Abstract

We study comprehensively using numerical simulations a new class of resonators, based on a circular photonic crystal reflector. The dependence of the resonator characteristics on the reflector design and parameters is studied in detail. The numerical results are compared to analytic results based on coupled mode theory. High quality factors and small modal volumes are found for a wide variety of design parameters.

©2005 Optical Society of America

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  1. C. K. Madsen and J. H. Zhao , Optical Filter Design and Analysis: A Signal Processing Approach , ( Wiley-Interscience, New York , 1999 ).
  2. B. E. Little , “ Second-order filtering and sensing with partially coupled traveling waves in a single resonator ,” Opt. Lett.   23 , 1570 – 1572 ( 1998 ).
    [Crossref]
  3. A. Melloni , R. Costa , P. Monguzzi , and M. Martinelli , “ Ring-resonator filters in silicon oxynitride technology for dense wavelength-division multiplexing systems ,” Opt. Lett.   28 , 1567 – 1569 ( 2003 ).
    [Crossref] [PubMed]
  4. J. E. Heebner and R. W. Boyd , “ ‘Slow’ and ‘fast’ light in resonator-coupled waveguides ,” J. Mod. Opt   49 , 2629 – 2636 ( 2002 ).
    [Crossref]
  5. A. Melloni , F. Morichetti , and M. Mertinelli , “ Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures ,” Opt. Quantum Electron.   35 , 365 ( 2003 ).
    [Crossref]
  6. J. Scheuer , G. T. Paloczi , J. K. S. Poon , and A. Yariv , “ Coupled Resonator Optical Waveguides: Towards Slowing and Storing of Light ,” Opt. Photon. News   16 , 36 – 40 ( 2005 ).
    [Crossref]
  7. A. Yariv , “ Critical coupling and its control in optical waveguide-ring resonator systems ,” IEEE Photonics Technol. Lett.   14 , 483 – 485 ( 2002 ).
    [Crossref]
  8. C. Y. Chao and L. J. Guo , “ Biochemical sensors based on polymer microrings with sharp asymmetrical resonance ,” Appl. Phys. Lett.   83 , 1527 – 1529 ( 2003 ).
    [Crossref]
  9. See, for example, K. J. Vahala , “ Optical microcavities ,” Nature ( London )   424 , 839 – 846 ( 2003 ), and references therein.
    [Crossref] [PubMed]
  10. J. Vuckovic , M. Loncar , H. Mabuchi , and A. Scherer , “ Design of photonic crystal microcavities for cavity QED ,” Phys. Rev. E   65 , 016608 ( 2001 ).
    [Crossref]
  11. O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
    [Crossref] [PubMed]
  12. H. Y. Ryu , M. Notomi , and Y. H. Lee , “ High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities ,” Appl. Phys. Lett.   21 , 4294 – 4296 ( 2003 ).
    [Crossref]
  13. H. Y. Ryu , M. Notomi , G. H. Kim , and Y. H. Lee , “ High quality-factor whispering-gallery mode in the photonic crystal hexagonal disk cavity ,” Opt. Express   12 , 1708 – 1719 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708 .
    [Crossref] [PubMed]
  14. Y. Akahane , T. Asano , B. S. Song , and S. Noda , “ High-Q photonic nanocavity in a two-dimensional photonic crystal ,” Nature   425 , 944 – 947 ( 2003 ).
    [Crossref] [PubMed]
  15. B. S. Song , S. Noda , T. Asano , and Y. Akahane , “ Ultra-high-Q photonic double-heterostructure nanocavity ,” Nature Materials   4 , 207 – 210 ( 2005 ).
    [Crossref]
  16. M. Lončar et al. “ High quality factors and room-temperature lasing in a modified single-defect photonic crystal cavity ,” Opt. Lett.   29 , 721 – 723 ( 2004 ).
    [Crossref] [PubMed]
  17. J. Scheuer and A. Yariv , “ Annular Bragg Defect mode Resonators ,” J. Opt. Soc. Am. B.   20 , 2285 – 2291 ( 2003 ).
    [Crossref]
  18. J. Scheuer and A. Yariv , “ Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators ,” IEEE J. Quantum Electron.   39 , 1555 – 1562 ( 2003 ).
    [Crossref]
  19. J. Scheuer and A. Yariv , “ Circular photonic crystal resonators ,” Physical Review E   70 , 036603 ( 2004 ).
    [Crossref]
  20. J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Low Threshold Two-Dimensional Annular Bragg Lasers ,” Opt. Lett.   29 , 2641 – 2643 ( 2004 ).
    [Crossref] [PubMed]
  21. J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ InGaAsP annular Bragg lasers: Theory, applications and modal properties ,” IEEE J. Sel. Top. Quantum Electron.   11 , 476 – 484 ( 2005 ).
    [Crossref]
  22. K. Srinivasan and O. Painter , “ Momentum space design of high-Q photonic crystal optical cavities ,” Opt. Express   10 , 670 – 684 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670 .
    [PubMed]
  23. J. Vučkovič et al., “ Optimization of the Q factor in photonic crystal microcavities ,” IEEE J. Quantum Electron.   38 , 850 – 856 ( 2002 ).
    [Crossref]
  24. J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Lasing from a circular Bragg nanocavity with and ultrasmall modal volume ,” Appl. Phys. Lett.   86 , 251101 ( 2005 ).
    [Crossref]
  25. G. N. Watson , Theory of Bessel Functions , 2nd ed. ( London, U.K. Cambridge Univ. Press , 1952 ).
  26. G. Mur , “ Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations ,” IEEE Tansactions on Electromagnetic Compatibility   EMC-23 , 377 – 382 ( 1981 ).
    [Crossref]

