Abstract

Finite-element analysis in time and frequency domains using perfectly matched layers and isoparametric curvilinear elements for finite-size photonic-crystal (PC) cavities is presented in this paper. The time-domain approach includes current sources, the full band scheme, and the slowly varying envelope approximation; consequently, bigger time steps can be used independent of the size of the elements. The resonant frequency, quality factor, effective modal area, and field distribution for each mode can be obtained in a single simulation. A strategy to compute the higher resonant modes by using only a quarter of the cavity and adequate boundary conditions is also presented.

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Opt. Express (1)

Opt. Lett. (1)

Other (14)

D. C. Dibben and R. Metaxas, "Frequency domain vs. time domain finite element methods for calculation of fields in multimode cavities", IEEE Trans. Magn., vol. 33, no. 2, pp. 1468-1471, Mar. 1997.

M. Koshiba, Y. Tsuji and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuit components", J. Lightw. Technol. , vol. 18, no. 1, pp. 102-110, Jan. 2000.

V. F. Rodríguez-Esquerre and H. E. Hernández-Figueroa, "Novel time-domain step-by-step scheme for integrated optical applications", IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 311 -313, Apr. 2001.

A. Cucinotta, S. Selleri, L. Vincetti and M. Zooboli, "Impact of the cell geometry on the spectral properties of photonic crystal structures", Appl. Phys. B, Photophys. Laser Chem. , vol. 73, pp. 595-600, Oct. 2001.

A. Niiyama, M. Koshiba and Y. Tsuji, "An efficient scalar finite element formulation for nonlinear optical channel waveguides", J. Lightw. Technol., vol. 13, no. 9, pp. 1919-1925, Sep. 1995.

G. R. Cowper, "Gaussian quadrature formulas for triangles", Int. J. Numer. Methods Eng., vol. 7, pp. 405 -408, 1973.

N. M. Newmark, "A method of computation for structural dynamics", J. Eng. Mechan. Divis., ASCE, vol. 85, pp. 67 -94, July 1959.

B. N. Parlet, The Symmetric Eigenvalue Problem, Englewood Cliffs, NJ: Prentice-Hall, 1990.

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton, NJ: Princeton Univ. Press, 1995, ch. 7.

K. Sakoda, Optical Properties of Photonic Crystals, New York: Springer-Verlag, 2001, ch. 6.

"Photonic Crystal", IEEE J. Quantum Electron , vol. 38, pp. 724-963, Jul. 2002.

K. Sakoda, "Numerical study on localized defect modes in two-dimensional triangular photonic crystals", J. Appl. Phys., vol. 84, pp. 1210-1214, Aug. 1998.

J. K. Hwang, S. B. Hyun, H. Y. Ryu and Y. H. Lee, "Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition", J. Opt. Soc. Amer. B, Opt. Phys., vol. 15, pp. 2316-2324, Aug. 1998.

J. Huh, J. K. Hwang, H. Y. Ryu and Y. H. Lee, "Nondegenerate monopole mode of single defect two-dimensional triangular photonic band-gap cavity", J. Appl. Phys., vol. 92, pp. 654-659, Jul. 2002.

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