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Soviet Journal of Quantum Electronics

PROPAGATION OF A LIGHT PULSE IN A MOVING TWO-LEVEL ABSORBING MEDIUM

Boris L Borovich, V. S. Zuev, V A Katulin, O Yu Nosach, E. L. Tyurin, Vladimir A. Shcheglov

Published Feb 28, 1972• 10 citations
Publisher

Abstract

A solution is obtained for the equations describing the passage of a monochromatic radiation pulse of arbitrary shape I0(t) across a two-level absorbing medium with an activeparticle density N0 = const. It is shown that, depending on the ratio of the velocity of the medium v(t) to v0 = 2I0/N0, two modes of propagation of bleaching waves can be observed and the boundary between these modes is v = v0. The treatment is applicable to a radiation source moving at an arbitrary velocity in an absorbing medium.

DOI
10.1070/qe1972v002n02abeh004406

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A solution is obtained for the equations describing the passage of a monochromatic radiation pulse of arbitrary shape I0(t) across a two-level absorbing medium with an activeparticle density N0 = const. It is shown that, depending on the ratio of the velocity of the medium v(t) to v0 = 2I0/N0, two modes of propagation of bleaching waves can be observed and the boundary between these modes is v = v0. The treatment is applicable to a radiation source moving at an arbitrary velocity in an absorbing medium.
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.
An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.
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.
An investigation is made of optical pulse propagation in a two-photon-absorbing medium in the incoherent regime. Simple analytic expressions describing the initial stage of evolution of arbitrarily shaped radiation pulses are derived in the long-wavelength approximation. The steady-state pulse shape is determined. In cases of self-modulation instability, the steady-state pulse is a harmonic wave whose period is governed by the properties of the medium and does not depend on the intensity of the propagating radiation. A qualitative investigation is made of the formation of steady-state 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.