Abstract

Waveguides that are composed of electromagnetically coupled optical microcavities [coupled resonator optical waveguides (CROWs)] can be used for light guiding, slowing, and storage. In this paper, we present a 2-D analysis of finite-size straight and curved CROW sections based on a rigorous Muller boundary integral equation method. We study the mechanisms of the coupling of whispering-gallery (WG) mode and guiding light around bends in CROWs composed of both identical and size-mismatched microdisk resonators. Our accurate analysis reveals the differences in WG modes coupling in the vicinity of bends in CROWs composed of optically large and wavelength-scale microcavities. We propose and discuss possible ways to design low-loss CROW bends and to reduce bend losses. These include selecting specific bend angles depending on the azimuthal order of the WG mode and tuning the radius of the microdisk positioned at the CROW bend.

© 2007 IEEE

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  1. T. M. Benson, S. V. Boriskina, P. Sewell, A. Vukovic, S. C. Greedy, A. I. Nosich, Frontiers of Planar Lightwave Circuit Technology: Design, Simulation and Fabrication (Springer-Verlag, 2005) pp. 39-70.
  2. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
  3. J. E. Heebner, R. W. Boyd, "‘Slow’ and ‘fast’ light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
  4. A. Melloni, F. Morichetti, M. Martinelli, "Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures ," Opt. Quantum Electron. 35, 365-379 (2003).
  5. A. Nakagawa, S. Ishii, T. Baba, "Photonic molecule laser composed of GaInAsP microdisks," Appl. Phys. Lett. 86, 330-332 (2005).
  6. S. V. Boriskina, "Theoretical prediction of a dramatic Q-factor enhancement and degeneracy removal of WG modes in symmetrical photonic molecules," Opt. Lett. 31, 338-340 (2006).
  7. S. V. Boriskina, "Spectrally-engineered photonic molecules as optical sensors with enhanced sensitivity: A proposal and numerical analysis," J. Opt. Soc. Amer. B, Opt. Phys. 23, 1565-1573 (2006).
  8. A. Yariv, Y. Xu, R. K. Lee, A. Scherer, "Coupled-resonator optical waveguide: A proposal and analysis," Opt. Lett. 24, 711-713 (1999).
  9. J. K. S. Poon, J. Scheuer, Y. Xu, A. Yariv, "Designing coupled-resonator optical waveguide delay lines," J. Opt. Soc. Amer. B, Opt. Phys. 21, 1665-1673 (2004).
  10. S. Deng, W. Cai, V. N. Astratov, "Numerical study of light propagation via whispering gallery modes in microcylinder coupled resonator optical waveguides," Opt. Express 12, 6468-6480 (2004).
  11. I. Chremmos, N. Uzunoglu, "Integral equation analysis of microring and microdisk coupled-resonator optical waveguides ," IEEE Photon. Technol. Lett. 18, 1173-1175 (2006).
  12. D. Barnes, S. M. Mahurin, A. Mehta, B. G. Sumpter, D. W. Noid, "Three-dimensional photonic “molecules” from sequentially attached polymer-blend microparticles," Phys. Rev. Lett. 88, 015 508 (2002).
  13. V. N. Astratov, J. P. Franchak, S. P. Ashili, "Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder," Appl. Phys. Lett. 85, 5508-5510 (2004).
  14. B. M. Möller, U. Woggon, M. V. Artemyev, "Coupled-resonator optical waveguides doped with nanocrystals," Opt. Lett. 30, 2116-2118 (2005).
  15. Z. Chen, A. Taflove, V. Backman, "Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres ," Opt. Lett. 31, 389-391 (2006).
  16. S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdr, U. Oesterl, "Miniband transmission in a photonic crystal coupled-resonator optical waveguide," Opt. Lett. 26, 1019-1021 (2001).
  17. E. Ozbay, M. Bayindir, I. Bulu, E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures ," IEEE J. Quantum Electron. 38, 837-843 (2002).
  18. S. Mookherjea, "Dispersion characteristics of coupled-resonator optical waveguides," Opt. Lett. 30, 2406-2408 (2005).
  19. A. Melloni, F. Morichetti, M. Martinelli, "Optical slow wave structures," Optics Photonics News 14, 44-48 (2003).
  20. J. Scheuer, G. T. Paloczi, J. K. S. Poon, A. Yariv, "Coupled resonator optical waveguides: Toward the slowing & storage of light," Optics Photonics News 16, 36-40 (2005).
  21. E. I. Smotrova, A. I. Nosich, T. M. Benson, P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," IEEE J. Sel. Topics Quantum Electron. 12, 78-85 (2006).
  22. S. V. Boriskina, P. Sewell, T. M. Benson, A. I. Nosich, "Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 393-402 (2004).
  23. Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 69, 056 604 (2004).
  24. S. Mookherjea, "Spectral characteristics of coupled resonators," J. Opt. Soc. Amer. B, Opt. Phys. 23, 1137-1145 (2006).
  25. L. B. Felsen, Symp. Math. (, 1975) pp. 39-56.
  26. G. Tayeb, D. Maystre, "Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities ," J. Opt. Soc. Amer. A, Opt. Image Sci. 14, 3323-3332 (1997).
  27. A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, C. Martijn de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 62, 5711-5720 (2000).
  28. A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 63, 046 612 (2001).
  29. M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, J. P. Reithmaier, "Optical demonstration of a crystal band structure formation," Phys. Rev. Lett. 83, 5374-5377 (1999).
  30. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mat. 2, 229-232 (2003).
  31. Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, A. Rogach, "Fine structure of coupled optical modes in photonic molecules," Phys. Rev. A, Gen. Phys. 70, 051 801(R) (2004).
  32. S. V. Boriskina, S. V. Pishko, T. M. Benson, P. Sewell, "Electromagnetic energy transport above and below the diffraction limit in mesoscale coupled-cavity photonic and plasmonic waveguides," Proc. MMET Int. Conf. (2006) pp. 213-215.
  33. S. V. Boriskina, T. M. Benson, P. Sewell, "Photonic molecules made of matched and mismatched microcavities: New functionalities of microlasers and optoelectronic components," Proc. SPIE 6452, (2007).

