Photonic Crystal Clusters - Guiding, Localisation and Emission

Optical communication technology is central to the information age. Sustained performance doubling in fibre technology every nine months will soon overwhelm current switching networks, rendering electronic technology uncompetitive. All-optical switching and routing requires development of optical integrated circuits which will likely be based on photonic crystal (the optical analogue of semiconductors. In this project we will investigate the effects of disorder and roughness on the guiding of signals through photonic crystal waveguides and couplers, and study competing radiation processes, quantifying their interplay and the transitions between them using a unique, purpose-built set of design tools based on powerful, new theoretical and computational methods that we have developed. These studies will extend our conceptual understanding of the radiation dynamics of photonic crystals and deliver design studies of photonic crystal waveguides and couplers.

Significant Achievements, Anticipated Outcomes and Future Work

Earlier phases of this project greatly enhanced our understanding of passive devices, especially PC waveguides. In particular, guiding in PC devices was characterised in terms of the Bloch modes of a guide. Monte Carlo simulations also allowed us to investigate the tolerance of such a guide to manufacturing defects.

During 2003 this work was extended to encompass the characterisation, in terms of Bloch modes, of more complex linear PC devices which may serve in the future as a basis for tunable optical circuit components – devices such as the folded directional coupler and Fabry-Perrot interferometers. Computational results have included studies of transmittance, using newly-developed codes for Bloch mode analysis of extended PC devices. Originally prototyped in Mathematica, the method has now been implemented in parallel codes using Fortran90 and OpenMP on the APAC National Facility SC machine. This has allowed us to undertake Monte Carlo studies of the effects of disorder in such devices. In particular, earlier work on the perfectly ordered case had indicated that the folded directional coupler might be suited for use as a notch rejection filter. Our preliminary studies on the disordered case indicate that although the notch rejection property is not as robust in the presence of disorder as is guiding in a simple PC waveguide, nevertheless the property remains observable in the presence of small but significant amounts of disorder. Further computational studies are currently in progress on the cluster at ac3.

This year has seen significant improvement in the efficiency and functionality of the code, as well as its application to the modelling of devices that may provide the building blocks of future integrated optical circuits. This work is now being undertaken as part of the research program of the ARC Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), which was established early in 2003. Future development of the project will be closely aligned with the principal aim of CUDOS – the investigation of integrated photonic devices. It is anticipated that this will involve both application of the current code to the modelling of novel devices and the development of new codes suited to the study of more general photonic materials. It is likely that this will include the use of more generic numerical methods such as Finite Difference Time Domain methods.

Computational Techniques Used

To date the project has been concerned with studies of two-dimensional photonic crystals. Models for such materials, in the absence of disorder, include both finite and infinite arrays of circular cylinders (of infinite length) of specified radius and refractive index, arranged on a rectangular lattice. Disorder may then be introduced in the radii, refractive indices and/or positions of individual cylinders. Waveguides may be constructed in such structures by removing lines of cylinders. More complex structures may be defined by removing more intricately structured sets of cylinders or by altering the properties of one or more cylinders.

The propagation of a field in a finite cluster of cylinders may be characterised by expanding the field as an infinite series of cylindrical harmonics, and then using a Rayleigh multipole method to identify the coefficients of the series as solutions of a large system of linear equations, derived by truncating the series expansion. The field may then be evaluated with speed and accuracy at points on a spatial grid. Thus the study of the behaviour of the field in a single crystal involves the solution of a (potentially very large) linear system, with the size of the matrix determined by the number of cylinders and the number of terms in the truncated series. Bloch mode models of extended linear devices are based on the computation of transfer matrices describing the field propagation through the layers of the structure, and the solution of a corresponding eigenvalue problem. To study the effects of disorder we use Monte Carlo simulation over an ensemble of crystals. The additional computational problems in this case are the estimation of the mean values and standard errors.

We have developed a substantial body of code implementing solutions to the analysis of both single crystals and ensembles. For single crystals we have used OpenMP within a node to implement loop parallelism in order to reduce walltime. We also make use of proprietary LaPack routines for efficient implementation of linear algebraic operations. For multiple realisations, which have formed the majority of the work undertaken during the last year, we have used shell scripts to implement task level parallelism across multiple processors and across multiple nodes. The code has been ported to the APAC National Facility LC cluster without the use of OpenMP, but preserving the use of proprietary libraries for efficiency. It has also been ported to the ac3 Beowulf cluster, again with reliance on OpenMP and LaPack.

