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With help of Green functions the transition rates for different types of two-photon absorption through diagram summations are calculated. The appearance of double-photon absorption characteristics in the photo-stimulated field emission is analyzed. It is shown that the two-step transitions can be discerned from the one-step excitations in this way. A convenient experimental technique is discussed.

The absorption coefficient of a number of potential i.r. laser window materials has been measured in the region of multiphonon absorption. Absorptions as low as 0·004 cm−1 have been detected by using thick samples and a differential technique with a dual-beam spectrophotometer. The absorption coefficients of LiF, CaF2, BaF2, SrF2, MgF2, Al2O3, KCl, NaCl and KBr all decrease exponentially with increasing wavenumber. The slope of the exponential bears a nearly constant relationship to the longitudinal optical phonon frequency, consistent with a multiphonon process whose strength depends on the number of phonons generated. Absorption data are also presented for Si, Ge, GaAs: Cr, GaAs: Fe, ZnSe and CdTe.

The expression of the two-photon absorption coefficient in crystals is discussed using explicitly the Wigner-Eckart theorem for finite symmetry groups. It is discussed how to separate the dynamical part, which contains appropriate reduced matrix elements of the momentum operator, from the geometrical part, which depends on the polarization vectors of both the radiation beams. For the geometrical part the standard results of the literature are recovered; detailed new information for the two-photon absorption rate is supplied by the dynamical part. To illustrate the procedure, the case of TICI is considered as a specific example. Nous traitons le facteur d'absorption optique pour transitions a deux photons dans les cristaux en appliquant explicitement le theoreme de Wigner-Eckart au groupe fini des operateurs de symmetrie ponctuelle. On etudie comme on peut separer la partie dynamique de la partie geometrique, la premiere etant determinee par les elements de matrice reduits de l'operateur d'impulsion, la deuxieme contenant les vecteurs de polarization des deux faisceaux incidents. Pour le facteur geometrique, nous retrouvons les resultats bien connus; le facteur dynamique fournit des detaillees nouvelles conaissances a propos du facteur d'absorption a deux photons. L'application de notre procedure pour le cristal de TICI est enfin donnee comme un exemple.

The $3S\ensuremath{-}5S$ transition of Na atoms is induced by absorption of two photons, one each from two circularly polarized beams traveling in opposite directions through the vapor. The beams are derived from a tunable, narrow-band pulsed dye laser. Doppler broadening is absent and the hyperfine structure is resolved. The hyperfine interaction constant ${A}_{5S}$ in the $5S$ state of the ${\mathrm{Na}}^{23}$ atom is determined to be 101\ifmmode\pm\else\textpm\fi{}15 MHz.

The coefficient for absorption during H2-H collisions was calculated for temperatures from 2000 to 7000 K and wave numbers between 100 and 40 000 cm-1 for LTE. Because only transitions with Δν = 1 were considered, the absorption was near the fundamental at 4161 cm-1 in the infrared. The model included mechanical anharmonicity, vibration-rotation interaction, excited vibrational states, and transverse components of the dipole moment. At 5500 cm-1, 3750° K, and 1 atm pressure, inclusion of H2-H vibrational absorption increased the absorption of pure hydrogen gas 48 per cent. An approximate formula for the H2-H absorption coefficient is given for rapid calculation.

The authors derive an expression for the rate of absorption by an atomic system (bound or free) of radiation from an ultra intense laser beam. The absorption characteristics are radically different from those of conventional weak-field absorption theory.

The two-photon absorption spectrum due to excitonic molecules is measured in CuCl at 77 and 4.2\ifmmode^\circ\else\textdegree\fi{}K. We measured values of the two-photon transition cross section of the order of ${10}^{\ensuremath{-}44}$ ${\mathrm{cm}}^{4}$ sec and estimated a peak value of ${10}^{\ensuremath{-}42}$. The binding energy of the molecule is found to be 255 ${\mathrm{cm}}^{\ensuremath{-}1}$.

A calorimetric method for continuous measurements of the optical absorption of bulk glasses over the spectrum extending from the visible to the near-infrared wavelength ranges is presented. A relation between the absorption and the induced temperature rise of the sample, at thermal equilibrium, is derived. Details for the most convenient arrangement of source, lens and monochromator are given. As an example, experimental results are plotted for a F2 glass.

The two-photon absorption spectra of crystalline naphthalene and of the naphthalene molecule in solution were measured over the energy range 31000–45000 cm −1 by monitoring the fluorescence excited by tunable dye lasers. The vibronically-induced odd-parity 1 A 1g a 1 B − 3u and 1 A 1g a 1 B 2u transitions and two even-parity allowed 1 A 1g a 1 B 1g , 1 A 1g a 1 A 1g transitions were identified.

