Page 206 - Photonics Essentials an introduction with experiments

Optical Fibers and Optical Fiber Amplifiers

200 Advanced Topics

Figure 9.7. Schematic diagram showing a light path incident on the core–cladding in-
terface at the critical angle.

The quantity sin( a ) is called the numerical aperture or NA of the
fiber (Fig. 9.8). The NA of a fiber having an index difference of 1% is
about 0.2. This corresponds to an angle of about 2 × 11° , or 22°. A typ-
ical optical fiber for telecommunications has a numerical aperture of
0.1. This implies a much smaller index step than 1%.

Example 9.1
Calculate the index difference between the core and the cladding of a
fiber with an NA of 0.1. We will solve this in two ways. First we will
make an estimate:
2
2
sin( a ) = n 1 – n 2 = NA = 0.1
2
2
n 1 – n 2 = 0.01
(n 1 – n 2 )(n 1 + n 2 ) = 0.01
(n 1 + n 2 ) = 0.01
0.01 0.01
= = 0.003448
n 1 + n 2 2.90
In this case, we assume that n 1 n 2 = 1.45

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