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Multiple Photon Ionization Processes in Atoms.

Edward J. Robinson

Published Jun 1, 1976• 0 citations
OpenAlex

Abstract

The advent of the laser has brought about a revolution in the kinds of experimental phenomena that can be investigated. In particular, ultra-high power monochromatic, collimated sources have intensities of sufficient magnitude to enable studies to be carried out in the regime where 'non-linear' effects are important, even dominant. Important among these are processes which are characterised by the simultaneous absorption of two or more optical photons. While multiple photon processes are not completely new, those in the optical part of the spectrum, like Raman scattering, have, until the advent of the laser, been thought of as linear in the incident intensity, or, like the two-quantum decay of the metastable 2s states of hydrogen-like atoms and ions, been confined to theory. Of the multiple photon, non-linear optical processes, multiquantum ionization is one of the more fruitful for detailed, quantitative measurements, and for comparison with theory, since (1) one does not require precise coincidence between the laser light and an absorption line (2) the ionizations can be detected unambiguously with 100% efficiency (3) atomic wave functions are simple, and sufficiently accurate to enable one to make reasonable precise calculations.

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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

Multiphoton Ionization of Hydrogen and Rare-Gas Atoms

H. Barry Bebb, Albert Gold

A perturbation theory of the ionization of atoms by simultaneous absorption of several photons, each of whose energy is less than the ionization potential, is developed from the evolution-operator formalism. A precise computation is made for the hydrogen atom, giving transition rates as a function of photon energy for two- through twelve-photon photoionization. The eighth-order ionization rate (in cgs units) at the 1.78-eV ruby-laser line is found to be \ensuremath{\sim}${10}^{\ensuremath{-}244}$\ifmmode\times\else\texttimes\fi{}${(\mathrm{photon}\mathrm{flux})}^{8}$ and should be observable using available techniques. Good agreement is obtained with Zernik's exact calculation of the two-photon ionization rate of metastable $2S$ hydrogen. Approximate calculations are made for the rare gases. Assuming "typical" experimental conditions of a gas density of \ensuremath{\sim}${10}^{20}$ atoms ${\mathrm{cm}}^{\ensuremath{-}3}$ and a ruby laser focused into a volume of \ensuremath{\sim}${10}^{\ensuremath{-}8}$ ${\mathrm{cm}}^{3}$, we find that the flux required to liberate one electron during a 10-nsec pulse is \ensuremath{\sim}${10}^{29}$ ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for Xe, Kr, and Ar and \ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}${10}^{30}$ photons ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne and He. These gases ionize with the simultaneous absorption of 7, 8, 9, 13, and 14 photons, respectively. The predicted rate for Xe is found to be in excellent agreement with the recent direct measurements of Voronov and Delone. We conclude that multiphoton ionization provides the initial electrons required for the optical breakdown of gases, though it does not account for the over-all growth of the discharge except possibly at very low pressures. Impurity atoms (particularly heavy rare gases) may be the source of "initiating" electrons in Ne and He.

Physical Review•Mar 4, 1966•439 citations

Two-photon ionization of many-electron atoms

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Until recently, the nonlinear interaction between light and matter has been restricted to only low photon energies produced by optical lasers. However, about a decade ago, the rise of free-electron laser facilities revolutionized the field of nonlinear light-matter interaction by delivering intense high-energy light pulses. Today, such lasers are used for research in materials science, chemical technology, biophysical science, solid state physics as well as fundamental research. It is the new experimental possibilities provided by free-electron lasers that motivated the work presented in this thesis. Two-photon ionization process is one of the simplest nonlinear interactions in which absorption of two photons by an atom (or a molecule) leads to promoting one of its bound electrons to continuum. This work presents studies of two-photon ionization of neutral atoms. After a brief historical introduction to the topic of nonlinear light-matter interaction, the density matrix describing the state of an atom and a photoelectron following two-photon ionization is derived. In each successive chapter, part of this density matrix is used to obtain characteristic quantities such as total two-photon ionization cross section, photoelectron angular distributions, ion polarization or degree of polarization of fluorescence photon produced by subsequent decay of the photoion. Physical properties of these quantities are studied and intriguing phenomena, such as elliptical dichroism, polarization transfer as well as relativistic and screening effects are investigated.

