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Applied Physics Letters

Third harmonic generation in phase-matched alkali metal vapors

D. M. Bloom, G. Bekkers, J. F. Young, Stephen E. Harris

Published Jun 15, 1975• 68 citations
Publisher

Abstract

We report improvements in conversion efficiency for third harmonic generation in sodium and rubidium vapor. 30-psec pulses of radiation at 1.064 μm have been converted to 0.3547 μm with an energy conversion efficiency of 10%. Factors limiting conversion efficiency are discussed.
DOI
10.1063/1.88036

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We report the generation of 0.3547-\ensuremath{\mu}m radiation by tripling 1.064-\ensuremath{\mu}m radiation in a phase-matched mixture of rubidium and xenon. We find $\ensuremath{\chi}(3\ensuremath{\omega})=1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}32}$ esu, which is about 106{10}^{6}106 times greater than that of He. Phase matching occurs for Xe and Rb atoms in the ratio 412:1.
We calculate the spectrum of third-harmonic generation (THG) for multimode fundamental input fields. We consider input fields from (1) a laser with gain on several cavity modes, (2) pulses with short temporal duration, and (3) frequency-modulated input fields. The effects of phase modulation in the nonlinear medium on the spectrum of the THG field are considered. Using the estimates by Miles and Harris [IEEE J. Quantum Electron. QE-9, 470 (1973)] for the nonlinear susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) and ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) in alkali-metal vapors, we find that phase modulation can profoundly affect the efficiency and the spectrum of the THG. Generally, the self-phase modulation of the fundamental will tend to reduce the phase matching of an intense fundamental field and the third harmonic and thereby lower the conversion efficiency. New frequencies not contained in the set of frequencies ${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{j}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{k}}$, where {${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$} are frequencies in the fundamental laser spectrum, are created even at relatively low conversion due to phase modulation. Effects of cross phase modulation are also studied.
The dependence of the third harmonic intensity on the medium length under completely phase-matched and resonant conditions is discussed. It is shown that the conversion efficiency in the coherent transient case is expected to exceed that in the steady state case in a long and/or dense medium when the incident light pulse has sufficient energy. The 3S-5S transition of sodium with a 602.3 nm light is studied experimentally as a model system. The efficiency as a function of the incident light frequency and intensity is in agreement with the predictions. By eliminating the phase-mismatching effect, the dependence on the medium density is also determined. It is demonstrated that the efficiency surely increases even in the higher density of sodium.
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.