Abstract

High-Q semiconductor microdisk resonators laterally coupled to optical waveguides serve as compact and robust components in wavelength-division-multiplexing systems. We present an efficient algorithm for the two-dimensional design of wavelength-selective filters based on waveguide-coupled whispering-gallery-mode (WGM) microresonators of arbitrary cross-sectional shape. A full-wave integral equation formulation enables us to accurately account for the coupling between the resonator and bus waveguide as well as for radiation and material losses. Furthermore, we apply this approach to the analysis of elliptic-resonator filters. Filter tuning by changing the resonator shape from circular to elliptic reduces the dependence of the coupling efficiency on the width of the air gap. Two alternative coupling designs are suggested for monolithic and hybrid integration technologies. One is based on increasing the coupling length, while the other exploits the field concentration at the increased-curvature portion of the deformed WGM resonator.

© 2003 IEEE

PDF Article

References

  • View by:
  • |

  1. D. Cros and P. Guillon, "Whispering gallery dielectric resonator modes for W-band devices", IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1667-1673, Nov. 1990.
  2. D. R. Rowland and J. D. Love, "Evanescent wave coupling of whispering gallery modes of dielectric cylinder", Inst. Elect. Eng. Proc.-J, vol. 140, no. 3, pp. 177-188, 1993.
  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-SiO microring resonator optical channel dropping filters", IEEE Photon. Technol. Lett., vol. 10, pp. 549-551, Apr. 1998.
  4. 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., vol. 15, pp. 2154-2165, Nov. 1997.
  5. S. V. Boriskina and A. I. Nosich, "Radiation and absorption losses of the whispering-gallery-mode dielectric resonators excited by a dielectric waveguide", IEEE Trans. Microwave Theory Tech., vol. 47, pp. 224-231, Feb. 1999.
  6. A. Sakai and T. Baba, "FDTD simulation of photonic devices and circuits based on circular and fan-shaped microdisks", J. Lightwave Technol., vol. 17, pp. 1493-1499, Aug. 1999.
  7. M. K. Chin and S. T. Ho, "Design and modeling of waveguide-coupled single-mode microring resonators", J. Lightwave Technol., vol. 16, pp. 1433-1446, Aug. 1998.
  8. R. G. Walker and C. D. W. Wilkinson, "Integrated optical ring resonators made by silver ion-exchange in glass", Appl. Opt., vol. 22, pp. 1029-1035, July 1983.
  9. M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao and S. T. Ho, "GaAs microcavity channel-dropping filter based on a race-track resonator", IEEE Photon. Technol. Lett., vol. 11, pp. 1620-1622, Dec. 1999.
  10. Y. Kogami, Y. Tomabechi and K. Matsumura, "Resonance characteristics of whispering gallery modes in an elliptic disc resonator", IEEE Trans. Microwave Theory Tech., vol. 44, pp. 473-475, Mar. 1996.
  11. T. Kitagawa, Y. Akahori, I. Ogawa and Y. Tohmori, "Hybrid integration technologies using planar lightwave circuits and developed components", IEICE Trans. Electron., vol. E85-C, pp. 1009-1017, Apr. 2002.
  12. G. L. Hower, R. G. Olsen, J. D. Earls and J. B. Schneider, "Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects", IEEE Trans. Antennas Propagat., vol. 41, pp. 982-986, July 1993.
  13. A. I. Nosich, "The method of analytical regularization in wave-scattering and eigenvalue problems: foundations and review of solutions", IEEE Antennas Propagat. Mag., vol. 41, pp. 34 -49, Mar. 1999.
  14. S. V. Boriskina, T. M. Benson, P. Sewell and A. I. Nosich, "Highly efficient design of specially engineered whispering-gallery-mode laser resonators", Optical Quantum Electron., vol. 35, no. 1, pp. 545 -559, Mar./Apr. 2002.
  15. D. Colton and R. Kress, Integral Equation Method in Scattering Theory, New York: Wiley, 1983.
  16. S. V. Boriskina, T. M. Benson, P. Sewell and A. I. Nosich, "Effect of a layered environment on the complex natural frequencies of 2D WG-mode dielectric-ring resonators", J. Lightwave Technol., vol. 20, pp. 1563-1572, Aug. 2002 .
  17. P. G. Petropoulos and G. A. Kriegsmann, "Optical theorems for electromagnetic scattering by inhomogeneities in layered dielectric media", IEEE Trans. Antennas Propagat., vol. 39, pp. 1119-1124, Aug. 1991.
  18. J. U. Nöckel, A. D. Stone and R. K. Chang, "Q spoiling and directionality in deformed ring cavities", Opt. Lett., vol. 19, pp. 1693-1695, 1994.
  19. S.A. Backes, A. P. Heberle, J. R. A. Cleaver and K. Köhler, "Shape dependence of emission from microdisk lasers", Physica Status Solidi B, vol. 204, no. 1, pp. 581-583, 1997.
  20. V. Van, P. P. Absil, J. V. Hryniewicz and P.-T. Ho, "Propagation loss in single-mode GaAs-AlGaAs microring resonators: Measurement and model", J. Lightwave Technol., vol. 19, pp. 1734-1738, Nov. 2001.
  21. A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton and R. A. Logan, "Directional light coupling from microdisk lasers", Appl. Phys. Lett., vol. 62, pp. 561-563, Feb. 1993 .
  22. B.-J. Li and P.-L. Liu, "Numerical analysis of microdisk lasers with rough boundaries", IEEE J. Quantum Electron., vol. 35, pp. 791-795, May 1997.
  23. M. Fujita and T. Baba, "Proposal and finite-difference time-domain simulation of whispering gallery mode microgear cavity", IEEE J. Quantum Electron., vol. 37, pp. 1253-1258, Oct. 2001.
  24. K. Djordjev, Se.-J. Choi, Sa.-J. Choi and P. D. Dapkus, "High-Q vertically coupled InP microdisk resonators", IEEE Photon. Technol. Lett., vol. 14, pp. 331 -333, Mar. 2002.

