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Physical Review Letters

Picosecond Studies of Optical Second Harmonic Generation in Atomic Vapor

Christopher S. Mullin, Doseok Kim, Marla B. Feller, Y. R. Shen

Published Apr 3, 1995• 9 citations
Publisher

Abstract

Picosecond laser pulses are used to study the forbidden resonant second harmonic generation (SHG) in atomic vapor. The results can be understood quantitatively by an ionization-initiated dc-field-induced SHG model taking into account the temporal buildup of the dc field and transient behavior of the two-photon coherent excitation of the vapor.

DOI
10.1103/physrevlett.74.2678

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Picosecond laser pulses were used to study the highly forbidden resonant second-harmonic generation (SHG) in potassium vapor. The input intensity dependence, vapor density dependence, buffer-gas pressure dependence, and spatial profile of the SHG were measured. A pump–probe experiment was conducted to probe the time dependence of the SHG signal. The experimental results can be understood from an ionization-initiated dc-field-induced SHG model. A theory of a dc-field-induced SHG model is developed that takes into account the time development of the dc electric field in detail. This temporal buildup of the dc field along with transient coherent excitation between two-photon-allowed transitions can explain the experimental results quantitatively, including the previous vapor SHG results with nanosecond laser pulses.

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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.

Physical Review A•Apr 1, 1979•43 citations
Picosecond laser pulses are used to study the forbidden resonant second harmonic generation (SHG) in atomic vapor. The results can be understood quantitatively by an ionization-initiated dc-field-induced SHG model taking into account the temporal buildup of the dc field and transient behavior of the two-photon coherent excitation of the vapor.
Picosecond laser pulses were used to study the highly forbidden resonant second-harmonic generation (SHG) in potassium vapor. The input intensity dependence, vapor density dependence, buffer-gas pressure dependence, and spatial profile of the SHG were measured. A pump–probe experiment was conducted to probe the time dependence of the SHG signal. The experimental results can be understood from an ionization-initiated dc-field-induced SHG model. A theory of a dc-field-induced SHG model is developed that takes into account the time development of the dc electric field in detail. This temporal buildup of the dc field along with transient coherent excitation between two-photon-allowed transitions can explain the experimental results quantitatively, including the previous vapor SHG results with nanosecond laser pulses.
It is well-known that the second-order nonlinear effects, such as second harmonic generation (SHG), difference frequency generation (DFG), and sum frequency generation (SFG), in atomic vapors are theoretically forbidden by symmetry on both a microscopic level because the individual atoms in the vapor do not possess a dipole, and on a macroscopic level because the atoms are isotropically distributed. However, SHG is vapor was first observed by Mossberg et al. (1978) in Tl and then in many other atomic vapors and some noble gases by other groups. Several explanations for this phenomenon have been presented. A model proposed by Mossberg et al. and later modified by Bethune (1981), attributes it to a DC field, which is created by laser-induced multi-photon ionization and spatial separation of free photoelectrons from the heavier ions either by the pondermotive potential of the laser or by the kinetic energy of photoelectrons and makes SHG allowed. All experiments reported so far have been carried out by using either nanosecond or picosecond laser pulses. The authors report the first femtosecond SHG in vapor. The experimental study is done in potassium vapor using femtosecond pulses from a mode-locked Ti:sapphire laser.>
SHG is forbidden in materials with centrosymmetry such as an atomic vapor, yet it has been observed with appreciable efficiency on atomic resonances in metal vapors with focused nanosecond lasers. We have used a 3 psec tunable laser pulse in a pump-probe geometry to determine how the symmetry is broken in atomic media. We observe a significant instantaneous response with a strong intensity dependence. Enhancement of the SHG of a delayed probe pulse by the pump pulse is weak up to 1 nsec. Other factors such as ionization of K vapor, linewidth and phase matching are also studied.
Second harmonic generation (SHG) in atomic Li vapor is studied when the 2 2 S 1/2 -3 2 S 1/2 two-photon transition is resonantly excited. This is an SHG in a medium with inversion symmetry, with no externally apptied electric or magnetic field, and with no apparent multipole moments associated with the resonant excitation. The SH polarization is found to be parallel to the intensity gradient of the incident laser beam when a cylindrical lens focusing is applied. The mechanism of this highly forbidden SHG is explained by the radial electric field induced by free expansion of photo-electrons around the laser beam axis.
It is shown that optical second-harmonic generation is possible in dispersive atomic vapors since a static electric field is spontaneously created by the fundamental laser beam. When multiphoton ionization of atoms occurs simultaneously in the interaction, the spontaneous field and second-harmonic generation are significantly enhanced. Our experimental results for atomic sodium vapor irradiated by picosecond Nd-doped yttrium-aluminum-garnet laser pulses agree well with the theoretical predictions.
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.