Abstract

Using coupled-mode theory, we have shown that there is a π phase jump between the input and the through/drop fields of a co-directional coupler when the gap width between the coupled-waveguides reaches certain values such that the length of the coupler equals to the odd integer (for through field) or even integer (for drop field) times of the Transfer Distance. We introduced an efficient numerical method based on combining the scattering matrix method and FDTD method for analyzing a microring that has material loss. By applying this method, we found that the phase jump phenomenon also occurs in a half-ring coupler when the gap width between the coupled half-ring waveguides reaches a critical value. We showed that, for a given operating bandwidth, it is important that the gap width between the rings has to be larger than a certain value in order to avoid the phase jump, or smaller in order to take advantage of the phase jump. Based on the phase jump phenomenon, we found that the through and the drop spectra of the single-arm and the double-arm microring can be manipulated to shift about one half free spectral range by selecting appropriate gap widths. A novel all-microring wavelength interleaver, based on the phase jump phenomenon, is proposed and numerically demonstrated.

© 2009 Optical Society of America

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References

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  1. M. C. M. Lee and M. C. Wu, "Tunable coupling regimes of silicon microdisk resonators using MEMS actuators," Opt. Express 14, 4703-4712 (2006).
    [CrossRef] [PubMed]
  2. A. Yariv and P. Yeh, Photonics:optical electronics in modern communications (Oxford University Press Inc., 2007), pp. 184-189.
  3. M. A. Popovic, C. Manolatou, and M. R. Watts, "Coupled-induced resonance frequency shifts in coupled dielectric multi-cavity filters," Opt. Express 14, 1208-1222 (2006).
    [CrossRef] [PubMed]
  4. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Effect of a layered environment on the complex nature frequencies of two-dimensional WGM dieletric-ring resonators," IEEE J. Lightwave Technol. 20, 1563-1572 (2002).
    [CrossRef]
  5. O. Schwelb, "On the nature of resonance splitting in coupled multiring optical resonators," Opt. Commun. 281, 1065-1071 (2008).
    [CrossRef]
  6. T. Barwicz, M. A. Popovic, P. T. Rakich, M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microringresonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437-1442 (2004).
    [CrossRef] [PubMed]
  7. T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, "Fabrication of add-drop filters based on frequency-matched microring resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
    [CrossRef]
  8. S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
    [CrossRef]
  9. C. K. Madsen and J. H. Zhao, Optical filter design and analysis: a signal processing approach (John Willey & Sons Inc., 1999), pp. 165-177.
  10. T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
    [CrossRef]
  11. K. Oda, N. Takato, H. Toba, and K. Nosu, "A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 6, 1016-1023 (1988).
    [CrossRef]
  12. M. Kohtoku, S. Oku, Y. Kadota, and Y. Yoshikuni, "200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interference with a ring resonator," IEEE Photon. Technol. Lett. 12, 1174-1176 (2000).
    [CrossRef]
  13. Z. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen, "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
    [CrossRef]
  14. J. Song, Q. Fang, S. H. Tao, M. B. Yu, G. Q. Lo, and D. L. Kwong, "Passive ring-assisted Mach-Zehnder interleaver on silicon-on-insulator," Opt. Express 16, 8359-8365 (2008).
    [CrossRef] [PubMed]
  15. C. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2000), Chap. 4.
  16. M. A. Popovic, T. Barwicz, M. R. Watts, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kartner, and H. I. Smith, "Multistage high-order microring-resonator add-drop filters," Opt. Lett. 31, 2571-2573 (2006).
    [CrossRef] [PubMed]
  17. S. Xiao, M. H. Khan, H. Shen, and M. Qi, "A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion," Opt. Express 15, 14765-14771 (2007).
    [CrossRef] [PubMed]
  18. S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Silicon-on-insulator microring add-drop filters with free spectral ranges over 30 nm," IEEE J. Lightwave Technol. 26, 228-236 (2008).
    [CrossRef]
  19. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
    [CrossRef]

