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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Method of statistical simulation of laser energy storage

V.I. Denisov

Published Jan 1, 1996• 0 citations
Publisher

Abstract

In this work the method of statistical simulation allowing to calculate an interaction of a laser pulse with nonlinear absorbing many-level medium when the time duration of the pulse is equal to longitudinal characteristic relaxation time has been suggested and realized. The two problems were solved by this method. The first problem was the one of laser energy storage on the metastable level of the medium atoms. The space and time characteristics of this inverted medium of plane geometry were calculated. The amplification coefficient of forbidden transition versus different parameters of this problem was obtained. Using Asl as an example the mechanism of two-step photoionization of atoms and mechanism of formation of inversion of the population between a metastable level and a ground state (mechanism of accumulation of laser radiation energy in volume) are investigated. It is shown that due to the "imprisonment" (trapping) of reemited photons leads to the sharp decrease both of the length of interaction between laser radiation and medium, and the length of accumulation of laser radiation energy in volume. In this case the gain factor of inverted medium is one order of magnitude less than that obtained by theoretical estimates (neglecting this effect). The algorithm suggested allows solving these problems within multi-pulse mode taking into account the collision and diffusion processes.

DOI
10.1364/cleo_europe.1996.cthi1

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In this work the method of statistical simulation allowing to calculate an interaction of a laser pulse with nonlinear absorbing many-level medium when the time duration of the pulse is equal to longitudinal characteristic relaxation time has been suggested and realized. The two problems were solved by this method. The first problem was the one of laser energy storage on the metastable level of the medium atoms. The space and time characteristics of this inverted medium of plane geometry were calculated. The amplification coefficient of forbidden transition versus different parameters of this problem was obtained. Using Asl as an example the mechanism of two-step photoionization of atoms and mechanism of formation of inversion of the population between a metastable level and a ground state (mechanism of accumulation of laser radiation energy in volume) are investigated. It is shown that due to the "imprisonment" (trapping) of reemited photons leads to the sharp decrease both of the length of interaction between laser radiation and medium, and the length of accumulation of laser radiation energy in volume. In this case the gain factor of inverted medium is one order of magnitude less than that obtained by theoretical estimates (neglecting this effect). The algorithm suggested allows solving these problems within multi-pulse mode taking into account the collision and diffusion processes.
In this work the method of statistical simulation allowing someone to calculate an interaction of laser pulse with nonlinear absorbing many-level medium when the time duration of pulse is equal to longitudinal characteristic relaxation time is suggested and realized. Two problems were solved by this method. The first problem was the one of laser energy storage on the metastable level of medium atoms. The space and time characteristics of this inverted medium of plane geometry were calculated. The amplification coefficient of forbidden transition versus different parameters of this problem was obtained. The second problem was the calculation of many-steps selective photoionization of the atomic beam. Under specific conditions a superradiance had an effect on output of ions during decay of resonant exciting level into metastable level.
Numerical integration of a system of equations describing the coherent interaction between radiation and a two-level medium (e.g., a semiconductor) is employed to analyze the effect of relaxation processes on the energy characteristics and dynamics of radiation pulses of duration τpΣ T '2 (T '2 is the irreversible polarization relaxation time). It is shown that the interaction of these pulses with the medium is strongly dependent on their area on entry to the medium and the attenuation of the pulses as a result of relaxation processes decreases with increasing pulse input power. This may be utilized for probing the medium in the resonant absorption range for short polarization relaxation times, in solution 42.65.Gv.
The growth of a radiation pulse traversing a medium with an inverted population is described by nonlinear, time-dependent photon transport equations, which account for the effect of the radiation on the medium as well as vice versa. The equations are solved in closed form for an arbitrary input pulse and an arbitrary initial distribution of inverted population. The solutions are discussed in detail for the particular cases of a square pulse and a Lorentzian pulse, both with a uniform initial population inversion.
A theoretical study has been made of the transmission of a monochromatic, well-collimated beam of radiation normally incident on idealized material containing only two energy levels. The nonlinear partial differential equations governing the variation of population and photon density in space and time have been solved exactly for arbitrary initial conditions under the assumption that spontaneous emission and thermal relaxation from the excited state can be neglected. These conditions are satisfied in practice when the radiation is in the form of a pulse whose duration is short compared with the characteristic times of these relaxation processes. Two cases are considered in detail: (a) when all atoms are in the ground state and the material absorbs; and (b) when there is a population inversion and the material amplifies. In case (a), the radiation, with a characteristic velocity, ``bores'' its way through an optically dense substance emerging delayed in time and leaving the material in a perfectly transparent or saturated state. In case (b), an incoming pulse is amplified and sharpened—to a degree determined by the gain of the medium. In addition to these cases, the dependence of the apparent spontaneous emission lifetime on the size and population distribution of the material is mentioned.
The interaction of intense laser fields with matter is accompanied by a multitude of phenomena, ranging from the generation of coherent radiation across various spectral ranges (from terahertz to soft X-rays) to the creation of beams of accelerated charged particles and micromodification of the volume and surface of various samples.To describe this diversity of phenomena, several theoretical approaches have been developed to date.These approaches utilize different approximations to address this complex nonlinear problem, allowing for the explanation of specific aspects of such interactions.The developed theoretical frameworks consider the interaction at both microscopic and macroscopic levels; at the microscopic level, they investigate the characteristics of single atoms interacting with laser fields, while at the macroscopic level, they analyze nonlinear susceptibilities that describe the nonlinear polarization of the medium during the propagation of laser radiation through it.This work presents an overview of methods describing some of the most commonly employed theoretical approaches to model the response of a medium at a microscopic (quantum-mechanical) level, as well as various methods for controlling the properties of generated coherent radiation.A model for the gas medium is described that accounts for both the response characteristics of individual atoms and allows for consideration of phase and quasiphase matching effects during radiation generation.The influence of medium parameters on the efficiency of generation and polarization properties of generated radiation is analyzed under both phase and quasi-phase matching conditions.A detailed description of an analytical method for calculating the nonlinear susceptibility of a gas medium is provided.The obtained values of nonlinear susceptibility for arbitrary orders may be useful in numerical calculations concerning the propagation of laser radiation in matter.Various channels for radiation generation are analyzed as parameters of the laser field are varied.
The results are given of a theoretical investigation of the interaction of a laser pulse with a molecular medium. Allowance for the vibrational relaxation processes is made within the diffusion approximation framework which makes it possible to describe relaxation as the diffusion of particles in continuous electron energy bands. A simultaneous solution is obtained of the diffusion equations for the medium and the equations for the radiation field in the special cases of slow and fast vibrational relaxation. It is shown that the fast relaxation, which prevents gain saturation, increases the signal energy compared with the case of slow relaxation in an amplifying medium and reduces this energy compared with such relaxation in an absorbing medium. Expressions are obtained for the functions which describe the distributions of the band particles established by the investigated signal. The analysis made shows that the diffusion model can be applied to the interaction between laser pulses and molecular media.