Abstract

The Padé approximation with Baker’s algorithm is compared with the least-squares Prony method and the generalized pencil-of-functions (GPOF) method for calculating mode frequencies and mode Q factors for coupled optical microdisks by FDTD technique. Comparisons of intensity spectra and the corresponding mode frequencies and Q factors show that the Padé approximation can yield more stable results than the Prony and the GPOF methods, especially the intensity spectrum. The results of the Prony method and the GPOF method are greatly influenced by the selected number of resonant modes, which need to be optimized during the data processing, in addition to the length of the time response signal. Furthermore, the Padé approximation is applied to calculate light delay for embedded microring resonators from complex transmission spectra obtained by the Padé approximation from a FDTD output. The Prony and the GPOF methods cannot be applied to calculate the transmission spectra, because the transmission signal obtained by the FDTD simulation cannot be expressed as a sum of damped complex exponentials.

© 2009 Optical Society of America

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References

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  1. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nature Photon. 1, 65-71 (2007).
    [CrossRef]
  2. J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
    [CrossRef]
  3. F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigureable on-chip delay line,” Opt. Express 16, 8395-8405 (2008).
    [CrossRef] [PubMed]
  4. L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
    [CrossRef]
  5. Q. Li, Z. Zhang, J. Wang, M. Qiu, and Y. Su, “Fast light in silicon ring resonator with resonance-splitting,” Opt. Express 17, 933-940 (2009).
    [CrossRef] [PubMed]
  6. A. Taflove, Advances in Computational Electrodynamics--The Finite-Difference Time-Domain Method (Artech House, 1998).
  7. W. L. Ko and R. Mittra, “A combination of FDTD and Prony's methods for analyzing microwave integrated circuits,” IEEE Trans. Microwave Theory Tech. 39, 2176-2181 (1991).
    [CrossRef]
  8. J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony's methods,” IEEE Microw. Guid. Wave Lett. 2, 431-433 (1992).
    [CrossRef]
  9. Y. Hua and T. K. Sarkar, “Generalized pencil-of-function method for extracting poles of an EM system from its transient response,” IEEE Trans. Antennas Propag. 37, 229-233 (1989).
    [CrossRef]
  10. J. Ritter and F. Arndt, “Efficient FDTD/matrix-pencil method for the full-wave scattering parameter analysis of waveguiding structures,” IEEE Trans. Microwave Theory Tech. 44, 2450-2456 (1996).
    [CrossRef]
  11. S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and Padé approximation,” IEEE Microw. Guid. Wave Lett. 8, 415-417 (1998).
    [CrossRef]
  12. G. A. Baker and J. L. Gammel, The Padé Approximant in Theoretical Physics (Academic,1970).
  13. W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
    [CrossRef]
  14. W. H. Guo, Y. Z. Huang, and Q. M. Wang, “Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Padé Approximation,” IEEE Photonics Technol. Lett. 12, 813-815 (2000).
    [CrossRef]
  15. Q. Chen, Y. Z. Huang, W. H. Guo, and L. J. Yu, “Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation,” Opt. Commun. 248, 309-315 (2005).
    [CrossRef]
  16. Y. Z. Huang, Q. Chen, W. H. Guo, and L. J. Yu, “Application of Padé approximation in simulating photonic crystals,” Chin. J. Semicond. 26, 1281-1286 (2005).
  17. Min Qiu, “Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately,” Microwave Opt. Technol. Lett. 45, 381-385 (2005).
    [CrossRef]
  18. Q. Chen, Y. D. Yang, and Y. Z. Huang, “Distributed mode coupling in microring channel drop filters,” Appl. Phys. Lett. 89, 061118 (2006).
    [CrossRef]
  19. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]
  20. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321-322 (2000).
    [CrossRef]

2009 (1)

2008 (3)

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
[CrossRef]

F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigureable on-chip delay line,” Opt. Express 16, 8395-8405 (2008).
[CrossRef] [PubMed]