2007 (1)

S. V. Boriskina, T. M. Benson, P. Sewell, "Photonic molecules made of matched and mismatched microcavities: New functionalities of microlasers and optoelectronic components," Proc. SPIE 6452, (2007).

2006 (6)

E. I. Smotrova, A. I. Nosich, T. M. Benson, P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," IEEE J. Sel. Topics Quantum Electron. 12, 78-85 (2006).

S. Mookherjea, "Spectral characteristics of coupled resonators," J. Opt. Soc. Amer. B, Opt. Phys. 23, 1137-1145 (2006).

S. V. Boriskina, "Theoretical prediction of a dramatic Q-factor enhancement and degeneracy removal of WG modes in symmetrical photonic molecules," Opt. Lett. 31, 338-340 (2006).

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

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

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

2005 (4)

S. Mookherjea, "Dispersion characteristics of coupled-resonator optical waveguides," Opt. Lett. 30, 2406-2408 (2005).

B. M. Möller, U. Woggon, M. V. Artemyev, "Coupled-resonator optical waveguides doped with nanocrystals," Opt. Lett. 30, 2116-2118 (2005).

A. Nakagawa, S. Ishii, T. Baba, "Photonic molecule laser composed of GaInAsP microdisks," Appl. Phys. Lett. 86, 330-332 (2005).

J. Scheuer, G. T. Paloczi, J. K. S. Poon, A. Yariv, "Coupled resonator optical waveguides: Toward the slowing & storage of light," Optics Photonics News 16, 36-40 (2005).

2004 (6)

S. V. Boriskina, P. Sewell, T. M. Benson, A. I. Nosich, "Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 393-402 (2004).

Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 69, 056 604 (2004).

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, A. Rogach, "Fine structure of coupled optical modes in photonic molecules," Phys. Rev. A, Gen. Phys. 70, 051 801(R) (2004).

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

S. Deng, W. Cai, V. N. Astratov, "Numerical study of light propagation via whispering gallery modes in microcylinder coupled resonator optical waveguides," Opt. Express 12, 6468-6480 (2004).

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

2003 (3)

A. Melloni, F. Morichetti, M. Martinelli, "Optical slow wave structures," Optics Photonics News 14, 44-48 (2003).

A. Melloni, F. Morichetti, M. Martinelli, "Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures ," Opt. Quantum Electron. 35, 365-379 (2003).

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mat. 2, 229-232 (2003).

2002 (3)

E. Ozbay, M. Bayindir, I. Bulu, E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures ," IEEE J. Quantum Electron. 38, 837-843 (2002).

