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Physical Review A

Semiclassical theory of resonant three-wave parametric interactions: Second-harmonic generation

Thomas A. DeTemple, L. A. Bahler, J. F. Osmundsen

Published Oct 1, 1981• 28 citations

Abstract

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.

DOI: 10.1103/physreva.24.1950

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The solution of the coupled-wave equations for second-harmonic generation in a near-resonant three-level system is extended to include absorption. It is shown, within second-order perturbation theory, that double resonance is the optimal conversion condition, despite absorption enhancement. We extend the solution numerically, using nonperturbative susceptibilities derived within the rotating-wave approximation, to saturating intensities and discuss the modifications to the perturbative conclusions as well as the regimes of validity for the various approximations.

The density-matrix approach, in the quasistatic or adiabatic limit, is applied to the case of resonant four-wave interactions in four-level systems resulting in explicit analytical expressions for the nonlinear optical parametric and nonparametric polarizations, including ac Stark effects. The results are applicable to any closed-linkage diagram of this type but are applied only to the specific case of resonant frequency tripling. The results revealed the presence of up to six Stark-shifted nonparametric resonances and the presence of saturation and interference effects on the parametric susceptibility. In particular, the third-order susceptibility is shown to saturate to a very small value under high-field conditions which restricts the range of useful pump intensities. Under near-resonant to resonant conditions, these imply that because of either nonparametric loss present at the pump or harmonic frequencies or power-dependent dispersive and saturation effects, conversion efficiencies higher than 25% may be difficult to realize in practice.

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.

A semiclassical density matrix treatment is developed for the parallel near-resonant interaction of three waves in a four-level atomic or molecular system. Explicit solutions are developed and contain implicit AC Stark-shift and splitting information. The role of splitting and AC Stark-shifts is discussed for a system of two competing emitted waves starting from a common optically pumped level; a situation encountered in many optically pumped lasers. Application of the results to a Raman-Raman competition situation in ammonia is illustrated.

The parametric resonances and the quasi-level structure of an atom strongly driven by a near-resonant amplitude-modulated optical field are studied theoretically. An approximate analytical solution of the density-matrix equations of motion is obtained for two-level and three-level atoms. Based on this solution the quasi-level shifts are analyzed, and the conditions for the quasi-levels to cross each other are derived. Expressions are given for the probe-wave absorption/gain spectrum near the parametric resonance and far from it. It is pointed out that the parametric resonances appear when the pumping field sidebands are tuned to resonance with some transitions among the quasi-levels.