Abstract

We study the dispersion relations in slow-light waveguide structures consisting of coupled microdisk resonators. A group theoretical analysis of the symmetry properties of the propagating modes reveals a fundamental phenomenon: The degeneracy of the CW and CCW rotating modes is removed, giving rise to two distinct transmission bands. This effect induces symmetry-based dispersion which may limit the usable bandwidth of such structures. The properties of this band splitting and its impact on CROW performance for optical communications are studied in detail.

©2010 Optical Society of America

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References

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  1. G J.P. Elliott and P.G. Dawber, Symmetry in physics (Oxford Univ. Press1979).
  2. N. W. Ashcroft and N. David Mermin, Solid state physics (Holt, Rinehart and Winston; Saunders, 1976).
  3. Kazuaki Sakoda, Optical Properties of Photonic Crystals 2nd ed., (Springer, 2004).
  4. Y. Chung, D. G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” IEEE J. Lightwave Technol. 24, 1865 (2006).
    [Crossref]
  5. O. Schwelb, “Band-limited optical mirrors based on ring resonators: analysis and design,” IEEE J. Lightwave Technol. 23, 3931 (2005).
    [Crossref]
  6. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Effect of a layered environment on the complex natural frequencies of two-dimensional WGM dielectric-ring resonators,” IEEE J. Lightwave Technol. 20, 1563 (2002).
    [Crossref]
  7. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau,“Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature (London)  409, 490 (2001).
    [Crossref] [PubMed]
  8. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
    [Crossref] [PubMed]
  9. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature,” Phys. Rev. Lett. 90, 113903 (2003).
    [Crossref] [PubMed]
  10. A.V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, and B. S. Ham, “Observation of Ultraslow and Stored Light Pulses in a Solid,” Phys. Rev. Lett. 88, 023602 (2002).
    [Crossref] [PubMed]
  11. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711 (1999).
    [Crossref]
  12. A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365 (2003).
    [Crossref]
  13. M. F. Yanik and S. Fan, “Stopping Light All Optically,” Phys. Rev. Lett. 92, 083901 (2004).
    [Crossref] [PubMed]
  14. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 93, 233903 (2004).
    [Crossref] [PubMed]
  15. J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides - Toward the slowing and storage of light,” Opt. Photonics News 16, 36 (2005).
    [Crossref]
  16. J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics,” J. Opt. Soc. Am. B 21, 1818 (2004).
    [Crossref]
  17. J. E. Heebner, R. W. Boyd, and Q-Han Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E 65, 036619 (2002)
    [Crossref]
  18. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
    [Crossref] [PubMed]
  19. S. V. Boriskina, “Spectral engineering of bends and branches in microdisk coupled-resonator optical waveguides,” Opt. Express 15, 17371David17379 (2007).
    [Crossref] [PubMed]
  20. J. W. Ryu, S. Y. Lee, C. M. Kim, and Y. J., “Directional interacting whispering-gallery modes in coupled dielectric microdisks,” Phys. Rev. A. 74, 013804 (2006).
    [Crossref]
  21. L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77051801(R) (2008).
    [Crossref]
  22. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Optical Coupling of Whispering-Gallery Modes of Two Identical Microdisks and Its Effect on Photonic Molecule Lasing,” IEEE J. Sel. Top. Quantum Electron. 12, 78–85 (2006).
    [Crossref]
  23. S. V. Boriskina, “Theoretical prediction of a dramatic Q-factor enhancement and degeneracy removal of whispering gallery modes in symmetrical photonic molecules,” Opt. Lett. 31, 338–340 (2006).
    [Crossref] [PubMed]
  24. A. Nakagawa, S. Ishii, and T. Baba, “Photonic molecule laser composed of GaInAsP microdisks,” Appl. Phy. Lett. 86, 041112 (2005).
    [Crossref]
  25. B. Z. Steinberg, “Rotating photonic crystals: A medium for compact optical gyroscopes,” Phys. Rev. E 71, 056621 (2005).
    [Crossref]
  26. J. Scheuer and A. Yariv, “Sagnac Effect in Coupled-Resonator Slow-Light Waveguide Structures,” Phys. Rev. Lett. 96, 053901 (2006)
    [Crossref] [PubMed]
  27. B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B. 24, 1216 (2007).
    [Crossref]
  28. M. Tinkham, Group theory and quantum mechanics (McGraw-Hill, New York, 1964).
  29. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669 (2002)
    [Crossref]
  30. A. Taflove, Computational electrodynamics : the finite-difference time-domain method, (Artech House, Boston, 1995).
  31. J. B. Khurgin, “Dispersion and loss limitations on the performance of optical delay lines based on coupled resonant structures,” Opt. Lett. 32, 133 (2007)
    [Crossref]
  32. P. J. Winzer and R.-J. Essiambre, “Advanced Optical Modulation Formats”, Proceed. IEEE 94, 952 (2006)
    [Crossref]
  33. O. Weiss and J. Scheuer, “Side coupled adjacent resonators CROW - formation of Mid-Band Zero Group Velocity”, Opt. Express 17, 14817 (2009).
    [Crossref] [PubMed]

