tes within each channel. However, if a channel has enough power to induce the effect on the refractive index of the material for another channel propa- gating through the same material (that is to say, in a WDM system) then impairment arises in this other channel. This effect is referred to as Cross-Phase Modulation (XPM). The total induced frequency chirp, AWNL(t), is given by AWNL(t) (5.63) where (5.64) Because the XPM term is twice that of a single channel in the first-order design of WDM, only the XPM term is taken into consideration. [2b] Stimulated Raman Scattering With an very intense incident optical wave, Stimulated Raman Scattering (SRS) can occur in which a forward-propagating wave, referred to as the Stokes wave, grows rapidly in the fiber SO that most of the energy of the incident wave is transferred into it. The incident radiation is also referred to as the pump. In a fiber the forward-scattered wave grows as L)=Iz(0)xexp(gRIpLeff-asL) (5.65) where gR is the Raman gain coefficient; Ip is the intensity of the incident radiation; Is(0) is the initial value of the forward-scattered wave; Leff is the effective length; as is the fiber loss at the wavelength of the Stokes wave; and L is the fiber length. The Raman gain, gR, in silica fiber extends over a large frequency range (up to 40 THz) with a broad peak near 13 THz. This behavior is due to the noncrystalline nature of silica glass. In amorphous materials such as fused silica, molecular vibrational frequencies spread out into bands that overlap and become a continuum, unlike most materials where Raman gain occurs at specific fre- quencies. The Raman gain for silica is shown in Figure 5.26 measured with a pump at 1.0 um. Chapter 5 Optical Fibers Fig. 5.26 Raman gain of silica fiber. Source: Based on Ramaswami and Sivarajan (2002) and Stolen (1980). Channel Separation (THz) The impact of the SRS on the performance of a single-channel optical system is negligi- ble because the threshold power required is Raman = 16 Aett (5.66) and for a fiber with Aeff =