Three nonlinear barriers and generalized reflectivity for TM waves in Kerr media
Year: 2026
Type: article
Abstract: We analyze transverse-magnetic (TM) wave propagation in Kerr media using a phase-amplitude formalism. From the algebraic constraints imposed by the conserved quantities we identify three distinct nonlinear barriers: a material barrier at $\varepsilon = 0$ intrinsic to epsilon-near-zero (ENZ) media, a propagation threshold at $\varepsilon = \beta^2$ (with $\beta$ the normalized propagation constant), and a geometrical barrier at $\varepsilon = 2\beta^2$ arising from waveguide boundary conditions. We prove that $\varepsilon = 0$ and $\varepsilon = 2\beta^2$ are impassable. For the $\varepsilon = 2\beta^2$ barrier we derive a switching intensity $I_{\mathrm{switch}} = |2\beta^2-\varepsilon_l|/|\alpha|$, valid for both self-focusing ($\alpha>0$) and self-defocusing ($\alpha<0$) Kerr nonlinearities, and for arbitrary linear permittivity $\varepsilon_l$. We also extend Kaplan's reflectivity theory to TM polarization, obtaining exact expressions for the reflection coefficient and incident intensity at a linear–nonlinear interface. This yields a generalized Snell's law and identifies intensity-dependent Brewster conditions where reflection vanishes. The two thresholds at $\varepsilon = \beta^2$ and $\varepsilon = 2\beta^2$ provide complementary switching mechanisms, both tunable via waveguide geometry. The results offer an analytical basis for designing polarization-selective photonic devices.
Source: Optics Continuum
Authors: O. Nyamsuren, G. Ochirbat
Institution: National University of Mongolia
Language: English
Topic: Nonlinear Photonic Systems
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,372
OpenAlex ID: W7154140456