We theoretically investigate the optical properties of a one-dimensional non-Hermitian dispersive layered system with saturable gain and loss. We solve the nonhomogeneous Helmholtz equation perturbatively by applying the modified transfer matrix method and we obtain closed-form expressions for the reflection or transmission coefficients for TM incident waves. The nonreciprocity of the scattering process can be directly inferred from the analysis of the obtained expressions. It is shown that by tuning the parameters of the layers we can effectively control the impact of nonlinearity on the scattering characteristics of the non-Hermitian layered structure. In particular, we investigate the asymmetric and nonreciprocal characteristics of the reflectance and transmittance of multilayered parity-time (PT)-symmetric slab. We demonstrate that incident electromagnetic wave may effectively tunnel through the PT-symmetric multilayered structures with zero reflection. The effect of nonlinearity to the scattering matrix eigenvalues is systematically examined.

中文翻译：

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具有饱和效应的非Hermitian多层的非线性散射

我们从理论上研究具有饱和增益和损耗的一维非Hermitian色散分层系统的光学特性。通过应用改进的传递矩阵方法，我们扰动地求解了非均质的亥姆霍兹方程，并获得了TM入射波的反射或透射系数的闭式表达式。散射过程的不可逆性可以从获得的表达式的分析中直接推断出来。结果表明，通过调整层的参数，我们可以有效地控制非线性对非Hermitian层状结构的散射特性的影响。特别是，我们研究了多层奇偶时间（PT）对称平板的反射率和透射率的不对称和不可逆的特性。我们证明了入射电磁波可以有效地隧穿具有零反射的PT对称多层结构。系统地研究了非线性对散射矩阵特征值的影响。