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Figure 3-2 Total Internal Reflection

The critical angle is fixed by the indices of refraction of the core and cladding and is computed using the following formula: qc = cos–1 (n2/n1)The critical angle can be measured from the normal or cylindrical axis of the core. If n1 = 1.557 and n2 = 1.343, for example, the critical angle is 30.39 degrees.

Figure 3-2 shows a light ray entering the core from the outside air to the left of the cable. Light must enter the core from the air at an angle less than an entity known as the acceptance angle (a): qa = sin–1 [(n1/n0) sin(qc)]In the formula, n0 is the refractive index of air and is equal to one. This angle is measured from the cylindrical axis of the core. In the preceding example, the acceptance angle is 51.96 degrees.The optical fiber also has a numerical aperture (NA). The NA is given by the following formula:

NA = Sin qa = ?(n12 – n22) From a three-dimensional perspective, to ensure that the signals reflect and travel correctly through the core, the light must enter the core through an acceptance cone derived by rotating the acceptance angle about the cylindrical fiber axis. As illustrated in Figure 3-3, the size of the acceptance cone is a function of the refractive index difference between the core and the cladding. There is a maximum angle from the fiber axis at which light can enter the fiber so that it will propagate, or travel, in the core of the fiber. The sine of this maximum angle is the NA of the fiber. The NA in the preceding example is 0.787. Fiber with a larger NA requires less precision to splice and work with than fiber with a smaller NA. Single-mode fiber has a smaller NA than MMF.

August 22, 2011
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