A new mechanism of absorption of infrared radiation by neutral donor-pair molecules in n-type III-V and II-VI semiconductors at helium temperatures is investigated at photon energies of about half the donor ionization energy. A simple formula for the absorption coefficient is derived and numerical results are presented. The absorption line position agrees very well with the position of photoconductivity peaks observed in these materials by the Clarendon Laboratory group.

A detailed analysis of the Herzberg-Tellere effects expected in the two-photon spectra of D 2h and D 6h molecules fixed in space is presented. The results are expected to be applicable to naphthalene and benzene moderate resolution two-photon spectra.

An atomic system represented by two-level systems interacts with a light field via two-photon transitions. For the case of two-photon absorption in one mode we calculate the time-dependent factorial moments of the light-field intensity and the probability to find n photons in the field.

Our aim is to study the two-photon induced luminescence in CdS crystals by using a low power CW laser (5 mW). We discuss briefly the possibility given by the electron-pulse-counting technique to detect weak optical signals. This technique enables us to investigate the luminescence spectra (which show two bands at 2.4 and 2.0 eV) and the dependence of the luminescence intensity on the laser power. The discussion of the experimental results makes it clear that the level responsible for the red emission is partially saturated at a laser intensity of 1023 photon/cm2 s.

Absorption bands have been found at 655 and 830 nm in a Mn2+-doped ZnS crystal under intense optical excitation. From the close correlation to the orange fluorescence, these bands are ascribed to the transitions from the emitting state 4 T 1 ( 4 G) of Mn2+. This observation of the excited-state absorption makes it possible for the first time to locate higher excited levels of impurity ions hidden behind the strong fundamental absorption of the host material by a direct optical absorption method. Assignments for the terminal states of the observed absorption transitions are discussed.

Optical absorption in MnF2 in the region from 50 to 350 cm−1 was studied. A search was made in particular for multiple-magnon processes previously reported in the literature. While, for example, four-magnon processes can be obtained theoretically from an expansion of the Heisenberg spin Hamiltonion, we found no temperature dependent absorption in the region studied other than the well-known two-magnon peak at 100 cm−1. All the observed peaks above 100 cm−1 could be attributed to phonons.

A simplified theory of small-signal two-photon absorption is developed, based on the solution of rate equations involving an infinitely short-living intimediate state. It is shown that in a first approximation this theory leads to results identical to those obtained using second-order perturbation techniques. Moreover, the present approach leads to a built-in saturation effect at high intensities depending on the parameters of the laser and of the absorbing medium. An analysis expression is given for the intensity dependent saturation.

The calculation of relative intensities of the optical absorption lines of the fourth order pair of Cr3+ ions in ruby has been performed assuming the electro-dipole character of the transitions.

Optical absorptions have been measured in chalcopyrite, CuFeS 2 , and Fe-doped CuAlS 2 and CuGaS 2 . An extra absorption band with two peaks is observed at the low energy region of the absorption edge for Fe-doped CuAlS 2 and CuGaS 2 .Energy positions of two absorption peaks are 1.3 eV and 2.0 eV for CuAlS 2 and 1.2 eV and 1.9 eV for CuGaS 2 , respectively. The intensity of this absorption band increases with the increase of doped Fe ions and grows into the absorption edge of CuFeS 2 . Its oscillator strength comes up to 7·10 -2 . In chalcopyrite photoconductivity is observed and its maximum is just at the same energy region of the absorption edge. By comparing our results with those of absorption measurements for Cu- or Fe-doped ZnS it is concluded that this absorption band originates from the charge transfer transitions relating to 3d electron of Fe ions and the absorption edge of CuFeS 2 rises from the band-to-band transition corresponding to this charge transfer transition.

A general theoretical expression is derived for the probability of a three-photon absorption process. It is concluded that three-photon absorption to a discrete level may be observed if the radiation field contains a laser beam and additional light with a continuous frequency distribution and that a transition to a continuum ofstates may be observed if the radiation field consists of laser light only. The selection rules for three-photon absorption are basically the same as for one-photon absorption.

The fundamental absorption band edge of NaClO 3 crystal showed a shift towards longer wavelengths with increase in temperature. There is also evidence of formation of a new band at temperature higher than about 120°C. The shift is nearly linear up to about 120°C, but it is much larger than the linear rate as the melting point (≈ 250°C) is approached. The excess absorption is assumed to be due to the thermally produced lattice disorder and analysis yielded 1·40±0·05 eV for the energy of formation of the defect. The anomalous thermal expansion of the crystal reported by earlier workers at temperatures above 120°C could also be analysed in a similar manner and the activation energy of 1·45±0·05 eV so obtained is in reasonable agreement with that obtained from optical absorption studies. The additional absorption may be attributed to the perturbation of the fundamental absorption band due to defects formed at higher temperatures.

