This chapter discusses nonlinear optical (NLO) properties of polymers. The topics related to certain theoretical aspects, concepts of material design, and evaluation techniques for second- and third-order NLO polymers as well as for two-photon absorbing organic and polymeric materials are discussed. The hyperpolarizability (β) and second-order bulk susceptibility (χ(2)) values have been measured for a large number of chromophores in solution and in polymeric films in attempts to identify efficient second-order NLO polymers. The product (μβ) obtained from electric-field-induced second-harmonic (EFISH) measurements of several second-order NLO polymers is tabulated. A number of poled side-chain NLO polymers have employed for second-harmonic generation (SHG) measurements. Third-harmonic generation (THG) is a coherent process and arises due to purely electronic contributions and does not depend on the population of the excited state. In a degenerate four-wave mixing (DFWM) process, three optical beams of the same frequency interact with the material to create a fourth beam of the same frequency. The optical Kerr gate (OKG) is a process that arises due to optically induced birefringence caused by a nonlinear phase shift. Self-focusing and defocusing (SFD) arise from the intensity dependence of the refractive index of the medium. The two-photon absorption (TPA) phenomenon is one of the important third-order NLO features. The observed TPA cross-sections of a large variety of organic and polymeric materials are in the range of several tens GM to the order of ~ 104 GM. The third-order NLO properties are very sensitive
to the length of the π-electron conjugation.