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Two-photon ionization of metastable helium

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There have been relatively few investigations of multiphoton ionization from metastable helium. Of particular interest has been the work of Haberland et al. 1987 and Haberland and Oschwald 1988. In both the 1987 and 1988 papers they have described the two photon ionization of metastable helium. In each of these studies they have reported the occurrence of unexplained structure along the wings of their resonance profiles. Upon the performance of similar measurements by this study, the unexplained structure is not seen and the agreement of the experiment's measurements with the theoretical shape of the resonance curves has been good. To experimentally verify these resonance effects, we have used a tunable dye laser in conjunction with a time of flight mass spectrometer to create and detect ions from metastable helium by two-photon absorption. The use of a metastable state instead of the ground state is advantageous because of its proximity to the ionization continuum and its extended lifetime. Using a metastable state as a starting point for multiphoton absorption requires fewer photons to reach the ionization threshold. The extended lifetime of the state also makes it easy to access experimentally. For helium the singlet metastable state 2$\sp1$S lies at 20.61 eV above the ground level with a natural lifetime of close to a millisecond. Two photons of 501.7 nm and 504.35 nm are required for the ionization processes in resonance with the 3$\sp1$P and the 3$\sp1$D states. This thesis is the accounting of the experimental process involved in the measurement of the dipole and quadrupole resonances of two photon ionization from singlet metastable helium. The study includes the description of the laser, electron gun assembly for metastable helium creation, and the time of flight mass spectrometer. A discussion of the theory of multiphoton processes is included along with the discussion of the data, its reduction and analysis, and a comparison with theoretical prediction. This study has not only involved the acquisition of definitive atomic spectra data sets, but has also established a facility for resonant ionization spectroscopy at The American University.

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One- and two-photon ionization

de Meijere, Jacob Louis Frederik

Detailed descriptions of one- and two-photon ionization are presented. We go beyond conventional perturbation theory to investigate the dynamics of both processes for a broad range of field intensities. The general theory of unstable decaying states is applied to the problem of one-photon ionization (the photoeffect). It is found that a non-trivial dependence of the transition dipole moment on the continuum state energy can lead to corrections to exponential decay, and even oscillations in the bound state population. As examples we consider the photoionization of hydrogen and atoms with autoionizing states. Only in the absence of autoionizing states corrections to exponential decay remain inconsequential for any experimentally relevant intensity. Our description of two-photon ionization is formulated in the Heisenberg picture. Besides the usual two-level atom projection operators we introduce explicitly the operators referring to the atomic continuum. By eliminating from the equations of motion the terms related to the electromagnetic self field as well as the terms referring to the continuum, transverse and longitudinal damping corresponding to spontaneous emission and photoionization is obtained. The use of field correlation functions allows us to account for the partial coherence of the applied field. We develop a technique to extract from the equations of motion a unique two-photon ionization rate. Such a characterization of the ionization process is not only instructive because of its simplicity, it is also in many cases completely satisfactory. The resulting general expression for the two-photon ionization rate is the central result of our treatment. From it we recover several familiar results in different limiting cases. In addition, our general rate expression provides the first description of the complete hierarchy of saturation effects that one should expect. We present a number of examples where we calculate the two-photon ionization rate as a function of the detuning, and where we emphasize the saturation and field correlation effects.

•Jan 1, 2016•0 citations

Fluorescence studies of multiple-photon ionization processes: Four- and five-photon ionization of Sr at wavelengths of 558–590 nm

Harold K. Haugen, Andreas Othonos

An ``all-optical'' technique is presented for the study of multiphoton-ionization processes, based on fluorescence detection of the ions which are produced. A vapor is utilized in a moderate-density regime (\ensuremath{\sim}${10}^{11}$--${10}^{15}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) such that collisional effects are negligible. The technique is applied to multiple-photon ionization of Sr in the wavelength range of 558--590 nm at laser intensities \ensuremath{\sim}1--50 GW/${\mathrm{cm}}^{2}$. Fine-structure-resolved emission of the ${\mathrm{Sr}}^{+}$ (5${p}^{2}$${P}_{3/2/,1/d}^{0}$) ions which are formed is observed at \ensuremath{\lambda}=407.8 and 421.5 nm, following either four- or five-photon absorption. No emission is observed from higher ionic states, with a detection sensitivity \ensuremath{\sim}${1:10}^{3}$ with respect to the ionic-resonance emission.

