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Soviet Journal of Quantum Electronics

Investigation of the properties of resonance holograms in a beam of sodium atoms

Igor' S Grigoriev, Vladimir V. Likhanskii, Alexandre F. Semerok, Valerii A Firsov, A. Chankin

Published Oct 31, 1987• 1 citation
Publisher

Abstract

Experimental and theoretical (using a two-level approximation) investigations were made of the properties of resonance holograms (excited-state gratings) created by monochromatic linearly polarized radiation from a cw dye laser in a beam of sodium atoms as a result of the 32P3/2– 32S1/2(F=2) transition. A good qualitative agreement was observed between the theory and experimental results. It was established that the maximum diffraction efficiency was attained when the intensity of the radiation used to form the hologram was of the order of the intensity needed to saturate the transition and the optical thickness of the beam was ~1.1. The sensitivity of the medium was ~1 nJ/cm2 for 1% diffraction efficiency.

DOI
10.1070/qe1987v017n10abeh010782

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•Jan 1, 2016•0 citations
Experimental and theoretical (using a two-level approximation) investigations were made of the properties of resonance holograms (excited-state gratings) created by monochromatic linearly polarized radiation from a cw dye laser in a beam of sodium atoms as a result of the 32P3/2– 32S1/2(F=2) transition. A good qualitative agreement was observed between the theory and experimental results. It was established that the maximum diffraction efficiency was attained when the intensity of the radiation used to form the hologram was of the order of the intensity needed to saturate the transition and the optical thickness of the beam was ~1.1. The sensitivity of the medium was ~1 nJ/cm2 for 1% diffraction efficiency.
The resonant excitation of the sodium D2 transition by laser radiation was investigated experimentally in this thesis. Line polarization measurement of the resonance fluorescence was employed to investigate the excitation process. The sodium atoms, which were collimated in a very narrow beam, were excited by a monochromatic laser beam with the frequency tuned to resonance with the 32S 112(F=2) - 32P312 hyperfine transition. The direction of the laser beam was perpendicular to the atomic beam and the fluorescence photons were detected along a direction perpendicular to both the laser and atomic beams. The experimental measurements were performed to determine the effect due to the variation of the laser intensity and frequency on the line polarization. A theoretical expression of the line polarization as a function of density matrix elements of the upper excited hyperfine sub -states was derived. A full quantum electrodynamic theory was used to derive an atomic operator equation of motion which was needed to calculate atomic operator elements. These elements then yielded the corresponding density matrix elements. The experimental results and the theoretical modelling were in a good agreement. The first experimental results for the line polarization of the highly excited states, 42D512 and 42D312, are also presented. The use of two lasers enabled these highly excited states to be excited. The line polarization of the fluorescence for transitions from the 4D level down to lower states is derived in terms of the density matrix elements of the upper excited states. Two limiting cases for the theoretical predictions of the line polarization are considered.
We have made measurements of the spectrum of resonance fluorescence emitted by sodium atoms in an intense, uniform, monochromatic field. The transition used in the experiment was between the 32S123^{2}S_{\frac{1}{2}}32S21​​ (F=2F=2F=2, mF=2{m}_{F}=2mF​=2) ground state and the 32P323^{2}P_{\frac{3}{2}}32P23​​ (${F}^{\ensuremath{'}}=3$, ${m}_{F}^{\ensuremath{'}}=3$) excited state. A separate light beam, circularly polarized and resonant with this transition, was used to prepare the sodium atoms in the F=2F=2F=2, mF=2{m}_{F}=2mF​=2 magnetic sublevel. This pumping scheme was used to obtain the spectrum for both on- and off-resonance excitations. The measurements are in good agreement with Mollow's calculation. In addition, we describe conditions under which we observed asymmetric spectra similar to those of earlier experiments.
This work presents theoretical and experimental studies of the energy efficiency of multiwave mixing in complex molecular media (dye solutions) exhibiting higher order nonlinearities. There is a great variety of such media, including the resonance ones revealing nonlinearities of higher orders due to the absorption saturation effect and transitions between different excited states of the molecules. However, the majority of previous studies of multiwave mixing have been performed in the resonant medium approximation disregarding the induced anisotropy effect. A new method for enhancement of multiwave mixing in solutions of laser dyes has been proposed and substantiated with the use of lasing as an additional light beam, whose absorption by the molecules in the excited states leads to the formation of thermal dynamic gratings resultant in the improved efficiency of the energy exchange. The theoretical models for the formation of nonlinear dynamic holograms adequately describing the control process over multiwave mixing by an independent light beam, the frequency of which is tuned into the induced absorption band from the molecules in the excited state, have been developed. Polarization multiwave mixing has been realized in Rhodamine-6G dye solution using nonlinearities up to the ninth order inclusive. It has been demonstrated that on orthogonal polarization of the hologram recording waves the diffraction efficiency is lowered by one-two orders, the diffracted wave polarization being dependent on the diffraction order (the polarization plane alignment is identical within the orders of the same evenness).
