Stationary one-dimensional dispersive shock waves

TL;DR

This paper demonstrates the formation of stable, localized stationary one-dimensional dispersive shock waves in dissipative media with gain and two-photon absorption, contrasting with their nonstationary nature in conservative media.

Contribution

It introduces the concept of stable stationary dispersive shock waves in dissipative media, highlighting the role of gain and two-photon absorption in their formation and stability.

Findings

Stationary dispersive shock waves can form in dissipative media with gain and absorption.

These shock waves can be stable if the defect strength is below a critical value.

The transverse extent of the shock waves can significantly exceed the defect size.

Abstract

We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defect in defocusing media with linear gain and two-photon absorption. We found that in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from defect or generating beam, the competition between gain and two-photon absorption in dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed certain critical value.