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arXiv 1702.07185physics.opticsquant-ph
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非线性谱奇异性与Laser输出强度

Nonlinear Spectral Singularities and Laser Output Intensity

Hamed Ghaemi-Dizicheh, Ali Mostafazadeh, Mustafa Sarisaman

摘要:

谱奇异性的数学概念允许用相应线性波动方程的纯输出解来描述。这导致了这个概念的一个非线性推广的非线性,在空间中被限制。本文研究了具有弱克尔非线性的无反射镜板条激光器在任意TE和TM模中的非线性光谱奇异性。这为确定这些模式的激光输出强度$I$提供了计算方案。特别是,我们提供了一个基本的数学推导的线性依赖的$I$上的增益系数$g$,并获得一个明确的解析表达式,其斜率。这表明,如果板的折射率的实部$η$不超过3,则$θ$上存在下限,低于该下限,TE和TM模式中的激光发射需要$η$偏移少量,因为$g$超过阈值增益。我们的研究结果表明,激光在倾斜TM模式的平板是禁止的,如果TM模式的入射(发射)角超过布鲁斯特角。

英文摘要:

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 $η$ of the refractive index of the slab does not exceed 3, there is a lower bound on $θ$ below which lasing in both its TE and TM modes requires $η$ 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.

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