2008 (3)

O. Schwelb, "On the nature of resonance splitting in coupled multiring optical resonators," Opt. Commun. 281, 1065-1071 (2008).
[CrossRef]

J. Song, Q. Fang, S. H. Tao, M. B. Yu, G. Q. Lo, and D. L. Kwong, "Passive ring-assisted Mach-Zehnder interleaver on silicon-on-insulator," Opt. Express 16, 8359-8365 (2008).
[CrossRef] [PubMed]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Silicon-on-insulator microring add-drop filters with free spectral ranges over 30 nm," IEEE J. Lightwave Technol. 26, 228-236 (2008).
[CrossRef]

2007 (2)

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion," Opt. Express 15, 14765-14771 (2007).
[CrossRef] [PubMed]

Z. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen, "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

2006 (5)

M. A. Popovic, T. Barwicz, M. R. Watts, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kartner, and H. I. Smith, "Multistage high-order microring-resonator add-drop filters," Opt. Lett. 31, 2571-2573 (2006).
[CrossRef] [PubMed]

M. C. M. Lee and M. C. Wu, "Tunable coupling regimes of silicon microdisk resonators using MEMS actuators," Opt. Express 14, 4703-4712 (2006).
[CrossRef] [PubMed]

M. A. Popovic, C. Manolatou, and M. R. Watts, "Coupled-induced resonance frequency shifts in coupled dielectric multi-cavity filters," Opt. Express 14, 1208-1222 (2006).
[CrossRef] [PubMed]

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, "Fabrication of add-drop filters based on frequency-matched microring resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
[CrossRef]

2004 (3)

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

T. Barwicz, M. A. Popovic, P. T. Rakich, M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microringresonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437-1442 (2004).
[CrossRef] [PubMed]

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

2002 (1)

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Effect of a layered environment on the complex nature frequencies of two-dimensional WGM dieletric-ring resonators," IEEE J. Lightwave Technol. 20, 1563-1572 (2002).
[CrossRef]

2000 (1)

M. Kohtoku, S. Oku, Y. Kadota, and Y. Yoshikuni, "200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interference with a ring resonator," IEEE Photon. Technol. Lett. 12, 1174-1176 (2000).
[CrossRef]

1988 (1)

K. Oda, N. Takato, H. Toba, and K. Nosu, "A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 6, 1016-1023 (1988).
[CrossRef]

Absil, P. P.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Barwicz, T.

Benson, T. M.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Effect of a layered environment on the complex nature frequencies of two-dimensional WGM dieletric-ring resonators," IEEE J. Lightwave Technol. 20, 1563-1572 (2002).
[CrossRef]

Boriskina, S. V.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Effect of a layered environment on the complex nature frequencies of two-dimensional WGM dieletric-ring resonators," IEEE J. Lightwave Technol. 20, 1563-1572 (2002).
[CrossRef]

Cao, S.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Chang, S. J.

Z. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen, "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Chen, Y. J.

Z. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen, "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Chu, S. T.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Damask, J. N.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Doerr, C. R.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Fang, Q.

Gill, D.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Guiziou, L.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Harvey, G.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Haus, H. A.

Hibino, Y.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Hryniewicz, J. V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Inoue, Y.

T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
[CrossRef]

Ippen, E. P.

Johnson, F. G.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Kadota, Y.

M. Kohtoku, S. Oku, Y. Kadota, and Y. Yoshikuni, "200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interference with a ring resonator," IEEE Photon. Technol. Lett. 12, 1174-1176 (2000).
[CrossRef]

Kartner, F. X.

Khan, M. H.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Silicon-on-insulator microring add-drop filters with free spectral ranges over 30 nm," IEEE J. Lightwave Technol. 26, 228-236 (2008).
[CrossRef]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion," Opt. Express 15, 14765-14771 (2007).
[CrossRef] [PubMed]

King, O.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Kitoh, T.