2007 (1)

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nature Photon. 1, 65-71 (2007).
[CrossRef]

2006 (1)

Q. Chen, Y. D. Yang, and Y. Z. Huang, “Distributed mode coupling in microring channel drop filters,” Appl. Phys. Lett. 89, 061118 (2006).
[CrossRef]

2005 (3)

Q. Chen, Y. Z. Huang, W. H. Guo, and L. J. Yu, “Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation,” Opt. Commun. 248, 309-315 (2005).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, and L. J. Yu, “Application of Padé approximation in simulating photonic crystals,” Chin. J. Semicond. 26, 1281-1286 (2005).

Min Qiu, “Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately,” Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

2001 (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

2000 (2)

W. H. Guo, Y. Z. Huang, and Q. M. Wang, “Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Padé Approximation,” IEEE Photonics Technol. Lett. 12, 813-815 (2000).
[CrossRef]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321-322 (2000).
[CrossRef]

1998 (1)

S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and Padé approximation,” IEEE Microw. Guid. Wave Lett. 8, 415-417 (1998).
[CrossRef]

1996 (1)

J. Ritter and F. Arndt, “Efficient FDTD/matrix-pencil method for the full-wave scattering parameter analysis of waveguiding structures,” IEEE Trans. Microwave Theory Tech. 44, 2450-2456 (1996).
[CrossRef]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

1992 (1)

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony's methods,” IEEE Microw. Guid. Wave Lett. 2, 431-433 (1992).
[CrossRef]

1991 (1)

W. L. Ko and R. Mittra, “A combination of FDTD and Prony's methods for analyzing microwave integrated circuits,” IEEE Trans. Microwave Theory Tech. 39, 2176-2181 (1991).
[CrossRef]

1989 (1)

Y. Hua and T. K. Sarkar, “Generalized pencil-of-function method for extracting poles of an EM system from its transient response,” IEEE Trans. Antennas Propag. 37, 229-233 (1989).
[CrossRef]

Arndt, F.

J. Ritter and F. Arndt, “Efficient FDTD/matrix-pencil method for the full-wave scattering parameter analysis of waveguiding structures,” IEEE Trans. Microwave Theory Tech. 44, 2450-2456 (1996).
[CrossRef]

Baker, G. A.

G. A. Baker and J. L. Gammel, The Padé Approximant in Theoretical Physics (Academic,1970).

Beausoleil, R. G.

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Chen, Q.

Q. Chen, Y. D. Yang, and Y. Z. Huang, “Distributed mode coupling in microring channel drop filters,” Appl. Phys. Lett. 89, 061118 (2006).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, and L. J. Yu, “Application of Padé approximation in simulating photonic crystals,” Chin. J. Semicond. 26, 1281-1286 (2005).

Q. Chen, Y. Z. Huang, W. H. Guo, and L. J. Yu, “Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation,” Opt. Commun. 248, 309-315 (2005).
[CrossRef]

Chen, W.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Chu, S.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Dey, S.

S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and Padé approximation,” IEEE Microw. Guid. Wave Lett. 8, 415-417 (1998).
[CrossRef]

Djordjevic, S. S.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Ferrari, C.

Fontaine, N. K.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Gammel, J. L.

G. A. Baker and J. L. Gammel, The Padé Approximant in Theoretical Physics (Academic,1970).

Guo, W. H.

Q. Chen, Y. Z. Huang, W. H. Guo, and L. J. Yu, “Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation,” Opt. Commun. 248, 309-315 (2005).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, and L. J. Yu, “Application of Padé approximation in simulating photonic crystals,” Chin. J. Semicond. 26, 1281-1286 (2005).

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

W. H. Guo, Y. Z. Huang, and Q. M. Wang, “Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Padé Approximation,” IEEE Photonics Technol. Lett. 12, 813-815 (2000).
[CrossRef]

Hua, Y.

