Abstract

We report a numerical and analytical study of mode field patterns and mode coupling in planar waveguide-coupled square microcavities, using two-dimensional (2-D) finite-difference time-domain (FDTD) method and k-space representation. Simulated mode field patterns can be identified by k-space modes. We observe that different mode number parities permit distinctly different mode field patterns and spectral characteristics. Simulation results suggest that k-space modes that nearly match the waveguide propagation mode have a relatively high coupling efficiency. Such preferential mode coupling can be modified by the mode number parity.

© 2003 Optical Society of America

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References

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  1. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
    [Crossref] [PubMed]
  2. S. C. Hagness, D Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
    [Crossref]
  3. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]
  4. D. J. W. Klunder, F. S. Tan, T. van der Veen, H. F. Bulthuis, G. Sengo, B. Docter, H. J. W. M. Hoekstra, and A. Driessen, “Experimental and numerical study of SiON microresonators with air and polymer cladding,” J. Lightwave Technol. 21, 1099–1110 (2003).
    [Crossref]
  5. R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
    [Crossref]
  6. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
    [Crossref]
  7. A. W. Poon, F. Courvoisier, and R. K. Chang, “Multimode resonances in square-shaped optical microcavities,” Opt. Lett. 26, 632–634 (2001).
    [Crossref]
  8. A. W. Poon, “Optical resonances of two-dimensional microcavities with circular and non-circular shapes,” PhD thesis, Yale University, 2001.
  9. Y. L. Pan and R. K. Chang, “Highly efficient prism coupling to whispering gallery modes of a square µ cavity,” Appl. Phys. Lett. 82, 487–489 (2003).
    [Crossref]
  10. M. Lohmeyer, “Mode expansion of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34, 541–557 (2002).
    [Crossref]
  11. M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective,” Opt. Commun. 214, 155–170 (2002).
    [Crossref]
  12. Y. F. Chen, K. F. Huang, H. C. Lai, and Y. P. Lan, “Observation of vector vortex lattices in polarization states of an isotropic microcavity laser,” Phys. Rev. Lett. 90, 053904 (2003).
    [Crossref] [PubMed]
  13. N. Ma, C. Y. Fong, F. K. L. Tung, K. C. Lam, W. N. Chan, and A. W. Poon, “Micro-pillar square resonant cavity channel add-drop filters on silicon-nitride-on-silica: design, fabrication and characterization,” in Proc. of Conf. Lasers Electro-Optics, Baltimore, MD, Jun. 2003.
  14. FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com.
  15. K. Okamoto, “Chapter 2” in Fundamentals of optical waveguides, (Academic, San Diego, CA, 2000).

2003 (4)

D. J. W. Klunder, F. S. Tan, T. van der Veen, H. F. Bulthuis, G. Sengo, B. Docter, H. J. W. M. Hoekstra, and A. Driessen, “Experimental and numerical study of SiON microresonators with air and polymer cladding,” J. Lightwave Technol. 21, 1099–1110 (2003).
[Crossref]

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Y. L. Pan and R. K. Chang, “Highly efficient prism coupling to whispering gallery modes of a square µ cavity,” Appl. Phys. Lett. 82, 487–489 (2003).
[Crossref]

Y. F. Chen, K. F. Huang, H. C. Lai, and Y. P. Lan, “Observation of vector vortex lattices in polarization states of an isotropic microcavity laser,” Phys. Rev. Lett. 90, 053904 (2003).
[Crossref] [PubMed]

2002 (2)

M. Lohmeyer, “Mode expansion of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34, 541–557 (2002).
[Crossref]

M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective,” Opt. Commun. 214, 155–170 (2002).
[Crossref]

2001 (1)

1999 (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

1998 (1)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

1997 (2)

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
[Crossref] [PubMed]

S. C. Hagness, D Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[Crossref]

Amarnath, K.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Bulthuis, H. F.

Calhoun, L. C.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Chan, W. N.

N. Ma, C. Y. Fong, F. K. L. Tung, K. C. Lam, W. N. Chan, and A. W. Poon, “Micro-pillar square resonant cavity channel add-drop filters on silicon-nitride-on-silica: design, fabrication and characterization,” in Proc. of Conf. Lasers Electro-Optics, Baltimore, MD, Jun. 2003.

Chang, R. K.

Y. L. Pan and R. K. Chang, “Highly efficient prism coupling to whispering gallery modes of a square µ cavity,” Appl. Phys. Lett. 82, 487–489 (2003).
[Crossref]

A. W. Poon, F. Courvoisier, and R. K. Chang, “Multimode resonances in square-shaped optical microcavities,” Opt. Lett. 26, 632–634 (2001).
[Crossref]

Chen, Y. F.

Y. F. Chen, K. F. Huang, H. C. Lai, and Y. P. Lan, “Observation of vector vortex lattices in polarization states of an isotropic microcavity laser,” Phys. Rev. Lett. 90, 053904 (2003).
[Crossref] [PubMed]

Chu, S. T.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

Courvoisier, F.

