Der eine ist stumm, der andere ein Blinder by Akif Pirincci

By Akif Pirincci

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5 (a) If i ≤ imax , light is guided. (b) If i > imax , light escapes from the core. Using Eq. 148), we obtain n21 sin2 ???? > n22 or n21 cos2 ???? < n21 − n22 . 4) Using Eqs. 4), it follows that, to have a total internal reflection, we should have the following condition: sin i < (n21 − n22 )1∕2 . 5) If (n21 − n22 )1∕2 > 1, total internal reflection occurs for any incidence angle i. But for most of the practical fiber designs, (n21 − n22 )1∕2 ≪ 1. In this case, as the angle of incidence i increases, ???? decreases and the light ray could escape the core–cladding interface without total internal reflection.

Let ????c be the critical angle. Consider a ray with an angle ???? > ????c , as shown in Fig. 2. This ray undergoes total internal reflection at B. The reflected ray BC undergoes total internal reflection again at C. This process continues till the output end and is called frustrated total internal reflection. With this mechanism, light is successfully transmitted from the input end to the output end of the fiber. 2 Signal propagation in a fiber by frustrated total internal reflection. 37 Optical Fiber Transmission Reflective coating Silica core Signal propagation in a fiber by repeated normal reflections.

5), the maximum value of sin i for a ray to be guided is given by sin imax = (n21 − n22 )1∕2 . 7) and imax is called the acceptance angle. Let us define the relative index difference as Δ= n1 − n2 . 8) If the difference between n1 and n2 is small, n1 + n2 ≈ 2n1 and Eq. 7) can be approximated as NA ≈ n1 (2Δ)1∕2 . 9) Let us construct a cone with the semi-angle being equal to imax , as shown in Fig. 5(a). If the incident ray is within the cone (i < imax ), it will be guided through the fiber. Otherwise, it will escape to the cladding and then to the jacket, as shown in Fig.

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