Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By J. Frances Monllor, J. Tervo, and C. Neipp

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The Split-Field Finite-Difference Time-Domain (SFFDTD) formulation is extended to periodic structures with Kerr-type nonlinearity. The optical Kerr effect is introduced by an iterative fixed-point procedure for solving the nonlinear system of equations. Using the method, formation of solitons inside homogenous nonlinear media is numerically observed. Furthermore, the performance of the approach with more complex photonic systems, such as high-reflectance coatings and binary phase gratings with high nonlinearity is investigated. The static and the dynamic behavior of the Kerr effect is studied and compared to previous works.

J. Frances Monllor, J. Tervo, and C. Neipp, "Split-Field Finite-Difference Time-Domain Scheme for Kerr-Type Nonlinear Periodic Media," Progress In Electromagnetics Research, Vol. 134, 559-579, 2013.

1. Kerr, J., "A new relation between electricity and light: Dielectri-fied media birefringent," Phil. Mag. J. Sci., Vol. 50, No. 3, 337-393, 1875.

2. Boyd, R. W., Nonlinear Optics, 2nd Edition, Academic Press, 2003.

3. Aberg, I., "High-frequency switching and Kerr effect - Nonlinear problems solved with nonstationary time domain techniques Summary," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 1, 85-90, 1998.

4. Joseph, R. M. and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag., Vol. 45, No. 3, 364-374, 1997.

5. Kosmidou, E. P. and T. D. Tsiboukis, "An unconditionally stable ADI-FDTD algorithm for nonlinear materials," Proc. ISTET, 2003.

6. Fujii, M., M. Tahara, I. Sakagami, W. Freude, and P. Russer, "High-order FDTD and auxiliary differential equation formulation of optical pulse propagation ," IEEE J. Quantum Electron., Vol. 40, No. 2, 175-182, 2004.

7. Balourdos, P. S., D. J. Frantzeskakis, M. C. Tsilis, and I. G. Tigelis, "Reflectivity of a nonlinear discontinuity in optical waveguides," Journal of Optics A: Pure and Applied Optics, Vol. 7, No. 1, 1-11, 1998.

8. Deering, W. D. and G. M. Molina, "Power switching in hybrid coherent couplers," IEEE J. Quantum Electron., Vol. 33, No. 3, 336-340, 1998.

9. Zhou, F., Y. Liu, Z.-Y. Li, and Y. Xia, "Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials," Opt. Express, Vol. 18, No. 15, 13337-13344, 2010.

10. Wang, S. M. and L. Gao, "Nonlinear responses of the periodic structure composed of single negative materials," Opt. Commun., Vol. 267, No. 1, 197-204, 2006.

11. Wang, S. M., C. G. Tang, T. Pan, and L. Gao, "Bistability and gap soliton in one-dimensional photonic crystal containing single-negative materials," Phys. Lett. A, Vol. 348, No. 3-6, 424-431, 2006.

12. Hedge, R. S. and H. G. Winful, "Optical bistability in periodic nonlinear structures containing left handled materials," Microw. Opt. Technol. Lett., Vol. 46, No. 36, 528-530, 2005.

13. Gao, D. and L. Gao, "Goos-Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability," Appl. Phys. Lett., Vol. 97, 041903, 2010.

14. Dong, L. Gao, and C.-W. Qiu, "Goos-Hänchen shift at the surface of chiral negative refractive media," Progress In Electromagnetic Research, Vol. 90, 255-268, 2009.

15. Brzozowski, L. and E. H. Sargent, "Optical signal processing using nonlinear distributed feedback structures," IEEE J. Quantum Electron., Vol. 36, No. 5, 550-555, 2000.

16. Qasymeh, M., M. Cada, and S. A. Ponomarenko, "Quadratic electro-optic Kerr effect: Applications to photonic devices," IEEE J. Quantum Electron., Vol. 44, No. 8, 740-746, 2008.

17. Wu, J.-W. and H.-B. Bao, "Simultaneous generation of ultrafast bright and dark pulse employing nonlinear processes based on the silicon waveguides," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 8-9, 1143-1154, 2009.

18. Li, Y. E. and X. P. Zhang, "Nonlinear optical switch utilizing long-range surface plasmon polaritons," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 17-18, 2363-2371, 2009.

19. Crutcher, S., A. Biswas, M. D. Aggarwal, and M. E. Edwards, "Oscillatory behavior of spatial solitons in two-dimensional waveguides and stationary temporal power law solitons in optical fibers," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 6, 761-772, 2006.

20. Ghafoori-Fard, H., M. J. Moghimi, and A. Rostami, "Linear and nonlinear superimposed Bragg grating: A novel proposal for all-optical multi-wavelength filtering and switching," Progress In Electromagnetic Research, Vol. 77, 243-266, 2007.