2005 (4)

J. Scheuer , G. T. Paloczi , J. K. S. Poon , and A. Yariv , “ Coupled Resonator Optical Waveguides: Towards Slowing and Storing of Light ,” Opt. Photon. News   16 , 36 – 40 ( 2005 ).
[Crossref]

B. S. Song , S. Noda , T. Asano , and Y. Akahane , “ Ultra-high-Q photonic double-heterostructure nanocavity ,” Nature Materials   4 , 207 – 210 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ InGaAsP annular Bragg lasers: Theory, applications and modal properties ,” IEEE J. Sel. Top. Quantum Electron.   11 , 476 – 484 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Lasing from a circular Bragg nanocavity with and ultrasmall modal volume ,” Appl. Phys. Lett.   86 , 251101 ( 2005 ).
[Crossref]

2004 (4)

2003 (8)

Y. Akahane , T. Asano , B. S. Song , and S. Noda , “ High-Q photonic nanocavity in a two-dimensional photonic crystal ,” Nature   425 , 944 – 947 ( 2003 ).
[Crossref] [PubMed]

J. Scheuer and A. Yariv , “ Annular Bragg Defect mode Resonators ,” J. Opt. Soc. Am. B.   20 , 2285 – 2291 ( 2003 ).
[Crossref]

J. Scheuer and A. Yariv , “ Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators ,” IEEE J. Quantum Electron.   39 , 1555 – 1562 ( 2003 ).
[Crossref]

A. Melloni , R. Costa , P. Monguzzi , and M. Martinelli , “ Ring-resonator filters in silicon oxynitride technology for dense wavelength-division multiplexing systems ,” Opt. Lett.   28 , 1567 – 1569 ( 2003 ).
[Crossref] [PubMed]

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

C. Y. Chao and L. J. Guo , “ Biochemical sensors based on polymer microrings with sharp asymmetrical resonance ,” Appl. Phys. Lett.   83 , 1527 – 1529 ( 2003 ).
[Crossref]

