Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media; such as, media in which the induced dielectric polarization responds nonlinearly to the electric field of the light. This nonlinearity is typically observed at very high light intensities such as those provided by pulsed lasers. In this chapter, we focus on the application of high bit-rate communications. We will see that the nonlinear Schrödinger (NLS) equation and the dispersion-managed nonlinear Schrödinger (DMNLS) equation play a central role.

Communications

In 1973 Hasegawa and Tappert (Hasegawa and Tappert, 1973a; Hasegawa and Kodama, 1995) showed that the nonlinear Schrödinger equation derived in Chapter 7 [see (7.26), and the subsequent discussion] described the propagation of quasi-monochromatic pulses in optical fibers. Motivated by the fact that the NLS equation supports special stable, localized, soliton solutions, Mollenauer et al. (1980) demonstrated experimentally that solitons can propagate in a real fiber. However, it was soon apparent that due to unavoidable damping in optical fibers, solitons lose most of their energy over relatively short distances. In the mid-1980s all-optical amplifiers (called erbium doped fiber amplifiers: EDFAs) were developed. However with such amplifiers there is always some additional small amount of noise. Gordon and Haus (1986) (see also Elgin, 1985) showed that solitons suffered seriously from these noise effects. The frequency and temporal position of the soliton was significantly shifted over long distances, thereby limiting the available transmission distance and speed of soliton-based systems.