Nonlinear Optical Coefficients

Second harmonic generation, optical rectification, and the linear electro-optic effect are particular aspects of a process in which two fields, E^c' and Eye'yt, generate a polarization P V ° ' = d^kyE%ifitEykeiyt. 913 (1) 914 TI-IE BELL SYSTEM T E C H N I C A L JOURNAL, M A Y - J U N E 1907 Our concern is with the tensor coefficients which (Nye 1 ) necessarily vanish in centric (centrosymmetric) crystals and which, in acentric crystals, are subject to symmetry restrictions, (Kleinman 2 ) which often leave only one or two independent components. Experimentally, the values of the allowed components of d in different materials and at different frequencies range from about 2.10 1 0 esu (cm/stat volt) to about 6.10 -5 esu. This range may be contrasted with the linear optical susceptibility x which is between 0.1 and 0.3 for the vast majority of materials and only quite exceptionally exceeds unity. There is, however, a connection between the tensor d and x which is expressed by an important empirical rule due to Miller. 3 If we write as daifk = xuxuxlk&ijk , (2)