Y. Hua and T. K. Sarkar, “Generalized pencil-of-function method for extracting poles of an EM system from its transient response,” IEEE Trans. Antennas Propag. 37, 229-233 (1989).
[CrossRef]

Huang, Y. Z.

Q. Chen, Y. D. Yang, and Y. Z. Huang, “Distributed mode coupling in microring channel drop filters,” Appl. Phys. Lett. 89, 061118 (2006).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, and L. J. Yu, “Application of Padé approximation in simulating photonic crystals,” Chin. J. Semicond. 26, 1281-1286 (2005).

Q. Chen, Y. Z. Huang, W. H. Guo, and L. J. Yu, “Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation,” Opt. Commun. 248, 309-315 (2005).
[CrossRef]

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

W. H. Guo, Y. Z. Huang, and Q. M. Wang, “Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Padé Approximation,” IEEE Photonics Technol. Lett. 12, 813-815 (2000).
[CrossRef]

Karalar, A. O.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Ko, W. L.

W. L. Ko and R. Mittra, “A combination of FDTD and Prony's methods for analyzing microwave integrated circuits,” IEEE Trans. Microwave Theory Tech. 39, 2176-2181 (1991).
[CrossRef]

Li, Q.

Li, W. J.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

Little, B. E.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Martinelli, M.

Melloni, A.

Mittra, R.

S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and Padé approximation,” IEEE Microw. Guid. Wave Lett. 8, 415-417 (1998).
[CrossRef]

W. L. Ko and R. Mittra, “A combination of FDTD and Prony's methods for analyzing microwave integrated circuits,” IEEE Trans. Microwave Theory Tech. 39, 2176-2181 (1991).
[CrossRef]

Morichetti, F.

Pan, Z.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Pereda, J. A.

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony's methods,” IEEE Microw. Guid. Wave Lett. 2, 431-433 (1992).
[CrossRef]

Prieto, A.

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony's methods,” IEEE Microw. Guid. Wave Lett. 2, 431-433 (1992).
[CrossRef]

Qiu, M.

Qiu, Min

Min Qiu, “Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately,” Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

Ritter, J.

J. Ritter and F. Arndt, “Efficient FDTD/matrix-pencil method for the full-wave scattering parameter analysis of waveguiding structures,” IEEE Trans. Microwave Theory Tech. 44, 2450-2456 (1996).
[CrossRef]

Sarkar, T. K.

Y. Hua and T. K. Sarkar, “Generalized pencil-of-function method for extracting poles of an EM system from its transient response,” IEEE Trans. Antennas Propag. 37, 229-233 (1989).
[CrossRef]

Sekaric, L.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nature Photon. 1, 65-71 (2007).
[CrossRef]

Song, M.

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
[CrossRef]

Su, Y.

Taflove, A.

A. Taflove, Advances in Computational Electrodynamics--The Finite-Difference Time-Domain Method (Artech House, 1998).

Vegas, A.

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony's methods,” IEEE Microw. Guid. Wave Lett. 2, 431-433 (1992).
[CrossRef]

Vielva, L. A.

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony's methods,” IEEE Microw. Guid. Wave Lett. 2, 431-433 (1992).
[CrossRef]

Vlasov, Y.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nature Photon. 1, 65-71 (2007).
[CrossRef]

Wang, J.

Wang, Q. M.

W. H. Guo, Y. Z. Huang, and Q. M. Wang, “Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Padé Approximation,” IEEE Photonics Technol. Lett. 12, 813-815 (2000).
[CrossRef]

Willner, A. E.

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
[CrossRef]

Wu, T.

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
[CrossRef]

Xia, F.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nature Photon. 1, 65-71 (2007).
[CrossRef]

Yang, C.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Yang, J.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Yang, Y. D.

Q. Chen, Y. D. Yang, and Y. Z. Huang, “Distributed mode coupling in microring channel drop filters,” Appl. Phys. Lett. 89, 061118 (2006).
[CrossRef]

Yariv, A.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321-322 (2000).
[CrossRef]

Yoo, S. J. B.

