Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Laser Intensity for Maximum Yield in Multiphoton Ionization

L. Allen, Robert W. Boyd, Jerzy S. Krasiński, Michelle S. Malcuit, Carlos R. Stroud

Published Jan 28, 1985• 14 citations
Publisher

Abstract

An optimum laser intensity that maximizes the photoionization yield is found in a two-photon resonant, three-photon ionization experiment. At laser intensities higher than this optimum, a negative value is obtained for the exponential index describing this multiphoton process, both at zero detuning and at the detuning for which the signal is maximized. Despite the presence of large (> 1 \AA{}A) optical Stark shifts, Gaussian beam-focusing effects produce an excitation spectrum peaked near zero detuning and reverse the sense of its skewness.

DOI
10.1103/physrevlett.54.309

Related papers

Saturation effects in multiphoton ionization

John A. Yeazell, Michelle S. Malcuit, Carlos R. Stroud +1 more

We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Theory of the effect of third-harmonic generation on three-photon resonantly enhanced multiphoton ionization in focused beams

M. G. Payne, W. R. Garrett

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 $n$-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.

Physical Review A•Dec 1, 1983•72 citations

Resonance shifts in the multiphoton ionization of cesium atoms

J. Morellec, Didier Normand, G. Petite

This work reports the multiphoton ionization of cesium atoms, via resonance with the $6F$ level, by interaction with a single transverse and longitudinal mode neodymium-glass laser beam. At a low rate of ion production, when the laser frequency is tuned through resonance, the laser intensity necessary to create a constant number of ions passes through a minimum, as expected, for a three-photon energy equal to the unperturbed $6S\ensuremath{\rightarrow}6F$ transition energy. But for a higher ionization rate, involving larger laser intensities, a departure from expectation is observed which is interpreted as a consequence of an energy shift of the transition. The level shifts are demonstrated in another way by their strong effect on the experimental order of nonlinearity of the interaction, ${K}_{\mathrm{expt}}$. A sharp variation of ${K}_{\mathrm{expt}}$ is observed when the energy shift of the $6S\ensuremath{\rightarrow}6F$ transition exactly compensates the wavelength detuning of the laser. The latter method gives shift values which are found to be independent of the large variations of the interaction volume under conditions of resonance. Both methods give a linear dependence of the shifts on the laser intensity. Identification of these shifts with energy shifts of the $6S\ensuremath{\rightarrow}6F$ transition is subject to theoretical reservations and needs further experimentation.

Physical Review A•Jul 1, 1976•107 citations

Theory of resonant multiphoton processes

C. S. Chang

The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order ${10}^{8}$ W/${\mathrm{cm}}^{2}$) is determined by the intensity-dependent level width ($6f$ configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order ${10}^{12}$ W/${\mathrm{cm}}^{2}$) are determined by both the intensity-dependent widths and shifts a$\stackrel{\mathrm{`}}{\mathrm{s}}$ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.

Physical Review A•May 1, 1974•14 citations

ATOMS INTERACTING WITH ELECTROMAGNETIC FIELDS, MULTIPHOTON IONIZATION

G. Mainfray

The non linear interaction between an intense laser radiation and atoms leads to ionization through the absorption of N photons from the laser radiation via laser-induced virtual states. The multiphoton ionization rate varies as a function of the laser intensity I as IN. We discuss the two most important effects which govern multiphoton ionization processes : resonance effects and laser-coherence effects. In a moderate laser intensity range (107 - 109 W cm-2) corresponding to the two, three or four-photon ionization of atoms, resonance effects play a dominant role while the photon statistics of the laser radiation are relatively unimportant. On the contrary, in the very high intensity range (1012 - 1013 W cm-2) required to observe large Nth - order ionization processes, coherence effects play a dominant role through N! enhancement in the N-photon ionization rate, while resonance effects are completely damped due to the high laser intensity. We conclude by reviewing the possible applications of multiphoton absorption processes in other fields.

