# Associate Professor Tim Langtry

**Associate Professor,**School of Mathematical Sciences

BAppSc (NSWIT), BA (Hons) (UNSW), MAppSc (NSWIT), PhD (UNSW)

Member, Australian Mathematical Society

**Phone**

+61 2 9514 2258

**Room**

CB01.15.37

### Research Interests

My main research interests are in numerical analysis and computational mathematics. Particular areas of interest include quasi-Monte Carlo methods for numerical multiple integration (eg rank 1 lattice rules) and, more recently, computational photonics.

My work in photonics has focussed on computational modelling of various aspects of photonic crystals - composite materials which exhibit a periodic variation in their refractive index, leading to novel and interesting optical properties. An example of some results of this work may be seen in the paper Effects of disorder in two-dimensional photonic crystal waveguides.

**Can supervise:**Yes

## Chapters

Botten, L.C., McPhedran, R.C., de Sterke, C.M., Nicorovici, N.A., Asatryan, A.A., Smith, G.H., Langtry, T., White, T., Fussell, D.P. & Kuhlmey, B. 2006, 'From Multipole Methods to Photonic Crystal Device modeling' in Yasumoto, K. (ed),

*Electromagnetic Theory and Applications for Photonic Crystals*, Taylor & Francis, Florida, USA, pp. 47-122. NA

Botten, L.C., McPhedran, R.C., Nicorovici, N.A., Asatryan, A.A., de Sterke, C.M., Robinson, P.A., Busch, K., Smith, G. & Langtry, T. 2003, 'Rayleigh multipole methods for photonic crystal calculations' in Priou, A. & Itoh, T. (eds),

*Electromagnetic applications of photonic band gap materials and structures*, Massachusetts Institute of Technology, USA, pp. 21-60. Langtry, T.N. 1998, 'A generalisation of ratios of Fibonacci numbers with application to numerical quadrature', SPRINGER, pp. 239-253.

Langtry, T. 1997, 'Bounds on the figure of merit of some lattice rules' in Niederreiter, H., Hellekalek, P., Larcher, G. & Zinterhof, P. (eds),

*Monte Carlo and Quasi-Monte Carlo Methods 1996*, Springer Verlag, New York, pp. 308-320. Langtry, T. 1993, 'Applications of Fibonacci Numbers: Volume 5' in Bergum, G.E., Philippou, A.N. & Horadam, A.F. (eds),

*Applications of Fibonacci Numbers: Volume 5*, Kluwer Academic Publishers, Dordrecht, pp. 331-343.## Conferences

Zinder, Y., Nicorovici, N.A. & Langtry, T. 2011, 'Mathematica based platform for self-paced learning',

*Proceedings of the 10th International Conference on Technology in Mathematics Teaching (ICTMT10)*, University of Portsmouth, United Kingdom, pp. 203-208. One of the major challenges in teaching applied mathematics is the large amount of calculation involved in many practical mathematical methods. On one hand, mastering these methods requires students to gain experience in performing all steps of a calculation. This experience is crucial for gaining an understanding of the methods, their capabilities and limitations, and cannot be replaced by black box type commercial software which simply displays the results of calculations and gives no insight into the nature of the operations performed. On the other hand, the calculations involved in many modern mathematical methods are tedious and time consuming with fatal results caused by even minor computational mistakes. The advent of computer algebra systems such as Mathematica opened new horizons in teaching mathematics. The ability to perform symbolic calculations in combination with powerful graphics and programming capabilities makes it possible to develop software that provides students with the opportunity for step by step exploration of mathematical procedures. We present the results of an ongoing research project aimed at the development of a Mathematica based platform which allows academics to develop software for self-paced learning.

Zinder, Y., Nicorovici, N. & Langtry, T. 2010, 'MATHEMATICA BASED PLATFORM FOR SELF-PACED LEARNING',

*EDULEARN10: INTERNATIONAL CONFERENCE ON EDUCATION AND NEW LEARNING TECHNOLOGIES*, IATED-INT ASSOC TECHNOLOGY EDUCATION A& DEVELOPMENT, pp. 323-330. Maher, A., Lake, M., Langtry, T. & Hill, C. 2007, 'A proteomics laboratory system and digital mentor',

*APAC07*, Australian Partnership for Advanced Computing, Canberra, Australia, pp. 1-19. The typical small biological laboratory is cmposed of electronic scientific equipment and wet laboratory equipment where staff record reesults into paper workbooks. There is oftern a lack of expert staff to guide new users, and hard won experience is locked away with individual staff and their workbooks. The Proteomics Laboratory System and Digital Mentor aims to: facilitate the capture, analysis and sharing of results; facilitate the creation and documentation of standardised work flows and experimental procedures; and mentore inexperienced users in best practice when engaged in particular procedures in the laboratory. In this paper we discuss the design of the system and report on the initial production release. This is nased on a relational database and web-server framework. A novel aspect of the system is the exploitation of custom extensions to a wiki-style interface that add functionality for non-expert end-users.

