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Physical Review A

Intensity fluctuations in a two-mode ring laser

M. M-Tehrani, L. Mandeļ

Published Feb 1, 1978• 37 citations
Publisher

Abstract

The light intensities of the two counter-rotating modes of a ring laser have been investigated by photoelectric counting measurements near the laser threshold and for various detunings. The results are found to be in good quantitative agreement with the theory. They confirm that, at the line center, competition effects prevent the light output in one mode from growing and becoming coherent as the pump parameter is increased. Instead the relative intensity fluctuations of this mode become unity, as for thermal light. Negative cross correlations between the intensity fluctuations of the two modes are also measured. The competition effects virtually disappear when the laser is detuned three natural linewidths from line center, and an intermediate situation is found for smaller detuning.

DOI
10.1103/physreva.17.694

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Physical Review A•Dec 1, 1979•55 citations
The light intensities of the two counter-rotating modes of a ring laser have been investigated by photoelectric counting measurements near the laser threshold and for various detunings. The results are found to be in good quantitative agreement with the theory. They confirm that, at the line center, competition effects prevent the light output in one mode from growing and becoming coherent as the pump parameter is increased. Instead the relative intensity fluctuations of this mode become unity, as for thermal light. Negative cross correlations between the intensity fluctuations of the two modes are also measured. The competition effects virtually disappear when the laser is detuned three natural linewidths from line center, and an intermediate situation is found for smaller detuning.
The fluctuations and correlations of the light intensities associated with the two counterrotating modes of a ring laser have been investigated by measurement of the photoelectric counting statistics. With the laser tuned to line center, it is found that the weaker mode intensity does not grow with increasing pump parameter above threshold and that its relative intensity fluctuations do not die out, as in a conventional laser, but become thermal instead. The cross-correlation coefficient tends toward a constant negative value. The results are all in substantial quantitative agreement with the theory.
Expressions for the fluctuations and correlations of the light emitted by a ring laser with counter-rotating traveling wave modes are derived theoretically. It is shown that the competition of the two modes for the excited atomic population leads to negative correlations between their intensity fluctuations, whose magnitude depends on the detuning of the laser cavity from the atomic line center. As a result of the mode competition, the relative intensity fluctuations do not die out in general as the working point of the laser is raised above threshold at line center, and the emitted light does not become fully coherent as in a conventional laser. The two-time amplitude and intensity correlation functions of the light are calculated at line center, and are shown to be expressible in terms of the eigenfunctions and eigenvalues of a certain Schr\"odinger equation, in complete analogy with the theory of the single-mode laser. However, the intensity correlation time increases with pump parameter above threshold, unlike that for the single-mode laser.
The intensity and amplitude correlation functions of the optical field of a ring laser at line center are calculated, under conditions when the two pump parameters corresponding to the counter-rotating traveling wave modes are not necessarily equal. This represents a generalization of earlier treatments by M-Tehrani and Mandel (1978) and Hioe (1978). The laser is assumed to be at rest. A perturbative technique is used to express the correlation functions for a small difference $\ensuremath{\epsilon}$ of pump parameters in terms of the solutions for $\ensuremath{\epsilon}=0$. It is found that the cross correlations are unchanged to the first order in $\ensuremath{\epsilon}$, whereas the autocorrelations both of the light amplitude and of the light intensity are modified. Curves are presented to illustrate the behavior.
The equations of motion for an inhomogeneously broadened laser operating off resonance in the neighborhood of threshold are solved. It is shown that the effects of detuning cannot be described just by a frequency-dependent laser pump parameter, but that the laser characteristics are modified in other ways also. The relative intensity fluctuations and the correlation time of the laser are calculated as a function of mean intensity and frequency, and it is shown that both are affected by detuning. These theoretical conclusions are then confirmed quantitatively by direct photoelectric counting and two-time correlation measurements of a He:Ne laser.
The two-mode inhomogeneously broadened ring laser with spontaneous-emission noise is investigated in the presence of backscattering. Using a linear transformation it is shown that this problem in the absence of detuning is equivalent to that of the ring laser without backscattering in the two following cases: (i) in-phase backcoupling case (R1{R}_{1}R1​=R2∗{R}_{2}^{\mathrm{*}}R2∗​), (ii) equal pump parameters and ``symmetric'' backscattering (\ensuremath{\Vert}R1{R}_{1}R1​\ensuremath{\Vert}=\ensuremath{\Vert}R2{R}_{2}R2​\ensuremath{\Vert}), where R1{R}_{1}R1​ and R2{R}_{2}R2​ are complex backscattering coefficients. We recover in this way the stationary probability density obtained by Christian and Mandel [Phys. Rev. A 34, 3932 (1986)]. Exact expressions for the mean values, fluctuations, and correlations of the two-mode intensities are derived. Our results show that the relative intensity fluctuations of both modes die out well above threshold. Mode-competition effects are reduced by symmetric backscattering. Exact formulas for the effective eigenvalue characterizing the initial decay of intensity correlation functions are given. These results are compared with the experimental data measured by Singh [Phys. Rep. 108, 217 (1984)].
The equations previously derived for the intensity fluctuations of a two-mode ring laser are applied to a homogeneously broadened laser. It is shown that the mean light intensity of the more lossy mode passes through a maximum and then tends to zero as the excitation is increased. The probability distribution of the intensity of each mode may exhibit two peaks, and spontaneous switching between the intensities associated with the peaks may occur. This is manifest in relative intensity fluctuations of the more lossy mode that can be much greater than unity. Estimates are given for the characteristic switching time.