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

The Influence Of Magnetic Field On The Diffraction Efficiency Of Holograms In Resonant Media

Alexander S. Rubanov, R. N. Onoshko, M. R. Kholodok

Published Apr 12, 1990• 0 citations
Publisher

Abstract

The influence of magnetic field on the wave-front conjugation at degenerate four-wave mixing in resonant-absorbing atomic iodine va-pors has been studied theoretically. It is shown that depending on the magnitude and direction of the magnetic field, interacting waves pola-rization, as well as on the interaction length and intensity of pump waves, the conjugation efficiency can both increase and decrease. The greatest increase in the wave-front conjugation efficiency of radia-tion with a frequency corresponding to the line centre F =4- r =3 is attained in a transverse magnetic field with the interacting waves polarization orthogonal to the field.

DOI
10.1117/12.963817

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Applied Physics Letters•Jun 15, 1981•39 citations
The influence of magnetic field on the wave-front conjugation at degenerate four-wave mixing in resonant-absorbing atomic iodine va-pors has been studied theoretically. It is shown that depending on the magnitude and direction of the magnetic field, interacting waves pola-rization, as well as on the interaction length and intensity of pump waves, the conjugation efficiency can both increase and decrease. The greatest increase in the wave-front conjugation efficiency of radia-tion with a frequency corresponding to the line centre F =4- r =3 is attained in a transverse magnetic field with the interacting waves polarization orthogonal to the field.
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.
This thesis describes the theoretical solution and experimental verification of phase conjugation via nondegenerate four-wave mixing in resonant media. The theoretical work models the resonant medium as a two-level atomic system with the lower state of the system being the ground state of the atom. Working initially with an ensemble of stationary atoms, the density matrix equations are solved by third-order perturbation theory in the presence of the four applied electro-magnetic fields which are assumed to be nearly resonant with the atomic transition. Two of the applied fields are assumed to be non-depleted counterpropagating pump waves while the third wave is an incident signal wave. The fourth wave is the phase conjugate wave which is generated by the interaction of the three previous waves with the nonlinear medium. The solution of the density matrix equations gives the local polarization of the atom. The polarization is used in Maxwell's equations as a source term to solve for the propagation and generation of the signal wave and phase conjugate wave through the nonlinear medium. Studying the dependence of the phase conjugate signal on the various parameters such as frequency, we show how an ultrahigh-Q isotropically sensitive optical filter can be constructed using the phase conjugation process. In many cases the pump waves may saturate the resonant medium so we also present another solution to the density matrix equations which is correct to all orders in the amplitude of the pump waves since the third-order solution is correct only to first-order in each of the field amplitudes. In the saturated regime, we predict several new phenomena associated with degenerate four-wave mixing and also describe the ac Stark effect and how it modifies the frequency response of the filtering process. We also show how a narrow bandwidth optical filter with an efficiency greater than unity can be constructed. In many atomic systems the atoms are moving at significant velocities such that the Doppler linewidth of the system is larger than the homogeneous linewidth. The latter linewidth dominates the response of the ensemble of stationary atoms. To better understand this case the density matrix equations are solved to third-order by perturbation theory for an atom of velocity v. The solution for the polarization is then integrated over the velocity distribution of the macroscopic system which is assumed to be a gaussian distribution of velocities since that is an excellent model of many real systems. Using the Doppler broadened system, we explain how a tunable optical filter can be constructed whose bandwidth is limited by the homogeneous linewidth of the atom while the tuning range of the filter extends over the entire Doppler profile. Since it is a resonant system, sodium vapor is used as the nonlinear medium in our experiments. The relevant properties of sodium are discussed in great detail. In particular, the wavefunctions of the 3S and 3P states are analyzed and a discussion of how the 3S-3P transition models a two-level system is given. Using sodium as the nonlinear medium we demonstrate an ultrahigh-Q optical filter using phase conjugation via nondegenerate four-wave mixing as the filtering process. The filter has a FWHM bandwidth of 41 MHz and a maximum efficiency of 4 x 10-3. However, our theoretical work and other experimental work with sodium suggest that an efficient filter with both gain and a narrower bandwidth should be quite feasible.
A theoretical analysis is made of the efficiency of wavefront reversal under conditions of a degenerate form of the four-wave interaction in a resonantly absorbing (amplifying) medium allowing for changes in the pump waves as a result of their natural resonant absorption (amplification). The coefficient of reflection into a reversed wave is obtained as a function of the optical thickness of a layer of the medium, the boundary values of the pump wave intensity, and the shift of the field frequency from the line center. The optimal values of these parameters and the corresponding maximum reflection coefficient are determined.
Phase conjugation of backward-and forward-wave produced by degenerate four-wave mixing using a nearly resonantly enhanced nonlinearity in four-level organic dye solutions was investigated. The conversion efficiency of 22% had been obtained in a 2.5 X 10-5 - molar solution of Chlorophyll A in methylalcohol with a 5 mm interaction length and a pumping energy of ～ 8 mJ from SH of a Q-switched Nd: YAG. Degene-rate four-wave mixing by two-photon resonant-enhancement in the solution of rhodamine 6G in alcohol was studied. Measurements were performed which described the dependence of nonlinear reflectivities on the molar concentrations of the media and the intensities of the pumping and object waves. Phase conjugation characteristics of forward-wave in four-wave mixing process were theoretically analysed. Experiments have cofirmed the theoretical prediction. The method of quartet degenerate four-wave mixing had been ex-tended to the doublet degenerate case. Using this method image conversion from 1.06 μm to 5320 ? had been realized with a conversion efficiency of 25% in a 5 mm long satu-rable absorber made of organic dye 9740 solution in dichloroethane. Theoretical analy-sis showed that using a medium, which is a near resonant absorber for the infrared object wave but is transparent for the visible reconstruction wave, the conversion efficiency may be well in excess of unity.
Phase conjugation of backward-and forward-wave produced by degenerate four-wave mixing using a nearly resonantly enhanced nonlinearity in four-level organic dye solutions was investigated. The conversion efficiency of 22% had been obtained in a 2.5 X 10-5 - molar solution of Chlorophyll A in methylalcohol with a 5 mm interaction length and a pumping energy of ～ 8 mJ from SH of a Q-switched Nd: YAG. Degene-rate four-wave mixing by two-photon resonant-enhancement in the solution of rhodamine 6G in alcohol was studied. Measurements were performed which described the dependence of nonlinear reflectivities on the molar concentrations of the media and the intensities of the pumping and object waves. Phase conjugation characteristics of forward-wave in four-wave mixing process were theoretically analysed. Experiments have cofirmed the theoretical prediction. The method of quartet degenerate four-wave mixing had been ex-tended to the doublet degenerate case. Using this method image conversion from 1.06 μm to 5320 ? had been realized with a conversion efficiency of 25% in a 5 mm long satu-rable absorber made of organic dye 9740 solution in dichloroethane. Theoretical analy-sis showed that using a medium, which is a near resonant absorber for the infrared object wave but is transparent for the visible reconstruction wave, the conversion efficiency may be well in excess of unity.
We present a study of atomic coherence effects in resonant degenerate four-wave mixing. We find for energy levels having magnetic degeneracies, the third-order nonlinear response resulting from two counterpropagating pump waves orthogonally polarized to an incident probe wave generates a signal whose polarization is phase conjugate to that of the incident probe wave. This effect is due to the coupling of different magnetic states resulting from coherent excitation giving rise to a net electric quadrupole. Experimental studies in Na on the D2 line at 5890 Å confirm the analysis.