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

Yu, L. J.

Q. Chen, Y. Z. Huang, W. H. Guo, and L. J. Yu, “Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation,” Opt. Commun. 248, 309-315 (2005).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, and L. J. Yu, “Application of Padé approximation in simulating photonic crystals,” Chin. J. Semicond. 26, 1281-1286 (2005).

Zhang, L.

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
[CrossRef]

Zhang, Z.

Zou, L.

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

Q. Chen, Y. D. Yang, and Y. Z. Huang, “Distributed mode coupling in microring channel drop filters,” Appl. Phys. Lett. 89, 061118 (2006).
[CrossRef]

Chin. J. Semicond. (1)

Y. Z. Huang, Q. Chen, W. H. Guo, and L. J. Yu, “Application of Padé approximation in simulating photonic crystals,” Chin. J. Semicond. 26, 1281-1286 (2005).

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321-322 (2000).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (2)

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony's methods,” IEEE Microw. Guid. Wave Lett. 2, 431-433 (1992).
[CrossRef]

S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and Padé approximation,” IEEE Microw. Guid. Wave Lett. 8, 415-417 (1998).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20, 1030-2032 (2008).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

W. H. Guo, Y. Z. Huang, and Q. M. Wang, “Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Padé Approximation,” IEEE Photonics Technol. Lett. 12, 813-815 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

Y. Hua and T. K. Sarkar, “Generalized pencil-of-function method for extracting poles of an EM system from its transient response,” IEEE Trans. Antennas Propag. 37, 229-233 (1989).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

J. Ritter and F. Arndt, “Efficient FDTD/matrix-pencil method for the full-wave scattering parameter analysis of waveguiding structures,” IEEE Trans. Microwave Theory Tech. 44, 2450-2456 (1996).
[CrossRef]

W. L. Ko and R. Mittra, “A combination of FDTD and Prony's methods for analyzing microwave integrated circuits,” IEEE Trans. Microwave Theory Tech. 39, 2176-2181 (1991).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

Min Qiu, “Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately,” Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

Nature Photon. (1)

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nature Photon. 1, 65-71 (2007).
[CrossRef]

Opt. Commun. (1)

Q. Chen, Y. Z. Huang, W. H. Guo, and L. J. Yu, “Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation,” Opt. Commun. 248, 309-315 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonics applications,” Opt. Lett. 17, 1978-1980 (2008).
[CrossRef]

Other (2)

G. A. Baker and J. L. Gammel, The Padé Approximant in Theoretical Physics (Academic,1970).

A. Taflove, Advances in Computational Electrodynamics--The Finite-Difference Time-Domain Method (Artech House, 1998).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of coupled microdisks of radius R and gap g between two disks.

Fig. 2
Fig. 2

Spectra obtained by the LS-Prony method from the 2 14 FDTD output at deci = 3 and resonant number M = 100 , 200, and 300.

Fig. 3
Fig. 3

Spectra obtained by the GPOF method from the 2 14 FDTD output at deci = 5 and the parameter R σ = 10 2 , 10 4 , and 10 6 .

Fig. 4
Fig. 4

Spectra obtained by the Padé approximation from the 2 14 FDTD output at deci = 3 , 4, and 5.

Fig. 5
Fig. 5

Embedded ring resonators of a racetrack and an inside ring coupled to two straight waveguides.

Fig. 6
Fig. 6

Spectra obtained by the Padé approximation, the LS-Prony method at M = 1300 , and the GPOF method at R σ = 10 8 from the 2 15 FDTD output for embedded ring resonators are plotted as the solid, the dashed, and the dashed-dotted curves.

Fig. 7
Fig. 7

(a) Transmission and (b) time delay spectra of the through port obtained by the FDTD technique and the Padé approximation are plotted as the open circles, and those by the transfer matrix method as the solid curves.

