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Soviet Journal of Quantum Electronics

Numerical modeling of the amplification of subpicosecond pulses in an XeCl excimer medium

Viktor T Platonenko, E.N. Tishina

Published Feb 28, 1988• 3 citations
Publisher

Abstract

The interaction between coherent subpicosecond ultraviolet radiation and an XeCl molecule was modeled numerically. It was established that a two-level model of the spectrum of a molecule having stable upper and rapidly decaying lower levels can be applied to study the amplification of 0.1–0.7 ps pulses. A numerical analysis was made of the amplification of 0.2–0.5 ps pulses and the influence of coherence effects was assessed. The conditions of validity of the Frantz–Nodvik equation to describe the energy characteristics of the amplified pulses were analyzed.

DOI
10.1070/qe1988v018n02abeh011472

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The Journal of Chemical Physics•Sep 15, 1988•30 citations
The interaction between coherent subpicosecond ultraviolet radiation and an XeCl molecule was modeled numerically. It was established that a two-level model of the spectrum of a molecule having stable upper and rapidly decaying lower levels can be applied to study the amplification of 0.1–0.7 ps pulses. A numerical analysis was made of the amplification of 0.2–0.5 ps pulses and the influence of coherence effects was assessed. The conditions of validity of the Frantz–Nodvik equation to describe the energy characteristics of the amplified pulses were analyzed.
Coherent amplification of short-pulse XeCl lasers is studied theoretically by using multilevel Maxwell–Bloch equations in which the vibrational–rotational structures of a XeCl gain spectrum are included. The model used considers 100 transitions each in the P and R branches for six different vibrational transitions of XeCl(B, υ = 0) → XeCl(X, υ′ = 0–5). Coherence components between sublevels in the B and X states are also properly calculated. The model can successfully predict coherent effects such as a quantum beat caused by the spectrum overlap of the several vibrational–rotational transitions involved in a short-pulse laser spectrum. During amplification, laser pulses experience some nonlinear effects caused by the complex gain spectrum structure and by the coherent interactions; thus a considerable change in the laser pulse shape and a substantial reduction in the duration of the amplified laser pulse are predicted. The Frantz–Nodvik equation in the rate-equation limit and even single-level Maxwell–Bloch equations are not applicable for short-pulse propagation analyses in inhomogeneously broadened gain media.
Coherent amplifications of short pulse XeCl lasers are theoretically studied using multi-level Maxwell-Bloch equations including real vibrational-rotational structures of a gain spectrum of XeCl. The model can successfully predict coherent effects such as the quantum beat caused by spectrum overlaptions of several vibrational-rotational transitions involved in the short pulse laser spectrum. Saturation of amplified energy caused by formation of a 2 π-pulse-like pulse. Since a pulse area necessary for the production of a 2π-pulse-like pulse which depletes all the upper state populations accessible to the laser spectrum depends on the laser pulse width, an effective saturation energy is a function of the laser pulse width. When absorption in the amplifier media is not negligible to the small-signal gain, an effective u-pulse-like pulse is generated instead of a 2π-pulse-like pulse. The laser pulse width is shortened by the π or 2π-pulse-like pulse formation, and even shorter pulses than the linear limitation defined by the gain spectrum width can be generated if the amplified pulse intensity becomes very strong.
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.
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.
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.