Blowing up Light: A nonlinear amplification scheme for electromagnetic waves

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.

arXiv commentExpanded version, 8 pages, 5 figures, to appear in J. Opt. Soc. Am. B

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Cited by in corpus (1)

• Blow-up solutions of Helmholtz equation for a Kerr slab with a complex linear and nonlinear permittivity