Abstract

The resonant properties of a closed and symmetric cyclic array of N coupled microring resonators (coupled-microring resonator regular N-gon) are for the first time determined analytically by applying the transfer matrix approach and Floquet theorem for periodic propagation in cylindrically symmetric structures. By solving the corresponding eigenvalue problem with the field amplitudes in the rings as eigenvectors, it is shown that, for even or odd N, this photonic molecule possesses 1 + N/2 or 1+N resonant frequencies, respectively. The condition for resonances is found to be identical to the familiar dispersion equation of the infinite coupled-microring resonator waveguide with a discrete wave vector. This result reveals the so far latent connection between the two optical structures and is based on the fact that, for a regular polygon, the field transfer matrix over two successive rings is independent of the polygon vertex angle. The properties of the resonant modes are discussed in detail using the illustration of Brillouin band diagrams. Finally, the practical application of a channel-dropping filter based on polygons with an even number of rings is also analyzed.

© 2007 Optical Society of America

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2007 (2)

Y. Yang and Y. Huang, "Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators," Phys. Rev. A 76, 023822 (2007).

S. V. Boriskina, "Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules," Opt. Lett. 32, 1557-1559 (2007).

2006 (13)

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).

Z. Chen, A. Taflove, and V. Backman, "Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres," Opt. Lett. 31, 389-391 (2006).

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, "Transmission and group delay of microring coupled-resonator optical waveguides," Opt. Lett. 31, 456-458 (2006).

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes," Opt. Lett. 31, 921-923 (2006).

S. Boriskina, "Spectrally engineered photonic molecules as optical sensors with enhanced sensitivity: a proposal and numerical analysis," J. Opt. Soc. Am. B 23, 1565-1573 (2006).

N.-S. Zhao, H. Zhou, Q. Guo, W. Hu, X.-B. Yang, S. Lan, and X.-S. Lin, "Design of highly efficient optical diodes based on the dynamics of nonlinear photonic crystal molecules," J. Opt. Soc. Am. B 23, 2434-2440 (2006).

J. Scheuer and A. Yariv, "Sagnac effect in coupled-resonator slow-light waveguide structures," Phys. Rev. Lett. 96, 053901 (2006).

A. L. Burin, "Bound whispering gallery modes in circular arrays of dielectric spherical particles," Phys. Rev. E 73, 066614 (2006).

S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006).

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).

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Ultralow lasing thresholds of π-type supermodes in cyclic photonic molecules composed of submicron disks with monopole and dipole modes," IEEE Photon. Technol. Lett. 18, 1993-1995 (2006).

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, "Directional emission, increased free spectral range and mode Q-factors in 2-D wavelength-scale optical microcavity structures," IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).

I. D. Chremmos and N. K. Uzunoglu, "Integral equation analysis of microring and microdisk coupled-resonator optical waveguides," IEEE Photon. Technol. Lett. 18, 1173-1175 (2006).

2005 (3)

2004 (6)

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 90-103 (2004).

J. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical waveguide delay lines," J. Opt. Soc. Am. B 21, 1665-1673 (2004).

B. Möller, U. Woggon, M. Artemyev, and R. Wannemacher, "Photonic molecules doped with semiconductor nanocrystals," Phys. Rev. B 70, 115323 (2004).

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, "Fine structure of coupled optical modes in photonic molecules," Phys. Rev. A 70, 051801(R) (2004).

V. N. Astratov, J. P. Franchak, and S. P. Ashili, "Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder," Appl. Phys. Lett. 85, 5508-5510 (2004).

J. Poon, J. Scheuer, and A. Yariv, "Wavelength-selective reflector based on a circular array of coupled microring resonators," IEEE Photon. Technol. Lett. 16, 1331-1333 (2004).

2003 (1)

2002 (1)

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).

2001 (3)

M. Bayindir, S. Tanriseven, and E. Ozbay, "Propagation of light through localized coupled-cavity modes in one dimensional photonic band-gap structures," Appl. Phys. A 72, 117-119 (2001).

G. Guttroff, M. Bayer, A. Forchel, P. A. Knipp, and T. L. Reinecke, "Isomeric photonic molecules formed from coupled microresonators," Phys. Rev. E 63, 036611 (2001).

