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Physical Review A

Interference between nonresonant three-photon absorption and third-harmonic generation and the cancellation of four-photon resonances

M. Elk, P. Lambropoulos, Xian Tang

Published Jul 1, 1991• 18 citations
Publisher

Abstract

We investigate the theory of cancellation by interference between the absorption of three fundamental laser photons and one third-harmonic photon. The theory is formulated in terms of the density matrix so as to take detunings, dephasing, and and laser bandwidth into account. The result is a theory of cancellation for finite detuning that explains how four-photon resonances can be canceled by a three-photon mechanism, if there is an atomic level at near three-photon resonance. We obtain explicit conditions for this to happen, and perform calculations pertaining to a recent experiment [D. Charalambdis et al., Phys. Rev. A (to be published)] where cancellation of 4+1 resonantly enhanced multiphoton ionization has been observed.

DOI
10.1103/physreva.44.r31

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Suppression of a four-photon resonance by four-wave mixing near an intermediate three-photon resonance

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

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 ${\mathit{I}}_{1}$\ensuremath{\simeq}7\ifmmode\times\else\texttimes\fi{}${10}^{9}$ W/${\mathrm{cm}}^{2}$, is nearly three-photon resonant with the 6s[3/2](J=1) resonance; the second, unfocused beam (${\mathit{I}}_{2}$\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}${10}^{7}$ W/${\mathrm{cm}}^{2}$) 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.

Physical Review A•Oct 1, 1992•12 citations
We investigate the theory of cancellation by interference between the absorption of three fundamental laser photons and one third-harmonic photon. The theory is formulated in terms of the density matrix so as to take detunings, dephasing, and and laser bandwidth into account. The result is a theory of cancellation for finite detuning that explains how four-photon resonances can be canceled by a three-photon mechanism, if there is an atomic level at near three-photon resonance. We obtain explicit conditions for this to happen, and perform calculations pertaining to a recent experiment [D. Charalambdis et al., Phys. Rev. A (to be published)] where cancellation of 4+1 resonantly enhanced multiphoton ionization has been observed.
We present a complete account of our recent work [Phys. Rev. A 44, 31 (1991)] in which we investigate the theory of cancellation by interference between the absorption of three fundamental laser photons and one third-harmonic photon. The theory is formulated in terms of the density matrix so as to take detunings, dephasing, and laser bandwidth into account. The result is a theory of cancellation for finite detuning that explains how four-photon resonances can be canceled by a three-photon mechanism if there is an atomic level at near-three-photon resonance. The treatment is extended to focused beams and the interplay between phase matching and cancellation is investigated. We obtain explicit conditions for cancellation to occur, and perform calculations pertaining to a recent experiment where cancellation of 4+1 resonantly enhanced multiphoton ionization has been observed.
The destructive interference between the three-photon and the third-harmonic one-photon absorption in the vicinity of the 6s[3/2]1{]}_{1}]1​ state of Xe has been studied in the resonantly enhanced multiphoton ionization via nf states, through the cancellation of the nf, J=2 resonances of the spectrum, accessible by four-photon absorption. The gas-pressure, i.e., phase-matching, dependence of the three-photon detuning range from the 6s[3/2]1{]}_{1}]1​ state for which cancellation occurs has been investigated in one- and two-color experiments, including positive detuning from this state in positively dispersive regions. For obtaining cancellation, the theoretically predicted requirement of optically thick medium at the third-harmonic frequency is corroborated by present observations for negative detunings. The different cancellation behavior of the nf[3/2]2{]}_{2}]2​ and nf[5/2]2{]}_{2}]2​ states observed indicates the dependence of the effect on the atomic parameters of the coupled four-photon resonance. The experimental results are found to be in partial agreement with existing theoretical models.
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.
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.
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.