Solitons in ${ \mathcal P }{ \mathcal T }$-symmetric optical Mathieu lattices

Abstract

We report the existence of stable optical spatial solitons in -symmetric optical Mathieu lattices. We find that Mathieu lattices allow a double phase transition between either having pure real or complex spectra by varying the particular continuous q parameter of the corresponding Mathieu lattice. We find that the q parameter can also modify the physical properties of the solitons, such as their shape, stability and dynamics. Moreover, this q parameter can be used to engineer the Mathieu lattice as an optical isolator for potential applications in light control.

Unidirectional flow of composite bright-bright solitons through asymmetric double potential barriers and wells

“…The nonlinear modes obtained are found to be stable below a certain threshold norm value [52]. Further, the parameter which allows controllability of the solitonic properties in PT-symmetric Mathieu lattices, namely, shape, dynamics and stability has also been pointed out for efficient light control [53]. Recently, the unidirectional flow of bright solitons through a specific combination of asymmetric potential wells was demonstrated where transmission of solitons were defined by the critical velocity, below which reflection dominates [42].…”

Solving ordinary differential equations using genetic algorithms and the Taylor series matrix method

“…y y y y 1 2 1 2 0; 0 1; 0 0, 21 3 such equation arrives from reducing the nonlinear-Schrödinger system in order to admit solitons, or nonlinear modes [16]. In fact, this equation has analytic solution given by:…”

“…Ordinary differential equations rule a wide spectrum of physical phenomena and they constitute the actual basis of our science and technology, being used to describe a plethora of processes, ranging from quantum mechanics [1], heat transfer [2], electrical circuits, optics [3] and all kinds of harmonic oscillations [4], population growth [5] to cosmology dynamics [6] and even to model nonlinear dynamics of interpersonal relationships [7], just to mention a few examples.…”