Nonlinear Spectral Singularities and Laser Output Intensity

Abstract

The mathematical notion of spectral singularity admits a description in terms of purely outgoing solutions of a corresponding linear wave equation. This leads to a nonlinear generalization of this notion for nonlinearities that are confined in space. We examine the nonlinear spectral singularities in arbitrary TE and TM modes of a mirrorless slab laser that involves a weak Kerr nonlinearity. This provides a computational scheme for the determination of the laser output intensity $I$ for these modes. In particular, we offer an essentially mathematical derivation of the linear-dependence of $I$ on the gain coefficient $g$ and obtain an explicit analytic expression for its slope. This shows that if the real part $\eta$ of the refractive index of the slab does not exceed 3, there is a lower bound on $\theta$ below which lasing in both its TE and TM modes requires $\eta$ to be shifted by a small amount as $g$ surpasses the threshold gain. Our results suggest that lasing in the oblique TM modes of the slab is forbidden if the incidence (emission) angle of the TM mode exceeds the Brewster's angle.

17 pages, 4 figures

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Cited by in corpus (11)

• Nonlinear Scattering and Its Transfer Matrix Formulation in One Dimension
• Spectral singularities and tunable slab lasers with 2D material coating
• Transport effects in non-Hermitian nonreciprocal systems: General approach
• Solving scattering problems in the half-line using methods developed for scattering in the full line
• Spectral Singularities, Threshold Gain, and Output Intensity for a Slab Laser with Mirrors
• Scattering Theory and $\mathcal{P}\mathcal{T}$-Symmetry
• Scattering of TE and TM waves and quantum dynamics generated by non-Hermitian Hamiltonians
• Perfectly absorbed and emitted currents by complex potentials in nonlinear media
• Blowing up Light: A nonlinear amplification scheme for electromagnetic waves
• Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium
• Spectral singularities and threshold gain of a slab laser under illumination of a focused Gaussian beam