2009 (1)

2008 (1)

L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77051801(R) (2008).
[Crossref]

2007 (3)

2006 (6)

J. W. Ryu, S. Y. Lee, C. M. Kim, and Y. J., “Directional interacting whispering-gallery modes in coupled dielectric microdisks,” Phys. Rev. A. 74, 013804 (2006).
[Crossref]

P. J. Winzer and R.-J. Essiambre, “Advanced Optical Modulation Formats”, Proceed. IEEE 94, 952 (2006)
[Crossref]

J. Scheuer and A. Yariv, “Sagnac Effect in Coupled-Resonator Slow-Light Waveguide Structures,” Phys. Rev. Lett. 96, 053901 (2006)
[Crossref] [PubMed]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Optical Coupling of Whispering-Gallery Modes of Two Identical Microdisks and Its Effect on Photonic Molecule Lasing,” IEEE J. Sel. Top. Quantum Electron. 12, 78–85 (2006).
[Crossref]

S. V. Boriskina, “Theoretical prediction of a dramatic Q-factor enhancement and degeneracy removal of whispering gallery modes in symmetrical photonic molecules,” Opt. Lett. 31, 338–340 (2006).
[Crossref] [PubMed]

Y. Chung, D. G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” IEEE J. Lightwave Technol. 24, 1865 (2006).
[Crossref]

2005 (4)

O. Schwelb, “Band-limited optical mirrors based on ring resonators: analysis and design,” IEEE J. Lightwave Technol. 23, 3931 (2005).
[Crossref]

A. Nakagawa, S. Ishii, and T. Baba, “Photonic molecule laser composed of GaInAsP microdisks,” Appl. Phy. Lett. 86, 041112 (2005).
[Crossref]

B. Z. Steinberg, “Rotating photonic crystals: A medium for compact optical gyroscopes,” Phys. Rev. E 71, 056621 (2005).
[Crossref]

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides - Toward the slowing and storage of light,” Opt. Photonics News 16, 36 (2005).
[Crossref]

2004 (4)

J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics,” J. Opt. Soc. Am. B 21, 1818 (2004).
[Crossref]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
[Crossref] [PubMed]

M. F. Yanik and S. Fan, “Stopping Light All Optically,” Phys. Rev. Lett. 92, 083901 (2004).
[Crossref] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

2003 (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365 (2003).
[Crossref]

2002 (4)

J. E. Heebner, R. W. Boyd, and Q-Han Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E 65, 036619 (2002)
[Crossref]

A.V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, and B. S. Ham, “Observation of Ultraslow and Stored Light Pulses in a Solid,” Phys. Rev. Lett. 88, 023602 (2002).
[Crossref] [PubMed]

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

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669 (2002)
[Crossref]

2001 (2)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau,“Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature (London)  409, 490 (2001).
[Crossref] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

1999 (1)

Ashcroft, N. W.

N. W. Ashcroft and N. David Mermin, Solid state physics (Holt, Rinehart and Winston; Saunders, 1976).

Baba, T.

A. Nakagawa, S. Ishii, and T. Baba, “Photonic molecule laser composed of GaInAsP microdisks,” Appl. Phy. Lett. 86, 041112 (2005).
[Crossref]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau,“Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature (London)  409, 490 (2001).
[Crossref] [PubMed]

Benson, T. M.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Optical Coupling of Whispering-Gallery Modes of Two Identical Microdisks and Its Effect on Photonic Molecule Lasing,” IEEE J. Sel. Top. Quantum Electron. 12, 78–85 (2006).
[Crossref]

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

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

Boag, A.

