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arXiv · 1807.00644

Blowing up Light: A nonlinear amplification scheme for electromagnetic waves

Ali Mostafazadeh·Hamed Ghaemi-Dizicheh·Sasan Hajizadeh
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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.

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Ali Mostafazadeh, Hamed Ghaemi-Dizicheh, Sasan Hajizadeh. 2018-07-02. Blowing up Light: A nonlinear amplification scheme for electromagnetic waves. https://doi.org/10.1364/josab.35.002986

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