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Soviet Journal of Quantum Electronics

Propagation of optical pulses under two-photon resonance absorption conditions

Leonid A Bol'shov, V. P. Reshetin

Published Mar 31, 1982• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1982v012n03abeh012173

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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.
An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.
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.
A numerical and analytic investigation is made of the self-interaction of Gaussian beams under two-photon resonance conditions when the pulse duration is shorter than the relaxation times and the frequency detuning from resonance exceeds appreciably the spectral width of the radiation (adiabatic model). An analysis is made of defocusing (up-detuning) and self-focusing processes (down-detuning) in two-photon resonance. Three characteristic adiabatic self-focusing regimes are identified: a steady-state waveguide and weak and strong quasiwaveguide propagation. Expressions are derived for the critical powers and minimal self-focusing length.
Paraxial equations for the intensity and eikonal of a light wave, and also a kinetic equation for the difference between the level populations are used to analyze deformation of the space–time structure of a laser pulse occurring in a medium exhibiting two-photon absorption under noncoherent interaction conditions. The analysis is made using time and space compression functions, and the results of a numerical solution of two-dimensional equations for the propagation of radiation. A determination is made of the principal laws governing the changes in the time and space distributions of the intensity of radiation under quasisteady and transient interaction conditions, and also in the case of a small signal. It is shown that two-photon absorption results in a significant inhomogeneity of the space–time structure of a pulse. The results are given of experimental investigations of changes in the time, space, and energy characteristics of a neodymium laser pulse undergoing two-photon absorption in gallium arsenide.
Coherent propagation of a circularly polarized pulse which is two-photon quasi-resonant with a medium of multi-level atoms is considered in the adiabatic following limit. The relevant pair of non-linear coupled partial differential equations are solved exactly for arbitrary pulse shapes. The development of the envelope and the phase of the pulse as it propagates through the medium is described analytically. Perturbation theoretical results are shown to apply only for small intensity or small distance of propagation or both. Qualitatively different results apply for higher intensities and longer distances of propagation. These include strong self-phase-modulation effects as well as reshaping of the pulse envelope.