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# Associate Professor Christopher Poulton

### Biography

Dr Chris Poulton is an Associate Professor in the Department of Mathematical Sciences. His research focus is on numerical analytical methods in electromagnetic wave propagation in composite materials, and he is the leader of the UTS node of CUDOS, the ARC Centre of excellence for Ultra-high bandwidth Devices and Optical Systems.

Dr Poulton received his PhD from the University of Sydney in 2000 for his work on electromagnetic and elastodynamic wave propagation in periodic materials. In 2000 he was appointed Lecturer in Applied Mathematics at the University of Liverpool, UK, where he worked on analytical models of photonic and phononic crystals and co-authored a book on asymptotic methods in electromagnetism. From 2002-2005 he was a post-doctoral fellow at the Institute for High-frequency and Quantum Electronics at the University of Karlsruhe, Germany, where he worked with experimentalists on developing integrated nonlinear devices. At the beginning of 2006 he joined the Max Planck Research Group (photonics and new materials) in Erlangen, Germany, where he worked on plasmonic interactions and guidance in photonic crystal fibres. He has been at UTS since July 2007.

Dr Poulton’s research interests are in numerical and analytical models of confined states, waveguides, metamaterials, and photon-phonon interactions.

### Professional

Centre for the Mathematical Modelling of Complex Systems (CeMMCoS): core member

Centre for Ultra-high bandwidth Devices and Optical Systems (CUDOS, ARC Centre of Excellence): Chief Investogator

Institute for Nanoscale Technology (INT): Associate member

Optical Society of America (OSA): member

Associate Professor, School of Mathematical Sciences
Core Member, Research Strength Materials and Technology for Energy Efficiency Member
Ph.D in Theoretical Physics

Phone
+61 2 9514 4370
Room
CB07.05.40

### Research Interests

Dr Poulton’s research focus is on the physics and modelling of advanced nanophotonic materials and devices. His reas of expertise is in the numerical and analytical modeling of confined states, waveguides, and metamaterials. Central to this work are photonic crystals and photonic crystal fibres; specially designed structures in which photons can be trapped, guided, or otherwise manipulated. An important part of this research involves the electromagnetic properties of metals at optical wavelengths – these problems are interesting from a computational point of view because they are so difficult to model, owing to the large momentum carried by the electron in comparison to the photon. Composites formed of metals and dielectrics also have exceptionally interesting optical properties – in particular there has recently been much excitement over a new class of materials, combining metals and dielectrics, known as metamaterials. These revolutionary new materials can be used to control the motion of light through space in a manner resembling a strong gravitational field. This leads to a number of interesting possibilities, including the electromagnetic cloaking of objects, as well as the resolution of images beyond the diffraction limit. Dr Poulton is also interested in the elastodynamic properties of periodic materials, including those possessing phononic band gaps, in which all sturctural vibrations propagating through the material are damped.

Can supervise: Yes

PhD student: Sayyed Mirnaziry

Topic: Photon-phonon interactions in nanophotonics

33190 Mathematical Modelling for Science (Autumn Semester)

33230 Mathematical Modelling 2 (Autumn Semester)

35484 EM Wave theory (Autumn semester)
35482 Boundary value problems (Spring semester)

A number of honours projects are offered each year. Interested students should contact me via email (address given above).

## Books

Movchan, A.B., Movchan, N.V. & Poulton, C.G. 2002, Asymptotic models of fields in dilute and densely packed composites, 1, Imperial College Press, London, UK.
This monograph provides a systematic study of asymptotic models of continuum mechanics for composite structures, which are either dilute (for example, two-phase composite structures with small inclusions) or densely packed (in this case inclusions may be close to touching). It is based on the results of recent research and includes a comprehensive analysis of dipole and multipole fields associated with defects in solids. The text covers static problems of elasticity in dilute composites as well as spectral problems. Applications of the mathematical models included in the book are in damage mechanics and in problems of design of composite structures that can be used as filters or polarisers of elastic waves.

## Chapters

Poulton, C.G., McPhedran, R.C., Nicorovici, N.A. & Botten, L.C. 2003, 'Localized Green's functions for a two-dimentional periodic material' in Gladwell, G.M.L. (ed), Solid Mechanics and its Applications vol 113: IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Kluwer, Netherlands, pp. 181-190.
We describe a method for the calculation of Green's functions for an array of dielectric cylinders. The method is to first construct quasi-periodic Greens functions, with Bloch vector kB. This function also obeys the appropriate electromagnetic boundary conditions on the surface of each cylinder. The Greens function for a single source in the array can then be calculated by averaging the quasi-periodic result over the Brillouin zone.
Zalipaev, V.V., Movchan, A.B., Poulton, C.G. & McPhedran, R.C. 2002, 'Phononic band structures for arrays of circular cavities in an elastic medium' in Abrahams, I.D. (ed), IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity, Kluwer, Netherlands, pp. 95-104.
We study the propagation of elastic waves in a two-dimensional solid containing a doubly periodic array of circular holes. The method of multipoles expansions is employed here, so that it takes into account a coupling between shear and dilatational waves (this coupling occurs via the traction bou~dary conditions). As a result, we obtain an infinite system of linear algebraic equations, which can be truncated and solved numerically in order to determine the frequencies of the propagating modes. The algorithm has been implemented as a computer code used to construct the dispersion diagrams and analyse the filtering properties of the composite structure.