Ding, T. N.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Docter, B.

Driessen, A.

Fan, S.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Fong, C. Y.

N. Ma, C. Y. Fong, F. K. L. Tung, K. C. Lam, W. N. Chan, and A. W. Poon, “Micro-pillar square resonant cavity channel add-drop filters on silicon-nitride-on-silica: design, fabrication and characterization,” in Proc. of Conf. Lasers Electro-Optics, Baltimore, MD, Jun. 2003.

Foresi, J. S.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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. Ippen, 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.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Hagness, S. C.

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
[Crossref] [PubMed]

S. C. Hagness, D Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[Crossref]

Hammer, M.

M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective,” Opt. Commun. 214, 155–170 (2002).
[Crossref]

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

Ho, P. T.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Ho, S. T.

S. C. Hagness, D Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[Crossref]

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
[Crossref] [PubMed]

Hoekstra, H. J. W. M.

Huang, K. F.

Y. F. Chen, K. F. Huang, H. C. Lai, and Y. P. Lan, “Observation of vector vortex lattices in polarization states of an isotropic microcavity laser,” Phys. Rev. Lett. 90, 053904 (2003).
[Crossref] [PubMed]

Ibrahim, T. A.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Ippen, E. P.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Kanakaraju, S.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Kimerling, L. C.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

Klunder, D. J. W.

Kuo, L. C.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Lai, H. C.

Y. F. Chen, K. F. Huang, H. C. Lai, and Y. P. Lan, “Observation of vector vortex lattices in polarization states of an isotropic microcavity laser,” Phys. Rev. Lett. 90, 053904 (2003).
[Crossref] [PubMed]

Lam, K. C.

N. Ma, C. Y. Fong, F. K. L. Tung, K. C. Lam, W. N. Chan, and A. W. Poon, “Micro-pillar square resonant cavity channel add-drop filters on silicon-nitride-on-silica: design, fabrication and characterization,” in Proc. of Conf. Lasers Electro-Optics, Baltimore, MD, Jun. 2003.

Lan, Y. P.

Y. F. Chen, K. F. Huang, H. C. Lai, and Y. P. Lan, “Observation of vector vortex lattices in polarization states of an isotropic microcavity laser,” Phys. Rev. Lett. 90, 053904 (2003).
[Crossref] [PubMed]

Leng, Y.

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

Little, B. E.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

Lohmeyer, M.

M. Lohmeyer, “Mode expansion of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34, 541–557 (2002).
[Crossref]

Ma, N.

N. Ma, C. Y. Fong, F. K. L. Tung, K. C. Lam, W. N. Chan, and A. W. Poon, “Micro-pillar square resonant cavity channel add-drop filters on silicon-nitride-on-silica: design, fabrication and characterization,” in Proc. of Conf. Lasers Electro-Optics, Baltimore, MD, Jun. 2003.

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Okamoto, K.

K. Okamoto, “Chapter 2” in Fundamentals of optical waveguides, (Academic, San Diego, CA, 2000).

Pan, Y. L.

Y. L. Pan and R. K. Chang, “Highly efficient prism coupling to whispering gallery modes of a square µ cavity,” Appl. Phys. Lett. 82, 487–489 (2003).
[Crossref]

Poon, A. W.

A. W. Poon, F. Courvoisier, and R. K. Chang, “Multimode resonances in square-shaped optical microcavities,” Opt. Lett. 26, 632–634 (2001).
[Crossref]

A. W. Poon, “Optical resonances of two-dimensional microcavities with circular and non-circular shapes,” PhD thesis, Yale University, 2001.

N. Ma, C. Y. Fong, F. K. L. Tung, K. C. Lam, W. N. Chan, and A. W. Poon, “Micro-pillar square resonant cavity channel add-drop filters on silicon-nitride-on-silica: design, fabrication and characterization,” in Proc. of Conf. Lasers Electro-Optics, Baltimore, MD, Jun. 2003.

Rafizadeh, D

S. C. Hagness, D Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[Crossref]

Rafizadeh, D.

Sengo, G.

Stair, K. A.

Steinmeyer, G.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

Taflove, A.

S. C. Hagness, D Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[Crossref]

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
[Crossref] [PubMed]

Tan, F. S.

Thoen, E. R.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

Tiberio, R. C.

Tung, F. K. L.

N. Ma, C. Y. Fong, F. K. L. Tung, K. C. Lam, W. N. Chan, and A. W. Poon, “Micro-pillar square resonant cavity channel add-drop filters on silicon-nitride-on-silica: design, fabrication and characterization,” in Proc. of Conf. Lasers Electro-Optics, Baltimore, MD, Jun. 2003.

van der Veen, T.

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Zhang, J. P.

