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Soviet Journal of Quantum Electronics

Short pulse evolution in two-photon-absorbing media as a function of frequency and initial energy

Konstantin N. Drabovich, L. M. Kocharyan

Published Nov 30, 1980• 1 citation
Publisher

Abstract

A numerical analysis is made of the frequency dependence of the evolution of the envelopes and energy loss of short optical pulses propagating under two-photon resonance conditions. It is established that for pulses with an initial energy situated in the range 2 π ( m +1)> θ o >2 π m , there are m intervals of resonance-frequency detunings within which the pulse evolution differs qualitatively. It is shown that a quasimultistage frequency dependence of the energy loss for a fixed length of medium may serve as a test for the coherence of the resonant interaction.

DOI
10.1070/qe1980v010n11abeh010321

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A numerical analysis is made of the frequency dependence of the evolution of the envelopes and energy loss of short optical pulses propagating under two-photon resonance conditions. It is established that for pulses with an initial energy situated in the range 2 π ( m +1)> θ o >2 π m , there are m intervals of resonance-frequency detunings within which the pulse evolution differs qualitatively. It is shown that a quasimultistage frequency dependence of the energy loss for a fixed length of medium may serve as a test for the coherence of the resonant interaction.
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An investigation is made of optical pulse propagation in a two-photon-absorbing medium in the incoherent regime. Simple analytic expressions describing the initial stage of evolution of arbitrarily shaped radiation pulses are derived in the long-wavelength approximation. The steady-state pulse shape is determined. In cases of self-modulation instability, the steady-state pulse is a harmonic wave whose period is governed by the properties of the medium and does not depend on the intensity of the propagating radiation. A qualitative investigation is made of the formation of steady-state pulses.
A theoretical investigation is made of collinear propagation of high-power optical pulses through a medium under conditions of two-photon resonance ω 0 ± ω s ≈ ω 21 ( ω 0 and ω s are the pulse frequencies, ω 21 is the frequency of an atomic transition in the medium). It is assumed that the condition for coherent interaction τ 0 , τ s < T 2 is satisfied ( τ 0 and τ s are the pulse durations at the entrance, T 2 is the phase relaxation time of the medium). By means of numerical integration of equations for the fields and the medium, it is shown that efficient generation of the harmonics ω 1 = 2 ω 0 ± ω s , ω 2 = 2 ω s ± ω 0 is possible under short and ultrashort pulse conditions.
We study the features of spatial and temporal evolution of two powerful short different-wavelength laser pulses interacting with optical dense three-level Lambda-type medium under condition of coherent population trapping for the general case of unequal transition oscillator strengths. The pulses are simultaneously sent into an atom. The durations of probe and coupling pulses T1,2T_{1,2}T1,2​ (T2>T1T_2>T_1T2​>T1​) are supposed to be shorter than all relaxation times in the medium. We present analytical and numerical solutions of the self-consistent set of coupled Schr\\"{o}dinger equations and reduced wave equations in adiabatic limit with taking into account the first non-adiabatic correction. The adiabaticity criterion with account of pulse propagation is studied. We find that propagation dynamics depends on the relationship between the transition oscillator strengths. It is shown that at the initial stage of propagation the envelopes of the pulses slightly change along the length of the medium. This distance can be large compared to one-photon resonant absorption length of the medium. Also it is possible a regime of complete reemitting of the probe pulse into the coupling one during propagation. A spatial evolution of the atomic Raman coherence is investigated in detail too.
The spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level \ensuremath{\Lambda}-type optical medium under coherent population trapping. The general case of unequal oscillator strengths of the transitions is considered. The durations of the probe pulse and the coupling pulse T1,2(T2>T1){T}_{1,2} {(T}_{2}>{T}_{1})T1,2​(T2​>T1​) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schr\"odinger equations and reduced wave equations in the adiabatic limit taking account of the first nonadiabatic correction. The adiabaticity criterion is also discussed taking account of pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that the envelopes of the pulses slightly change throughout the medium length in the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. An effect of localization of the atomic coherence was observed similar to the one predicted by Fleischhauer and Lukin [Phys. Rev. Lett. 84, 5094 (2000)].
The spatial and temporal dynamics of two short pulses propagating in an optically dense medium of resonant three-level Λ-atoms is investigated numerically and analytically. The maximum coherence for the Raman transition due to coherent population trapping. It is shown that, at the initial stage of propagation, the waveforms of such pulses only slightly change along the length of the medium, which may considerably exceed the length of linear absorption for a single weak pulse. As the length of the absorbing medium increases, the energy of the probe (first) pulse is completely transferred into the second (control) pulse.