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.
Highlights
There has been great interest in new type of electromagnetic materials called left-handed media [1]
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
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 left-handed meta-material (LHM)
Summary
There has been great interest in new type of electromagnetic materials called left-handed media [1]. Akhmediev et al [7] explained the stability behavior of antisymmetric and symmetric solutions of a linear core sandwiched between two nonlinear media They showed that the antisymmetric wave is stable at high values of the propagation constant, in contrast to the symmetric wave. Shabat and Mousa have studied the stability of nonlinear surface waves along the boundary of linear semiconductor [13] and along the boundary of lateral antiferromagnetic/nonmagnetic superlattice (LANS) [14] These studies were carried out in a media with positive refractive index. To study the stability of the corresponding surface waves, it is necessary to select a particular form of the frequency dependence of the electric permittivity h and magnetic permeability h of the LHM, I solve this problem by using computer simulation method [15]. The coordinate system is such that, the y axis is normal to the interface and the wave vector is directed along the x axis
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