Solitons in a ${\cal PT}$- symmetric $\chi^{(2)}$ coupler

TL;DR

This paper investigates the existence, stability, and interactions of solitons in a ${ m PT}$-symmetric $oldsymbol{ m \chi^{(2)}}$ coupler, revealing how gain and loss balance can stabilize solitons and reducing the model to an effective Kerr-type nonlinear system.

Contribution

It introduces two types of ${ m PT}$-symmetric solitons in a $oldsymbol{ m \chi^{(2)}}$ coupler and demonstrates their stabilization through gain-loss balancing, including a reduction to an effective Kerr model.

Findings

Gain and loss balance stabilizes solitons.

Two families of ${ m PT}$-symmetric solitons are identified.

Interaction of stable solitons is demonstrated.

Abstract

We consider the existence and stability of solitons in a $\chi^{(2)}$ coupler. Both the fundamental and second harmonics undergo gain in one of the coupler cores and are absorbed in the other one. The gain and losses are balanced creating a parity-time (${\cal PT}$) symmetric configuration. We present two types of families of ${\cal PT}$-symmetric solitons, having equal and different profiles of the fundamental and second harmonics. It is shown that gain and losses can stabilize solitons. Interaction of stable solitons is shown. In the cascading limit the model is reduced to the ${\cal PT}$-symmetric coupler with effective Kerr-type nonlinearity and balanced nonlinear gain and losses.