Time-dependent optical anisotropy

In interacting systems the optical and orientation factors in a are no longer separable quantities. The induced optical effect is determined both by the single particle scattering [form factor P q)] and by the pair distribution function [structure factor 5( )], the latter being direction-dependent [42]. Since in addition to orientation the electric field causes particle translation, even for spherical particles the radial distribution function g q, /) and the "static" structure factor attain time-dependent induced anisotropy. The deformed surface potential also contributes to this effect. 

The application of an external field onto many materials will induce optical anisotropy. If the applied field oscillates, a time-dependent modulation of the polarization of the light transmitted by the device will result. Modulators of this sort include photoelastic modulators (PEM) [30,31], Faraday cells [32], Kerr cells [32], and Pockel cells. 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

The relationship between the structure of a polymer chain and it dynamics has long been a focus for work in polymer science. It is on the local level that the dynamics of a polymer chain are most directly linked to the monomer structure. The techniques of time-resolved optical spectroscopy provide a uniquely detailed picture of local segmental motions. This is accomplished through the direct observation of the time dependence of the orientation autocorrelation function of a bond in the polymer chain. Optical techniques include fluorescence anisotropy decay experiments (J ) and transient absorption measurements(7 ). A common feature of these methods is the use of polymer chains with chromophore labels attached. The transition dipole of the attached chromophore defines the vector whose reorientation is observed in the experiment. A common labeling scheme is to bond the chromophore into the polymer chain such that the transition dipole is rigidly affixed either para 1 lei (1-7) or perpendicular(8,9) to the chain backbone. 

Time-resolved optical experiments rely on a short pulse of polarized light from a laser, synchrotron, or flash lamp to photoselect chromophores which have their transition dipoles oriented in the same direction as the polarization of the exciting light. This non-random orientational distribution of excited state transition dipoles will randomize in time due to motions of the polymer chains to which the chromophores are attached. The precise manner in which the oriented distribution randomizes depends upon the detailed character of the molecular motions taking place and is described by the orientation autocorrelation function. This randomization of the orientational distribution can be observed either through time-resolved polarized fluorescence (as in fluorescence anisotropy decay experiments) or through time-resolved polarized absorption. 

As noted above, the in-phase and quadrature spectra represent components of dynamic optical anisotropy caused by the re-orientational behaviour characteristic of the type and local environment of each group. Reorientation processes tend to synchronize if there is a specific chemical interaction or connectivity between them, and herein lies the value of correlation analysis, in that it provides a valuable method for studying the time dependent variation of infrared dichro-ism signals. 

In semiconductor nanostructures, local field effects are mostly due to a surface charge polarization contribution, which is essentially a macroscopic classical term, that is very important in optical properties calculations. For instance, surface polarization is responsible for a strong optical anisotropy of elongated nanocrystals [36]. We can say that the one-particle contribution represents the optical properties of an isolated, stand-alone nanocrystal, the intrinsic properties due to the delocalized states and the quantum confinement effects. One-particle contributions do not take into account the influence of the external environment into the optical properties, such as the macroscopic polarization of the surface bonds. On the contrary, the methods beyond one-particle calculations, based on the inversion of the dielectric matrix or, as we will see below, a time-dependent tight-binding formulation, take into account more properly the influence of the external environment, in particular the charge transfer within the nanocrystals and at the surface. 

Three basic types of physical phenomenon are responsible for electroopti-cal behavior of a macromolecule in solution dipole moment, diffusion coefficients, and extinction coefficients. Amplitudes and time constants depend on both the properties of the macromolecules and experimental conditions. The sum of relaxation amplitudes is related to the linear dichroism of the solution at saturation, and depends on both the electric and optical properties of the molecule under investigation. The saturating behavior of linear dichroism calculated for a pure permanent moment, a pure induced moment or a mixed orientational mechanism is traditionally used in determining electrical responses and optical anisotropy by fitting the experimental results to a theoretical curve.Pqj. molecules with effective cylindrical symmetry (regarding their orientational behavior), the optical signal observed in the experiment can be represented as a product of orientational factor, < )(j, and a limiting reduced dichroism at infinite field. 

The in-phase and quadrature spectra represent orthogonal components of the dynamic optical anisotropy caused by the reorientation of electric dipole transition moments. The in-phase spectrum is proportional to the instantaneous extent of strain. The quadrature spectrum, on the other hand, represents the component of reorientation proportional to the rate of strain, which is n/2 out of phase with the extent of strain. Figure 36 shows an example of the in-phase and quadrature spectrum. These two component spectra contain the same amount of information content displayed in the set of time-resolved spectra shown in Figure 35. In other words, the entire time-dependence of the dichroism signals can be reconstructed from the linear combinations of the two orthogonal component spectra. 

Fig. 3.9 shows the V J) and C(J) dependences for the types of transitions discussed. As can be seen for Q Q i transitions the quantum mechanical solutions already at J > 5 differ little from the J —> oo limit. At the same time, in the case ofPj. Pj.or.Pj. RI. type transitions, even at such high values as J = 50 the difference from the classical limit still constitutes a value of the order of 1% of that of the degree of polarization or of anisotropy. This may lead to considerable error if one uses classical expressions from Table 3.5 for V x) dependences of the type presented in Fig. 3.8 for the determination of parameter x Table 3.6 also presents the values of 7Z(x), P(x) and C(x) in the limit of very strong optical depopulation for x > oo- It is noteworthy that in this case the corresponding values for P-excitation are identically equal to zero, independently of J, whilst in the other cases they behave either as 1/J or as 1/J2 see Fig. 3.9. 

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