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Soviet Journal of Quantum Electronics

Changes in the polarization properties of an electromagnetic wave caused by atoms in external fields

Nikolai L. Manakov, V. D. Ovsyannikov

Published Sep 30, 1975• 3 citations
Publisher

Abstract

A theoretical analysis is made of changes in the polarization parameters of an electromagnetic wave as a result of its passage through a medium with an anisotropic refractive index. Formulas are obtained for the transformation of the Stokes parameters corresponding to the Faraday, Cotton–Mouton, and Kerr effects in a partly polarized wave. A study is made of changes in the polarization parameters of a weak wave in the presence of strong radiation. The rotation of the polarization ellipse of strong radiation in a nonlinear isotropic medium is discussed. Nonlinear susceptibilities governing the cited effects are calculated for atomic gases by the model pseudopotential method.

DOI
10.1070/qe1975v005n09abeh011893

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A theoretical analysis is made of changes in the polarization parameters of an electromagnetic wave as a result of its passage through a medium with an anisotropic refractive index. Formulas are obtained for the transformation of the Stokes parameters corresponding to the Faraday, Cotton–Mouton, and Kerr effects in a partly polarized wave. A study is made of changes in the polarization parameters of a weak wave in the presence of strong radiation. The rotation of the polarization ellipse of strong radiation in a nonlinear isotropic medium is discussed. Nonlinear susceptibilities governing the cited effects are calculated for atomic gases by the model pseudopotential method.
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 theoretical analysis is made of the resonant interaction between a traveling monochromatic light wave of arbitrary intensity and polarization and the 1/21/2 and 10 transitions in gas atoms in a magnetic field. An analysis is made of the influence of atomic collisions and coherence of the Zeeman sublevels of the terms on the structure of nonlinear magnetooptic resonances in the amplitude and polarization characteristics of the wave. Some features of nonlinear magnetooptic resonances for laser excitation of atoms from the ground state are noted. A study is made of the Faraday rotation and self-rotation of the polarization ellipse of the radiation as a function of the detuning of the wave frequency, the saturation parameter, and the optical density of the gas. The stability of the polarization of light in the medium is discussed. It is noted that these laws may be used to analyze and control the radiation characteristics of lasers and amplifiers when the level of saturation of a resonant gaseous medium in a magnetic field is high.
Theoretical treatment of the magnetoelectric Jones birefringence and dichroism is developed through the bilinearity in static electric and magnetic field dipole-forbidden corrections to the amplitude of Rayleigh scattering. In particular cases of orientation of the static fields relative to the polarization and wave vectors of monochromatic radiation, the amplitude determines corrections to the refractive index of atomic gas responsible for (i) the Jones birefringence and dichroism, (ii) linear birefringence and dichroism and (iii) directional anisotropy for the monochromatic wave. The analytical equations and numerical data for the indicated corrections, calculated for alkaline-earth-like atoms, determine optimal conditions for observing the effects in vapours. For resonance on 1D2 state essential enhancement is discovered in the frequency dependence for the ratio of refractive index anisotropy of the Jones effect to the square-root product of corresponding anisotropies determining the Kerr and Cotton–Mouton effects.
The quantum theory of polarizing light and the Stokes operators are applied to the study of the evolutions of polarization states of light in the processes of i nteraction with atoms in the case with or without Kerr medium. The non_classic b ehavior in the fluctuations of Stokes parameters for the polarizing light and th eir squeezing are investigated. The polarization ellipse, the degree of polariza tion of the field in quantum optics and the signal_to_noise ratio in the Stokes parameters are discussed. It is shown that the modulated oscillations appear in the evolutions of Stokes parameters and their fluctuations. These oscillations c ollapse and revive intermittently. The polarization ellipse does not vary in the interaction with atoms but the degree of polarization will oscillate. Kerr medi um changes these oscillations distinctly.
The propagation of strongly polarized electromagnetic waves through a resonance medium, with arbitrary angular momenta of the levels, is investigated in the adiabatic-following approximation. Exact wavefunctions of the two-level atomic system with degenerate levels in the field of a circularly (linearly) polarized wave are constructed and the picture of the shift of energy level splittings is discussed. Exact formulae for the nonlinear refractive index of the medium in the field of the circularly (linearly) polarized wave are found. The propagation of counterpropagating polarized waves—an intense pump wave and a probe light signal—through the resonance medium is studied. The studies are carried out in the scope of a two-level (one-photon resonance) and a three-level (one- and two-photon resonances) medium. Formulae are found for the induced rotation of the plane of polarization for the probing signal that are exact in terms of the intensity of the pump wave. The spectral dependence of the angle of rotation is studied, and it is shown that a series of Stark-shifted resonance poles of atomic absorption and a three-photon scattering process arise.
A phenomenological analysis of the nonlinear susceptibility tensor of an isotropic medium is used to show the possibility of existence of nonreciprocal effects in the course of propagation of arbitrarily polarized opposite waves of the same intensity and frequency. A system for producing amplitude and phase nonreciprocal effects is discussed. The dependence of the effects on the polarizations (ellipticities and azimuths) and on the coefficients of nonlinear interaction between the opposite waves is analyzed for small amplitude and phase changes.