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Soviet Journal of Quantum Electronics

Natural fluctuations in a multimode standing-wave laser

Vladimir R. Mironenko, Vladimir I. Yudson

Published Nov 30, 1982• 3 citations
Publisher

Abstract

It is shown theoretically that the relative fluctuations in the numbers of photons in individual modes of a multimode standing-wave laser with a homogeneously broadened gain profile is extremely sensitive to the degree of filling of the resonator with the active medium. If this medium fills the whole resonator, the spatial effects result in strong suppression of fluctuations in the individual modes. In the opposite case of a thin medium the statistical properties of a multimode standing-wave laser are close to those of a traveling-wave laser. The conclusions reached are used in an analysis of the quantitative discrepancy between the results of published experimental studies of the statistics of multimode lasing.

DOI
10.1070/qe1982v012n11abeh006142

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It is shown theoretically that the relative fluctuations in the numbers of photons in individual modes of a multimode standing-wave laser with a homogeneously broadened gain profile is extremely sensitive to the degree of filling of the resonator with the active medium. If this medium fills the whole resonator, the spatial effects result in strong suppression of fluctuations in the individual modes. In the opposite case of a thin medium the statistical properties of a multimode standing-wave laser are close to those of a traveling-wave laser. The conclusions reached are used in an analysis of the quantitative discrepancy between the results of published experimental studies of the statistics of multimode lasing.
A model using rate equations which allow for quantum noise is used to make a theoretical analysis of the steady-state lasing regime of a cw dye laser. Equations describing the laser performance are derived in the adiabatic approximation neglecting spatial inhomogeneities in the burnup of the active medium. An investigation is made of the stability of steady-state multimode laser action and it is found that this is weak in certain modes. Calculations are made of correlation functions describing fluctuations in the numbers of photons in the modes and fluctuations in the total intensity. Although the fluctuations in individual modes are large, the integrated intensity fluctuates negligibly. An analysis is made of the influence of quantum intensity fluctuations on the attainment of maximum sensitivity in intracavity laser spectroscopy.
Theoretical and experimental results of investigations into the quantum noise of multimode laser radiation are considered. The feasibility of generating light with a photon-number-squeezed (sub-Poissonian) photon distribution by a multimode laser with a homogeneously broadened line is analyzed. The conditions of noisy and noiseless (regular) pumping are considered. Photon-number fluctuations of the net laser radiation summed over all generated modes are calculated in the approximation of equidistant equal modes, as are photon-number fluctuations in an individual mode inside and outside the resonator. Output-radiation noise spectra and photon-number fluctuations are calculated for solid-state (neodymium glass, Nd:YAG) and semiconductor lasers. Theoretical results are compared with a number of experimental data obtained for semiconductor lasers in recent years.
A set of strong-field Maxwell–Bloch equations is derived for a multimode, standing-wave, homogeneously broadened laser such as a dye laser, which obeys the atomic rate-equation limit. Numerical solutions show that the energy in the cavity oscillates between the field and the gain medium at multiples of the cavity mode spacing. By using these Maxwell–Bloch equations, intensity autocorrelation functions of a dye-laser system under varying conditions are calculated. We find that the numerical results qualitatively agree with recent experimental data.
The mechanism for quantum noise suppression in a multimode laser with a homogeneously broadened line is explained. It is shown that the spontaneous emission noise and pump noise contribution to the photon number fluctuations inside the laser cavity may be suppressed infinitely (up to their complete elimination) when the number of modes participating in the generation is increased. Low-frequency spectral squeezing for an individual output field mode in optimal conditions tends to 100% as the total number of modes increases. The low-frequency spectral squeezing for the total output field may reach 50% below the shot noise level under optimal conditions. The noise suppression of the laser light is explained by the saturation effect of an atomic transition and inter-mode correlation. A multimode laser is an accessible source of light with potentially fully suppressed quantum noise.
A stochastic, semiclassical model is developed for a multimode, homogeneously broadened laser with rapid dipole dephasing, appropriate for semiconductor, Ti:sapphire, or dye lasers. The theory self-consistently incorporates population dynamics including temporal beating effects and relaxation oscillations, spatial hole burning, coherent-wave mixing, and quantum noise. The model is valid for single- and compound-cavity lasers in which the mode frequencies are well defined. We pay particular attention to finding a useful mode basis in the case that the gain medium does not completely fill the cavity. This situation can lead to coupled-cavity effects. For typical systems the model is valid for pump rates up to several times threshold and is tractable for numerical simulations. The theoretical development described in this paper is applied to an experimental system in a companion paper (J. Opt. Soc. Am. B14, 180 (1997)].