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.

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Cited by in corpus (3)

• Stable and oscillating solitons of $\mathcal{P}\mathcal{T}$-symmetric couplers with gain and loss in fractional dimension
• Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: I. Inherited and genuine singularities