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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Theoretical Studies Of Coherent Amplification Of Ultrashort Laser Pulses In An XeCL Laser Medium

Fumihiko Kannari, Minoru Obara

Published May 31, 1989• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.951323

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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.
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.
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.
Equations appropriate for amplification of short pulses in the multilevel atomic iodine amplifier are developed from the Maxwell-Bloch equations with homogeneous line broadening. The equations are implemented in the form of a two-dimensional time-dependent finite-difference computer code with six population densities, six medium polarization densities, and adaptive propagation capabilities. The Sandia atomic iodine laser was used to examine the adequacy of the theoretical description for amplification conditions covering the full range of gain saturation. Whole-beam self-focusing is observed with a strongly saturating small-waist beam in agreement with predictions. Calculations predict that this self-focusing instability may be controlled by tuning the multiline amplifier bandwidth.
A one-dimensional model of the coherent amplification in a high- and swept-gain amplifier in the presence of strong spontaneous emission is presented and applied to seeding an x-ray laser with a high harmonic pulse. The atomic structure of the amplifying medium includes level degeneracy, and the Maxwell-Bloch equations are used to describe the propagation and interaction processes. This analysis elucidates, in the most comprehensive way, the influence of the random spontaneous emission on the coherent amplification process, as reflected in the basic pulse parameters such as its shape, polarization, and coherence.
Pulse propagation in maser-type traveling-wave amplifiers with a homogeneously broadened transition is treated by a formalism analogous to the Bloch equations. Phenomenological dephasing (T2) and recovery (T1) times are defined, and a linear (nonsaturable) loss mechanism is included. In the numerical calculations, only the case of negligible excitation during the time it takes a pulse to pass is considered. When pulses are allowed to grow until the amplifier is ``saturated,'' steady-state pulses having a unique shape and intensity independent of the initial pulse are found. The parameters of these steady-state pulses depend only on the ratio of the linear loss and gain coefficients. Steady-state pulses have a peak intensity that decreases monotonically from infinity to zero as the linear loss coefficient varies from zero to the gain coefficient, while the pulse width correspondingly varies from zero to infinity, and the pulse energy varies from a finite value to zero. Steady-state pulses propogate at a velocity less than that of the small signal velocity in the medium.
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.