Page 715 - Introduction to Information Optics

12.3. Design of Optical Network Transport 69^
be increased as the light source line width becomes wider than the Brillouin
line width [26]. Another practical approach is to dither the laser source. Slight
dither in frequency, for example, tens of MHz, can increase the SBS threshold
by more than an order of magnitude. Although the SRS threshold is higher, in
DWDM systems it still causes power transfer from the low-wavelength
channels to the high ones and therefore leads to SRS cross talk between
channels. Large fiber dispersion and power equalization between channels are
usually used to alleviate the SRS negative impacts of SRS.

12.3.2,2. Self-Phase Modulation and Cross-Phase Modulation

Both self-phase modulation (SPM) and cross-phase modulation (XPM) in
optical fiber arise from nonlinear refraction that refers to the intensity depend-
ence of the refractive index. SPM has been well depicted in [35]. The refractive
index can be expressed as

P
n(io) = n 0(oj) + n 2—- , (12.17)

where n 0(o>) is a linear component and n 2 is the nonlinear refraction index
20 2
coefficient, which is ~3 x 10~ m /w for silica fibers. This nonlinear refrac-
tion results in a nonlinear phase shift to the light traveling in a fiber [27]

(12.18)

where y is the nonlinear coefficient, and

(12.19)

where /. is the wavelength of the light. Although the nonlinearity of the silica
material itself is very small, the confined optical power inside the fiber and the
long propagation length lead to significant nonlinear phase shift.
SPM is caused by phase shift from the optical field itself. The peak of a pulse
induces a higher nonlinear coefficient and travels slower in the fiber than the
wings. As a result, in the wavelength domain the leading edge of the pulse
acquires shift toward red (longer wavelength) and the trailing edge acquires
shift toward blue (shorter wavelength). The signal broadening in the frequency
domain is

(12.20)