Asatryan, A.A., Botten, L.C., McPhedran, R.C., de Sterke, C.M., Langtry, T. & Nicorovici, N.A. 2004, 'Conductance of photons and Anderson localization of light',

*Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies*, Optical Society of America, USA, pp. 860-861. Conductance properties of photons in disordered two-dimensional photonic crystals is calculated using exact multipole expansions technique. The Landauers two-terminal formula is used to calculate average of the conductance, its variance and the probability density distribution.

Langtry, T., Botten, L.C., Asatryan, A.A., Byrne, M.A. & Bourgeois, A. 2004, 'Localisation and disorder in the design of 2D photonic crystal devices',

*ANZIAM Journal - 11th Biennial Computational Techniques and Applications Conference: CTAC-2003*, Cambridge University Press, Australia, pp. 744-758. Photonic crystals are meta-materials that can inhibit the propagation of light in all directions for specific wavelength ranges. Material or structural defects can be introduced into the crystal to cause localised modes, providing the ability to mould the flow of light on the wavelength scale and allowing the development of miniaturised, integrated photonic devices. For this reason, photonic crystals will likely be key building blocks for future micro-optical and communication technology. In this paper, we examine the Bloch mode modelling of 2D photonic crystal structures with application to the analysis of photonic crystal waveguides and their susceptibility to disorder, which provides a framework for studying fabrication tolerances in realistic devices.

Asatryan, A.A., Botten, L.C., White, T.P., de Sterke, C.M., McPhedran, R.C. & Langtry, T. 2003, 'Modelling of complex waveguides structures embedded in photonic crystals',

*COIN/ACOFT 2003. Proceedings on the Optical Internet and Optical Fibre Technology*, COIN/ACOFT 2003, Melbourne, Australia, pp. 145-148. de Sterke, C.M., Botten, L.C., White, T.P., McPhedran, R.C., Asatryan, A.A. & Langtry, T. 2003, 'Photonic bandgap effects as a basis for novel compact devices',

*COIN/ACOFT 2003. Conference Proceedings on the Optical Internet and Optical Fibre Technology*, COIN/ACOFT 2003, Melbourne, Australia, pp. 133-136. Langtry, T., Botten, L.C., Asatryan, A.A., Byrne, M.A., Bourgeois, A. & McPhedran, R.C. 2003, 'Computational modelling of photonic crystals',

*Proceedings of the APAC Conference and Exhibition on Advanced Computing, Grid Application and eResearch*, Australian Partnership for Advanced Computing (APAC, Gold Coast, QLD, pp. 1-19. Botten, L.C., Asatryan, A.A., Langtry, T., de Sterke, C.M. & McPhedran, R.C. 2002, 'Propagation of Photonic Crystal Waveguides',

*Proceedings of the Australian Institute of Physics 15th Biennial Congress 2002.*, Australian Institute of Physics, Sydney, Australia, pp. 289-291. Langtry, T., Botten, L.C., de Sterke, C.M., Asatryan, A.A. & McPhedran, R.C. 2002, 'Effects of Disorder in Photonic Crystal Waveguides',

*Proceedings of the Australian Institute of Physics 15th Biennial Congress 2002.*, Australian Institute of Physics, Sydney, Australia, pp. 310-312. Langtry, T., Botten, L.C., Asatryan, A.A. & McPhedran, R.C. 2001, 'Local Density of States Calculations for Photonic Crystals',

*Proceedings of HPC Asia 2001*, Queensland Parallel Supercomputing Facilty and Australian Partnership for Advasnced Computing, Brisbane, pp. 0-0. Langtry, T.N. 2000, 'A discrepancy-based analysis of figures of merit for lattice rules',

*MONTE CARLO AND QUASI-MONTE CARLO METHODS 1998*, SPRINGER-VERLAG BERLIN, pp. 296-310.## Journal articles

Jay, K., Chaumet, P.C., Langtry, T. & Rahmani, A. 2010, 'Optical binding of electrically small magnetodielectric particles',

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*Journal of Nanophotonics*, vol. 4, pp. 1-9.View/Download from: Publisher's site