See, for example, K. J. Vahala , “ Optical microcavities ,” Nature ( London )   424 , 839 – 846 ( 2003 ), and references therein.
[Crossref] [PubMed]

H. Y. Ryu , M. Notomi , and Y. H. Lee , “ High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities ,” Appl. Phys. Lett.   21 , 4294 – 4296 ( 2003 ).
[Crossref]

2002 (4)

K. Srinivasan and O. Painter , “ Momentum space design of high-Q photonic crystal optical cavities ,” Opt. Express   10 , 670 – 684 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670 .
[PubMed]

J. Vučkovič et al., “ Optimization of the Q factor in photonic crystal microcavities ,” IEEE J. Quantum Electron.   38 , 850 – 856 ( 2002 ).
[Crossref]

J. E. Heebner and R. W. Boyd , “ ‘Slow’ and ‘fast’ light in resonator-coupled waveguides ,” J. Mod. Opt   49 , 2629 – 2636 ( 2002 ).
[Crossref]

A. Yariv , “ Critical coupling and its control in optical waveguide-ring resonator systems ,” IEEE Photonics Technol. Lett.   14 , 483 – 485 ( 2002 ).
[Crossref]

2001 (1)

J. Vuckovic , M. Loncar , H. Mabuchi , and A. Scherer , “ Design of photonic crystal microcavities for cavity QED ,” Phys. Rev. E   65 , 016608 ( 2001 ).
[Crossref]

1999 (1)

O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
[Crossref] [PubMed]

1998 (1)

1981 (1)

G. Mur , “ Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations ,” IEEE Tansactions on Electromagnetic Compatibility   EMC-23 , 377 – 382 ( 1981 ).
[Crossref]

Akahane, Y.

B. S. Song , S. Noda , T. Asano , and Y. Akahane , “ Ultra-high-Q photonic double-heterostructure nanocavity ,” Nature Materials   4 , 207 – 210 ( 2005 ).
[Crossref]

Y. Akahane , T. Asano , B. S. Song , and S. Noda , “ High-Q photonic nanocavity in a two-dimensional photonic crystal ,” Nature   425 , 944 – 947 ( 2003 ).
[Crossref] [PubMed]

Asano, T.

B. S. Song , S. Noda , T. Asano , and Y. Akahane , “ Ultra-high-Q photonic double-heterostructure nanocavity ,” Nature Materials   4 , 207 – 210 ( 2005 ).
[Crossref]

Y. Akahane , T. Asano , B. S. Song , and S. Noda , “ High-Q photonic nanocavity in a two-dimensional photonic crystal ,” Nature   425 , 944 – 947 ( 2003 ).
[Crossref] [PubMed]

Boyd, R. W.

J. E. Heebner and R. W. Boyd , “ ‘Slow’ and ‘fast’ light in resonator-coupled waveguides ,” J. Mod. Opt   49 , 2629 – 2636 ( 2002 ).
[Crossref]

Chao, C. Y.

C. Y. Chao and L. J. Guo , “ Biochemical sensors based on polymer microrings with sharp asymmetrical resonance ,” Appl. Phys. Lett.   83 , 1527 – 1529 ( 2003 ).
[Crossref]

Costa, R.

Dapkus, P. D.

O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
[Crossref] [PubMed]

DeRose, G.

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ InGaAsP annular Bragg lasers: Theory, applications and modal properties ,” IEEE J. Sel. Top. Quantum Electron.   11 , 476 – 484 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Lasing from a circular Bragg nanocavity with and ultrasmall modal volume ,” Appl. Phys. Lett.   86 , 251101 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Low Threshold Two-Dimensional Annular Bragg Lasers ,” Opt. Lett.   29 , 2641 – 2643 ( 2004 ).
[Crossref] [PubMed]

Green, W. M. J.

