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Mainly with respect to the mathematical part of the article by Kruglov and Harvey [Phys. Rev. A 98, 063811 (2018)] some (supplementary) remarks on the solution method, on the conditions of existence, and on the parameter dependence are presented. For elucidation, numerical examples are included.

The parameter dependence and power flow of guided TE-waves in a lossless cubic nonlinear, dielectric, magnetic planar three-layer structure is studied as follows. Using a travelling wave ansatz with stationary amplitude, Maxwell’s equations are transformed to a system of ordinary nonlinear differential equations. The solutions of the system are presented compactly (in terms of hyperbolic and elliptic functions).The nonnegative and bounded (“physical”) solutions are determined by using a phase diagram condition (PDC) that is applied to express the continuity (transmission) conditions at the interfaces leading to the dispersion relation (DR).Based on the PDC, the parameter dependence and stability of the solutions to the DR and corresponding power flow are studied numerically for permittivities and permeabilities that may be appropriate to describe metamaterial.

The nonlinear Schrödinger equation is the basis of the traditional stability analysis of nonstationary guided waves in a nonlinear three-layer slab structure. The stationary (independent of the propagation distance) solutions of the nonlinear Schrödinger equation are used as “initial data” in this analysis. In the present paper, we propose a method to investigate the dependence of these solutions on the experimental parameters and discuss their stability with respect to the parameters. The method is based on the phase diagram condition (PDC) and compact representation (in terms of Weierstrass’ elliptic function and its derivative) of the dispersion relation (DR). The problem’s parameters are constrained to certain regions in parameter space by the PDC. Dispersion curves inside (or at boundaries) of these regions correspond to possible physical solutions of Maxwell’s equations as ”start” solutions for a traditional stability analysis. Numerical evaluations of the PDC, DR, and power flow including their parameter dependence are presented.