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Physical Review A

Effects of four-wave mixing on four-photon resonance excitation and ionization in the presence of a three-photon intermediate state resonance enhancement

M. G. Payne, J. C. Miller, Roger C. Hart, W. R. Garrett

Published Dec 1, 1991• 19 citations
Publisher

Abstract

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}${\mathit{k}}_{\mathit{r}}$L\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}${\mathit{k}}_{\mathit{r}}$ 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}${\mathit{k}}_{\mathit{r}}$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.

DOI
10.1103/physreva.44.7684

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Physical Review A•Aug 1, 1998•10 citations
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 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 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 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.
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.
Several extensions are made in theoretical studies of multiphoton ionization associated with third-harmonic fields that are generated near three-photon resonances in gaseous media. The treatment includes the strong coherent cancellation effect which occurs between three-photon pumping of a resonant level and pumping by the third-harmonic field that is generated in the same medium. The incomplete spoiling of the cancellation effect with counterpropagating beams is quantitatively described. Also, treatment of the multiphoton-ionization problem involving phase-matched, third-harmonic fields is generalized to include quantitative effects of index changes due to a buffer gas, absorption due to dimers, and collisional dephasing of coherent excitations. Finally, we show how measurements of linewidths, phase-matching positions, and pressure dependences of ionization yields associated with third-harmonic generation and subsequent absorption can be used to determine oscillator strengths of a resonant level, absorption coefficients for a resonant species and a buffer-gas species, and the refractive index of the buffer gas at the third-harmonic frequency.
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.