## Conferences

Wolff, C., Steel, M.J., Eggleton, B.J. & Poulton, C.G. 2014, 'Stimulated brillouin scattering in high index-contrast optical waveguides: Energy, forces and symmetries', Frontiers in Optics, FiO 2014, Optical Society of America (OSA).
We theoretically investigate the important physical processes for Stimulated Brillouin Scattering in high-contrast optical waveguides. We explore the relevant forces and scattering mechanisms, their symmetry properties and their relationships based on the conservation of energy.
Poulton, C.G., Aryanfar, I., Wolff, C., Casas-Bedoya, A., Steel, M.J. & Eggleton, B.J. 2014, 'Stimulated Brillouin Scattering, hybrid acoustic modes and nonreciprocal mode-conversion in nanophotonic waveguides', Optics InfoBase Conference Papers, Optical Society of American (OSA).
We theoretically investigate non-reciprocal mode-conversion arising from Stimulated Brillouin Scattering (SBS) in sub-micron nanophotonic waveguides. We find that hybrid acoustic modes can be efficiently generated via radiation pressure, leading to enhancement of SBS-based mode conversion. 2014 OSA.
Fisher, C., Botten, L.C., Poulton, C.G., McPhedran, R.C. & Martijn de Sterke, C. 2014, 'Efficient end-fire coupling of surface plasmons in metallic waveguide', Frontiers in Optics, FiO 2014, Optical Society of America (OSA).
We theoretically investigate the end-fire coupling mechanism of surface plasmons into an interface, bounded by an ideally grounded waveguide, with respect to incident beam parameters, media permittivities and waveguide width. Efficiencies of s 80% were observed.
Krylova, A.K., Lapine, M., Poulton, C.G., McPhedran, R.C., Kivshar, Y.S. & Belov, P.A. 2013, 'Tailoring lattice parameters for broadband artificial diamagnetism', 2013 7th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, METAMATERIALS 2013, IEEE Computer Society, pp. 34-36.
We report a strategy to achieve the values of the effective magnetic permeability close to zero by using anisotropic metamaterial made of dense arrays of conductive loops. We present an extensive parametric analysis of the role of lattice parameters and symmetry, and also of the geometry of the loops. The magnitudes of the real part of the permeability reach 0.05 and are observed in a very broad frequency span, accompanied with negligible dissipation. Importantly, our analysis is applicable in a wide range of absolute sizes, being appropriate up to the THz range. Finally, we assess the dielectric properties of the optimal diamagnetic meta-materials, providing a complete picture of its interaction with the electromagnetic waves. 2013 IEEE.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & De Sterke, C.M. 2013, 'Positional disorder in nanowire array photovoltaics', Conference Record of the IEEE Photovoltaic Specialists Conference, Institute of Electrical and Electronics Engineers Inc., pp. 322-325.
Nanowire arrays are the focus of considerable research for incorporation into next generation solar cells. For these structures to be economically viable they must be designed to achieve high efficiencies in the presence of fabrication variations. Here we report on a systematic study of arrays of clustered nanowires, which reveals how the underlying physics of absorption enhancement in nanowire arrays is altered by the introduction of positional disorder. We find that positional disorder in fact enhances absorption efficiency over the majority of the parameter space due to the formation of additional modes in the structure and subsequently broadened absorption peaks. 2013 IEEE.
Pant, R., Li, E., Poulton, C.G., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2013, 'Brillouin dynamic grating on a photonic chip', 2013 Conference on Lasers and Electro-Optics, CLEO 2013, IEEE Computer Society.
We demonstrate an on-chip dynamic grating using stimulated Brillouin scattering in a 6.5cm long chalcogenide waveguide. The measured grating reflectivity is comparable to that measured in tens-of-meter long fiber and the On-Off ratio is ?28dB. 2013 The Optical Society.
Watts, A.L., Singh, N., Poulton, C.G., Magi, E., Kabakova, I.V., Hudson, D. & Eggleton, B.J. 2013, 'Characterization of axial quantization in WGM chalcogenide microfiber resonators', Optics InfoBase Conference Papers, Optical Society of America.
We experimentally and numerically characterize the axial quantization in whispering gallery mode (WGM) microfiber resonators exploiting a positive photoinduced index perturbation. Experimental results are in good agreement with numerical calculations. OSA 2013.
Pant, R., Byrnes, A., Li, E., Choi, D.-.Y., Poulton, C.G., Fan, S., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2013, 'Photonic chip based tunable and dynamically reconfigurable microwave photonic filter using stimulated brillouin scattering', Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, BGPP 2012.
We report the first demonstration of on-chip tunable narrowband microwave photonic filter with shape reconfiguration. Stimulated Brillouin scattering is exploited in a chalcogenide chip to demonstrate a microwave filter with 3dB bandwidth ~23MHz over 2-12GHz. OSA 2012.
Pant, R., Li, E., Poulton, C.G., Choi, D.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2013, 'Brillouin dynamic grating on a photonic chip', CLEO: Science and Innovations, CLEO_SI 2013.
We demonstrate an on-chip dynamic grating using stimulated Brillouin scattering in a 6.5cm long chalcogenide waveguide. The measured grating reflectivity is comparable to that measured in tens-of-meter long fiber and the On-Off ratio is ~28dB. OSA 2013.
Gao, F., Pant, R., Li, E., Poulton, C.G., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B. 2013, 'On-chip high sensitivity laser frequency sensing with brillouin mutually-modulated cross-gain modulation', CLEO: Science and Innovations, CLEO_SI 2013.
We report the first demonstration of a photonic-chip based laser frequency sensor using Brillouin mutually-modulated cross-gain modulation (MMXGM) in a 7cm long chalcogenide waveguide. A large sensitivity (9.45mrad/kHz) of the modulation phase shift was demonstrated. OSA 2013.
Eggleton, B.J., Poulton, C.G., Marpaung, D., Morrison, B., Kabakova, I.V., Choi, D.Y., Madden, S.J., Luther-Davies, B. & Pant, R. 2013, 'On-chip stimulated Brillouin scattering and its applications', Proceedings of SPIE - The International Society for Optical Engineering.
We review recent demonstration of stimulated Brillouin scattering in a chalcogenide photonic chip and its application to optical and microwave signal processing tasks. The interaction between light and sound via stimulated Brillouin scattering (SBS) was exploited in chalcogenide photonic circuits to achieve on-chip SBS slow and fast light, microwave photonic filters, and dynamic gratings using travelling-wave geometry. Using a ring-resonator geometry, photonic-chip based Brillouin laser was demonstrated. 2013 SPIE.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & de Sterke, C.M. 2012, 'Disorder in silicon nanowire arrays for photovoltaic applications', Frontiers in Optics, FIO 2012.
We study the effect of non-uniform radii on the optical absorption of silicon nanowire arrays. Whilst previous studies have shown that radius disorder can increase the efficiency, the mechanism is unclear. To elucidate this we study structures with a small supercell, forming a regular nanowire array with two distinct radii. We find that these arrays have new electromagnetic resonances, not present in arrays with uniform radii, leading to increased absorption. OSA 2012.
Pant, R., Byrnes, A., Poulton, C.G., Li, E., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'On-chip slow and fast light using stimulated brillouin scattering', Integrated Photonics Research, Silicon and Nanophotonics, IPRSN 2012.
We report the first demonstration of on-chip SBS slow and fast light using stimulated Brillouin scattering. Slow (~2307 km/s), fast and negative (~-6818 km/s) group velocities were observed in a 7cm long chalcogenide waveguide. 2012 OSA.
Byrnes, A., Pant, R., Poulton, C.G., Li, E., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'On-chip, tunable, narrow-bandpass microwave photonic filter using stimulated brillouin scattering (SBS)', CLEO: Science and Innovations, CLEO_SI 2012.
We report the first demonstration of a narrow-bandpass (~20MHz), on-chip, tunable, photonic filter for RF signals, using SBS in a chalcogenide waveguide. Extinction ratios of over 20dB for a frequency range of 2-12GHz were realized. OSA 2012.
Byrnes, A., Pant, R., Poulton, C.G., Li, E., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'On-chip, tunable, narrow-bandpass microwave photonic filter using stimulated Brillouin scattering (SBS)', 2012 Conference on Lasers and Electro-Optics, CLEO 2012.
We report the first demonstration of a narrow-bandpass (?20MHz), on-chip, tunable, photonic filter for RF signals, using SBS in a chalcogenide waveguide. Extinction ratios of over 20dB for a frequency range of 2-12GHz were realized. 2012 OSA.
Pant, R., Byrnes, A., Poulton, C.G., Li, E., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'Photonic chip based tunable slow and fast light via stimulated Brillouin scattering', 2012 Conference on Lasers and Electro-Optics, CLEO 2012.
We report the first demonstration of on-chip tunable slow- and fast-light via stimulated Brillouin scattering. We observe group-index ranging from ?-44 to +130 in a 7cm long chalcogenide waveguide at a low gain of ?23dB. 2012 OSA.
Pant, R., Byrnes, A., Poulton, C.G., Li, E., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'Photonic chip based tunable slow and fast light via stimulated Brillouin scattering', Proceedings of SPIE - The International Society for Optical Engineering.
The ability to control the speed of light on an optical chip is fundamental to the development of nanophotonic components for alloptical signal processing and sensing [1-7]. However this is a significant challenge, because chip-scale waveguides require very large changes in group index (?n g) to achieve appreciable pulse delays. Here, we use Stimulated Brillouin Scattering (SBS) to report the demonstration of on-chip slow, fast and negative group velocities with ?n g ranging from -44 to +130, and delays of up to 23ns at a pump power of ?300mW and propagation length of 7cm. These results are obtained using a highly-nonlinear chalocogenide (As 2S 3) rib waveguide, in which the confinement of both photons and phonons results in strong interaction. SBS can be used to achieve controllable pulse delays at room temperature over a large wavelength and signal-bandwidth [5]. These results open up a new set of photonic applications ranging from microwave photonics [8] to spectrometry [4]. 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).
Chen, P.Y., Poulton, C.G., Asatryan, A.A., Steel, M.J., Botten, L.C., Martijn De Sterke, C. & McPhedran, R.C. 2011, 'Folded bands in metamaterial photonic crystals', New Journal of Physics.
The dispersion relation of periodic structures that include metamaterials or materials with large anomalous dispersion can give bands with infinite group velocity points. These bands do not span the entire first Brillouin zone but are instead localized in k-space. We show that these points arise when both positive and negative elements are present, with the group index rather than the refractive index being the controlling quantity. A rigorous condition and two approximations are derived, each showing that an appropriate weighted average of group index being zero leads to infinite group velocity points. IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., Martijn de Sterke, C. & McPhedran, R.C. 2011, 'Analysis of enhanced absorption in dense silicon nanowire arrays', Optics InfoBase Conference Papers, pp. 1136-1138.
We analyze the absorption of solar radiation by dense silicon nanowire arrays, which are being considered for use in solar cells. Though it is known that these structures absorb sunlight much more efficiently than bulk silicon, the mechanism is complicated and not understood. Using a novel, semi-analytic model, we show that the enhanced absorption can be attributed to a few modes of the array, which couple well to incident light, overlap well with the silicon, and exhibit strong Fabry-Prot resonances. For some frequencies the absorption is further enhanced by slow light effects. 2011 AOS.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., Martijn de Sterke, C. & McPhedran, R.C. 2011, 'Absorption of silicon nanowire arrays on silicon and silica substrates', Optics InfoBase Conference Papers.
Nanowire arrays are promising structures for 3rd generation photovoltaics, due to their absorption enhancement over thin films and reduction in material usage. Having previously studied the absorption mechanism of silicon nanowire arrays suspended in air, we now extend the analysis to arrays on substrates. We find that the absorption mechanism continues to be dominated by one (or more) well coupled, well concentrated, resonant modes. Whilst the substrates reduce the strength of the resonances, they can simultaneously increase short wavelength absorption. The ultimate efficiency of the arrays remains significantly greater than that of silicon thin films and with a silicon substrate exceeds that of arrays suspended in air. 2011 OSA.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., Martijn De Sterke, C. & McPhedran, R.C. 2011, 'Angular dependence of absorption in silicon nanowire arrays', Optics InfoBase Conference Papers.
We use a novel modal simulation method to study the optical absorption properties of silicon nanowire arrays, which are being considered for 3rd generation photovoltaics. We have previously found the strong absorption to be derived from a small number of resonant modes and we now study the absorption as a function of angle of incidence. We find that the same few modes dominate the absorption mechanism and that the absorption remains high up to 35 off-normal irradiation. 2011 OSA.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., Martijn de Sterke, C. & McPhedran, R.C. 2011, 'Simulations of silicon nanowire arrays for photovoltaics- more absorption with less silicon', Optics InfoBase Conference Papers.
Using a novel numerical method we calculate the energy absorption of a silicon nanowire array, for photovoltaics. We show that dilute arrays deliver optimal integrated absorption on a per-silicon-volume basis, and identify the enhancement mechanism. OSA/ CLEO 2011.
Kan, D.J., Botten, L.C., Poulton, C.G., Asatryan, A.A. & Dossou, K.B. 2011, 'Semi-analytical formulations for the surface modes of photonic woodpiles', 2011 Int. Quantum Electron. Conf., IQEC 2011 and Conf. Lasers and Electro-Optics, CLEO Pacific Rim 2011 Incorporating the Australasian Conf. Optics, Lasers and Spectroscopy and the Australian Conf., pp. 2130-2132.
We describe semi-analytical methods for modeling the optical surface modes of finite and semi-infinite photonic woodpiles, and find that the behavior of the surface modes depends greatly on the whether the number of layers is even or odd. We also demonstrate analytically that coupling between the top and bottom surfaces can occur even when the top layer is orthogonal to the bottom layer. The coupling strength exhibits a strong dependence on the direction of propagation; for certain directions, decoupling occurs even when the number of layers is small. The dispersion curves of two different coupled modes can anticross or be interwoven. We also describe the conditions under which coupled surface modes will exist when two woodpiles are used to create a Fabry-Prot cavity. 2011 IEEE.
Dossou, K.B., Botten, L.C., Asatryan, A.A., Sturmberg, B.P.C., Byrne, M.A., Poulton, C.G., McPhedran, R.C. & De Sterke, C.M. 2011, 'Novel modeling techniques for photonic devices', Proceedings of the International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD, pp. 107-108.
The combination of purely numerical methods, such as the finite element method, with an analytical treatment can lead to a powerful semi-analytical technique. We present such a technique, which combines the finite element method with a modal approach, with a focus on the modeling three-dimensional photonic structures. 2011 IEEE.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., De Sterke, C.M. & McPhedran, R.C. 2011, 'Simulations of silicon nanowire arrays for photovoltaics More absorption with less silicon', 2011 Conference on Lasers and Electro-Optics: Laser Science to Photonic Applications, CLEO 2011.
Using a novel numerical method we calculate the energy absorption of a silicon nanowire array, for photovoltaics. We show that dilute arrays deliver optimal integrated absorption on a per-silicon-volume basis, and identify the enhancement mechanism. 2011 OSA.
Rahmani, A., Poulton, C.G., Steel, M.J., Chaumet, P.C. & Bryant, G.W. 2011, 'Purcell effect in a magnetic cavity', Optics InfoBase Conference Papers.
We study dipole emission inside a homogeneous, magnetic sphere. For fixed refractive index, the largest emission rate for an electric source is observed, in general, when the magnetic permeability is maximized. The corresponding result for a magnetic source follows by symmetry. 2010 Optical Society of America.
Poulton, C.G., Rahmani, A. & Steel, M.J. 2011, 'Radiation dynamics in a magneto-dielectric metamaterial cylinder', Optics InfoBase Conference Papers, pp. 1830-1831.
We study the radiation dynamics of an electric line current source in a homogeneous, magneto-dielectric cylinder. We find that radiation by the source is most enhanced by maximizing the magnetic response of the cylinder. 2011 AOS.
Rahmani, A., Poulton, C.G., Steel, M.J., Chaumet, P.C. & Bryant, G.W. 2011, 'Purcell effect in a magnetic cavity', 2011 Conference on Lasers and Electro-Optics: Laser Science to Photonic Applications, CLEO 2011.
We study dipole emission inside a homogeneous, magnetic sphere. For fixed refractive index, the largest emission rate for an electric source is observed, in general, when the magnetic permeability is maximized. The corresponding result for a magnetic source follows by symmetry. 2011 OSA.
Dossou, K.B., Botten, L.C., Asatryan, A.A., Sturmberg, B.C.P., Byrne, M.A., Poulton, C.G., McPhedran, R.C. & Martijn de Sterke, C. 2011, 'Modal formulation for scattering on the absorbing silicon nanowire arrays for photovoltaic applications', Optics InfoBase Conference Papers.
We develop a modal method for modeling the scattering off absorbing silicon nanowire arrays for photovoltaic applications. This semi-analytic approach allows the efficient, accurate calculation of absorption and gives insight into the absorption mechanism. OSA/CLEO 2011.
Dossou, K.B., Botten, L.C., Asatryan, A.A., Sturmberg, B.C.P., Byrne, M.A., Poulton, C.G., McPhedran, R.C. & Martijn De Sterke, C. 2011, 'Modal formulation for scattering on the absorbing silicon nanowire arrays for photovoltaic applications', Optics InfoBase Conference Papers.
We develop a modal method for modeling the scattering off absorbing silicon nanowire arrays for photovoltaic applications. This semi-analytic approach allows the efficient, accurate calculation of absorption and gives insight into the absorption mechanism. 2011 OSA.
Chen, P.Y., McPhedran, R.C., Asatryan, A.A., Botten, L.C., Poulton, C.G., Steel, M.J. & De Sterke, C.M. 2011, 'Fast simulation of slab photonic crystal structures using modal methods', Optics InfoBase Conference Papers, pp. 71-72.
A faster method of simulating 2D slabs, both metallic and dielectric, with cylindrical inclusions is proposed. The method is applicable to photonic crystal defect-row waveguides and extraordinary transmssion through metallic films, capable of producing both in-plane dispersion relations and transmission spectra. 2011 AOS.
Chen, P.Y., McPhedran, R.C., Asatryan, A.A., Botten, L.C., Poulton, C.G., Steel, M.J. & De Sterke, C.M. 2011, 'Fast simulation of slab photonic crystal structures using modal methods', 2011 Int. Quantum Electron. Conf., IQEC 2011 and Conf. Lasers and Electro-Optics, CLEO Pacific Rim 2011 Incorporating the Australasian Conf. Optics, Lasers and Spectroscopy and the Australian Conf., pp. 71-72.
A faster method of simulating 2D slabs, both metallic and dielectric, with cylindrical inclusions is proposed. The method is applicable to photonic crystal defect-row waveguides and extraordinary transmssion through metallic films, capable of producing both in-plane dispersion relations and transmission spectra. 2011 IEEE.
Dossou, K.B., Botten, L.C., Asatryan, A.A., Sturmberg, B.C.P., Byrne, M.A., Poulton, C.G., McPhedran, R.C. & De Sterke, C.M. 2011, 'Modal formulation for scattering on the absorbing silicon nanowire arrays for photovoltaic applications', 2011 Conference on Lasers and Electro-Optics: Laser Science to Photonic Applications, CLEO 2011.
We develop a modal method for modeling the scattering off absorbing silicon nanowire arrays for photovoltaic applications. This semi-analytic approach allows the efficient, accurate calculation of absorption and gives insight into the absorption mechanism. 2011 OSA.
Chen, P., McPhedran, R.C., Poulton, C.G., Steel, M.J., Asatryan, A.A., Botten, L.C. & de Sterke, C.M. 2010, 'Calculating complex group velocity from modal fields of a lossy periodic structure', Photonic and Electromagnetic Crystal Structures, Instituto de Ciencia de Materiales de Madrid, Granada, Spain, pp. 1-1.
Mahmoodian, S., Dossou, K.B., Poulton, C.G., McPhedran, R.C., Botten, L.C. & De Sterke, C.M. 2010, 'Engineering cavity modes in photonic crystal double-heterostructures', Optics InfoBase Conference Papers.
We present results from a new method that allows us to design the mode fields for 3D photonic crystal heterostructure cavities, in the domain where the perturbation used to create the cavity is weak. The method, based on a perturbation treatment from solid-state physics, enables the rapid computation of the main features of 3D cavity modes for an arbitrary perturbation and is several orders of magnitude faster than direct numerical methods. We use this method to study optimal confinement of resonant states in these structures. 2010 Optical Society of America.
Asatryan, A.A., Kan, D., Dossou, K.B., Poulton, C.G. & Botten, L.C. 2010, 'Formulation for Modeling Lossless Waveguides in Photonic Woodpiles Using the Fictitious Source Superposition Method', Photonic and Electromagnetic Crystal Structures, insituto de ciencia de materiales de madrid, Granada, Spain.
Asatryan, A.A., Botten, L.C., Dossou, K.B., Poulton, C.G., Chen, P., McPhedran, R.C. & De Sterke, C.M. 2009, 'The local density of states of metamaterial photonic crystals', Optics InfoBase Conference Papers, Optical Society of America.
We study the local density of states (LDOS) of photonic crystals made with metamaterial inclusions and show that the introduction of metamaterial components substantially widens and deepens band gaps in comparison with normal photonic crystals. 2009 Optical Society of America.
Asatryan, A.A., Botten, L.C., Dossou, K.B., Poulton, C.G., Chen, P., McPhedran, R.C. & De Sterke, C.M. 2009, 'The local density of states of metamaterial photonic crystals', Optics InfoBase Conference Papers.
We study the local density of states (LDOS) of photonic crystals made with metamaterial inclusions and show that the introduction of metamaterial components substantially widens and deepens band gaps in comparison with normal photonic crystals. 2009 Optical Society of America.
Lee, M.W., Grillet, C., Poulton, C.G., Monat, C., Smith, C.L.C., Mgi, E., Freeman, D., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2009, 'An expanded k-space evanescent coupling technique for characterizing photonic crystal waveguides', Optics InfoBase Conference Papers.
We demonstrate an expanded k-space evanescent coupling technique for characterizing the dispersion and loss of photonic crystal waveguides (PCWG) by measuring the Fabry-Prot spectrum of a closed waveguide using a highly curved taper. 2009 Optical Society of America.
Lee, M.W., Grillet, C., Poulton, C.G., Monat, C., Smith, C.L.C., Mgi, E., Freeman, D., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2009, 'An expanded k-space evanescent coupling technique for characterizing photonic crystal waveguides', 2009 Conference on Lasers and Electro-Optics and 2009 Conference on Quantum Electronics and Laser Science Conference, CLEO/QELS 2009.
We demonstrate an expanded k-space evanescent coupling technique for characterizing the dispersion and loss of photonic crystal waveguides (PCWG) by measuring the Fabry-Prot spectrum of a closed waveguide using a highly curved taper. 2009 Optical Society of America.
Poulton, C.G., Mahmoodiar, S., Dossou, K.B., McPhedran, R.C., Botten, L.C. & De Sterke, C.M. 2009, 'Semi-analytical models for resonant states near photonic crystal band edges', AIP Conference Proceedings, pp. 78-80.
We present a semi-analytical method for the computation and analysis of localised resonant states with frequencies close to photonic crystal band edges. The method results in a differential equation for the envelope function of the confined state that is readily solved to determine good approximations to both frequencies and fields. We examine the formation and evolution of confined states near the band-edge for both cavities and waveguides in photonic crystals. 2009 American Institute of Physics.
Asatryan, A.A., Botten, L.C., Dossou, K.B., Poulton, C.G., Chen, P., McPhedran, R.C. & De Sterke, C.M. 2009, 'The local density of states of metamaterial photonic crystals', 2009 Conference on Lasers and Electro-Optics and 2009 Conference on Quantum Electronics and Laser Science Conference, CLEO/QELS 2009.
We study the local density of states (LDOS) of photonic crystals made with metamaterial inclusions and show that the introduction of metamaterial components substantially widens and deepens band gaps in comparison with normal photonic crystals. 2009 Optical Society of America.
Prill Sempere, L.N., Schmidt, M., Tyagi, H.K., Poulton, C.G. & Russell, P.S. 2008, 'Metal nanowire arrays in photonic crystal fibers', Winter Topical Meeting Series, 2008 IEEE/LEOS, IEEE/LEOS, Piscataway, NJ, pp. 206-207.
Metallic nanowire arrays are created by pumping molten metal into the hollow channels of silica glass PCF. Measurements show that, at certain wavelengths, the core-guided light couples to leaky surface plasmon modes on the nanowires.
Dossou, K.B., Botten, L.C., Mahmoodian, S., McPhedran, R.C., Poulton, C.G., Asatryan, A.A. & Martijn de Sterke, C. 2008, 'Modes of composite defects in 2D photonic crystals', 2008 Joint Conference of the Opto-Electronics and Communications Conference and the Australian Conference On Optical Fibre Technology, OECC/ACOFT 2008.
We demonstrate the existence of a class of defects in 2D photonic crystals, for which the eigenstates depend only on the defect geometry, and not on details like photonic crystal parameters or defect size.
Schwefel, H.G., Poulton, C.G. & Wang, L.J. 2008, 'Numerically efficient multipole method for photonic molecules', Proceedings of 2008 10th Anniversary International Conference On Transparent Optical Networks (ICTON) vol 4, IEEE/LEOS, New Jersey, USA, pp. 230-233.
A novel and numerically efficient multipole formulation for the calculation of resonances of photonic molecules is presented. Photonic molecules are often modeled as two dimensional coupled dielectric disks. We use the multipole expansion of the individual fields and formulate the boundary conditions in terms of a generalized eigenvalue problem. The complex root search is simplified by studying the flow of the eigenvalues, where we argue that the motion of the eigenvalues in the complex plane is analytic with respect to a two parameter family. Based on this analytic behavior we present a numerical algorithm to compute a range of photonic molecule resonances and field distributions using only two diagonalizations.
Dossou, K.B., Botten, L.C., Poulton, C.G., McPhedran, R.C., Asatryan, A.A. & Martijn de Sterke, C. 2008, 'Evolution of defect states in 2D photonic crystals', Optics InfoBase Conference Papers, Optical Society of America.
We study the evolution of defect states from the band-edges of a 2D photonic crystal. A simple exponential relation is derived for the dispersion of the state, and we investigate the connection with Bloch modes. 2008 Optical Society of America.
Dossou, K.B., Botten, L.C., Poulton, C.G., McPhedran, R.C., Asatryan, A.A. & Martijn de Sterke, C. 2008, 'Evolution of defect states in 2D photonic crystals', Optics InfoBase Conference Papers, Optical Society of America.
We study the evolution of defect states from the band-edges of a 2D photonic crystal. A simple exponential relation is derived for the dispersion of the state, and we investigate the connection with Bloch modes. 2008 Optical Society of America.
Dossou, K.B., Botten, L.C., Poulton, C.G., McPhedran, R.C., Asatryan, A.A. & De Sterke, C.M. 2008, 'Evolution of defect states in 2D photonic crystals', 2008 Conference on Quantum Electronics and Laser Science Conference on Lasers and Electro-Optics, CLEO/QELS.
We study the evolution of defect states from the band-edges of a 2D photonic crystal. A simple exponential relation is derived for the dispersion of the state, and we investigate the connection with Bloch modes. 2008 Optical Society of America.
Dossou, K.B., Botten, L.C., Poulton, C.G., McPhedran, R.C., Asatryan, A.A. & De Sterke, C.M. 2008, 'Evolution of defect states in 2D Photonic crystals', Conference on Quantum Electronics and Laser Science (QELS) - Technical Digest Series.
We study the evolution of defect states from the band-edges of a 2D photonic crystal. A simple exponential relation is derived for the dispersion of the state, and we investigate the connection with Bloch modes. 2008 Optical Society of America.
Prill Sempere, L.N., Schmidt, M., Tyagi, H.K., Poulton, C.G. & Russell, P.S. 2007, 'Metal nanowire arrays in photonic crystal fibres', Frontiers in Optics, Technical Digest, Optical Society of America, CD, pp. 1-3.
Nanowire arrays are produced by pumping molten metal into the holes of silica PCF. Distinct dips in the transmitted spectra coincide with the coupling of the core-guided light to leaky plasmonic resonances in the nanowires
Poulton, C.G., Schmidt, M., Pearce, G.J., Kakarantzas, G. & Russell, P.S. 2007, 'Guided Modes in arrays of metallic nanowires', Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies 2007 Technical Digest, Optical Society of America, USA, pp. 1-2.
We study numerically the formation of photonic band gaps and guided "defect" modes within two dimensional arrays of metallic nanowires. Attenuations as low as 1.7 dB/cm are predicted for silver wires at 1550 nm wavelength.
Fujii, M., Takashima, T., Maitra, A., Leuthold, J., Freude, W. & Poulton, C.G. 2007, 'Nonreciprocal transmission and low-threshold bistability in strongly modulated asymmetric nonlinear WBGs', Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies 2007 Technical Digest, Optical Society of America, USA, pp. 1-2.
Nonreciprocal optical bistability is numerically investigated in InGaAsP/InP nonlinear waveguide Bragg gratings having a strong and asymmetric sidewall modulation. Minimum switching power as low as 77 mW is predicted by choosing optimal switching conditions.
Wilcox, S., Botten, L.C., McPhedran, R.C., de Sterke, C.M. & Poulton, C.G. 2005, 'Exact modeling of defect modes in photonic crystals', Optics InfoBase Conference Papers, Optical Society of America.
An exact model for defect modes in PC devices with infinite cladding is presented. Its accuracy is demonstrated, as is its role in corroborating that the fundamental mode of a conven-tional PCF has no cutoff. 2005 Optical Society of America.
Wilcox, S., Botten, L.C., McPhedran, R.C., Martijn De Sterke, C. & Poulton, C.G. 2005, 'Exact modeling of defect modes in photonic crystals', Quantum Electronics and Laser Science Conference (QELS), pp. 711-713.
An exact model for defect modes in PC devices with infinite cladding is presented. Its accuracy is demonstrated, as is its role in corroborating that the fundamental mode of a conventional PCF has no cutoff. 2005 Optical Society of America.
Servant, J., Guenneau, S., Movchan, A.B. & Poulton, C.G. 2003, 'Vibrations of a circular cylinder in oblique incidence revisited', Solid Mechanics and its Applications vol 113: IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Kluwer, Netherlands, pp. 95-104.
In this paper, we analyse the propagation of elastodynamic waves in a circular cylinder in the case of oblique incidence. We use a scattering matrix approach and derive an algebraic linear system which allows us to get a complete picture of the dispersion curves. This derivation is of the foremost importance, since it provides the right form for the algebraic system associated to a singular cylinder, basis of its generalisation to a doubly periodic array of circular cylinders
Spence, A. & Poulton, C.G. 2003, 'Inverse iteration for nonlinear eigenvalue problems in electromagnetic scattering', Solid Mechanics and its Applications vol 113: IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Kluwer, Netherlands, pp. 585-594.
We present an extension of the well-known method of 'inverse iteration' for the standard eigenvalue problem to the nonlinear problem of finding dispersion relations for electromagnetic waves moving through a doublyperiodic structure. Numerical results are presented to illustrate the performance of the technique. A further improvement is described that allows an e cient path following algorithm where a curve of solutions is computed in (?, Kbloch) space. We present dispersion relations calculated via this new method and compare the efficiency of this algorithm with that of more traditional methods.
Poulton, C.G., Guenneau, S., Nicolet, A. & Movchan, A.B. 2003, 'Transverse propagating waves in perturbed periodic structures', Solid Mechanics and its Applications vol 113: IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Kluwer, Netherlands, pp. 147-158.
We present here an analysis of electromagnetic waves propagating through a doubly periodic array of inclusions which are not necessarily circular. A small perturbation to a circular boundary is introduced, and this can be used to derive the e ective boundary conditions for the perturbed inclusion. We examine the e ect of this perturbation on the dispersion curves for the material, and compare this with a finite element modelling of the perturbed structure.
Poulton, C.G., McPhedran, R.C., Nicorovici, N.A., Botten, L.C. & Movchan, A.B. 2001, 'Asymptotics of photonic band structures for doubly-periodic arrays', IUTAM SYMPOSIUM ON MECHANICAL AND ELECTROMAGNETIC WAVES IN STRUCTURED MEDIA, SPRINGER, pp. 227-238.

