Circular polarization modeling

Figure 9.20 Intensity of s-polarized second-harmonic signal generated in transmitted direction for glass-side incidence as function of rotation angle of quarter waveplate. Note significant difference in response for right- (45° and 225°) and left-hand (135° and 315°) circularly polarized light. Points represent experimental data, solid line fit to the model described in Section 3 with nonvanishing g, and the dashed line the fit with vanishing g.

A useful model for explanation of optical rotation considers that a beam of plane-polarized light is the vector resultant of two oppositely rotating beams of circularly polarized light. This will be clearer if we understand that circularly polarized light has a component electric field that varies in direction but not in magnitude so that the field traverses a helical path in either a clockwise or counterclockwise direction, as shown in Figure 19-2. 

Drude first proposed that the rotatory power of a dissymmetric substance could be understood if its absorption of light involved the motion of a charged particle along a helical path within the molecule [8]. This type of motion would result in the simultaneous production of an electric dipole from the translatory motion and a magnetic dipole from the rotatory motion. The model requires that the electric and dipole moments have at least some components which are collinear with each other, or else stereospecific interaction with circularly polarized light would not be possible. 

Modeling EM solitary waves in a plasma is quite a challenging problem due to the intrinsic nonlinearity of these objects. Most of the theories have been developed for one-dimensional quasi-stationary EM energy distributions, which represent the asymptotic equilibrium states that are achieved by the radiation-plasma system after long interaction times. The analytical modeling of the phase of formation of an EM soliton, which we qualitatively described in the previous section, is still an open problem. What are usually called solitons are asymptotic quasi-stationary solutions of the Maxwell equations that is, the amplitude of the associated vector potential is either an harmonic function of time (for example, for linear polarization) or it is a constant (circular polarization). Let s briefly review the theory of one-dimensional RES. 

Finally, magnetically induced circularly polarized emissions ("MICE") have been reported for several charge transfer emitters containing ruthenium(II) and analyzed in terms of Crosby s proposed model for MLCT excited states (177). 

To illustrate the exchange of the phase information between the atomic transition and the multipole field, consider the electric dipole Jaynes-Cummings model (34). Assume that the field consists of two circularly polarized components in a coherent state each. The atom is supposed to be initially in the ground state. Then, the time-dependent wave function of the system has the form [53]... 

Pyrene excimer formation still continues to be of interest and importance as a model compound for various types of study. Recent re-examinations of the kinetics have been referred to in the previous section. A non a priori analysis of experimentally determined fluorescence decay surfaces has been applied to the examination of intermolecular pyrene excimer formation O. The Kramers equation has been successfully applied to the formation of intermolecular excimer states of 1,3-di(l-pyrenyl) propane . Measured fluorescence lifetimes fit the predictions of the Kramer equation very well. The concentration dependence of transient effects in monomer-excimer kinetics of pyrene and methyl 4-(l-pyrenebutyrate) in toluene and cyclohexane have also been studied . Pyrene excimer formation in polypeptides carrying 2-pyrenyl groups in a-helices has been observed by means of circular polarized fluorescence" . Another probe study of pyrene excimer has been employed in the investigation of multicomponent recombination of germinate pairs and the effect on the form of Stern-Volmer plots ". 

Materials Photoacoustic measurements were made on a component-assembled PAS spectrometer consisting of a 9W argon ion laser (Spectra Physics), a 0.5 cc internal volume PAS cell equipped with a sensitive electret microphone (Radio Shack, 3.2 mV/Pa). Circular polarization modulation was achieved with a special low frequency (220 Hz) photoelastic modulator (15) (Hinds International). Signals were detected and processed with a vector tracking lock-in amplifier (PAR model 5204), and intensity modulation was done with a 30-slot blade mechanical chopper (Ortec). Syntheses of all compounds were by well established literature methods. 

Pyrene photophysics has produced the usual, and now to be expected, crop of papers on diverse topics. Aggregation in concentrated solutions has been evidenced by the Shpol ski effect and two photon excitation spectra have yielded new electronic state assignments. The maximum entropy method, mentioned earlier, for the determination of fluorescence lifetimes shows that in dipyrenylpropane the data for luminescence decay do not fit a simple 3-state model.This study adds more information upon a system hitherto open to much dispute. It is unlikely that the problem will be considered as solved. The presence of a ground state dimer of pyrene moieties has been shown by NMR in the bichromophoric molecules of (pyrenylcarboxyl) alkanesand also with racemic and meso dipyrenyl alkanes. Strong circular polarization in excimer emission has been detected from pairs of pyrene groups linked to a polypeptide chain. ... 

The spin splitting of the energy bands of semiconductors without inversion symmetry has other interesting and presumably also technological consequences. Photoemitted electrons from GaAs are spin polarized when the light used for the irradiation is circularly polarized.[49,50] (such effects may also be observed for metals, see for example [51]). The so-called three step model for photomission considers the three processes, optical excition from a valence-band state to a state in the conduction band, transport of the excited electron to the surface, and — finally — emission through the... 

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