Evolution of rectangular and triangular initial beam profiles in positive Kerr local medium

Abstract

The hyperbolic secant (Sech) shape, as the initial beam profile, is the well-know profile that compensates the diffraction and self-focusing effect during propagation in Kerr medium, and evolves as the bright spatial soliton. The Sech beam can be confined in the Kerr medium andinduces its own waveguide. In this work, two initial beam profiles, rectangular and triangular functions, that are different than Sech profile, are considered, and the propagation of these beam profiles in third-order nonlinear (Kerr) medium is investigated. As a result, the initialbeam-width played an important role in confining the beam profiles in direction of propagation. In addition, the intensity profiles change to the Sech profile after some initial step of propagation. All the calculations and simulations have been done by the Split-Step numericalmethod with MATLAB program.

Electromagnetic curves and Rytov’s law in the optical fiber with Maxwellian evolution via alternative moving frame

“…If the electric field is presumed to be Rytov parallel transported in w direction, then comparing (32) and (35) implies that:…”

“…where and v have the same values at all points and (s, c, w) and u space, time variables, where E is electric field and V is magnetic field. If we consider that the electric field is perpendicular to the tangent direction and ( 19), (35), and (45), we can calculate,…”

“…In the same way, noting that E is right angle to the tangent directional and ( 19), (35), and (46), we can compute…”

“…Amor et al studied the relationship between the Burgers' equation and the pseudo-null vortex filament equation in Minkowski space [34]. Hesami et al, researched the evolution of two profiles, in a positive Kerr medium and the effect of initial beam-width [35]. Authors indicated numerically that it is possible to generate bright spatial quasi-solitons, in media that are defined via the (1+1)-Dimensional local and nonlocal Nonlinear Schrödinger Equation, via initial condition field distributions that are aside from the analytical solution [36].…”

Surface waves propagating along the interface between a parabolic graded-index medium and a self-focusing nonlinear medium: exact analytical solution

“…Of particular interest are spatially localized optical structures [14][15][16][17], the diversity of which is manifested in photonics [18][19][20][21][22][23][24][25]. Results of numerical investigations of intense beam light propagation in Kerr nonlinear (positive and negative) media (local and nonlocal) could be found in [26][27][28][29].…”