volume | PIER Journals

Abstract

A method for modeling and designing of coupled resonators photonic crystal (PC) filters for wavelength division multiplexing (WDM) systems is presented. This proposed method is based on coupling coefficients of intercoupled resonators and the external quality factors of the input and output resonators based on the circuit approach. A general formulation for extracting the two types of parameters from the physical structure of the PC filters is given. At last, we redesign a third-order Chebyshev filter which has a center frequency of 193.55 THz, a flat bandwidth of 50GHz, and ripples of 0.1 dB in the pass-band. The filter's structure derived from the proposed method is more compact.

1. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, "Photonic Crystal: Molding the Flow of Light ," Princeton Univ. Press, Princeton, 1995.

2. Yanik, M. F., H. Altug, J. Vuckovic, and S. Fan, "Submicrometer all-optical digital memory and integration of nanoscale photonic devices without isolator," IEEE J. Lightw. Techno., Vol. 22, 2316-2322, 2004.
doi:10.1109/JLT.2004.833811

3. Koshiba, M., "Wavelength division multiplexing and demultiplex-ing with photonic crystal waveguide coupler ," IEEE J. Lightw. Techno., Vol. 19, 1970-1975, 2001.
doi:10.1109/50.971693

4. Mekis, M. Meier, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, "Lasing mechanism in two dimensional photonic crystal lasers," Appl. Phys. A, Vol. 69, 111-114, 1999.
doi:10.1007/s003390050981

5. Yanik, M. F., S. Fan, M. Soljacic, and J. D. Joannopoulos, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Optics Letters, Vol. 28, 2506-2508, 2003.
doi:10.1364/OL.28.002506

6. Chen, J. C., H. A. Haus, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Optical filters from photonic band gap air bridges," IEEE J. Lightw. Techno., Vol. 14, 2575-2580, 1996.
doi:10.1109/50.548157

7. Imada, M., 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. Lightw. Techno., Vol. 20, 873-878, 2002.
doi:10.1109/JLT.2002.1007943

8. Costa, R., A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Techno. Letters, Vol. 15, 401-403, 2003.
doi:10.1109/LPT.2002.807953

9. Park, D., S. Kim, I. Park, and H. Lim, "Higher order optical resonant filters based on coupled defect resonators in photonic crystals," IEEE J. Lightw. Techno., Vol. 23, 1923-1928, 2005.
doi:10.1109/JLT.2005.846897

10. Li, X. C., J. Xu, K. Xu, A. Q. Liu, and J. T. Lin, "A side-coupled photonic crystal filter with sidelobe suppression," Appl. Phys. A, Vol. 89, 327-332, 2007.
doi:10.1007/s00339-007-4116-4

11. Haus, H. A., Wave and Fields in Optoelectronics, Prentice-Hall, 1984.

12. Fan, S., P. Villeneuve, and J. Joannopoulos, "Channel drop filters in photonic crystals," Opt. Express, Vol. 3, 4-11, 1998.
doi:10.1364/OE.3.000004

13. Chen, C., X. Li, H. Li, K. Xu, J. Wu, and J. Lin, "Bandpass filters based on phase-shifted photonic crystal waveguide gratings," Opt. Express, Vol. 15, 11278-11284, 2007.
doi:10.1364/OE.15.011278

14. Fasihi, K. and S. Mohammadnejad, "Highly efficient channel-drop filter with a coupled cavity-based wavelength-selective reflection feedback," Opt. Express, Vol. 17, 8983-8997, 2009.
doi:10.1364/OE.17.008983

15. Akahane, , Y., T. Asano, H. Takano, B. S. Song, Y. Takana, and S. Noda, "Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response," Opt. Express, Vol. 13, 2512-2530, 2005.
doi:10.1364/OPEX.13.002512

16. Ashcroft, N. W. and N. D. Mermin, Solid State Physics, Saunders College, Philadelphia, 1976.

17. Kouwenhoven, L. P., C. M. Marcus, P. L. McEuen, S. Tarucha, R. M. Westervelt, and N. S. Wingreen, "Electron transport in quantum dots," Proceedings of the NATO Advanced Study Institute on Mesoscopic Electron Transport, Curacao, Netherlands, Antilles, 1996.

18. Mohtashami, A., J. Zarbakhsh, and K. Hingerl, "Advances impedance matching in photonic crystal waveguides," Opt. Quant. E, Vol. 39, 387-394, 2007.
doi:10.1007/s11082-007-9080-x

19. Biswas, R., Z. Y. Li, and K. M. Ho, "Impedance of photonic crystals and photonic crystal waveguides," App. Physics Letters, Vol. 84, 1254-1256, 2004.
doi:10.1063/1.1649815

20. Momeni, B., A. A. Eftekhar, and A. Adibi, "Effective impedance model for analysis of reflection at the interfaces of photonic crystals," Optics Letters, Vol. 32, 778-780, 2007.
doi:10.1364/OL.32.000778

21. Miri, M., A. Khavasi, K. Mehrany, and B. Rashidian, "Transimission-line model to design matching stage for light coupling into two-dimensional photonic crystals," Optics Letters, Vol. 35, 115-117, 2010.
doi:10.1364/OL.35.000115

22. Cameron, R. J., "General coupling matrix synthesis methods for chebyshev filtering functions," IEEE Trans. on MTT, Vol. 47, 433-442, 1999.
doi:10.1109/22.754877

23. Hong, J. S. and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, John Wiley and Sons, Inc., 2001.
doi:10.1002/0471221619.ch12

24., http://www.rsoftdesign.com/.

Dr. Zuo-Xing Dai

Dr. Jia-Li Wang

Dr. Yan Heng