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AIP conference proceedings

New coherent cancellation effect involving four-photon excitation and the related ionization

M. G. Payne, W. R. Garrett, J. P. Judish, M. P. McCann

Published Jan 1, 1989• 0 citations
Publisher

Abstract

We describe here an effect which occurs when a first laser is tuned near a dipole allowed three‐photon resonance and a second laser is used to complete a dipole allowed four‐photon resonance between the ground state ‖ 0≳ and an excited state ‖ 2≳. In this process three photons are absorbed from the first laser and one photon from the second; so that if the ‖ 0≳ to ‖ 2≳ transition is two‐photon allowed the transition is also pumped resonantly by the third harmonic field due to the first laser and the second laser field. When the second laser is strong enough to cause strong absorption of the third harmonic light, and the phase mismatch, Δk is large and dominated by the nearby resonance, a destructive interference occurs between the pumping of the ‖ 0≳ to ‖ 2≳ transition by two‐ and four‐photon processes.

DOI
10.1063/1.38563

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Physical Review A•Aug 1, 1998•10 citations
We describe here an effect which occurs when a first laser is tuned near a dipole allowed three‐photon resonance and a second laser is used to complete a dipole allowed four‐photon resonance between the ground state ‖ 0≳ and an excited state ‖ 2≳. In this process three photons are absorbed from the first laser and one photon from the second; so that if the ‖ 0≳ to ‖ 2≳ transition is two‐photon allowed the transition is also pumped resonantly by the third harmonic field due to the first laser and the second laser field. When the second laser is strong enough to cause strong absorption of the third harmonic light, and the phase mismatch, Δk is large and dominated by the nearby resonance, a destructive interference occurs between the pumping of the ‖ 0≳ to ‖ 2≳ transition by two‐ and four‐photon processes.
We describe here an effect which occurs when a first laser is tuned near a dipole allowed three-photon resonance and a second laser is used to complete a dipole allowed four-photon resonance between the ground state /vert bar/0 > and an excited state /vert bar/2 >. In this process three photons are absorbed from the first laser and one photon from the second; so that if the /vert bar/0 >--/vert bar/2 > transition is two-photon allowed the transition is also pumped resonantly by the third harmonic field due to the first laser and the second laser field. When the second laser is strong enough to cause strong absorption of the third harmonic light, and the phase mismatch, /DELTA/kappa is large and dominated by the nearby resonance, a destructive interference occurs between the pumping of the /vert bar/0 >--/vert bar/2 > transition by two- and four-photon process. 7 refs.
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.
Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for nnn-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.
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 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.