Bound rays

A ray is reflected from the interface back into the core at angle 0 regardless of whether partial or total reflection occurs. If we repeat this procedure at successive reflections from the interfaces, we construct the zig-zag paths, or trajectories, of Fig. 1-4. Path (a) is for a ray that is totally reflected at every reflection. We refer to this as a bound ray, since its path is entirely confined within the core. Path (b) is for a ray that is partly reflected at each reflection. We refer to this as a refracting ray. The rays may be categorized by the value of 0 according to... 

Since the power of a bound ray is totally reflected back into the core at every reflection, the ray can propagate indefinitely without any loss of power. A... 

Fig. 1-4 Zig-zag paths within the core of a step-profile planar waveguide for (a) bound rays and (b) refracting rays.

Fig. 1-8 Sinusoidal-like bound-ray path within the core of a graded-profile planar waveguide.

Fig. 1-9 Ray half-period Zp for a bound ray in the core of a graded-proiile planar waveguide. The path length Lp is measured along the path from P and Q.

The ray-path parameters are calculated with reference to Fig. 1-9 which shows a bound-ray path between successive turning points P and Q, separated by the ray half-period Zp measured along the axis. The path length Lp and the optical path length Lg are defined by path integrals... 

Fig. 2-7 Schematic distribution of rays on circular fibers according to the value of the invariants andTfor (a) the step-profile of Eq. (2-8) and (b) the clad power-law fibers of Eq. (2-43) [3]. Shading denotes tunneling rays (TR) and hatching denotes refracting rays (RR). Bound rays (BR) occupy the unshaded regions.

The range of values of 0 (r) for bound rays at radius r is then... 

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