## Journal articles

Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & Sterke, C.M.D. 2014, 'Nanowire array photovoltaics: Radial disorder versus design for optimal efficiency', Appl. Phys. Lett., vol. 101, p. 173902.
Solar cell designs based on disordered nanostructures tend to have higher efficiencies than structures with uniform absorbers, though the reason is poorly understood. To resolve this, we use a semi-analytic approach to determine the physical mechanism leading to enhanced efficiency in arrays containing nanowires with a variety of radii. We use our findings to systematically design arrays that outperform randomly composed structures. An ultimate efficiency of 23.75% is achieved with an array containing 30% silicon, an increase of almost 10% over a homogeneous film of equal thickness.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & de Sterke, C.M. 2014, 'Optimizing Photovoltaic Charge Generation of Nanowire Arrays: A Simple Semi-Analytic Approach', ACS PHOTONICS, vol. 1, no. 8, pp. 683-689.
Wolff, C., Steel, M.J., Eggleton, B.J. & Poulton, C.G. 2014, 'Stimulated Brillouin Scattering in integrated photonic waveguides: forces, scattering mechanisms and coupled mode analysis'.
Recent theoretical studies of Stimulated Brillouin Scattering (SBS) in nanoscale devices have led to an intense research effort dedicated to the demonstration and application of this nonlinearity in on-chip systems. The key feature of SBS in integrated photonic waveguides is that small, high-contrast waveguides are predicted to experience powerful optical forces on the waveguide boundaries, which are predicted to further boost the SBS gain that is already expected to grow dramatically in such structures because of the higher mode confinement alone. In all recent treatments, the effect of radiation pressure is included separately from the scattering action that the acoustic field exerts on the optical field. In contrast to this, we show here that the effects of radiation pressure and motion of the waveguide boundaries are inextricably linked. Central to this insight is a new formulation of the SBS interaction that unifies the treatment of light and sound, incorporating all relevant interaction mechanisms --- radiation pressure, waveguide boundary motion, electrostriction and photoelasticity --- from a rigorous thermodynamic perspective. Our approach also clarifies important points of ambiguity in the literature, such as the nature of edge-effects with regard to electrostriction, and of body-forces with respect to radiation pressure. This new perspective on Brillouin processes leads to physical insight with implications for the design and fabrication of SBS-based nanoscale devices.
Bttner, T.F.S., Kabakova, I.V., Hudson, D.D., Pant, R., Poulton, C.G., Judge, A.C. & Eggleton, B.J. 2014, 'Phase-locking and Pulse Generation in Multi-Frequency Brillouin Oscillator via Four Wave Mixing', Scientific Reports, vol. 4.
There is an increasing demand for pulsed all-fibre lasers with gigahertz repetition rates for applications in telecommunications and metrology. The repetition rate of conventional passively mode-locked fibre lasers is fundamentally linked to the laser cavity length and is therefore typically ?10-100 ...MHz, which is orders of magnitude lower than required. Cascading stimulated Brillouin scattering (SBS) in nonlinear resonators, however, enables the formation of Brillouin frequency combs (BFCs) with GHz line spacing, which is determined by the acoustic properties of the medium and is independent of the resonator length. Phase-locking of such combs therefore holds a promise to achieve gigahertz repetition rate lasers. The interplay of SBS and Kerr-nonlinear four-wave mixing (FWM) in nonlinear resonators has been previously investigated, yet the phase relationship of the waves has not been considered. Here, we present for the first time experimental and numerical results that demonstrate phase-locking of BFCs generated in a nonlinear waveguide cavity. Using real-time measurements we demonstrate stable 40 ...ps pulse trains with 8 ...GHz repetition rate based on a chalcogenide fibre cavity, without the aid of any additional phase-locking element. Detailed numerical modelling, which is in agreement with the experimental results, highlight the essential role of FWM in phase-locking of the BFC.
Wolff, C., Stee, M.J. & Poulton, C.G. 2014, 'Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers', Optics Express, vol. 22, no. 26, pp. 32489-32501.
We derive formal selection rules for Stimulated Brillouin Scattering (SBS) in structured waveguides. Using a group-theoretical approach, we show how the waveguide symmetry determines which optical and acoustic modes interact for both forward and backward SBS. We present a general framework for determining this interaction and give important examples for SBS in waveguides with rectangular, triangular and hexagonal symmetry. The important role played by degeneracy of the optical modes is illustrated. These selection rules are important for SBS-based device design and for a full understanding the physics of SBS in structured waveguides.
Aryanfar, I., Wolff, C., Steel, M.J., Eggleton, B.J. & Poulton, C.G. 2014, 'Mode conversion using stimulated Brillouin scattering in nanophotonic silicon waveguides', Optics Express, vol. 22, no. 23, pp. 29270-29282.
We theoretically and numerically investigate Stimulated Brillouin Scattering generated mode conversion in high-contrast suspended silicon nanophotonic waveguides. We predict significantly enhanced mode conversion when the linked effects of radiation pressure and motion of the waveguide boundaries are taken into account. The mode conversion is more than 10 times larger than would be predicted if the effect of radiation pressure is not taken into account: we find a waveguide length of 740 ?m is required for 20dB of mode conversion, assuming a total pump power of 1W. This is sufficient to bring the effect into the realm of chip-scale photonic waveguides. We explore the interaction between the different types of acoustic modes that can exist within these waveguides, and show how the presence of these modes leads to enhanced conversion between the different possible optical modes.
Donnelly, J.L., Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & De Sterke, C.M. 2014, 'Mode-based analysis of silicon nanohole arrays for photovoltaic applications', Optics Express, vol. 22, no. SUPPL. 5.
We investigate the optical properties of silicon nanohole arrays for application in photovoltaic cells in terms of the modes within the structure. We highlight three types of modes: fundamental modes, important at long wavelengths; guided resonance modes, which enhance absorption for wavelengths where the intrinsic absorption of silicon is low; and channeling modes, which suppress front-surface reflection. We use this understanding to explain why the parameters of optimized nanohole arrays occur in specific ranges even as the thickness is varied. 2014 Optical Society of America.
Wolff, C., Soref, R., Poulton, C.G. & Eggleton, B.J. 2014, 'Germanium as a material for stimulated Brillouin scattering in the mid-infrared', Optics Express, vol. 22, no. 25, pp. 30735-30747.
In a theoretical design study, we propose buried waveguides made of germanium or alloys of germanium and other group-IV elements as a CMOS-compatible platform for robust, high-gain stimulated Brillouin scattering (SBS) applications in the mid-infrared regime. To this end, we present numerical calculations for backward-SBS at 4mm in germanium waveguides that are buried in silicon nitride. Due to the strong photoelastic anisotropy of germanium, we investigate two different orientations of the germanium crystal with respect to the waveguide's propagation direction and find considerable differences. The acoustic wave equation is solved including crystal anisotropy; acoustic losses are computed from the acoustic mode patterns and previously published material parameters.
Smith, M.J.A., Meylan, M.H., McPhedran, R.C. & Poulton, C.G. 2014, 'A short remark on the band structure of free-edge platonic crystals', Waves in Random and Complex Media.
A corrected version of the multipole solution for a thin plate perforated in a doubly periodic fashion is presented. It is assumed that free-edge boundary conditions are imposed at the edge of each cylindrical inclusion. The solution procedure given here exploits a well-known property of Bessel functions to obtain the solution directly, in contrast to the existing incorrect derivation. A series of band diagrams and an updated table of values are given for the resulting system (correcting known publications on the topic), which shows a spectral band at low frequency for the free-edge problem. This is in contrast to clamped-edge boundary conditions for the same biharmonic plate problem, which features a low-frequency band gap. The numerical solution procedure outlined here is also simplified relative to earlier publications, and exploits the spectral properties of complex-valued matrices to determine the band structure of the structured plate. 2014 2014 Taylor & Francis.
Kabakova, I.V., Marpaung, D., Poulton, C.G. & Eggleton, B.J. 2014, 'Driving acoustic waves optically on a chip', Australian Physics, vol. 51, no. 3, pp. 84-88.
Stimulated Brillouin scattering (SBS) is an important nonlinear effect in optical fibers and waveguides that has been traditionally exploited for high-sensitivity distributed sensing, coherent lasers and gyroscopes. Recent advances in nanofabrication led to the extensive growth of SBS research. The ability to generate SBS in nanoscale devices has opened numerous opportunities for photonic integration, resulting in on-chip Brillouin lasers, microwave generation, Brillouin cooling and quantum optomechanics. In this paper we briefly describe principles of inelastic Brillouin scattering and review our recent developments in optical signal manipulation and lasing using on-chip SBS.
Pant, R., Marpaung, D., Kabakova, I.V., Morrison, B., Poulton, C.G. & Eggleton, B.J. 2014, 'On-chip stimulated brillouin scattering for microwave signal processing and generation', Laser and Photonics Reviews, vol. 8, no. 5, pp. 653-666.
Demonstration of continuously tunable delay, low-noise lasers, dynamically controlled gratings, and optical phase shifting using the stimulated Brillouin scattering (SBS) process has lead to the emergence of SBS as a promising technology for microwave photonics. On-chip realization of SBS enables photonic integration of microwave photonic signal processing and offers significantly enhanced performance and improved efficiency. On-chip stimulated Brillouin scattering is reviewed in the context of slow-light based tunable delay, low-noise narrow linewidth lasers and filtering for integrated microwave photonics. A discussion on key material and device properties, necessary to enable on-chip Brillouin scattering using both the single-pass and resonator geometry, is presented along with an outlook for photonic integration of microwave signal processing and generation in other platforms. On-chip realization of stimulated Brillouin scattering (SBS) enables photonic integration of microwave photonic signal processing and offers significantly enhanced performance and improved efficiency. On-chip SBS is reviewed in the context of slow-light based tunable delay, low-noise narrow linewidth lasers and filtering for integrated microwave photonics. A discussion on key material and device properties, necessary to enable on-chip Brillouin scattering using both the single-pass and resonator geometry, is presented along with an outlook for photonic integration of microwave signal processing and generation in other platforms. 2014 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Lapine, M., Krylova, A.K., Belov, P.A., Poulton, C.G., McPhedran, R.C. & Kivshar, Y.S. 2013, 'Broadband diamagnetism in anisotropic metamaterials', Physical Review B - Condensed Matter and Materials Physics, vol. 87, no. 2.
We discuss the strategy for achieving the values of the effective magnetic permeability much smaller than unity by employing an appropriate arrangement of metamaterial elements ("meta-atoms"). We demonstrate that strong diamagnetism over a very wide frequency range can be realized in metamaterials by employing nonresonant elements with deeply subwavelength dimensions. We analyze the effect of the lattice parameters on the diamagnetic response and find that selecting an appropriate lattice type is crucial for optimal performance. Finally, we discuss the optimal characteristics required to obtain the lowest possible values of magnetic permeability and point out an efficient tuning possibility. 2013 American Physical Society.
Pant, R., Li, E., Poulton, C.G., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2013, 'Observation of Brillouin dynamic grating in a photonic chip', Optics Letters, vol. 38, no. 3, pp. 305-307.
We report demonstration of a Brillouin dynamic grating (BDG) in a photonic chip. A BDG was characterized in a 6.5 cm long chalcogenide (As 2S3) rib waveguide using CW pumps in x polarization and read using a CW probe in y polarization. The measured reflectivity, on-off ratio, and 3 dB bandwidth (f3dB) for the BDG were 0.4%, ?28 dB, and ?6 GHz, respectively. 2013 Optical Society of America.
Gao, F., Pant, R., Li, E., Poulton, C.G., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2013, 'On-chip high sensitivity laser frequency sensing with Brillouin mutually-modulated cross-gain modulation', 2013 Conference on Lasers and Electro-Optics, CLEO 2013.
We report the first demonstration of a photonic-chip based laser frequency sensor using Brillouin mutually-modulated cross-gain modulation (MMXGM) in a 7cm long chalcogenide waveguide. A large sensitivity (9.45mrad/kHz) of the modulation phase shift was demonstrated. 2013 The Optical Society.
Watts, A.L., Singh, N., Poulton, C.G., Magi, E.C., Kabakova, I.V., Hudson, D.D. & Eggleton, B.J. 2013, 'Photoinduced axial quantization in chalcogenide microfiber resonators', Journal of the Optical Society of America B: Optical Physics, vol. 30, no. 12, pp. 3249-3253.
We investigate axial quantization in chalcogenide (As2S3) whispering gallery mode microfiber resonators. A microcavity is fabricated using a positive photoinduced index perturbation in the microfiber, and the modes are excited through evanescent field coupling with a tapered silica fiber. We show that the modes of the unperturbed fiber split into ladders of modes due to the confinement along the axial direction of the fiber. The axial quantization of the modes is reproduced with a combination of numerical models. Due to the high nonlinearity and photosensitive properties of chalcogenide glasses, microcavities in these materials offer unique potential in nonlinear optics and sensing applications. 2013 Optical Society of America.
