A three-layered waveguide structure containing the Kerr nonlinear medium separated by an optical linear interlayer from a parabolic graded-index layer is considered. Exact solutions of the wave equation corresponding to several types of transverse electric waves existing in different ranges of values of the effective refractive index are found. The types of waves differ from each other by the presence or absence of oscillations in the interlayer and in the graded-index layer, as well as the form of attenuation in a nonlinear medium. The wave types obtained can be divided into two main groups. The first group includes such waves that can propagate with an arbitrarily varying effective refractive index in the allowable range of values. The second one includes such waves that can propagate at certain discrete values of the effective refractive index. Such values of the effective refractive index of waveguide modes are determined by the wavelength of the incident ray, difference between the dielectric constants of a parabolic graded-index layer, and its width. Even and odd waveguide modes are described separately. Field oscillations can be observed only in the interlayer for waves of the first group. Field oscillations can also be observed in the graded-index layer for waves of the second group. The field profile is a self-focusing nonlinear medium flatter than in a defocusing one for all types of waves. An increase in the same parameters has a different effect on the profiles of the different types of waves. The possibility of controlling the distribution of the wave energy between the layers of the waveguide structure by changing the angle of incidence is shown.

中文翻译：

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介电常数、光学线性和非线性层具有抛物线空间分布的三层波导结构中的横向电波

考虑包含克尔非线性介质的三层波导结构，该介质通过光学线性夹层与抛物线渐变折射率层分开。找到了不同有效折射率值范围内几种横向电波对应的波动方程的精确解。波的类型因中间层和渐变折射率层中是否存在振荡以及非线性介质中的衰减形式而彼此不同。获得的波浪类型可分为两大类。第一组包括能够以在允许值范围内任意变化的有效折射率传播的波。第二个包括可以以有效折射率的某些离散值传播的波。波导模式的有效折射率的值由入射光线的波长、抛物线渐变折射率层的介电常数之间的差异及其宽度决定。偶数和奇数波导模式分开描述。对于第一组波，只能在夹层中观察到场振荡。在第二组波的渐变折射率层中也可以观察到场振荡。对于所有类型的波，场分布是一种比散焦介质更平坦的自聚焦非线性介质。相同参数的增加对不同类型的波的轮廓有不同的影响。显示了通过改变入射角来控制波导结构各层之间波能分布的可能性。