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Journal of Physics B Atomic Molecular and Optical Physics

Modification of a strong resonance radiation polarization in media with Doppler-broadened transitions of 0 to 1 and 1 to 0 types and in the presence of a DC electric field

Sergey V. Fomichev

Published Sep 14, 1995• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/28/17/015

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•Dec 1, 1998•4 citations
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.
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.
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 general nonlinear stationary theory of propagation of an elliptically polarized pulse that resonantly interacts with the 1/2-1/2 transition is developed taking into account relaxation processes. It is shown that interference of magnetic sublevels in the field of polarized radiation that optically pumps atoms results in inversionless amplification of radiation. Taking into account the Doppler broadening of spectral lines shows that there exists a certain optimal length of the resonant medium along which the radiation that emerges from the medium is maximally amplified.
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.
We present the theory of resonant backward degenerate four-wave mixing in gaseous media for Doppler-broadened degenerate two-level systems. The degeneracy of the atomic levels as well as the influence of the polarization of the incident fields are taken into account within the framework of a tensorial formalism. The amplitude, line shape, and polarization of the reemitted phase-conjugate field are calculated up to the third order in the incident fields. The velocity average is performed in the approximation of large Doppler linewidths. One considers in detail the influence of depolarizing relaxation processes and the effects of pump-probe angular separation. In particular, the importance of the residual Doppler effect (shortening of the lifetime of the optically induced gratings by the atomic motion) associated with the pump-probe angle is emphasized. We show that the polarization of the reemitted fields is governed by very simple laws as soon as the residual Doppler effect overcomes the lifetimes of the atomic levels. Phase-conjugate mirrors can be simply characterized by a linear dichroism (parallel pump polarizations) or a birefringence (cross-polarized pumps). Vectorial phase conjugation is also analyzed, in the case of counter-rotating circular polarizations of the pumps. Finally, the case of two-photon transition is studied and compared with the case of a resonant transition.
Under the light of recent developments of the theory of matter-radiation interaction in the presence of magnetic field applied to non-LTE spectropolarimetry in astrophysics, we have revisited the theory of anisotropic resonance line scattering in moving media by means of the density-matrix formulation. This has led us to present a theoretical method of determination of the matter velocity field vector in the solar wind acceleration region. The example of the O Vi 103.2 nm line has been chosen for putting this theory into operation. It has been observed by the ultraviolet spectrograph \textsc{Sumer} of \textsc{Soho} in different regions of the solar wind acceleration region; it is partially formed by resonance scattering of the incident underlying transition region radiation which competes (and can predominate) with electron collisional excitation at the low densities which prevail at these high altitudes. The theory which is developed hereafter not only shows that this line is shifted and its intensity dimmed by the Doppler effect, due to the matter velocity field of the solar wind, but also predicts that it is linearly polarized, owing to the anisotropy of the incident radiation field; its two linear polarization parameters, degree and direction of polarization, are sensitive to the matter velocity field vector. Our results show that the interpretation of polarimetric data, associated to the shift and the Doppler-dimming effect, may offer a method of diagnostic of the complete velocity field vector, provided that the partial anisotropy of the incident radiation field be taken into account. In fact such a diagnostic is currently missing. Yet its interest is crucial to understand various problems in astrophysics, such as stellar winds, and especially the acceleration mechanisms of the solar wind. It is also essential for a dynamical modelling of solar structures.