Refracting rays step-profile fiber

The transmission coefficients of Eqs. (7-15) and (7-19) apply to all tunneling rays on graded- and step-profile fibers, except in the limit where a tunneling ray becomes a refracting ray, i.e. when - p. In this limit, the value of the transmission coefficient is relatively large compared to its value for tunneling rays close to the bound-ray limit, i.e. when - oo. Consequently, for certain... 

For situations where the above assumption cannot be adopted, expressions for the transmission coefficient in the transition region between tunneling and refracting rays are available [4,8]. The values of Tare plotted as curve (i) in Fig. 7-2(b) for a skew leaky ray with I = 0.033 on a clad parabolic fiber. To the left of the vertical dashed line, the curve corresponds to tunneling rays and coincides with the local plane-wave expression of Eq. (7-18) as increases [8]. Similarly, to the r ght of the vertical dashed line, the curve corresponds to refracting rays Ind coincides with the local plane-wave expression of Eq. (7-6) as decreases. A similar transition occurs for skew leaky rays on a step-profile fiber [16]. 

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.

Within the core of a step-profile fiber, we use the Fresnel coefficient to describe the fraction of power lost by rays which undergo refraction at the interface. In Fig. 35-1 (b), the incident and transmitted rays make angles O and a, respectively, with the normal, or radial, direction. If we ignore polarization, then Eq. (35-20) is replaced by... 

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.

Figure 21.21 Step-index optical fiber design, (a) Fiber cross section, (ft) Fiber radial index of refraction profile, (c) Input hght pulse, (d) Internal reflection of hght rays, (e) Output light pulse.

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