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Soviet Journal of Quantum Electronics

Role of collision anisotropy in two-photon processes in a magnetic field. Phenomenological analysis

G. N. Nikolaev, Sergei G Rautian

Published May 31, 1984• 0 citations
Publisher

Abstract

It is shown that the nonlinear susceptibility tensor of an isotropic medium is axially symmetric because of the anisotropy of collisions characterized by a symmetry axis along the field wave vectors. In the collinear geometry a two-photon process is described by six functions of the frequencies and wave vectors of the fields, whereas in the case of a mirror-symmetric medium it is described by three such functions. A new difference method is proposed for separating just the collision anisotropy contribution to the signal of a two-photon process in a magnetic field. The method makes it possible to obtain several types of difference signal. In a probe field variant the number of possible signals is four and eight for mirror-symmetric and mirror-asymmetric media, respectively. In a variant involving observation of fluorescence at right-angles to the magnetic field and also parallel to the direction of propagation of the exciting light, the number of possible difference signals is eight and sixteen for mirror-symmetric and mirror-asymmetric media, respectively, whereas in the case of observations along a magnetic field there is only one type of signal. An analysis is made of the parity of the difference resonances relative to reversal of the magnetic field direction.

DOI
10.1070/qe1984v014n05abeh005127

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It is shown that the nonlinear susceptibility tensor of an isotropic medium is axially symmetric because of the anisotropy of collisions characterized by a symmetry axis along the field wave vectors. In the collinear geometry a two-photon process is described by six functions of the frequencies and wave vectors of the fields, whereas in the case of a mirror-symmetric medium it is described by three such functions. A new difference method is proposed for separating just the collision anisotropy contribution to the signal of a two-photon process in a magnetic field. The method makes it possible to obtain several types of difference signal. In a probe field variant the number of possible signals is four and eight for mirror-symmetric and mirror-asymmetric media, respectively. In a variant involving observation of fluorescence at right-angles to the magnetic field and also parallel to the direction of propagation of the exciting light, the number of possible difference signals is eight and sixteen for mirror-symmetric and mirror-asymmetric media, respectively, whereas in the case of observations along a magnetic field there is only one type of signal. An analysis is made of the parity of the difference resonances relative to reversal of the magnetic field direction.
The functional relations have been presented between the complex amplitude (including polarization) of reflected wave on the one hand and amplitudes, polarizations of pump and probe waves, the third-order nonlinear susceptibility on the other hand, for degenerate four-wave mixing (DFWM) in isotropic medium, in which the polarizations are linear and/or circular, and the geometry is collinear or non-collinear. In the non-collinear geometry, when the polarizations of pump waves are parallel to each other, one can determine the ratio x1111/x1221 from the angles between polarization directions of probe and reflected waves; when the polarizations of pump are circular polarizations of the same handedness, one can get the ideal complex conjugate wave in this geometry. In the collinear geometry, there are always some non-conjugate component in the reflected wave, and the functional relation between reflection coefficient of amplitude and the thickness of sample can have the form of tangent function, hyperbolic tangent function and linear function; when the polarizations of pump waves are parallel to each other and |x1221|> |x1122|, this geometry is capable of generating self-oscillation; when polarizations of pump are circular ones of different handedness, DFWM acts as an ideal plane-mirror for probe wave with circular polarization, etc. The results can be used to explain some well-known experimental results and provide some theoretical guidance for designing new experiments.
Using semiclassical radiation theory and a density matrix formalism we analyze the nonlinear characteristics of a gas laser amplifier operating with two optical frequency signals of arbitrary polarization and having an axial magnetic field. Both perturbational solutions, valid for relatively weak intensities and solutions valid for arbitrarily strong fields are obtained for two nonlinear effects: the saturation interaction of the electromagnetic waves, and the generation of combination tones. An arbitrary amount of Doppler broadening is considered throughout. The detailed treatment of J = 1 to J = 0 model yields the frequency, magnetic field and polarization dependence of the nonlinear effects. The results are presented analytically and graphically and are discussed using physical