International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395 -0056
Volume: 04 Issue: 04 | Apr -2017
p-ISSN: 2395-0072
www.irjet.net
Study of surface Soliton at the interface between a semidiscrete onedimensional Kerr-nonlinear system and a continuous medium (slab waveguide) O. P. Swami1, Vijendra Kumar2, A. K. Nagar3 1,2,3 Department
of Physics, Govt. Dungar college, Bikaner, Rajasthan, India, 334001 ---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract – In this paper, we study the existence of Surface
Soliton at the interface between a semidiscrete one dimension Kerr-nonlinear system and a continuous medium in form of optical waveguide. We investigate that a power threshold is required for the existence of surface. Below which no excitation found. Power threshold is calculated numerically and analytically with the function of propagation constant (keeping fix value of coupling constant). We also found that increasing the strength of coupling constant between the waveguides increases the light intensity in the excited waveguide resulting in a smoother soliton. Key Words: Surface Soliton, Waveguides, Discrete nonlinear Schrodinger equation, Kerr-nonlinear system, Refractive index.
1. INTRODUCTION AND REVIEW OF SOME PREVIOUS WORK The presence of an interface between different materials can profoundly affect the evolution of nonlinear excitations. Such interface can support stationary surface waves. These were encountered in various areas of physics including solid-state physics [1], near surface optics [2], plasmas [3], and acoustics [4]. In nonlinear optics, surface waves were under active consideration since 1980. The progress in their experimental observation was severely limited because of unrealistically high power levels required for surface wave excitation at the interfaces of natural materials. However, shallow refractive index modulations accessible in a technologically fabricated waveguide array (or lattice) may facilitate the formation of surface waves at moderate power levels at the edge of semi-infinite arrays as was suggested in Ref. [5]. This has led to the observation of one-dimensional surface solitons in arrays with focusing nonlinearity [6]. Defocusing lattice interfaces are also capable to support surface gap solitons [7, 8 & 9]. Surface lattice solitons may exist not only in cubic and saturable materials, but also in quadratic [10] and nonlocal [11] media, as well as at the interfaces of complex arrays [12]. The femtosecond laser direct writing technique [13] allows fabrication of waveguide arrays along arbitrary paths [14] and with various topologies, such as square [15], hexagonal [16] and circular [17], where multiple waveguides © 2017, IRJET
|
Impact Factor value: 5.181
|
can be specifically excited [18]. Since the nonlinearity of the waveguides is affected by the writing parameters [19], it is possible to tune it for specific purposes, such as excitation of 1D and 2D discrete solitons [20 & 21]. Surface solitons have also been predicted at the interface between two different semi-infinite waveguide arrays [22], as well as at the boundaries of two-dimensional (2D) nonlinear lattices [23, 24, 25, 26 & 27]. It has been shown that surface solitons of the vectorial [28 & 29] and vertical [6.77] types, as well as surface kinks [30], can exist too. The existence of surface Soliton required a power threshold below which no excitation found. In my present work the value of power threshold is calculated numerically and analytically with the function of propagation constant (keeping fix value of coupling constant). I also found that increasing the strength of coupling constant C between the waveguides increases the light intensity in the excited waveguide resulting in a smoother Soliton.
2. PROBLEM FORMULATION To analyze the problem of nonlinear surface waves, consider a semi-infinite Kerr-nonlinear lattice shown schematically in Figure 1. The discrete nonlinear schrodinger equation (DNLSE) that describes the evolution of complex modal field amplitudes for this system can be written as i
i
d0 2 C1 0 0 0 dz
d n 2 C ( n 1 n 1 ) n n 0 dz
(1)
(2)
In this model of the array of optical waveguides, the evolution variable z is the distance of the propagation of electromagnetic signals along the waveguides, and β is the coefficient of the on-site nonlinearity, the self focusing and self-defocusing nonlinearities corresponding, respectively, to β > 0 and β < 0. Equation (1) governs the evolution of the field at the edge of the array, which corresponds to site n = 0, and Eq. (2) applies at every other site, with n ≥ 1. The actual ISO 9001:2008 Certified Journal
|
Page 1094