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Physical review. B, Condensed matter

Interference effects in the degenerate-wave-mixing spectroscopy of alexandrite

T. Catunda, Luiz A. O. Nunes

Published May 1, 1992• 5 citations
Publisher

Abstract

The degenerate-multiwave-mixing spectroscopy of alexandrite at 77 K using a pulsed dye laser in resonance with the ${\mathit{R}}_{1\mathit{m}}$ line was studied in this work. Unusual asymmetric line shapes that can be explained by an interference effect between resonant and nonresonant contributions of the media susceptibility were observed. The resonant effect is caused by the saturation of the two-level system susceptibility and the nonresonant contribution comes from the linear polarizability difference between excited and ground states. The present work shows an observation of this kind of interference phenomena in degenerate-wave-mixing experiments. Furthermore, we note that it is an observation of saturation line splitting in degenerate wave mixing in a narrow line in solids.

DOI
10.1103/physrevb.45.10087

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The degenerate-multiwave-mixing spectroscopy of alexandrite at 77 K using a pulsed dye laser in resonance with the R1m{\mathit{R}}_{1\mathit{m}}R1m​ line was studied in this work. Unusual asymmetric line shapes that can be explained by an interference effect between resonant and nonresonant contributions of the media susceptibility were observed. The resonant effect is caused by the saturation of the two-level system susceptibility and the nonresonant contribution comes from the linear polarizability difference between excited and ground states. The present work shows an observation of this kind of interference phenomena in degenerate-wave-mixing experiments. Furthermore, we note that it is an observation of saturation line splitting in degenerate wave mixing in a narrow line in solids.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.
The interaction of two closely spaced resonances in degenerate four-wave-mixing spectra is investigated theoretically. Degenerate four-wave-mixing spectra for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integrating the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and summing the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision and Doppler broadened are considered. The homogeneously broadened results are found to agree with the results of the widely used Abrams–Lind expression for the case of stationary absorbers exposed to a steady-state excitation. We examine the effects of power broadening, pressure broadening, transition dipole moment, and population on the spectra of two neighboring homogeneously broadened resonances. As the laser power is increased, the real parts of the resonance susceptibilities destructively interfere with each other in the region between the lines, resulting in a significant and persistent dip in reflectivity. When Doppler broadening is included in the calculations, similar interference effects are observed, although at first the interference dip begins to disappear until the homogeneous part of the line shapes is broadened significantly by saturation. Using this numerical approach, we obtain good agreement with experimental results of primarily Doppler-broadened neighboring resonances.
The nonlinear effect in Cr+3 doped crystals has been studied by populating the excited metastable level 2E through the 4T2 absorption band due to its higher absorption cross section compared with the R lines. The excited state 2E has a complex susceptibility different from that of the ground state so the material susceptibility changes in proportion to the excited state population.1 However, when the laser is sintonized near one of the R lines (the direct transitions between the ground and excited states), we must also consider the effect of this resonant interaction on the nonlinearity.
In this paper we analyze theoretically the influence of the local-field effects on reflection spectra of a degenerate four-wave mixing in a dense medium of two-level atoms. We discuss the spectral dependence of the nonlinear absorption and dispersion of the signal and probe fields as well as their coupling for various strengths of the external field and atomic densities. For weak external fields the local-field effects reduce to the well known Lorentz redshift of the reflection spectra. When the external field saturates the transition in a dense sample significant modifications of the probe reflectivity and of the wave mixing spectra occur, resulting in asymmetric, multipeak line shapes. \textcopyright{} 1996 The American Physical Society.
Nonlinear refraction spectroscopy measurements were performed in resonance with absorption lines in Nd3+ and Cr3+ doped crystals. The observed line shapes can be explained by the interference of resonant and nonresonant contributions to the nonlinear refractive index. These effects were fully discriminated using a pump and probe configuration, in which a dispersive line shape was observed on the top of a plateau that was attributed to the polarizability difference between excited and ground states (Deltaalpha). A theoretical model was used to obtain Deltaalpha from the experimental data, and the results are in agreement with several previous experiments. Slow and fast light propagation are also discussed.
Steady-state interactions of one, two, and three waves with two-photon two-level media are treated semiclassically. Dynamic Stark shifts as well as dynamic Stark splittings are included in the theory. The intermediate levels are assumed to be nonresonant, and one wave is allowed to have arbitrarily large intensity. The theory parallels the one-photon theory of multiwave mixing couched in terms of population pulsations. We find the one-, two-, and three-wave two-photon absorption coefficients and the three-wave coupling coefficients. We find similarities and significant differences between the one- and two-photon polarizations of the medium. The work treats two-photon saturation spectroscopy, laser- and optical-bistability instabilities, and phase conjugation with a unified formalism.