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Applied Physics Letters

On the theory of frequency chirped pulse coherent amplification in inhomogeneously broadened gain medium

É. M. Belenov, Peter G. Kryukov, A. Nazarkin

Published Jul 13, 1992• 0 citations
Publisher

Abstract

Frequency chirped pulse interaction with inhomogeneously broadened two-level active medium when the pulse width is shorter than the homogeneous relaxation time T2 (coherent interaction) is studied theoretically. It is shown that, unlike the case of incoherent interaction when only half an energy stored can be converted into field, in the nonlinear coherent regime full extraction of active medium energy is possible. The analogy of the effect with Landau–Zener transition between crossing molecular curves is pointed out. Giving high-energy output at relatively low peak intensities, this nonlinear mechanism of energy extraction can be useful for excimer lasers.

DOI
10.1063/1.108250

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 31, 1989•0 citations
Frequency chirped pulse interaction with inhomogeneously broadened two-level active medium when the pulse width is shorter than the homogeneous relaxation time T2 (coherent interaction) is studied theoretically. It is shown that, unlike the case of incoherent interaction when only half an energy stored can be converted into field, in the nonlinear coherent regime full extraction of active medium energy is possible. The analogy of the effect with Landau–Zener transition between crossing molecular curves is pointed out. Giving high-energy output at relatively low peak intensities, this nonlinear mechanism of energy extraction can be useful for excimer lasers.
It is shown that induced transitions of an ensemble of two-level articles with an inhomogeneously broadened line in the field of a phase-modulated pulse are analogous to Landau-Zener inelastic transitions in molecules when their terms cross. Even for T% T:, where T and T: are, respectively, the pulse width and the inhomogeneous relaxation time of the medium, a transition of particles of the entire spectrum ( T:) - ' from an upper to a lower level is possible, signifying the complete removal by the pulse of the energy stored in the active medium. Analysis of the dynamics of a phase-modulated pulse by means of the Maxwell-Bloch equations shows, in addition, the possibility of amplifying it without the development of field-amplitude oscillations.
Generation of single-cycle pulses from a laser passively mode locked by the technique of coherent mode locking is theoretically demonstrated for the case when resonant lines of both the gain and absorbing media are inhomogeneously broadened. In contrast to conventional mode-locked lasers, for which the inhomogeneous nature of line broadening sets a severe limitation on their performance, here, the stable single-cycle pulse operation is shown to persist even when the spectral widths of the inhomogeneously broadened lines of the amplifier and the absorber become nearly as wide as the central resonance frequency of their two-level transitions. This study is aimed at showing the potential for application of the coherent-mode-locking technique for quantum-dot lasers, which are typically characterized by a great amount of inhomogeneous broadening.
Introduction When an electromagnetic wave propagates through amedium stimulated emissions increase the intensity of the wave, while absorptions diminish it. The overall intensity will increase if the number of stimulated emissions can be made larger than the number of absorptions. If we can create such a situation then we have built an amplifier that operates through the mechanism of stimulated emission. This laser amplifier , in common with electronic amplifiers, has useful gain only over a particular frequency bandwidth. Its operating frequency range will be determined by the lineshape of the transition, and we expect the frequency width of its useful operating range to be of the same order as the width of the lineshape. It is very important to consider how this frequencywidth is related to the various mechanisms by which transitions between different energy states of a particle are smeared out over a range of frequencies. This line broadening affects in a fundamental way not only the frequency bandwidth of the amplifier, but also its gain. A laser amplifier can be turned into an oscillator by supplying an appropriate amount of positive feedback. The level of oscillation will stabilize because the amplifier saturates. Laser amplifiers fall into two categories, which saturate in different ways. A homogeneously broadened amplifier consists of a number of amplifying particles that are essentially equivalent, whereas an inhomogeneously broadened amplifier contains amplifying particles with a distribution of amplification characteristics. Homogeneous line broadening All energy states, except the lowest energy state of a particle (the ground state) cover a range of possible energies.
Recent advances in laser technology have led to the production of ultrashort electromagnetic pulses of very high peak power. In this paper we develop a theory which describes the transient behavior of such pulses in a laser amplifier. The effects of atomic coherence and inhomogeneous broadening, necessary for a complete treatment of the problem, are included. In the present development, the degree of homogeneous and inhomogeneous broadening is variable. The two-level active atoms are characterized by a phase memory time T2{T}_{2}T2​ and an inhomogeneous frequency distribution (which leads to a reversible decay time T2∗T_{2}^{}{}_{}{}^{*}T2​​∗). The field (Maxwell) and atomic (Schr\"odinger) equations are coupled in a self-consistent manner as in Lamb's theory of an optical maser. The resulting equations are solved analytically in certain limits, while the general case is integrated numerically. The emphasis is placed on the situation in which T2∗T_{2}^{}{}_{}{}^{*}T2​​∗ and the pulse width are much shorter than T2{T}_{2}T2​. Thus our main effort is devoted to the physics of the inhomogeneously broadened system. The theory itself, however, contains the effects of both forms of broadening. The basic difference between inhomogeneous and homogeneous broadening is discussed. In the former case, the decay of radiation is caused by the dephasing of dipoles, and is reversible. The atomic memory is retained during the dephasing, and an internal reflection of the atomic coordinates, as is exemplified in the "photon echo" process, will cause the dipoles to rephase. The phonon interruptions or atomic collisions that bring about the homogeneous broadening are random processes which lead to an irreversible destruction of the atomic phase memory. The implications of the reversible versus irreversible decay processes are seen to have important consequences in the problem of pulse amplification.
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.