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Progress In Electromagnetics Research
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MULTIPLE-SCALE ANALYSIS OF PLANE WAVE REFRACTION AT A DIELECTRIC SLAB WITH KERR-TYPE NONLINEARITY

By K. Z. Aghaie and M. Shahabadi

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Abstract:
Multiple-scale analysis is employed for the analysis of plane wave refraction at a nonlinear slab. It will be demonstrated that the perturbation method will lead to a nonuniformly valid approximation to the solution of the nonlinear wave equation. To construct a uniformly valid approximation, we will exploit multiplescale analysis. Using this method, we will derive the zerothorder approximation to the solution of the nonlinear wave equation analytically. This approximate solution clearly shows the effects of self-phase modulation (SPM) and cross-phase modulation (XPM) on plane wave refraction at the nonlinear slab. In fact, the obtained zeroth-order approximation is very accurate and there is not any need for derivation of higher-order approximations. As will be shown, the proposed method can be generalized to the rigorous study of nonlinear wave propagation in one-dimensional photonic band-gap structures.

Citation:
K. Z. Aghaie and M. Shahabadi, "Multiple-Scale Analysis of Plane Wave Refraction at a Dielectric Slab with Kerr-Type Nonlinearity," Progress In Electromagnetics Research, Vol. 56, 81-92, 2006.
doi:10.2528/PIER05051701
http://www.jpier.org/PIER/pier.php?paper=0505171

References:
1. Winful, H. G., J. H. Marburger, and E. Garmire, "Theory of bistability in nonlinear distributed feedback structures," Appl. Phys. Lett., Vol. 35, No. 5, 379-381, 1979.
doi:10.1063/1.91131

2. Christodoulides, D. N. and R. I. Joseph, "Slow Bragg solitons in nonlinear periodic structures," Phys. Rev. Lett., Vol. 62, No. 15-10, 1746-1749, 1989.
doi:10.1103/PhysRevLett.62.1746

3. Broderick, N. G. R., D. J. Richardson, and M. Ibsen, "Nonlinear switching in a 20-cm long fiber Bragg grating," Opt. Lett., Vol. 25, No. 8, 536-538, 2000.

4. Senthilnathan, K., P. Malathi, and K. Porsezian, "Dynamics of nonlinear pulse propagation through a fiber Bragg grating with linear coupling," J. Opt. Soc. Am. B, Vol. 20, No. 2, 366-372, 2003.

5. Slusher, R. E. and B. J. Eggleton (Eds.), Nonlinear Photonic Crystals, Springer-Verlag, Berlin, 2003.

6. Hayata, K., M. Nagai, and M. Koshiba, "Finite-element formalism for nonlinear slab-guided waves," IEEE Trans. Microw. Theory Tech., Vol. 36, No. 7, 1207-1215, 1988.
doi:10.1109/22.3657

7. Polstyanko, S. V., R. Dyczij-Edlinger, and J. F. Lee, "A full vectorial analysis of a nonlinear slab waveguide based on the nonlinear hybrid vector finite-element method," Opt. Lett., Vol. 21, No. 2, 98-100, 1996.

8. Van, V. and S. K. Chaudhuri, "A hybrid implicit-explicit FDTD scheme for nonlinear optical waveguide modeling," IEEE Trans. Microw. Theory Tech., No. 5, 540-545, 1999.
doi:10.1109/22.763152

9. Bender, C. M. and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, Singapore, 1978.

10. Joseph, R. M. and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propagat., Vol. 45, No. 3, 364-374, 1997.
doi:10.1109/8.558652

11. Ogusu, K., "Self-switching in hollow waveguides with a Kerrlike nonlinear permittivity," IEEE J. Lightwave Technol., Vol. 8, No. 10, 1541-1547, 1990.
doi:10.1109/50.59194


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