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Phase Conjugation Progress in Ensemble of Double-Lambda Atoms

Rozhdestvensky, Yury

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

Recently experiments on investigation of four wave mixing in sodium vapor cell have been performed by group of Dr P. Hemmer. It has been shown in these experiments that generation of a phase-conjugate wave takes place at large detuning of a pumping wave from the resonant transition in a double Lambda system of atomic levels only (so called case of Raman interaction). Moreover, the experiments demonstrated high efficiency of such Raman interaction for generation of the conjugate wave with low intensities of the exciting waves that indicates realization of new type of Raman laser. The aim of our work is theoretical analysis and numerical simulation of the experiment on the basis of exact solution of self-consistent system of Maxwell-Bloch equations. The atom-field interaction scheme is shown in the report. A peculiarity of this scheme is that the same pumping wave interacts with both transitions 1 ---> 3 and 2 ---> 4 simultaneously.

Related papers

Phase Conjugation via Four-Wave Mixing in a Resonant Medium

Joseph Nilsen

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.

•Jan 1, 1982•0 citations

Bloch vector model of Raman coupled system

Christopher C. Gerry

I study the coherent interaction of a three-level atom in the lambda configuration with pump, Stoke, and anti-Stokes laser fields. The pump laser field drives transitions from the two non-degenerate lower levels to the excited state which is highly detuned for either transition. This excited state is also coupled to each of the lower states by Stokes or anti-Stokes transitions so that this system may represent a model of four-wave mixing. Assuming large detunings, the excited state is adiabatically eliminated from obtaining an effective two-level system with Raman coupling between the levels. Optical Bloch equations are obtained for this effective two-level system, and phenomenological damping terms are added for collisional dephasing of the Raman transitions. The equations are solved for the steady-state as well as by the method of adiabatic following. From these solutions we obtain the polarization.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

Self-pumped phase conjugation in sodium vapor

Celestino J. Gaeta, Juan Francisco Lam, R. C. Lind

We have used a two-wave mixing gain process in sodium vapor to construct a self-pumped phase conjugator. This was done by forming a resonator around a quartz sodium cell equipped with Brewster angle windows. A pump beam is then directed into the sodium cell at a small angle to the longitudinal axis of the resonator. At sufficiently high cw pump intensities, the ac-Stark effect pro- vides sufficient gain to achieve oscillation. Although this gain is unidirectional it occurs on the wings of the sodium resonance so that the backward traveling optical field in the resonator does not experience loss due to sodium absorption. The counterpropagating optical fields in the resonator interact with the pump in an internal four- wave mixing process to produce a fourth optical field (phase conjugate to the pump field). Our experiment was conducted at the sodium D2 resonance. The pump laser was a 699 autoscan single frequency ring dye laser providing pump intensities up to several hundred watts per square centimeter.

Annual Meeting Optical Society of America•Jan 1, 1988•1 citation

Optical phase conjugation with a sodium Raman laser

Joanne DiFrancisco‐Donoghue, Jonathan S. Kane, Philip Hemmer

Recently, there has been increased interest in the use of resonant atomic systems for performing optical-wavefront conjugation. This interest has arisen because resonant systems are inherently fast, with response times in the nanosecond range. However, resonant systems tend to have lower efficiencies and greater optical power requirements than do photorefractive crystals, such as BaTiO3. In this paper, we explore the possibility of using a highly efficient Raman laser1 in a sodium-vapor cell to obtain efficient phase conjugation at greatly reduced optical power densities. In this demonstration we use a self-pumped (linear-cavity) conjugator for simplicity. With this setup, we have achieved phase- conjugate reflectivities of 2% with input powers of only 20 W/cm2. This is only 2% of the optical power density previously reported2 to obtain comparable reflectivity with a self-pumped scheme in sodium vapor.

Quantum Electronics and Laser Science Conference•May 12, 1991•0 citations

Phase conjugation by nondegenerate four-wave mixing with excited-state Zeeman coherences

Ragini Saxena, G. S. Agarwal

Nondegenerate four-wave mixing on the j=0\ensuremath{\rightarrow}j=1 transition, in a ``V '' system, using orthogonal, circularly polarized pump beams is used to study theoretically the generation of the phase-conjugate signals. The efficiency of generation of the conjugate wave is studied as a function of the various system parameters such as pump-probe detuning, Zeeman splitting, pump-atom detuning, collisional parameters, and the intensities of the pump beams. The origin of the various resonances in the reflectivity is explained. For weak pump fields, some resonances are shown to have subnatural linewidths. In the degenerate case, the reflectivity as a function of pump-atom detuning has, in contrast to a two-level system, a doublet structure for moderate absorption-length parameters and field strengths. The reflectivity is shown to have additional resonances due to pump imbalance. The phase-conjugate signal is also shown to exhibit the pressure-induced extra resonances.

Physical Review A•Feb 1, 1985•7 citations

High-gain optical phase conjugation using degenerate four-wave mixing via coherent population trapping in moving atoms

X. Xia, D. S. Hsiung, M. S. Shahriar +2 more

Summary form only given. Previously, we have used four-wave mixing via coherent population trapping to achieve optical phase conjugation (OPC) with high gain, using two dye lasers and a sodium vapor cell. The /spl Lambda/ transition used involved the two hyperfine ground states and one excited state, so that two different optical frequencies were needed to satisfy the two-photon resonant condition between the probe and one of the pump beams. Later, we demonstrated in rubidium that a single hyperfine transition with Zeeman sublevels is enough to achieve OPC with equally high gain, thus eliminating the need for high-frequency sideband generation. However, in order to guarantee that the diffraction from the grating is primarily dispersive, the backward pump beam had to be detuned by about 60 MHz from the probe and the forward pump. One of the key disadvantages of such a nondegenerate scheme is that applications such as phase-conjugate mirrors are hard to implement. Here, we report the observation of optical phase conjugation in rubidium with equally high gain, but all the frequencies are degenerate.

