Ray-optics approach

Light propagation in optical waveguides is exactly described by Maxwell s equations. Yet, for multimode waveguides, which obey the condition 1 

We now consider a light wave with 1 = polarized in the x-direction, traveling in the waveguide between the two interfaces, waveguide-cover and waveguide-substrate. The wave will be reflected at the interfaces with angles cpc and (ps for cover and substrate, respectively. Since we assume the electric held is parallel to the interfaces, a phase shift of Tj will occur at each interface according to Fresnel s formulas, while the amplitude and polarization remain the same. Additionally, we assume for simplicity that (pc = Ps = V- 

After two reflections, the reflected wave is at a distance of AC — AB = Idsin p from the original wave  

The phase shift upon reflection at the interfaces depends on both the angle of reflection ip and on the polarization of the electromagnetic wave (TE or TM). 

For TE (electric field is perpendicular to the plane of incidence spanned by the wave normal and the normal to the interface), the phase shift is 

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According to the statistical ray optics approach [82], the relation between internal and external intensity of light is... 

In the framework of the geometric optics approach to seismic problems, the traveltime r(r, r ) of the seismic ray can be related to the local seismic velocity c(r) by the relationship... 

Fig. 2 Light intensity distribution along the main diameter inside a large particle, calculated using the geometrical optics approach and considering the first internal reflection of rays. (1), Kp = 0.06 (2), 0.23 (3), 1.22 (4), 6.1 — 1.2, however, the...

The phase information is lost by simply recording a transmission image. In order to meastue (x, z) or 5 (x, z)/5x, some devices are necessary in X-ray optics. Figure 8 shows five approaches demonstrated for micro X-ray CT based on X-ray phase information. Some details of the individual methods are described below. 

In this chapter we review some of the most important developments in recent years in connection with the use of optical teclmiques for the characterization of surfaces. We start with an overview of the different approaches available to tire use of IR spectroscopy. Next, we briefly introduce some new optical characterization methods that rely on the use of lasers, including nonlinear spectroscopies. The following section addresses the use of x-rays for diffraction studies aimed at structural detenninations. Lastly, passing reference is made to other optical teclmiques such as ellipsometry and NMR, and to spectroscopies that only partly depend on photons. 

Although experimental studies of DNA and RNA structure have revealed the significant structural diversity of oligonucleotides, there are limitations to these approaches. X-ray crystallographic structures are limited to relatively small DNA duplexes, and the crystal lattice can impact the three-dimensional conformation [4]. NMR-based structural studies allow for the determination of structures in solution however, the limited amount of nuclear overhauser effect (NOE) data between nonadjacent stacked basepairs makes the determination of the overall structure of DNA difficult [5]. In addition, nanotechnology-based experiments, such as the use of optical tweezers and atomic force microscopy [6], have revealed that the forces required to distort DNA are relatively small, consistent with the structural heterogeneity observed in both DNA and RNA. 

The first theoretical attempts in the field of time-resolved X-ray diffraction were entirely empirical. More precise theoretical work appeared only in the late 1990s and is due to Wilson et al. [13-16]. However, this theoretical work still remained preliminary. A really satisfactory approach must be statistical. In fact, macroscopic transport coefficients like diffusion constant or chemical rate constant break down at ultrashort time scales. Even the notion of a molecule becomes ambiguous at which interatomic distance can the atoms A and B of a molecule A-B be considered to be free Another element of consideration is that the electric field of the laser pump is strong, and that its interaction with matter is nonlinear. What is needed is thus a statistical theory reminiscent of those from time-resolved optical spectroscopy. A theory of this sort was elaborated by Bratos and co-workers and was published over the last few years [17-19]. 

Spin-state transitions have been studied by the application of numerous physical techniques such as the measurement of magnetic susceptibility, optical and vibrational spectroscopy, the Fe-Mbssbauer effect, EPR, NMR, and EXAFS spectroscopy, the measurement of heat capacity, and others. Most of these studies have been adequately reviewed. The somewhat older surveys [3, 19] cover the complete field of spin-state transitions. Several more recent review articles [20, 21, 22, 23, 24, 25] have been devoted exclusively to spin-state transitions in compounds of iron(II). Two reviews [26, 27] have considered inter alia the available theoretical models of spin-state transitions. Of particular interest is the determination of the X-ray crystal structures of spin transition compounds at two or more temperatures thus approaching the structures of the pure HS and LS electronic isomers. A recent survey [6] concentrates particularly on these studies. 

Processes such as film extrusion, fiber spinning, injection molding, and drawing tend to impart orientation to products made from semicrystalline polymers. Mechanical, dielectric, and optical properties, to mention only three, are often strongly influenced by orientation. X-ray diffraction offers a direct approach to studying crystallite orientation because the Intensity that is diffracted into a detector placed at an appropriate position is directly proportional to the number of crystal lattice planes that are in the correct orientation for diffraction. The principles of such measurements are well described in textbooks 0,2). 

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