B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B. 24, 1216 (2007).
[Crossref]

Boriskina, S. V.

Boyd, R. W.

J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics,” J. Opt. Soc. Am. B 21, 1818 (2004).
[Crossref]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

J. E. Heebner, R. W. Boyd, and Q-Han Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E 65, 036619 (2002)
[Crossref]

Chak, P.

Chipouline, A.

L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77051801(R) (2008).
[Crossref]

Chung, Y.

Y. Chung, D. G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” IEEE J. Lightwave Technol. 24, 1865 (2006).
[Crossref]

Dagli, N.

Y. Chung, D. G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” IEEE J. Lightwave Technol. 24, 1865 (2006).
[Crossref]

Dawber, P.G.

G J.P. Elliott and P.G. Dawber, Symmetry in physics (Oxford Univ. Press1979).

Deych, L. I.

L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77051801(R) (2008).
[Crossref]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau,“Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature (London)  409, 490 (2001).
[Crossref] [PubMed]

Elliott, G J.P.

G J.P. Elliott and P.G. Dawber, Symmetry in physics (Oxford Univ. Press1979).

Essiambre, R.-J.

P. J. Winzer and R.-J. Essiambre, “Advanced Optical Modulation Formats”, Proceed. IEEE 94, 952 (2006)
[Crossref]

Fan, S.

M. F. Yanik and S. Fan, “Stopping Light All Optically,” Phys. Rev. Lett. 92, 083901 (2004).
[Crossref] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

Ham, B. S.

A.V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, and B. S. Ham, “Observation of Ultraslow and Stored Light Pulses in a Solid,” Phys. Rev. Lett. 88, 023602 (2002).
[Crossref] [PubMed]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau,“Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature (London)  409, 490 (2001).
[Crossref] [PubMed]

Heebner, J. E.

J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics,” J. Opt. Soc. Am. B 21, 1818 (2004).
[Crossref]

J. E. Heebner, R. W. Boyd, and Q-Han Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E 65, 036619 (2002)
[Crossref]

Huang, Y.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
[Crossref] [PubMed]

Ishii, S.

A. Nakagawa, S. Ishii, and T. Baba, “Photonic molecule laser composed of GaInAsP microdisks,” Appl. Phy. Lett. 86, 041112 (2005).
[Crossref]

Khurgin, J. B.

Kim, C. M.

J. W. Ryu, S. Y. Lee, C. M. Kim, and Y. J., “Directional interacting whispering-gallery modes in coupled dielectric microdisks,” Phys. Rev. A. 74, 013804 (2006).
[Crossref]

Kim, D. G.

Y. Chung, D. G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” IEEE J. Lightwave Technol. 24, 1865 (2006).
[Crossref]

Kippenberg, T. J.

Lee, R. K.

Lee, S. Y.

J. W. Ryu, S. Y. Lee, C. M. Kim, and Y. J., “Directional interacting whispering-gallery modes in coupled dielectric microdisks,” Phys. Rev. A. 74, 013804 (2006).
[Crossref]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau,“Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature (London)  409, 490 (2001).
[Crossref] [PubMed]

Lukin, M. D.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365 (2003).
[Crossref]

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365 (2003).
[Crossref]

Mermin, N. David

N. W. Ashcroft and N. David Mermin, Solid state physics (Holt, Rinehart and Winston; Saunders, 1976).

Mookherjea, S.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
[Crossref] [PubMed]

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365 (2003).
[Crossref]

Musser, J. A.

A.V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, and B. S. Ham, “Observation of Ultraslow and Stored Light Pulses in a Solid,” Phys. Rev. Lett. 88, 023602 (2002).
[Crossref] [PubMed]

Nakagawa, A.

A. Nakagawa, S. Ishii, and T. Baba, “Photonic molecule laser composed of GaInAsP microdisks,” Appl. Phy. Lett. 86, 041112 (2005).
[Crossref]

Nosich, A. I.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Optical Coupling of Whispering-Gallery Modes of Two Identical Microdisks and Its Effect on Photonic Molecule Lasing,” IEEE J. Sel. Top. Quantum Electron. 12, 78–85 (2006).
[Crossref]

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

Paloczi, G. T.

