Solitons in a $\mathcal{P}\mathcal{T}$- symmetric ${\chi }^{(2)}$ coupler

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 ($\mathcal{P}\mathcal{T}$) symmetric configuration. We present two types of families of $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-symmetric coupler with effective Kerr-type nonlinearity and balanced nonlinear gain and losses.

References in corpus (2)

• Making Sense of Non-Hermitian Hamiltonians
• XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

Cited by in corpus (1)

• Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions