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Physical Review A

Competition between two-photon-resonant three-photon ionization and four-wave mixing in Xe

Hidekazu Nagai, Taisuke Nakanaga

Published Dec 6, 2011• 3 citations
Publisher

Abstract

Competitive inhibition of a resonance enhanced multiphoton ionization process by a resonant four-wave mixing has been observed in Xe atoms. When an intense IR (1064 nm) laser was applied to a sample of Xe which was also being irradiated by a UV laser tuned to the two-photon absorption line of Xe, the two-photon-resonant three-photon ionization signals decreased with increasing IR laser power. This phenomenon is dependent on the resonant states of Xe and the polarization of the two laser beams. Three 6$s$ excited states [5/2]${}_{2}$, [3/2]${}_{2}$, and [1/2]${}_{0}$ were examined. At the [1/2]${}_{0}$ resonant state, the ion signals were not decreased but slightly increased with the increase of the IR laser power. No suppression of the ion signal was observed at the [5/2]${}_{2}$ resonant state, when the polarization directions of the lasers were perpendicular to each other. The result of the polarization dependence reflects the selection rules of four-wave mixing. A simple rate equation analysis including the contribution of two-photon ionization from the [1/2]${}_{0}$ state by the IR laser well represents the IR laser-power dependence of the ion signal.

