Polarized optical spectroscopy electrical fields

A diagrannnatic approach that can unify the theory underlymg these many spectroscopies is presented. The most complete theoretical treatment is achieved by applying statistical quantum mechanics in the fonn of the time evolution of the light/matter density operator. (It is recoimnended that anyone interested in advanced study of this topic should familiarize themselves with density operator fonnalism [8, 9, 10, H and f2]. Most books on nonlinear optics [13,14, f5,16 and 17] and nonlinear optical spectroscopy [18,19] treat this in much detail.) Once the density operator is known at any time and position within a material, its matrix in the eigenstate basis set of the constituents (usually molecules) can be detennined. The ensemble averaged electrical polarization, P, is then obtained—tlie centrepiece of all spectroscopies based on the electric component of the EM field. 

Fig. 3.5. Experimental apparatus for time-resolved THz transmission spectroscopy. The sample is excited with a visible laser pulse delivered by delay line 3. A singlecycle THz electric-field transient probes the polarization response of the sample after time delay tv scanned by delay line 1. The transmitted THz amplitude is monitored via ultrabroadband electro-optic sampling in a THz receiver as a function of time T scanned by delay line 2. From [13]...

An important consequence of the presence of the metal surface is the so-called infrared selection rule. If the metal is a good conductor the electric field parallel to the surface is screened out and hence it is only the p-component (normal to the surface) of the external field that is able to excite vibrational modes. In other words, it is only possible to excite a vibrational mode that has a nonvanishing component of its dynamical dipole moment normal to the surface. This has the important implication that one can obtain information by infrared spectroscopy about the orientation of a molecule and definitely decide if a mode has its dynamical dipole moment parallel with the surface (and hence is undetectable in the infrared spectra) or not. This strong polarization dependence must also be considered if one wishes to use Eq. (1) as an independent way of determining ft. It is necessary to put a polarizer in the incident beam and use optically passive components (which means polycrystalline windows and mirror optics) to avoid serious errors. With these precautions we have obtained pretty good agreement for the value of n determined from Eq. (1) and by independent means as will be discussed in section 3.2. 

Fluctuations in the dielectric properties near the interface lead to scattering of the EW as well as changes in the intensity of the internally reflected wave. Changes in optical absorption can be detected in the internally reflected beam and lead to the well-known technique of attenuated total reflectance spectroscopy (ATR). Changes in the real part of the dielectric function lead to scattering, which is the main topic of this review. Polarization of the incident beam is important. For s polarization (electric field vector perpendicular to the plane defined by the incident and reflected beams or parallel to the interface), there is no electric held component normal to the interface, and the electric field is continuous across the interface. For p polarization (electric field vector parallel to the plane defined by the incident and reflected beams), there is a finite electric field component normal to the interface. In macroscopic electrodynamics this normal component is discontinuous across the interface, and the discontinuity is related to the induced surface charge at the interface. Such discontinuity is unphysical on the molecular scale [4], and the macroscopic formalism may have to be re-examined if it is applied to molecules within a few A of the interface. 

Optical models of the interaction of polarized radiation with plane parallel layers are based on Maxwell s equations. Many derivations have ajqieared in the literature. The most generalized models treat the probed material as an n-layered system with an arbitrary variation in optical properties with distance. Optical modeling was first applied to an isotropic monolayer deposited on an aqueous subphase by Dluhy (25). In this work, it was established that when the optical constants of the substrate are lower than the monolayer, non-zero electric field intensities exist in three dimensions, unlike the cases of grazing-angle reflection from metal surfaces or normal transmission spectroscopy. 

The electric field of laser light need not oscillate in a single plane, and often optics are employed to produce other polarizations with a degree of circularity. Circular polarizations are important in forms of laser spectroscopy which exploit angular momentum selection rules, because the photons carry unit quanta of angular momentum. With chiral substances, a small degree of sensitivity to the handedness of the radiation is also manifest in the circular differential response. For two-photon and higher-order processes, however, even the spectra of reasonably symmetrical molecules display a marked dependence on polarization. 

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