 waveguide dispersion, and polarization mode dispersion. The reason waveguide dispersion and polarization mode dispersion became important is the low value of the material dispersion. The normalized frequency parameter, V, plays an important role in single-mode fiber. The parameter V is given by (5.38) where the symbols have their usual meaning. Single-mode operation takes place above a theoretical cutoff wavelength Ac given from equation 5.38 as (5.39) where Vc is the cutoff normalized frequency. With the help of equation 5.38, equation 5.39 can be written as (5.40) For a step index single-mode fiber-that is, Chapter 5 Optical Fibers (5.41) cladding V = 2.405 and the cutoff wavelength is given by Ac-2.405 (5.42) For operation at 1300 nm the recommended cutoff wavelength ranges from 1100 to 1280 nm. With this choice for the cutoff wavelength, operation at 1300 nm is free of modal noise and intermodal dispersion. The material dispersion for silica glass with a step index single-mode fiber is given by (5.43) where d2n1/d22 is the second derivative of the refractive index with respect to the wavelength. The value of Dm(A) is usually estimated from fiber measurements, but for theoretical work a simple equation with two parameters offers a reasonable approximation. The equa- tion is (5.44) where So and 20 are the slope at 20 and the zero material dispersion wavelength, respectively. For standard single-mode fiber the slope at 20 is in the range 0.085 to 0.095 ps/nm2 X km. The Corning single-mode fiber SMF-28e+ is a typical example of high-quality modern fiber whose key parameters are summarized next. For this Corning fiber, equation 5.44 is valid for the range 1200 a 1625 nm. Tables 5.3, 5.4, and 5.5 summarize the performance of the Corning SMF-28e+ fiber. Single-mode fibers of similar performance are also available from other fiber manufacturers. After material dispersion the next important dispersion component is waveguide dis- persion. The physical origin of waveguide dispersion is the wave-guiding effects, and eve