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Physical Review Letters

Quantum Fluctuations, Pump Noise, and the Growth of Laser Radiation

Rajarshi Roy, Anthony W. Yu, Shijun Zhu

Published Dec 16, 1985• 112 citations
Publisher

Abstract

We have measured the distribution of times for single-mode laser radiation to grow from an equilibrium spontaneous-emission background to a prescribed value of the intensity. These passage-time distributions are compared with the results of Monte Carlo simulations and demonstrate a new technique for the description of statistical fluctuations in lasers.

DOI
10.1103/physrevlett.55.2794

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We have measured the distribution of times for single-mode laser radiation to grow from an equilibrium spontaneous-emission background to a prescribed value of the intensity. These passage-time distributions are compared with the results of Monte Carlo simulations and demonstrate a new technique for the description of statistical fluctuations in lasers.
Laser fluctuations are measured and characterized with a new technique based on the concept of first-passage-time distributions. This first-passage-time technique makes it possible to discern quantum noise in a dye laser even in the presence of pump fluctuations that are many orders of magnitude larger. We report new analytic and experimental results for the mean, variance, and skewness of the first-passage-time distributions. The analytic results agree well with numerical computations and experimental measurements. Our technique is particularly suited to the quantitative description of laser fluctuations above threshold; it complements the conventional photoelectric counting and correlation methods which are valuable for lasers below and near threshold but are difficult to implement for lasers far above threshold. The limits of validity of the theory containing a cubic nonlinearity are examined in the context of passage-time measurements. The effects of multiplicative noise and saturation on the variance of the intensity fluctuations are also discussed. A new signature of multiplicative noise is predicted.
Statistical properties of dye laser transients are analyzed by first-passage-time technique. Both pump and quantum fluctuations effece the establishment of steady states in a dye laser. These two kinds of noise play different roles in laser transients. Meanwhile it is difficult to discern them since the pump fluctuations are six orders of magnitude larger than the quantum noise. In this paper a model of single mode dye laser with pump fluctuations simplified by white noise is presented and the analytic results of the mean, variance and skewness of first-passage-time distributions are obtained through a Fokker-Planck equation. Compared with experimental measurements and curves from Monte Carlo simulations, excellent agreement is obtained.
We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with NNN stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.
We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with NNN stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.
We have measured the evolution of the intensity emitted by a random laser during a pump pulse that is comparable in duration to the spontaneous emission decay time. The time traces of our random laser, consisting of titanium dioxide particles and sulforhodamine B dye, show clear relaxation oscillations. We compare our experimental results to an analytic, conventional model based on the four-level rate equations for a single-mode laser. The measured frequency of well-resolved fluctuation oscillations suggests an effective mode lifetime of 5 ps.
The steady-state intensity distribution for a laser operating somewhat above threshold is determined by solving a master equation. The master equation describes the interaction between a single radiation mode and NNN two-level atoms, it contains the effects of pumping and radiation loss from the cavity, and it is applicable to both homogeneous and Doppler broadening. Forms of the master equation applicable to both three- and four-level lasers are considered. Solutions are obtained under the assumption that the distribution of atoms and radiation intensity is a bivariate Gaussian. Fluctuations in the output of giant-pulse lasers are also considered.