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Theoretical studies of Resonance Enhanced Stimulated Raman Scattering (RESRS) of frequency doubled Alexandrite laser wavelengths in cesium vapor

N. M. Lawandy

Published Jan 14, 1986• 0 citations
OpenAlex

Abstract

This work focused on understanding the effects of arbitrary transverse and longitudinal relaxation rates on the susceptibilities of coherently driven three-level systems. The approximation of a single relaxation rate often made in previous work is strongly invalidated by the variation in the spontaneous emission lifetime between various atomic level pairs in systems such as cesium. It is of great importance to the problem of nonlinear infrared generation to determine the dependence of both real and imaginary susceptibility on relaxation rates. The imaginary susceptibility on the pump transition determines the absorption of pump photons and the imaginary susceptibility on the laser transition determines the spectral dependence of the gain. This is of particular importance for pure Raman emission (i.e., absorption at linecenter of the gain transition) as it determines the tunability characteristics we are aiming to predict. The real susceptibility is important when cavities are used at the signal field as this will determine the loaded resonance of the Raman oscillator. Researchers show that in some cases which result from having different relaxation rates mode splitting may result, allowing more than one frequency to have the same Raman wavelength, possibly resulting in a temporal instability.

Related papers

Theoretical studies of Resonance Enhance Stimulated Raman Scattering (RESRS) of frequency doubled Alexandrite laser wavelengths in cesium vapor

N. M. Lawandy

It is well known that the presence of a real atomic level which is nearly resonant with the pump field can greatly enhance the Raman emission cross section. In order to accurately calculate the Raman gain in systems where resonance enhancement plays a dominant role, expressions for the pump and signal susceptibilities must be derived. These expressions should be valid for arbitrary field strengths in order to allow for pump and signal saturation. In addition, the theory should allow for arbitrary longitudinal and transverse relaxation rates. This latter point is extremely vital for three level atomic systems such as the alkali earth metals since they do not have population reservoirs and can have widely varying spontaneous lifetimes on the three pertinent transitions. Moreover, the dephasing rates are strong functions of electron states and are therefore also different for the three coupled pairs of levels. These considerations are not as important when molecular systems are concerned since the large reservoir of rotational states serve to produce essentially equal longitudinal recovery rates for the population of the three levels. The three level system with three arbitrary longitudinal and transverse relaxation rates was solved. There is no need for setting either pair of rates equal and the expressions are valid for arbitrarily strong fields.

•Jan 1, 1986•0 citations

Nonlinear infrared generation in alkali metal vapors: Steady state susceptibilities and dynamic behavior. Effective relaxation rates and preliminary Raman gain predictions for the Cs system

N. M. Lawandy

Effective relaxation rates for atomic cesium pumped by doubled Alexandrite radiation are presented. Laser radiation levels are 8S 1/2 and 9S 1/2; resonance levels 3 = 8P 1/2 and 8P 1/2, respectively. In addition, Raman gain is represented in two graphs which plot chi per atom (10 to the -13 power) at Raman peak versus the infrared wave number per centimeter and the corresponding doubled Alexandrite wave number. One graph covers resonance level 8P, the other 9P; in both cases cesium is pumped with a peak pulse height of 0.5 MW in a 200 micron diameter spot size.

•Dec 18, 1986•0 citations

Effect of the pump absorption on generation of infrared stimulated electronic Raman scattering in alkali-metal vapors

A. I. Agafonov, G. G. Grigoryan, Nikolay V Znamenskiy +5 more

The main properties of infrared stimulated electronic Raman scattering (SERS) at the 6 2 S 1/2 -7 2 S 1/2, 3/2 transitions in cesium atoms are studied theoretically and experimentally as functions of the atomic concentration, which was varied from 10 11 to 10 16 cm −3 . It is found that the efficiency of generation of Stokes radiation strongly depends on one-photon absorption of the pump radiation tuned near frequencies of the 6 2 S 1/2 -7 2 P 1/2, 3/2 transitions. By using the equation for the density matrix, which describes the evolution of a three-level system, the theory of resonance excitation of IR radiation upon one-photon absorption at an adjacent transition is developed. The theory describes well the main features of IR SERS in alkali-metal vapors.

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Four-wave processes in cesium vapor involving electronic stimulated Raman scattering

A. K. Popov, V.P. Ran'shikov, V. P. Timofeev +2 more

Experimental and theoretical investigations were made of four-wave frequency mixing of the ?4? = ?1 ? ?2 ? ?3 type in cesium vapor enhanced by a Raman resonance (the field at the frequency ?2 is formed as a result of electronic stimulated Raman scattering of the pump field ?1). A strong dependence of the mixing characteristics on the conditions for excitation of electronic stimulated Raman scattering was identified and analyzed. Recommendations are given on the choice of optimal conditions for efficient frequency mixing in Raman resonance systems.

