Analytic study of orthogonally polarized solitons interacting in highly birefringent optical fibers

Abstract

We examine analytically, numerically, and experimentally the phase shift incurred by a soliton pulse when it collides with a copropagating, orthogonally polarized soliton pulse in a highly birefringent optical fiber. Use of a well-known average variational principle and a Gaussian ansatz reduces the dynamics to a set of ordinary differential equations for which an approximate analytic solution is found in the case of highly birefringent fibers. The analytic approximation is shown to be in good agreement with the full numerical model and experimental data, allowing it to be used as an evaluation tool for the design of nonlinear optical loop mirror switches.

Bright optical spatial solitons in a photovoltaic photorefractive waveguide exhibiting the two photon photorefractive effect

“…Secondly, numerically computed exact profiles do not differ widely from the Gaussian one in most of the cases and thirdly, Gaussian profile is qualitatively very close to sech profile as it has almost the same half width and also the integral of the two profiles are comparable [47]. Finally, analytical simplification is not expected by using sech ansatz in most cases [58]. Since we use an approximate solution, we can term these solutions as quasisolitons and henceforth the term soliton will refer to such quasi-solitons.…”

“…[47], Anderson set a trend by suggesting the use of Gaussian profile in variational methods. Subsequently, this was implemented by many researchers in nonlinear optics [12,19,[49][50][51][52][53][54][55][56][57][58]. Gaussian ansatz is most widely used for approximating solutions for non integrable systems and most widely used by the nonlinear optics and soliton community.…”

Variational approach for walking solitons in birefringent fibres

“…This diagram was obtained by means of the above described variational method. The solid lines represent the solutions given by equations (4). Di erent sets of almost parallel curves correspond to di erent values of the parameter¯whilst the value of v hardly in¯uences the shape of these curves, ®xing solely the minimum allowed value of q.…”

“…We must however bear in mind that the last terms in equation (1) are the only ones responsible for energy transfer between both polarizations. And although averaging out the fast oscillatory terms has proven to be a good approximation to describe most of the observed phenomena [3,4,17] in the picosecond regime, we will go further by retaining these terms in the analysis.…”

Two-component spatial holographic solitons supported by cross-phase modulation

“…In both numerical and approximate analytical methods, occasionally the sech profile is used as it is the closest profile to the exact solitonic shape in many cases. However, most widely used approximate solutions for nonintegrable systems are of Gaussian type [26][27][28][29] instead of sech. The justification of using the Gaussian ansatz is manifold.…”