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Physical Review A

Third-harmonic generation and multiphoton ionization in Bessel beams

Viktor E. Peet, R.V. Tsubin

Published Aug 1, 1997• 61 citations
Publisher

Abstract

Three-photon resonance enhancement of third-harmonic generation and multiphoton ionization have been studied in xenon under excitation by the Bessel and the focused annular laser beams. It has been shown that the transformation of a Gaussian beam into a Bessel or an annular one leads to significant changes of third-harmonic excitation profiles and ionization spectra. These changes result from a principal difference of the beams, where either collinear (Gaussian beams) or noncollinear (Bessel and focused annular beams) excitation geometries are realized. It has been shown that the noncollinear ring-type phase matching shifts the maximum of the generated third harmonic to the longer wavelength toward the atomic resonance. Numerical calculations of third-harmonic excitation spectra have been carried out and compared with experimental results. The efficiency of frequency tripling in collinear and noncollinear excitation geometries have been compared. Cancellation of the three-photon $6s$ resonance and the influence of harmonic photons on the excitation of the four-photon $4f$ resonance in the Bessel beams are discussed.

DOI
10.1103/physreva.56.1613

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Physical Review A•Jan 8, 2001•8 citations
Three-photon resonance enhancement of third-harmonic generation and multiphoton ionization have been studied in xenon under excitation by the Bessel and the focused annular laser beams. It has been shown that the transformation of a Gaussian beam into a Bessel or an annular one leads to significant changes of third-harmonic excitation profiles and ionization spectra. These changes result from a principal difference of the beams, where either collinear (Gaussian beams) or noncollinear (Bessel and focused annular beams) excitation geometries are realized. It has been shown that the noncollinear ring-type phase matching shifts the maximum of the generated third harmonic to the longer wavelength toward the atomic resonance. Numerical calculations of third-harmonic excitation spectra have been carried out and compared with experimental results. The efficiency of frequency tripling in collinear and noncollinear excitation geometries have been compared. Cancellation of the three-photon 6s6s6s resonance and the influence of harmonic photons on the excitation of the four-photon 4f4f4f resonance in the Bessel beams are discussed.
Three-photon-resonant excitation and subsequent ionization of xenon at high concentrations has been studied utilizing both Bessel and Gaussian beams. Comparisons of analogous results with the two modes of focusing are made. The excitation-ionization profiles can be analyzed on the basis of the well-studied interference effect involving combined contributions of three- and one-photon transition amplitudes in resonant atomic excitation. We show that the principal features of the excitation problem with Bessel beams can be simulated by a simple picture involving crossed plane-wave beams. Using this approach it has been shown that pressure-broadened and shifted lines that result from the interference-based cooperative Lorentzian line shift constitutes the main pressure-dependent peak of off-resonance excitation profiles produced in Bessel beams.
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 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.
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.
Multiphoton ionization profiles in xenon under three-photon excitation by azimuthally segmented conical laser beams have been studied and analyzed on the basis of the interference-based cooperative shift of the atomic resonance line. Segmentation of the conical wave front with various geometrical slits reduces the possible three-photon azimuthal sub-beam combinations in the third order process and a principal (or ``homogeneous'') Lorentzian component can be selected from the overall excitation profile. This Lorentzian is identical to the pressure-broadened atomic line shifted by the cooperative shift. A possibility of controlling the nonlinear response by spatial selection of interacting waves in conical beams is discussed.