 to give Ntot= (6.34) in which Ntot is the total refractive index, Nin is the familiar refractive index from linear optics, and NNL is known as the nonlinear refractive index. I is the optical intensity (W/m2). We Remark on two properties of the nonlinear refractive index. The first is that it acts on a sub-picosecond timescale and so, even with channels at or slightly above 160 Gbit/s, any effects resulting from it can be regarded as instantaneous. The second is that the value of NNL depends on the composition of the optical fiber's glass (especially its GeO2 content), for which various values have been reported according to the measurement technique used. Agrawal (2001) recommends that for standard single-mode fibers we use 2.6 x 10-20 m²/W for pulses in excess of 1 ns but 2.2 x 10-20 m ²/W for pulses between 1 ps and 1 ns. Slightly greater values are required for germania-rich fibers, such as DCF. Self-Phase Modulation The dependence of the refractive index on intensity exerts an additional phase change on a propagating wave according to (6.35) BlinL is the phase shift used in linear optics, and it acts together with the second group of terms, which include the launched pump power, Pin. Aeff is the fiber's effective area to account for the radial distribution of the guided mode; and Leff is the "effective length" to account for the progressive reduction of signal power due to the fiber's loss. By integrating P(z) = Pin exp[-az] over the fiber's length, we obtain r==[1-exp(-a.)]/a (6.36) Leff can be interpreted as the length over which the same nonlinear phase shift would occur if the fiber were of zero loss. (Recall from equation 6.10 that the small signal theory of fiber Raman amplifiers also uses an effective length but its loss term is at the pump wavelength.) The logical 1s in an RZ or NRZ transmission system are in the form of pulses that can usually be approximated as Gaussians or super-Gaussians in the time domain. In either case, the intensity at the peak of a pulse is higher than at its extremities, a