 Fiber Length Fig. 5.22 Concept of the effective length, Leff, in nonlinear optical effects. Aeff  r (5.49) where ro is the mode field radius. The concept is illustrated in Figure 5.21. The second is the effective length, Leff, and it is defined by (5.50) where L is the fiber length and a is the attenuation coefficient of the fiber, which here is not in dBs. The attenuation coefficient of the fiber in this equation is derived from the loss in decibels through the equation (5.51) For low-loss fiber Leff = L and for high loss fiber, Leff = 1/a Because the fiber for optical transmission has low loss, the first approximation is usually used. The physical meaning of Leff is simple. We know that for low power the nonlinear effects are negligible, SO there is a "threshold" of power above which the propagation is nonlinear and below which it is linear. This concept is illustrated in Figure 5.22. For example, consider a fiber with a loss of 1.8 dB/km and length of 25 km. Using the approximation for low loss, Leff = L. If we use equation 5.50 the result is 15.5 km. In a system with optical amplifiers, the effective length of the system is given by (5.52) Chapter 5 Optical Fibers where Ltotal is now the total system length and Al the spacing between amplifiers. It is clear that to reduce the system effective length it is better to use as few amplifiers as possible. The nonlinear effects relevant to fiber communications are [1] Single-channel systems [1a] Self-Phase Modulation (SPM) [1b] Stimulated Brillouin Scattering (SBS) [2] Multichannel systems [2a] Cross-Phase Modulation (XPM) [2b] Stimulated Raman Scattering (SRS) [2c] Four-Wave Mixing (FWM) [1a] Self-Phase Modulation To understand the self-phase modulation effect, one has to understand the effect of high intensity on the refractive index of the material. This impact of optical power on the refrac- tive index can be stated mathematically as (5.53) where N1 is the conventional refractive index of the silica glass and N2 is the nonlinear refrac- tive index. The value of