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ InGaAsP annular Bragg lasers: Theory, applications and modal properties ,” IEEE J. Sel. Top. Quantum Electron.   11 , 476 – 484 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Lasing from a circular Bragg nanocavity with and ultrasmall modal volume ,” Appl. Phys. Lett.   86 , 251101 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Low Threshold Two-Dimensional Annular Bragg Lasers ,” Opt. Lett.   29 , 2641 – 2643 ( 2004 ).
[Crossref] [PubMed]

Guo, L. J.

C. Y. Chao and L. J. Guo , “ Biochemical sensors based on polymer microrings with sharp asymmetrical resonance ,” Appl. Phys. Lett.   83 , 1527 – 1529 ( 2003 ).
[Crossref]

Heebner, J. E.

J. E. Heebner and R. W. Boyd , “ ‘Slow’ and ‘fast’ light in resonator-coupled waveguides ,” J. Mod. Opt   49 , 2629 – 2636 ( 2002 ).
[Crossref]

Kim, G. H.

Kim, I.

O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
[Crossref] [PubMed]

Lee, R. K.

O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
[Crossref] [PubMed]

Lee, Y. H.

H. Y. Ryu , M. Notomi , G. H. Kim , and Y. H. Lee , “ High quality-factor whispering-gallery mode in the photonic crystal hexagonal disk cavity ,” Opt. Express   12 , 1708 – 1719 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708 .
[Crossref] [PubMed]

H. Y. Ryu , M. Notomi , and Y. H. Lee , “ High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities ,” Appl. Phys. Lett.   21 , 4294 – 4296 ( 2003 ).
[Crossref]

Little, B. E.

Loncar, M.

M. Lončar et al. “ High quality factors and room-temperature lasing in a modified single-defect photonic crystal cavity ,” Opt. Lett.   29 , 721 – 723 ( 2004 ).
[Crossref] [PubMed]

J. Vuckovic , M. Loncar , H. Mabuchi , and A. Scherer , “ Design of photonic crystal microcavities for cavity QED ,” Phys. Rev. E   65 , 016608 ( 2001 ).
[Crossref]

Mabuchi, H.

J. Vuckovic , M. Loncar , H. Mabuchi , and A. Scherer , “ Design of photonic crystal microcavities for cavity QED ,” Phys. Rev. E   65 , 016608 ( 2001 ).
[Crossref]

Madsen, C. K.

C. K. Madsen and J. H. Zhao , Optical Filter Design and Analysis: A Signal Processing Approach , ( Wiley-Interscience, New York , 1999 ).

Martinelli, M.

Melloni, A.

A. Melloni , R. Costa , P. Monguzzi , and M. Martinelli , “ Ring-resonator filters in silicon oxynitride technology for dense wavelength-division multiplexing systems ,” Opt. Lett.   28 , 1567 – 1569 ( 2003 ).
[Crossref] [PubMed]

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

Mertinelli, M.

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

Monguzzi, P.

Morichetti, F.

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

Mur, G.

G. Mur , “ Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations ,” IEEE Tansactions on Electromagnetic Compatibility   EMC-23 , 377 – 382 ( 1981 ).
[Crossref]

Noda, S.

B. S. Song , S. Noda , T. Asano , and Y. Akahane , “ Ultra-high-Q photonic double-heterostructure nanocavity ,” Nature Materials   4 , 207 – 210 ( 2005 ).
[Crossref]

Y. Akahane , T. Asano , B. S. Song , and S. Noda , “ High-Q photonic nanocavity in a two-dimensional photonic crystal ,” Nature   425 , 944 – 947 ( 2003 ).
[Crossref] [PubMed]

Notomi, M.

H. Y. Ryu , M. Notomi , G. H. Kim , and Y. H. Lee , “ High quality-factor whispering-gallery mode in the photonic crystal hexagonal disk cavity ,” Opt. Express   12 , 1708 – 1719 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708 .
[Crossref] [PubMed]

H. Y. Ryu , M. Notomi , and Y. H. Lee , “ High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities ,” Appl. Phys. Lett.   21 , 4294 – 4296 ( 2003 ).
[Crossref]

O’Brien, J. D.

