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Physical Review A

Two-photon resonant, optical third-harmonic generation in cesium vapor

K. M. Leung, John Francis Ward, Brian J. Orr

Published Jun 1, 1974• 59 citations
Publisher

Abstract

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 $9d^{2}D_{\frac{3}{2}}$ 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 ${10}^{8}$ 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.

DOI
10.1103/physreva.9.2440

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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{10}^{\ensuremath{-}30}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.
This work examines the use of higher order multiphoton resonances in higher harmonic generation together with judicious exploitation of coherent interaction properties to achieve efficient harmonic generation. A detailed experimental study on third harmonic generation in two photon resonant coherent interaction and a theoretical study on four photon resonant coherent interaction have been conducted. Two photon resonant coheren propagation in lithium vapor (2S-4S and 2S-3D interaction) has been studied in detail as a function of phase and delay of the interacting pulse sequence. Under coherent lossless propagation of 90 phase shifted pulse pair, third harmonic generation is enhanced. A maximum energy conversion efficiency of 1% was measured experimentally. This experiment shows that phase correlated pulse sequence can be used to control multiphoton coherent resonant effects. A larger two photon resonant enhancement does not result in more efficient harmonic generation, in agreement with the theoretical prediction. An accurate (to at least 0.5 A°) measurement of intensity dependent Stark shift has been done with the newly developed "interferometric wavemeter." Stark shifts as big as several pulse bandwidths (of picosecond pulses) result in a poor tuning of multiphoton resonance and become a limiting factor of resonant harmonic generation. A complete theory has been developed for harmonic generation in a four photon resonant coherent interaction. A numerical application of the theory to the Hg atom successfully interprets the experimental observations in terms of the phase dependent stimulated Raman scattering. With the intensity required for four photon resonant transition, the calculation predicts a dramatic Stark shift effect which completely destroys the resonance condition. This model provides a basis for the development of future schemes for efficient higher order coherent upconversion.
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.
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The authors present a detailed theoretical analysis of two-photon resonant third- and fifth-harmonic generation in metal vapors with picosecond laser pulses. These processes are described by self-consistent Maxwell-Bloch equations which take into account the effects of optical Stark shifts, multiphoton ionization, Doppler broadening, two-photon absorption, the reaction of the third-harmonic field on the fundamental, and a nonlinear index of refraction. As an example, a quantitative analysis of third- and fifth-harmonic generation in lithium vapor ($2s\ensuremath{-}4s$ transition) is presented. The limitations on energy conversion efficiency and the temporal as well as spectral characteristics of the harmonic pulses are investigated for two kinds of low-loss propagation fundamental pulses. It is shown that 90\ifmmode^\circ\else\textdegree\fi{} phase-shifted fundamental pulses (zero area) are more efficient than $2\ensuremath{\pi}m$ pulses. Energy conversion efficiencies of 6.5% for third-harmonic (190 nm) and 0.07% for cascade fifth-harmonic (114 nm) pulses are predicted.