Le Journal de Physique Colloques•Nov 1, 1982•1 citation

Resonance-enhanced multiphoton ionization of atomic hydrogen

L. R. Brewer, Fritz Buchinger, Martin Ligare +1 more

We have measured the resonance-enhanced four-photon ionization of atomic hydrogen. The degenerate four-photon process occurs via a three-photon resonance between the 1s and the 2p levels, with subsequent one-photon ionization near threshold. We have studied the highly asymmetric resonance-enhanced profile, i.e., the photoion yield as a function of laser detuning from three-photon resonance between the 1s and 2p levels. In particular, we have determined the width, shift, peak, and asymmetry of the profile as a function of laser intensity. The experimental results are compared to theoretical models. These models involve both the properties of the atom in an intense near-resonant radiative field, and a detailed model for the multimode laser field, particularly the field fluctuations due to mode beating. The asymmetric resonance-enhanced photoionization profile is well reproduced by both a random-phase and a chaotic-light model.

Physical Review A•Apr 1, 1989•21 citations
An optimum laser intensity that maximizes the photoionization yield is found in a two-photon resonant, three-photon ionization experiment. At laser intensities higher than this optimum, a negative value is obtained for the exponential index describing this multiphoton process, both at zero detuning and at the detuning for which the signal is maximized. Despite the presence of large (> 1 \AA{}A) optical Stark shifts, Gaussian beam-focusing effects produce an excitation spectrum peaked near zero detuning and reverse the sense of its skewness.
We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.
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.
This work reports the multiphoton ionization of cesium atoms, via resonance with the 6F6F6F level, by interaction with a single transverse and longitudinal mode neodymium-glass laser beam. At a low rate of ion production, when the laser frequency is tuned through resonance, the laser intensity necessary to create a constant number of ions passes through a minimum, as expected, for a three-photon energy equal to the unperturbed $6S\ensuremath{\rightarrow}6F$ transition energy. But for a higher ionization rate, involving larger laser intensities, a departure from expectation is observed which is interpreted as a consequence of an energy shift of the transition. The level shifts are demonstrated in another way by their strong effect on the experimental order of nonlinearity of the interaction, Kexpt{K}_{\mathrm{expt}}Kexpt​. A sharp variation of Kexpt{K}_{\mathrm{expt}}Kexpt​ is observed when the energy shift of the $6S\ensuremath{\rightarrow}6F$ transition exactly compensates the wavelength detuning of the laser. The latter method gives shift values which are found to be independent of the large variations of the interaction volume under conditions of resonance. Both methods give a linear dependence of the shifts on the laser intensity. Identification of these shifts with energy shifts of the $6S\ensuremath{\rightarrow}6F$ transition is subject to theoretical reservations and needs further experimentation.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.
The non linear interaction between an intense laser radiation and atoms leads to ionization through the absorption of N photons from the laser radiation via laser-induced virtual states. The multiphoton ionization rate varies as a function of the laser intensity I as IN. We discuss the two most important effects which govern multiphoton ionization processes : resonance effects and laser-coherence effects. In a moderate laser intensity range (107 - 109 W cm-2) corresponding to the two, three or four-photon ionization of atoms, resonance effects play a dominant role while the photon statistics of the laser radiation are relatively unimportant. On the contrary, in the very high intensity range (1012 - 1013 W cm-2) required to observe large Nth - order ionization processes, coherence effects play a dominant role through N! enhancement in the N-photon ionization rate, while resonance effects are completely damped due to the high laser intensity. We conclude by reviewing the possible applications of multiphoton absorption processes in other fields.
We have measured the resonance-enhanced four-photon ionization of atomic hydrogen. The degenerate four-photon process occurs via a three-photon resonance between the 1s and the 2p levels, with subsequent one-photon ionization near threshold. We have studied the highly asymmetric resonance-enhanced profile, i.e., the photoion yield as a function of laser detuning from three-photon resonance between the 1s and 2p levels. In particular, we have determined the width, shift, peak, and asymmetry of the profile as a function of laser intensity. The experimental results are compared to theoretical models. These models involve both the properties of the atom in an intense near-resonant radiative field, and a detailed model for the multimode laser field, particularly the field fluctuations due to mode beating. The asymmetric resonance-enhanced photoionization profile is well reproduced by both a random-phase and a chaotic-light model.