DOI
10.1103/physreva.84.063408

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Competitive inhibition of a resonance enhanced multiphoton ionization process by a resonant four-wave mixing has been observed in Xe atoms. When an intense IR (1064 nm) laser was applied to a sample of Xe which was also being irradiated by a UV laser tuned to the two-photon absorption line of Xe, the two-photon-resonant three-photon ionization signals decreased with increasing IR laser power. This phenomenon is dependent on the resonant states of Xe and the polarization of the two laser beams. Three 6sss excited states [5/2]2{}_{2}2​, [3/2]2{}_{2}2​, and [1/2]0{}_{0}0​ were examined. At the [1/2]0{}_{0}0​ resonant state, the ion signals were not decreased but slightly increased with the increase of the IR laser power. No suppression of the ion signal was observed at the [5/2]2{}_{2}2​ resonant state, when the polarization directions of the lasers were perpendicular to each other. The result of the polarization dependence reflects the selection rules of four-wave mixing. A simple rate equation analysis including the contribution of two-photon ionization from the [1/2]0{}_{0}0​ state by the IR laser well represents the IR laser-power dependence of the ion signal.
Partial cancellation of the ionization signal in the four-photon-resonant five-photon ionization via J=2 4f and 5f resonances in Xe has been observed at increased gas pressures. Experiments with one and two counterpropagating laser beams provide strong evidence that cancellation is due to destructive interference at the three-photon step between the coherent three- and one-photon excitation channels, the latter involving one vacuum ultraviolet photon of the third-harmonic generation that occurs above the 6s[3/2]1o{]}_{1}^{\mathit{o}}]1o​ state. The well-known destructive interference for the ``on-resonance'' case is now shown to occur also for large detuning from the resonance (up to 2000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) probed by four-photon-resonant five-photon ionization. This type of cancellation may provide a new insight in interference effects involved in multiphoton-excitation processes.
Partial cancellation of the ionization signal in the four-photon-resonant five-photon ionization via J = 2 4f and 5f resonances in Xe has been observed at increased gas pressures. Experiments with one and two counterpropagating laser beams provide strong evidence that cancellation is due to destructive interference at the three-photon step between the coherent three- and one-photon excitation channels, the latter involving one vacuum ultraviolet photon of the third-harmonic generation that occurs above the 6s[3/2]1o state. The well-known destructive interference for the ''on-resonance'' case is now shown to occur also for large detuning from the resonance (up to 2000 cm-1) probed by four-photon-resonant five-photon ionization. This type of cancellation may provide new insight in interference effects involved in multiphoton-excitation processes.
We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​L\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​ is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​b\ensuremath{\Vert}\ensuremath{\gg}1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.
We use resonance ionization involving two colors in single-pass and retroreflected geometries to study the suppression of excitation of a four-photon resonance by an interference involving four-wave sum-frequency generation occurring near an intermediate three-photon resonance. The 6p[1/2](J=0) state of xenon is excited by three blue photons plus one infrared photon. One beam, focused to I1{\mathit{I}}_{1}I1​\ensuremath{\simeq}7\ifmmode\times\else\texttimes\fi{}109{10}^{9}109 W/cm2{\mathrm{cm}}^{2}cm2, is nearly three-photon resonant with the 6s[3/2](J=1) resonance; the second, unfocused beam (I2{\mathit{I}}_{2}I2​\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}107{10}^{7}107 W/cm2{\mathrm{cm}}^{2}cm2) is tuned to maintain exact four-photon resonance with the 6p[1/2](J=1) state. One additional blue photon ionizes from the four-photon level. Third-harmonic light is generated by the first, nearly three-photon-resonant beam by four-wave sum-frequency mixing. One third-harmonic photon plus one photon from the second laser form a second excitation pathway to the four-photon level; destructive interference between the two pathways results in a reduction in the observed ionization. The degree of reduction depends on the xenon density and the detuning (both positive and negative) from three-photon resonance. This interference may be overcome by retroreflecting the nearly three-photon-resonant beam to provide an additional excitation pathway which generates no third harmonic.The study provides detailed information on the pressure-dependent range from exact resonance over which the familiar three-photon cancellation effect is operative; it shows that the interference occurs in high- and low-energy regions about three-photon resonance; and it establishes that interference is produced for large values of the phase mismatch even if the absorption of the interfering field is low. We compare our measurements of the reduction in ionization with predictions published by us elsewhere [M. G. Payne, J. C. Miller, R. C. Hart, and W. R. Garrett, Phys. Rev. A 44, 7684 (1991)]; excellent agreement is observed. We also report the observation of suppression of pressure-induced wing absorption into the three-photon state observed in a classic ``hybrid'' resonance mode of excitation.
Two independently tunable, linearly polarized dye lasers have been used to study multiphoton ionization of gaseous xenon. One laser is tuned near three-photon resonance with the allowed 6s[3/2]J=1° resonance, which is not observed with one laser at these pressures because of the destructive interference between the three-photon-excitation and third-harmonic-excitation pathways to the 6s[3/2]J=1° state. The second laser is tuned to resonance with higher allowed np and np′ states of xenon. The missing ionization signal is seen to be dramatically restored by the addition of the second laser beam; however, the signal again disappears as the pressure is increased. These results are discussed in relation to recent experimental and theoretical studies of cancellation effects between three-photon excitation and third-harmonic generation. Spectroscopic information obtained from tuning each dye laser, together with data on the angular distributions resulting from rotating the plane of polarization of one laser relative to that of the second laser, clearly shows that two different ionization mechanisms are operative. In addition, these experiments unambiguously illustrate the importance of dissociative ionization of quasi-dimers of xenon over a rather broad frequency range.
We present a theory for two- and three-photon excitation, optical shifting, and four-wave mixing when a first laser is tuned onto, or near, a two-photon resonance and a second much more intense laser is tuned near or on resonance between the two-photon resonance and a second excited state. When the second excited state has a dipole-allowed transition back to the ground state and the concentration is sufficiently high, a destructive interference is produced between three-photon coupling of the ground state and the second excited state and one-photon coupling between the same states by the internally generated four-wave mixing field. This interference leads to several striking effects. For instance, as the onset of the interference occurs, the optical shifts in the two-photon resonance excitation line shape become smaller in copropagating geometry so that the line shapes for multiphoton ionization enhanced by the two-photon resonance eventually become unaffected by the second laser. In the same range of concentrations the four-wave mixing field evolves to a concentration-independent intensity. With counterpropagating laser beams the line shape exhibits normal optical shifts like those observed for both copropagating and counterpropagating laser beams at very low concentrations. The theoretical work presented here extends our earlier works by including the effect of laser bandwidth and by removing the restriction of having the second laser be tuned far from three-photon resonance. In this way we have now included, as a special case, the effect of both laser bandwidth and interference on laser-induced transparency. Unlike other effects related to odd-photon destructive interference, the effect of a broad bandwidth is to bring about the predicted effects at much lower concentrations. Studies in rubidium show good agreement between theory and experiment for both ionization line shapes and four-wave mixing intensity as a function of concentration.