Abstract

We study the linear resonance properties of several types of microrings in a two-dimensional photonic crystal (PC) consisting of a square lattice with air holes in dielectric using the plane-wave expansion method and the FDTD method. Moreover we investigate the nonlinear responses, especially optical bistability when an intense optical pulse is incident into the microrings. In this paper, Ag-As-Se chalcogenide glass is assumed as nonlinear dielectric, which has a high third-order nonlinearity. Although line-defect waveguides in an air-hole-type PC are usually multimoded, we can obtain interesting unique properties such as counter rotation of intracavity fields, transmission to all output ports, and unstable nonlinear oscillations in the multimoded PC microring. We can improve the resonance characteristics by partly introducing single-mode waveguides into microrings and can obtain stable optical bistability.

© 2008 Optical Society of America

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2007 (3)

2006 (2)

Q. Xu and M. Lipson, "Carrier-induced optical bistability in silicon ring resonators," Opt. Lett. 31, 341-343 (2006).
[CrossRef] [PubMed]

A. R. Alija, L. J. Martinez, P. A. Postigo, C. Seassal, and P. Viktorovitch, "Coupled-cavity two-dimensional photonic crystal waveguide ring laser," Appl. Phys. Lett. 89, 101102 (2006).
[CrossRef]

2005 (1)

2004 (3)

2003 (2)

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

S. H. Kim and Y. H. Lee, "Symmetry relations of two-dimensional photonic crystal cavity modes," IEEE J. Quantum Electron. 39, 1081-1085 (2003).
[CrossRef]

2002 (4)

M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81, 1163-1165 (2002).
[CrossRef]

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-P. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

2001 (2)

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightwave Technol. 19, 1970-1975 (2001).
[CrossRef]

2000 (2)

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

1999 (1)

1998 (3)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop filters in photonic crystals," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

H. Li and K. Ogusu, "Analysis of optical instability in a double-coupler nonlinear fiber ring resonator," Opt. Commun. 157, 27-32 (1998).
[CrossRef]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

1996 (4)

H. Benisty, "Modal analysis of optical guides with two-dimensional photonic band-gap boundaries," J. Appl. Phys. 79, 7483-7492 (1996).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

K. Ogusu, "Dynamic behavior of reflection optical bistability in nonlinear fiber ring resonator," IEEE J. Quantum Electron. 32, 1537-1543 (1996).
[CrossRef]

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

1995 (1)

Absil, P. P.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-P. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Alija, A. R.

A. R. Alija, L. J. Martinez, P. A. Postigo, C. Seassal, and P. Viktorovitch, "Coupled-cavity two-dimensional photonic crystal waveguide ring laser," Appl. Phys. Lett. 89, 101102 (2006).
[CrossRef]

Azizi, K.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Benisty, H.

Cassagne, D.

Chan, Y. J.

Chen, C. C.

Chen, J. C.

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

Chien, H. T.

Chiu, W. Y.

Choi, Y. S.

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

Chu, S. T.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Chutinan, A.

A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

De La Rue, R. M.

Eppen, E. P.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Fan, S.

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop filters in photonic crystals," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

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

Fink, Y.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Foresi, J. S.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Greene, W.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Grover, R.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-P. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Haus, H. A.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop filters in photonic crystals," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

Ho, P.-P.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-P. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Hou, C. H.

Houdre, R.

Huang, T. W.

Ibanescu, M.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Ibrahim, T. A.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-P. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Jaskorzynska, B.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Jeong, S. H.

Joannopoulos, J. D.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop filters in photonic crystals," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

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

Johnson, F. G.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-P. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Johnson, S. G.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

Jouanin, C.

Karlsson, A.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Kim, G. H.

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

Kim, J. O.

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

Kim, S. H.

S. H. Kim and Y. H. Lee, "Symmetry relations of two-dimensional photonic crystal cavity modes," IEEE J. Quantum Electron. 39, 1081-1085 (2003).
[CrossRef]

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

Kimerling, L. C.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Kira, G.

Kitao, M.

Komori, K.

Koshiba, M.

Krauss, T. F.

Kumar, V. D.

V. D. Kumar, T. Srinivas, and A. Selvarajan, "Investigation of ring resonators in photonic crystal circuits," Photon. Nanostruct. Fundam. Appl. 2, 199-206 (2004).
[CrossRef]

Kuramochi, E.

Kurland, I.

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

Labilloy, D.

Lee, Y. H.

S. H. Kim and Y. H. Lee, "Symmetry relations of two-dimensional photonic crystal cavity modes," IEEE J. Quantum Electron. 39, 1081-1085 (2003).
[CrossRef]

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

Li, H.

H. Li and K. Ogusu, "Analysis of optical instability in a double-coupler nonlinear fiber ring resonator," Opt. Commun. 157, 27-32 (1998).
[CrossRef]

Lipson, M.

Little, B. E.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Maeda, S.

