Sources endface illumination

The source is located in a uniform medium of refractive index Mq is assumed to be sufficiently large that it fully illuminates at least the core cross-section of the fiber endface, as is normally the case in practice. A ray from the source is incident on the endface z = 0 at Q in Fig. 4-4, and makes angle 0q with the normal QN, or axial, direction. The polar coordinates of Q on the endface are (r, (f>) relative to the x-axis. We consider only rays incident over the core a ray incident over the cladding cannot become a bound ray in the core. 

We can now calculate the source power carried by bound rays when the fiber is illuminated by the diffuse source. In this part of the chapter we determine the total source power, the total bound-ray power and the radial distribution of bound-ray power over the core cross-section. Later in the chapter we show how to derive the distribution of power among the various bound-ray directions. We assume that the source of Fig. 4-3(a) is placed against the fiber endface in Fig. 4—4, and its surface covers at least the core cross-section. Only the portion of the source within the core cross-section can excite bound rays, so we ignore any effects due to the source outside of this region. The excitation of leaky rays by sources is examined in Chapter 8. 

In Section 4—6 we showed how to determine the total bound-ray power and the radial distribution of bound-ray power within the core of the fiber when illuminated by a uniform diffuse source which abuts the endface. Here we determine the distribution of source power among the bound-ray directions. This distribution can be conveniently described in terms of the ray invariants by defining a distribution function F(fi, I) such that [6]... 

The diffuse source of Fig. 4-3 (a) illuminates the endface of a step-profile fiber in Fig. 4-4. This source excites all tunneling and refracting rays, as well as bound rays. In order to determine the power entering the tunneling rays, we must first determine the distribution function. 

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)... 

In the previous chapter we examined the excitation of modes of a fiber by illumination of the endface with beams and diffuse sources, i.e. by sources external to the fiber. Here we investigate the power of bound modes and the power radiated due to current sources distributed within the fiber, as shown in Fig. 21-1. Our interest in such problems is mainly motivated by the following chapter, where we show that fiber nonuniformities can be modelled by current sources radiating within the uniform fiber. Thus, isolated nonuniformities radiate like current dipoles and surface roughness, which occurs at the core-cladding interface, can be modelled by a tubular current source. 

When the source of excitation is specified, either as a current distribution J within the fiber, or as illuminating fields E, and H, over the endface, the aj Q) are given explicitly by Eqs. (25-12) and (25-11), respectively. In either case, we substitute the expression for aj Q) into Eq. (26-1), and take advantage of the symmetry properties of the integrand to extend the range of integration to Q= — 00. For the step-profile fiber, each cartesian, or scalar component, of the field is proportional to an integral / of the form... 

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