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536 Fiber Optic Communications

where
2
3 (3)
0
= (B.27)
2
8c A
eff 0

is the nonlinear coefficient. Note that multiplication by Ω in the frequency domain leads to the operator i in
t
the time domain. Eq. (B.26) in the absence of the right-hand side terms is called the nonlinear Schrödinger
equation (NLSE). The third term on the left-hand side represents self-phase modulation, which is discussed
in Section 10.5. The second term on the right-hand side of Eq. (B.26) is responsible for self-steepening.
The terms on the right-hand side of Eq. (B.26) become important for ultra-short pulses (pulse width < 1ps).
Eq. (B.26) in the presence of the right-hand-side terms is called the modified nonlinear Schrödinger equation
(MNLSE). From Eq. (10.53), we have
3 (3)
n = . (B.28)
2
8n
0
Using Eq. (B.28) in Eq. (B.27) and noting that ≅ n ∕c, we obtain
0 0
0
n 0
2
= . (B.29)
cA eff