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APPLICATION OF PROBABILITY METHOD FOR CALCULATION OF OPTICAL CHARACTERISTICS OF QUANTUM GENERATORS OF LIGHT

Boris I Stepanov, Viktor P. Gribkovskii

Published May 26, 1965• 0 citations
OpenAlex

Abstract

Abstract : On the basis of the probability method and the resonator theory, it is possible to explain the basic properties of quantum generators of light and in a number of the most important cases to obtain quite accurate correlation with experiment. During use of probability method of calculation, energy levels and probability of transition between them are used as initial data. The main problem is reduced to determination of populations of separate levels depending upon intensity of irradiation, with subsequent calculation of number of optical transitions. In quantum generators it is necessary to consider transitions between levels which appear under the action of pumping radiation, as well as under action of the generated radiation itself.

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Abstract : On the basis of the probability method and the resonator theory, it is possible to explain the basic properties of quantum generators of light and in a number of the most important cases to obtain quite accurate correlation with experiment. During use of probability method of calculation, energy levels and probability of transition between them are used as initial data. The main problem is reduced to determination of populations of separate levels depending upon intensity of irradiation, with subsequent calculation of number of optical transitions. In quantum generators it is necessary to consider transitions between levels which appear under the action of pumping radiation, as well as under action of the generated radiation itself.
The problem of research of spectroscopic converters of the optical and near-range range is considered in this paper. The theoretical model of such spectrogenerators operating in conditions of self-excitation of the system itself is offered. A model based on quantum radiation laws and interaction of radiation with matter has been developed. The block diagram of the spectrotransformer and the scheme of the unified transformation of wavelengths are presented. The method of transformation of the wavelengths of light waves is proposed based on the information-energy transformation of the light spectrum. The proposed method for transforming the wavelengths of light waves on the basis of the information-energy transformation of the light spectrum includes an effective working environment of resonant optical pumping of alkali metal vapors, which allows the population of the upper atomic levels to occur and predetermines the inverse population of relatively lower energy levels. This creates the possibility of spectral transformation of waves of a wide cosmic range in a predetermined interval of wavelengths. The problem of the investigation of spectroscopic and optical converters of the optical and near- range range is presented in this paper. The theoretical model of such spectrogenerators operating in conditions of self-excitation of the system itself is offered. The developed model is based on the quantum laws of radiation and the interaction of radiation with matter. The basis of this theory is the Schrödinger equation and its separate solutions are presented. Theoretical investigations of spectroenergetic converters are carried out. A systematic analysis of the quantum theory of radiation and its interaction with the most suitable media has been carried out. The obtained laws are suitable for solving the problem of energy transformation of different ranges of the energy spectrum.
Abstract The calculations of the preceding chapter display some of the inadequacies of the Einstein theory of interaction of light with atoms. The theory itself gives no prescription for computing the values of the A and B coefficients appropriate to a given atomic transition. For this one must look to the quantum-mechanical theory of transition probabilities. As light beams are generated by emission from atoms and measurements on light beams ultimately depend on the absorption of light by atoms, it is essential to cover the theory of the atomic interaction processes, even though the main interest of the book is the quantum nature of the light itself. More seriously, the Einstein theory is applicable only for broad-band illumination of the atom, where the energy in the incident light is distributed smoothly across the frequencies within the linewidth of the atomic transition. By contrast, many experiments with laser sources use light beams whose frequency distributions are much narrower than atomic transition linewidths.
A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given.
We study here level-degeneracy effects in super-radiance, using the quantum "small-system" model whose interest and limitations are discussed. First, we show that this model allows one to understand the physical origin of these effects and to describe their qualitative influence on the properties of the emitted light. We also present and analyze numerical results obtained for the case of a dipole transition between two degenerate levels of angular momenta \textonehalf{}. We show that in this particular case one can define a basis of collective states which is well adapted to the invariance properties of the master equation. It is then possible to solve the master equation and to compute expectation values for the radiated field (intensity radiated with a given polarization, quantum fluctuations of this intensity) for various initial conditions and for small but already significant values of the number of individual systems. A detailed analysis of these results and a comparison with analogous calculations in the case where the degeneracy is supposed to be removed allows us to estimate the individual influence of the different types of effects (interference effects and the two sorts of competition effects, inhibition and initiation). We also compare the total intensity radiated to the intensity radiated by the same number of two (nondegenerate) level atoms. This comparison can be simply understood if one studies the partition of the population of the collective energy levels between the different states of these levels, and it appears that the most populated states are these which are able to radiate the most. Finally, it is shown how level degeneracy affects the quantum fluctuations of the intensity.
A theory is presented of induced Raman emission in a three-level system whose parameters are appropriate for microwave to optical frequencies. Solutions of the time-dependent Schrödinger equation are obtained for arbitrary intensity of the pump and signal radiations, which are assumed to be not too many line-widths off resonance. It is shown how the quantum-mechanical aspects of the problem may be separated from the statistical-mechanical aspects, in contrast to the density matrix techniques. The frequency dependence of the Raman emission on the frequency and intensity of the pumping radiation obtained by this method is presented and compared with the results we have obtained by other methods. The intensity and line shape of the Raman emission when the pump frequency is far off resonance are also obtained. The case of three interacting fields is also considered.