Fig. 8
Fig. 8

Transmission coefficients versus time with the time from 0 to (a) 7 ps and (b) 90 ps at the through and the drop ports for injecting a continuous exciting source at wavelength 1493.65 nm of the transmission peak.

Fig. 9
Fig. 9

Mode field pattern obtained by FDTD simulation after (a) 0.1, (b) 3, and (c) 90 ps transmission of the injected continuous wave exciting source at the wavelength 1493.65 nm of the transmission peak.

Tables (1)

Tables Icon

Table 1 Q Factors Obtained by the Three Methods for the TM Modes at λ = 2066 , 1843, and 1674 nm

Equations (37)

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f ( z ) = n = 0 c n z n
n = 0 c n z n P ( z ) R ( z ) = O ( z M + N + 1 ) ,
P ( z ) = n = 0 M a n z n ,
R ( z ) = 1 + n = 1 N b n z n .
U ( , f ) = n = 0 S ( n Δ t ) exp ( i 2 π f n Δ t ) .
F ( z , f ) = n = 0 C n z n ,
η 2 j ( z ) θ 2 j ( z ) = [ N j , j ] F ( z , f ) ,
η 2 j + 1 ( z ) θ 2 j + 1 ( z ) = [ N j 1 , j ] F ( z , f ) ,
η 2 j + 2 ( z ) θ 2 j + 2 ( z ) = η ¯ 2 j + 1 η 2 j ( z ) z η ¯ 2 j η 2 j + 1 ( z ) η ¯ 2 j + 1 θ 2 j ( z ) z η ¯ 2 j θ 2 j + 1 ( z ) ,
η 2 j + 3 ( z ) θ 2 j + 3 ( z ) = η ¯ 2 j + 2 η 2 j + 1 ( z ) η ¯ 2 j + 1 η 2 j + 2 ( z ) η ¯ 2 j + 2 θ 2 j + 1 ( z ) η ¯ 2 j + 1 θ 2 j + 2 ( z ) ,
η 0 = n = 0 N C n z n , θ 0 = 1.0 ,
η 1 = n = 0 N 1 C n z n , θ 1 = 1.0 .
I ( f ) = | [ N 2 , N 2 ] F ( 1 , f ) | 2 .
S n = k = 1 M a k z k n , n = 0 , 1 , 2 , , N ,
z k = exp ( ( j 2 π f k α k ) Δ t ) ,
S n = k = 1 M b k S n k , n = M , M + 1 , , N ,
P ( z ) = z M + b 1 z M 1 + + b M ,
f k = Im ( ln ( z k ) ) 2 π Δ t ,
α k = Re ( ln ( z k ) ) Δ t ,
Q k = π f k α k .
I ( f ) = | k = 1 M a k j 2 π ( f k f ) α k | 2 .
Y 1 = [ y 0 , y 1 , , y L 1 ] ,
Y 2 = [ y 1 , y 2 , , y L ] ,
Y 1 = Z 1 A Z 2 ,
Y 2 = Z 1 A Z 0 Z 2 ,
Z 1 ( l , m ) = z m l 1 ( 1 m M , 1 l N L ) ,
Z 2 ( m , l ) = z m l 1 ( 1 l L , 1 m M ) ,
Z 0 = diag [ z 1 , z 2 , , z M ] ,
A = diag [ a 1 , a 2 , , a M ] .
Y 1 + Y 2 = Z 2 + Z 0 Z 2 ,
Y 1 + Y 2 p i = z i p i .
Y 1 = U D 1 V H ,
Y 1 + = V 0 D 0 1 U 0 H .
( Z z k I ) q k = 0 , k = 1 , 2 , , M ,
Z = D 0 1 U 0 H Y 2 V 0 ,
P ( x , y , t ) = exp [ ( t t 0 ) 2 t w 2 ] cos ( 2 π f t )
τ = d φ d ω ,

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