Diffuse illumination partially

So far in this chapter we have considered mode excitation due to a single beam directed at a particular angle to the fiber axis. Let us now consider the effect on mode excitation when the illumination is composed of a family of beams which differ in their angles of incidence at the endface, e.g. the source of diffuse illumination depicted in Fig. 20-6(a). Such sources are known as (partially)... 

When an n-type semiconductor which is in contact with a metal ion-containing electrolyte is illuminated, then two equal partial currents occur under open-circuit conditions (Fig. 11.25a). The anodic photocurrent is due to O2 formation in H2O, whereas the cathodic partial current corresponds to the reduction of the metallic ions. Since the holes cannot diffuse very far, most of them collect at the illuminated interface. In the case of an n-type semiconductor, sufficient electrons are availabe everywhere, so that metal deposition should occur at illuminated as well as at dark surface sites (Fig. 11.25b), according to which conclusion, selective deposition would be impossible. Experimentally, however, selective metal deposition has been observed, e.g. at CdS at illuminated surfaces [130] and at Ti02 at the dark sites [131]. In the case of CdS, this phenomenon was interpreted as a downward shift of the energy bands at the illuminated surface which is more favorable to an electron transfer there [130]. The result obtained with Ti02 has been explained by strong internal and external recombination... 

In the "diffusion flame" method developed by von Hartel and Polanji (Z. physikal. Chem. B 1930,11, 97) sodium vapour is introduced throu a nozzle into an excess of organic halide and the extent of penetration before it is completely consumed by reaction is measured. In an experiment made by Cvetanovic and Le Roy (J. Chem. Phys. 1952, 20, 1016) at 532.7 K, a stream of sodium vapour at a partial pressure = 8.3 x 10" mm Hg in nitrogen carrier gas was passed through a nozzle of radius r = 0.125 cm into a stream of nitrogen and ethyl chloride vapour at a partial pressure p = 2.5 x 10" mm Hg. The radius R of the spherical zone of reaction made visible by illumination with sodium D-line resonance radiation was 1.55 cm. The partial pressure P of sodium at the visibility limit was estimated to be 7 X 10" mm Hg. The diffusion coef5cient D of sodium in the reaction mixture is 130 cm s. ... 

In the last five sections we have shown how a lens, on the one hand can increase source efficiency for collimated beam illumination of a fiber, while, on the other hand, it is ineffective at increasing the efficiency of the diffuse source. If we couple these facts with the description of the diffuse source as a superposition of collimated beams, it is evident that the efficiency of a partially diffuse source can be increased by a lens. The situation is illustrated in Fig. 4—8. We assume the step-profile fiber is weakly guiding so that 9 1, and the focal length satisfies... 

The partially diffuse source of Fig. 20-6(a) illuminates a single-mode fiber. We showed in Sections 20-7 and 20-12 that the fundamental mode is most efficiently excited by on-axis beams. Thus, it is intuitive that the more diffuse the source, i.e. the larger 0 , the lower the efficiency of the source in exciting the fundamental mode. To demonstrate this behavior quantitatively, we consider a source with a Gaussian intensity... 

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