Molecular Transition Frequencies Research Articles

Nonlinear optical line shapes of disordered molecular aggregates: Motional narrowing and the effect of intersite correlations

We theoretically investigate nonlinear optical line shapes of linear molecular aggregates with Gaussian disorder in the molecular transition frequencies. A perturbative treatment in the disorder is used, within which the joint stochastic distribution function of the frequencies of all multiexciton states of an aggregate can be determined analytically. It is shown that motional narrowing, which is characteristic for the linear absorption spectra of aggregates, also occurs for nonlinear line shapes. An important aspect of our disorder model is that it allows for general correlations between the transition frequencies of molecules within one aggregate, thereby interpolating between continuous energy disorder and a segment or kink model. The general theory is applicable for nonlinearities of any order. Specific applications are discussed for linear absorption, nonlinear absorption, and two-color pump–probe spectra. Our theory suggests that pump–probe experiments provide a novel and very promising approach to obtain microscopic information on aggregate systems; in particular, this technique can be used to determine both the magnitude of the molecular disorder and its degree of intersite correlation within aggregates.

Classical model of femtosecond time-resolved absorption spectra of dissociating molecules

We present a simple classical model for understanding time-resolved absorption spectra of molecules that are in the process of dissociating. The model applies to absorption spectra that are obtained by measuring the spectral power density of an ultrafast, continuum probe pulse after transmission through the sample. We show that the classical model can yield results in good agreement with quantum-mechanical wave packet propagation calculations. In a close analogy with collisional line broadening, the time-resolved absorption spectra are shown to have an impact region near the separated-atom transition frequency and a far-wing region. The impact region is due to radiation emitted after the molecule has separated into atomic fragments, and the far-wing region is due to radiation emitted during the time of strong molecular interaction. The spectrum in the impact region depends upon an effective phase shift for a ‘‘partial’’ collision, which begins at the time that the probe pulse sweeps through the molecular transition frequency. For narrow wave packets, this phase shift can be directly measured, and the molecular transition frequency can be recovered as a function of time along the path of dissociation. For very broad wave packets, the time-resolved absorption spectra approach a statistical limit, in which the absorption line shape becomes an image in frequency space of the probability density in configuration space at the time of excitation by the probe pulse. In all cases, the frequency-integrated absorption is proportional to the net population of molecules that are excited by the probe pulse. In principle, this result can be used to obtain the strength of the transition dipole moment as a function of internuclear separation. We also consider fluorescence induced by a short optical probe pulse, as in the experiments of Zewail and co-workers. Fluorescence measurements are shown to be fundamentally different from measurements of the transmitted spectral power density: fluorescence depends upon the net population excited by the probe pulse, whereas the transmitted spectral power density depends upon interference between the incident probe field and the polarization field. Thus these two experimental techniques are sensitive to different aspects of the dissociation process.

Time-resolved absorption spectra of dissociating molecules.

We present a simple model of time-resolved absorption spectra of molecules that are in the process of dissociating. Within an ``impact approximation,'' the spectra are shown to be superpositions of Lorentzian and dispersion profiles with relative weights determined by a net phase shift. New methods are proposed for obtaining molecular transition frequencies and relative transition dipole moments as functions of internuclear separation. Experimental data on TlI are compared to theoretical predictions, with good overall agreement.

Spectral hole burning and holography. III. Electric field induced interference of holograms

The electric field induced superposition of holograms recorded by spectral hole burning is investigated. Holograms have been burned at adjacent positions in a plane defined by wavelength and electric field. Application of an appropriate electric field to the sample causes the components of adjacent holograms to overlap as the spectral holes split due to Stark shifts of molecular transition frequencies. The diffraction efficiency of such superimposed holograms depends on their relative phase and has been studied theoretically and experimentally. It is shown that for zero phase difference, constructive interference leads to a strong diffraction efficiency whereas for a phase difference of π, the gratings cancel leading to zero diffraction efficiency. Experiments have been performed with the dye cresyl violet in a polyvinylbutyral film at a temperature of 1.7 K and the data are compared with computer simulations.

Influence of the gain inhomogeneity on the frequency shift of a laser standard

It is shown that a transverse inhomogeneity of the pumping results in a blue shift of the frequency of a stabilized laser relative to a molecular transition frequency. This shift does not depend on the laser field intensity and may be an appreciable fraction of the homogeneous line width of the molecular transition.

Rotovibrational collision-induced absorption by nonpolar gases and mixtures (H2-He pairs): Symmetry of line profiles.

