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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
CB01.15.33

### 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

Chen, P.Y., 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, IOP PUBLISHING LTD.
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', Frontiers in Optics, Optical Society of America, USA, pp. 1-2.
We present a new method for designing mode fields of 3D photonic crystal heterostructure cavities. The method is several orders of magnitude faster than existing numerical methods and enables rapid design of heterostructure cavity resonances.
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', Conference on Lasers and Electro-Optics/The International Quantum Electronics Conference (IQEC), Optical Society of America, Washington, DC, USA, pp. 1-2.
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.
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. & de Sterke, C.M. 2008, 'Modes of composite defects in 2D photonic crystals', Joint Conference Of The Opto-Electronics And Communications Conference 2008 And The Australian Conference On Optical Fibre Technology, Vols 1 And 2, IEEE, Piscataway, USA, pp. 1-2.
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 Re 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. & de Sterke, C.M. 2008, 'Evolution of defect states in 2D photonic crystals', CLEO/QELS 2008 (Conference on Lasers and Electro-Optics Conference on Quantum Electronics and Laser Science), IEEE, USA, pp. 1-2.
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.
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.
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. Using this formalism, we study the limitations on different technologically important structures, discuss the effect of inelastic contributions to the forces, and show how finite-length effects can be used to either increase or reduce the SBS gain in nanoscale devices. 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., 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.', Sci Rep, vol. 4, p. 5032.
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., Steel, M.J. & Poulton, C.G. 2014, 'Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers'.
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.', Opt 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., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & Martijn de Sterke, C. 2014, 'Mode-based analysis of silicon nanohole arrays for photovoltaic applications.', Opt Express, vol. 22 Suppl 5, pp. A1343-A1354.
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.
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.', Opt Lett, 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(2)S(3)) 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 (f(3 dB)) for the BDG were 0.4%, ~28 dB, and ~6 GHz, respectively.
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.', Opt 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.
Watts, A., Singh, N., Poulton, C.G., Magi, E., Kabakova, I., Hudson, 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 co
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'.
We examine the effect of acoustic mode confinement on Stimulated Brillouin Scattering 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 non-confined 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.
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, slow- and fast-light, microwave signal processing, Brillouin dynamic gratings, and nonreciprocal devices.
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, pp. A964-A969.
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 $t\rightarrow \infty$.
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 IMAGE SCIENCE AND VISION, vol. 29, no. 5, pp. 817-831.
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.', Opt Lett, 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(2)S(3)) 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.
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
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.
Sturmberg, B.C.P., Dossou, K.B., Botten, L.C., Asatryan, A.A., Poulton, C.G., McPhedran, R.C. & de Sterke, C.M. 2012, 'Nanowire array photovoltaics: Radial disorder versus design for optimal efficiency', APPLIED PHYSICS LETTERS, vol. 101, no. 17.
Smith, M.J., 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 numer
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.', Opt Express, vol. 20, no. 19, pp. 21235-21246.
We propose a scheme for on-chip isolation in chalcogenide (As?S?) 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.
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.', Opt Express, vol. 20, no. 17, pp. 18836-18845.
We report the first demonstration of a photonic chip based dynamically reconfigurable, widely tunable, narrow pass-band, high 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 spectrum, we 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.
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.
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, vol. 86, no. 4.
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.', Opt 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 cm long waveguide with a cross-section 4 ?m x 850 nm 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 x 10(-9) m/W. A probe gain of 16 dB was obtained for a CW pump power of ~300 mW.
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, vol. 84, no. 4.
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.', Opt Lett, 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 (As?S?) 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 1.34 W. Anti-Stokes waves due to four-wave mixing between the pump and the Stokes wave were observed in the forward spectrum.
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.
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., 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.', Opt Express, vol. 19 Suppl 5, pp. A1067-A1081.
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.
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. & de Sterke, C.M. 2010, 'Paired modes of heterostructure cavities in photonic crystal waveguides with split band edges', OPTICS EXPRESS, vol. 18, no. 25, pp. 25693-25701.
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.
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.
Grujic, T., Kuhlmey, B., 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 ..., 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.
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 ..., 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.
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.
Lee, M.W., Grillet, C., Poulton, C.G., Monat, C., Smith, C.L., Mgi, E., Freeman, D., Madden, S., Luther-Davies, B. & Eggleton, B.J. 2008, 'Characterizing photonic crystal waveguides with an expanded k-space evanescent coupling technique.', Opt 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.
Dossou, K.B., Botten, L.C., McPhedran, R.C., Poulton, C.G., Asatryan, A.A. & de Sterke, C.M. 2008, 'Shallow defect states in two-dimensional photonic crystals', PHYSICAL REVIEW A, vol. 77, no. 6.
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.', Phys Rev E Stat Nonlin Soft Matter Phys, vol. 71, no. 5 Pt 2, p. 056606.
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.
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.