T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
[CrossRef]

Kohtoku, M.

M. Kohtoku, S. Oku, Y. Kadota, and Y. Yoshikuni, "200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interference with a ring resonator," IEEE Photon. Technol. Lett. 12, 1174-1176 (2000).
[CrossRef]

Kwong, D. L.

Lee, M. C. M.

Li, H.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Little, B. E.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Lo, G. Q.

Manolatou, C.

Mizuno, T.

T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
[CrossRef]

Ni, C. Y.

Z. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen, "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Nosich, A. I.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Effect of a layered environment on the complex nature frequencies of two-dimensional WGM dieletric-ring resonators," IEEE J. Lightwave Technol. 20, 1563-1572 (2002).
[CrossRef]

Nosu, K.

K. Oda, N. Takato, H. Toba, and K. Nosu, "A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 6, 1016-1023 (1988).
[CrossRef]

Oda, K.

K. Oda, N. Takato, H. Toba, and K. Nosu, "A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 6, 1016-1023 (1988).
[CrossRef]

Oguma, M.

T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
[CrossRef]

Oku, S.

M. Kohtoku, S. Oku, Y. Kadota, and Y. Yoshikuni, "200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interference with a ring resonator," IEEE Photon. Technol. Lett. 12, 1174-1176 (2000).
[CrossRef]

Popovic, M. A.

Qi, M.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Silicon-on-insulator microring add-drop filters with free spectral ranges over 30 nm," IEEE J. Lightwave Technol. 26, 228-236 (2008).
[CrossRef]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion," Opt. Express 15, 14765-14771 (2007).
[CrossRef] [PubMed]

Rakich, P. T.

Schwelb, O.

O. Schwelb, "On the nature of resonance splitting in coupled multiring optical resonators," Opt. Commun. 281, 1065-1071 (2008).
[CrossRef]

Seiferth, F.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Sewell, P.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Effect of a layered environment on the complex nature frequencies of two-dimensional WGM dieletric-ring resonators," IEEE J. Lightwave Technol. 20, 1563-1572 (2002).
[CrossRef]

Shen, H.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Silicon-on-insulator microring add-drop filters with free spectral ranges over 30 nm," IEEE J. Lightwave Technol. 26, 228-236 (2008).
[CrossRef]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion," Opt. Express 15, 14765-14771 (2007).
[CrossRef] [PubMed]

Shibata, T.

T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
[CrossRef]

Smith, H. I.

Socci, L.

Song, J.

Suzuki, S.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Takahashi, H.

T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
[CrossRef]

Takato, N.

K. Oda, N. Takato, H. Toba, and K. Nosu, "A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 6, 1016-1023 (1988).
[CrossRef]

Tao, S. H.

Toba, H.

K. Oda, N. Takato, H. Toba, and K. Nosu, "A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 6, 1016-1023 (1988).
[CrossRef]

Trakalo, M.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Van, V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Wang, Z.

Z. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen, "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Watts, M. R.

Wu, K. Y.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Wu, M. C.

Xiao, S.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Silicon-on-insulator microring add-drop filters with free spectral ranges over 30 nm," IEEE J. Lightwave Technol. 26, 228-236 (2008).
[CrossRef]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion," Opt. Express 15, 14765-14771 (2007).
[CrossRef] [PubMed]

Xie, P.

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

Yoshikuni, Y.

M. Kohtoku, S. Oku, Y. Kadota, and Y. Yoshikuni, "200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interference with a ring resonator," IEEE Photon. Technol. Lett. 12, 1174-1176 (2000).
[CrossRef]

Yu, M. B.

