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Soviet Journal of Quantum Electronics

Effect of relaxation processes on the coherent interaction between radiation and a two-level medium

Dmitrii I. Gruev

Published Sep 30, 1978• 0 citations
Publisher

Abstract

Numerical integration of a system of equations describing the coherent interaction between radiation and a two-level medium (e.g., a semiconductor) is employed to analyze the effect of relaxation processes on the energy characteristics and dynamics of radiation pulses of duration τpΣ T '2 (T '2 is the irreversible polarization relaxation time). It is shown that the interaction of these pulses with the medium is strongly dependent on their area on entry to the medium and the attenuation of the pulses as a result of relaxation processes decreases with increasing pulse input power. This may be utilized for probing the medium in the resonant absorption range for short polarization relaxation times, in solution 42.65.Gv.

DOI
10.1070/qe1978v008n09abeh010748

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Numerical integration of a system of equations describing the coherent interaction between radiation and a two-level medium (e.g., a semiconductor) is employed to analyze the effect of relaxation processes on the energy characteristics and dynamics of radiation pulses of duration τpΣ T '2 (T '2 is the irreversible polarization relaxation time). It is shown that the interaction of these pulses with the medium is strongly dependent on their area on entry to the medium and the attenuation of the pulses as a result of relaxation processes decreases with increasing pulse input power. This may be utilized for probing the medium in the resonant absorption range for short polarization relaxation times, in solution 42.65.Gv.
The propagation of two ultrashort radiation pulses interacting via an intermediate level is analyzed by numerical integration of a system of equations describing coherent interaction between radiation and a three-level medium. It is shown that the propagation of the pulses depends strongly on their areas on entry to the medium and on the relationship between the dipole moments of transitions between neighboring levels. Substantial temporal narrowing was established for fairly high-power pulses (4π and 6π pulses) and this may be utilized to control their durations. Investigations are also made of the influence of relaxation processes, delay of pulses relative to one another on entry to the medium, and nonresonant dispersion during pulse propagation under the specified conditions.
The evolution of radiation under conditions of electromagnetically induced transparency in the scheme of degenerate quantum transitions J = 0 → J = 1 → J = 2 in the pulsed interaction regime of the fields and with allowance for the Doppler broadening of spectral lines has been analyzed numerically. It has been shown that, if the input coupling radiation is linearly polarized, the circularly polarized input probe pulse splits in the medium into pulses with mutually perpendicular linear polarizations. The direction of polarization of one of these pulses coincides with the direction of polarization of the input coupling field. The distance that the probe pulse travels in the medium until it completely decays decreases with a decrease in both the duration of the input probe pulse and the intensity of the input coupling radiation. A change in the power of the input probe pulse hardly affects the distance required for the decay and the velocity of propagation of linearly polarized pulses in the medium. An increase in the Doppler broadening of spectral lines leads to a decrease in this distance and, simultaneously, to an increase in the energy losses of the probe radiation. Qualitative considerations that explain the physical reason for the investigated effects have been presented.
Transmission characteristics in an excited absorbing medium are discussed on the basis of the photon transport-equation and the rate equations. An increasing power of the C W laser beam passing through the medium is considered when this medium is excited at the same time by a different pulse of radiation. A typical example of a square excitation-pulse states that the transmittance recovers to its original value after it once reaches a maximum value. The time response of the medium depends upon the total number of absorbing centers M, the absorption cross-section σ, and the relaxation time τ as well as the intensity of radiation sources I. The decay time of the increased transmittance is proportional to τ/σM if the quantity (1-M/2τI) is kept constant. As a numerical example the relaxation time of SF6 is estimated to be 2×10-6 s at a pressure of 3.7 Torr in comparison with an experimental result.
The effect of slowing down pulses of probe radiation in a medium consisting of two-level quantum systems whose longitudinal and transverse relaxation times strongly differ is studied. The conditions for the occurrence of “slow light” in a transparency window are obtained. Regimes are discovered in which the medium becomes transparent or amplifies the probe radiation, with the high dispersion of the refractive index being conserved. The parameters at which the delay time of the probe radiation reaches a maximum or the group velocity of this radiation decreases to a maximal possible value under the condition of exact resonance with the strong field are found.
Abstract The interest in unipolar pulses in optics is related to the possibility of their efficient action on quantum objects. In this work, we study the interaction of a short rectangular unipolar pulse with a two-level resonant medium under conditions that the pulse duration is shorter than the relaxation times of the medium. It is paradoxical that the polarization and the population difference of the medium oscillate not at the Rabi frequency, but, rather, at a frequency that is proportional to the sum of the squared frequency of the resonant transition of the medium and the squared Rabi frequency of the pulse. This phenomenon is similar to the Stark effect, which consists of a shift of the transition frequencies of a medium in a constant external electric field. The possibility of generating radiation at frequencies that exceed the resonant transition frequency of the medium upon its excitation by a rectangular unipolar pulse is discussed.