In polar semiconductors with direct energy gaps, optical absorption is observed for photons with energies well below that corresponding to the energy gap. It is now established that the absorption tail (Urbach's law) is due to indirect phonon-assisted optical transitions involving the absorption of one or more optical phonons of energy kθ. In the present paper we have considered the effect of a magnetic field on the optical absorption in that region of the Urbach tail where second-order processes are dominant. In contrast to the normal direct interband absorption coefficient, the absorption reflects the Landau level structure of valence band and conduction band separately. A discussion is given of the conditions under which such an effect should be observable.

The magnon sidebands and other structure in the optical spectrum of antiferromagnetic Mn${\mathrm{F}}_{2}$ have been studied under various conditions of magnetic fields, uniaxial stress, and temperature. We present the results of such experiments for the $^{4}T_{1}(\mathrm{I})$, $^{4}A_{1}$, $^{4}E(\mathrm{I})$, $^{4}T_{2}(\mathrm{II})$, $^{4}T_{1}(\mathrm{II})$, and $^{4}E(\mathrm{II})$ states of ${\mathrm{Mn}}^{++}$ in Mn${\mathrm{F}}_{2}$. The magnon sideband shapes have been fitted as well as possible by density-of-states calculations in which the normal magnon dispersion and an adjustable exciton dispersion were used. It has been possible in this way to identify and give the magnitude of the pair moment for the principal exchange mechanism responsible for each sideband absorption, and to give the exciton parameters for the best fit. The discrepancies in this fitting process are probably ascribable to exciton-magnon binding, and indeed one line appears to represent a bound state of an exciton and a magnon.

The optical constants of degenerate CdO films were measured at about 10 K in the spectral range around the LO lattice frequency (5 to 24 μm). Besides the free carrier absorption and a tail of the lattice absorption an additional absorption is found above the LO frequency which can be explained by the theory of free polarons. At higher frequencies it is superimposed by further absorption processes with noticeable structure which are unexplained until now. Die optisehen Konstanten entarteter CdO-Schichten wurden bei etwa 10 K in der Umgebung der LO-Gitterschwingungsfrequenz (5 bis 24 μm)gemessen. Neben der Absorption durch freie Ladungstrager und einem Auslaufer der Gitterabsorption wurde oberhalb der LO-Frequenz ein weiterer Absorptionsbeitrag gefunden, der durch die Theorie des groBen Polarons erklart werden kann. Ihm uberlagert ist bei hoheren Frequenzen eine starker strukturierte Absorption, fur die bis jetzt keine Deutung vorliegt.

Two‐photon‐absorption cross sections were determined in the energy range 3.10–3.56 eV for crystalline anthracene and for the anthracene molecule in solution. The experimental method was based on the measurement of the excitation spectrum for fluorescence induced by two‐photon absorption from a Raman‐shifted ruby laser. From these results we conclude that: (a) a symmetry‐forbidden two‐photon transition corresponding to the 1A1g → 1B2u excitation was observed both in the crystal and in the solution; (b) this transition is vibronically induced by a nontotally symmetric vibration of the frequency 1200 ± 400 cm−1; (c) a crystal state is observed at 3.5–3.6 eV which has no counterpart in the solution spectrum; (d) this crystal state is tentatively assigned to a g‐symmetry‐type charge‐transfer state; (e) the possible observation of a quadrupole two‐photon 1A1g → 1B2u to the 0–0 band seems likely since the dipole two‐photon transition is forbidden and vibronic mixing within the true 0–0 band does not occur.

Measurements have been made, using polarized light, of the anisotropy of the visible absorption of centres induced in quartz by x-ray, gamma and neutron irradiation. The ratio of the integrated absorption when the electric vector is parallel to the c-axis to that when it is perpendicular, is 1 ·5. An experiment is described which suggests that the optical absorption is associated with substitutional aluminium impurity. It is shown that a value of 1·3 would be expected from the O'Brien and Pryce model of the magnetic resonance centre which is induced under similar conditions.

Saturated absorption techniques are being used increasingly often to measure optical resonances having such narrow bandwidths that they would otherwise be obscured by Doppler broadening. The principle underlying these techniques is reviewed using four simple thought or "gedanken" experiments. A rudimentary explanation is based on Bennett's " hole-burning" picture. Two configurations of typical saturated absorption experiments are described. One illustrates absorption outside and the other inside of a laser cavity. The intracavity technique is recommended for weak absorbers and when especially simple compact apparatus is needed. For most other experiments, the gaseous absorber is better located outside the laser cavity.

