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Soviet Journal of Quantum Electronics

Theory of propagation of ultrashort light pulses in a threelevel medium

Maria V. Bogdanova, Tamara M. Il'inova

Published Oct 31, 1975• 0 citations
Publisher

Abstract

The results are given of a theoretical investigation of the interaction between two ultrashort pulses J1 and J2 of frequencies ω31 and ω21 with a three-level amplifying medium. It is assumed that the signal J1 of frequency ω31 is a steady-state π pulse and the signal J2 is weak so that its influence on the level populations can be ignored. The case when the signal J2 has a steady-state amplitude profile and an exponential gain is considered. The analysis is made ignoring the group delay effects and also allowing for the mismatch of the group velocities of the signals. The results obtained can be used in studies of the amplification of ultrashort pulses in molecular media such as organic dyes or CO2 molecules.

DOI
10.1070/qe1975v005n10abeh012036

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The results are given of a theoretical investigation of the interaction between two ultrashort pulses J1 and J2 of frequencies ω31 and ω21 with a three-level amplifying medium. It is assumed that the signal J1 of frequency ω31 is a steady-state π pulse and the signal J2 is weak so that its influence on the level populations can be ignored. The case when the signal J2 has a steady-state amplitude profile and an exponential gain is considered. The analysis is made ignoring the group delay effects and also allowing for the mismatch of the group velocities of the signals. The results obtained can be used in studies of the amplification of ultrashort pulses in molecular media such as organic dyes or CO2 molecules.
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The Maxwell–Schrödinger equations describing the ultrashort laser pulse propagation in multilevel molecular media are shown to be analytically solvable and to reduce to nonlinear multisine-Gordon equations for certain models of the field–molecule system. Special cases of level schemes are shown to lead to soliton propagation. A numerical study is presented in order to examine the effect of nonresonant (virtual) transitions on pulse propagation and amplification in a three-level molecular system as a function of intensity and detuning.
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.
An analysis is made of the interaction of radiation with a two-level medium at a high particle density. An explicit allowance is made in the interaction Hamiltonian for the interaction between dipoles induced by a resonance field. A semiclassical description is used to obtain a system of equations describing the propagation of a pulse in the active medium. The equations contain nonlinear terms allowing for the interaction in question. An approximate solution of the equations is obtained for the case of amplification of a weak noncoherent pulse describing pulse compression in the amplifying medium. The theory is compared with experimental results.