Construction of ray paths

Construction of ray paths 1-3 Ray invariant 1-4 Ray-path parameters 1-5 Ray transit time... 

Most of the chapter is devoted to the construction of ray paths and their classification on circular fibers with axisymmetric profiles. However, we also consider noncircular fibers since cross-sections can differ from circular symmetry in practice, e.g. elliptical fibers. Finally, since this chapter parallels Chapter 1 to a large extent, it may be helpful to compare the results of corresponding sections. 

The construction of ray paths within the core of the step-profile waveguides of Chapters 1 and 2 is based on straight-line trajectories, which are solutions of the ray-path equation of Eq. (1-18) in a uniform medium. When the core is graded, the cartesian component equations of the ray-path equation follow directly, as in Eqs. (1-19) and (2-49). Here we derive the corresponding component equations in directions defined by the cylindrical polar coordinates (r, 0, z) of Fig. 2-1, for application to fibers with graded profiles n(r) in Chapter 2, and, by simple generalization, to slowly varying fibers with profiles n(r, z) in Chapter 5. 

FIGURE 4.19 A beam of x-rays (not shown) is striking two scattering centers that emit scattered radiation. The difference in the lengths of the paths followed by the scattered waves determines whether they interfere (a) constructively or (b) destructively. 

When a beam of X-rays falls on a crystal plane composed of regularly arranged atoms, molecules or ions, the X-rays are diffracted. Waves from the diffracted X-rays may produce constructive or destructive interference. For constructive interference, the path difference must be equal to an integral multiple of the wavelength (Figure 21.26). 

CRT, the abbreviation for cathode-ray tube, was once a familiar acronym. Before liquid crystal display (LCD) was available, the CRT was the heart of computer monitors and TV sets. The first cathode-ray tube was made by Michael Faraday (1791-1867) about 150 years ago. When he passed electricity through glass tubes from which most of the air had been evacuated, Faraday discovered cathode rays, a type of radiation emitted by the negative terminal or cathode. The radiation crossed the evacuated tube to the positive terminal or anode. Later scientists found that cathode rays travel in straight lines and have properties that are independent of the cathode material (that is, whether it is iron, platinum, and so on). The construction of a CRT is shown in Figure 2-6. The cathode rays produced in the CRT are invisible, and they can be detected only by the light emitted by materials that they strike. These materials, called phosphors, are painted on the end of the CRT so that the path of the cathode rays can be revealed. Fluorescence is the term used to describe the emission of light by a phosphor when it is struck by... 

Figure 5.7 Derivation of Bragg s law of X-ray diffraction. Parallel X-rays strike the surface at an angle 0, and are reflected from successive planes of crystals of interplanar spacing d. The path difference between reflections from successive planes is given by AB + BC, which, by geometry, is equal to 2dsin0. For constructive interference, this must be equal to a whole number of wavelengths of the incoming radiation.

---