Appl. Opt. (1)

J. Lightwave Technol. (5)

Opt. Lett. (1)

Other (17)

S.A. Backes, A. P. Heberle, J. R. A. Cleaver and K. Köhler, "Shape dependence of emission from microdisk lasers", Physica Status Solidi B, vol. 204, no. 1, pp. 581-583, 1997.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton and R. A. Logan, "Directional light coupling from microdisk lasers", Appl. Phys. Lett., vol. 62, pp. 561-563, Feb. 1993 .

B.-J. Li and P.-L. Liu, "Numerical analysis of microdisk lasers with rough boundaries", IEEE J. Quantum Electron., vol. 35, pp. 791-795, May 1997.

M. Fujita and T. Baba, "Proposal and finite-difference time-domain simulation of whispering gallery mode microgear cavity", IEEE J. Quantum Electron., vol. 37, pp. 1253-1258, Oct. 2001.

K. Djordjev, Se.-J. Choi, Sa.-J. Choi and P. D. Dapkus, "High-Q vertically coupled InP microdisk resonators", IEEE Photon. Technol. Lett., vol. 14, pp. 331 -333, Mar. 2002.

P. G. Petropoulos and G. A. Kriegsmann, "Optical theorems for electromagnetic scattering by inhomogeneities in layered dielectric media", IEEE Trans. Antennas Propagat., vol. 39, pp. 1119-1124, Aug. 1991.

S. V. Boriskina and A. I. Nosich, "Radiation and absorption losses of the whispering-gallery-mode dielectric resonators excited by a dielectric waveguide", IEEE Trans. Microwave Theory Tech., vol. 47, pp. 224-231, Feb. 1999.

D. Cros and P. Guillon, "Whispering gallery dielectric resonator modes for W-band devices", IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1667-1673, Nov. 1990.

D. R. Rowland and J. D. Love, "Evanescent wave coupling of whispering gallery modes of dielectric cylinder", Inst. Elect. Eng. Proc.-J, vol. 140, no. 3, pp. 177-188, 1993.

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-SiO microring resonator optical channel dropping filters", IEEE Photon. Technol. Lett., vol. 10, pp. 549-551, Apr. 1998.

M. K. Chin, C. Youtsey, W. Zhao, T. Pierson, Z. Ren, S. L. Wu, L. Wang, Y. G. Zhao and S. T. Ho, "GaAs microcavity channel-dropping filter based on a race-track resonator", IEEE Photon. Technol. Lett., vol. 11, pp. 1620-1622, Dec. 1999.

Y. Kogami, Y. Tomabechi and K. Matsumura, "Resonance characteristics of whispering gallery modes in an elliptic disc resonator", IEEE Trans. Microwave Theory Tech., vol. 44, pp. 473-475, Mar. 1996.

T. Kitagawa, Y. Akahori, I. Ogawa and Y. Tohmori, "Hybrid integration technologies using planar lightwave circuits and developed components", IEICE Trans. Electron., vol. E85-C, pp. 1009-1017, Apr. 2002.

G. L. Hower, R. G. Olsen, J. D. Earls and J. B. Schneider, "Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects", IEEE Trans. Antennas Propagat., vol. 41, pp. 982-986, July 1993.

A. I. Nosich, "The method of analytical regularization in wave-scattering and eigenvalue problems: foundations and review of solutions", IEEE Antennas Propagat. Mag., vol. 41, pp. 34 -49, Mar. 1999.

S. V. Boriskina, T. M. Benson, P. Sewell and A. I. Nosich, "Highly efficient design of specially engineered whispering-gallery-mode laser resonators", Optical Quantum Electron., vol. 35, no. 1, pp. 545 -559, Mar./Apr. 2002.

D. Colton and R. Kress, Integral Equation Method in Scattering Theory, New York: Wiley, 1983.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.