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Computation of the Filtering Properties of Photonic Crystal Waveguide Discontinuities Using the Mode Matching Method

Authors: Athanasios Theoharidis, Thomas Kamalakis, Ioannis Neokosmidis, Thomas Sphicopoulos

Abstract:

In this paper, the application of the Mode Matching (MM) method in the case of photonic crystal waveguide discontinuities is presented. The structure under consideration is divided into a number of cells, which supports a number of guided and evanescent modes. These modes can be calculated numerically by an alternative formulation of the plane wave expansion method for each frequency. A matrix equation is then formed relating the modal amplitudes at the beginning and at the end of the structure. The theory is highly efficient and accurate and can be applied to study the transmission sensitivity of photonic crystal devices due to fabrication tolerances. The accuracy of the MM method is compared to the Finite Difference Frequency Domain (FDFD) and the Adjoint Variable Method (AVM) and good agreement is observed.

Keywords: Optical Communications, Integrated Optics, Photonic Crystals, Optical Waveguide Discontinuities.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082097

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References:


[1] J.D Joannopoulos, R.D. Meade and J.N. Winn, Photonic Crystals, Molding the flow of Light, Princeton University Press, 1995.
[2] K. Sakoda, Optical Properties of Photonic Crystals, Springer-Verlag Berlin, 2001.
[3] A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve and J. D. Joannopoulos, "High Transmission through Sharp Bends in Photonic Crystal Waveguides", Phys. Rev. Lett. 77, 3787-3790, 1996.
[4] Y. Hibino, "Recent Advances in High-Density and Large Scale AWG Multi/Demultiplexers With Higher Index Contrast-Based PLCs", IEEE J. Selected Topics in Quant. Elec. Vol. 8, No. 6, November 2002, pp. 1090-1101.
[5] I. Vurgaftman and J. R. Meyer "Photonic-Crystal Distributed-Feedback Quantum Cascade Lasers", IEEE J. Quantum Electronics, Vol. 38, No. 6, June 2002, pp. 592-602.
[6] M. F. Yanik and S. Fan, M. Soljaˇcic' and J. D. Joannopoulos "Alloptical transistor action with bistable switching in a photonic crystal cross-waveguide geometry", OSA Optics Letters Vol. 28, No. 24 December 2003, pp. 2506-2508.
[7] M. Koshiba, "Wavelength Division Multiplexing and Demultiplexing With Photonic Crystal Waveguide Couplers", Vol. 19, No. 12, December 2001, pp. 1970-1975.
[8] T. Matsumoto and T. Baba, "Photonic Crystal k-Vector Superprism", IEEE Journal of Lightwave Technlogy, Vol. 22, No. 3, March 2004, pp. 917-922.
[9] M. Imada, S. Noda A. Chutinan, M. Mochizuki and T. Tanaka "Channel Drop Filter Using a Single Defect in a 2-D Photonic Crystal Slab Waveguide", IEEE J. Lightwave Technology, Vol. 20, No. 5, May 2002, pp. 873-878.
[10] R. Costa, A. Melloni and M. Martinelli, "Bandpass Resonant Filters in Photonic-Crystal Waveguides", IEEE Photon. Techn. Letters, Vol. 15, No. 3, March 2003, pp. 401-403.
[11] D. Park, S. Kim, I. Park and H. Lim, "Higher Order Optical Resonant Filters Based on Coupled Defect Resonators in Photonic Crystals", IEEE J. Lightwave Technology Vol. 23, May 2005, No. 5 pp. 1923-1928.
[12] A. Tafflove and S. Hagness Computational Electrodynamics: the finite difference time-domain method, Artech House Publishers,2000.
[13] M. Koshiba, Y. Tsuji, S. Sasaki "High-Performance Absorbing Boundary Conditions for Photonic Crystal Waveguide Simulations", IEEE Microwave and Wireless Components Letters ,Vol. 11,No.4 ,April 2001, pp. 152-154.
[14] S. D. Wu and E. N. Glytsis, "Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finitedifference frequency-domain method", J. Opt. Soc. Am. A, Vol. 19, No. 10, October 2002, pp. 2018.
[15] G. Veronis, R.W. Dutton, S. Fan, "Method for sensitivity analysis of photonic crystal devices", OSA Optics Letters, Vol. 29, No. 19, October 2004, pp. 2288-2290.
[16] R.E. Collin, Field Theory of Guided Waves, McGraw Hill, 1992
[17] M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O. Weisberg, T.D. Engeness, M. Soljacic, S.A. Jacobs and Y. Fink, "Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarizarion-mode dispersion and group-velocity dispersion", OSA J. Optical Soc. Am. B, Vol. 19, No. 12, Dec 2002, pp. 2867.
[18] S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals", Phys. Rev. E 66, 066608 (2002).
[19] M. L. Povinelli, S. G. Johnson, E. Lidorikis, J. D. Joannopoulos, "Effect of a photonic band gap on scattering from waveguide disorder", Applied Physics Letters, Vol. 84, No. 12, May 2004, pp. 3639.
[20] D. Marcuse, Theory of Dielectric Optical Waveguides, Academic Press Inc, Second Edition 1997.
[21] G. A. Gesell, I. R. Ciric, "Recurrence model analysis for multiple waveguide discontinuities and its application to circular structures", IEEE Transactions on Microwave Theory and Techniques, Vol. 41, No. 3, March 1993, pp. 484 - 490.