A new method of investigating energy band structure is proposed which makes use of the angular dependence of two-photon absorption coefficient of polarized beams. The angular dependences of the allowed transitions are calculated and tabulated for 32 crystal point groups. The exciton as well as interband transitions are discussed, and the method will be explained for the cases of NaCl–, CsCl–, ZnS– and diamond-type crystals how to determine the points of extremum vertical energy separation in the Brillouin zone with the help of associated tables and figures.

Thin films of MnF2, ZnF2, and ZnF2:Mn have been prepared by evaporation, and their optical absorption spectra have been measured from 1500 to 2600A. The absorption coefficient of MnF2 has a maximum of 8.64×104 cm−1 at 1613A, corresponding to an oscillator strength of 0.042; while there appears to be a maximum of lower value at 1470A for ZnF2. An unresolved weaker band at 2050A is also evident for MnF2. For the phosphor, ZnF2:Mn, the absorption coefficient is intermediate between those of ZnF2 and MnF2, but the peak characteristic of the Mn++ activator is shifted to 1666A and the oscillator strength of the transition is increased to 1.2.The relative excitation spectrum of ZnF2:Mn was determined, and maximum response occurred between 1600 and 1670A, indicating that radiation in the strong absorption band characteristic of the activator is most effective in exciting luminescence. Less efficient excitation occurs to 2200A.It is concluded that a transition to an excited atomic state of the activator, rather th...

The absorption spectra of CdCl 2 and CdBr 2 single crystals doped with cuprous or cupric halides were measured. Optical bleaching of the absorption bands due to Cu + gives rise to new absorption bands which suggest the conversion of Cu + →Cu 2+ . This was confirmed also by detecting the growth in ESR signals characteristic of Cu 2+ centers.

We consider the effect of molecular symmetry on the two‐photon absorption constants of a randomly oriented sample of molecules. It is shown that a complete polarization study of an allowed two‐photon transition of a fluid generally yields enough information to permit an unequivocal identification of the symmetry species of the excited state. Ambiguities occur in only a few cases. Thus, oriented molecule studies for symmetry assignment will be largely unnecessary in two‐photon molecular spectroscopy. Symmetry assignment rules are given for all of the 32 crystallographic point groups and for the two groups of linear molecules. It is shown that certain transitions, which are allowed for two photons of different energies, are forbidden for two photons of the same energy. The application of this formalism to Raman scattering problems is discussed.

We treat theoretically the simultaneous two-photon absorption and sum-frequency generation associated with exciton polaritons in noncentrosymmetric crystals. Expressions are derived for the two-photon absorption coefficient and for the intensity of the polariton beam. We describe the symmetry properties of two-photon absorption by longitudinal excitons and by transverse polaritons.

The absorption spectra of solid films of six photoconductive dyes are reported. The transitions in the solid state correspond to those of the ``isolated'' cations in solution. However, the longest‐wavelength singlet‐singlet absorption band is split into components separated by 1000 cm—1 or more. Other bands are unaffected, except for a general decrease of oscillator strength. The results are interpreted in terms of light absorption by a single molecule, followed by exciton motion in the lowest excited state.

In amorphous and hexagonal selenium optical absorption and photoconductivity were studied in their dependence on temperature. The absorption edge shifts for amorphous selenium toward shorter wavelengths with decreasing temperature. For a temperature change from 300° to 90°K and a layer thickness of 98μ, for example, a shift from 6600 to 6100A is observed at an optical density of 3; for higher densities (shorter wavelengths) the shift is smaller. It can be shown that this shift is related to the thermal excitation of vibrational levels. At higher temperatures the population of the higher vibration levels increases and the separation of these from the excited state diminishes.At low temperature (ca 90°K) photoconductivity is observed only after the light quanta exceed 2.5 ev and the absorption coefficient has reached 105 cm−1. Increase of temperature brings about a shift of the photoconductive threshold toward longer wavelengths, paralleling the absorption‐edge shift. The absorption coefficient has been fol...

A double beam spectrophotometer has been developed which uses a logarithmic amplifier to obtain absorption coefficients and the area under absorption curves. The wavelength range is from 3000 A to 2.3 μ and resolution is determined by the grating monochromator to which the system is attached. With a resolution of 1 A an absorption coefficient of 0.02 is easily measurable. The optical and electronic system of the instrument and its performance are described.

Depending upon the circumstances, the phenomena which accompany or are the consequences of two‐photon absorption may be quite varied. The effects which have been reported to date are luminescence, internal and external photoelectric generation, and initiation of chemical reactions. In this paper, we point out that generation of sound waves may also be expected on a theoretical basis, and we present experimental results which we believe may have demonstrated this effect in liquids consisting of solutions of molecules such as benzanthracene and benzpyrene.