Publications, Awards and External Funding

External Funding and Awards

ARC Discovery-Project Grant (2002 – 2004): Light emission and localisation in photonic clusters and random lasers: L. C. Botten and R. C. McPhedran, $58,000 per annum.
ARC Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS): $200,000 per annum, plus $66,000 matching UTS funding.
UTS University Research Group (2002-2005): Photonic Crystal Technology, LC Botten, TN Langtry, GH Smith, AA Asatryan et al, $30,000 per annum.
UTS Research Excellence Grants Scheme (2004): Photon Conductance in Photonic Crystal Devices, AA Asatryan, LC Botten, TN Langtry and GH Smith, $20,000.

Publications

Book Chapter
LC Botten, RC McPhedran, NA Nicorovici, AA Asatryan, CM de Sterke, PA Robinson, K Busch, GH Smith, TN Langtry. ‘Rayleigh multipole methods for photonic crystal calculations’, in PIER Special Issue on ``Electromagnetic Applications of PBG Materials and Structures'', (eds T Itoh & A Priou), 2003, pp 21–60.

Journal articles

L C Botten, A A Asatryan, T N Langtry, T P White, C M de Sterke and R C McPhedran. Semi-analytic treatment for propagation in finite photonic crystal waveguides. Optics Lett., 28, No. 10 2003, pp 854–856.
T N Langtry, L C Botten, A A Asatryan, and R C McPhedran, Monte Carlo modelling of imperfections in two-dimensional photonic crystals, Mathematics and Computers in Simulation, .62, 385-393, 2003
A A Asatryan, K Busch, L C Botten, R C McPhedran, C M de Sterke: Two dimensional Green’s tensor and local density of states in finite sized two-dimensional photonic crystals, Waves in Random Media, 13, 9-25, 2003
A A Asatryan, P A Robinson, R C McPhedran, L C Botten, C M de Sterke, T N Langtry, N A Nicorovici, Diffusion and anomalous diffusion of light in two-dimension photonic crystals, Phys Rev E, 67, 03660, 2003
T N Langtry, L C Botten, C M de Sterke, A A Asatryan and R C McPhedran, Effects of disorder in two-dimensional photonic crystal waveguidess, Phys Rev E, 68, 026611, 2003
R C McPhedran, N A Nicorovici, D R McKenzie, G Rouse, M Large, L C Botten, A Parker, V Welch, V Vardeny, M Wohlgennant, Structural Colours through Photonic Crystals, Physica B, 338, 182-185, 2003.
D. P. Fussell, R. C. McPhedran, C. M. de Sterke and A. A. Asatryan, Three dimensional local density of states in a finite two-dimensional photonic crystal composed of cylinder, Phys. Rev. E 67, 04560, 2003.
R C McPhedran, L C Botten, J McOrist, A A Asatryan, C M de Sterke, N A Nicorovici, Density of states functions for photonic crystals, Phys Rev E, in press.
A A Asatryan, L C Botten, T N Langtry, C M de Sterke, R C McPhedran, P A Robinson, Conductance of photons in disordered photonic crystals, submitted to Phys. Rev. Lett.
T N Langtry, L C Botten, A A Asatryan, M A Byrne and A Bourgeouis. ‘Localisation and disorder in the design of 2D photonic crystal devices’, ANZIAM J., in press.

Conference (full written paper, refereed proceedings)

L C Botten, T P White, A A Asatryan, T N Langtry, C M de Sterke, R C McPhedran, ‘An analytic treatment of propagation in straight and bent photonic crystal waveguides’, CLEO/QELS 2003 Technical Digest, paper CWA23, ISBN 1-55752-733-4, June 1-6, 2003, Baltimore, Maryland.
T N Langtry, L C Botten, A A Asatryan, M A Byrne, A Bourgeois, R C McPhedran, ‘Computational modelling of photonic crystals’, APAC ‘03, Gold Coast Queensland, September 2003, Proceedings of the APAC Conference on Advanced Computing, Grid Applications and eResearch, September 2003 (on CD-ROM).
C M de Sterke, L C Botten, T P White, R C McPhedran, A A Asatryan, T N Langtry, ‘Photonic bandgap effects as a basis for novel compact devices’, Proceedings of COIN’03/ACOFT’03, July 2003, pp.133-136.
A A Asatryan, L C Botten, T P White, C M deSterke, R C McPhedran, T N Langtry. ‘Modelling of complex waveguide structures embedded in photonic crystals’, Proceedings of COIN’03/ACOFT’03, July 2003, pp. 145-148.