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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Mathematical model of laser generation on the basis of Markov processes theory

Dmitry V. Zaitsev

Published Mar 1, 1996• 1 citation
Publisher

Abstract

The discrete nature of active media atoms, laser light photons and their Poisson distribution law allow us to apply correctly Markov processes theory with discrete states and continuous time to the description of laser generation process. The equations of photons quantity in laser resonator and population inversion are deduced. The results coincide with known equations. Equations of photons quantity dispersion and population inversion dispersion are deduced also. The analysis of these equations permits us to explain the operation of spiking pulsed multimode lasers.

DOI
10.1117/12.234169

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The discrete nature of active media atoms, laser light photons and their Poisson distribution law allow us to apply correctly Markov processes theory with discrete states and continuous time to the description of laser generation process. The equations of photons quantity in laser resonator and population inversion are deduced. The results coincide with known equations. Equations of photons quantity dispersion and population inversion dispersion are deduced also. The analysis of these equations permits us to explain the operation of spiking pulsed multimode lasers.
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This chapter begins with a heuristic derivation of atomic population rate equations which include changes to level populations due to stimulated transitions as well as level relaxations and pump. These equations are used to study the saturation of population inversion with increasing light intensity and its dependence on the type of gain medium (three-level gain media vs. four-level gain media), lineshape and nature of line broadening (homogeneous vs inhomogeneous broadening). How saturation affects lineshape and thus gain and absorption giving rise to phenomena like power broadening and spectral hole burning is also discussed. The chapter summarizes the equations of motion for atomic polarization, inversion and the cavity field describing their nonlinear dynamical coupling. These equations, known as the Maxwell-Bloch equations, provide a complete description of atom-field interaction in a laser. Approximations of these equations, including the rate equation approximation, to deal with different laser classes are briefly described. These will be used in the next few chapters to explore and understand the rich and varied behavior of lasers. The chapter ends with a summary of select gain media for different types of commonly used lasers.
The dynamics of a multimode high-intensity gas laser including some velocity-changing-collision effects is investigated theoretically. Using a spatial Fourier expansion method for the density matrix of the active medium, one obtains the system of equations which contain only the Fourier components of the population inversion. To obtain the approximate solutions in the high-intensity case, the saturation terms due to hole burning and the population-pulsation terms are treated separately. The former are calculated exactly and the result is equivalent to the rate-equation approximation. The latter are treated by the perturbation method. The equations of motion for mode amplitudes have a similar form to those of Lamb's perturbation theory but can be applied to a high-intensity multimode laser. Experimental results of three-mode oscillation of a He-Ne laser are compared with the theory.
Using one-dimensional semiclassical Maxwell — Bloch equations with account for the coherent polarisation dynamics, we have studied spike generation regimes of a superradiant distributed feedback laser in the case of inhomogeneous broadening of the spectral line of an active medium. By analysing the dynamic spectra of inversion of the active medium and laser radiation, we have revealed the relationship of individual spikes of radiation and their modulation with specific parts in the spectral line of the active medium and mode beatings. It has been shown that the broadening and shift of the lasing spectrum with respect to the initial electromagnetic Bragg-cavity modes is accompanied by a strong spectral gradient of inversion that is typical of the superradiant regimes.