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Soviet Journal of Quantum Electronics

Optical Stark effect in an active medium

R F Mardanov, Yu. E. Pol’skii

Published Feb 28, 1976• 0 citations
Publisher

Abstract

The semiclassical approximation is used in an analysis of the nonlinear shift of the frequency of an electric dipole transition in a high-power radiation field. It is shown that the shift can only increase the frequency. The magnitude of the shift is proportional to the field intensity but independent of its frequency. Secondapproximation relationships are derived for the calculation of the parameters of the interaction of the field with an active medium. Numerical estimates of the Stark effect are obtained for some gaseous active media.

DOI
10.1070/qe1976v006n02abeh010956

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•Jan 1, 1978•0 citations
The semiclassical approximation is used in an analysis of the nonlinear shift of the frequency of an electric dipole transition in a high-power radiation field. It is shown that the shift can only increase the frequency. The magnitude of the shift is proportional to the field intensity but independent of its frequency. Secondapproximation relationships are derived for the calculation of the parameters of the interaction of the field with an active medium. Numerical estimates of the Stark effect are obtained for some gaseous active media.
An expression is obtained for the nonlinear susceptibility governing the addition of frequencies under resonance conditions. Allowance is made for the Stark shift, changes in populations, and transient response of the medium. Analysis is made of the stimulated emission of the third harmonic as a result of two-photon resonance in parallel and focused beams. It is shown that the saturation effect limits seriously the conversion coefficient of a nonlinear medium of fixed length. Optimal intensities of the fundamental-frequency radiation are found. It is shown that when a beam is focused sharply in a nonlinear medium, the saturation effect and Stark shift make it possible to add frequencies in media with normal dispersion. The relationship between four-photon parametric effects and coherent resonant processes such as self-induced transparency is established for ultrashort pulses.
A new semiclassical model of the active medium of a gas laser and a description of its interaction with a classical electromagnetic field are reported. The model is based upon an exact microscopic formulation of the density of the active medium in a suitably defined semiclassical state space. Field-medium interaction mechanisms are studied by coupling the equation describing the dynamics of this density with Maxwell's field equations and the Schr\"odinger wave equation. Coupled stochastic nonlinear equations are formulated and quasilinear techniques are employed to effect their solutions. Wave-dipole correlations, the dominant nonlinearity, is shown to effect stability, produce the phenomena of hole burning, mode coupling, and frequency conversion, and to provide the mechanism whereby nonresonant pump field energy is converted into resonant laser oscillations.
The amplification of intense light pulses in resonance active media with an optical Stark effect and coherence effects is examined theoretically. In the course of the amplification, the pulse may go through a stage of an incoherent Stark quasisoliton. The envelope of this quasisoliton has an approximately constant, highly asymmetric shape. The energy of the quasisoliton is approximately constant. Upon further amplification, the Stark quasisoliton "breaks up" into a train of shorter pulses. Over a sufficiently long amplification distance, a true soliton may form in the active medium. In general, this true soliton is not the same as a standard π pulse in a medium without a Stark effect.
A formalism is developed to calculate radiative processes, and applied to the shift of resonance frequency due to the radiation field itself. The zeroth approximation gives the Bohr resonance condition, while the next approximation gives a shift proportional to the photon density. The first-order shift is made of two terms: electric and magnetic. They can be interpreted as second-order Stark effect and Zeeman effect due to the oscillating field, respectively. A comparison with experimental data on the Cs atom is made. A good agreement is obtained by choosing the value of parameters suitably. These values of parameters can be checked by a future experiment.
An analysis is made of the interaction of radiation with a two-level medium at a high particle density. An explicit allowance is made in the interaction Hamiltonian for the interaction between dipoles induced by a resonance field. A semiclassical description is used to obtain a system of equations describing the propagation of a pulse in the active medium. The equations contain nonlinear terms allowing for the interaction in question. An approximate solution of the equations is obtained for the case of amplification of a weak noncoherent pulse describing pulse compression in the amplifying medium. The theory is compared with experimental results.
The first part of this work describes theoretical and experimental studies of Stark-induced three-wave mixing in gaseous NH2D. Application of a dc electric field to a gaseous system destroys the basic inversion symmetry and allows two-photon mixing processes to occur. A theoretical derivation of this effect under conditions of resonantly enhanced non-linearities is given for a three-level system. Calculations are presented for mixing of a CO2 laser with a 4 GHz microwaves in the molecule NH2D, producing single lower sideband radiation. Experimental observation of resonantly enhanced, dc-induced, three-wave mixing in gaseous NH2D is presented. The dependence of this effect on gas pressure, microwave frequency, applied dc field, and microwave power are presented and compared with theoretical predictions. The experiment was done at Hughes Research Laboratories by Abrams and his coworkers. The second part of this work describes the propagation of electromagnetic waves in periodic layered media. The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-finite and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. The theory of electromagnetic Bloch waves in periodic stratified media is then applied to the problems of birefringence, and group velocity in these media. The relevance of periodic media to phase matching in nonlinear mixing experiments-and to laser action in the x-ray region is discussed. New types of guided waves such as Bragg guided waves and optical surface waves are theoretically predicted and experimentally observed.