Physical Review A•Apr 1, 1989•11 citations
The advent of the laser has brought about a revolution in the kinds of experimental phenomena that can be investigated. In particular, ultra-high power monochromatic, collimated sources have intensities of sufficient magnitude to enable studies to be carried out in the regime where 'non-linear' effects are important, even dominant. Important among these are processes which are characterised by the simultaneous absorption of two or more optical photons. While multiple photon processes are not completely new, those in the optical part of the spectrum, like Raman scattering, have, until the advent of the laser, been thought of as linear in the incident intensity, or, like the two-quantum decay of the metastable 2s states of hydrogen-like atoms and ions, been confined to theory. Of the multiple photon, non-linear optical processes, multiquantum ionization is one of the more fruitful for detailed, quantitative measurements, and for comparison with theory, since (1) one does not require precise coincidence between the laser light and an absorption line (2) the ionizations can be detected unambiguously with 100% efficiency (3) atomic wave functions are simple, and sufficiently accurate to enable one to make reasonable precise calculations.
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.
A perturbation theory of the ionization of atoms by simultaneous absorption of several photons, each of whose energy is less than the ionization potential, is developed from the evolution-operator formalism. A precise computation is made for the hydrogen atom, giving transition rates as a function of photon energy for two- through twelve-photon photoionization. The eighth-order ionization rate (in cgs units) at the 1.78-eV ruby-laser line is found to be \ensuremath{\sim}${10}^{\ensuremath{-}244}$\ifmmode\times\else\texttimes\fi{}(photonflux)8{(\mathrm{photon}\mathrm{flux})}^{8}(photonflux)8 and should be observable using available techniques. Good agreement is obtained with Zernik's exact calculation of the two-photon ionization rate of metastable 2S2S2S hydrogen. Approximate calculations are made for the rare gases. Assuming "typical" experimental conditions of a gas density of \ensuremath{\sim}1020{10}^{20}1020 atoms ${\mathrm{cm}}^{\ensuremath{-}3}$ and a ruby laser focused into a volume of \ensuremath{\sim}${10}^{\ensuremath{-}8}$ cm3{\mathrm{cm}}^{3}cm3, we find that the flux required to liberate one electron during a 10-nsec pulse is \ensuremath{\sim}1029{10}^{29}1029 ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for Xe, Kr, and Ar and \ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}1030{10}^{30}1030 photons ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne and He. These gases ionize with the simultaneous absorption of 7, 8, 9, 13, and 14 photons, respectively. The predicted rate for Xe is found to be in excellent agreement with the recent direct measurements of Voronov and Delone. We conclude that multiphoton ionization provides the initial electrons required for the optical breakdown of gases, though it does not account for the over-all growth of the discharge except possibly at very low pressures. Impurity atoms (particularly heavy rare gases) may be the source of "initiating" electrons in Ne and He.
Until recently, the nonlinear interaction between light and matter has been restricted to only low photon energies produced by optical lasers. However, about a decade ago, the rise of free-electron laser facilities revolutionized the field of nonlinear light-matter interaction by delivering intense high-energy light pulses. Today, such lasers are used for research in materials science, chemical technology, biophysical science, solid state physics as well as fundamental research. It is the new experimental possibilities provided by free-electron lasers that motivated the work presented in this thesis. Two-photon ionization process is one of the simplest nonlinear interactions in which absorption of two photons by an atom (or a molecule) leads to promoting one of its bound electrons to continuum. This work presents studies of two-photon ionization of neutral atoms. After a brief historical introduction to the topic of nonlinear light-matter interaction, the density matrix describing the state of an atom and a photoelectron following two-photon ionization is derived. In each successive chapter, part of this density matrix is used to obtain characteristic quantities such as total two-photon ionization cross section, photoelectron angular distributions, ion polarization or degree of polarization of fluorescence photon produced by subsequent decay of the photoion. Physical properties of these quantities are studied and intriguing phenomena, such as elliptical dichroism, polarization transfer as well as relativistic and screening effects are investigated.
