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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Propagation of two counter waves in ensemble of three-level Λ- and V-systems

Julia V. Bogdanova

Published Jan 12, 2004• 0 citations
Publisher

Abstract

To model the signals of magnetic and frequency scanning of the rarefied gas, the problem of resonant interaction of two monochromatic waves and particles with active transition J = 0↔J = 1 in stationary magnetic field is solved by method of density matrix. The resonance with the sign depending on gas pressure, waves’ intensity and magnetic field strength was found for the system with a split ground state. Solution of wave equations for slow amplitudes.

DOI
10.1117/12.545695

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To model the signals of magnetic and frequency scanning of the rarefied gas, the problem of resonant interaction of two monochromatic waves and particles with active transition J = 0↔J = 1 in stationary magnetic field is solved by method of density matrix. The resonance with the sign depending on gas pressure, waves’ intensity and magnetic field strength was found for the system with a split ground state. Solution of wave equations for slow amplitudes.
Summary form only given. Results are presented of theoretical studies into the resonances of the saturated absorption and saturated dispersion in an external absorption cell. The theory has been worked out by means of combining methods of mathematical theory of diffraction and quantum mechanical method for computing the polarization of active media. This made it possible for the first time to find a self-consisting spatial solution of the density matrix equation for the two-level system and the Helmholtz equation for electromagnetic field and to solve the problem of propagation of two counterpropagating monochromatic waves though an absorbing nonlinear medium taking into consideration the transverse transit-time effect.
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.
A theoretical investigation is carried out through the interaction of the plane running monochromatic light wave, having an arbitrary intensity, with atoms (molecules) of a rarefied gas in the plane cell (at the normal incidence of the wave). Cases of closed and open resonance transitions from the non-degenerate ground (or metastable) quantum level are considered. Possible sub-Doppler resonances are analysed in the wave absorption, caused by the transient establishment of the optical coherence on the transition, Rabi oscillations between its levels, and optical pumping during the free flights of particles between the walls of the cell. Results of the previous works on given problems are generalized, which were obtained at definite restrictions on the wave intensity and cell length. Moreover, non-trivial sub-Doppler spectral structures, resulting as a consequence of the dependence of the absorption saturation on the transit relaxation of particles, have been established and investigated. Such structures may consist of a number of peaks and dips caused by Rabi oscillations between the transition levels. The results obtained can be used in sub-Doppler spectroscopy and for the stabilization of laser frequencies in thin gas cells.
The effect of collisions on the resonance fluorescence spectrum of three-level atoms with a V-configuration of levels when excited by two monochromatic resonance fields has been theoretically investigated. The analysis has been carried out for the systems with a small Doppler broadening compared to the collision frequency (high buffer gas pressures) and for the general case of an arbitrary change (from complete failure to complete preservation) of the phase memory at any of the three transitions in the V-system. It has been shown that in the three-level V-type atoms excited by two monochromatic fields, the resonant fluorescence spectrum (the number of spectral lines and their widths) at one of the transitions strongly depends on the presence of resonant radiation at the adjacent transition. Under certain conditions, the line widths will be completely determined by the relaxation characteristics of the adjacent transition and, in particular, can be repeatedly narrowed with an increase in the radiation intensity at the adjacent transition. It has been shown that despite the homogeneous nature of the broadening of the absorption lines, the resonance fluorescence spectrum has a pronounced anisotropy with respect to the mutual orientation of the wave vectors of spontaneous and exciting radiation. It has been established that the line widths in the resonance fluorescence spectrum are proportional to the diffusion coefficient of the atoms interacting with radiation under certain conditions. This fact can serve as the basis for a spectroscopic method for measuring the transport frequencies of the collisions of the radiation-absorbing particles with the buffer ones. It has been shown that the effects of phase memory in the collisions lead to a strong qualitative and quantitative modification of the resonance fluorescence spectrum.
The effect of a force of resonance pressure of light on the amplitude and frequency properties of saturated-absorption resonance in a gas of two-level atoms was studied. On the basis of numerical solutions of the Liouville and Fokker-Planck equations, dynamics of changes in the velocity-distribution function of an ensemble of atomic particles, depending on the saturation parameter and time of their interaction with a strong field of light, was evaluated. The shape of a resonance line, related to saturated absorption, and its location relative to the frequency of the atomic transition were determined taking into account the dynamics of the distribution function. The results of the calculations are compared with the experimental data.
In the intense radiation fields with power density from 104W/cm2 to 109W/cm2 the essential modification of electronic states of atoms occurs displaying, in particular, in modifications of resonant fluorescence (rf) spectra. We use 'Fermi golden rule' for calculations of relative intensities and frequencies for rf multiplet for real multilevel initially unexcited atoms in two monochromatic laser fields of arbitrary intensity resonant to adjacent transitions of (Xi) or (Lambda) types and magnetic field, giving the level splittings of different values from Zeeman to Paschen-Back effect. The dependence of quasienergies on parameters obtained with the help of a sorting program permits us to define the values of parameters for which the states of the system are mixed and so to receive the correct probability amplitudes for instantaneous or adiabatic regimes of switching the perturbation. The analysis of the quasienergies and form of rf spectra permits us to get relations between the form of the spectra and modifications of electronic structure of the atom due to radiation fields and external magnetic field.