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Physical Review Letters

Laser with a Fluctuating Pump: Intensity Correlations of a Dye Laser

Ronald F. Fox, Glenn E. James, Rajarshi Roy

Published May 14, 1984• 21 citations
Publisher

Abstract

A new, first-principles derivation of the equations for a quantized single-mode laser field pumped by a semiclassical stochastic field in a four-level molecular pumping scheme is presented. Computer simulations are used to generate fits to measured correlation functions for a single-mode dye laser.
DOI
10.1103/physrevlett.52.1778

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We examine from first principles the effects of a stochastic pump on the output fluctuations of a laser. The Hamiltonian for a four-level molecule interacting with a stochastic semiclassical pump field and quantized laser field is used to obtain density-matrix equations of motion. Noise from the pump field and from spontaneous emission is introduced systematically, as opposed to the ad hoc inclusion of random forces in the semiclassical equations. The relationship of this theory with previous quantum and semiclassical equations is described. New equations are derived on which computer simulations are performed to compare our theoretical results to experimental data for a single-mode dye laser.
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The probability distribution p(n)p(n)p(n) for the detection of nnn photons emitted by a single-mode dye laser in a short time at various excitations is measured, together with the distribution of time intervals between pairs of detected photons. The first measurement yields the probability density p(I)\mathcal{p}(I)p(I) and the moments of the light intensity III, and the second one the two-time intensity-correlation function. Measurements are also performed at three different wavelengths. p(I)\mathcal{p}(I)p(I) is found to have a two-component structure, and the relative intensity fluctuations $\frac{〈{(\ensuremath{\Delta}I)}^{2}〉}{{〈I〉}^{2}}$ grow, apparently without limit, as the excitation tends to zero, so that no thermal state is reached. A possible explanation in terms of pumping fluctuations is discussed. The correlation function has the form of a sum of three exponential functions, and the amplitudes and decay constants of the three components are derived. The effective decay-time constant exhibits a thirteenth-power-law dependence on frequency of the laser light.