O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
[Crossref] [PubMed]

Painter, O.

K. Srinivasan and O. Painter , “ Momentum space design of high-Q photonic crystal optical cavities ,” Opt. Express   10 , 670 – 684 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670 .
[PubMed]

O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
[Crossref] [PubMed]

Paloczi, G. T.

J. Scheuer , G. T. Paloczi , J. K. S. Poon , and A. Yariv , “ Coupled Resonator Optical Waveguides: Towards Slowing and Storing of Light ,” Opt. Photon. News   16 , 36 – 40 ( 2005 ).
[Crossref]

Poon, J. K. S.

J. Scheuer , G. T. Paloczi , J. K. S. Poon , and A. Yariv , “ Coupled Resonator Optical Waveguides: Towards Slowing and Storing of Light ,” Opt. Photon. News   16 , 36 – 40 ( 2005 ).
[Crossref]

Ryu, H. Y.

H. Y. Ryu , M. Notomi , G. H. Kim , and Y. H. Lee , “ High quality-factor whispering-gallery mode in the photonic crystal hexagonal disk cavity ,” Opt. Express   12 , 1708 – 1719 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708 .
[Crossref] [PubMed]

H. Y. Ryu , M. Notomi , and Y. H. Lee , “ High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities ,” Appl. Phys. Lett.   21 , 4294 – 4296 ( 2003 ).
[Crossref]

Scherer, A.

J. Vuckovic , M. Loncar , H. Mabuchi , and A. Scherer , “ Design of photonic crystal microcavities for cavity QED ,” Phys. Rev. E   65 , 016608 ( 2001 ).
[Crossref]

O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
[Crossref] [PubMed]

Scheuer, J.

J. Scheuer , G. T. Paloczi , J. K. S. Poon , and A. Yariv , “ Coupled Resonator Optical Waveguides: Towards Slowing and Storing of Light ,” Opt. Photon. News   16 , 36 – 40 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Lasing from a circular Bragg nanocavity with and ultrasmall modal volume ,” Appl. Phys. Lett.   86 , 251101 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ InGaAsP annular Bragg lasers: Theory, applications and modal properties ,” IEEE J. Sel. Top. Quantum Electron.   11 , 476 – 484 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Low Threshold Two-Dimensional Annular Bragg Lasers ,” Opt. Lett.   29 , 2641 – 2643 ( 2004 ).
[Crossref] [PubMed]

J. Scheuer and A. Yariv , “ Circular photonic crystal resonators ,” Physical Review E   70 , 036603 ( 2004 ).
[Crossref]

J. Scheuer and A. Yariv , “ Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators ,” IEEE J. Quantum Electron.   39 , 1555 – 1562 ( 2003 ).
[Crossref]

J. Scheuer and A. Yariv , “ Annular Bragg Defect mode Resonators ,” J. Opt. Soc. Am. B.   20 , 2285 – 2291 ( 2003 ).
[Crossref]

Song, B. S.

B. S. Song , S. Noda , T. Asano , and Y. Akahane , “ Ultra-high-Q photonic double-heterostructure nanocavity ,” Nature Materials   4 , 207 – 210 ( 2005 ).
[Crossref]

Y. Akahane , T. Asano , B. S. Song , and S. Noda , “ High-Q photonic nanocavity in a two-dimensional photonic crystal ,” Nature   425 , 944 – 947 ( 2003 ).
[Crossref] [PubMed]

Srinivasan, K.

Vahala, K. J.

See, for example, K. J. Vahala , “ Optical microcavities ,” Nature ( London )   424 , 839 – 846 ( 2003 ), and references therein.
[Crossref] [PubMed]

Vuckovic, J.

