OPJ  Vol.2 No.2 , June 2012
Stability of Nonlinear Te Surface Waves along the Boundary of Left-Handed Material
Abstract: This paper is concerned with the stability characteristics of nonlinear surface waves propagating along a left-handed substrate (LHM) and a non-linear dielectric cover. These characteristics have been simulated numerically by using the perturbation method. The growth rate of perturbation is computed by solving the dispersion equation of perturbation. I found that the stability of nonlinear surface waves is affected by the frequency dependence of the electric permittivity εh and magnetic permeability μh of the LHM. The spatial evolution of the steady state field amplitude is determined by using computer simulation method. The calculations show that with increasing the effective refractive index nx at fixed saturation parameter μp, the field distribution is sharpened and concentrated in the nonlinear medium. The waves are stable of forward and backward behavior. At higher values of nx, attenuated backward waves are observed.
Cite this paper: H. Mousa, "Stability of Nonlinear Te Surface Waves along the Boundary of Left-Handed Material," Optics and Photonics Journal, Vol. 2 No. 2, 2012, pp. 123-128. doi: 10.4236/opj.2012.22017.

[1]   L. Hu and S. T. Chui, “Characteristics of Electromagnetic Wave Propagation in Uniaxially Anisotropic Left-Handed Materials,” Physical Review: B, Vol. 66, No. 8, 2002, pp. 085108-085115. doi:10.1103/PhysRevB.66.085108

[2]   V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of Permittivity and Permeability,” Soviet Physics Uspekhi, Vol. 10, No. 4, 1967, p. 509. doi:10.1070/PU1968v010n04ABEH003699

[3]   I. V. Shadrivov, A. A. Sukhorakov and Y. S. Kivshar, “Nonlinear Surface Waves in Left-Handed Material,” Physical Review: E, Vol. 69, No. 1, 2004, p. 016617. doi:10.1103/PhysRevE.69.016617

[4]   D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser and S. Schultz, “Composite Medium with Simultaneously Negative permeability and Permittivity,” Physical Review Letters, Vol. 84, No. 18, 2000, p. 4184. doi:10.1103/PhysRevLett.84.4184

[5]   J. V. Moloney, J. Ariyasu and G. I. Stegeman, “Stability of Nonlinear Stationary Waves Guided by a Thin Film Bounded by Nonlinear Media,” Applied Physics Letter, Vol. 48, No. 13, 1986, p. 826. doi:10.1063/1.96680

[6]   H. T. Tran, “Stability of Stationary Dark Waves Guided by Nonlinear Surfaces and Waveguides,” Journal of the Optical Society of America B, Vol. 11, No. 5, 1994, pp. 789-797. doi:10.1364/JOSAB.11.000789

[7]   N. Akhmediev, A. Ankiewicz and H.-T. Tan, “Stability Analysis of Even and Odd Waves of Symmetric Nonlinear Planar Optical Waveguides,” Journal of the Optical Society of America B, Vol. 10, No. 1, 1993, pp.230-236. doi:10.1364/JOSAB.10.000230

[8]   N. N. Akhmediev, “Nonlinear Surface Electromagnetic Phenomena,” In: H. E. Ponath and G. I. Stegeman, Eds., The Problem of Stability and Excitation of Nonlinear Surface Waves, Elsevier, Horth Holland, 1991, p. 289.

[9]   A. Hasegawa, “Soliton Effects in Optical Waveguides,” Reports on Progress in Physics, Vol. 65, No. 6, 2002, pp. 999-1024. doi:10.1088/0034-4885/65/6/203

[10]   A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg and Y. Silberberg, “Spatial Optical Solitons in Waveguide Arrays,” IEEE Journal of Quantum Electron, Vol. 39, No. 1, 2003, pp. 31-50. doi:10.1109/JQE.2002.806184

[11]   M. Johansson, A. A. Sukhorukov and Y. S. Kivshar, “Discrete Reduced-Symmetry Solitons and Second Band Vortices in Two Dimensional Nonlinear Waveguide Arrays,” Physical Review: E, Vol. 80, No. 4, 2009, pp. 046604046619. doi:10.1103/PhysRevE.80.046604

[12]   F. Setzpfandt, A. A. Sukhorukov and T. Pertsch, “Discrete Quadratic Solitons with Competing Second-Harmonic Components,” Physical Review A, Vol. 84, No. 5, 2011, pp. 053843-053851. doi:10.1103/PhysRevA.84.053843

[13]   H. M. Mousa and M. M. Shabat, “Stability of Nonlinear TE Surface Waves along the Boundary of Linear Gyrodielectric Media,” International Journal of Modern Physics B, Vol. 21, No. 26, 2007, pp. 4487-4493. doi:10.1142/S0217979207038009

[14]   M. M. Shabat and H. M. Mousa, “Stability of Nonlinear Te Surface Waves along the Interface of Nonlinear Dielectric and Superlattices Media,” The Islamic University Journal, Vol. 14, No. 1, 2006, pp. 135-145.

[15]   “Maple Software,” Version 9, 615 Kumpf Drive, Waterloo, 2004.