Intermolecular-interaction potentials depend on the vibrational coordinates of the molecules involved. We study the effect of this v dependence (as we will call it for brevity) on the symmetry of line shapes of rotovibrational collision-induced-absorption (RVCIA) spectra of collisional complexes such as ${\mathrm{H}}_{2}$-He or ${\mathrm{H}}_{2}$-${\mathrm{H}}_{2}$. If the v dependence is ignored, individual line shapes \ensuremath{\Gamma}(\ensuremath{\omega}) of CIA spectra satisfy the widely used ``detailed balance'' relationship \ensuremath{\Gamma}(-\ensuremath{\omega})=${e}^{\mathrm{\ensuremath{-}}\ensuremath{\Elzxh}\ensuremath{\omega}/\mathrm{kT}}$\ensuremath{\Gamma}(\ensuremath{\omega}), where \ensuremath{\omega} designates the frequency shift relative to the molecular transition frequency, and T the temperature. However, if one accounts for the v dependence, the symmetry of a computed profile is modified significantly, the more so the higher the temperature and the higher the vibrational overtones one considers. These differing symmetries are described in quantitative terms that are of interest in modeling or analyzing RVCIA spectra. This paper may be considered the second, concluding part of our theoretical study of the influence of the v dependence on RVCIA spectra; the previous part [Phys. Rev. A 36, 4700 (1987)] deals with the influence of the v dependence on the integrated intensities (spectral moments) of RVCIA spectra.

Effective polarizabilities in absorbing regions of molecular crystals

A technique is developed to deduce the complex effective polarizability tensor from the complex optical susceptibility tensor of molecular crystals. A simple algebraic treatment is used to compare the polarizability and susceptibility behaviour near an isolated absorption. Peaks in the imaginary part of the effective polarizability are related to the site-shifted molecular transition frequencies of exciton theory. Results for pyromellitic dianhydride (PMDA) illustrate the technique and confirm that it gives realistic polarizabilities as a function of frequency.

The microwave and far-infrared spectra of the O-(18)H radical

Far-infrared laser magnetic resonance (LMR) spectroscopy was used to calculate the frequencies, wavelengths, and line strengths for transitions of O-(18)H molecules at microwave and far-infrared frequencies. In this experiment, a molecular transition frequency is tuned into coincidence with that of a fixed frequency laser by the application of a variable magnetic field. The O-(18)H radicals, detected in natural abundance (0.20 percent), were produced by the reaction of hydrogen atoms with nitrogen dioxide. These data together with microwave frequencies ascertained by Gottlieb, Redford, and Smith (1974) were used to determine the parameters of an effective Hamiltonian. Rotational levels up to J = 5.5 were involved. Results are indicated schematically and the low-lying energy levels of O-(18)H are shown. It is concluded that the frequencies of transitions between levels studied directly in the LMR experiment are reliable.

Saturated absorption in a molecular gas mixture to find line frequencies

Saturated abosorption on a low-pressure mixture of CO2 and CH3OH inside a hot cell is used to demonstrate how the frequencies of molecular infrared transitions in near coincidence with a CO2 laser emission can be obtained with sub-Doppler resolution.

Accelerated energy transfer between molecules near a solid particle

The Forster-Dexter theory of energy transfer between molecules is generalized to include the effects of a nearby solid state particle. It is found that the energy transfer rate between a donor and acceptor molecule may be enhanced by many orders of magnitude when the molecular transition frequencies lie in the vicinity of the resonance frequency of the particle and when the particle possesses sharp features. Due to increased damping near the particle, however, this may or may not lead to increased acceptor molecule radiation.

Adiabatic rapid passage within a Doppler-broadened line: A technique for level lifetime measurements

Adiabatic rapid passage (ARP) experiments have been done in which the ARP frequency sweep covers only a fraction of a Doppler-broadened linewidth. The population inversion thus produced is monitored by suddenly shifting the laser back into resonance with the excited molecules and then observing the size of the optical nutation signal they produce. By employing a variable time delay before the sudden shift is made, the relaxation of the population difference and hence, the level lifetimes can be determined. The technique was demonstrated using a CO2 laser and transitions in N14H3 and N15H3, with the frequency sweep and shift being done by varying the molecular transition frequency via the Stark effect. The results, which are in good agreement with those found by delayed optical nutation measurements, are presented and their physical interpretation is discussed.

Transitions at the Rabi frequency in the AC Stark effect: a dressed-molecule description

Studies are made of a system consisting of a molecule interacting with both an intense electromagnetic field resonant with a molecular transition frequency and a weak RF probe field at the Rabi frequency. An earlier study of this system (Freedhoff et al., ibid., vol.8, p.L209 (1975)) is extended to include the effects of photon cascades and of laser detuning. The method of calculation is the dressed-atom description and master-equation approach of Cohen-Tannoudji and Reynaud (1977). Unlike the earlier study, the present treatment produces quantitatively correct expressions for the emission and absorption spectra both in the visible and in the RF regions. More importantly, however, the predicted absorption intensity is greatly enhanced over that in the earlier study, and, for negative detuning of the laser, amplification of the RF signal is predicted.