arguments. It is found that only saturation but no combination tone generation occurs for two opposite circularly polarized input signals while both are, in general, present for two arbitrary linearly or elliptically polarized fields. For two opposite circular waves the interaction is found to comprise three parts, each with a different behavior: self saturation, common level mutual saturation and a coherent double quantum interaction. The total interaction (coupling) between the two fields is always weak. The limiting case of a single linearly polarized field is considered separately, the zero magnetic field dip and the nonlinear behavior of the Faraday rotation is discussed. For two linearly (or elliptically) polarized waves the three nonlinear processes listed above take place between opposite circular components. In addition a modulation of the population inversion densities occurs due to the presence of two different frequencies with the same circular polarization. This results in the generation of new frequencies and also contributes to the coupling between the input fields. The coupling depends on the magnetic field, and on the frequency separation and the polarization states of the signals. The limiting case of zero magnetic field is examined. It is found that the medium is made effectively anisotropic by the nonlinear interactions. The polarization vectors of two linearly polarized fields rotate apart unless the angle between them is zero or 90 degrees. The results are extended to the general Ja to Jb transition. In zero magnetic field the nonlinear effects are found to depend on ΔJ, while for nonzero magnetic field resonances in the interaction occur whenever the frequency difference between two opposite circularly polarized transitions that have common level equals the frequency separation of the input fields. Combination tone generation takes place for all but two opposite circularly polarized signals.
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.
For isotropic media, the magnetic field applied across the light propagation direction affects their optical properties only in the second order, and its effect proves to be much weaker than in the longitudinal field. In this work, we show that, under resonant excitation well beyond the linear regime, the situation changes drastically: A small magnetic linear anisotropy considerably increases, and an even stronger new quadrupole dichroism emerges. The latter manifests itself as the ${90}^{\ensuremath{\circ}}$-periodic azimuthal dependence of the transmission and anisotropic rotation of the probe polarization plane. These effects are described microscopically in a toy model, and their symmetry analysis is presented. Both are observed experimentally on the D2D2D2 resonance of cesium vapor and agree with the theoretical predictions. The large magnitude of the quadrupole dichroism makes it promising for magnetometric applications and for studying the effects of anisotropic bleaching.
In this work a theoretical study of the interaction between a light beam and an anisotropic nonlinear interferometer has been considered and methods to control the transmission of the microcavity using optical and magnetic fields have been developed. It has been demonstrated that anisotrophy of intracavity media determines the differences in transmission functions for various polarization modes and produces polarization instability. Varying spectroscopic parameters of the resonant medium and parameters of the anisotropic element, different types of intensity self-oscillations for different polarization modes can be obtained. To control the characteristics of nonlinear interferometer, it is proposed to use an additional light beam whose frequency is tuned into the absorption band from the excited level. The propagation characteristics of periodic magento-optical and dielectric multilayer films made of alternating layers of these materials having a symmetric periodicity with the center of the structure under a magnetic field is analyzed. The magnetic induction on this type of materials is temperature dependent and modifies the transmission and reflection characteristics of these structures. This kinds of structures, gives us the possibilities for an additional controlling of the characteristics of nonlinear interferometer.
For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions a theory of nonlinear magneto-optic polarization phenomena is developed. The theory is valid in the case of both arbitrary resonance linearly-polarized radiation intensity and arbitrary external magnetic field spatial orientation. The Faraday and Voigt geometries are analysed in detail, and in the case of the Faraday geometry the effect is considered of a noncompensated magnetic field transverse component on the shape of a dependence relating the radiation polarization plane rotation angle to a magnetic field longitudinal component. In the case of the Voigt geometry an essential effect is found of the angle between the radiation initial polarization and transverse magnetic field vectors on the character of the dependence relating the radiation polarization plane rotation angle to the transverse magnetic field magnitude.