Page 451 - High Power Laser Handbook

418 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 419

y
x

LP 01
LP 01 LP 11 LP 21
LP 11

LP 02 LP 12 LP 22

Figure 15.3 The first few modes of an optical fiber. The arrows represent the
direction of the electric field.

The first two modes of an optical fiber (LP and LP ) are illus-
01
11
trated in Fig. 15.3. The fundamental mode has two degenerate modes,
and the second mode has four nearly degenerate modes in an optical
fiber with perfect circular symmetry. This degeneracy of the two
orthogonally polarized modes can lead to easy coupling between
them, inducing depolarization after a short propagation length assum-
ing a linearly polarized input. The degeneracy can be broken by intro-
ducing a noncircular symmetry, which is what happens in a polarization
maintaining (PM) fiber, leading to much improved polarization pres-
ervation. The normalized propagation constant b of all LP modes in a
step-index fiber are plotted in Fig. 15.4 for V < 10. It can be seen that

1.0

0.8
Normalized propagation constant (b) 0.6 01 11 21 31 02 12 41 03

0.4
22
0.2
13
32 51 61
42
0.0
0 2 4 6 8 10
Normalized frequency (V )
Figure 15.4 Normalized propagation constant for all LP modes with
normalized frequency V < 10 for a step-index fiber.