Parametric gap solitons in PT-symmetric optical structures

Abstract

It is well known that quadratic nonlinearity and feedback through Bragg periodicity are the basis for parametric gap solitons. The major part of the relevant investigations refers to passive systems. At the same time, optical systems supplemented with active elements can demonstrate unusual properties. Asymmetry intrinsic to structures with parity-time (PT) symmetry is a bright confirmation of this statement. The interplay of nonlinearity, Bragg reflection and gain/loss profile can lead to the complicated pattern of wave interactions and novel results. In this study we address the properties of two-color solitons in complex PT symmetric periodic structures with quadratic nonlinearity. We focus on the case of single Bragg resonance. We reveal the region of parameters where stable parametric solitons may exist. We demonstrate that characteristics of forming solitons depend on the order of alteration of amplifying and absorbing layers.

Self-similar light beams at the second harmonic generation in a PT-symmetry structure with strong Bragg coupling at both frequencies

“…A system similar to system (3.1) - (3.4), but in a different normalization, was obtained in 12,13 in a passive medium and without taking into account diffraction by the x variable. Similar equations in the active medium were presented in 19,20 .…”

“…The second scheme is similar to the scheme used in 19,20 . An active periodic structure is surrounded by a homogeneous linear medium with permittivity 0  , so that the periodic structure is located between the coordinates…”

“…By now, optical pulse propagation is intensively studied in non-conservative layered media with Kerr nonlinearity 17 and with quadratic one 18 . In our works on trapping and stable propagation of two-color Bragg solitons in PT-symmetric systems we take a counter propagating wave model as a base for numerical simulation [19][20] . Studying diffracting beams of the fundamental and second harmonics we demonstrated that the width of the initial beam of the first harmonic influences reflection and transmission properties of both active and passive layered systems.…”