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Physical Review

Laser and Two-Photon Processes

David A. Kleinman

Published Jan 1, 1962• 102 citations
Publisher

Abstract

The possibility of observing two-photon processes using the intense beam of the ruby optical maser is considered theoretically for two general types of experiment. The essential approximation in the theory is the hypothesis that excited states exist which connect both the initial and final states by electric dipole transitions having a total oscillator strength $f\ensuremath{\sim}1$. Simple formulas are obtained for the two-photon absorption which do not depend on the details of the electronic structure. Recent experiments on the Ca${\mathrm{F}}_{2}$: ${\mathrm{Eu}}^{++}$ system are in quantitative agreement with the predictions of the theory.

DOI
10.1103/physrev.125.87

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Spectroscopy and Optical Maser Action in Sr F2 : Sm2+

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Multiple Photon Ionization Processes in Atoms.

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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.

•Jun 1, 1976•0 citations
The possibility of observing two-photon processes using the intense beam of the ruby optical maser is considered theoretically for two general types of experiment. The essential approximation in the theory is the hypothesis that excited states exist which connect both the initial and final states by electric dipole transitions having a total oscillator strength f\ensuremath∼1f\ensuremath{\sim}1f\ensuremath∼1. Simple formulas are obtained for the two-photon absorption which do not depend on the details of the electronic structure. Recent experiments on the CaF2{\mathrm{F}}_{2}F2​: Eu++{\mathrm{Eu}}^{++}Eu++ system are in quantitative agreement with the predictions of the theory.
The observation of two-photon absorption by a very efficient up-converted emission is reported for Ho3+{\mathrm{Ho}}^{3+}Ho3+ in CaF2{\mathrm{F}}_{2}F2​, SrF2{\mathrm{F}}_{2}F2​, and CdF2{\mathrm{F}}_{2}F2​ with both cw- and pulse-laser excitations. The two-photon excitation spectra are found to be highly structured and consist of two bands: The band AAA is excited by the dye-laser photons of frequencies 15 400-15 700 ${\mathrm{cm}}^{\ensuremath{-}1}$: The band BBB is excited by the dye-laser photons of frequencies 15 800-16 400 ${\mathrm{cm}}^{\ensuremath{-}1}$. No one-photon absorption is observed for Ho3+{\mathrm{Ho}}^{3+}Ho3+ in the above lattices at twice these frequencies. Studies of concentration dependence, temperature dependence, and dependence on the pulse repetition rate are used for the assignment of the band. The investigation shows that the two bands AAA and BBB arise from two different modes of two-photon excitation. The band AAA is assigned to arise from a sequential (stepwise) two-photon excitation $^{5}I_{8}\ensuremath{\rightarrow}^{5}F_{5}\ensuremath{\rightarrow}^{5}D_{2}$. The band BBB is assigned to arise from the direct two-photon absorption $^{5}I_{8}\ensuremath{\rightarrow}^{3}L_{8}$. Our results are in agreement with the prediction of the Judd-Ofelt theory of lanthanide transition intensities.
A crystal of SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ was operated as a pulsed optical maser at temperatures close to 4.2\ifmmode^\circ\else\textdegree\fi{}K. The 6969 \AA{} output corresponds to the wavelength of an exceedingly sharp line ($\ensuremath{\Delta}\ensuremath{\nu}<0.6$ ${\mathrm{cm}}^{\ensuremath{-}1}$) in which almost all of the low-temperature fluorescence is concentrated. In contrast to what prevails in CaF2{\mathrm{F}}_{2}F2​: Sm+2{\mathrm{Sm}}^{+2}Sm+2 masers, the output is characterized by strong relaxation oscillations. This may be explained by the large difference in the fluorescent lifetimes in the two systems. While in CaF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ the value of $\ensuremath{\tau}$ is approximately 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec, in SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ it has a value of 15 msec. The reason for the large difference in $\ensuremath{\tau}$ values, in turn, depends upon the relative proximity of the long-wavelength edge of the red band to the position of the metastable 5D0^{5}D_{0}5D0​ level from which fluorescence occurs. Absorption measurements taken at helium temperatures on SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ show that the lowest vibrational level of the lowest lying $4f\ensuremath{-}5d$ band lies \ensuremath{\sim}600 ${\mathrm{cm}}^{\ensuremath{-}1}$ above the position of the 5D0^{5}D_{0}5D0​ level while in CaF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ there is near coincidence of the corresponding levels and consequently strong configurational mixing. Crystals of SrCl2{\mathrm{Cl}}_{2}Cl2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ were also studied in this regard and display an expected close similarity in spectral characteristics to SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+. The vibrational structure on the $4f\ensuremath{-}5d$ bands is much more pronounced, however, than in CaF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ and SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+, indicating weaker coupling to the lattice in the excited 5d5d5d state. A tentative interpretation for the splitting of the red band seen in the absorption spectra of Sm2+{\mathrm{Sm}}^{2+}Sm2+ ions is given.
The theory of one- and two-photon transitions between a given pair of impurity levels of the same parity is developed. As is well known, lattice vibrations assist the otherwise forbidden one-photon transition, increasing its intensity with temperature. The two-photon transition rate is shown to have a complementary decrease with increasing temperature. A measurement of both temperature dependences determines the effective frequency and coupling constant for the interaction. The formalism is applied to predicting the two-photon transition rate for the $4{d}^{10}\ensuremath{-}4{d}^{9}5s$ transition of the silver ion in NaCl:Ag. For an experiment using a ruby laser and an ultraviolet beam the maximum absorption coefficient predicted for the ultraviolet beam is $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}48}\mathrm{FN}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ at low temperatures, where FFF is the flux (photons/cm2{\mathrm{cm}}^{2}cm2 sec) of the laser and NNN is the Ag+{\mathrm{Ag}}^{+}Ag+ concentration. This should be within reach of present experimental techniques.
The physics of the two-photon absorption process is investigated for a three-state system. The density-matrix equations for the two-photon interaction are solved in the steady-state limit assuming that the pump laser radiation is monochromatic. Collisional broadening, saturation, and Stark shifting of the two-photon resonance are investigated in detail by numerical solution of the steady-state density-matrix equations. Analytical expressions for the saturation intensity and the Stark shift are derived for the case where the single-photon transitions between the intermediate state and the initial and final states are far from resonance with the pump laser. For this case, it is found that the direction of the Stark shift is dependent on the relative magnitudes of the dipole-moment matrix elements for the single-photon transitions that couple the intermediate state with the initial and final states. Saturation and Stark shifting are also investigated for the case where the single-photon transitions between the intermediate state and the initial and final states are close to resonance with the pump laser.
We investigate the process of photon absorption by atoms or molecules shortly interacting with a laser beam in the dipole approximation. Assuming that the interaction time $\ensuremath{\tau}$ is much smaller than the lifetime of the corresponding excited state, we examine the absorption probability as a function of $\ensuremath{\tau}$. In addition, we incorporate Doppler broadening due to nonzero temperature of the atoms (molecules). It is demonstrated that in the case of a zero detuning and without Doppler broadening the absorption probability is quadratic in $\ensuremath{\tau}$. Once Doppler broadening is taken into account or the laser beam is off from the resonant frequency, the absorption probability becomes linear in $\ensuremath{\tau}$. Our findings are expected to be important for experimental studies in optical cells or cavities where atoms or molecules traverse continuous laser beams. The experimental prospects of searching for the electric dipole moment of the electron are discussed in detail.
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.