There have been relatively few investigations of multiphoton ionization from metastable helium. Of particular interest has been the work of Haberland et al. 1987 and Haberland and Oschwald 1988. In both the 1987 and 1988 papers they have described the two photon ionization of metastable helium. In each of these studies they have reported the occurrence of unexplained structure along the wings of their resonance profiles. Upon the performance of similar measurements by this study, the unexplained structure is not seen and the agreement of the experiment's measurements with the theoretical shape of the resonance curves has been good. To experimentally verify these resonance effects, we have used a tunable dye laser in conjunction with a time of flight mass spectrometer to create and detect ions from metastable helium by two-photon absorption. The use of a metastable state instead of the ground state is advantageous because of its proximity to the ionization continuum and its extended lifetime. Using a metastable state as a starting point for multiphoton absorption requires fewer photons to reach the ionization threshold. The extended lifetime of the state also makes it easy to access experimentally. For helium the singlet metastable state 2$\sp1$S lies at 20.61 eV above the ground level with a natural lifetime of close to a millisecond. Two photons of 501.7 nm and 504.35 nm are required for the ionization processes in resonance with the 3$\sp1$P and the 3$\sp1$D states. This thesis is the accounting of the experimental process involved in the measurement of the dipole and quadrupole resonances of two photon ionization from singlet metastable helium. The study includes the description of the laser, electron gun assembly for metastable helium creation, and the time of flight mass spectrometer. A discussion of the theory of multiphoton processes is included along with the discussion of the data, its reduction and analysis, and a comparison with theoretical prediction. This study has not only involved the acquisition of definitive atomic spectra data sets, but has also established a facility for resonant ionization spectroscopy at The American University.
Detailed descriptions of one- and two-photon ionization are presented. We go beyond conventional perturbation theory to investigate the dynamics of both processes for a broad range of field intensities. The general theory of unstable decaying states is applied to the problem of one-photon ionization (the photoeffect). It is found that a non-trivial dependence of the transition dipole moment on the continuum state energy can lead to corrections to exponential decay, and even oscillations in the bound state population. As examples we consider the photoionization of hydrogen and atoms with autoionizing states. Only in the absence of autoionizing states corrections to exponential decay remain inconsequential for any experimentally relevant intensity. Our description of two-photon ionization is formulated in the Heisenberg picture. Besides the usual two-level atom projection operators we introduce explicitly the operators referring to the atomic continuum. By eliminating from the equations of motion the terms related to the electromagnetic self field as well as the terms referring to the continuum, transverse and longitudinal damping corresponding to spontaneous emission and photoionization is obtained. The use of field correlation functions allows us to account for the partial coherence of the applied field. We develop a technique to extract from the equations of motion a unique two-photon ionization rate. Such a characterization of the ionization process is not only instructive because of its simplicity, it is also in many cases completely satisfactory. The resulting general expression for the two-photon ionization rate is the central result of our treatment. From it we recover several familiar results in different limiting cases. In addition, our general rate expression provides the first description of the complete hierarchy of saturation effects that one should expect. We present a number of examples where we calculate the two-photon ionization rate as a function of the detuning, and where we emphasize the saturation and field correlation effects.
An ``all-optical'' technique is presented for the study of multiphoton-ionization processes, based on fluorescence detection of the ions which are produced. A vapor is utilized in a moderate-density regime (\ensuremath{\sim}1011{10}^{11}1011--1015{10}^{15}1015 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) such that collisional effects are negligible. The technique is applied to multiple-photon ionization of Sr in the wavelength range of 558--590 nm at laser intensities \ensuremath{\sim}1--50 GW/cm2{\mathrm{cm}}^{2}cm2. Fine-structure-resolved emission of the Sr+{\mathrm{Sr}}^{+}Sr+ (5p2{p}^{2}p2P3/2/,1/d0{P}_{3/2/,1/d}^{0}P3/2/,1/d0​) ions which are formed is observed at \ensuremath{\lambda}=407.8 and 421.5 nm, following either four- or five-photon absorption. No emission is observed from higher ionic states, with a detection sensitivity \ensuremath{\sim}1:103{1:10}^{3}1:103 with respect to the ionic-resonance emission.