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CAOL . International Conference on Advanced Optoelectronics and Lasers

Spatial inhomogeneity of the absorption and re-emission properties of an optically active medium in a resonator

Андрій Сіжук, Konstantin E. Dorfman, C. H. Raymond Ooi

Published Sep 1, 2019• 0 citations
Publisher

Abstract

The spatial inhomogeneity of absorption coefficient of the space between mirrors, filled by an optically active gas, is analyzed in quantum optical terms. It was theoretically shown, that the quantization of electromagnetic field in a cavity (optical resonator) can reveal the spatial inhomogeneity of absorption or re-emission ability of the optically active medium. It appears from the analytical calculations, the inhomogeneity is caused by the Doppler frequency shifts (including recoil effects) during the atom-photon collisions and the non-zero initial frequency width of the scanning signal. The proposed analytical representation of the absorption coefficient through the additive quantum optical terms gives deeper insight into intrinsic processes in the interacting with light matter.

DOI
10.1109/caol46282.2019.9019445

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The spatial inhomogeneity of absorption coefficient of the space between mirrors, filled by an optically active gas, is analyzed in quantum optical terms. It was theoretically shown, that the quantization of electromagnetic field in a cavity (optical resonator) can reveal the spatial inhomogeneity of absorption or re-emission ability of the optically active medium. It appears from the analytical calculations, the inhomogeneity is caused by the Doppler frequency shifts (including recoil effects) during the atom-photon collisions and the non-zero initial frequency width of the scanning signal. The proposed analytical representation of the absorption coefficient through the additive quantum optical terms gives deeper insight into intrinsic processes in the interacting with light matter.
A method of calculation of the absorption coefficient in the terms of quantum optics with regard for the quantization of the electromagnetic field and the Doppler effect is presented. It is shown that the local value of the absorption coefficient non-linearly depends on the atomic density and initial intensity. The analytically derived results are demonstrated in graphs for the the local absorption coefficient as a function of the frequency. The relatively strong dependence of the absorptance on the path length of an optical light beam is caused by the interatomic coupling through the intermediary of an electromagnetic field. The splitting of the absorption line induced by the Doppler effect in the system placed between mirrors is demonstrated.
Quantum optical theory of absorption properties of interacting atoms is developed. The concept of local absorptance is introduced as a derivative of the logarithm of intensity with respect to the distance in the vicinity of a given spatial point and a moment of time. The intensity is represented by the quantum and statistically averaged normal product of creation and annihilation operators of the electromagnetic field. The development of an analytical method of the estimation for the kinetic and optical parameters for the system is proposed here. The calculation method of the absorption coefficient includes thermal atomic motion, Doppler effect, and the short-range interaction between atoms. The absorption coefficient explicitly takes into account the quantum nature of the optical field. The ability of the system to absorb or emit quanta is quantitatively expressed through the special form of interaction integrals. The specific form of integrals results from the structure of the quantum brackets. The interplay between the collective (virtual photon exchange) and binary (optically induced inter-particle bonding) processes determines the system behavior. The spectral profile of the local absorption coefficient for different atomic densities and time intervals is simulated for realistic parameters.
An analysis is made of the spectrum of absorption of a weak probe electromagnetic by two-level atoms in a strong resonant laser field, undergoing collision with buffer gas atoms. The analysis is made using an approach that allows for the direct influence of a strong electromagnetic on the dynamics of an elastic collision between an active atom and a buffer gas atom. Rate equations are analyzed for a combined atom–strong electromagnetic field system (an atom dressed by the field) allowing for spontaneous and optical collisional transitions, and also for the interaction with the probe field. In the steady-state case, an expression is derived for the electric susceptibility of the medium at the small-signal frequency. This expression contains the rates of the optical collisional transitions that depend nontrivially on the parameters of the strong electromagnetic field. The phenomenological characteristics of optical collisional transitions generally used are only valid at low intensities and for small frequency detunings of the strong electromagnetic field, i.e., in the impact limit.
The quantum optical theory of absorption/reemission properties of a system of interacting atoms is discussed. The calculation method of the absorption coefficient is developed with regard for the quantization of field, thermal atomic motion, Doppler effect, and the model interaction between atoms. It is shown that the formulation of the absorption coefficient in the quantum optical context is based on the commutation relation between the operators of electric field and intensity. The revealed non-linear dependence of the absorption coefficient on the atomic density, even in the case of negligible binary interaction, can be referred to a certain kind of quantum-optic collective effects.
An investigation is made of the influence of spatial inhomogeneity of the electromagnetic field on the process of resonance ionization of atoms. It is shown that the result of averaging over the spatial distribution of the field depends on the mechanism for formation of a dispersion dependence of the ionization probability on the radiation frequency. For all known initiating mechanisms, analytic expressions are derived to determine the line profile of the dispersion curve in a spatially inhomogeneous field having a Gaussian distribution over the transverse coordinate. It is found that if the extreme value of the energy shift of the transition due to the dynamic Stark effect αF02 is greater than the width of the dispersion curve in a homogeneous field, allowance for spatial inhomogeneity results in additional broadening of the dispersion curve, its actual order-of-magnitude width being αF02.