Problem of reproducibility of the output frequency of a CO2/OsO4laser

Two frequency-stabilized CO2/OsO4 lasers were used in an investigation of the behavior of the peak of a narrow nonlinear resonance in the spectrum of the 192OsO4 molecule. The investigation was carried out in a wide range of laser radiation intensities and OsO4 pressures in an external absorption cell. There were no power or collisional shifts of the molecular transition frequency to within ~2×10–11.

Theory of time- and frequency-resolved resonance Raman and resonance fluorescence induced by realistic coherent pulses of arbitrary strength

Closed-form expressions are derived for the time-resolved and frequency-resolved resonance fluorescence (RF) and resonance Raman (RR) produced by coherent, realistic, quasi-rectangular pulses of arbitrary strength. Saturation effects, such as optical nutation, dynamic Stark splitting and dynamic Stark shifts of RF and RR are shown to be strongly dependent on the rise and fall times of the pulse. It is predicted that at high pulse intensities, optical nutation and the intensity of RF, but not of RR, disappear rapidly with increasing frequency offset Δω = ω - ω mn of the average pulse frequency ω from the molecular transition frequency ω mn . This result strongly influences the saturation effects in Doppler-broadened time- and frequency-resolved spectra and points to the necessity of revising the interpretation of recent experimental observations.

Theory of resonance hyper-Raman induced by realistic coherent pulses

We present a theory of time-resolved and frequency-resolved resonance hyper-Raman induced by realistic, coherent, quasi-rectangular pulses. In particular, we treat the case where the mean frequency ω of the incident pulse is in near-resonance with the molecular transition frequency ω mn . New peaks are predicted and saturation effects are discussed.

Stark shift of molecular transition frequencies in a resonant optical field

Theoretical formulas are derived for the Stark shift of molecular transition frequencies in a resonant optical field. The formulas are obtained for one-photon vibrational-rotational and electronic transitions and for twophoton vibrational-rotational transitions. The influence of the hyperfine splitting on the Stark frequency shift is considered. Numerical estimates are obtained for the frequency shift of transitions in CO, HCl, CH4, and I2 molecules in a resonant optical field.

Radiative transitions at the doublet splitting frequency in the resonant Stark effect

Preliminary studies have been made of a system which consists of a molecule placed in an intense electromagnetic field resonant with a molecular transition frequency, and a probe field containing frequencies in the neighbourhood of the resulting dynamic Stark splitting frequency 2 epsilon . In these studies, only a single decay process was considered. Both emission and absorption of radiation by the system are predicted at frequencies near 2 epsilon , provided that the molecule has different permanent dipole moments in its lower and its upper states. A correct treatment, which allows for a cascade of emitted photons, is expected to bring about some quantitative changes in the shape of the predicted spectrum, but to leave unchanged the basic prediction of transitions at frequency 2 epsilon .

Calculation of improved12C16O molecular constants and rotational-vibrational transition frequencies

We report the calculation of12C16O molecular constants and rotational-vibrational transition frequencies of the electronic ground state with improved accuracy. It is based on a recent paper containing results of accurate frequency measurements of a few CO lines. By using these data new rotational constants have been determined, they are then utilized to calculate band center frequencies of four bands. Futhermore, four vibrational constants were computed by means of the calculated band center frequencies. Tables of band center frequencies, andP andR branch transition frequencies are given for the bands 1–0 to 20–19. It was not possible to obtain standard deviations of line frequencies. It is shown, however, that the best molecular constants published lead to line frequencies with deviations of a few hundred MHz. Line frequencies calculated with the new molecular constants coincide exactly with frequencies measured. Finally, it is shown that there are pairs of transitions whose frequencies are close together. By measuring frequency differences of a number of such pairs it should be possible to further improve CO molecular constants.

Accurate frequencies of molecular transitions used in laser stabilization: the 3.39-μm transition in CH4 and the 9.33- and 10.18-μm transitions in CO2

The frequencies of three lasers stabilized to molecular absorptions were measured with an infrared-frequency synthesis chain extending upwards from the cesium frequency standard. The measured values are 29.442 483 315 (25) THz for the 10.18-μm R(30) transition in CO2, 32.134 266 891 (24) THz for the 9.33-μm R(10) transition in CO2, and 88.376 181 627 (50) THz for the 3.39-μm P(7) transition in CH4. The frequency of methane, when multiplied by the measured wavelength reported in the following letter, yields 299 792 456.2(1.1) m/sec for the speed of light.

Qualitative Theory of the Senftleben Effects

A qualitative description is given of the general properties of the magnetic (and electric) field dependence of the transport coefficients of nonionized gases. This description is based on partial phase randomization which is in turn governed by the ratios of the molecular transition frequencies to ``the'' collision frequency. Applications of this qualitative picture are given to gases in low and high (Paschen-Back) magnetic fields. The viscosity is used throughout to exemplify the theory.