• Topic
• Acknowledgements
• Further reading

Topic

The present work concentrates on the theoretical understanding and the numerical computation of photonic crystals. It provides an introduction into the basic theory, shows some computation results and their interpretation by means of a few sample crystals, and proposes some measurement methods to evaluate the predicted behaviour. The interested user finds some additional software information, a couple of computation results and some images of an earlier made photonic crystal in the annexes.

In this work, the MIT Photonic-Bands software package was used for all of the numerical computations. The software was successfully installed on a personal workstation at home and on a server at the Laboratoire d'Optique Biomédicale. Its capabilities and its functionality were tried out. The program was judged to work reliable. It yields the more accurate results the more time was spent for the computation, and it finds repeatedly the same results for the same task even on different machines and program versions. Then, the results were passed to MATLAB for a powerful postprocessing and a graphical representation. You may download the MATLAB functions written for this task.

A total of three photonic crystal samples were designed by numerical computation and layout. Each sample covers a particular function:

1. a simple band gap filter
2. a high-Q cavity
3. an integrated wave-guide

It was shown that a high dielectric contrast is decisive to design large band gaps that are quite robust against fabrication errors.

Before spending more time for simulation, this work may be continued by the fabrication and test of the designed photonic crystals.

Acknowledgements

I would like to thank Dr. Ivo Utke, Kay Hassler, Prof. Olivier J.F. Martin, MER Patrick Hoffmann and Prof. Theo Lasser for their generous assistance.

Lausanne, 11/7/2002

Marcel Leutenegger

Further reading

1. Ivo Utke, 7x7 photonic crystal, (2001)
2. M. Paulus, O. J.F. Martin
   A fully vectorial technique for scattering and propagation in three-dimensional stratified photonic structures
   Opt. Quantum Electr. 33, 315-325 (2001)
3. M. Paulus, P. Gay-Balmaz, O. J. F. Martin
   Accurate and efficient computation of the Green's tensor for stratified media
   Phys. Rev. E 62, 5797-5807 (2000)
4. S. Johnson, J. Joannopoulos
   Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis
   Opt. Express 8, 173-190 (2001)
5. M. Paulus, O. J.F. Martin
   Green's tensor technique for scattering in two-dimensional stratified media
   Phys. Rev. E 63, 066615 (2001)
6. M. Paulus, O. J.F. Martin
   Light propagation and scattering in stratified: a Green's tensor approach
   J. Opt. Soc. Am. A 18, 854-861 (2001)
7. Bruce E. Kahn, Scanning electron microscopy, (2000)