Computation of the Filtering Properties of Photonic Crystal Waveguide Discontinuities Using the Mode Matching Method
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:62965", author = "Athanasios Theoharidis and Thomas Kamalakis and Ioannis Neokosmidis and Thomas Sphicopoulos", title = "Computation of the Filtering Properties of Photonic Crystal Waveguide Discontinuities Using the Mode Matching Method", 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.", volume = "2", number = "6", pages = "1252-5", }