IEEE J. Lightwave Technol. (6)

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Effect of a layered environment on the complex nature frequencies of two-dimensional WGM dieletric-ring resonators," IEEE J. Lightwave Technol. 20, 1563-1572 (2002).
[CrossRef]

T. Mizuno, T. Kitoh, M. Oguma, Y. Inoue, T. Shibata and H. Takahashi, "Uniform wavelength spacing Mach-Zehnder interference using phase-generating couplers," IEEE J. Lightwave Technol. 24, 3217-3226 (2006).
[CrossRef]

K. Oda, N. Takato, H. Toba, and K. Nosu, "A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 6, 1016-1023 (1988).
[CrossRef]

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, "Fabrication of add-drop filters based on frequency-matched microring resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

S. Cao, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K. Y. Wu, and P. Xie, "Interleaver technology: comparisons and applications requirements," IEEE J. Lightwave Technol. 22, 281-289 (2004).
[CrossRef]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Silicon-on-insulator microring add-drop filters with free spectral ranges over 30 nm," IEEE J. Lightwave Technol. 26, 228-236 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

M. Kohtoku, S. Oku, Y. Kadota, and Y. Yoshikuni, "200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interference with a ring resonator," IEEE Photon. Technol. Lett. 12, 1174-1176 (2000).
[CrossRef]

Z. Wang, S. J. Chang, C. Y. Ni, and Y. J. Chen, "A high-performance ultracompact optical interleaver based on double-ring assisted Mach-Zehnder interferometer," IEEE Photon. Technol. Lett. 19, 1072-1074 (2007).
[CrossRef]

Opt. Commun. (1)

O. Schwelb, "On the nature of resonance splitting in coupled multiring optical resonators," Opt. Commun. 281, 1065-1071 (2008).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Other (3)

C. K. Madsen and J. H. Zhao, Optical filter design and analysis: a signal processing approach (John Willey & Sons Inc., 1999), pp. 165-177.

C. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2000), Chap. 4.

A. Yariv and P. Yeh, Photonics:optical electronics in modern communications (Oxford University Press Inc., 2007), pp. 184-189.

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Figures (12)

Fig. 1.
Fig. 1.

Symmetrical co-directional coupler

Fig. 2.
Fig. 2.

(a)Transfer distance (Lc ). (b)KaL/π. (c)ϕ 11. (d)ϕ 21. (e)∣s ll∣. (f)∣s 2l∣. vs. gaP width g for the symmetrical co-directional coupler of Fig. 1. (ncore =2.5, ncladding =1.5, a=300 nm, L=6 μm, and λ=1550 nm. - ○ -: Calculated with coupled mode theory (rCMT), -∆-: Calculated with weak coupled mode theory (wCMT).)

Fig. 3.
Fig. 3.

Symmetrical half-ring coupler. (ncore =2.5, ncladding =1.5, guide widths=300 nm, and αmat =0 dB/cm).

Fig. 4.
Fig. 4.

(a)∣s 11∣, and ∣s 21∣ (b)ϕ 11, and ϕ 21 vs. gap width g for the symmetrical half-ring coupler of Fig. 3.

Fig. 5.
Fig. 5.

(a)∣s 11∣, and ∣s 21∣ (b)ϕ 11, and ϕ 21 vs. free-space wavelength for the symmetrical half-ring coupler of Fig. 3.

Fig. 6.
Fig. 6.

g vs. λc for the symmetrical half-ring coupler of Fig. 3.

Fig. 7.
Fig. 7.

(a)Ithrough /Ii with g L =350 nm. (b)Ithrough /Ii with g S =20 nm for single-arm microring. (Black line: calculated from the S-matrix method, Red line: calculated from the full-domain FDTD method.)

Fig. 8.
Fig. 8.

Ithrough /Ii and Idrop /Ii for (a) Type I and (b) Type II for double-arm microring with g L =350 nm and g S =20 nm. (Black line: calculated from the S-matrix method, Red line: calculated from the full-domain FDTD method.)

Fig. 9.
Fig. 9.

All-microring wavelength interleaver.