Martinez, L. J.

A. R. Alija, L. J. Martinez, P. A. Postigo, C. Seassal, and P. Viktorovitch, "Coupled-cavity two-dimensional photonic crystal waveguide ring laser," Appl. Phys. Lett. 89, 101102 (2006).
[CrossRef]

Mekis, A.

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

Minakata, M.

Mitsugi, S.

Noda, S.

A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

Notomi, M.

Oesterle, U.

Ogusu, K.

K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, "Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching," Opt. Lett. 29, 265-269 (2004).
[CrossRef] [PubMed]

H. Li and K. Ogusu, "Analysis of optical instability in a double-coupler nonlinear fiber ring resonator," Opt. Commun. 157, 27-32 (1998).
[CrossRef]

K. Ogusu, "Dynamic behavior of reflection optical bistability in nonlinear fiber ring resonator," IEEE J. Quantum Electron. 32, 1537-1543 (1996).
[CrossRef]

K. Ogusu, H. Shigekuni, and Y. Yokota, "Dynamic transmission properties of a nonlinear fiber ring resonator," Opt. Lett. 20, 2288-2290 (1995).
[CrossRef] [PubMed]

Okano, M.

Park, H. G.

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

Postigo, P. A.

A. R. Alija, L. J. Martinez, P. A. Postigo, C. Seassal, and P. Viktorovitch, "Coupled-cavity two-dimensional photonic crystal waveguide ring laser," Appl. Phys. Lett. 89, 101102 (2006).
[CrossRef]

Qiang, Z.

Qiu, M.

M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81, 1163-1165 (2002).
[CrossRef]

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Rattier, M.

Ryu, H. Y.

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

Schwelb, O.

Seassal, C.

A. R. Alija, L. J. Martinez, P. A. Postigo, C. Seassal, and P. Viktorovitch, "Coupled-cavity two-dimensional photonic crystal waveguide ring laser," Appl. Phys. Lett. 89, 101102 (2006).
[CrossRef]

Selvarajan, A.

V. D. Kumar, T. Srinivas, and A. Selvarajan, "Investigation of ring resonators in photonic crystal circuits," Photon. Nanostruct. Fundam. Appl. 2, 199-206 (2004).
[CrossRef]

Shigekuni, H.

Shinya, A.

Smith, C. J. M.

Soljacic, M.

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Soref, R. A.

Srinivas, T.

V. D. Kumar, T. Srinivas, and A. Selvarajan, "Investigation of ring resonators in photonic crystal circuits," Photon. Nanostruct. Fundam. Appl. 2, 199-206 (2004).
[CrossRef]

Steinmeyer, G.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Sugisaka, J.

Swillo, M.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Tanabe, T.

Thoen, E. R.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Van, V.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-P. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Viktorovitch, P.

A. R. Alija, L. J. Martinez, P. A. Postigo, C. Seassal, and P. Viktorovitch, "Coupled-cavity two-dimensional photonic crystal waveguide ring laser," Appl. Phys. Lett. 89, 101102 (2006).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop filters in photonic crystals," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

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

Weisbuch, C.

Wu, Y. H.

Xu, Q.

Yamamoto, N.

Yamasaki, J.

Yanik, M. F.

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

Yokota, Y.

Zhou, W.

Appl. Phys. Lett. (4)

S. H. Kim, H. Y. Ryu, H. G. Park, G. H. Kim, Y. S. Choi, Y. H. Lee, and J. O. Kim, "Two-dimensional photonic crystal hexagonal waveguide ring laser," Appl. Phys. Lett. 81, 2499-2501 (2002).
[CrossRef]

A. R. Alija, L. J. Martinez, P. A. Postigo, C. Seassal, and P. Viktorovitch, "Coupled-cavity two-dimensional photonic crystal waveguide ring laser," Appl. Phys. Lett. 89, 101102 (2006).
[CrossRef]

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81, 1163-1165 (2002).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Ogusu, "Dynamic behavior of reflection optical bistability in nonlinear fiber ring resonator," IEEE J. Quantum Electron. 32, 1537-1543 (1996).
[CrossRef]

S. H. Kim and Y. H. Lee, "Symmetry relations of two-dimensional photonic crystal cavity modes," IEEE J. Quantum Electron. 39, 1081-1085 (2003).
[CrossRef]

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

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-P. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Eppen, L. C. Kimerling, and W. Greene, " Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

J. Appl. Phys. (1)

H. Benisty, "Modal analysis of optical guides with two-dimensional photonic band-gap boundaries," J. Appl. Phys. 79, 7483-7492 (1996).
[CrossRef]

J. Lightwave Technol. (3)

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

Opt. Commun. (1)

H. Li and K. Ogusu, "Analysis of optical instability in a double-coupler nonlinear fiber ring resonator," Opt. Commun. 157, 27-32 (1998).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Photon. Nanostruct. Fundam. Appl. (1)

V. D. Kumar, T. Srinivas, and A. Selvarajan, "Investigation of ring resonators in photonic crystal circuits," Photon. Nanostruct. Fundam. Appl. 2, 199-206 (2004).
[CrossRef]

Phys. Rev. B (4)

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

Phys. Rev. E (1)

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

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

Other (2)

H. M. Gibbs, Optical bistability: Controlling light with light (Academic Press, 1985).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).

