Abstract
A finite difference time domain (FDTD) study of two-dimensional photonic crystals containing nonlinear materials is presented in this paper. An appropriate Z-transform oriented formulation of the FDTD method for the simulation of third-order nonlinear Kerr- and Raman-type media is analyzed and applied to model nonlinear photonic crystal waveguide structures. For their reflectionless termination a novel perfectly matched layer (PML) is proposed and evaluated comparatively to other periodic and inhomogeneous absorbers. Furthermore, the absorbing efficiency of the proposed PML is investigated varying its parameters.
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Bayindir, M., B. Temelkuran and E. Ozbay. Appl. Phys. Lett. 77 3902, 2000.
Berenger, J.-P. J. Comput. Phys. 114 185, 1994.
El-Kady, I., M.M. Sigalas, R. Biswas and K.M. Ho. IEEE J. Lightwave Tech. 17 2042, 1999.
Fang, J. and Z. Wu. IEEE Trans. Microwave Theory Tech. 44 2216, 1996.
Joannopoulos, J.D., R.D. Meade and J.N. Winn. Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, NJ, 1995.
Joseph, R.M. and A. Taflove. IEEE Trans. Antennas Prop. 45, 364, 1997.
Kelly, P.K. and M. Piket-May. IEEE J. Lightwave Tech. 17 1008, 1999.
Koshiba, M., Y. Tsuji and S. Sasaki. IEEE Microwave Wireless Comp. Lett. 11 152, 2001.
Mekis, A., J.C. Chen, I. Kurland, S. Fan, P. Villeneuve and J.D. Joannopoulos. Phys. Rev. Lett. 77 3787, 1996.
Mekis, A., S. Fan and J.D. Joannopoulos. IEEE Microwave Guided Wave Lett. 9 502, 1999.
Mingaleev, S. and Y. Kivshar. Opt. Photon. News 48, 2002.
Qiu, M. and S. He. Physica B 299 187, 2001.
Scholz, S., O. Hess and R. Ruhle. Opt. Expr., 3 28, 1998.
Stoffer, R., H.J.W.M. Hoekstra, R.M. De Ridder, E. Van Groesen and F.P.H. Van Beckum. Opt. Quant. Electron. 32 947, 2000.
Sullivan, D.M. IEEE Trans. Microwave Theory Tech. 43 676, 1995.
Taflove, A. Advances in Computational Electrodynamics, Artech House, Norwood, MA, 1998.
Thèvenot, M., A. Reineix and B. Jecko. J. Opt. A: Pure Appl. Opt. 1, 495, 1999.
Tanaka, T., S. Noda, A. Chutinan, T. Asano and N. Yamamoto. Opt. Quant. Electron. 34 37, 2002.
Tran, P. Optics Lett. 21, 1138, 1996.
Zhao, A.P. Application of the material-independent PML absorbers to the FDTD analysis of electromagnetic waves in nonlinear media. IEEE Trans. Microwave Theory Tech. 46 1511, 1998.
Ziolkowski, R.W. and M. Tanaka. Opt. Quant. Electron. 31 843, 1999.
Yablonovitch, E. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58 2059, 1987.
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Kosmidou, E.P., Tsiboukis, T.D. An FDTD analysis of photonic crystal waveguides comprising third-order nonlinear materials. Optical and Quantum Electronics 35, 931–946 (2003). https://doi.org/10.1023/A:1025122517879
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DOI: https://doi.org/10.1023/A:1025122517879