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Physics Physique Fizika

Translucency waves in optically dense media

V. E. Khartsiev

Published Jun 1, 1967• 4 citations
Publisher

Abstract

The phenomena which take place during the time of propagation of a monochromatic pulse of a resonance radiation through optically dense on the transition frequency medium containing resonance absorbing centers are considered. Due to the action of the pulse of the resonance radiation the saturation of absorption in the layer of the medium takes place. As a result the absorption decreases in the layer and the radiation penetrates into the next layer. Thus translucent region continuously moves deeper into the medium and the process is wavelike.When the density of the initial photon flux is constant and the distribution of absorbing centers is homogeneous the absorption coefficient and the photon density in the depth of the media depends only on the variable $t\phantom{\rule{0.15em}{0ex}}\ensuremath{-}\phantom{\rule{0.15em}{0ex}}x/v$. The velocity of translucency wave v may be by several orders of magnitude less than the velocity of light. The mechanism of the saturation can be various. The small value of the loss of photons in the transluced region of the medium is the necessary condition for the rise of translucent waves. The condition of realization of translucent wave is fulfilled for a large number of condensed states having intense absorption lines. These conditions are the most favourable in the case of presence of methastable levels between the levels 1 and 2 (type-ruby system). The effect of the translucent waves is general for various ranges of spectrum of electromagnetic radiation and may be realized in astrophysical scale.

DOI
10.1103/physicsphysiquefizika.3.129

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The phenomena which take place during the time of propagation of a monochromatic pulse of a resonance radiation through optically dense on the transition frequency medium containing resonance absorbing centers are considered. Due to the action of the pulse of the resonance radiation the saturation of absorption in the layer of the medium takes place. As a result the absorption decreases in the layer and the radiation penetrates into the next layer. Thus translucent region continuously moves deeper into the medium and the process is wavelike.When the density of the initial photon flux is constant and the distribution of absorbing centers is homogeneous the absorption coefficient and the photon density in the depth of the media depends only on the variable t\ensuremath−x/vt\phantom{\rule{0.15em}{0ex}}\ensuremath{-}\phantom{\rule{0.15em}{0ex}}x/vt\ensuremath−x/v. The velocity of translucency wave v may be by several orders of magnitude less than the velocity of light. The mechanism of the saturation can be various. The small value of the loss of photons in the transluced region of the medium is the necessary condition for the rise of translucent waves. The condition of realization of translucent wave is fulfilled for a large number of condensed states having intense absorption lines. These conditions are the most favourable in the case of presence of methastable levels between the levels 1 and 2 (type-ruby system). The effect of the translucent waves is general for various ranges of spectrum of electromagnetic radiation and may be realized in astrophysical scale.
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.
Summary form only given. Results are presented of theoretical studies into the resonances of the saturated absorption and saturated dispersion in an external absorption cell. The theory has been worked out by means of combining methods of mathematical theory of diffraction and quantum mechanical method for computing the polarization of active media. This made it possible for the first time to find a self-consisting spatial solution of the density matrix equation for the two-level system and the Helmholtz equation for electromagnetic field and to solve the problem of propagation of two counterpropagating monochromatic waves though an absorbing nonlinear medium taking into consideration the transverse transit-time effect.
A theoretical analysis is made of the transformation of light waves by optically induced amplitude-phase gratings of different order in a saturable absorbing medium. Allowance is made for gratings appearing; due to the absorption saturation and inhomogeneous heating of the medium. It is shown that, under certain conditions, the higher-order gratings may play a considerable role in the diffraction process. The contributions made by multistage and direct mechanisms to the n-th order diffraction are calculated. Estimates are obtained of the conditions which must be satisfied by the intensity and duration of radiation pulses, as well as by the optical properties and thickness of the absorbing medium, for these contributions to be comparable.
A theoretical investigation is made of the propagation of two-frequency laser radiation in an optically dense Λ medium in the presence of an rf field which is in resonance with a transition between the lower levels of a Λ-like system of an atom. It is shown that, depending on the phase and amplitude of the rf field and on the initial phases and intensities of the laser waves, one laser wave may be amplified at the expense of the energy of the other wave, or coherent bleaching of the medium (propagation of both waves without intensity losses) may take place.
The distinctive features of the propagation of the two-component electromagnetic pulses in an anisotropic media are studied in the frameworks of the system of equations of the resonance of long and short waves. It is shown that an interaction of the light with the quantum systems, which have a constant dipole momentum nonequal to zero, occurs not only in the usual mode of the self-induced transparency, but also in two new modes. In the first one (supertransparency), the pulse propagation causes the significant change of the population density of quantum levels, while its group velocity remains close to linear one. In the second mode (extraordinary transparency), the group velocity of the pulse changes significantly, but the population of the levels is practically invariable. It is also noted that the largest change of the population takes place, if the carrier frequency of the solitons is less than the resonant frequency, at that the detuning value depends on the duration of the pulses.
Propagation of broad-band ultimately short light pulses in a partially absorbing medium is analyzed in the framework of the three-level model. Nonlinear wave equations are obtained describing propagation of light pulses in media with quadratic (all three transitions are allowed) or cubic (one of the transitions is forbidden) nonlinearity in the range of optical transparency or with the sine-Gordon-type nonlinearity in the region of absorption. Using the averaged variational principle, the approximate solutions of equations in the form of unipolar soliton-like signals are found and conditions of their transverse stability are determined. A stable propagation of a broad-band pulse is shown to be possible under conditions when monochromatic signals exhibit self-focusing.