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Soviet Journal of Quantum Electronics

Third harmonic generation in two-photon interaction between high-power coherent optical pulses and resonant media

I A Poluéktov, A. Nazarkin

Published Dec 31, 1979• 10 citations
Publisher

Abstract

A numerical investigation is made of third harmonic generation (THG) under conditions of two-photon resonance between the fundamental frequency and a selected transition in the atoms of a medium. It is shown that under conditions of coherent interaction between the pump pulse and the medium, a THG efficiency of ∼20% or higher may be achieved. In this case, THG in the form of high-power ultrashort pulses may be obtained. It is shown that experimental observation of similar effects in specific media should not present particular difficulties.

DOI
10.1070/qe1979v009n12abeh009802

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Quantum theory of third-harmonic generation in a gaseous system - Part II

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IEEE Journal of Quantum Electronics•Feb 1, 1982•2 citations
A numerical investigation is made of third harmonic generation (THG) under conditions of two-photon resonance between the fundamental frequency and a selected transition in the atoms of a medium. It is shown that under conditions of coherent interaction between the pump pulse and the medium, a THG efficiency of ∼20% or higher may be achieved. In this case, THG in the form of high-power ultrashort pulses may be obtained. It is shown that experimental observation of similar effects in specific media should not present particular difficulties.
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.
The dependence of the third harmonic intensity on the medium length under completely phase-matched and resonant conditions is discussed. It is shown that the conversion efficiency in the coherent transient case is expected to exceed that in the steady state case in a long and/or dense medium when the incident light pulse has sufficient energy. The 3S-5S transition of sodium with a 602.3 nm light is studied experimentally as a model system. The efficiency as a function of the incident light frequency and intensity is in agreement with the predictions. By eliminating the phase-mismatching effect, the dependence on the medium density is also determined. It is demonstrated that the efficiency surely increases even in the higher density of sodium.
An analysis is made of the evolution of high-power laser pulses in the case of coherent two-photon interaction with resonant media. It is shown that pulses of frequencies ω 0 and ω s satisfying the equalit ω 0 ±ω 0 =ω 21 (ω 21 is the resonance frequency of the medium) experience splitting into separate subpulses followed by a reduction in their duration and increase in their power. The efficiency of this process depends on the initial ratio of the amplitudes E 0 and E s . It is shown that such effects can be observed in paramagnetic acoustic resonance.
This work examines the use of higher order multiphoton resonances in higher harmonic generation together with judicious exploitation of coherent interaction properties to achieve efficient harmonic generation. A detailed experimental study on third harmonic generation in two photon resonant coherent interaction and a theoretical study on four photon resonant coherent interaction have been conducted. Two photon resonant coheren propagation in lithium vapor (2S-4S and 2S-3D interaction) has been studied in detail as a function of phase and delay of the interacting pulse sequence. Under coherent lossless propagation of 90 phase shifted pulse pair, third harmonic generation is enhanced. A maximum energy conversion efficiency of 1% was measured experimentally. This experiment shows that phase correlated pulse sequence can be used to control multiphoton coherent resonant effects. A larger two photon resonant enhancement does not result in more efficient harmonic generation, in agreement with the theoretical prediction. An accurate (to at least 0.5 A°) measurement of intensity dependent Stark shift has been done with the newly developed "interferometric wavemeter." Stark shifts as big as several pulse bandwidths (of picosecond pulses) result in a poor tuning of multiphoton resonance and become a limiting factor of resonant harmonic generation. A complete theory has been developed for harmonic generation in a four photon resonant coherent interaction. A numerical application of the theory to the Hg atom successfully interprets the experimental observations in terms of the phase dependent stimulated Raman scattering. With the intensity required for four photon resonant transition, the calculation predicts a dramatic Stark shift effect which completely destroys the resonance condition. This model provides a basis for the development of future schemes for efficient higher order coherent upconversion.
In Part I [1], we presented a quantum theory of third-harmonic generation (THG) under two-photon absorption in a two-level atomic medium. We studied the time evolution of the third-harmonic field and its coherence properties by neglecting the depletion of the pump power. In this paper we extend the theory by taking the depletion of pump power into account. The density matrix for the third-harmonic field is derived. The study of the growth rate of the density matrix in time shows the quantum mechanical effects more clearly. The effects of detuning in the two-photon interactions and atomic motion are pointed out. The results are compared with the earlier results and differences are brought out.