On the theory of lasing at vibronic transitions in impurity crystals

Some aspects of lasing at vibronic transitions in impurity crystals are theoretically studied. The threshold conditions for a vibronic laser are shown to be dependent on the strength of the interaction of optical centers with a local vibration, which forms the vibronic spectrum, and the crystal lattice temperature. The theory can easily be generalized to the spectrum containing a structureless phonon sideband and well agrees with the experimental temperature dependence of the output power of a Mg₂SiO₄:Cr⁴⁺ forsterite laser.     

Self-induced three-level echo

A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the ³ P ₀-³ H ₆ transition in impurity praseodymium ions in the LaF₃ matrix upon ultrashort coherent excitation of the adjacent optically allowed ³ H ₄-³ P ₀ transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the ³ P ₀-³ H ₆ generation transition and completely eliminates polarization at the ³ H ₄-³ P ₀ excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden ³ H ₆-³ H ₄ transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.     

Electron paramagnetic resonance and optical spectroscopy of K3Na(CrO4)2 ferroelastics activated by MnO 4 2− molecular impurity ions

Crystals of a proper ferroelastic K₃Na(CrO₄)₂ containing molecular impurity ions MnO ₄ ^2? are studied using electron paramagnetic resonance (EPR) and optical spectroscopy. The EPR spectrum of the Mn⁶⁺ ion contained in the molecular impurity ion MnO ₄ ^2? is identified at low temperatures (T ≤ 20 K). The intensity of this spectrum decreases unusually fast as the temperature increases. A broad IR luminescence band with a vibronic structure well resolved at a temperature of 8 K is revealed. Theoretical treatment of the Mn⁶⁺ ion involved in the molecular impurity ions MnO ₄ ^2? of the K₃Na(CrO₄)₂ ferroelastic crystal suggests that an important role in this case is played by the pseudo-Jahn-Teller. The pseudo-Jahn-Teller effect offers an explanation for the appearance of a fine structure in the vibronic replicas in the luminescence spectrum, on the one hand, and accounts for the fast decrease in the intensity of the EPR spectrum of K₃Na(CrO₄)₂: MnO ₄ ^2? with increasing temperature, on the other.     

Crystal structure,spectroscopy and magnetism of binuclear complexes of mercury and lanthanides; the Ln(NCS)(HMPA)4(μ-SCN)2HgCl(SCN) type

A series of lanthanide compounds of type Ln(NCS)(HMPA)₄,(μ-SCN)₂HgCl(SCN) (Ln = Pr, Nd, Eu) were synthesized and grown in the form of single crystals.

The crystal structure of the neodymium complex was determined by X-ray diffraction. Its space group is Cc, with the following unit cell parameters; a = 17.338(3) Å, b = 15.795(3) Å, c = 21.828(4) Å, β = 107.65(3)°. The structure has an unexpected architecture in which one Cl^? ion, four SCN^? ions, and four oxygen atoms of HMPA groups are engaged in the metal ion coordination.

The binuclear complex is composed of two types of subunits; seven coordinated Nd (III) and four coordinated Hg (II). The results obtained were compared with the earlier published data on the crystal structures of polynuclear complexes with ions of the IIa group (Zn or Cd). Luminescence, excitation of luminescence and absorption spectra of lanthanide (Pr, Nd, Eu) single crystals, as well as vibrational IR and Raman spectra at 293, 77 and 4K, were recorded. Non-trivial results of reabsorption of the d-level of Pr(III) emission by ³H₄ → ³ P_J, ₁D² transitions were observed with simultaneous detection of emission from the ³P₀ level after excitation in the UV region. The experimental oscillator strengths of the transitions were determined from the absorption spectra and parametrized in terms of the Judd-Ofelt intensity parameters Ω_λ (λ = 2, 4, 6).

