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Optical Fiber Transmission 53

1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
–1 –0.5 0 0.5 1

Figure 2.21 Optical field and power distributions of LP mode. V = 10.3and b = 0.456.
22
In analogy with a 1-dimensional plan wave (Section 1.6.1), the phase speed of this mode can be written as

= . (2.72)

The phase speed of an electromagnetic wave propagating in a uniform medium of refractive index n is
eff
c
= . (2.73)
n
eff
Combining Eqs. (2.72) and (2.73), we find

= n eff = k n . (2.74)
0 eff
c
Thus, n can be interpreted as the effective index “seen” by the mode with propagating constant . Guided
eff
modes occur if k n < < k n or n < n < n .
0 2 0 1 2 eff 1
2.4.4 2-Dimensional Planar Waveguide Analogy
Consider a 2-D planar waveguide as shown in Fig. 2.22. Let
{
n 1 for |x| < d∕2
n(x)=
n 2 otherwise

Figure 2.22 A 2-dimensional planar waveguide.