Blowing up Light: A nonlinear amplification scheme for electromagnetic waves

TL;DR

This paper introduces a nonlinear resonance amplification scheme for electromagnetic waves using blow-up solutions of nonlinear Helmholtz equations, enabling narrowband wave amplification and filtering through a specially designed Kerr slab setup.

Contribution

It proposes a novel nonlinear resonance method employing blow-up solutions in a Kerr slab configuration for wave amplification and filtering.

Findings

Transmission coefficient diverges as (k - k_*)^{-4} near critical wavenumber

Setup achieves narrow spectral band amplification of electromagnetic waves

Uses nonlinear transfer matrix and unidirectionally invisible potentials

Abstract

We use blow-up solutions of nonlinear Helmholtz equations to introduce a nonlinear resonance effect that is capable of amplifying electromagnetic waves of particular intensity. To achieve this, we propose a scattering setup consisting of a Kerr slab with a negative (defocusing) Kerr constant placed to the left of a linear slab in such a way that a left-incident coherent TE wave with a specific incidence angle and intensity realizes a blow-up solution of the corresponding Helmholtz equation whenever its wavenumber $k$ takes a certain critical value, $k_\star$. For $k=k_\star$, the solution blows up at the right-hand boundary of the Kerr slab. For $k<k_\star$, the setup defines a scattering system with a transmission coefficient that diverges as $(k-k_\star)^{-4}$ for $k\to k_\star$. By tuning the distance between the slabs we can use this setup to amplify coherent waves with a wavelength in an extremely narrow spectral band. For nearby wavelengths the setup serves as a filter. Our analysis makes use of a nonlinear generalization of the transfer matrix of the scattering theory as well as properties of unidirectionally invisible potentials.