Satisfactory results for the calculation with low errors of estimation of the parameters were obtained for a crystal of the Nd-Hg compound, which reproduced the intensities of the electronic transitions well. Positive values of Ω_λ were evaluated for Pr(III) after including the ³H₄ → ³F₂ hypersensitive transition (obeying selection rules δJ = 2, δL = 2) in the calculations.

Based on the above results, the radiative rate constant can be determined. Strong vibronic components were found in the low temperature spectra for both types of ligands involved in metal ion coordination. The vibronic transitions are mainly associated with modes of groups directly coordinated to the metal ions. Electron-phonon coupling including the resonant vibronic effect was analysed based on IR and Raman data.

Magnetic susceptibility measurements were carried out down to 1.7 K. Correlation of the spectra and magnetic properties with details of the structure of the title compound was studied.     

Giant natural circular dichroism of vibronic transitions in HoAl3(BO3)4

The giant natural optical activity of vibronic replicas of the f–f ⁵ I ₈ → ⁵ F ₂ transition in HoAl₃(BO₃)₄ is observed. It exceeds the optical activity related to purely electronic transitions by two orders of magnitude and corresponds to the almost complete circular polarization of the transitions. This effect is explained by the local distortions of the crystal in the excited electronic state, which lead to the mixing of electron and vibrational wavefunctions and, as a consequence, to the delocalization of the vibronic wavefunction and the enhancement of spatial dispersion, which is responsible for the optical activity.     

Calculation and interpretation of the absorption and fluorescence spectra of indole in the isolated state and aqueous solution

We have calculated the vibronic absorption and fluorescence spectra of the first (¹ L _b ) and second (¹ L _a ) electronic transitions of indole in the isolated state and aqueous solution. The vibrational structure of the absorption and fluorescence spectra has been interpreted. The influence of the aqueous solution on the vibronic spectra has been shown.     

Manifestation of the vibronic analogue of the Fermi resonance in quasi-line spectra of porphyrins: Experiment and theoretical analysis

The quasi-line low-temperature (4.2 K) fluorescence excitation spectra of two porphyrins, meso-tetraazaporphin and meso-tetrapropylporphin introduced into an n-octane matrix are measured in the range of the S ₀ → S ₂ electronic transition. A characteristic feature of these spectra is that a conglomerate of quasi-lines—a structured complex band—is observed instead of one 0–0 quasi-line of the S ₀ → S ₂ transition. In this band, the intensity distributions for the two main types of impurity centers considerably differ from each other. The occurrence of such conglomerates is interpreted as a result of nonadiabatic electronic-vibrational interactions between vibronic S ₂ and S ₁ states (the complex vibronic analogue of the Fermi resonance). The frequencies and intensities of individual transitions determined from the deconvolution of complex conglomerates are used as the initial data for solving the inverse spectroscopic problem: the determination of the unperturbed electronic and vibrational levels of states involved in the resonance and the electronic-vibrational interaction matrix elements between them. This problem is solved with a method developed previously. The energy intervals between the S ₂ and S ₁ electronic levels of the two main types of impurity centers formed by molecules of a given porphyrin in the crystal matrix are found to significantly differ from each other (～100 cm^?1). At the same time, the energies of the unperturbed vibrational states of the S ₁ electronic level partcipating in the resonance are very close to each other for these two types of impurity centers.     

Vibronic state and optical spectrum of the N i2+ impurity ion in CaO

The relative intensities of vibronic splitting components of the³A_2g→¹T_2g optical electronic dipole transition induced by odd local vibrations and spin-orbit interaction are calculated for an impurity center with O _h point-group symmetry. The polarization dependences and magnetic circular dichroism (MCD) are found for the vibronic components in an external magnetic field. In contrast with the previous works, the calculation is not confined to the nearest-term approximation. It is shown that measurements of the polarization dependences and MCD allow one to identify unambiguously the vibronic components. A comparison with the experiment is carried out for theNi ²⁺ ion in CaO. A. M. Gor'kii Ural State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 19–23, June, 1999.     