J. E. Heebner, R. W. Boyd, "‘Slow’ and ‘fast’ light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).

D. Barnes, S. M. Mahurin, A. Mehta, B. G. Sumpter, D. W. Noid, "Three-dimensional photonic “molecules” from sequentially attached polymer-blend microparticles," Phys. Rev. Lett. 88, 015 508 (2002).

2001 (2)

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

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 63, 046 612 (2001).

2000 (2)

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, C. Martijn de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 62, 5711-5720 (2000).

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).

1999 (2)

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

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, J. P. Reithmaier, "Optical demonstration of a crystal band structure formation," Phys. Rev. Lett. 83, 5374-5377 (1999).

1997 (1)

G. Tayeb, D. Maystre, "Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities ," J. Opt. Soc. Amer. A, Opt. Image Sci. 14, 3323-3332 (1997).

Appl. Phys. Lett. (2)

A. Nakagawa, S. Ishii, T. Baba, "Photonic molecule laser composed of GaInAsP microdisks," Appl. Phys. Lett. 86, 330-332 (2005).

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

IEEE J. Quantum Electron. (1)

E. Ozbay, M. Bayindir, I. Bulu, E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures ," IEEE J. Quantum Electron. 38, 837-843 (2002).

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

E. I. Smotrova, A. I. Nosich, T. M. Benson, P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," IEEE J. Sel. Topics Quantum Electron. 12, 78-85 (2006).

IEEE Photon. Technol. Lett. (2)

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

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).

J. Mod. Opt. (1)

J. E. Heebner, R. W. Boyd, "‘Slow’ and ‘fast’ light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).

J. Opt. Soc. Amer. A, Opt. Image Sci. (2)

S. V. Boriskina, P. Sewell, T. M. Benson, A. I. Nosich, "Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 393-402 (2004).

G. Tayeb, D. Maystre, "Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities ," J. Opt. Soc. Amer. A, Opt. Image Sci. 14, 3323-3332 (1997).

J. Opt. Soc. Amer. B, Opt. Phys. (3)

S. Mookherjea, "Spectral characteristics of coupled resonators," J. Opt. Soc. Amer. B, Opt. Phys. 23, 1137-1145 (2006).

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

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

Nature Mat. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mat. 2, 229-232 (2003).

Opt. Express (1)

Opt. Lett. (6)

Opt. Quantum Electron. (1)

A. Melloni, F. Morichetti, M. Martinelli, "Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures ," Opt. Quantum Electron. 35, 365-379 (2003).

Optics Photonics News (2)

A. Melloni, F. Morichetti, M. Martinelli, "Optical slow wave structures," Optics Photonics News 14, 44-48 (2003).

J. Scheuer, G. T. Paloczi, J. K. S. Poon, A. Yariv, "Coupled resonator optical waveguides: Toward the slowing & storage of light," Optics Photonics News 16, 36-40 (2005).

Phys. Rev. A, Gen. Phys. (1)

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, A. Rogach, "Fine structure of coupled optical modes in photonic molecules," Phys. Rev. A, Gen. Phys. 70, 051 801(R) (2004).

Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. (3)

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, C. Martijn de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 62, 5711-5720 (2000).

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 63, 046 612 (2001).

Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 69, 056 604 (2004).

Phys. Rev. Lett. (2)

D. Barnes, S. M. Mahurin, A. Mehta, B. G. Sumpter, D. W. Noid, "Three-dimensional photonic “molecules” from sequentially attached polymer-blend microparticles," Phys. Rev. Lett. 88, 015 508 (2002).

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, J. P. Reithmaier, "Optical demonstration of a crystal band structure formation," Phys. Rev. Lett. 83, 5374-5377 (1999).

Proc. SPIE (1)

S. V. Boriskina, T. M. Benson, P. Sewell, "Photonic molecules made of matched and mismatched microcavities: New functionalities of microlasers and optoelectronic components," Proc. SPIE 6452, (2007).

Other (3)

T. M. Benson, S. V. Boriskina, P. Sewell, A. Vukovic, S. C. Greedy, A. I. Nosich, Frontiers of Planar Lightwave Circuit Technology: Design, Simulation and Fabrication (Springer-Verlag, 2005) pp. 39-70.

S. V. Boriskina, S. V. Pishko, T. M. Benson, P. Sewell, "Electromagnetic energy transport above and below the diffraction limit in mesoscale coupled-cavity photonic and plasmonic waveguides," Proc. MMET Int. Conf. (2006) pp. 213-215.

L. B. Felsen, Symp. Math. (, 1975) pp. 39-56.

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