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Soviet Journal of Quantum Electronics

Theory of resonant second harmonic generation and frequency summation under adiabatic conditions

Արթուր Մելիքյան, S. G. Saakyan

Published Aug 31, 1984• 0 citations
Publisher

Abstract

A theory is developed of resonant second harmonic generation in a medium consisting of three-level atoms (molecules). Reduced equations for wave propagation are solved without expanding a nonlinear polarization as a series in powers of the field intensities, so that the theory is applicable also to strong resonances. The case of a strong two-photon resonance is investigated and it is shown how the results differ from those obtained using the conventional theory which applies to the nonresonance cases. It is shown that the proposed theory can be generalized to the processes of generation of sum and difference frequencies.

DOI
10.1070/qe1984v014n08abeh005348

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A theory is developed of resonant second harmonic generation in a medium consisting of three-level atoms (molecules). Reduced equations for wave propagation are solved without expanding a nonlinear polarization as a series in powers of the field intensities, so that the theory is applicable also to strong resonances. The case of a strong two-photon resonance is investigated and it is shown how the results differ from those obtained using the conventional theory which applies to the nonresonance cases. It is shown that the proposed theory can be generalized to the processes of generation of sum and difference frequencies.
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The propagation of strongly polarized electromagnetic waves through a resonance medium, with arbitrary angular momenta of the levels, is investigated in the adiabatic-following approximation. Exact wavefunctions of the two-level atomic system with degenerate levels in the field of a circularly (linearly) polarized wave are constructed and the picture of the shift of energy level splittings is discussed. Exact formulae for the nonlinear refractive index of the medium in the field of the circularly (linearly) polarized wave are found. The propagation of counterpropagating polarized waves—an intense pump wave and a probe light signal—through the resonance medium is studied. The studies are carried out in the scope of a two-level (one-photon resonance) and a three-level (one- and two-photon resonances) medium. Formulae are found for the induced rotation of the plane of polarization for the probing signal that are exact in terms of the intensity of the pump wave. The spectral dependence of the angle of rotation is studied, and it is shown that a series of Stark-shifted resonance poles of atomic absorption and a three-photon scattering process arise.
Resonantly enhanced sum-frequency generation of pulsed laser radiation is treated theoretically for the case of a three-level system. The density-matrix equations of motion are solved using second-order, time-dependent perturbation theory with the inclusion of transient effects. The energy and spectrum of the generated radiation are calculated as functions of laser detunings, laser pulse lengths, and temporal overlap of the laser pulses. The tuning characteristics and output pulse characteristics are found to differ qualitatively depending on whether or not the excitation pulses satisfy the adiabatic following criteria generalized for the case of a three-level atom.
Motivated by recent experiments on second-harmonic generation in three-level systems [K. S. Yngvesson and E. L. Kollberg, Appl. Phys. Lett. 36, 104 (1980)], a semiclassical description of resonant three-wave parametric interactions in three nondegenerate levels is considered. Within the limitations of the rotating-wave approximation, analytical nonperturbative solutions for the nonlinear polarization are derived, which are then coupled to Maxwell's equations and integrated numerically. The results of sample calculations for second-harmonic generation show (a) a maximum harmonic conversion occurs on full resonance, (b) the conversion efficiency can be > 50% but requires a strongly saturating pump, (c) the conversion distance increases with pumping intensity, and (d) the inclusion of ac Stark splittings is crucial for the achievement of high conversion efficiency. The role of level splittings is further explored for the case of a resonant parametric oscillator.
We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization, temporal (frequency), and spatial dispersions. The method is based on the reduced Maxwell equation, atomic density matrix formalism, and adiabatic approximation. In order to demonstrate the efficiency of our method we investigate in detail the case of propagation of the pulses under conditions of coherent population trapping in a medium of two-level atoms with degenerate energy levels. Equations describing the evolution of various field parameters are derived. It is shown that pulses of ellipticity and spatial orientation of polarization ellipse propagate with slowing. Analytical expressions for the slowing factor are obtained. Previously unknown effects of the stimulated phase modulation and the generation of a phase pilot pulse by the variation of spatial orientation of the polarization ellipse are predicted.