The potentialities of diffraction methods for wavefront transformations may be considerably widened due to the use of nonlinear recording of dynamic holograms enabling multiwave mixing in media with the fifth and higher order nonlinearities. There is a great variety of such media including the resonant ones for which the presence of higher order nonlinearities is conditioned by the absorption saturation effect and transitions between different excited states of the molecules. However, in the majority of previous studies of multiwave mixing the resonant medium approximation has been used disregarding the induced anisotropy effect. This work presents a theoretical model and experimental studies of the energy efficiency of multiwave mixing in complex molecular media exhibiting higher order nonlinearities, in two cases: when the nonlinear cavity is introduced in the Fabry-Perot interferometer (IFP), and without it. Owing to the use of different combinations of mutually aligning polarizations for interacting waves, one is enabled to determine the contribution into the interaction efficiency by various dynamic gratings and nonlinearity mechanisms. The role of polarization gratings resultant from spatial modulation of the light field polarization state at the orthogonal polarization of the hologram recording waves has been established. Comparisons between the contributions of the above gratings and “normal” gratings recorded by identically polarized light beams into the process of multiwave mixing have demonstrated that the relation of these contributions is dependent on the intensity of interacting waves, and also it has been found that polarization of the diffracted wave is dependent on the diffraction order.
The subject of this thesis is the construction of a stabilized cw dye laser and its use with a sodium atomic beam to gain information about the range of validity of certain atomic radiation theories. By lengthening the laser cavity, cooling the dye solution and adding many other refinements the bandwidth of a single mode cw dye laser was reduced to 3 MHz over a period of ten seconds. The laser was designed so that by the insertion of three uncoated glass etalons single mode tunable operation was achieved. The purpose of stabilizing the dye laser was to be able to perform experiments on the hyperfine structure of sodium at high enough resolution and intensity to see any possible differences in the theoretical predictions of Quantum Electrodynamics, the optical Bloch equations, and Neoclassical Radiation Theory. The traditional method of eliminating Doppler shifting was used, that is a well-collimated thermal atomic beam of sodium was constructed. By crossing the atomic and laser beams at right angles the natural linewidth of 10 MHz was observable with only one or two MHz residual broadening. Two types of experiments were carried out: those studying the absorption spectrum, and those studying the emission spectrum. In the first experiments Lorentzian lineshapes were observed for all applied field strengths. This proved that if the Lamb shift of Neoclassical Theory exists at all it is small compared with 10 MHz for the sodium D lines. Further, the sharply peaked spectrum predicted by Neoclassical Theory for a certain field strength was not observed. The width of the absorption at high field strengths was not in good agreement with either theory. In the second type of experiment the observed emission spectra were in qualitative, but not good quantitative, agreement with Quantum Electrodynamics when the effects of nearby levels were included. The results are in disagreement with a two-level neoclassical treatment, and we have been unable thus far to obtain better agreement in more sophisticated treatments. Undoubtedly a better multi-level calculation is required in all theories since our system is not really two-level. In addition, we have found that a factor of 2 increase in the critical intensity calibration would bring QED into reasonable agreement with most of the experiments. However, we have been unable to establish the origin of such a factor. While these results were not sufficient to finally and absolutely settle the controversy regarding Quantum Electrodynamics and Neoclassical Theory they did provide a great deal of new information. For the first time the dynamic Stark effect was observed near resonance in the optical region with data that could be compared to theory. Also, the measurements of the absorption spectrum were the most complete and among the highest resolution measurements yet obtained by direct optical techniques. And finally, a number of of optical pumping phenomena were observed.