S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdre, and U. Oesterle, "Miniband transmission in a photonic crystal coupled-resonator optical waveguide," Opt. Lett. 26, 1019-1021 (2001).

1999 (3)

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Mode-coupling analysis of multipole symmetric resonant add/drop filters," IEEE J. Quantum Electron. 35, 1451-1460 (1999).

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).

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).

1998 (1)

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2586 (1998).

Appl. Phys. A (1)

M. Bayindir, S. Tanriseven, and E. Ozbay, "Propagation of light through localized coupled-cavity modes in one dimensional photonic band-gap structures," Appl. Phys. A 72, 117-119 (2001).

Appl. Phys. Lett. (3)

V. N. Astratov, J. P. Franchak, and S. P. Ashili, "Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder," Appl. Phys. Lett. 85, 5508-5510 (2004).

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).

A. Nakagawa, S. Ishii, and T. Baba, "Photonic molecule laser composed of GaInAsP microdisks," Appl. Phys. Lett. 86, 041112 (2005).

IEEE J. Quantum Electron. (1)

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Mode-coupling analysis of multipole symmetric resonant add/drop filters," IEEE J. Quantum Electron. 35, 1451-1460 (1999).

IEEE J. Sel. Top. Quantum Electron. (3)

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, "Directional emission, increased free spectral range and mode Q-factors in 2-D wavelength-scale optical microcavity structures," IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).

S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006).

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).

IEEE Photon. Technol. Lett. (3)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Ultralow lasing thresholds of π-type supermodes in cyclic photonic molecules composed of submicron disks with monopole and dipole modes," IEEE Photon. Technol. Lett. 18, 1993-1995 (2006).

I. D. Chremmos and N. K. Uzunoglu, "Integral equation analysis of microring and microdisk coupled-resonator optical waveguides," IEEE Photon. Technol. Lett. 18, 1173-1175 (2006).

J. Poon, J. Scheuer, and A. Yariv, "Wavelength-selective reflector based on a circular array of coupled microring resonators," IEEE Photon. Technol. Lett. 16, 1331-1333 (2004).

J. Opt. Soc. Am. B (3)

Opt. Express (2)

Opt. Lett. (9)

Y. P. Rakovich, J. J. Boland, and J. F. Donegan, "Tunable photon lifetime in photonic molecules: a concept for delaying an optical signal," Opt. Lett. 30, 2775-2777 (2005).

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).

Z. Chen, A. Taflove, and V. Backman, "Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres," Opt. Lett. 31, 389-391 (2006).

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, "Transmission and group delay of microring coupled-resonator optical waveguides," Opt. Lett. 31, 456-458 (2006).

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes," Opt. Lett. 31, 921-923 (2006).

S. V. Boriskina, "Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules," Opt. Lett. 32, 1557-1559 (2007).

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).

S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdre, and U. Oesterle, "Miniband transmission in a photonic crystal coupled-resonator optical waveguide," Opt. Lett. 26, 1019-1021 (2001).

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, "Photonic molecule lasing," Opt. Lett. 28, 2437-2439 (2003).

Phys. Rev. A (2)

Y. Yang and Y. Huang, "Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators," Phys. Rev. A 76, 023822 (2007).

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, "Fine structure of coupled optical modes in photonic molecules," Phys. Rev. A 70, 051801(R) (2004).

Phys. Rev. B (1)

B. Möller, U. Woggon, M. Artemyev, and R. Wannemacher, "Photonic molecules doped with semiconductor nanocrystals," Phys. Rev. B 70, 115323 (2004).

Phys. Rev. E (2)

A. L. Burin, "Bound whispering gallery modes in circular arrays of dielectric spherical particles," Phys. Rev. E 73, 066614 (2006).

G. Guttroff, M. Bayer, A. Forchel, P. A. Knipp, and T. L. Reinecke, "Isomeric photonic molecules formed from coupled microresonators," Phys. Rev. E 63, 036611 (2001).

Phys. Rev. Lett. (3)

J. Scheuer and A. Yariv, "Sagnac effect in coupled-resonator slow-light waveguide structures," Phys. Rev. Lett. 96, 053901 (2006).

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).

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2586 (1998).

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