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Chinese Physics Letters

Semiclassical analysis of noise in two-photon lasers

Sun Songgen

Published Feb 1, 1988• 0 citations
OpenAlex

Abstract

Lamb's semiclassical theory of the laser is used to analyze the effect of shot noise and thermal noise on laser performance. A Fokker--Planck equation is derived for the probability distribution of the laser field when shot noise and thermal noise are present. Conditions for bunching or antibunching are derived and the results are compared with those for one-photon lasers.

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Lamb's semiclassical theory of the laser is used to analyze the effect of shot noise and thermal noise on laser performance. A Fokker--Planck equation is derived for the probability distribution of the laser field when shot noise and thermal noise are present. Conditions for bunching or antibunching are derived and the results are compared with those for one-photon lasers.
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The quantum-statistical properties of the optical field of a two-mode laser with two coupled transitions have been studied by means of a generalization of the Scully and Lamb theory. The photon number distribution and the mode intensity distribution are obtained in the steady state for a system of homogeneously broadened atoms in resonance with the laser field. It is shown that the mode-coupling constant $\ensuremath{\xi}$ is unity and that near threshold the results of earlier treatments are recovered. Furthermore, it is shown that certain limit measures for the relative intensity fluctuations predicted by the semiclassical Fokker-Planck treatments based on the third-order theory are valid even in the limit of arbitrarily high gain levels.
A two-photon laser is modeled as NNN two-level atoms interacting via a two-photon transition with a single resonant-cavity field mode. The quadratic form of this interaction makes such a system a candidate to exhibit reduced quantum fluctuations (squeezing) in one quadrature of the output field. A Fokker-Planck equation containing all leading quantum noise terms is derived following the method of Haken. A linearized fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing may be present in two-photon optical bistability. Our calculations confirm the results of Lugiato and Strini, who adopted a factorization of moment equations.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
The analogy of a laser with an autocatalytic chemical reaction is used to write down a macroscopic stochastic master equation of the birth-and-death type for the photon probability function in a semiclassical laser formalism. This equation may be solved exactly in the steady state using a generating function. This leads to a prescription for calculating all the higher-order moments of the photon number as well as providing a unique truncation of the hierarchy of moment equations at any given order. Further, the variance is given by a Poisson distribution, in agreement with the strong-signal Scully-Lamb theory. This master equation is also shown to lead to an exact Fokker-Planck equation by using a modified Kramers-Moyal expansion. A comparison between our results and the (microscopic) Scully-Lamb theory shows that the two approaches give the same results at large photon number.