ABSTRACT
Second harmonic generation (SHG) has been the most investigated nonlinear optical process, since its discovery by Franken in the 1960s [1]. In SHG processes the frequency of an incoming beam, ω, is doubled due to second-order optical susceptibility χ ijk 2 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429062575/094681f2-6da1-4fd2-99d6-ea568776de0a/content/eqn_31.tif"/> (−2ω,ω,ω) of the nonlinear material. Within the electric-dipole approximation, the third-rank tensor χ ijk 2 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429062575/094681f2-6da1-4fd2-99d6-ea568776de0a/content/eqn_32.tif"/> , or equivalently the d ˜ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429062575/094681f2-6da1-4fd2-99d6-ea568776de0a/content/eqn_33.tif"/> tensor components, d ijk = (1/2) χ ijk 2 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429062575/094681f2-6da1-4fd2-99d6-ea568776de0a/content/eqn_34.tif"/> , present nonvanishing terms only if the material has a non-centrosymmetric crystal structure, that is, it belongs to a group symmetry without center of inversion, thus giving rise to the so-called bulk or electric dipole induced SHG. Several nonlinear optical techniques have been developed, in order to allow the different components of the third-rank tensor χ ijk 2 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429062575/094681f2-6da1-4fd2-99d6-ea568776de0a/content/eqn_35.tif"/> to be determined with reference to a well-characterized sample, which is usually α-quartz, KDP, or BBO.
