Introduction

Abstract

Research on nonlinear optics has been performed, since soon after the invention of lasers in 1960. The responses of materials to an optical field, such as dielectric polarization and absorption, are approximately linear with respect to the field amplitude. However, they deviate from the linear dependence for large amplitudes. The deviations are generally called nonlinear-optic effects. They are classified into second-order nonlinearity, i.e., the component of the response proportional to the square of the field amplitude, and third-order nonlinearity, i.e., the component proportional to the cube of the amplitude. While the second-order nonlinearity is observed only in noncentrosymmetric crystals, the third-order nonlinearity is observed more or less in all materials. Since the coherent radiation produced by lasers can be concentrated into a very narrow range in spatial, temporal, and spectral domains, the field amplitude often becomes very large, and hence nonlinear-optic effects are observed significantly. The resulting nonlinear optic phenomena themselves are a subject of academic interest. More importantly, the nonlinear-optic effects not only provide a variety of possibilities in understanding the properties of materials as a means of characterization, but also enable implementation of many functions that are not feasible with linear optics and electronics. They include optical wavelength conversion by harmonic generation, mixing of frequencies, and amplification and generation of coherent radiation by parametric processes. Coherent radiation can be generated at wavelengths where no appropriate laser is available. The functions also include ultrafast temporal and spatial control of an optical wave by another optical wave, and measurements of ultrashort optical pulses by autocorrelation. They have found many important applications in many areas of science. A comprehensive review of nonlinear optics is given in Refs. [1.1]–[1.8].