Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide have received a great deal of attention in the recent years. Our goal in this paper is to study the propagation characteristics of that pulse in a nonlinear optical fiber. In analyzing these characteristics, the nonlinear effects along with the dispersion are taking into account. Additionally, the considered nonlinear effects include self phase modulation (SPM) and stimulated Raman scattering (SRS). The problem to be processed is modeled using the finite difference time domain (FDTD) technique which represents an efficient tool in achieving the required purpose. Because of the symmetrical structure of the optical waveguide, the FDTD modeling of bodies of revolution (BOR) in cylindrical coordinates is the most preferable algorithm in analyzing our problem. The FDTD treatment of dispersion and nonlinearity of the optical waveguide is accomplished through the direct integration method. In addition, the Lorentzian model is chosen to represent the dielectric properties of the optical fiber. The azimuthal symmetry of optical fiber enables us to use a two-dimensional difference lattice through the projection of the three-dimensional coordinates (r, φ, z) into the (r, z) plane. Extensive numerical results have been obtained for various cavity structures.
2. Jin, G. H., J. Harari, J. P. Vilcot, and D. Decoster, "An improved time-domain beam propagation method for integrated optics components," IEEE Photonics Technol. Lett., Vol. 9, No. 3, 348-350, 1997.
3. 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, Mar. 1997.
4. Sullivan, D. M., "Nonlinear FDTD formulations using Z transforms," IEEE Trans. Microw. Theory Techn., Vol. 43, No. 3, 676-682, Mar. 1995.
5. Luebbers, R., F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider, "A frequency-dependent finite difference time-domain formulation for dispersive media," IEEE Trans. Elect. Mag. Compat., Vol. 32, No. 3, 222-227, Aug. 1990.
6. 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 Electronics, Vol. 28, No. 10, 2416-2422, Oct. 1992.
7. Joseph, R. M., P. M. Goorjian, and A. Taflove, "Direct time integration of Maxwell's equations in 2-D dielectric waveguides for propagation and scattering of femtosecond electromagnetic solitons," Opt. Lett., Vol. 18, 491-493, Apr. 1993.
8. Zhou, D., W. P. Huang, C. L. Xu, D. G. Fang, and B. Chen, "The perfectly matched layer boundary condition for scalar finite-difference time-domain method," IEEE Photonics Technol. Lett., Vol. 13, No. 5, 454-456, May 2001.
9. Sullivan, D., J. Liu, and M. Kuzyk, "Three-dimensional optical pulse simulation using the FDTD method," IEEE Trans. Microw. Theory Techn., Vol. 48, No. 7, 1127-1133, July 2000.
10. El Mashade, M. B., M. Ashry, and A. Nasr, "Theoretical analysis of quantum-dot infrared photodetectors," Semicond. Sci. Technol., Vol. 18, 891-900, 2003.
11. Buchanan, W. J., "Analysis of electromagnetic wave propagation using the 3D finite-difference time domain method with parallel processing,", Ph.D. Thesis, Napier University, Mar. 1996.
12. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time-domain Method, Artech House, Boston, 2000.
13. Perez-Ocon, F., A. M. Pozo, J. R. Jimenez, and E. Hita, "Fast single-mode characterization of optical fiber by finite-difference time-domain method," J. Light Wave Technology, Vol. 24, No. 8, 3129-3136, Aug. 2006.
14. Crando, J., "FDTD computation of dispersive effects for a body of revolution," IEEE Antennas and Propagation Society International Symposium, Vol. 1, 48-51, July 8-13, 2001.
15. Chen, Y., R. Mittra, and P. Harms, "Finite-difference time-domain algorithm for solving Maxwell's equations in rotationally symmetric geometries," IEEE Trans. Microw. Theory Techn., Vol. 44, No. 6, 832-839, June 1996.
16. Blow, K. and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electronics, Vol. 25, No. 12, 2665-2673, Dec. 1989.