Cross Section laser frequency dependence

There have been extensive theoretical treatments of resonant and preresonant Raman scattering, which reveal the important factors affecting the magnitude of p. However, it is difficult to theoretically predict p from molecular structure, and the theory is normally used to predict laser frequency dependence and deduce the relationship between resonance Raman spectra and molecular structure. Albrecht and Hutley (22) derived an expression for the laser frequency dependence of the cross section ... 

The strength of a photon—molecule interaction is deterrnined by the frequency-dependent cross section 0 (v), expressed in cm for absorption and related to a(y) in equation 1 or by the differential cross section (k5(y) jin units of cm /sr for scattering (14). The latter specifies the likelihood that active species scatter some portion of the incident laser fluence (photons /cm ) into a viewing soHd angle, AQ, measured in steradians (Fig. 1). The cross sections can be expressed as in equation 5 ... 

The stretching and bending modes of zeolite lattices have weak Raman cross sections, which makes measuring high quality Raman spectra difficult. Laser induced fluorescence is also a common problem with dehydrated zeolites, although this can be overcome with the Fourier transform technique. As with the corresponding infrared spectra, the frequencies of the Raman active lattice modes depend on both the local structure and the composition of the zeolite lattice. 

Frequency upconversion of 800 nm ultrashort 175 fs optical pulses by two-photon absorption in a stilbenoid compound-doped polymer (PMMA) optical fiber was reported [28]. By the intensity-dependent transmission method, the two-photon absorption cross section was deduced. The combination of a well-designed organic chromophore incorporated into a fiber geometry is appealing for the development of an upconversion blue polymer laser. Upconversion fluorescence and optical power limiting effects based on the two- and three-photon absorption process of a frans-4,4 bis(pyrrolidinyl)stilbene were investigated [29]. The molecular TPA cross section three-photon absorption (3PA) cross section g3 at 720-1000 nm were measured. The 3PA-induced optical power-limiting properties were also illustrated at 980 nm. 

The fact that such an experimental window for coherent control in liquids does actually exist was verified in experiments on the selective multiphoton excitation of two distinct electronically and structurally complex dye molecules in solution (Brixner et al. 2001(b)). In these experiments, despite the failure of single-parameter variation (wavelength, intensity or linear chirp control), adaptive femtosecond pulse shaping revealed that complex laser fields could achieve chemically selective molecular excitation. These results prove, first, that the phase coherence of complex molecules persists for more than 100 fs in a solvent environment. Second, this is direct proof that it is the nontrivial coherent manipulation of the excited state and not of the frequency-dependent two-photon cross sections that is responsible for the coherent control of the population of the excited molecular state. 

With infrared-radiation pump lasers, where the frequency of the exciting photons approaches the energy of the direct band gap of several semi-conductos (e.g., InSb, PbTe), the effective mass m becomes very small and the light scattering cross section can approach one million times that of the free electron. The SFR cross section furthermore depends on the magnetic field strength. 

After having passed a A/4 plate v/hich produces a circular polarization, the pump beam travels in the opposite direction through the sample cell. When the laser frequency ca is tuned to a molecular transition (J", M")- (J, M ), molecules in the lower level (J", M") can absorb the pump wave. The quantum number M, which describes the projection of J onto the direction of light propagation, follows the selection rule aM = +1 for transitions M" ->M induced by left-hand circularly polarized light (M" M = M" + 1). Due to saturation the degenerate M sublevels of the rotational level J" become partially or completely depleted. The degree of depletion depends on the pump intensity I, the absorption cross section a(J", M" O, M ), and on possible relaxation processes which may repopulate the level (J", M"). The cross... 

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