Nonlinear Spectral Singularities and Lasing Threshold Condition

Abstract

A spectral singularity is a mathematical notion with an intriguing physical realization in terms of certain zero-width resonances. In optics it manifests as lasing at the threshold gain. We explore the application of their recently-developed nonlinear generalization in the study of the effect of a nonlinearity on the lasing threshold condition for an infinite planar slab of gain medium. In particular, for a Kerr nonlinearity, we derive an explicit expression for the intensity of the emitted waves from the slab and discuss the implications of our results for the time-reversed system that acts as a coherent perfect absorber.

4 pages

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• Coupling approach for the realization of a $\mathcal{P}\mathcal{T}$-symmetric potential for a Bose-Einstein condensate in a double well
• Reciprocal and unidirectional scattering of parity-time symmetric structures
• Asymmetric transmission through a flux-controlled non-Hermitian scattering center
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• Spectral Singularities in the Surface Modes of a Spherical Gain Medium
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• Spectral Singularity in confined PT symmetric optical potential
• Spectral Singularities and CPA-Laser Action in a Weakly Nonlinear PT-Symmetric Bilayer Slab
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• Spectral singularities and tunable slab lasers with 2D material coating
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• Time evolution of decay for purely absorptive potentials: The effect of spectral singularities
• Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points
• Unidirectional Reflection and Invisibility in Nonlinear Media with an Incoherent Nonlinearity
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• Spectral Singularities, Threshold Gain, and Output Intensity for a Slab Laser with Mirrors
• Spectral singularities and threshold gain of a slab laser under illumination of a focused Gaussian beam
• Invisibility and PT Symmetry: A Simple Geometrical Viewpoint