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Suppression and shifting of odd-photon resonant excitations and stimulated hyper-Raman emissions

W. R. Garrett, M. G. Payne

When a principal atomic transition (dipole allowed from the ground state) is driven by odd- multi-photon excitation or by stimulated hyper-Raman scattering, a nonlinear multi-wave mixing field is generated at the transition frequency. A number of dramatic effects on such odd-photon mediated processes can ensue as a result of the internally generated wave-mixing fields. Excellent agreement between theory and experimental studies in Xe and in metal vapors is illustrated for a number of predicted effects including: suppression and strong shifting of resonance lines and hyper-Raman emissions under single and multi-laser excitation. We illustrate the dependence of the interference-related effects on pressure, oscillator strength, wavelength combination and relative propagation directions of pump laser beams. Contrary to most other nonlinear effects, we show that none of the features (in the semi-classical regime) depends on the intensity of the driving laser field.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 1, 1992•0 citations

Theory of Optical Frequency Mixing Using Resonant Phenomena

Ali Javan, A. Szöke

The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by $\frac{\mathrm{rN}}{T}$, where $N$ is the total number of atoms, $T$ is the average time of coherent interaction of atoms and the radiation field, and $r$ is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.

Physical Review•Jan 18, 1965•15 citations
This work focused on understanding the effects of arbitrary transverse and longitudinal relaxation rates on the susceptibilities of coherently driven three-level systems. The approximation of a single relaxation rate often made in previous work is strongly invalidated by the variation in the spontaneous emission lifetime between various atomic level pairs in systems such as cesium. It is of great importance to the problem of nonlinear infrared generation to determine the dependence of both real and imaginary susceptibility on relaxation rates. The imaginary susceptibility on the pump transition determines the absorption of pump photons and the imaginary susceptibility on the laser transition determines the spectral dependence of the gain. This is of particular importance for pure Raman emission (i.e., absorption at linecenter of the gain transition) as it determines the tunability characteristics we are aiming to predict. The real susceptibility is important when cavities are used at the signal field as this will determine the loaded resonance of the Raman oscillator. Researchers show that in some cases which result from having different relaxation rates mode splitting may result, allowing more than one frequency to have the same Raman wavelength, possibly resulting in a temporal instability.
It is well known that the presence of a real atomic level which is nearly resonant with the pump field can greatly enhance the Raman emission cross section. In order to accurately calculate the Raman gain in systems where resonance enhancement plays a dominant role, expressions for the pump and signal susceptibilities must be derived. These expressions should be valid for arbitrary field strengths in order to allow for pump and signal saturation. In addition, the theory should allow for arbitrary longitudinal and transverse relaxation rates. This latter point is extremely vital for three level atomic systems such as the alkali earth metals since they do not have population reservoirs and can have widely varying spontaneous lifetimes on the three pertinent transitions. Moreover, the dephasing rates are strong functions of electron states and are therefore also different for the three coupled pairs of levels. These considerations are not as important when molecular systems are concerned since the large reservoir of rotational states serve to produce essentially equal longitudinal recovery rates for the population of the three levels. The three level system with three arbitrary longitudinal and transverse relaxation rates was solved. There is no need for setting either pair of rates equal and the expressions are valid for arbitrarily strong fields.
Effective relaxation rates for atomic cesium pumped by doubled Alexandrite radiation are presented. Laser radiation levels are 8S 1/2 and 9S 1/2; resonance levels 3 = 8P 1/2 and 8P 1/2, respectively. In addition, Raman gain is represented in two graphs which plot chi per atom (10 to the -13 power) at Raman peak versus the infrared wave number per centimeter and the corresponding doubled Alexandrite wave number. One graph covers resonance level 8P, the other 9P; in both cases cesium is pumped with a peak pulse height of 0.5 MW in a 200 micron diameter spot size.
The main properties of infrared stimulated electronic Raman scattering (SERS) at the 6 2 S 1/2 -7 2 S 1/2, 3/2 transitions in cesium atoms are studied theoretically and experimentally as functions of the atomic concentration, which was varied from 10 11 to 10 16 cm −3 . It is found that the efficiency of generation of Stokes radiation strongly depends on one-photon absorption of the pump radiation tuned near frequencies of the 6 2 S 1/2 -7 2 P 1/2, 3/2 transitions. By using the equation for the density matrix, which describes the evolution of a three-level system, the theory of resonance excitation of IR radiation upon one-photon absorption at an adjacent transition is developed. The theory describes well the main features of IR SERS in alkali-metal vapors.
Experimental and theoretical investigations were made of four-wave frequency mixing of the ?4? = ?1 ? ?2 ? ?3 type in cesium vapor enhanced by a Raman resonance (the field at the frequency ?2 is formed as a result of electronic stimulated Raman scattering of the pump field ?1). A strong dependence of the mixing characteristics on the conditions for excitation of electronic stimulated Raman scattering was identified and analyzed. Recommendations are given on the choice of optimal conditions for efficient frequency mixing in Raman resonance systems.
When a principal atomic transition (dipole allowed from the ground state) is driven by odd- multi-photon excitation or by stimulated hyper-Raman scattering, a nonlinear multi-wave mixing field is generated at the transition frequency. A number of dramatic effects on such odd-photon mediated processes can ensue as a result of the internally generated wave-mixing fields. Excellent agreement between theory and experimental studies in Xe and in metal vapors is illustrated for a number of predicted effects including: suppression and strong shifting of resonance lines and hyper-Raman emissions under single and multi-laser excitation. We illustrate the dependence of the interference-related effects on pressure, oscillator strength, wavelength combination and relative propagation directions of pump laser beams. Contrary to most other nonlinear effects, we show that none of the features (in the semi-classical regime) depends on the intensity of the driving laser field.
The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by rNT\frac{\mathrm{rN}}{T}TrN​, where NNN is the total number of atoms, TTT is the average time of coherent interaction of atoms and the radiation field, and rrr is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.