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Loss-compensated active nonlinear layered structures with gain saturation

In this paper, we investigate the possibility of using gain material to overcome losses in periodic semiconductor layered metamaterial. A generic approach, based on the modified transfer matrix method and perturbation theory, was devised here to take into account a gain saturation effect. It is demonstrated that the introduction of nonlinear saturation of the linear gain leads to nonreciprocal response of the system. Taking advantage of the conservation relation, we determine the relation between the gain coefficient and geometrical parameters of the layers to get full compensation of the losses in the nonlinear stack. It is obtained that depending on the parameters of the layers and angle of electromagnetic wave incidence, the full gain–loss balance in the nonlinear system can be maintained taking the gain coefficient above or below the threshold determined for the lossless linear stack. It is shown that the input intensity strongly affects the reflection and transmission coefficients for the nonlinear periodic stack and can be used as the additional mechanism to mitigate the losses.