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides - Toward the slowing and storage of light,” Opt. Photonics News 16, 36 (2005).
[Crossref]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
[Crossref] [PubMed]

Park, Q-Han

J. E. Heebner, R. W. Boyd, and Q-Han Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E 65, 036619 (2002)
[Crossref]

Pereira, S.

Pertsch, T.

L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77051801(R) (2008).
[Crossref]

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

Poon, J. K. S.

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides - Toward the slowing and storage of light,” Opt. Photonics News 16, 36 (2005).
[Crossref]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
[Crossref] [PubMed]

Ryu, J. W.

J. W. Ryu, S. Y. Lee, C. M. Kim, and Y. J., “Directional interacting whispering-gallery modes in coupled dielectric microdisks,” Phys. Rev. A. 74, 013804 (2006).
[Crossref]

Sakoda, Kazuaki

Kazuaki Sakoda, Optical Properties of Photonic Crystals 2nd ed., (Springer, 2004).

Scherer, A.

Scheuer, J.

O. Weiss and J. Scheuer, “Side coupled adjacent resonators CROW - formation of Mid-Band Zero Group Velocity”, Opt. Express 17, 14817 (2009).
[Crossref] [PubMed]

B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B. 24, 1216 (2007).
[Crossref]

J. Scheuer and A. Yariv, “Sagnac Effect in Coupled-Resonator Slow-Light Waveguide Structures,” Phys. Rev. Lett. 96, 053901 (2006)
[Crossref] [PubMed]

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides - Toward the slowing and storage of light,” Opt. Photonics News 16, 36 (2005).
[Crossref]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
[Crossref] [PubMed]

Schmidt, C.

L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77051801(R) (2008).
[Crossref]

Schwelb, O.

O. Schwelb, “Band-limited optical mirrors based on ring resonators: analysis and design,” IEEE J. Lightwave Technol. 23, 3931 (2005).
[Crossref]

Sewell, P.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Optical Coupling of Whispering-Gallery Modes of Two Identical Microdisks and Its Effect on Photonic Molecule Lasing,” IEEE J. Sel. Top. Quantum Electron. 12, 78–85 (2006).
[Crossref]

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

Shahriar, M. S.

A.V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, and B. S. Ham, “Observation of Ultraslow and Stored Light Pulses in a Solid,” Phys. Rev. Lett. 88, 023602 (2002).
[Crossref] [PubMed]

Sipe, J. E.

Smotrova, E. I.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Optical Coupling of Whispering-Gallery Modes of Two Identical Microdisks and Its Effect on Photonic Molecule Lasing,” IEEE J. Sel. Top. Quantum Electron. 12, 78–85 (2006).
[Crossref]

Spillane, S. M.

Steinberg, B. Z.

B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B. 24, 1216 (2007).
[Crossref]

B. Z. Steinberg, “Rotating photonic crystals: A medium for compact optical gyroscopes,” Phys. Rev. E 71, 056621 (2005).
[Crossref]

Sudarshanam, V. S.

A.V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, and B. S. Ham, “Observation of Ultraslow and Stored Light Pulses in a Solid,” Phys. Rev. Lett. 88, 023602 (2002).
[Crossref] [PubMed]

Suh, W.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

Taflove, A.

A. Taflove, Computational electrodynamics : the finite-difference time-domain method, (Artech House, Boston, 1995).

Tinkham, M.

M. Tinkham, Group theory and quantum mechanics (McGraw-Hill, New York, 1964).

Tünnermann, A.

L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77051801(R) (2008).
[Crossref]

Turukhin, A.V.

A.V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, and B. S. Ham, “Observation of Ultraslow and Stored Light Pulses in a Solid,” Phys. Rev. Lett. 88, 023602 (2002).
[Crossref] [PubMed]

Vahala, K. J.

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

Wang, Z.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

Weiss, O.

Winzer, P. J.

P. J. Winzer and R.-J. Essiambre, “Advanced Optical Modulation Formats”, Proceed. IEEE 94, 952 (2006)
[Crossref]

Xu, Y.