Fluorescence and fluorescence excitation spectra of jet-cooled carbazole

The fluorescence excitation spectra of jet-cooled carbazole molecules at vibrational temperatures of 55 and 80 K and the fluorescence spectrum of these molecules excited by radiation at the frequency of a pure electronic transition are measured. As the vibrational temperature increases, the excitation spectra exhibit a series of lines of the same symmetry, which are caused by the interaction of the active vibration with a subensemble of optically inactive vibrations. The final symmetry of the totally and nontotally symmetric vibrations is determined from the shape of the rotational contours of the lines of vibronic transitions. The values of a decrease in the frequency of the nontotally symmetric vibrations in the first excited electronic state S ₁ due to their interaction with the electronic state S ₂ are calculated to be up to 100 cm^?1. The frequencies of the pure electronic transitions in the absorption and fluorescence spectra coincide with each other and are equal to 30809 cm^?1, the frequencies of vibrations in the ground state S ₀ exceeding the frequencies of the corresponding vibrations in the excited state S ₁. The degree of polarization of the integral fluorescence is determined for a series of vibronic transitions of the a ₁ and b ₂ final symmetry that are observed in the fluorescence excitation spectra, and the contribution of the intensity with the borrowed polarization θ_⊥ to the integral fluorescence is calculated. It is found that the intensity θ_⊥ is higher for the transitions of the b ₂ symmetry and can reach ≈50%.     

Electron-beam excitation of vacuum ultraviolet hydrogen laser

Stimulated emission of the Lyman-Band transitions of H₂ near 1600 Å has been achieved using a commercial electron-beam generator as an energy source. A 10⁴ A, 3 ns pulse of 400 keV electrons propagated 1.5m, through H₂ at pressures of 10–100 torr. Electron-molecule collisions produced inversion and superradiance at the kW power level.     

Two-photon vibronic spectroscopy of allene at 7.0–10.5 eV: experiment and theory

2?+?1 resonance-enhanced multiphoton ionization (REMPI) spectra of allene at 7.0–10.5?eV have been observed. The excited vibronic symmetry has been determined from polarization-ratio measurements. Based on the vibronic energies and peak intensities calculated using ab initio MO and time-dependent density functional theory, the very congested REMPI spectra have been assigned as due to π*?←?π, 3p?←?π, 4s?←?π, 4p?←?π, and 4d?←?π transitions. Vibrational progressions related to the CH₂ twisting (ν₄ ～770?cm^?1) have been observed for several excited electronic states. Calculated Franck–Condon factors also confirm that CH₂ twisting is the most active mode in the vibronic spectra of allene. In this study, theoretical calculations of two-photon intensities and polarization ratios have been made through the ab initio computed one-photon transition dipole moments to various electronic states as intermediates. As a starting point to interpret the complicated vibronic spectrum of allene, the theoretical approach, without vibronic couplings, has been applied to predict the peak positions, spectral intensities, and polarization ratios of Rydberg states, and qualitatively shows a considerable agreement with experimental observations.     

Effect of the fluorine substitution in ethyl groups of 1,4-distyrylbenzene on the fine structure fluorescence and fluorescence excitation spectra

The fine-structure fluorescence and fluorescence excitation spectra of conjugated chain compounds, 1,4-distyrylbenzene (DSB) and its fluorine-substituted derivative α,ω-1,4-distyrylbenzene, have been obtained by the Shpolskii method in an n-octane matrix at a temperature of 4.2 K. These spectra have been simulated by representing the band of each of the vibronic transitions as the sum of a zero-phonon line and a phonon wing with the corresponding parameters, such as the half-widths of the spectral lines and the Debye-Waller factors. Based on this simulation, the relative intensities of vibronic transitions have been determined and the frequencies of normal vibrations in the S ₀ and S ₁^* states have been refined. It has been found that the energy of the purely electronic transition in the molecule of the fluorine-substituted derivative is higher by 950 cm⁻¹ compared to the unsubstituted DSB. The parameters of the Franck-Condon and Herzberg-Teller interactions have been determined. The observed violation of the mirror symmetry between the conjugated spectra is explained by the interference of intramolecular interactions.     