An ensemble of spherical particles with arbitrary dielectric permittivity and magnetic penneability was considered in the dipole approximation. Each particle was described by complex electric and magnetic polarizabilities. A computational approach based on the coupled dipole method, also called the discrete dipole approximation, was used to derive the optical force experienced by each particle due to an incident electromagnetiG..Ji.eld and the fields scattered by all other particles. This approach is general and can handle material dispersion and losses. In order to illustrate this approach, we studied the case of two spherical particles separated by a distance d, and illuminated by an incident plane wave whose wave vector is normal to the axis of the particles. We computed the optical force experienced by each particle in the direction of the beam (radiation pressure), and perpendicular to the beam (optical binding) for particles with positive and negative refractive indices. We also considered the effect of material losses.

Jay, K., Chaumet, P.C., Langtry, T.N. & Rahmani, A. 2010, 'Optical binding of electrically small magnetodielectric particles',

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*JOURNAL OF NANOPHOTONICS*, vol. 4.View/Download from: Publisher's site

Asatryan, A.A., Botten, L.C., Byrne, M.A., Langtry, T.N., Nicorovici, N.A., McPhedran, R.C., de Sterke, C.M. & Robinson, P.A. 2005, 'Conductance of photons in disordered photonic crystals',

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*PHYSICAL REVIEW E*, vol. 71, no. 3.View/Download from: Publisher's site

Botten, L.C., White, T.P., de Sterke, C.M., McPhedran, R.C., Asatryan, A.A. & Langtry, T.N. 2004, 'Photonic crystal devices modelled as grating stacks: matrix generalizations of thin film optics',

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*OPTICS EXPRESS*, vol. 12, no. 8, pp. 1592-1604.View/Download from: Publisher's site

White, T.P., Botten, L.C., de Sterke, C.M., McPhedran, R.C., Asatryan, A.A. & Langtry, T.N. 2004, 'Bloch mode scattering matrix methods for modeling extended photonic crystal structures. II. Applications',

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*PHYSICAL REVIEW E*, vol. 70, no. 5.View/Download from: Publisher's site

Langtry, T., Botten, L.C., Asatryan, A.A., Byrne, M.A. & Bourgeois, A. 2004, 'Localisation and disorder in the design of 2D photonic crystal devices',

*ANZIAM Journal*, vol. 45, pp. 744-758. Photonic crystals are meta-materials that can inhibit the propagation of light in all directions for specific wavelength ranges. Material or structural defects can be introduced into the crystal to cause localised modes, providing the ability to mould the flow of light on the wavelength scale and allowing the development of miniaturised, integrated photonic devices. For this reason, photonic crystals will likely be key building blocks for future micro-optical and communication technology. In this paper, we examine the Bloch mode modelling of 2D photonic crystal structures with application to the analysis of photonic crystal waveguides and their susceptibility to disorder, which provides a framework for studying fabrication tolerances in realistic devices.

Botten, L.C., White, T.P., Asatryan, A.A., Langtry, T.N., de Sterke, C.M. & McPhedran, R.C. 2004, 'Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory',

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*PHYSICAL REVIEW E*, vol. 70, no. 5.View/Download from: Publisher's site

White, T.P., Botten, L.C., de Sterke, C.M., McPhedran, R.C., Asatryan, A.A. & Langtry, T.N. 2004, 'Bloch mode scattering matrix methods for modeling extended photonic crystal structures. II. Applications.',

*Phys Rev E Stat Nonlin Soft Matter Phys*, vol. 70, no. 5 Pt 2, p. 056607. The Bloch mode scattering matrix method is applied to several photonic crystal waveguide structures and devices, including waveguide dislocations, a Fabry-Prot resonator, a folded directional coupler, and a Y-junction design. The method is an efficient tool for calculating the properties of extended photonic crystal (PC) devices, in particular when the device consists of a small number of distinct photonic crystal structures, or for long propagation lengths through uniform PC waveguides. The physical insight provided by the method is used to derive simple, semianalytic models that allow fast and efficient calculations of complex photonic crystal structures. We discuss the situations in which such simplifications can be made and provide examples.

Botten, L.C., White, T.P., Asatryan, A.A., Langtry, T.N., de Sterke, C.M. & McPhedran, R.C. 2004, 'Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory.',

*Phys Rev E Stat Nonlin Soft Matter Phys*, vol. 70, no. 5 Pt 2, p. 056606. We present a rigorous Bloch mode scattering matrix method for modeling two-dimensional photonic crystal structures and discuss the formal properties of the formulation. Reciprocity and energy conservation considerations lead to modal orthogonality relations and normalization, both of which are required for mode calculations in inhomogeneous media. Relations are derived for studying the propagation of Bloch modes through photonic crystal structures, and for the reflection and transmission of these modes at interfaces with other photonic crystal structures.