Y. J.,

J. W. Ryu, S. Y. Lee, C. M. Kim, and Y. J., “Directional interacting whispering-gallery modes in coupled dielectric microdisks,” Phys. Rev. A. 74, 013804 (2006).
[Crossref]

Yanik, M. F.

M. F. Yanik and S. Fan, “Stopping Light All Optically,” Phys. Rev. Lett. 92, 083901 (2004).
[Crossref] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

Yariv, A.

J. Scheuer and A. Yariv, “Sagnac Effect in Coupled-Resonator Slow-Light Waveguide Structures,” Phys. Rev. Lett. 96, 053901 (2006)
[Crossref] [PubMed]

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides - Toward the slowing and storage of light,” Opt. Photonics News 16, 36 (2005).
[Crossref]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
[Crossref] [PubMed]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711 (1999).
[Crossref]

Appl. Phy. Lett. (1)

A. Nakagawa, S. Ishii, and T. Baba, “Photonic molecule laser composed of GaInAsP microdisks,” Appl. Phy. Lett. 86, 041112 (2005).
[Crossref]

IEEE J. Lightwave Technol. (3)

Y. Chung, D. G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” IEEE J. Lightwave Technol. 24, 1865 (2006).
[Crossref]

O. Schwelb, “Band-limited optical mirrors based on ring resonators: analysis and design,” IEEE J. Lightwave Technol. 23, 3931 (2005).
[Crossref]

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

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

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Optical Coupling of Whispering-Gallery Modes of Two Identical Microdisks and Its Effect on Photonic Molecule Lasing,” IEEE J. Sel. Top. Quantum Electron. 12, 78–85 (2006).
[Crossref]

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

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

B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B. 24, 1216 (2007).
[Crossref]

Nature (1)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau,“Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature (London)  409, 490 (2001).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Express. (1)

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90 (2004).
[Crossref] [PubMed]

Opt. Lett. (4)

Opt. Photonics News (1)

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, “Coupled Resonator Optical Waveguides - Toward the slowing and storage of light,” Opt. Photonics News 16, 36 (2005).
[Crossref]

Opt. Quantum Electron. (1)

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365 (2003).
[Crossref]

Phys. Rev. A (1)

L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77051801(R) (2008).
[Crossref]

Phys. Rev. A. (1)

J. W. Ryu, S. Y. Lee, C. M. Kim, and Y. J., “Directional interacting whispering-gallery modes in coupled dielectric microdisks,” Phys. Rev. A. 74, 013804 (2006).
[Crossref]

Phys. Rev. E (2)

J. E. Heebner, R. W. Boyd, and Q-Han Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E 65, 036619 (2002)
[Crossref]

B. Z. Steinberg, “Rotating photonic crystals: A medium for compact optical gyroscopes,” Phys. Rev. E 71, 056621 (2005).
[Crossref]

Phys. Rev. Lett. (6)

J. Scheuer and A. Yariv, “Sagnac Effect in Coupled-Resonator Slow-Light Waveguide Structures,” Phys. Rev. Lett. 96, 053901 (2006)
[Crossref] [PubMed]

M. F. Yanik and S. Fan, “Stopping Light All Optically,” Phys. Rev. Lett. 92, 083901 (2004).
[Crossref] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[Crossref] [PubMed]

A.V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, and B. S. Ham, “Observation of Ultraslow and Stored Light Pulses in a Solid,” Phys. Rev. Lett. 88, 023602 (2002).
[Crossref] [PubMed]

Proceed. IEEE (1)

P. J. Winzer and R.-J. Essiambre, “Advanced Optical Modulation Formats”, Proceed. IEEE 94, 952 (2006)
[Crossref]

Other (5)

A. Taflove, Computational electrodynamics : the finite-difference time-domain method, (Artech House, Boston, 1995).

M. Tinkham, Group theory and quantum mechanics (McGraw-Hill, New York, 1964).

G J.P. Elliott and P.G. Dawber, Symmetry in physics (Oxford Univ. Press1979).

N. W. Ashcroft and N. David Mermin, Solid state physics (Holt, Rinehart and Winston; Saunders, 1976).

Kazuaki Sakoda, Optical Properties of Photonic Crystals 2nd ed., (Springer, 2004).