J. Vučkovič et al., “ Optimization of the Q factor in photonic crystal microcavities ,” IEEE J. Quantum Electron.   38 , 850 – 856 ( 2002 ).
[Crossref]

J. Vuckovic , M. Loncar , H. Mabuchi , and A. Scherer , “ Design of photonic crystal microcavities for cavity QED ,” Phys. Rev. E   65 , 016608 ( 2001 ).
[Crossref]

Watson, G. N.

G. N. Watson , Theory of Bessel Functions , 2nd ed. ( London, U.K. Cambridge Univ. Press , 1952 ).

Yariv, A.

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Lasing from a circular Bragg nanocavity with and ultrasmall modal volume ,” Appl. Phys. Lett.   86 , 251101 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ InGaAsP annular Bragg lasers: Theory, applications and modal properties ,” IEEE J. Sel. Top. Quantum Electron.   11 , 476 – 484 ( 2005 ).
[Crossref]

J. Scheuer , G. T. Paloczi , J. K. S. Poon , and A. Yariv , “ Coupled Resonator Optical Waveguides: Towards Slowing and Storing of Light ,” Opt. Photon. News   16 , 36 – 40 ( 2005 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Low Threshold Two-Dimensional Annular Bragg Lasers ,” Opt. Lett.   29 , 2641 – 2643 ( 2004 ).
[Crossref] [PubMed]

J. Scheuer and A. Yariv , “ Circular photonic crystal resonators ,” Physical Review E   70 , 036603 ( 2004 ).
[Crossref]

J. Scheuer and A. Yariv , “ Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators ,” IEEE J. Quantum Electron.   39 , 1555 – 1562 ( 2003 ).
[Crossref]

J. Scheuer and A. Yariv , “ Annular Bragg Defect mode Resonators ,” J. Opt. Soc. Am. B.   20 , 2285 – 2291 ( 2003 ).
[Crossref]

A. Yariv , “ Critical coupling and its control in optical waveguide-ring resonator systems ,” IEEE Photonics Technol. Lett.   14 , 483 – 485 ( 2002 ).
[Crossref]

O. Painter , R. K. Lee , A. Scherer , A. Yariv , J. D. O’Brien , P. D. Dapkus , and I. Kim , “ Two-dimensional photonic band-gap defect mode laser ,” Science   284 , 1819 – 1821 ( 1999 ).
[Crossref] [PubMed]

Zhao, J. H.

C. K. Madsen and J. H. Zhao , Optical Filter Design and Analysis: A Signal Processing Approach , ( Wiley-Interscience, New York , 1999 ).

Appl. Phys. Lett. (3)

C. Y. Chao and L. J. Guo , “ Biochemical sensors based on polymer microrings with sharp asymmetrical resonance ,” Appl. Phys. Lett.   83 , 1527 – 1529 ( 2003 ).
[Crossref]

H. Y. Ryu , M. Notomi , and Y. H. Lee , “ High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities ,” Appl. Phys. Lett.   21 , 4294 – 4296 ( 2003 ).
[Crossref]

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ Lasing from a circular Bragg nanocavity with and ultrasmall modal volume ,” Appl. Phys. Lett.   86 , 251101 ( 2005 ).
[Crossref]

IEEE J. Quantum Electron. (2)

J. Scheuer and A. Yariv , “ Coupled-Waves Approach to the Design and Analysis of Bragg and Photonic Crystal Annular Resonators ,” IEEE J. Quantum Electron.   39 , 1555 – 1562 ( 2003 ).
[Crossref]

J. Vučkovič et al., “ Optimization of the Q factor in photonic crystal microcavities ,” IEEE J. Quantum Electron.   38 , 850 – 856 ( 2002 ).
[Crossref]

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

J. Scheuer , W. M. J. Green , G. DeRose , and A. Yariv , “ InGaAsP annular Bragg lasers: Theory, applications and modal properties ,” IEEE J. Sel. Top. Quantum Electron.   11 , 476 – 484 ( 2005 ).
[Crossref]