Supplementary Material (8)

» Media 1: AVI (1662 KB)     
» Media 2: AVI (3964 KB)     
» Media 3: AVI (1644 KB)     
» Media 4: AVI (1800 KB)     
» Media 5: AVI (1735 KB)     
» Media 6: AVI (1800 KB)     
» Media 7: AVI (1843 KB)     
» Media 8: AVI (1801 KB)     

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Figures (17)

Fig. 1.
Fig. 1.

Dispersion curves of the guided modes in (a) a W1 waveguide and (b) a W0.7 waveguide. The PC is a square lattice of air holes (r=0.46a) in dielectric (n=3.1). The gray areas are the projected band structure of the perfect crystal.

Fig. 2.
Fig. 2.

(a) Square PC ring resonator consisting of the W1 waveguide. The two bus waveguides are the W0.7 waveguide. (b) Corresponding directional coupler for calculating the coupling strength into the ring resonator.

Fig. 3.
Fig. 3.

(a)Linear transmission spectra at three output ports of the PC ring resonator shown in Fig. 2(a) and (b) field pattern in the ring resonator at ω=0.2830(2πc/a). (c) Mode pattern with a resonance frequency of 0.2796(2πc/a) in the isolated square PC ring resonator, which was calculated by using the PWE method. [Media 1]

Fig. 4.
Fig. 4.

Transmission to three output ports of the directional coupler consisting of the W0.7 and W1 waveguides shown in Fig. 2 (b) as a function of coupler length L.

Fig. 5.
Fig. 5.

Temporal shapes of the transmitted pulses from three output ports of the nonlinear PC ring resonator (n=3.1 and n 2=9.0×10-17m2/W) shown in Fig. 2(a) when a triangular pulse is incident into it for a few values of the peak power P 0 and initial detuning Δω=ω 0-ω.

Fig. 6.
Fig. 6.

(a) Enlarged temporal variation of the transmitted pulse from port D for Δω=0.002 ω 0 and P 0=24 W/µm in Fig. 5. (b) Instantaneous electric field distribution in the PC ring resonator corresponding to (a). [Media 2]

Fig. 7.
Fig. 7.

(a) Temporal shape of the transmitted pulse from port D when a triangular pulse with τ=10 ps and P 0=226 W/µm is incident into the PC ring resonator with Δω=0.002 ω 0. (b) Corresponding input-output characteristics.

Fig. 8.
Fig. 8.

(a) Single-mode PC waveguide (decreased-index waveguide) where the radii rs of a line of air holes is decreased. (b) Its dispersion curves of the guided modes for rs =0.35a.

Fig. 9.
Fig. 9.

Two kinds of waveguide-coupled PC ring resonators constructed of the decreased-index waveguide with rs =0.35a.

Fig. 10.
Fig. 10.

Linear transmission spectra (a) and (b) at three output ports of the PC ring resonators shown in Figs. 9(a) and 9(b), respectively.

Fig. 11.
Fig. 11.

Instantaneous electric field distributions in the PC ring resonators at resonant points A-C marked in Fig. 10. Figures (a), (b), and (c) correspond to resonant points A, B, and C, respectively.[Media 3][Media 4][Media 5]

Fig. 12.
Fig. 12.

(a) and (b) Temporal shapes of the transmitted pulses from ports B and D of the nonlinear PC ring resonator shown in Fig. 9(b), respectively, when the triangular pulse in incident into it for two values of Δω=ω 0-ω (where ω 0=0.2763(2πc/a), which is marked by C in Fig. 10(b)) and P 0. (c) and (d) Input-output characteristics corresponding to (a) and (b), respectively.

Fig. 13.
Fig. 13.

(a) (11) waveguide defined by removing one row of air holes in the (11) direction of the PC. (b)Its dispersion relations.

Fig. 14.
Fig. 14.

Three types (R1, R2, and R3) of PC ring resonators incorporating the (11) waveguides.

Fig. 15.
Fig. 15.

Linear transmission spectra of the three PC ring resonators shown in Fig. 13.[Media 6][Media 7][Media 8]

Fig. 16.
Fig. 16.

Temporal variation of the transmitted pulses from ports B, C, and D when the triangular pulse with τ=30 ps and P 0=58 W/µm is incident into port A of ring resonator R3 with ω 0=0.2846(2πc/a) for three values of the initial detuning Δω.

Fig. 17.
Fig. 17.

Input-output characteristics of ring resonator R3 corresponding to Fig. 16.

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