Conference on Lasers and Electro-Optics•Jan 1, 1998•1 citation
Recently experiments on investigation of four wave mixing in sodium vapor cell have been performed by group of Dr P. Hemmer. It has been shown in these experiments that generation of a phase-conjugate wave takes place at large detuning of a pumping wave from the resonant transition in a double Lambda system of atomic levels only (so called case of Raman interaction). Moreover, the experiments demonstrated high efficiency of such Raman interaction for generation of the conjugate wave with low intensities of the exciting waves that indicates realization of new type of Raman laser. The aim of our work is theoretical analysis and numerical simulation of the experiment on the basis of exact solution of self-consistent system of Maxwell-Bloch equations. The atom-field interaction scheme is shown in the report. A peculiarity of this scheme is that the same pumping wave interacts with both transitions 1 ---> 3 and 2 ---> 4 simultaneously.
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.
I study the coherent interaction of a three-level atom in the lambda configuration with pump, Stoke, and anti-Stokes laser fields. The pump laser field drives transitions from the two non-degenerate lower levels to the excited state which is highly detuned for either transition. This excited state is also coupled to each of the lower states by Stokes or anti-Stokes transitions so that this system may represent a model of four-wave mixing. Assuming large detunings, the excited state is adiabatically eliminated from obtaining an effective two-level system with Raman coupling between the levels. Optical Bloch equations are obtained for this effective two-level system, and phenomenological damping terms are added for collisional dephasing of the Raman transitions. The equations are solved for the steady-state as well as by the method of adiabatic following. From these solutions we obtain the polarization.
We have used a two-wave mixing gain process in sodium vapor to construct a self-pumped phase conjugator. This was done by forming a resonator around a quartz sodium cell equipped with Brewster angle windows. A pump beam is then directed into the sodium cell at a small angle to the longitudinal axis of the resonator. At sufficiently high cw pump intensities, the ac-Stark effect pro- vides sufficient gain to achieve oscillation. Although this gain is unidirectional it occurs on the wings of the sodium resonance so that the backward traveling optical field in the resonator does not experience loss due to sodium absorption. The counterpropagating optical fields in the resonator interact with the pump in an internal four- wave mixing process to produce a fourth optical field (phase conjugate to the pump field). Our experiment was conducted at the sodium D2 resonance. The pump laser was a 699 autoscan single frequency ring dye laser providing pump intensities up to several hundred watts per square centimeter.
Recently, there has been increased interest in the use of resonant atomic systems for performing optical-wavefront conjugation. This interest has arisen because resonant systems are inherently fast, with response times in the nanosecond range. However, resonant systems tend to have lower efficiencies and greater optical power requirements than do photorefractive crystals, such as BaTiO3. In this paper, we explore the possibility of using a highly efficient Raman laser1 in a sodium-vapor cell to obtain efficient phase conjugation at greatly reduced optical power densities. In this demonstration we use a self-pumped (linear-cavity) conjugator for simplicity. With this setup, we have achieved phase- conjugate reflectivities of 2% with input powers of only 20 W/cm2. This is only 2% of the optical power density previously reported2 to obtain comparable reflectivity with a self-pumped scheme in sodium vapor.
Nondegenerate four-wave mixing on the j=0\ensuremath{\rightarrow}j=1 transition, in a ``V '' system, using orthogonal, circularly polarized pump beams is used to study theoretically the generation of the phase-conjugate signals. The efficiency of generation of the conjugate wave is studied as a function of the various system parameters such as pump-probe detuning, Zeeman splitting, pump-atom detuning, collisional parameters, and the intensities of the pump beams. The origin of the various resonances in the reflectivity is explained. For weak pump fields, some resonances are shown to have subnatural linewidths. In the degenerate case, the reflectivity as a function of pump-atom detuning has, in contrast to a two-level system, a doublet structure for moderate absorption-length parameters and field strengths. The reflectivity is shown to have additional resonances due to pump imbalance. The phase-conjugate signal is also shown to exhibit the pressure-induced extra resonances.
Summary form only given. Previously, we have used four-wave mixing via coherent population trapping to achieve optical phase conjugation (OPC) with high gain, using two dye lasers and a sodium vapor cell. The /spl Lambda/ transition used involved the two hyperfine ground states and one excited state, so that two different optical frequencies were needed to satisfy the two-photon resonant condition between the probe and one of the pump beams. Later, we demonstrated in rubidium that a single hyperfine transition with Zeeman sublevels is enough to achieve OPC with equally high gain, thus eliminating the need for high-frequency sideband generation. However, in order to guarantee that the diffraction from the grating is primarily dispersive, the backward pump beam had to be detuned by about 60 MHz from the probe and the forward pump. One of the key disadvantages of such a nondegenerate scheme is that applications such as phase-conjugate mirrors are hard to implement. Here, we report the observation of optical phase conjugation in rubidium with equally high gain, but all the frequencies are degenerate.