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Journal of Modern Optics

Coupling effects in the propagation of harmonics

M. Ll. Pons, Luis Plaja

Published Sep 1, 1996• 1 citation
Publisher

Abstract

We present numerical solutions of the propagation of harmonics in a dense nonlinear medium, constituted by two-level atoms. The propagation of the harmonics is analysed taking into account the nonlinear atomic response to all the harmonics generated in the sample. We compare our results with the case in which only generation from the fundamental is considered, finding that the profile of the harmonics inside the medium changes drastically from one situation to the other. These results indicate that the role of the phase mismatch could be much less severe than previously expected.

DOI
10.1080/09500349608232862

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We present numerical solutions of the propagation of harmonics in a dense nonlinear medium, constituted by two-level atoms. The propagation of the harmonics is analysed taking into account the nonlinear atomic response to all the harmonics generated in the sample. We compare our results with the case in which only generation from the fundamental is considered, finding that the profile of the harmonics inside the medium changes drastically from one situation to the other. These results indicate that the role of the phase mismatch could be much less severe than previously expected.
The interaction of femtosecond pulse with an extended medium of the two-level atoms or molecules is considered. It is shown that in the ultrahigh intensity layer field the atomic response is extremely nonmonochromatic due to the nonlinearity appropriate to the two-level system. The theoretical analyses shows that the two-level system tends to the generation of harmonics of the driving field. The results of the computer simulations show that in the ultrahigh fields the spectrum of the medium response is unusually broad in comparison with that for the fields of moderate intensity.
As a succession of two pulses propagates through a medium which exhibits a resonance (single or multiphoton), the resonant parts of the susceptibility will depend on the relative phase of the two pulses, provided the delay between the pulses is shorter than the phase relaxation time of the interaction. As a result of this "coherent interaction", the reradiation of the sample (the fluorescence, the absorption and the generation of harmonics) will be a periodic function of the phase difference and delay between the two pulses of the sequence 1. The study of these coherent effects is important, because one expect to find conditions under which the maximum harmonic conversion to much shorter wavelengths can be greatly enhanced 2. The presence of the multiphoton resonance enhances the nonlinear susceptibility responsible for the harmonic generation, but reduces also the maximum achievable conversion efficiency because of resonant losses (depletion of the fundamental by multiphoton absorption). The latter effect can be eliminated by a judicious choice of the pulse sequencing and phasing. In addition to demonstrating, for the first time, coherent interaction enhancement in harmonic generation, the data of third harmonic versus relative phase of the pulse sequences enable us to measure the phase angle of the third order susceptibility (hence the contribution of the continuum relative to that of the resonance).
The method of characteristics is used to analyse the system of five nonlinear partial differential equations describing ultrashort optical pulse propagation through a medium of two-level atoms. Contrary to previous suggestions it is shown rigorously that the system is causal: no physical speeds exceed c. The method is well adapted to numerical integration. It can take full account of both back scattering and the effect of a surface to the dielectric. A number of new physical results obtained this way are briefly reported.
Combinations of quadratic nonlinear crystals with different phase mismatches are studied numerically in terms of amplitude squeezing in the second-harmonic generation. It is predicted that an appropriate choice of phase mismatches can lead to large amplitude squeezing in the fundamental field with much larger stability than in the phase-matched case. It is also predicted that another choice of phase mismatches can yield amplitude squeezing in the harmonic field beyond the theoretical limit of the phase-matched case.
The production of squeezed states in second-harmonic generation is discussed theoretically from the viewpoint of the structure of the nonlinear medium, phase-matching conditions, and the polarization state of the fields. The nonlinear coupling constants are derived in explicit form for all 102 magnetic symmetry groups for crystalline as well as electrically polarized isotropic media. The phase-matching conditions are discussed in detail. Phase mismatch is shown to accumulate along the optical path, and is calculated in full detail for various media and geometries. We refer to this as the mismatch accumulation effect. General formulae for normally ordered variances of the second-harmonic and fundamental fields are derived by perturbative procedure, and are specified for some special cases of practical interest.
We study the effects of propagation through an extended sample of two- and three-level atoms on the coherent accumulation of excitation by an ultrashort pulse train. In the two-level case, previous pulses in the train may prepare the medium such that a later pulse may experience amplification and absorption in different positions inside the sample. For a large number of pulses, the atomic medium may be saturated by the train, and some pulses propagate without experiencing either absorption or amplification. In general, absorption of the resonant pulse frequency during propagation compromises the accumulation efficiency. In the three-level case, the coherent accumulation of excitation leads to electromagnetically induced transparency of the pulse train, and the pulses exit the medium without any distortion in their temporal profile.