Refracting rays fiber endface

We now determine the behavior of a ray as it passes from the source, across the fiber endface and into the core. If the refractive index Hq of the medium... 

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. 

Fig. 4-4 Reflection and refraction of a source ray at Q on the fiber endface. Polar coordinates (r, ) define the position of Q, and the projection of the ray path onto the endface makes angle 0 with the azimuthal direction at Q.

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. 

Fig. 8-9 Intensity pattern over the endface of a step-profile fiber, showing (a) a bright circle due to bound rays and (b) a dark band due to refracting rays, and lighter regions due to tunneling rays.

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