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Figures (14)

Fig. 1.
Fig. 1. Schematic of a CROW structure and field amplitudes definitions.
Fig. 2.
Fig. 2. Dimensions and definitions of the simulated structure.
Fig. 3.
Fig. 3. Symmetric (a) and anti-symmetric (b) modes of an individual microdisk
Fig. 4.
Fig. 4. Dispersion relations of the Anti-symmetric (red) and symmetric (blue) bands of a CROW.
Fig. 5.
Fig. 5. Dependence of the differences in the self-frequency shifts (a) and in the delay per resonator (b) on the inter-resonator gap.
Fig. 6.
Fig. 6. Transmission bands of the Anti-symmetric (red) and symmetric (blue) Bloch modes of a CROW for different gaps.
Fig. 7.
Fig. 7. Transmission bands of the Anti-symmetric (red) and symmetric (blue) Bloch modes of a CROW for different m’s.
Fig. 8.
Fig. 8. Maximal delay as a function of the bandwidth.
Fig. 9.
Fig. 9. Delay-bandwidth product as a function of the bandwidth.
Fig. 10.
Fig. 10. Eye-opening penalty as a function of the number of resonators for a 40Gbs RZ signal.
Fig. 11.
Fig. 11. Eye-opening penalty as a function of the number of resonators for different data-rates.
Fig. 12.
Fig. 12. Eye-opening penalty as a function of the number of resonators for different Q factors.
Fig. 13.
Fig. 13. Eye-opening penalty as a function of the number of resonators for different Q factors for the symmetric branch only.
Fig. 14.
Fig. 14. Schematic modal field profiles of the (a) anti-symmetric and (b) symmetric modes for m=1.

Tables (2)

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Table 1. Traces of the C2v covering operation

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Table A.1 Character table of the C2v group.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

v n = a + a b + b n T .
v n + 1 = M · v n ,
v n + 1 = v n exp ( iK Λ ) ,
( M e iK Λ ) · v = 0 ,
( M e iK Λ ) · v = 0 ,
[ M , D i ] = 0 D i g ,
η μ = β Γ β Γ χ ̄ μ ( β ) χ R ( β ) ,
P μ R = g d μ Γ χ ̄ μ ( g ) D i ( g ) ,
P A 1 R = 1 4 ( E + C 2 + σ x + σ y ) P A 2 R = 1 4 ( E + C 2 σ x σ y ) P B 1 R = 1 4 ( E C 2 + σ x σ y ) P B 2 R = 1 4 ( E C 2 σ x + σ y ) ,
v 1 = ( 1 1 1 1 ) , v 2 = ( 1 1 1 1 ) , v 3 = ( 1 1 1 1 ) , v 4 = ( 1 1 1 1 )
Δ ω K = 1 2 ΩΔ α κ Ω cos ( K Λ ) ,
T d S , AS N r κ S , AS Ω + 1 2 N r · ( ω Ω 1 2 Δ α S , AS ) 2 ( κ S , AS Ω ) 3 ,
Ω 0 = Ω ( 1 + 1 2 δ Δ α ) ,
T d S , AS N r κ S , AS Ω + 1 2 N r · ( Δ ω I S , AS 1 2 Ω δ Δ α ) 2 ( κ S , AS Ω ) 3 ,
T d max = N r κ S Ω + 1 2 N r · ( Δ ω + 1 2 Ω δ Δ α ) 2 ( κ S Ω ) 3 , T d min = N r κ AS Ω ,
N r ( κ S 1 κ AS 1 ) Ω + 1 2 N r . [ 4 ln ( 2 ) B + 1 2 Ω δ Δ α ] 2 ( κ S Ω ) 3 1 4 B ,
E out 1 = 1 2 E in [ exp ( i K S Λ N r ) + exp ( i K AS Λ N r ) ] E out 2 = 1 2 E in [ exp ( i K S Λ N r ) exp ( i K AS Λ N r ) ] ,
P out ( ω ) = P in ( ω ) e α c n T d ( ω ) = P in ( ω ) e Ω Q T d ( ω ) ,
E = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] ; C 2 = [ 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 ] σ x = [ 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 ] ' σ y = [ 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 ] ,

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