Dossou, K.B., Botten, L.C. & Poulton, C.G. 2013, 'Semi-analytic impedance modeling of three-dimensional photonic and metamaterial structures', JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, vol. 30, no. 10, pp. 2034-2047.
Poulton, C.G., Pant, R. & Eggleton, B.J. 2013, 'Acoustic confinement and stimulated Brillouin scattering in integrated optical waveguides', Journal of the Optical Society of America B: Optical Physics, vol. 30, no. 10, pp. 2657-2664.
We examine the effect of acoustic mode confinement on stimulated Brillouin scattering (SBS) in optical waveguides that consist of a guiding core embedded in a solid substrate. We find that SBS can arise due to coupling to acoustic modes in three different regimes. First, the acoustic modes may be guided by total internal reflection; in this case, the SBS gain depends directly on the degree of confinement of the acoustic mode in the core, which is in turn determined by the acoustic V parameter. Second, the acoustic modes may be leaky but may nevertheless have a sufficiently long lifetime to have a large effect on the SBS gain; the lifetime of acoustic modes in this regime depends not only on the contrast in acoustic properties between the core and the cladding but is also highly dependent on the waveguide dimensions. Finally, SBS may occur due to coupling to free modes, which exist even in the absence of acoustic confinement; we find that the cumulative effect of coupling to these nonconfined modes results in significant SBS gain. We show how the different acoustic properties of core and cladding lead to these different regimes and discuss the feasibility of SBS experiments using different material systems. 2013 Optical Society of America.
Eggleton, B.J., Poulton, C.G. & Pant, R. 2013, 'Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits', Advances in Optics and Photonics, vol. 5, no. 4, pp. 536-587.
We review recent progress in inducing and harnessing stimulated Brillouin scattering (SBS) in integrated photonic circuits. Exciting SBS in a chip-scale device is challenging due to the stringent requirements on materials and device geometry. We discuss these requirements, which include material parameters, such as optical refractive index and acoustic velocity, and device properties, such as acousto-optic confinement. Recent work on SBS in nano-photonic waveguides and micro-resonators is presented, with special attention paid to photonic integration of applications such as narrow-linewidth lasers, slowand fast-light, microwave signal processing, Brillouin dynamic gratings, and nonreciprocal devices. 2013 Optical Society of America.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & De Sterke, C.M. 2013, 'Absorption enhancing proximity effects in aperiodic nanowire arrays', Optics Express, vol. 21, no. 22.
Aperiodic Nanowire (NW) arrays have higher absorption than equivalent periodic arrays, making them of interest for photovoltaic applications. An inevitable property of aperiodic arrays is the clustering of some NWs into closer proximity than in the equivalent periodic array. We focus on the modes of such clusters and show that the reduced symmetry associated with cluster formation allows external coupling into modes which are dark in periodic arrays, thus increasing absorption. To exploit such modes fully, arrays must include tightly clustered NWs that are unlikely to arise from fabrication variations but must be created intentionally. 2013 Optical Society of America.
McPhedran, R.C. & Poulton, C.G. 2013, 'The Riemann Hypothesis for Symmetrised Combinations of Zeta Functions'.
This paper studies combinations of the Riemann zeta function, based on one defined by P.R. Taylor, which was shown by him to have all its zeros on the critical line. With a rescaled complex argument, this is denoted here by ${\cal T}_-(s)$, and is considered together with a counterpart function ${\cal T}_+(s)$, symmetric rather than antisymmetric about the critical line. We prove that ${\cal T}_+(s)$ has all its zeros on the critical line, and that the zeros of both functions are all of first order. We establish a link between the zeros of ${\cal T}_-(s)$ and of ${\cal T}_+(s)$ with those of the zeros of the Riemann zeta function $\zeta(2 s-1)$, which enables us to prove that, if the Riemann hypothesis holds, then the distribution function of the zeros of $\zeta (2 s-1)$ agrees with those for ${\cal T}_-(s)$ and of ${\cal T}_+(s)$ in all terms which do not remain finite as $t\rightarrow \infty$.
Gao, F., Pant, R., Li, E., Poulton, C.G., Choi, D.-.Y., Madden, S.J., Luther-Davies, B. & Eggleton, B.J. 2013, 'On-chip high sensitivity laser frequency sensing with Brillouin mutually-modulated cross-gain modulation', Optics Express, vol. 21, no. 7, pp. 8605-8613.
We report the first demonstration of a photonic-chip laser frequency sensor using Brillouin mutually-modulated cross-gain modulation (MMXGM). A large sensitivity (?9.5 mrad/kHz) of the modulation phase shift to probe carrier frequency is demonstrated at a modulation frequency of 50 kHz using Brillouin MMXGM in a ?7 cm long chalcogenide rib waveguide. 2013 Optical Society of America.
Dossou, K.B., Botten, L.C., Asatryan, A.A., Sturmberg, B.C.P., Byrne, M.A., Poulton, C.G., McPhedran, R.C. & De Sterke, C.M. 2012, 'Modal formulation for diffraction by absorbing photonic crystal slabs', Journal of the Optical Society of America A: Optics and Image Science, and Vision, vol. 29, no. 5, pp. 817-831.
A finite element-based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications. The semianalytic approach allows efficient and accurate calculation of the absorption of an array with a complex unit cell. This approach gives direct physical insight into the absorption mechanism in such structures, which can be used to enhance the absorption. The verification and validation of this approach is applied to a silicon nanowire array, and the efficiency and accuracy of the method is demonstrated. The method is ideally suited to studying the manner in which spectral properties (e.g., absorption) vary with the thickness of the array, and we demonstrate this with efficient calculations that can identify an optimal geometry. 2012 Optical Society of America.
Pant, R., Byrnes, A., Poulton, C.G., Li, E., Choi, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'Photonic chip based tunable slow and fast light via stimulated Brillouin scattering', CLEO: Science and Innovations, CLEO_SI 2012.
We report the first demonstration of on-chip tunable slow- and fast-light via stimulated Brillouin scattering. We observe group-index ranging from ~-44 to +130 in a 7cm long chalcogenide waveguide at a low gain of ~23dB. OSA 2012.
Poulton, C.G., Movchan, A.B., Movchan, N.V. & Mcphedran, R.C. 2012, 'Analytic theory of defects in periodically structured elastic plates', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 468, no. 2140, pp. 1196-1216.
We consider the problem of localized flexural waves in thin plates that have periodic structure, consisting of a two-dimensional array of pins or point masses. Changing the properties of the structure at a single point results in a localized mode within the bandgap that is confined to the vicinity of the defect, while changing the properties along an entire line of points results in a waveguide mode. We develop here an analytic theory of these modes and provide semi-analytic expressions for the eigenfrequencies and fields of the point defect states, as well as the dispersion curves of the defect waveguide modes. The theory is based on a derivation of Green's function for the structure, which we present here for the first time. We also consider defects in finite arrays of point masses, and demonstrate the connection between the finite and infinite systems. 2011 The Royal Society.
Mahmoodian, S., Sipe, J.E., Poulton, C.G., Dossou, K.B., Botten, L.C., McPhedran, R.C. & De Sterke, C.M. 2012, 'First-principles method for high-Q photonic crystal cavity mode calculations', Optics Express, vol. 20, no. 20, pp. 22763-22769.
We present a first-principles method to compute radiation properties of ultra-high quality factor photonic crystal cavities. Our Frequency-domain Approach for Radiation (FAR) can compute the far-field radiation pattern and quality factor of cavity modes ? 100 times more rapidly than conventional finite-difference time domain calculations. We explain how the radiation pattern depends on the perturbation used to create the cavity and on the Bloch modes of the photonic crystal. 2012 Optical Society of America.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & Martijn De Sterke, C. 2012, 'Nanowire array photovoltaics: Radial disorder versus design for optimal efficiency', Applied Physics Letters, vol. 101, no. 17.
Solar cell designs based on disordered nanostructures tend to have higher efficiencies than structures with uniform absorbers, though the reason is poorly understood. To resolve this, we use a semi-analytic approach to determine the physical mechanism leading to enhanced efficiency in arrays containing nanowires with a variety of radii. We use our findings to systematically design arrays that outperform randomly composed structures. An ultimate efficiency of 23.75 is achieved with an array containing 30 silicon, an increase of almost 10 over a homogeneous film of equal thickness. 2012 American Institute of Physics.
Smith, M.J.A., McPhedran, R.C., Poulton, C.G. & Meylan, M.H. 2012, 'Negative refraction and dispersion phenomena in platonic clusters', Waves in Random and Complex Media, vol. 22, no. 4, pp. 435-458.
We consider the problem of Gaussian beam scattering by finite arrays of pinned points, or platonic clusters, in a thin elastic plate governed by the biharmonic plate equation. Integral representations for Gaussian incident beams are constructed and numerically evaluated to demonstrate the different behaviours exhibited by these finite arrays. We show that it is possible to extend the scattering theory from infinite arrays of pinned points to these finite crystals, which exhibit the predicted behaviour well. Analytical expressions for the photonic superprism parameters p, q and r, which are measures for dispersion inside the crystal, are also derived for the pinned plate problem here. We demonstrate the existence of negative refraction, beam splitting, Rayleigh anomalies, internal reflection, and near-trapping on the first band surface, giving examples for each of these behaviours. 2012 Taylor and Francis Group, LLC.
Poulton, C.G., Pant, R., Byrnes, A., Fan, S., Steel, M.J. & Eggleton, B.J. 2012, 'Design for broadband on-chip isolator using stimulated Brillouin scattering in dispersion-engineered chalcogenide waveguides', Optics Express, vol. 20, no. 19, pp. 21235-21246.
We propose a scheme for on-chip isolation in chalcogenide (As 2S3) rib waveguides, in which Stimulated Brillouin Scattering is used to induce non-reciprocal mode conversion within a multi-moded waveguide. The design exploits the idea that a chalcogenide rib buried in a silica matrix acts as waveguide for both light and sound, and can also be designed to be multi-moded for both optical and acoustic waves. The enhanced opto-acoustic coupling allows significant isolation (> 20 dB) within a chip-scale (cm-long) device (< 10 cm). We also show that the bandwidth of this device can be dramatically increased by tuning the dispersion of the waveguide to match the group velocity between optical modes: we find that 20 dB isolation can be extended over a bandwidth of 25 nm. 2012 Optical Society of America.
Pant, R., Byrnes, A., Li, E., Choi, D.-.Y., Poulton, C.G., Fan, S., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'Photonic chip based tunable and dynamically reconfigurable microwave photonic filter using stimulated Brillouin scattering', Optics InfoBase Conference Papers.
We report the first demonstration of on-chip tunable narrowband microwave photonic filter with shape reconfiguration. Stimulated Brillouin scattering is exploited in a chalcogenide chip to demonstrate a microwave filter with 3dB bandwidth ~23MHz over 2-12GHz. OSA 2012.
Chen, P.Y., Byrne, M.A., Asatryan, A.A., Botten, L.C., Dossou, K.B., Tuniz, A., McPhedran, R.C., De Sterke, C.M., Poulton, C.G. & Steel, M.J. 2012, 'Plane-wave scattering by a photonic crystal slab: Multipole modal formulation and accuracy', Waves in Random and Complex Media, vol. 22, no. 4, pp. 531-570.
The optical properties of photonic crystal slabs are often simulated with general three-dimensional methods such as finite-difference time-domain. Here we develop a multipole modal method, which is specialized to exploit two symmetries of the photonic crystal slab: the slab's vertically invariant nature allows the field to be expressed in Bloch modes, while the cylindrical inclusions allow the Bloch modes themselves to be expressed in the multipole basis. We find the multipole method to be fast and efficient in finding the Bloch modes, with convergence approaching the numerical accuracy possible. By matching the Bloch modes to plane waves at the top and bottom interfaces of the photonic crystal, the field scattered by the slab is calculated. Values of transmittance and reflectance accurate to 2-3 digits are easily and quickly achieved, whereas 5-6 digits are possible with greater numbers of modes and plane waves in field expansions. Higher accuracy is limited by Gibbs-related phenomena arising from the matching at the interface of necessarily discontinuous Bloch modes to necessarily continuous plane waves. We believe this limit may be present in all modal methods that use Bloch modes to expand the field within the photonic crystal. 2012 Taylor and Francis Group, LLC.
Mahmoodian, S., Sipe, J.E., Poulton, C.G., Dossou, K.B., Botten, L.C., McPhedran, R.C. & De Sterke, C.M. 2012, 'Double-heterostructure cavities: From theory to design', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 86, no. 4.
We derive a frequency-domain-based approach for radiation from double-heterostructure cavity (DHC) modes. We use this to compute the quality factors and radiation patterns of DHC modes. The semianalytic nature of our method enables us to provide a general relationship between the radiation pattern of the cavity and its geometry. We use this to provide general designs for ultrahigh-quality-factor DHCs with radiation patterns that are engineered to emit vertically. 2012 American Physical Society.
Byrnes, A., Pant, R., Li, E., Choi, D.-.Y., Poulton, C.G., Fan, S., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'Photonic chip based tunable and reconfigurable narrowband microwave photonic filter using stimulated Brillouin scattering', Optics Express, vol. 20, no. 17, pp. 18836-18845.
