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Annual Meeting Optical Society of America

Multibeam gain competition deduced from intensity statistics of amplified spontaneous emission

Gregory M. Alman, Neal Broadus Abraham

Published Jan 1, 1990• 0 citations
Publisher

Abstract

The univariate and bivariate intensity statistics of amplified spontaneous emission (ASE) from continuously excited HeNe and HeXe gas discharges have been measured for the purpose of characterizing the dependence of ASE fluctuations on gain length and degree of homogeneous broadening. Comparison with theoretical results from a model for intensity fluctuations in heavily saturated multimode systems confirms that increasing the homogeneous broadening lowers the number of competing "modes" in the system. Intrinsic to this simple coupled-intensity model are unique combinations of cumulants that are independent of the number of modes and the strength of their coupling. These combinations have been measured, and they are independent of the degree of homogeneous broadening and are constant as the discharge length is increased. The normalized cumulants and cross-correlations for coprapogating and counterpropagating orthogonal, circularly polarized beams in a HeXe homogeneously broadened medium are consistently smaller in magnitude than those for orthogonal, linearly polarized beams. Comparison of results for neon and xenon discharges will distinguish whether this is the result of back-reflections or is a property of the counterpropagating beams quasiresonant with these noble-gas transitions, which differ in their upper- and lowerstate angular momenta.

DOI
10.1364/oam.1990.tunn6

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Amplified spontaneous emission. IV. Beam divergence and spatial coherence

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For pt. III see abstr. A54492 of 1971. The origins of beam divergence in amplified spontaneous emission are discussed and theoretical models are developed to predict what their effect would be in real systems. The divergence of the beam is experimentally investigated for the 3.39 mu m He-Ne and the 0.614 mu m Ne systems and compared with the theories. Good agreement is achieved in pure neon for a theory which depends upon the parametric relationship between intensity and length of active medium. In the case of He-Ne although the theory gives the correct qualitative prediction, the absolute magnitude of the effect is wrong by a factor of about 1.7. Measurements of the degree of spatial coherence as a function of length and inversion density of the medium and for the variation of spatial coherence across the tube for a given length and inversion density of medium, are presented for the neon system.