Asatryan, A.A., Robinson, P.A., McPhedran, R.C., Botten, L.C., de Sterke, C.M., Langtry, T.L. & Nicorovici, N.A. 2003, 'Diffusion and anomalous diffusion of light in two-dimensional photonic crystals',

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*PHYSICAL REVIEW E*, vol. 67, no. 3.View/Download from: Publisher's site

Langtry, T., Coupland, M.P. & Moore, B.J. 2003, 'Mathematica in context',

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*International Journal of Mathematical Education in Science & Technology*, vol. 34, no. 5, pp. 699-718.View/Download from: Publisher's site

Langtry, T., Botten, L.C., Asatryan, A.A. & McPhedran, R.C. 2003, 'Monte Carlo modelling of imperfections in two-dimensional photonic crystals',

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*Mathematics And Computers In Simulation*, vol. 62, no. 3-6, pp. 385-393.View/Download from: Publisher's site

In this paper we describe a Monte Carlo simulation of imperfections in photonic crystals, a new class of materials with optical properties that offer promise in a range of potential applications in the areas of information and communications technology. We describe the relevant physical and structural properties of these materials and outline the derivation of a theoretical model. We then present a Monte Carlo investigation of the tolerance of these materials to fabrication defects.

Botten, L.C., Asatryan, A.A., Langtry, T.N., White, T.P., de Sterke, C.M. & McPhedran, R.C. 2003, 'Semianalytic treatment for propagation in finite photonic crystal waveguides',

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*OPTICS LETTERS*, vol. 28, no. 10, pp. 854-856.View/Download from: Publisher's site

Langtry, T.N., Asatryan, A.A., Botten, L.C., de Sterke, C.M., McPhedran, R.C. & Robinson, P.A. 2003, 'Effects of disorder in two-dimensional photonic crystal waveguides',

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*PHYSICAL REVIEW E*, vol. 68, no. 2.View/Download from: Publisher's site

Thornton, B.S., Nguyen, H.T., Hung, A., Hirst, C., Thornton-Benko, E. & Langtry, T. 2001, 'Breast Screening Outcomes: Communications Problems, Chaos Relationship and Control Theory',

*Canadian Applied Mathematics Quarterly*, vol. 9, no. 4, pp. 377-401. Langtry, T.N. 2001, 'A construction of higher-rank lattice rules',

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*MATHEMATICS AND COMPUTERS IN SIMULATION*, vol. 55, no. 1-3, pp. 103-111.View/Download from: Publisher's site

Langtry, T.N. 1999, 'Lattice rules of minimal and maximal rank with good figures of merit',

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*JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS*, vol. 112, no. 1-2, pp. 147-164.View/Download from: Publisher's site

Langtry, T.N. 1996, 'An application of diophantine approximation to the construction of rank-1 lattice quadrature rules',

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*MATHEMATICS OF COMPUTATION*, vol. 65, no. 216, pp. 1635-1662.View/Download from: Publisher's site

LANGTRY, T.N. 1995, 'THE DETERMINATION OF CANONICAL-FORMS FOR LATTICE QUADRATURE-RULES',

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*JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS*, vol. 59, no. 2, pp. 129-143.View/Download from: Publisher's site

Thornton, B.S. & Langtry, T.N. 1988, 'Prescheduling graphic displays for optimal cancer therapies to reveal possible tumor regression or stabilization.',

*J Med Syst*, vol. 12, no. 1, pp. 31-41. The paper describes an adaptive control approach to the problem of the treatment of solid tumors. The evolution with time t of the state of a tumor is modelled by a two-compartment system, governed by two differential equations forming an autonomous system under therapy control u, (formula; see text) where y1 and y2 are the number of proliferating and nonproliferating cells, respectively. The output is analyzed in the phase plane y1y2. The control problem is that of restricting the tumor state to a predetermined region of the plane by selecting a suitable change in therapy control u, e.g., modality and dosage, when the state solution intersects the boundary of this region and the ratio y1/y2 of proliferating to nonproliferating cells is displayed together with an elapsed time scale. Then, consequent selection of a suitable therapeutic sequence may be assisted by the use of a data base as part of an expert system. The process is repeated at each intersection of the prescribed boundary. Such sequences may lead to stabilization of the system through the appearance on a computer display screen of a stable equilibrium point or a limit cycle.