We report the first demonstration of a photonic chip based dynamically reconfigurablewidely tunablenarrow pass-bandhigh Q microwave photonic filter (MPF). We exploit stimulated Brillouin scattering (SBS) in a 6.5 cm long chalcogenide (As2S3) photonic chip to demonstrate a MPF that exhibited a high quality factor of ?520 and narrow bandwidth and was dynamically reconfigurable and widely tunable. It maintained a stable 3 dB bandwidth of 23 2MHz and amplitude of 20 2 dB over a large frequency tuning range of 2-12 GHz. By tailoring the pump spectrumwe reconfigured the 3 dB bandwidth of the MPF from ?20 MHz to ?40 MHz and tuned the shape factor from 3.5 to 2 resulting in a nearly flat-topped filter profile. This demonstration represents a significant advance in integrated microwave photonics with potential applications in on-chip microwave signal processing for RADAR and analogue communications. 2012 Optical Society of America.
Pant, R., Byrnes, A., Poulton, C.G., Li, E., Cho, D.-.Y., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2012, 'Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering', Optics Letters, vol. 37, no. 5, pp. 969-971.
We report the first (to our knowledge) demonstration of photonic chip based tunable slow and fast light via stimulated Brillouin scattering. Slow, fast, and negative group velocities were observed in a 7 cm long chalcogenide (As 2S3) rib waveguide with a group index change ranging from ? ? 44 to +130, which results in a maximum delay of ?23 ns at a relatively low gain of ?23 dB. Demonstration of large tunable delays in a chip scale device opens up applications such as frequency sensing and true-time delay for a phased array antenna, where integration and delays ?10 ns are highly desirable. 2012 Optical Society of America.
Pant, R., Poulton, C.G., Choi, D.-.Y., Li, E., Madden, S.J., Luther-Davies, B. & Eggleton, B.J. 2011, 'On-chip stimulated Brillouin scattering', Proceedings of SPIE - The International Society for Optical Engineering, vol. 8095.
We report the first demonstration of on-chip stimulated Brillouin scattering (SBS). SBS is characterized in a chalcogenide (As2S 3) photonic chip where the measured Brillouin shift and full-width at half-maximum (FWHM) linewidth are 7.7 GHz and 34 MHz respectively. The measured Brillouin gain coefficient (gB) is 0.715 x 10-9 m/W, consistent with the theoretical estimate. 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).
Kan, D.J., Botten, L.C., Poulton, C.G., Asatryan, A.A. & Dossou, K.B. 2011, 'Semi-analytical formulations for the surface modes of photonic woodpiles', Optics InfoBase Conference Papers, pp. 2130-2132.
We describe semi-analytical methods for modeling the optical surface modes of finite and semi-infinite photonic woodpiles, and find that the behavior of the surface modes depends greatly on the whether the number of layers is even or odd. We also demonstrate analytically that coupling between the top and bottom surfaces can occur even when the top layer is orthogonal to the bottom layer. The coupling strength exhibits a strong dependence on the direction of propagation; for certain directions, decoupling occurs even when the number of layers is small. The dispersion curves of two different coupled modes can anticross or be interwoven. We also describe the conditions under which coupled surface modes will exist when two woodpiles are used to create a Fabry-Prot cavity. 2011 AOS.
Pant, R., Li, E., Choi, D.-.Y., Poulton, C.G., Madden, S.J., Luther-Davies, B. & Eggleton, B.J. 2011, 'Cavity enhanced stimulated brillouin scattering in an optical chip for multiorder Stokes generation', Optics Letters, vol. 36, no. 18, pp. 3687-3689.
We report the first demonstration of on-chip cascaded stimulated Brillouin scattering (SBS). Cascaded SBS is characterized in a 4 cm long chalcogenide (As2S3) rib waveguide where the end facet reflections provide a monolithic Fabry-Perot (FP) resonator. The presence of the FP cavity reduces the Brillouin gain threshold, which enables observation of cascaded SBS at reduced pump powers. We observe up to three orders of Stokes waves in the backscattered signal at a coupled peak power of 1:34W. Anti-Stokes waves due to four-wave mixing between the pump and the Stokes wave were observed in the forward spectrum. 2011 Optical Society of America.
Kan, D.J., Asatryan, A.A., Poulton, C.G., Dossou, K.B. & Botten, L.C. 2011, 'Modeling waveguides in photonic woodpiles using the fictitious source superposition method', Journal of the Optical Society of America B: Optical Physics, vol. 28, no. 4, pp. 746-755.
We extend the fictitious source superposition method in order to model linear defects in photonic woodpiles, and we use the method to model a waveguide that is created by changing either the radius or refractive index of a single rod of an infinite woodpile composed of chalcogenide glass cylinders. In one instance, a nearly constant dispersion was observed over a sizable kx interval, where kx is the Bloch vector in the waveguiding direction, making this a compelling geometry for slow-light waveguides. The principal advantage of the method is that it does not rely on a supercell, thus avoiding what is possibly the greatest source of inefficiency present in most of the other methods that are used for modeling these structures. Instead, the method proceeds by placing an artificial source inside each rod of the defect layer and then subsequently taking an appropriate field superposition to remove all but one of these sources. The remaining source can then be used to mimic the fields that would be produced by a defect rod. 2011 Optical Society of America.
Chen, P., Poulton, C.G., Asatryan, A.A., Steel, M.J., Botten, L.C., de Sterke, C.M. & McPhedran, R.C. 2011, 'Folded Bands In Metamaterial Photonic Crystals', New Journal of Physics, vol. 13, pp. 1-18.
The dispersion relation of periodic structures that include metamaterials or materials with large anomalous dispersion can give bands with infinite group velocity points. These bands do not span the entire first Brillouin zone but are instead localized in k-space. We show that these points arise when both positive and negative elements are present, with the group index rather than the refractive index being the controlling quantity. A rigorous condition and two approximations are derived, each showing that an appropriate weighted average of group index being zero leads to infinite group velocity points.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., De Sterke, C.M. & McPhedran, R.C. 2011, 'Modal analysis of enhanced absorption in silicon nanowire arrays', Optics Express, vol. 19, no. 19.
We analyze the absorption of solar radiation by silicon nanowire arrays, which are being considered for photovoltaic applications. These structures have been shown to have enhanced absorption compared with thin films, however the mechanism responsible for this is not understood. Using a new, semi-analytic model, we show that the enhanced absorption can be attributed to a few modes of the array, which couple well to incident light, overlap well with the nanowires, and exhibit strong Fabry-Prot resonances. For some wavelengths the absorption is further enhanced by slow light effects. We study the evolution of these modes with wavelength to explain the various features of the absorption spectra, focusing first on a dilute array at normal incidence, before generalizing to a dense array and off-normal angles of incidence. The understanding developed will allow for optimization of simple SiNW arrays, as well as the development of more advanced designs. 2011 Optical Society of America.
Kan, D.J., Botten, L.C., Poulton, C.G., Asatryan, A.A. & Dossou, K.B. 2011, 'Semianalytical formulations for the surface modes of photonic woodpiles', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 84, no. 4.
We have developed semianalytical methods that allow us to perform a comprehensive analysis of the surface modes of photonic woodpiles. The surface modes of both finite and semi-infinite woodpiles are characterized using transfer matrix and plane-wave matrix formulations, and, in the case of finite structures, we give a general analytical description of the "double- interface" modes, which propagate simultaneously along the top and bottom surfaces. We show that if the number of layers is even, then such modes will only exist for specific directions of the Brillouin zone. However, if the number of layers is odd, then every surface mode is a double-interface mode, and, in this case, the direction of propagation plays an important role in determining the coupling strength between the two surfaces: for certain directions, the coupling is negligible even when the number of layers is small. The dispersion curves of two different double-interface modes can anticross or be interwoven, depending on the symmetry of the modes. We also describe the conditions under which coupled surface modes will exist when two woodpiles are used to create a Fabry-Prot cavity. 2011 American Physical Society.
Pant, R., Poulton, C.G., Choi, D.-.Y., Mcfarlane, H., Hile, S., Li, E., Thevenaz, L., Luther-Davies, B., Madden, S.J. & Eggleton, B.J. 2011, 'On-chip stimulated Brillouin scattering', Optics Express, vol. 19, no. 9, pp. 8285-8290.
We demonstrate on-chip stimulated Brillouin scattering (SBS) in an As2S3 chalcogenide rib waveguide. SBS was characterized in a 7cm long waveguide with a cross-section 4?m x 850nm using the backscattered signal and pump-probe technique. The measured Brillouin shift and its full-width at half-maximum (FWHM) linewidth were ?7.7 GHz and 34 MHz, respectively. Probe vs. pump power measurements at the Brillouin shift were used to obtain the gain coefficient from an exponential fit. The Brillouin gain coefficient obtained was 0.715 10-9 m/W. A probe gain of 16 dB was obtained for a CW pump power of ?300 mW. 2011 Optical Society of America.
Kan, D.J., Asatryan, A.A., Poulton, C.G. & Botten, L.C. 2010, 'Multipole method for modeling linear defects in photonic woodpiles', JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, vol. 27, no. 2, pp. 246-258.
Liu, W., Sukhorukov, A., Miroshnichenko, A., Poulton, C., Xu, Z., Neshev, D. & Kivshar, Y. 2010, 'Complete spectral gap in coupled dielectric waveguides embedded into metal', Appl. Phys. Lett., vol. 97, p. 021106.
We study a plasmonic coupler involving backward (TM_01) and forward (HE_11) modes of dielectric waveguides embedded into infinite metal. The simultaneously achievable contradirectional energy flows and codirectional wavevectors in different channels lead to a spectral gap, despite the absence of periodic structures along the waveguide. We demonstrate that a complete spectral gap can be achieved in a symmetric structure composed of four coupled waveguides.
Mahmoodian, S., Sukhorukov, A.A., Ha, S., Lavrinenko, A.V., Poulton, C.G., Dossou, K.B., Botten, L.C., McPhedran, R.C. & Martijn De Sterke, C. 2010, 'Paired modes of heterostructure cavities in photonic crystal waveguides with split band edges', Optics Express, vol. 18, no. 25, pp. 25693-25701.
We investigate the modes of double heterostructure cavities where the underlying photonic crystal waveguide has been dispersion engineered to have two band-edges inside the Brillouin zone. By deriving and using a perturbative method, we show that these structures possess two modes. For unapodized cavities, the relative detuning of the two modes can be controlled by changing the cavity length, and for particular lengths, a resonant-like effect makes the modes degenerate. For apodized cavities no such resonances exist and the modes are always non-degenerate. 2010 Optical Society of America.
Poulton, C.G., McPhedran, R.C., Movchan, N.V. & Movchan, A.B. 2010, 'Convergence properties and flat bands in platonic crystal band structures using the multipole formulation', Waves in Random and Complex Media, vol. 20, no. 4, pp. 702-716.
We present converged band diagrams for Bloch-Floquet bending waves in a thin elastic plate containing a square array of circular perforations, using the multipole formulation developed by Movchan et al. (2007) and applied in the situation where the perforations are no longer considered to be small in comparison with the lattice pitch. We give tables of converged frequencies and the number of multipoles necessary to achieve them, for a range of radii of the perforations for both clamped-edge and free-edge boundary conditions. We find that the larger filling fraction leads to extremely flat bands within the band structure; this can be explained by considering the energy of the vibrational modes. We derive the energy balance relation as well as convenient expressions for the group velocity of eigenmodes, which reveal the interplay between the Helmholtz and the modified Helmholtz components of the eigenfield. 2010 Taylor & Francis.
Nicorovici, N.-.A.P., McPhedran, R.C., Botten, L.C., Poulton, C.G. & Asatryan, A.A. 2010, 'Green's functions and relative local density of states in two-dimensional lossy structured systems', Waves in Random and Complex Media, vol. 20, no. 4, pp. 656-677.
The local density of states (LDOS) is a function of spatial position and frequency which governs the radiation properties of sources placed within structured optical systems. We show how the enhancement or suppression of the relative LDOS, comparing two-dimensional systems, may be computed from Green's tensors obeying the two-dimensional Helmholtz equation and electromagnetic boundary conditions, both around and within a coated, lossy, non-magnetic cylinder. We illustrate the spatial and spectral variation of this relative LDOS with numerical results for both principal cases of polarization, with either the magnetic or the electric field of the Green's function source along the cylinder axis. 2010 Taylor & Francis.
Chen, P.Y., McPhedran, R.C., de Sterke, C.M., Poulton, C.G., Asatryan, A.A., Botten, L.C. & Steel, M.J. 2010, 'Group velocity in lossy periodic structured media', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 82, no. 5.
In lossless periodic media, the concept of group velocity is fundamental to the study of propagation dynamics. When spatially averaged, the group velocity is numerically equivalent to energy velocity, defined as the ratio of energy flux to energy density of modal fields. However, in lossy media, energy velocity diverges from group velocity. Here, we define a modal field velocity which remains equal to the complex modal group velocity in homogeneous and periodicmedia. The definition extends to the more general situation of modal fields that exhibit spatial or temporal decay due to lossy elements or Bragg reflection effects. Our simple expression relies on a generalization of the concepts of energy flux and density. Numerical examples, such as a two-dimensional square array of silver rods in vacuum, are provided to confirm the result. Examples demonstrate how the dispersion relation of the periodic structure, the properties of its modes, and their group velocities change markedly in lossy media. 2010 The American Physical Society.
Grujic, T., Kuhlmey, B.T., De Sterke, C.M. & Poulton, C.G. 2009, 'Modelling of photonic crystal fiber based on layered inclusions', Journal of the Optical Society of America B: Optical Physics, vol. 26, no. 10, pp. 1852-1861.