Journal of physics. A, Proceedings of the Physical Society. General•Apr 1, 1972•30 citations
The univariate and bivariate intensity statistics of amplified spontaneous emission (ASE) from continuously excited HeNe and HeXe gas discharges have been measured for the purpose of characterizing the dependence of ASE fluctuations on gain length and degree of homogeneous broadening. Comparison with theoretical results from a model for intensity fluctuations in heavily saturated multimode systems confirms that increasing the homogeneous broadening lowers the number of competing "modes" in the system. Intrinsic to this simple coupled-intensity model are unique combinations of cumulants that are independent of the number of modes and the strength of their coupling. These combinations have been measured, and they are independent of the degree of homogeneous broadening and are constant as the discharge length is increased. The normalized cumulants and cross-correlations for coprapogating and counterpropagating orthogonal, circularly polarized beams in a HeXe homogeneously broadened medium are consistently smaller in magnitude than those for orthogonal, linearly polarized beams. Comparison of results for neon and xenon discharges will distinguish whether this is the result of back-reflections or is a property of the counterpropagating beams quasiresonant with these noble-gas transitions, which differ in their upper- and lowerstate angular momenta.
Spontaneous emission from incoherently excited atoms has a negative exponential intensity probability distribution function (IPDF) In an optical amplifier when the gam is non-lincar (due to gam saturation), the intensity lluctuation statistics is sigmllcanlly altered from that of spontaneous emission as is evidenced by experimental results We have derived the expressions for (i) univariate cumulants of intensity lluctuations up to tenth order from a single mode IPDF and (ii) bi\ariate moments of intensity fluctuations up to fifth order starting from a bivariate IPDF 3'he IPDFs arc negative polynomials (whose powers depend on the number of interactive modes), which rest on the assumption that the variation of intensity has a maximum entropy distribution with the constraint that the total intensity is constant This approximation holds for a heavily saturated source of amplified spontaneous emission (ASI-) and some other coupled-mode optical systems Both the normalized cumulants and bivariate moments have shown unique features that depend only on the number of interacting modes m the system The theoretical results have been compared with the experimental ones for ASH The comparison is useful to lest the model and to identify the number of interacting modes m coupled-mode optical systems Keywords Amplified spontaneous emission, coupled-mode optical systems, univariate cumulants and bivariate moments PAC^S Nos.42 50 Ar, 02 70 --c
In an optical amplifier, when the gain is non-linear due to gain saturation, the intensity fluctuation statistics are significantly altered from the statistics of the negative-exponential intensity probability distribution function (IPDF) for spontaneous emission and unsaturated amplifiers. We have systematically computed bivariate moments, trivariate moments and central moments, tetravariate moments, as well as bivariate and trivariate cumulants of intensity fluctuations for non-linear coupled-mode optical systems starting from a k -variable multivariate IPDF of a system of n ( k < n ) coupled modes. The multivariate IPDF is a negative polynomial that rests on the assumption that the variation of intensity has a maximum-intensity distribution with the constraint that the total intensity is constant. The assumption holds for multimode optical systems including a thin, long, mirrorless, gas laser where under heavy gain saturation the output tends to become constant although the intensity of any mode displays rapid fluctuations about the average intensity. The multivariate IPDF reduces to the negative-exponential IPDF of spontaneous emission when n is infinite, as expected. The new results for the multivariate characteristics of the intensity fluctuations have shown characteristic signatures that depend on the number of interacting modes, n . The results are also useful for testing the multivariate IPDFs and identifying n for heavily saturated coupled-mode optical systems.
Intensity fluctuation characteristics of amplified-spontaneous emission are found using intensity rate equations and the noise-amplifier approximation for saturation coupling between two and four competing modes. The existence of more than one mode leads to the retention of relatively large fluctuations in each mode even as the amplifier gain is saturated, an operating regime which by contrast has been shown to reduce significantly the fluctuations when only a single beam is present. The noise-amplifier approximation is found to be an adequate approximation of the effects of the spontaneous emission distributed along the length of a laser amplifier. The intensity fluctuations in all cases approach limiting distributions functions as the amplifier becomes heavily saturated. Characteristics of these limiting distributions are found for one, two, and four beams; for combinations of beams copropagating and counterpropagating; in the presence and absence of loss; for differences in gain; and for saturation of the sources due to high intensities.
Competition between amplified spontaneous emission (ASE) and the four-wave-mixing (FWM) process has been observed under conditions of two-photon resonant excitation of the sodium 3d level. The nature of the competition is that the FWM process is able to prevent the occurrence of ASE, even though the gain of the ASE process calculated in the absence of competition effects is much larger than that of FWM. The ASE is suppressed because the fields generated by the FWM process create a new excitation pathway connecting the ground and 3d levels, and under quite general conditions this pathway interferes destructively with that due solely to the applied laser field. These effects are modeled theoretically by solving perturbatively the density-matrix equations of the atomic system, thereby determining the population in the upper level and the nonlinear polarization of the medium. The coupling between the various optical fields due to the nonlinear polarization is described by coupled amplitude equations. The solution to these equations predicts that when the wave-vector mismatch is not too large the fields evolve spatially to reach steady-state values, and that the population excited to the 3d level by the total steady-state optical field is much smaller than that due to the incident laser field alone. We have observed experimentally the suppression of ASE by FWM and have observed that this suppression does not occur when the medium is excited with counterpropagating beams that cannot efficiently excite the FWM process. In addition, we have conducted a series of experiments that shows that the degree of suppression of ASE depends on the intensity and focusing characteristics of the incident laser as expected on the basis of our theoretical model.
Paraxial Maxwell-Bloch theory is used to describe amplified spontaneous emission (ASE) in strongly inverted media. Counterpropagation of waves coupled through gain saturation and diffraction, and pumping by a laser beam which propagates transverse to the amplifier are included in the treatment. The reactive part of the medium polarization is calculated by population-rate equations in the limit of rapid dephasing of the atomic dipoles. The spontaneous emission noise source needed for the numerical simulation of Maxwell's equations is derived from microscopic theory by coarse-graining, thereby establishing the compatibility of the spherically symmetric microscopic source with paraxial propagation theory. The three coupled Maxwell equations for the counterpropagating ASE waves and the transversely propagating pump wave are solved numerically in time and two spatial dimensions. This simulation is used to calculate the longitudinal profile of the transverse fluorescence, which measures the saturation of the gain, the longitudinal profile of the transmitted pump wave, which measures the saturation of pump absorption, and the transverse coherence function of the radiation emitted from the ends of the amplifier.
For pt. III see abstr. A54492 of 1971. The origins of beam divergence in amplified spontaneous emission are discussed and theoretical models are developed to predict what their effect would be in real systems. The divergence of the beam is experimentally investigated for the 3.39 mu m He-Ne and the 0.614 mu m Ne systems and compared with the theories. Good agreement is achieved in pure neon for a theory which depends upon the parametric relationship between intensity and length of active medium. In the case of He-Ne although the theory gives the correct qualitative prediction, the absolute magnitude of the effect is wrong by a factor of about 1.7. Measurements of the degree of spatial coherence as a function of length and inversion density of the medium and for the variation of spatial coherence across the tube for a given length and inversion density of medium, are presented for the neon system.