Page 71 - Fiber Optic Communications Fund

52 Fiber Optic Communications

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 2.19 Optical field and power distributions of LP mode. V = 5.3and b = 0.278.
02

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 2.20 Optical field and power distributions of LP mode. V = 4and b = 0.44.
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In this case, using Eq. (2.53) in Eq. (2.59), we find V = a and with m = 1, Eq. (2.57) becomes
1
J (V)= 0. (2.70)
0
The first zero of the zeroth-order Bessel function (Fig. 2.14) occurs at V = 2.4048. Therefore, LP ceases
11
to exist if V < 2.4048. Thus, when 0 < V < 2.4048, the fiber supports only LP mode. In other words, to
01
ensure that the fiber is single-moded, V should be smaller than 2.4048.

2.4.3 Effective Index

From Eq. (2.39), we find that the forward-propagating mode can be written as
(r,, z, t)= A R(r)Φ() exp [−i(t − z)]. (2.71)
1