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arXiv quant-ph/0011003quant-ph
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好腔laser的量子限制线宽:从阈值附近到阈值附近的解析理论

Quantum-limited linewidth of a good-cavity laser: An analytical theory from near to far above threshold

Ulrike Herzog, János A. Bergou

摘要:

重新讨论了好腔激光器的量子限制或本征线宽问题。从Scully-Lamb主方程出发,给出了一种完全解析的方法,确定了稳态腔场的关联函数和谱。为此,我们开发了一种解析近似方法,隐式地结合了微观波动的相位和强度的字段,此外,充分考虑到饱和的非线性增益。我们的主要结果是一个简单的公式的量子限制的线宽是有效的,从近到远高于阈值,也包括热光子的存在。接近阈值时,线宽是忽略强度波动的标准相扩散处理所预测的两倍,甚至高于阈值50%的增加仍然是相当大的。一般来说,只要光子数分布不是严格的泊松分布,强度的量子涨落就存在并继续影响线宽。这种内在的关系是由一个公式显示的线宽和曼德尔Q参数。超过100%以上阈值的线宽被发现是小于预测的标准治疗,因为简单的相位扩散模型越来越高估的相位波动率忽略增益饱和。在极大平均光子数的极限下,得到了理想的完全相干经典场。

英文摘要:

The problem of the quantum-limited or intrinsic linewidth of a good-cavity laser is revisited. Starting from the Scully-Lamb master equation, we present a fully analytical treatment to determine the correlation function and the spectrum of the cavity field at steady state. For this purpose, we develop an analytical approximation method that implicitly incorporates the microscopic fluctuations of both the phase and intensity of the field, and, in addition, takes full account of the saturation of the nonlinear gain. Our main result is a simple formula for the quantum-limited linewidth that is valid from near to far above threshold and also includes the presence of thermal photons. Close to the threshold, the linewidth is twice as large as predicted by the standard phase-diffusion treatment neglecting intensity fluctuations, and even 50% above threshold the increase is still considerable. In general, quantum fluctuations of the intensity are present and continue to influence the linewidth as long as the photon-number distribution is not strictly Poissonian. This inherent relationship is displayed by a formula relating the linewidth and the Mandel Q-parameter. More than 100% above treshold the linewidth is found to be smaller than predicted by the standard treatment, since the simple phase-diffusion model increasingly overestimates the rate of phase fluctuations by neglecting gain saturation. In the limit of a very large mean photon number the expected perfectly coherent classical field is obtained.

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