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Soviet Journal of Quantum Electronics

Nonlinearity of the refractive index of doped insulators

G. B. Altshuler, S. A. Kozlov

Published Apr 30, 1985• 3 citations
Publisher

Abstract

Relationships are obtained for the nonlinear resonant polarization of a multilevel system in the field of a monochromatic light wave under noncoherent interaction conditions allowing for anharmonicity of the electron oscillator and the dynamic Stark shift. Estimates are made of the resonant nonlinear refractive index of glasses and crystals activated with Cr 3+ and Nd 3+ ions and it is found that this may be of the order of (or greater than) the same index of the insulating base of the active medium.

DOI
10.1070/qe1985v015n04abeh006941

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Relationships are obtained for the nonlinear resonant polarization of a multilevel system in the field of a monochromatic light wave under noncoherent interaction conditions allowing for anharmonicity of the electron oscillator and the dynamic Stark shift. Estimates are made of the resonant nonlinear refractive index of glasses and crystals activated with Cr 3+ and Nd 3+ ions and it is found that this may be of the order of (or greater than) the same index of the insulating base of the active medium.
The mechanism for refractive-index changes that accompany changes in population during pumping and amplification of an optical beam is studied in a Nd:YAG laser crystal by both resonant four-wave mixing and interferometric techniques. It is found that these refractive-index changes (connected with the difference in polarizability of excited and unexcited Nd3+ ions) have two components: a small noninertial component that accompanies an amplified optical pulse and the major changes that are intensified with a delay time of ∼3 µs. The latter effect is explained by population (or depopulation) of a higher-lying energy level 2(F2)5/2 of the 4f electron shell of Nd3+ ions, which has large polarizability in near-IR and visible light. The real part of the nonlinear optical resonant susceptibility of the inverted Nd:YAG caused by the refractive-index changes is also discussed.
A theoretical analysis is made of the nonlinear (in respect of the radiation intensity) rotation of the plane of polarization occuring in an atomic medium subjected to a static magnetic field near one-photon (two-level atoms) and two-photon (three-level atoms) resonances. A study is also made of the influence of a strong monochromatic pump wave on the propagation of a weak nonmonochromatic wave. The wave functions and quasienergies are calculated for a three-level system in static magnetic and monochromatic electromagnetic fields near a two-photon resonance. It is shown that the Verdet constant and the refractive index of such a system depend on the magnitude and relative sign of the frequency detuning from resonance. Proximity to a two-photon resonance destroys the polarizability of a medium for either sign of the detuning.
A polarising interferometer was used to investigate changes in the refractive index of an Nd:YAG laser crystal associated with changes in the populations of the electronic energy levels characterised by different polarisabilities. The study was carried out on diode-pumped crystals as well as on crystals which were flashlamp-pumped under conditions of saturation of the gain experienced by the optical beam. The changes in the refractive index depended nonlinearly on the pump power. The ratio of the real and imaginary parts of the nonlinear susceptibility of an Nd:YAG laser amplifier was determined: this ratio rose from 0.2 to 1.2 when the gain increased from 0.2 to 0.45 cm -1 .
A novel method is reported for calculating the nonlinear resonant change in refractive index of a doped saturable medium at the short-pulse excitation. The derived system of equations for energy density and phase of a short pulse propagating in the doped medium allows one to address a rather general case of the resonant index non-linearity caused by the dope's population perturbation (bleaching) effect. As an example, the energy-dependent changes in the refractive index and transmission coefficient of a Cr4+:YAG crystal under the ns-range (wavelength 1.06 μm) excitation are modeled.
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.
Starting from a Hamiltonian which describes the interaction of the many-electron system of a crystal with the quantized light field, we derive nonlinear coupled equations of motion for the light-field amplitude, the electron-hole-pair amplitude, and the inversion. These equations yield the basis for the investigation of space-dependent nonlinear interaction effects between light and electrons in direct band-to-band transitions. With the aid of these equations we investigate the saturation behavior of direct band-to-band transitions for an incident monochromatic electromagnetic plane wave. We determine the nonlinear absorption coefficient and nonlinear refractive index. We compute the nonlinear transmissivity taking into account the boundary conditions at the end faces of the crystal and discuss the effect of optical bistability.