Abstract

Coupled resonator optical waveguide (CROW) may play an important role in future integrated optical devices. In this paper, a closed form formula for the calculation of the transfer function of a photonic crystal (PC) CROW coupled to an input and an output PC waveguide is derived. Coupled mode theory (CMT) is initially used for the derivation of a semi-analytical transfer function model. This model requires the computation of the inverse of a matrix containing the coupling coefficients of the device. The model is compared to the results obtained by the finite-difference time domain (FDTD) and good agreement is obtained. Using the tight-binding approximation, the semi-analytical model is used to derive an analytical solution for the transfer function of the structure directly from the coupling coefficients of the device. Based on this analytical model, the resonant frequencies of the structure are determined.

© 2008 IEEE

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  1. A. Yariv, Y. Xu, R. K. Lee, A. Scherer, "Coupled-resonator optical waveguide: A proposal and analysis," Opt. Lett. 24, 711-713 (1999).
  2. S. Mookherjea, A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Topics Quantum Electron. 8, 448-456 (2002).
  3. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
  4. N. Stefanou, A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133 (1999).
  5. C. K. Madsen, "General IIR optical filter design for WDM applications using all-pass filters," IEEE J. Lightw. Technol. 18, 860-868 (2000).
  6. F. Xia, L. Sekaric, M. O'Boyle, Y. Vlasov, "Coupled resonator optical waveguides based on silicon-on-insulator photonic wires," Appl. Phys. Lett. 041122-041122 (2006).
  7. J. K. S. Poon, J. Scheuer, Y. Xu, A. Yariv, "Designing coupled resonator optical waveguide delay lines," J. Opt. Soc. Amer. B 21, 1665-1673 (2004).
  8. Y. Xu, R. K. Lee, A. Yariv, "Propagation and second-harmonic generation of electromagnetic waves in coupled resonator optical waveguides," J. Opt. Soc. Amer. B 17, 387-399 (2000).
  9. A. Tafflove, S. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method (Artech House, 2000).
  10. T. Kamalakis, T. Sphicopoulos, "Analytical expressions for the resonant frequencies and modal fields of finite coupled cavity chains," IEEE J. Quantum Electron. 41, 1419-1425 (2005).
  11. H. A. Haus, W. P. Huang, "Mode coupling in tapped structures," IEEE J. Lightw. Technol. 7, 729-730 (1989).
  12. T. Kamalakis, T. Sphicopoulos, "Frequency dependence of the coupling coefficients and resonant frequency detuning in a nanophotonic waveguide-cavity system," IEEE J. Quantum Electron. 42, 827-837 (2006).
  13. T. Kamalakis, T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using coupled mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).
  14. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  15. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).
  16. R. E. Collin, Field Theory of Guided Waves (IEEE Press, 1990).
  17. M. Koshiba, Y. Tsuji, S. Sasaki, "High performance absorbing boundary conditions for photonic crystal waveguide simulations," IEEE Microw. Compon. Lett. 11, 152-154 (2001).

2006 (2)

F. Xia, L. Sekaric, M. O'Boyle, Y. Vlasov, "Coupled resonator optical waveguides based on silicon-on-insulator photonic wires," Appl. Phys. Lett. 041122-041122 (2006).

T. Kamalakis, T. Sphicopoulos, "Frequency dependence of the coupling coefficients and resonant frequency detuning in a nanophotonic waveguide-cavity system," IEEE J. Quantum Electron. 42, 827-837 (2006).

2005 (2)

T. Kamalakis, T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using coupled mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).

T. Kamalakis, T. Sphicopoulos, "Analytical expressions for the resonant frequencies and modal fields of finite coupled cavity chains," IEEE J. Quantum Electron. 41, 1419-1425 (2005).

2004 (1)

J. K. S. Poon, J. Scheuer, Y. Xu, A. Yariv, "Designing coupled resonator optical waveguide delay lines," J. Opt. Soc. Amer. B 21, 1665-1673 (2004).

2002 (1)

S. Mookherjea, A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Topics Quantum Electron. 8, 448-456 (2002).

2001 (1)

M. Koshiba, Y. Tsuji, S. Sasaki, "High performance absorbing boundary conditions for photonic crystal waveguide simulations," IEEE Microw. Compon. Lett. 11, 152-154 (2001).

2000 (2)

C. K. Madsen, "General IIR optical filter design for WDM applications using all-pass filters," IEEE J. Lightw. Technol. 18, 860-868 (2000).

Y. Xu, R. K. Lee, A. Yariv, "Propagation and second-harmonic generation of electromagnetic waves in coupled resonator optical waveguides," J. Opt. Soc. Amer. B 17, 387-399 (2000).

1999 (2)

A. Yariv, Y. Xu, R. K. Lee, A. Scherer, "Coupled-resonator optical waveguide: A proposal and analysis," Opt. Lett. 24, 711-713 (1999).

N. Stefanou, A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133 (1999).

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

1989 (1)

H. A. Haus, W. P. Huang, "Mode coupling in tapped structures," IEEE J. Lightw. Technol. 7, 729-730 (1989).

Appl. Phys. Lett. (1)

F. Xia, L. Sekaric, M. O'Boyle, Y. Vlasov, "Coupled resonator optical waveguides based on silicon-on-insulator photonic wires," Appl. Phys. Lett. 041122-041122 (2006).

IEEE J. Lightw. Technol. (1)

C. K. Madsen, "General IIR optical filter design for WDM applications using all-pass filters," IEEE J. Lightw. Technol. 18, 860-868 (2000).

IEEE J. Lightw. Technol. (1)

H. A. Haus, W. P. Huang, "Mode coupling in tapped structures," IEEE J. Lightw. Technol. 7, 729-730 (1989).

IEEE J. Quantum Electron. (3)

T. Kamalakis, T. Sphicopoulos, "Frequency dependence of the coupling coefficients and resonant frequency detuning in a nanophotonic waveguide-cavity system," IEEE J. Quantum Electron. 42, 827-837 (2006).

T. Kamalakis, T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using coupled mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).

T. Kamalakis, T. Sphicopoulos, "Analytical expressions for the resonant frequencies and modal fields of finite coupled cavity chains," IEEE J. Quantum Electron. 41, 1419-1425 (2005).

IEEE J. Sel. Topics Quantum Electron. (1)

S. Mookherjea, A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Topics Quantum Electron. 8, 448-456 (2002).

IEEE Microw. Compon. Lett. (1)

M. Koshiba, Y. Tsuji, S. Sasaki, "High performance absorbing boundary conditions for photonic crystal waveguide simulations," IEEE Microw. Compon. Lett. 11, 152-154 (2001).

J. Opt. Soc. Amer. B (1)

J. K. S. Poon, J. Scheuer, Y. Xu, A. Yariv, "Designing coupled resonator optical waveguide delay lines," J. Opt. Soc. Amer. B 21, 1665-1673 (2004).

J. Opt. Soc. Amer. B (1)

Y. Xu, R. K. Lee, A. Yariv, "Propagation and second-harmonic generation of electromagnetic waves in coupled resonator optical waveguides," J. Opt. Soc. Amer. B 17, 387-399 (2000).

Opt. Lett. (1)

Phys. Rev. B (1)

N. Stefanou, A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133 (1999).

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

Other (4)

A. Tafflove, S. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method (Artech House, 2000).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

R. E. Collin, Field Theory of Guided Waves (IEEE Press, 1990).

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