Fig. 10.
Fig. 10.

(a)I drop1/Ii . (b)I drop2/Ii . (c)Ithrough /Ii . for all-microring wavelength interleaver with g L =350 nm and g S =20 nm.

Fig. 11.
Fig. 11.

Single-arm microring resonator.

Fig. 12.
Fig. 12.

Double-arm microring resonator.

Equations (46)

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[A1B1]=[s11s12s21s22] [A0B0]
[A1B1]=[s11exp(jϕ11)s12exp(jϕ12)s21exp(jϕ21)s221exp(jϕ22)][A0B0]
s11=cos(KaL)exp(jΓL)
s21=jsin(KaL)exp(jΓL)
s12=jsin(KaL)exp(jΓL)
s22=cos(KaL)exp(jΓL)
K=ω2μ0ε0(ncore2ncladding2)2βa/2a/2E1E2dxE12dx
C=E1E2dxE12dx
X=ω2μ0ε0(ncore2ncladding2)2βg+a/2g+3a/2E12dxE12dx
A1=s11A0
B1=s21A0
s11=s22=cos(KL)=cos(πL/2Lc)
s12=s212=jsin(KL)=jsin(πL/2Lc)
L=nLc
A1=s11A0+s12 B0
B1=s21A0+s22 B0
B0=B1exp[πR(αring/2+jβring)]
A1={s11+s12s21exp[πR(αring/2+jβring)]}A0/{1-s22exp[πR(αring/2+jβring)]}
Ithrough/Ii=1Imax/Ii1+(2/π)2sin2(θ/2)
r=s22exp(αringπR)
θ=ϕ22+βringπR
Imax/Ii=P1+(P2P3P4) / (1r)2
P1=(1s112) [1+(2/π)2sin2(θ/2)]
P2=2exp (αringπR) s11 s12s21s22cos(ϕ11ϕ12ϕ21+ϕ22)
P3=2exp (αringπR/2) s11 s12s21cos(ϕ11ϕ12ϕ21βringπR)
P4=s122 ∣∣s212 exp (αringπR)
[A1B1]=S(1)[A0B0]=[s11(1)s12(1)s21(1)s22(1)][A0B0]=
[s11(1)exp(jϕ11(1))s12(1)exp(jϕ12(1))s21(1)exp(jϕ21(1))s22(1)exp(jϕ22(1))][A0B0]
[B0C0]=S(2)[B1C1]=[s11(2)s12(2)s21(1)s22(1)][B1C1]=
[s11(2)exp(jϕ11(2))s12(2)exp(jϕ12(2))s21(2)exp(jϕ21(2))s22(2)exp(jϕ22(2))][B1C1]
B0=B1 s11(2)
B1=B0 s22(1) +A0s21(1)
C0=B1 s21(2)
C0=s21(1)s21(2)A0/(1s11(2)s22(1))
A1=B0s12(1)+A0s11(1)
A1=[s11(1)+s11(2)s21(1)s12(1)/(1s11(2)s22(1))] A0
Idrop/Ii=Imax,drop/Ii1+(2/π)2sin2(θ/2)
Ithrough/Ii=1Imax,through/Ii1+(2/π)2sin2(θ/2)
r=s22(1)s11(2)
θ=ϕ22(1)+ϕ11(2)
Imax,drop/Ii=s21(1)2s21(2)2/(1r)2
Imax,through / Ii=Q1+(Q2Q3Q4)/(1r)2
Q1=(1s11(1)2)[1+(2/π)2sin2(θ/2)]
Q2=2s11(2)2s11(1)s12(1) s21(1) s22(1) cos (ϕ21(1)+ϕ12(1)ϕ11(1)ϕ22(2))
Q3=2s11(2)s11(1)s12(1)s21(1)cos(ϕ21(1)+ϕ11(2)+ϕ12(1)ϕ11(1))
Q4=s12(1)2s21(1)2s11(2)2

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