Crystal Optics General

Optical Materials High-Frequency Properties 4.4.2.1 Crystal Optics General 

The dielectric properties of a medium at optical frequencies are given by 

In this general case, two waves of different velocity may propagate through the crystal. The relative dielectric impermeabilities are defined as the reciprocals of the principal dielectric constants  

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The general dispersion formula obtained for the coupling of the vibrational equations with the Maxwell field can be brought into the form of Fresnel s wellknown equation for the wave normal from crystal optics. It is usually written in the form... 

The measured crystal optical activity, in general, can be either of molecular origin or due to the chiral helical arrangement of chiral or achiral molecules in the crystal, or both. The two factors are difficult to separate. Kobayashi defined a chirality factor r = (pc — ps)/pc = 1 — pslpc, where pc is the rotatory power per molecule of a randomly oriented crystal aggregate derived from the gyration tensors determined by HAUP, and ps that in solution [51]. It is a measure of the 4 crystal lattice structural contribution to the optical activity and represents the severity of the crystal lattice structural contribution to the optical activity, and represents the severity of the restriction of the freedom of molecular orientation by forming a crystal lattice. Quartz is a typical example of r = 1, as it does not contain chiral molecules or ions and its optical activity vanishes in random orientation (ps = 0). 

It is known that excitons and polaritons in general have properties that can be considered within the framework of electrodynamics of continuous media. These properties were described in a monograph by V. M. Agranovich and V. L. Ginzburg ( Crystal Optics with Spatial Dispersion, and Excitons , Springer, 1984) where we used a mainly phenomenological approach. In the present book I provide a microscopical theory of excitations in organic solids and nanostruc-... 

To measure a crystal - or general any phase -along the optical axis of a uniaxial phase where the eigenstates are circularly polarized. 

Liquid crystals are generally characterized by the strong correlation between molecules, which respond cooperatively to external perturbations. That strong molecular reorientation (or director reorientation) can be easily induced by a static electric or magnetic field is a well-known phenomenon. The same effect induced by optical fields was, however, only studied recently. " Unusually large nonlinear optical effects based on the optical-field-induced molecular reorientation have been observed in nematic liquid-crystal films under the illumination of one or more cw laser beams. In these cases, both the static and dynamical properties of this field-induced molecular motion are found to obey the Ericksen-Leslie continuum theory, which describe the collective molecular reorientation by the rotation of a director (average molecular orientation). 

A large and perfect crystal scatters electrons into a diffraction pattern of sharp spots. General interpretation of this pattern requires a knowledge of crystallography. There are many texts in this field [18-20], with some specifically aimed at microscopists [21, 22]. Books on crystal optics (Section 2.3) contain basic summaries [23, 24]. There are also many texts on diffraction from materials 125-27], some concentrating on electron diffraction [28, 29]. The most common use of a crystal diffraction pattern is to find the orientation of a crystal of known structure. Wunderhch [30] contains a listing of many polymer crystal structures. 

The optical properties of transition-metal (TM) ions in crystals have generally analyzed by the ligand-field theory developed by Sugano et al. In the ligand-field theory, the multiplet energies of the TM ions in the octahedral (or tetrahedral) symmetry are expressed in terms of the Racah parameters B and C) and the crystal-field parameter (A). However, in the analysis based on this theory, the parameters axe determined from the experimental optical spectra under a certain trial assignment of the observed peaks. Therefore, correct parameters cannot be obtained unless the optical spectrum of the material is available and well understood. Even if the correct parameters are... 

X- radiation is very energetic and has been very difficult to manipulate. It can be focused either coherently by Fresnel zone plates and Bragg Fresnel lenses, or incoherently by bent crystal optics and coated fiber optics (generally speaking by highly reflective materials, e.g. super mirrors etc.). However, for many applications, such as X-ray microscopy and spectroscopy, the spot size at the exit of the aperture is too large and the beam stmcture is difficult to control. Moreover, in order to use X-ray in non-invasive medical treatments there is a need for an X-ray waveguide. 

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