Abstract

Using iterative methods we demonstrate that, for a structure consisting of N-coupled microspheres or ring resonators, the morphology-dependent resonances split into N higher-Q modes, in direct analogy with other types of oscillators. Moreover, for odd numbers of identical lossless coupled rings, the circulating intensity in the innermost ring increases exponentially with N when there is strong coupling to even-numbered rings and weak coupling to odd-numbered rings.

© 2003 Optical Society of America

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2002 (3)

2001 (1)

2000 (3)

1999 (3)

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).

1996 (2)

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565–3572 (1996).

C. Pedersen and T. Skettrup, “Laser modes and threshold conditions in N-mirror resonators,” J. Opt. Soc. Am. B 13, 926–937 (1996).

1991 (1)

1989 (1)

Absil, P. P.

Boyd, R. W.

Braunstein, D.

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565–3572 (1996).

Chu, S. T.

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25, 344–346 (2000).

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).

Fuller, K. A.

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).

Heebner, J. E.

Hryniewicz, J. V.

Jimba, Y.

H. Miyazaki and Y. Jimba, “Ab Initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).

Khazanov, A. M.

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565–3572 (1996).

Koganov, G. A.

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565–3572 (1996).

Kuwata-Gonokami, M.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).

Lee, R. K.

Little, B. E.

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25, 344–346 (2000).

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).

Melloni, A.

Miyazaki, H.

H. Miyazaki and Y. Jimba, “Ab Initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).

Mukaiyama, T.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).

Park, Q. H.

J. E. Heebner, R. W. Boyd, and Q. H. Park, “SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides,” J. Opt. Soc. Am. B 19, 722–731 (2002).

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

Pedersen, C.

Scherer, A.

Shuker, R.

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565–3572 (1996).

Skettrup, T.

Smith, D. D.

Takeda, K.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).

Xu, Y.

Yariv, A.

Appl. Opt. (2)

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).

J. Opt. Soc. Am. B (4)

Opt. Lett. (4)

Phys. Rev. A (1)

D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, “Lowering of threshold conditions for nonlinear effects in a microsphere,” Phys. Rev. A 53, 3565–3572 (1996).

Phys. Rev. B (1)

H. Miyazaki and Y. Jimba, “Ab Initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).

Phys. Rev. E (1)

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

Phys. Rev. Lett. (1)

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).

Other (1)

K. A. Fuller and D. W. Mackowski, “Electromagnetic scattering by compounded spherical particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, New York, 2000), pp. 225–272.

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