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arXiv:1610.04628

On the nature of periodically pulsating radiation sources

A. V. Kirichok, Volodymyr M. Kuklin, Anatolij G. Zagorodny

Published Oct 14, 2016• 0 citations
arXivHTMLPDF

Abstract

A change in the character of maser generation in a two-level system is found when the initial population inversion exceeds some threshold value proportional to the square root of the total number of atoms. Above this threshold, the number of photons begins to grow exponentially with time and the pulse with short leading edge and broadened trailing edge is generated. In this work, we attempt to explain the nature of this threshold. Coherent pulse duration estimated by its half-width increases significantly with increasing inversion, if all other parameters are fixed and the absorption is neglected. The inclusion of the energy loss of photons leads to the fact that the duration of coherent pulse is almost constant with increasing inversion, at least well away from the threshold. If there is exist a recovery mechanism for the population inversion, the pulsating mode of stimulated emission generation becomes possible. The integral radiation intensity at this may be increased several times. This approach can be used for analysis of the cosmic radiation that might help explain a great variety of pulsating radiation sources in space.

DOI
10.48550/arxiv.1610.04628

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A change in the character of maser generation in a two-level system is found when the initial population inversion exceeds some threshold value proportional to the square root of the total number of atoms. Above this threshold, the number of photons begins to grow exponentially with time and the pulse with short leading edge and broadened trailing edge is generated. In this work, we attempt to explain the nature of this threshold. Coherent pulse duration estimated by its half-width increases significantly with increasing inversion, if all other parameters are fixed and the absorption is neglected. The inclusion of the energy loss of photons leads to the fact that the duration of coherent pulse is almost constant with increasing inversion, at least well away from the threshold. If there is exist a recovery mechanism for the population inversion, the pulsating mode of stimulated emission generation becomes possible. The integral radiation intensity at this may be increased several times. This approach can be used for analysis of the cosmic radiation that might help explain a great variety of pulsating radiation sources in space.
The presence of an internal layer with an active medium in a hot radiation source is considered, which can be described by a quantum two-level system located near equilibrium. The population of the upper and lower levels is approximately equal. It is shown that during convection from deeper hot layers, which supports the inversion of the populations of the active system, generation of induced radiation pulses is possible, the intensity of which is comparable to or greater than the intensity of the background spontaneous radiation of the source. With a sufficient thickness of the surface layers due to the effects of radiation scattering in them, the emission spectrum of a completely black body may well form there. Pulse generation near a previously detected new threshold of induced radiation can lead to a periodic change in the radiation intensity of the source as a whole. This threshold is determined by the equality of the squared population inversion to the total number of states. The generation of pulses of induced radiation is considered both in Einstein's representation, on the basis of balanced equations, and using a semiclassical description for small values of population inversion and for low levels of electric field intensity, when the Rabi frequency is less than the line width. The description of the induced radiation process is reduced to a one-parameter system of equations. Periodic solutions are represented by closed trajectories on the phase plane (relative density of quanta, relative density of population inversion). A similar layer with an active medium, which can be described by a quantum two-level system located near equilibrium, can exist in stars and is most likely localized in the photosphere. If there is significant convection in the star’s atmosphere, conditions can be realized for generating pulses of induced radiation. It turns out that one can see the similarity of the obtained solutions with known observations of changes in the luminosity of Cepheid stars (Cepheus delta and the North Star).
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 paper presents the transition to the regime of induced radiation of a system of oscillators in the classical and the quantum cases. This transition occurs due to synchronization by the integral field of the phases of a small part of oscillator-emitters. In the quantum analogue of this model, it is shown that the formation of an induced (and, therefore, coherent, as noted by Ch. Towns) pulse of the field is due to the interference of nutation of population inversion in different regions of the system of oscillators. The law of spatial variation of the field intensity is deter-mined by the dispersion characteristics of the system and the level of absorption or output of the radiation energy. Only a small fraction of oscillators provide induced radiation: 8% in the classical case and half as much in the case of a quantum system, where a change in the sign of population inversion in the regions of the highest field values significantly affects the limitation of the radiation intensity.
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