volume | PIER Journals

2004-09-14

Full-Wave Analysis of Coupled Waveguides in a Two-Dimensional Photonic Crystal

Zahra Ghattan,

Dr. Zahra Ghattan

Department of Electrical and Computer Engineering

University of Tehran

Iran

Homepage

Nasrin Hojjat,

Dr. Nasrin Hojjat

Department of Electrical and Computer Engineering

University of Tehran

Homepage

Mahmoud Shahabadi

Dr. Mahmoud Shahabadi

School of Electrical and Computer Engineering

University of Tehran

Iran

Homepage

, Vol. 49, 291-307, 2004

doi:10.2528/PIER04042901

Abstract

It is shown that the modal analysis of coupled waveguides in a two-dimensional photonic crystal can be reduced to the evaluation of natural frequencies of an equivalent network. This network is constituted of ideal transmission lines and transformers and is directly derived from Maxwell's equations without any simplifying assumptions. The natural frequencies of the proposed equivalent network are computed after its subdivision into a series of cascaded sub-networks. These sub-networks are then described by their multiport impedance matrices so that the entire network can be described by the cascaded connection of these matrices. Resonance conditions of this cascaded connection yield the natural frequencies and consequently the propagation constants of various modes of the original coupled photonic-crystal waveguides. Under the resonance condition, the voltages and currents of the equivalent network are nonzero, and they can be used to determine all the field components of the corresponding mode. The obtained numerical results verify the fact that the coupling length of photonic-crystal directional couplers can be reduced considerably.

Citation

Copy Export

Zahra Ghattan, Nasrin Hojjat, and Mahmoud Shahabadi, "Full-Wave Analysis of Coupled Waveguides in a Two-Dimensional Photonic Crystal," , Vol. 49, 291-307, 2004.
doi:10.2528/PIER04042901

References

1. Snyder, A. W., et al. Optical Waveguide Theory, Chapman and Hall, 1995.

2. Vorobeichik, I. and M. Orenstein, "Intermediate-mode-assisted optical directional couplers via embedded periodic structure," IEEE J. Quantum Electron., Vol. 34, 1772-1781, 1998.
doi:10.1109/3.709596

3. Yonekura, J., M. Ikeda, and T. Baba, "Analysis of finite 2- D photonic crystal of columns and lightwave devices using the scattering matrix method," J. Lightwave Technol., Vol. 17, 1500-1508, 1999.
doi:10.1109/50.779177

4. Koshiba, M., "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightwave Technol., Vol. 19, 1970-1975, 2001.
doi:10.1109/50.971693

5. Martinez, A., F. Cuesta, and J. Marti, "Ultrashort 2-D photonic crystal directional couplers," IEEE Photonics Tech. Lett., Vol. 15, 694-696, 2003.
doi:10.1109/LPT.2003.810258

6. Boscolo, S., M. Midrio, and C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. of Quantum Electron., Vol. 38, 47-53, 2002.
doi:10.1109/3.973318

7. Kuchinsky, S., V. Y. Golyatin, A. Y. Kutikov, T. R. Pearsall, and D. Nedeljkovic, "Coupling between photonic crystal waveguides," IEEE J. of Quantum Electron., Vol. 38, 1349-1352, 2002.
doi:10.1109/JQE.2002.802954

8. Shahabadi, M. and K. Schunemann, "Millimeter-wave holographic power splitting/combining," IEEE Trans. Microwave Theory Tech., Vol. 45, No. 12, 2316-2323, 1997.
doi:10.1109/22.643836

9. Shahabadi, M.S. Atakaramians, and N. Hojjat, "Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals," to appear in IEE Proc..

10. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton Univ. Press, 1995.

11. Shahabadi, M., "Application of holography to millimeter-wave power combining," Ph.D. Dissertation, 1998.