IEEE Photonics Technol. Lett. (1)

A. Yariv , “ Critical coupling and its control in optical waveguide-ring resonator systems ,” IEEE Photonics Technol. Lett.   14 , 483 – 485 ( 2002 ).
[Crossref]

IEEE Tansactions on Electromagnetic Compatibility (1)

G. Mur , “ Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations ,” IEEE Tansactions on Electromagnetic Compatibility   EMC-23 , 377 – 382 ( 1981 ).
[Crossref]

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J. E. Heebner and R. W. Boyd , “ ‘Slow’ and ‘fast’ light in resonator-coupled waveguides ,” J. Mod. Opt   49 , 2629 – 2636 ( 2002 ).
[Crossref]

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

J. Scheuer and A. Yariv , “ Annular Bragg Defect mode Resonators ,” J. Opt. Soc. Am. B.   20 , 2285 – 2291 ( 2003 ).
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Y. Akahane , T. Asano , B. S. Song , and S. Noda , “ High-Q photonic nanocavity in a two-dimensional photonic crystal ,” Nature   425 , 944 – 947 ( 2003 ).
[Crossref] [PubMed]

See, for example, K. J. Vahala , “ Optical microcavities ,” Nature ( London )   424 , 839 – 846 ( 2003 ), and references therein.
[Crossref] [PubMed]

Nature Materials (1)

B. S. Song , S. Noda , T. Asano , and Y. Akahane , “ Ultra-high-Q photonic double-heterostructure nanocavity ,” Nature Materials   4 , 207 – 210 ( 2005 ).
[Crossref]

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J. Scheuer , G. T. Paloczi , J. K. S. Poon , and A. Yariv , “ Coupled Resonator Optical Waveguides: Towards Slowing and Storing of Light ,” Opt. Photon. News   16 , 36 – 40 ( 2005 ).
[Crossref]

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A. Melloni , F. Morichetti , and M. Mertinelli , “ Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures ,” Opt. Quantum Electron.   35 , 365 ( 2003 ).
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J. Scheuer and A. Yariv , “ Circular photonic crystal resonators ,” Physical Review E   70 , 036603 ( 2004 ).
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Figures (6)

Fig. 1.
Fig. 1. Circular PC reflector structure. (a) rectangular lattice (b) triangular lattice (c) sunflower lattice

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Fig. 2.
Fig. 2. Field Profile of (a) high Q and (b) low Q for a “sunflower” resonator with l=70, αr=0 and αθ=0.1

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Fig. 3.
Fig. 3. Comparison between theoretical (red) and numerical (green) radial field profile

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Fig. 4.
Fig. 4. Quality factor and resonance (angular) frequency vs. Angular Perturbation

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Fig. 5.
Fig. 5. Dependence of the Q and resonant frequency on (a) αθ and (b) on αr

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Fig. 6.
Fig. 6. Impact of neff on the Q and resonant frequency

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Equations (6)

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

H z ( x ) = A · H m ( 1 ) ( x ) + B · H m ( 2 ) ( x )
H z ( x ) = A ( x ) · H m ( 1 ) ( x ) + B ( x ) · H m ( 2 ) ( x )
ε x θ = { n 0 2 − ( n 0 2 − n p 2 ) ℑ [ 2 φ ( H m ( 1 ) ( x ) ) , α r ] ℑ [ lθ , α θ ] , x > x 0 n 0 2 , x ≤ x 0
ℑ y α = { 0 , sin ( y ) < α 1 , sin ( y ) ≥ α
H z ( x ) = { J m ( x ) x < x 0 J m ( x ) exp [ − ∣ k ∣ ( x − x 0 ) ] x ≥ x 0
Δ ε 0 = − 2 ∙ ( n 0 2 − n p 2 ) cos [ sin − 1 ( α r ) ] ∙ cos − 1 ( α θ ) π 2

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