21. Morgan, S. A., R. J. Ballagh, and K. Burnett, "Solitary-wave solutions to nonlinear Schrödinger equations," Phys. Rev. A, Vol. 55, No. 6, 4338-4345, 1997.

22. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag., Vol. 14, No. 3, 302-307, 1966.

23. Taflove, A. and S. C. Hagness, "Computational Electrodynamics: The Finite-Difference Time-Domain Method," Artech House, Norwood, MA, 2004.

24. Lee, K. H., I. Ahmed, R. S. M. Goh, E. H. Khoo, E. P. Li, and T. G. G. Hung, "Implementation of the FDTD method based on Lorentz-Drude dispersive model on GPU for plasmonics applications," Progress In Electromagnetic Research, Vol. 116, 441-456, 2011.

25. Francés, J., C. Neipp, M. Pérez-Molina, and A. Beléndez, "Rigorous interference and diffraction analysis of diffractive optic elements using the finite-difference time-domain method," Comput. Phys. Commun., Vol. 181, No. 12, 1963-1973, 2010.

26. Francés, J., C. Neipp, A. Márquez, A. Beléndez, and I. Pascual, "Analysis of reflection gratings by means of a matrix approach," Progress In Electromagnetic Research, Vol. 118, 167-183, 2011.

27. Kalaee, P. and J. Rashed-Mohassel, "Investigation of dipole radiation pattern above a chiral media using 3D BI-FDTD approach," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 1, 75-86, 2009.

28. Kao, Y. C. and R. G. Atkins, "A finite-difference time-domain approach for frequency selective surfaces at oblique incidence," Proceedings of Antennas and Propagation Society International Symposium, 1432-1435, 1996.

29. Roden, J. A., S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, "Time-domain analysis of periodic structures at oblique incidence: Orthogonal and nonorthogonal FDTD implementation," IEEE Trans. Microw. Theory Tech., Vol. 46, No. 4, 420-427, 1998.

30. Veysoglu, M. E., R. T. Shin, and J. A. Kong, "A finite-difference time-domain analysis of wave scattering from periodic surfaces: Oblique incidence case," Journal of Electromagnetic Waves and Applications, Vol. 7, No. 12, 1595-1607, 1993.

31. Mao, Y., B. Chen, H.-Q. Liu, J.-L. Xia, and J.-Z. Tang, "A hybrid implicit-explicit spectral FDTD scheme for oblique incidence problems on periodic structures," Progress In Electromagnetic Research, Vol. 128, 153-170, 2012.

32. Shahmansouri, A. and B. Rashidian, "Comprehensive three-dimensional split-field finite-difference time-domain method for analysis of periodic plasmonic nanostructures: Near- and far-field formulation," J. Opt. Soc. Am. B, Vol. 28, No. 11, 2690-2700, 2011.

33. Shahmansouri, A. and B. Rashidian, "GPU implementation of split-field finite-difference time-domain method for Drude-Lorentz dispersive media," Progress In Electromagnetic Research, Vol. 125, 55-77, 2012.

34. Goorjian, P. M., A. Taflove, R. M. Joseph, and S. C. Hagness, "Computational modeling of femtosecond optical solitons from Maxwell's equations," IEEE J. Quantum Electron., Vol. 28, No. 10, 2416-2422, 1992.

35. Goorjian, P. M. and A. Taflove, "Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons," Opt. Lett., Vol. 17, No. 3, 180-182, 1992.

36. Zhang, Y.-Q. and D.-B. Ge, "A unified FDTD approach for electromagnetic analysis of dispersive objects," Progress In Electromagnetic Research, Vol. 96, 155-172, 2009.

37. Gedney, S. D., "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas Propag., Vol. 44, No. 12, 1630-1639, 1996.

38. Zheng, G., A. A. Kishk, A. W. Glisson, and A. B. Yakovlev, "Implementation of Mur's absorbing boundaries with periodic structures to speed up the design process using finite-difference time-domain method," Progress In Electromagnetic Research, Vol. 58, 101-114, 2006.

39. Oh, C. and M. Escuti, "Time-domain analysis of periodic anisotropic media at oblique incidence: An efficient FDTD implementation," Opt. Express, Vol. 14, No. 24, 11870-11884, 2006.

40. Ammann, M., "Non-trivial materials in EM-FDTD," , Master's Thesis, Department of Physics, Swiss Federal Institute of Technology, 2007.

41. Pinto, D., S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, "FDTD analysis of nonlinear Bragg grating based optical devices," Opt. Quant. Electron., Vol. 38, No. 15, 1217-1238, 2006.

42. Macleod, H. A., Thin-Film Optical Filters, 2nd Edition, Taylor & Francis, 2001.
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