Mode degeneracies and the petermann excess-noise factor for unstable lasers
Mode degeneracies and the petermann excess-noise factor for unstable lasers
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DOI：
10.1080/09500340308234532
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发表时间：
2003-01
影响因子：
1.3
通讯作者：
M. Berry
中科院分区：
文献类型：
--
作者：
M. Berry
不稳定激光的线宽超过量子最小值的彼得曼因子K，这取决于（非酉）往返波算子的左右特征向量之间的重叠。当K被绘制成菲涅耳数N的函数时，发生了强共振，这与简并态N在复N平面中靠近实轴的N c有关。对于一定的放大倍数，简并可以位于实轴上，K为无穷大。本文采用了Horwitz-Southwell谱渐近理论，以一种非常精确的形式和流线型的推导，证明了峰出现在N = s - 1/8 （s整数）附近，并给出了N = c的共振宽度和简并的其他特征的可靠公式。低洼共振具有与模式切换相关的不连续剖面，其中特征值的绝对值交叉（这些不是简并）。
Abstract The linewidth of an unstable laser exceeds the quantum minimum by the Petermann factor K, which depends on the overlap between left and right eigenvectors of the (non-unitary) round-trip wave operator. When K is plotted as a function of the Fresnel number N, strong resonances occur, which are associated with degeneracies N c lying close to the real axis in the complex N plane. For certain values of the magnification, degeneracies can lie on the real axis, and K is infinite. The Horwitz-Southwell asymptotic theory of the spectrum, presented here in a very accurate form and with a streamlined derivation, is used to show that the peaks occur near N = s - 1/8 (s integer), and to give reliable formulae for the resonance widths Im N c and other features of the degeneracies. Low-lying resonances have discontinuous profiles associated with mode switching where the absolute values of the eigenvalues cross (these are not degeneracies).