Appl. Phys. Lett. (1)

Y. L. Pan and R. K. Chang, “Highly efficient prism coupling to whispering gallery modes of a square µ cavity,” Appl. Phys. Lett. 82, 487–489 (2003).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

IEEE Photon. Technol. Lett. (2)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, 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]

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun, and P. T. Ho, “Laterally coupled InP-based single-mode microracetrack notch filter,” IEEE Photon. Technol. Lett. 15, 1082–1084(2003).
[Crossref]

J. Lightwave Technol. (2)

D. J. W. Klunder, F. S. Tan, T. van der Veen, H. F. Bulthuis, G. Sengo, B. Docter, H. J. W. M. Hoekstra, and A. Driessen, “Experimental and numerical study of SiON microresonators with air and polymer cladding,” J. Lightwave Technol. 21, 1099–1110 (2003).
[Crossref]

S. C. Hagness, D Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[Crossref]

Opt. Commun. (1)

M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective,” Opt. Commun. 214, 155–170 (2002).
[Crossref]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

M. Lohmeyer, “Mode expansion of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34, 541–557 (2002).
[Crossref]

Phys. Rev. Lett. (1)

Y. F. Chen, K. F. Huang, H. C. Lai, and Y. P. Lan, “Observation of vector vortex lattices in polarization states of an isotropic microcavity laser,” Phys. Rev. Lett. 90, 053904 (2003).
[Crossref] [PubMed]

Other (4)

N. Ma, C. Y. Fong, F. K. L. Tung, K. C. Lam, W. N. Chan, and A. W. Poon, “Micro-pillar square resonant cavity channel add-drop filters on silicon-nitride-on-silica: design, fabrication and characterization,” in Proc. of Conf. Lasers Electro-Optics, Baltimore, MD, Jun. 2003.

FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com.

K. Okamoto, “Chapter 2” in Fundamentals of optical waveguides, (Academic, San Diego, CA, 2000).

A. W. Poon, “Optical resonances of two-dimensional microcavities with circular and non-circular shapes,” PhD thesis, Yale University, 2001.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of a planar waveguide-coupled square µ-cavity channel add-drop filter.

Fig. 2.
Fig. 2.

FDTD simulated throughput (blue), drop (green) and add (red dashed line) spectra (normalized with input intensity) of a planar waveguide-coupled square µ-cavity filter. a=2.2 µm, w=0.2 µm, g=0.2 µm and TM-polarized. The dominant resonances in the throughput spectrum are indexed as (mx, my) modes according to the corresponding mode-field patterns. The indexed (mx, my) modes are clustered according to the integer number of wavelengths M.

Fig. 3.
Fig. 3.

FDTD simulated odd M (=15) mode field patterns of a planar waveguide-coupled square µ-cavity filter at (6,9) mode (λ=1538 nm). a=2.2 µm, w=0.2 µm, g=0.2 µm and TM-polarized. (a) t=t0, (b) t≈t0+T/8, (c) t≈t0+T/4, (d) t≈t0+3T/8 and (e) t≈t0+T/2.

Fig. 4.
Fig. 4.

FDTD simulated odd M (=15) mode field patterns of a planar waveguide-coupled square µ-cavity filter at (7,8) mode (λ=1562.5 nm). a=2.2 µm, w=0.2 µm, g=0.2 µm and TM-polarized. (a) t=t0, (b) t≈t0+T/6, (c) t≈t0+T/4, (d) t≈t0+2T/6 and (e) t≈t0+T/2. Calculated mode field patterns of a discrete square cavity using Eq. (2) with A=0.7 for (7,8) mode, B=0.3 for (8,7) mode, and δ=π/2. (f) ωt=0, (g) ω t=2π/6, (h) ωt=π/2, (i) ωt=4π/6 and (j) ωt=π.

Fig. 5.
Fig. 5.

FDTD simulated even M (=16) mode field patterns of a planar waveguide-coupled square µ-cavity filter. a=2.2 µm, w=0.2 µm, g=0.2 µm and TM-polarized. (a) (7,9)π mode (λ=1446.5 nm), (b) (6,10)π mode (λ=1417.1 nm), (c) (7,9)0 mode (λ=1454.5 nm) and (d) (8,8) mode (λ=1461.2 nm). Calculated mode field patterns of a discrete square cavity using Eq. (2) with A=B. (e) (7,9)π mode, (f) (6,10)π mode, (g) (7,9)0 mode and (h) (8,8) mode. The dashed-line box in (b) and (f) denotes a “vortex.”

Fig. 6.
Fig. 6.

Calculated k-space (mx, my) modes (filled and open dots) of a discrete square cavity of a=2.36 µm. The y-axis is the mode angle θ and the x-axis is the wavelength λ. Only the modes that satisfy θc<θ <90°-θc are represented (θc≈16.6° for n=3.5). The modes of the same M values are distributed along various parabola curves. The dominant modes in Fig. 2 are represented by filled dots. The dashed line shows the waveguide fundamental mode angle ϕ (w=0.2 µm) in TM polarization.

Equations (3)

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E mx , my ( x , y ) e iωt = A e iωt sin ( m x π x a ) sin ( m y π y a ) ,
E mx , my ( x , y ) e iωt = A e iωt sin ( m x π x a ) sin ( m y π y a )
+ B e i ( ω t δ ) sin ( m y π x a ) sin ( m x π y a ) ,

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