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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 3 — Mar. 1, 2000
  • pp: 387–400

Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide

Youg Xu, Reginald K. Lee, and Amnon Yariv  »View Author Affiliations

JOSA B, Vol. 17, Issue 3, pp. 387-400 (2000)

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Using both the tight-binding approximation and the finite-difference time domain method, we analyze two types of coupled-resonator optical waveguide (CROW), a coupled-microdisks waveguide and a waveguide composed of coupled defect cavities in a two-dimensional photonic crystal. We find that the dispersion relation of the CROW band can be simply described by a small coupling parameter κ, and the spatial characteristics of the CROW modes remain the same as those of the single-resonator high Q modes. As applications of these unique properties, we demonstrate that CROW’s can be utilized in constructing waveguides without cross talk and enhance the efficiency of second-harmonic generation.

© 2000 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.7370) Optical devices : Waveguides

Youg Xu, Reginald K. Lee, and Amnon Yariv, "Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide," J. Opt. Soc. Am. B 17, 387-400 (2000)

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  1. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  2. P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19, 427–430 (1976).
  3. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
  4. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
  5. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
  6. O. Painter, J. Vuckovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
  7. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
  8. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
  9. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1995).
  10. S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
  11. N. C. Frateschi and A. F. Levi, “The spectrum of microdisk lasers,” J. Appl. Phys. 80, 644–653 (1996).
  12. See, for example, N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).
  13. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
  14. A. Taflove, ed. Advances in Computational Electromagnetics: the Finite Difference Time Domain Method (Artech House, Boston, Mass., 1998).
  15. K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: solutions of inhomogeneous Maxwell’s equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
  16. K. Sakoda and K. Ohtaka, “Sum-frequency generation in a two-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
  17. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
  18. J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
  19. J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59, 1551–1554 (1999).
  20. J. Martorell and R. Corbalan, “Enhancement of second harmonic generation in a periodic structure with a defect,” Opt. Commun. 108, 319–323 (1994).
  21. J. Trull, R. Vilaseca, J. Martorell, and R. Corbalan, “Second-harmonic generation in local modes of a truncated periodic structure,” Opt. Lett. 20, 1746–1748 (1995).
  22. T. Hattori, N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
  23. J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
  24. K. Sakoda, “Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals,” Opt. Expr. 4, 167–176 (1999).
  25. M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
  26. X. Feng and Y. Arakawa, “Off-plane angle dependence of photonic band gap in a two-dimensional photonic crystal,” IEEE J. Quantum Electron. 32, 535–542 (1996).
  27. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
  28. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
  29. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
  30. See, for example, J. Mathews and R. L. Walker, Mathematical Methods of Physics (Wiley, New York, 1970).
  31. S. G. Johnson, C. Manolatou, S. Fan, P. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23, 1855–1857 (1998).
  32. A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1997).
  33. See, for example, C. Cohen-Tannoudji, B. Piu, and F. Laloe, Quantum Mechanics (Wiley, New York, 1977).

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