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Physical Review Letters

Saturation of Two-Photon-Resonant Optical Processes in Cesium Vapor

John Francis Ward, A. V. Smith

Published Sep 8, 1975• 75 citations
Publisher

Abstract

We report observations of saturation of two-photon-resonant third-harmonic generation and of fluorescence following two-photon absorption in cesium vapor. Weakening dependence of these processes on fundamental power and broadening of the resonance line with increased fundamental power are both seen. It is shown that hole burning is important in a certain power range with the resonance becoming predominantly homogeneously broadened at higher power levels.

DOI
10.1103/physrevlett.35.653

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Physical Review A•May 1, 1974•14 citations
We report observations of saturation of two-photon-resonant third-harmonic generation and of fluorescence following two-photon absorption in cesium vapor. Weakening dependence of these processes on fundamental power and broadening of the resonance line with increased fundamental power are both seen. It is shown that hole burning is important in a certain power range with the resonance becoming predominantly homogeneously broadened at higher power levels.
Resonant enhancement of optical third-harmonic generation in cesium vapor has been observed when twice the energy of the fundamental photon becomes equal to the energy difference between the 9d2D329d^{2}D_{\frac{3}{2}}9d2D23​​ level and the ground state of the cesium atom. The measured, effective coefficient is ${10}^{\ensuremath{-}30}$ esu/atom, which is more than a factor 108{10}^{8}108 larger than the corresponding coefficient for the helium atom. An effective coefficient is synthesized by first calculating the coefficient for a single cesium atom at rest and then including the effects of Doppler broadening and the fundamental laser spectrum. The calculated value is in satisfactory agreement with experiment.
We have investigated three resonant nonlinear processes in atomic cesium vapor. They are third harmonic generation, two photon absorption, and parametric frequency conversion. Resonant enhancement of each is provided by tuning the ruby laser half the 6S - 9D transition frequency of 28828.90 cm. The parametric process involves, in addition, a resonance with one of the P states. We have studied the variation of each of the three processes with laser intensity and frequency. At exact resonance the THG is found to be proportional to the square of the laser intensity and the TPA is proportional to laser intensity over a large power range. The resonance lineshape for both processes is found to be power dependent. A detailed analysis of these two processes based on steady state density matrix calculations and including A. C. Stark shifts, photoionization, and beam geometry is shown to accurately describe most of our observations.
The density-matrix formalism is used to develop the theory of two-photon-resonant third-harmonic generation in metal vapors taking into account saturation, ionization, laser-induced Stark shifts, and variations in the wave-vector mismatch as a result of population redistribution. It is shown that for third-harmonic generation in the ultraviolet and the vacuum-ultraviolet regions, where $3\ensuremath{\omega}$ exceeds the ionization limit of the metal vapor, two-photon-resonant three-photon ionization will be the main limiting process. This will also be true for four-wave parametric processes. For efficient energy conversion, the two-photon-resonant metal vapor must be phase matchable to allow large vapor density and cell length. Otherwise, the low incident intensity limits, set by the saturation and the ionization effects, cannot be efficiently converted in only one coherence length. The theory is applied to two-photon-resonant tripling of the ruby laser in cesium vapor.
Four-photon interactions involving both a two-photon resonance with the9d^{2}D_{3/2}level and a one-photon resonance with an np2P level (n = 7-10) are investigated in detail. Gain, gain saturation, gain threshold, and forward-to-backward generation ratios are measured. Comparison with numerical estimates indicates that9d^{2}D_{3/2}tonp^{2}Plasing is the dominant gain mechanism but that a doubly resonant four-photon parametric oscillation makes a significant contribution. Gain saturation is dominated by population of np2P levels. Ionization is important, especially at higher pump powers.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.