Photonic crystal fibers often consist of rotationally symmetric inclusions in an otherwise uniform background medium. The band diagrams and modes of such structures can be efficiently calculated using geometry-specific methods that exploit this rotational symmetry. Until now, these have only been applied to fibers in which the inclusions are circular and have a uniform refractive index. Here, we generalize this to arbitrary rotationally symmetric inclusions using a transfer matrix approach, and we implement this approach in an approximate scalar method, which is valid for low-index contrasts and in the rigorous Rayleigh multipole method. We apply the methods to structures incorporating inclusions with graded refractive indices and to structures incorporating metal rings. 2009 Optical Society of America.
Schwefel, H.G. & Poulton, C.G. 2009, 'An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane.', Opt Express, vol. 17, no. 15, pp. 13178-13186.
We present a numerically improved multipole formulation for the calculation of resonances of multiple disks located at arbitrary positions in a 2-d plane, and suitable for the accurate computation of the resonances of large numbers of disks and of high-wavenumber eigenstates. Using a simple reformulation of the field expansions and boundary conditions, we are able to transform the multipole formalism into a linear eigenvalue problem, for which fast and accurate methods are available. Observing that the motion of the eigenvalues in the complex plane is analytic with respect to a two parameter family, we present a numerical algorithm to compute a range of multiple-disk resonances and field distributions using only two diagonalizations. This method can be applied to photonic molecules, photonic crystals, photonic crystal fibers, and random lasers.
Movchan, N.V., Mcphedran, R.C., Movchan, A.B. & Poulton, C.G. 2009, 'Wave scattering by platonic grating stacks', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 465, no. 2111, pp. 3383-3400.
We address the problem of scattering of flexural waves obeying the biharmonic equation by a stack of a finite number of gratings.We express the solution of the scattering problem for a single grating in terms of reflection and transmission matrices, incorporating the effects of both propagating and evanescent incident waves. The plane wave expansion coefficients above and below the grating are linked to multipole coefficients within the grating using the grating sums and the Rayleigh identities. We derive the recurrence procedure giving the reflection and transmission matrices of the stack in terms of those of individual layers. Trapped waves between a pair of gratings are investigated. 2009 The Royal Society.
Mahmoodian, S., Poulton, C.G., Dossou, K.B., McPhedran, R.C., Botten, L.C. & De Sterke, C.M. 2009, 'Modes of shallow photonic crystal waveguides: Semi-analytic treatment', Optics Express, vol. 17, no. 22, pp. 19629-19643.
We investigate the formation of photonic crystal waveguide (PCW) modes within the framework of perturbation theory. We derive a differential equation governing the envelope of PCW modes constructed from weak perturbations using an effective mass formulation based on the Luttinger-Kohn method from solid-state physics. The solution of this equation gives the frequency of the mode and its field. The differential equation lends itself to simple analytic approximations which reduce the problem to that of solving slab waveguide modes. By using this model, we demonstrate that the nature of the projected band structure and corresponding Bloch functions are central to the behaviour of PCW modes. With this understanding, we explain why the odd mode in a hexagonal PCW spans the entire Brillouin zone while the even mode is cut off. 2009 Optical Society of America.
Mahmoodian, S., McPhedran, R.C., De Sterke, C.M., Dossou, K.B., Poulton, C.G. & Botten, L.C. 2009, 'Single and coupled degenerate defect modes in two-dimensional photonic crystal band gaps', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 79, no. 1.
We investigate the formation and coupling of defect modes in two-dimensional photonic crystal (PC) band gaps associated with degenerate edges. Using a method based on Green's functions and perturbation theory, we derive a condition for the degeneracy of a defect mode in a PC band gap. We show that the interaction between multiple degenerate defects splits this degeneracy and provide a semi-analytic model for the splitting using a 44 tight-binding matrix. We observe that the structure of this tight-binding matrix is related to the overlap and corresponding symmetry of the defect modes. We confirm our analysis by comparing with numerical results. 2009 The American Physical Society.
Dossou, K.B., Poulton, C.G., Botten, L.C., Mahmoodian, S., Mcphedran, R.C. & De Sterke, C.M. 2009, 'Modes of symmetric composite defects in two-dimensional photonic crystals', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 80, no. 1.
We consider the modal fields and resonance frequencies of composite defects in two-dimensional photonic crystals (PCs). Using an asymptotic method based on Green's functions, we show that the coupling matrices for the composite defect can be represented as circulant or block-circulant matrices. Using the properties of these matrices, specifically that their eigenvectors are independent of the values of the matrix elements, we obtain modal properties such as dispersion relations, modal cutoff, degeneracy, and symmetry of the mode fields. Using our formulation, we investigate defects arranged on the vertices of regular polygons as well as PC ring resonators with defects arranged on the edges of polygons. Finally, we discuss the impact of band-edge degeneracies on composite-defect modes. 2009 The American Physical Society.
Lee, M.W., Grillet, C., Poulton, C.G., Monat, C., Smith, C.L.C., Mgi, E., Freeman, D., Madden, S., Luther-Davies, B. & Eggletons, B.J. 2008, 'Characterizing photonic crystal waveguides with an expanded k-space evanescent coupling technique', Optics Express, vol. 16, no. 18, pp. 13800-13808.
We demonstrate a direct, single measurement technique for characterizing the dispersion of a photonic crystal waveguide (PCWG) using a tapered fiber evanescent coupling method. A highly curved fiber taper is used to probe the Fabry-Prot spectrum of a closed PCWG over a broad k-space range, and from this measurement the dispersive properties of the waveguide can be found. Waveguide propagation losses can also be estimated from measurements of closed waveguides with different lengths. The validity of this method is demonstrated by comparing the results obtained on a 'W1' PCWG in chalcogenide glass with numerical simulation. 2008 Optical Society of America.
Dossou, K.B., Botten, L.C., McPhedran, R.C., Poulton, C.G., Asatryan, A.A. & Martijn De Sterke, C. 2008, 'Shallow defect states in two-dimensional photonic crystals', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 77, no. 6.
We investigate localized defect states near the edge of a band gap in a two-dimensional photonic crystal. An asymptotic approach based on Green's functions leads to analytical results both for the frequency and for the spatial behavior of the defect states. In particular, we find a simple exponential law which relates the change in frequency of the defect states to the relative change in electrical energy of the Bloch modes on the band edge, and to the density of states in the photonic crystal. We find that the symmetries of the Bloch modes at band extrema play an important role in the manifestation and evolution of defect states. We confirm the analysis with numerical simulations based on the fictitious source superposition method. 2008 The American Physical Society.
Schmidt, M.A., Sempere, L.N.P., Tyagi, H.K., Poulton, C.G. & Russell, P.S.J. 2007, 'Waveguiding and Plasmon Resonances in Two-Dimensional Photonic Lattices of Gold and Silver Nanowires'.
We report the fabrication of triangular lattices of parallel gold and silver nanowires of high optical quality, with diameters down to 500 nm and length-to-diameter ratios as high as 100,000. The nanowires are supported by a silica glass matrix and are disposed around a central solid glass core, i.e., a missing nanowire. These cm-long structures make it possible to trap light within an array of nanowires and characterize the plasmon resonances that form at specific optical frequencies. Such nanowire arrays have many potential applications, e.g., to imaging on the sub-wavelength scale.
Pearce, G.J., Wiederhecker, G.S., Poulton, C.G., Burger, S. & St J Russell, P. 2007, 'Models for guidance in kagome-structured hollow-core photonic crystal fibres.', Opt Express, vol. 15, no. 20, pp. 12680-12685.
We demonstrate by numerical simulation that the general features of the loss spectrum of photonic crystal fibres (PCF) with a kagome structure can be explained by simple models consisting of thin concentric hexagons or rings of glass in air. These easily analysed models provide increased understanding of the mechanism of guidance in kagome PCF, and suggest ways in which the high-loss resonances in the loss spectrum may be shifted.
Podlipensky, A., Szarniak, P., Joly, N.Y., Poulton, C.G. & Russell, P.S. 2007, 'Bound soliton pairs in photonic crystal fiber.', Opt Express, vol. 15, no. 4, pp. 1653-1662.
We demonstrate experimentally the formation and stable propagation of bound soliton pairs in a highly nonlinear photonic crystal fiber. The bound pairs occur at a particular power as the consequence of high-order soliton fission. They propagate over long distances with constant inter-soliton frequency and time separation. During propagation, the soliton self-frequency shift causes the central frequency of the pairs to move towards longer wavelength. The formation and characteristics of the bound soliton pairs are confirmed numerically. We believe this to be the first experimental observation of such bound soliton pairs.
Koos, C., Jacome, L., Poulton, C.G., Leuthold, J. & Freude, W. 2007, 'Nonlinear silicon-on-insulator waveguides for all-optical signal processing', Optics Express, vol. 15, no. 10, pp. 5976-5990.
Values up to gamma = 7106/(Wkm) for the nonlinear parameter are feasible if silicon-on-insulator based strip and slot waveguides are properly designed. This is more than three orders of magnitude larger than for state-of-the-art highly nonlinear fibers, and it enables ultrafast all-optical signal processing with nonresonant compact devices. At lambda = 1.55m we provide universal design curves for strip and slot waveguides which are covered with different linear and nonlinear materials, and we calculate the resulting maximum gamma
Koos, C., Poulton, C.G., Zimmerman, L., Jacome, L., Leuthold, J. & Freude, W. 2007, 'Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides', Photonics Technology Letters, IEEE, vol. 19, no. 11, pp. 819-821.
Bend designs for single-mode operation of low-loss overmoded waveguides are presented. A class of contour trajectories for minimum radiation loss is derived analytically, and numerical optimization is used to find ideal trajectory parameters. Three-dimensional finite-difference time-domain simulations predict bend losses below 0.1 dB for 180deg-bends of overmoded silicon-on-insulator waveguides with a radius of R=1.5 mum. These findings are supported experimentally
Poulton, C.G., Wang, J., Maitra, A., Freude, W. & Leuthold, J. 2007, 'Temporal Dynamics of the Alpha Factor in Semiconductor Optical Amplifiers', Journal of Lightwave Technology, vol. 25, no. 3, pp. 891-900.
The temporal evolution of the alpha-factor during pump-probe experiments in semiconductor optical amplifiers (SOAs) is not constant but varies strongly with time. It even takes on negative values for short periods of time. As a consequence, cross-phase modulation (XPM) effects usually lag behind cross-gain modulation effects by several picoseconds. This delay has important consequences for ultrafast operation of all-optical devices based on SOAs. It actually means that not every scheme will be suited for ultrafast operation. In order to properly model the XPM and phase variations within an SOA during a pump-probe experiment, a new parameterization for the alpha-factor is introduced. Inclusion of this model leads to an excellent agreement with the recent 160-Gb/s experiments for both phase and amplitude evolutions of the respective signals with time.
Poulton, C.G., Schmidt, M.A., Pearce, G.J., Kakarantzas, G. & Russell, P.S. 2007, 'Numerical study of guided modes in arrays of metallic nanowires.', Opt Lett, vol. 32, no. 12, pp. 1647-1649.
We numerically investigate the band structure and guided modes within arrays of metallic nanowires. We show that bandgaps appear for a range of array geometries and that these can be used to guide light in these structures. Values of attenuation as low as 1.7 dB/cm are predicted for arrays of silver wires at communications wavelengths. This is more than 100 times smaller than the attenuation of the surface plasmon polariton modes on a single silver nanowire.
Koos, C., Fujii, M., Poulton, C.G., Steingrueber, R., Leuthold, J. & Freude, W. 2006, 'FDTD-Modelling of Dispersive Nonlinear Ring Resonators: Accuracy Studies and Experiments', IEEE Journal of Quantum Electronics, vol. 42, no. 12, pp. 1215-1223.
The accuracy of nonlinear finite-difference time-domain (FDTD) methods is investigated by modeling nonlinear optical interaction in a ring resonator. We have developed a parallelized 3-D FDTD algorithm which incorporates material dispersion, (3)-nonlinearities and stair-casing error correction. The results of this implementation are compared with experiments, and intrinsic errors of the FDTD algorithm are separated from geometrical uncertainties arising from the fabrication tolerances of the device. A series of progressively less complex FDTD models is investigated, omitting material dispersion, abandoning the stair-casing error correction, and approximating the structure by a 2-D effective index model. We compare the results of the different algorithms and give guidelines as to which degree of complexity is needed in order to obtain reliable simulation results in the linear and the nonlinear regime. In both cases, incorporating stair-casing error correction and material dispersion into a 2-D effective index model turns out to be computationally much cheaper and more effective than performing a fully three-dimensional simulation without these features.
Fujii, M., Koos, C., Poulton, C.G., Sakagami, I., Leuthold, J. & Freude, W. 2006, 'A simple and rigorous technique for the nonlinear FDTD algorithm by optical parametric four-wave mixing', Microwave and Optical Technology Letters, vol. 48, no. 1, pp. 88-91.