Intensity and bandwidth of multiphonon vibronic transitions of rare-earth ions in crystals

The theory of multiphonon vibronic coupling to electronic transitions is applied in analysing fluorescence spectra of Eu²⁺ in BaFCI, which consist of the 4f⁷(⁶P_7/2,) → 4f⁷(⁸S_7/2) and 4f⁶5d → 4f⁷ transitions, and the 4f⁷-4f⁶5d excitation spectrum of Ce³⁺ in YPO⁴. The 4f electrons are weakly coupled to lattice vibration modes so that only weak one- and two-phonon sidebands are observable in the 4f-4f optical transitions, whereas the electron-phonon coupling is significantly stronger for a 5d electron. Accordingly, intensive multiphonon vibronic transitions overwhelmingly dominate the 4f⁶5d → 4f⁷ spectrum. It is shown that the extended Judd-Ofelt theory for weak vibronic coupling in the framework of the M-process is equivalent to the Huang-Rhys theory for the δ-process. In the analysis of experimental data, contributions from local ligand modes and lattice acoustic modes are separated, and the coupling strength is evaluated, in terms of the Huang-Rhys parameter S, for the 4f-4f and 5d-4f vibronic transitions.     

IR,UV and visible absorption of X irradiated single crystals of sodium nitrite

X irradiation of NaNO₂ single crystals, induces a motion of some NO₂^? ions, mainly around the axis perpendicular to their planes (a axis). The change in the orientation of NO₂^? is observed on the v₂ vibration of NO₂^? (by IR absorption) and on the vibronic structures associated with the NO₂^? electronic transitions (by UV and visible absorption). Other centers, like no₃^?, are also produced by irradiation. Their evolution with temperature is studied.     

Dependence of the Er<Subscript>2</Subscript>O<Subscript>3</Subscript> selective emission on the intensity of laser thermal excitation

The dependence of the selective emission (SE) spectra of erbium oxide (Er₂O₃) in the visible and near-IR spectral ranges on the laser excitation intensity at a wavelength of 10.6 μ m is experimentally studied. The intensity ratio for the Er³⁺ electronic and vibronic transitions in the SE spectra is varied with an increase in the laser intensity to 10 kW/cm². The mechanism for the multiphonon fluctuation excitation of electronic states and a possibility for the SE application in the observation of the thermo-photo-laser effect are discussed.     

Temperature dependence of superradiance intensity

Using the idea of exchange interaction in a system of two-level atoms participating in a superradiance process, we derive from first principles the superradiance Hamiltonian of such a system, which is found to be analogous to the Heisenberg Hamiltonian. We consistently calculate the coupling constant of the interaction that leads to the emergence of a superradiance state in the system. We also predict the existence of isospin excitations in the superradiance state, whose presence reduces the intensity of the corresponding superradiance pulse. Finally, we calculate the temperature dependence of the intensity of the superradiance pulse and find it be analogous to the Bloch T ^3/2-law for spin systems. Zh. éksp. Teor. Fiz. 116, 1148–1160 (October 1999)     

Evidence of equal Jahn-Teller coupling to Eg and T2g modes in KMgF3:Fe2+ from far infrared studies

From a study of the dependence of the far infrared (f.i.r.) spectra of KMgF₃:Fe²⁺ on impurity concentration and temperature, we identify them as due to magnetic dipole transition between the J = 1 and J = 2 states of Fe²⁺ and a resonant mode. The novelty of the work lies in demonstrating that in KMgF₃:Fe²⁺ the electronic orbital triplet is equally coupled to the E_g and T_2g modes of vibration and consequently vibronic interactions maintain the J-degeneracies.     

