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Journal of Physics B Atomic and Molecular Physics

Modification of radiation polarisation due to propagation in a resonant medium

G. G. Adonts, D G Akopyan, K V Arutunyan

Published Dec 28, 1986• 9 citations
Publisher

Abstract

The optical-pumping theory of the passage of polarised radiation through a resonant medium was developed in the irreducible tensorial formalism. Transitions with arbitrary momenta J 1.2 are considered in the cubic approximation. For transitions with small values of momenta (J 1 =1 to J 2 =0; J 1 = 1 / 2 to J 2 = 1 / 2 ) the vector form of the equation system in density-matrix notation allows the problem to be solved exactly for light intensity. In the general case of an elliptically polarised wave, the equation systems for the interaction between circular components of polarisation of light in a resonant medium are obtained. Numerical calculations for deformation and rotation of the polarisation ellipse in a medium subject to saturation effects are also carried out. Irrespective of the initial state the polarisation tends either to a linear or to a circular form as it propagates, depending on times of collisional relaxation of orientation and alignment. The polarisation of linearly and circularly polarised waves does not change as the waves propagate, but the values of the saturation power for these polarisations differ considerably.

DOI
10.1088/0022-3700/19/24/013

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Journal of Modern Optics•Mar 1, 1988•0 citations
The optical-pumping theory of the passage of polarised radiation through a resonant medium was developed in the irreducible tensorial formalism. Transitions with arbitrary momenta J 1.2 are considered in the cubic approximation. For transitions with small values of momenta (J 1 =1 to J 2 =0; J 1 = 1 / 2 to J 2 = 1 / 2 ) the vector form of the equation system in density-matrix notation allows the problem to be solved exactly for light intensity. In the general case of an elliptically polarised wave, the equation systems for the interaction between circular components of polarisation of light in a resonant medium are obtained. Numerical calculations for deformation and rotation of the polarisation ellipse in a medium subject to saturation effects are also carried out. Irrespective of the initial state the polarisation tends either to a linear or to a circular form as it propagates, depending on times of collisional relaxation of orientation and alignment. The polarisation of linearly and circularly polarised waves does not change as the waves propagate, but the values of the saturation power for these polarisations differ considerably.
The problem of the interaction of radiation with arbitrary polarisation and intensity with the resonance transitions 1/2-1/2 and 1-0 is solved. Exact expressions for the orientation vectors of the ground and excited states for the transition 1/2-1/2 and for the orientation vector and alignment tensor of the transition 1-0 have been obtained. In the case of longitudinal propagation the system of equations for the absorption of an elliptically polarised wave is obtained. It is shown that, irrespective of the initial state, the polarisation at the transition 1-0 tends either to the linear or to the circular form as it propagates depending on the times of collisional relaxation of orientation and alignment and on the magnetic field value. In the case of transverse propagation the dependence of the saturation intensity of a linearly polarised wave on the magnetic field value and on relaxation widths is obtained.
The theory of polarised light phase conjugation (PC) in non-degenerate four-wave mixing in a resonant medium has been developed in the irreducible tensorial formalism. The theory is applied to a wave with any polarisation in a resonant medium with levels of arbitrary momentum in the absence of pump-induced saturation effects. The formula for the non-linear susceptibility of the medium has been found and it is shown that the change of the polarisation at PC is essentially connected with the relaxation of the atomic multipole momenta (population, orientation and alignment). Wave equations were investigated for different pump-wave polarisations and three different physical mechanisms of the PC are discussed. The influence of the different relaxation rates of the atomic multipole momenta on the PC reflectivity has been investigated. The spectral dependence of the reflectivity and the spectral ranges which depend on the wave polarisation are found. For motionless atoms with small momenta (J 1 = 1 / 2 to J 2 = 1 / 2 , J 1 =1 to J 2 =0), exact formulae for the non-linear susceptibility of the medium as a function of pump intensity were found. The spontaneous decay of higher level to the lower one was taken into account. Because of optical pumping, saturation effects can be shown at considerably smaller intensities than in the usual two-level system. The exact expressions for the PC reflectivity at different polarisations of the pump waves are given.
The propagation of a strongly polarised electromagnetic wave 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) polarised wave are constructed and the picture of the energetic level splitting and shift is discussed. Exact formulae for the non-linear refractive index of the medium in the field of the circularly (linearly) polarised wave are found. The propagation of counterpropagating polarised 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 pump angle of rotation of the ellipse (plane) of polarisation 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.
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 non-linear optical polarization phenomena in the presence of a DC electric field is developed. The theory is valid in the case of both arbitrary resonance radiation intensity and arbitrary external DC electric field spatial orientation. The intensity-dependent contributions to variation of radiation polarization are analysed in detail in the Doppler limit. Special attention is paid to the case of linear polarization of incident radiation; in this case as well as in the presence of a DC electric field, the Doppler-enhanced non-linear optical contributions determining the emerging ellipticity and the rotation angle of polarization, respectively, are of the same order of magnitude (unlike the case of external magnetic field, in which the key effect is the rotation of polarization). It is shown, however, that in the case of the strictly transverse geometry and if the angle between the electric field direction and the initial polarization vector is equal to 45 degrees , the Doppler-enhanced non-linear optical contribution to the rotation angle becomes anomalously small. The effect of the presence of a longitudinal component of electric field on the non-linear optical polarization phenomena is investigated. In addition, although in the case of a purely longitudinal geometry for the considered transitions the electric field effect on radiation polarization modification is absent, some analytic results concerning self-rotation and deformation of a polarization ellipse in the Doppler limit for an intense initially elliptically polarized radiation are also presented.
Nonstationary polarisation effects in a medium with the Λ-scheme of energy levels with the quantum numbers of the total angular momentum equal to 0, 2, and 1 are numerically simulated. The analysis is performed in the slowly varying envelope approximation taking into account the inhomogeneous broadening of quantum transition lines. It is assumed that the lower-frequency (signal) radiation at the input to a resonance medium is considerably weaker than the higher-frequency (pump) radiation. It is shown that the polarisation of the signal pulse inside the medium is quasi-elliptic in the general case and is independent of the input-pulse polarisation. If the 'area' of the input pump pulse in the absence of signal radiation admits the formation of only one 2π-pulse, then the major axes of polarisation ellipses for the signal inside the medium and input pump radiation are collinear, however, the directions of rotation of the electric field strengths of these radiations are mutually opposite. For higher-power pump pulses, the polarisation structure of the signal pulse in the medium becomes considerably more complicated.
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.