A rigorous quantitative verification technique is presented for nonlinear finite-difference time-domain (FDTD) algorithms by analyzing parametric four-wave mixing (FWM) in an optical Kerr medium without involving other numerical techniques. This technique allows quick and reliable verification of complicated nonlinear FDTD algorithms, hence enhancing the application of nonlinear FDTD analysis to more realistic optical problems.
Poulton, C.G., Koos, C., Fujii, M., Freude, W., Leuthold, J., Pfrang, A. & Schimmel, T. 2006, 'Radiation modes and roughness loss in high index-contrast waveguides', IEEE Journal of Selected Topics in Quantum Electronics, vol. 12, no. 6, pp. 1306-1321.
We predict the scattering loss in rectangular high index-contrast waveguides, using a new variation of the classical approach of coupled-mode theory. The loss predicted by this three-dimensional (3-D) model is considerably larger than that calculated using previous treatments that approximate the true 3-D radiation modes with their two-dimensional counterparts. The 3-D radiation modes of the ideal waveguide are expanded in a series of cylindrical harmonics, and the coupling between the guided and radiation modes due to the sidewall perturbation is computed. The waveguide attenuation can then be calculated semianalytically. It is found that the dominant loss mechanism is radiation rather than reflection, and that the transverse electric polarization exhibits much larger attenuation than transverse magnetic polarization. The method also gives simple rules that can be used in the design of low-loss optical waveguides. The structural properties of sidewall roughness of an InGaAs/InP pedestal waveguide are measured using atomic force microscopy, and the measured attenuation is found to compare well with that predicted by the model.
Fujii, M., Maitra, A., Poulton, C.G., Leuthold, J. & Freude, W. 2006, 'Non-reciprocal transmission and Schmitt trigger operation in strongly modulated asymmetric WBGs', Optics Express, vol. 14, no. 26, pp. 12782-12793.
We investigate numerically a non-reciprocal switching behavior in strongly modulated waveguide Bragg gratings (WBGs) having a longitudinally asymmetric stopband configuration. The minimum power predicted for a stable switching operation is found to be approximately 77 mW for a realistic waveguide structure made of prospective materials; we assume in this paper a nano-strip InGaAsP/InP waveguide having longitudinally asymmetric modulation of the waveguide width. The analysis has been performed with our in-house nonlinear finite-difference time-domain (FDTD) code adapted to parallel computing. The numerical results clearly show low-threshold Schmitt trigger operation, as well as non-reciprocal transmission property where the switching threshold for one propagation direction is lower than that for the other direction. In addition, we discuss the modulation-like instability phenomena in such nonlinear periodic devices by employing both an instantaneous Kerr nonlinearity and a more involved saturable nonlinearity model.
Fujii, M., Koos, C., Poulton, C.G., Leuthold, J. & Freude, W. 2006, 'Nonlinear FDTD analysis and experimental verification in InGaAsP-InP racetrack microresonators', Photonics Technology Letters, IEEE, vol. 18, no. 1-4, pp. 361-363.
We demonstrate for the first time a nonlinear finite-difference time-domain (FDTD) analysis of optical parametric four-wave mixing (FWM) in an actual InGaAsP-InP-based racetrack microresonator, and the results are compared with measurements on an experimental prototype. It has been found from the two-dimensional (2-D) and three-dimensional FDTD analyses that the resonance frequencies can be reasonably predicted by an FDTD model by considering the strong material dispersion of the waveguide medium and that the wavelength conversion by FWM is not sensitive to the dimensionality of the model; thus, it is efficiently predicted by the 2-D FDTD model.
Maitra, A., Poulton, C.G., Wang, J., Leuthold, J. & Freude, W. 2005, 'Low switching threshold using nonlinearities in stopband-tapered waveguide Bragg gratings', IEEE Journal of Quantum Electronics, vol. 41, no. 10, pp. 1303-1308.
We numerically study the nonlinear switching characteristics in a waveguide grating with a linearly tapered stopband. This type of design shows promising results in decreasing the threshold switching power, while simultaneously preserving a significant extinction ratio. We find that the switching threshold changes linearly with the tapering coefficient. The physical explanation for these phenomena is discussed. Potential applications for this type of device include all-optical switches and isolators.
Poulton, C.G., Mueller, M. & Freude, W. 2005, 'Scattering from sidewall deformations in photonic crystals', Journal of the Optical Society of America B: Optical Physics, vol. 22, no. 6, pp. 1211-1220.
We present results from a new method for the solution of electromagnetic scattering from finite sets of two-dimensional cylinders exhibiting sidewall deformations. Our model treats the sidewall deviation as a small perturbation on a circle; the response of a single cylinder to an arbitrary external field can then be calculated, and the interactions between the cylinders can be computed with a multipole method. This leads to a series of model problems for successively higher asymptotic orders. Because most of the computation time is taken up with solving the original, unperturbed problem, a large number of additional types of perturbation can be examined at little extra numerical cost.
Spence, A. & Poulton, C.G. 2005, 'Photonic band structure calculations using nonlinear eigenvalue techniques', Journal of Computational Physics, vol. 204, no. 1, pp. 65-81.
This paper considers the numerical computation of the photonic band structure of periodic materials such as photonic crystals. This calculation involves the solution of a Hermitian nonlinear eigenvalue problem. Numerical methods for nonlinear eigenvalue problems are usually based on Newtons method or are extensions of techniques for the standard eigenvalue problem. We present a new variation on existing methods which has its derivation in methods for bifurcation problems, where bordered matrices are used to compute critical points in singular systems. This new approach has several advantages over the current methods. First, in our numerical calculations the new variation is more robust than existing techniques, having a larger domain of convergence. Second, the linear systems remain Hermitian and are nonsingular as the method converges. Third, the approach provides an elegant and efficient way of both thinking about the problem and organising the computer solution so that only one linear system needs to be factorised at each stage in the solution process. Finally, first- and higher-order derivatives are calculated as a natural extension of the basic method, and this has advantages in the electromagnetic problem discussed here, where the band structure is plotted as a set of paths in the (?,k) plane.
Fujii, M., Omaki, N., Tahara, M., Sakagami, I., Poulton, C.G., Freude, W. & Russer, P. 2005, 'Optimization of nonlinear dispersive APML ABC for the FDTD analysis of optical solitons', IEEE Journal of Quantum Electronics, vol. 41, no. 3, pp. 448-454.
We have investigated the parameter optimization for the nonlinear dispersive anisotropic perfectly matched layer (A-PML) absorbing boundary conditions (ABCs) for the two- and the three-dimensional (2D and 3D) finite-difference time-domain (FDTD) analyses of optical soliton propagation. The proposed PML is applied to the FDTD method of the standard and the high-spatial-order schemes. We first searched for the optimum values of the loss factor, permittivity, and the order of polynomial grading for particular numbers of APML layers in a two-dimensional (2-D) setting with Kerr and the Raman nonlinearity and Lorentz dispersion, and then we applied the optimized APML to a full three-dimensional (3-D) analysis of nonlinear optical pulse propagation in a glass substrate. An optical pulse of spatial and temporal soliton profile has been launched with sufficient intensity of electric field to yield a soliton pulse, and a reflection of -60dB has been typically obtained both for the 2-D and the 3-D cases.
Wilcox, S., Botten, L.C., McPhedran, R.C., Poulton, C.G. & De Sterke, C.M. 2005, 'Modeling of defect modes in photonic crystals using the fictitious source superposition method', Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 71, no. 5.
We present an exact theory for modeling defect modes in two-dimensional photonic crystals having an infinite cladding. The method is based on three key concepts, namely, the use of fictitious sources to modify response fields that allow defects to be introduced, the representation of the defect mode field as a superposition of solutions of quasiperiodic field problems, and the simplification of the two-dimensional superposition to a more efficient, one-dimensional average using Bloch mode methods. We demonstrate the accuracy and efficiency of the method, comparing results obtained using alternative techniques, and then concentrate on its strengths, particularly in handling difficult problems, such as where a mode is highly extended near cutoff, that cannot be dealt with in other ways. 2005 The American Physical Society.
Guenneau, S., Movchan, A.B., Poulton, C.G. & Nicolet, A. 2004, 'Coupling between electromagnetic and mechanical vibrations of thin-walled structures', Quarterly Journal of Mechanics and Applied Mathematics, vol. 57, no. 3, pp. 407-428.
The paper addresses the issue of coupling between the electromagnetic and elastic vibrations and deals with the following three classes of problems: vibration of thin bodies in an electromagnetic field; a coupling that occurs due to perturbation of boundaries within a deformed solid; and a coupling within regions of localized stress in a composite structure with defects. It is shown that the coupling effect is negligibly small in the first case, while it becomes important in the last two classes of problems. For vibrations of thin-walled conducting solids placed in an electromagnetic field we present a systematic new asymptotic scheme. It is observed that the magnetic field induces a `viscous force, which is similar to certain problems that occur in magnetic fluids flows. When we deal with electromagnetic waves propagating through a thin-walled periodic structure subject to regular perturbation of the boundary, an asymptotic method is applied to derive the effective boundary conditions for the perturbed inclusion within the array. We examine the effect of this perturbation on the dispersion curves for the corresponding spectral problem, and compare the asymptotic results with a finite element modelling of the perturbed structure. Finally, we show exciting results describing coupling between electromagnetic and elastic fields due to the localization associated with a defect mode in a doubly periodic structure.
Guenneau, S., Poulton, C.G. & Movchan, A.B. 2003, 'Conical propagation of electromagnetic waves through an array of cylindrical inclusions', Physica B: Condensed Matter, vol. 338, no. 1, pp. 149-152.
This paper presents properties of electromagnetic waves propagating through a doubly periodic array of cylindrical channels in oblique incidence. A new method, based on a multipole scattering approach, has been proposed to reduce this spectral problem for partial differential equations to a certain algebraic problem of the Rayleigh-type. We also address the question of a singular perturbation induced by the conical incidence and discuss some effective properties for ferro-magnetic photonic crystal fibers in the long wavelength limit.
Guenneau, S., Poulton, C.G. & Movchan, A.B. 2003, 'Oblique propagation of electromagnetic and elastic waves for an array of cylindrical fibres', Proceedings Of The Royal Society A: Mathematical Physical And Engineering Sciences, vol. 459, no. 2037, pp. 2215-2263.
This paper presents analysis of electromagnetic and elastodynamic waves propagating through a doubly periodic array of cylindrical channels in oblique incidence. A new method, based on a multipole scattering approach, has been proposed to reduce these spectral problems for partial differential equations to certain algebraic problems of the Rayleigh type. We obtain a formulation in terms of an eigenvalue problem that enables us to construct the high-order dispersion curves and to study both photonic and phononic band-gap structures in oblique incidence. We also address the question of a singular perturbation induced by the conical incidence and discuss some effective properties for ferromagnetic photonic crystal fibres in the long-wavelength limit.
Zalipaev, V.V., Movchan, A.B., Poulton, C.G. & McPhedran, R.C. 2002, 'Elastic waves and homogenization in oblique periodic structures', Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences, vol. 458, no. 2024, pp. 1887-1912.
A mathematical model has been constructed to describe elastic waves propagating in a twodimensional solid containing a doubly periodic parallelogram array of circular holes. A multipole expansion method is employed which takes into account a coupling between shear and dilatational waves via the traction boundary conditions and determines the structure of the propagating modes. It is important that the homogenized elastic structure be anisotropic; this follows from analysis presented here. The algorithm has been implemented into a computer code, which was used to construct the dispersion diagrams and analyse the filtering properties of the composite structure. It is of particular interest to study the hexagonal and rhombic types of parallelogram lattices, which can be shown to exhibit phononic bandgaps.
Guenneau, S., Poulton, C.G. & Movchan, A.B. 2002, 'Probleme spectral pour la propagation conique des ondes elastiques dans un reseau de fibres', Comptes Rendus Mathematique, vol. 330, pp. 491-497.
This Note is devoted to the analysis of elastic waves conically propagating through a doubly periodic array of cylindrical channels. A new method, based on a multiple scattering approach, has been proposed to reduce the problem to an algebraic system of the Rayleigh type. We obtain an eigenvalue problem formulation that enables us to construct the high-order dispersion curves and to study phononic band gap structures in oblique propagation. We note an effect of singular perturbation associated with a small angle of conical propagation
Poulton, C.G., Botten, L.C., McPhedran, R.C., Nicorovici, N.A. & Movchan, A.B. 2001, 'Noncommuting limits in electromagnetic scattering: Asymptotic analysis for an array of highly conducting inclusions', SIAM JOURNAL ON APPLIED MATHEMATICS, vol. 61, no. 5, pp. 1706-1730.
Bao, K.D., McPhedran, R.C., Nicorovici, N.A., Poulton, C.G. & Botten, L.C. 2000, 'The electromagnetic modes and homogenization for a cubic lattice of spheres', PHYSICA B, vol. 279, no. 1-3, pp. 162-163.