Computer Resolution and Franck-Condon Analysis of the Electronic Absorption Spectrum of KMnO4 in Water

Abstract

The electronic absorptíon spectrum of KMnO₄ in water solution was analyzed. The spectral contour was resolved into component bands and then Franck-Condon approach was applied. In the investigated range of 13000–48000 cm^?1 a presence of three structureless and of two vibronic strong bands was stated. The change in the Mn-O equilibrium bond length was found to be 10.5pm for 2e·1t₁ transition (vibronic band about 18000cm^?1) and to be 16pm for the 2e·3t₂ transition (vibronic band about. 30000cm_?1). The appropriate wavenumber of the vibrational mode in these excited electronic states was found to be 735cm^?1 and about 780cm^?1, respectively. The ground electronic state wavenumber of the totally symmetric vibrational mode was fitted to be equal to 828cm^?1. Details of the proposed method of computer elaboration of electronic spectra with vibrational structure were discussed.

Electronic absorption spectra of some inorganic comppunds consist of a number of strongly overlapped bands due to their vibronic structure.^1–5 A detailed analysis of spectral contours of such compounds provides some useful information about their structure in both ground excited electronic states.

The electronic spectrum of permanganate ion is the typical example of vibronic spectra.¹ The main part of the past works based on the analysis of permanganate ion spectra in low temperatures and different polarizations. In such conditions the vibronic structure is rather good resolved and can be effectively studies.^1,3,6 Spectra of solutions as a rule are relatively poor resolved so their analysis has to be more sophisticated.

The main purpose of this work is a presentation of a new computer method for an effective study of vibronic spectra of solutions. This method has been applied to the electronic absorption spectrum of KMnO₄ in water. The method allowed us to fit the geometric parameters of spectral contour, to establish the origins and parameters of two progressions in the UV/VIS range as well as to calculate the changes in the Mn-0 equilibrium bond lengths and vibrational energy resulting from the electronic excitations of the soluted permanganate ion.     

Spectroscopic properties of alexandrite crystals II

Several aspects of the optical spectroscopic properties of alexandrite crystals not previously investigated are reported here. For Cr³⁺ ions occupying the Al³⁺ lattice sites with mirror symmetry in BeAl₂O₄, the positions of the zero-phonon lines for absorption transitions to the ²T_1g and ⁴T_2g levels are identified, and vibronic transition peaks in the fluorescence spectrum are compared to transitions appearing in the Raman spectrum and Stokes excitation spectrum. In addition, the effects of radiation trapping are shown to lengthen the fluorescence lifetime of the ²E_g - ⁴A_2g transition for ions in these sites at low temperatures. For Cr³⁺ ions occupying the Al³⁺ lattice with inversion symmetry, the ground state splitting of the ²E_g - ⁴A_2g transition is reported and the decrease of the fluorescence lifetime with temperature is shown to be due to the increase in vibronic emission probability as well as increased probability of direct radiationless decay.     

Vibronic-spin-orbit coupling in octachlorodibenzo-p-dioxin

The dipole moments of vibronic transitions P _0R caused by vibronic-spin-orbit coupling along the coordinates of out-of-plane vibration modes R (to which the most intense vibronic lines of the fine-structure phosphorescence spectrum correspond) were calculated for the ³ B _1u (π π*) → S ₀ electronic transition in an octachlorodibenzo-p-dioxin molecule. The dependence of distribution (P _0R )² over R on the constant of spin-orbit coupling ?_A in different atomic groups (A = C, O, α-Cl, and β-Cl) of the molecule is ascertained. The contribution of these atomic groups (related to ?_A) to the value of P _0R ⁱ for the transitions from various triplet i-sublevels of the electronic state is determined. The obtained results about the different effect of the α-Cl and β-Cl atoms on the vibronic P _0R ⁱ and pure electronic transition dipole moments are discussed in connection with experimental data on the weak influence of the amount of chlorine atoms in polychlorinated dioxins on the phosphorescence decay time.