Excitation of Second Harmonic Signal
Just as bulk second harmonic generation, surface SHG arises out of the second-order susceptibility tensor χ(2). While the χ(2) tensor contains 27 elements, many of these elements are reduced by symmetry arguments. The exact nature of these arguments depends on the application. When determining molecular orientation, it is assumed that χ(2) is rotationally invariant around the z-axis (normal to the surface). The number of tensor elements reduces from 27 to the following 7 independent quantities: χZZZ, χZXX = χZYY, χXZX = χYZY, χXXZ = χYYZ, χXYZ = -χYXZ, χXZY = -χYZX, χZXY = -χZYX. Second Harmonic Generation further restricts the independent terms by requiring the tensor is symmetric in the last two indices reducing the number of independent tensor terms to 4: χZZZ, χZXX (equivalently χZYY), χXXZ (equivalently χXZX, χYZY, χYYZ), χXYZ (equivalently χXZY, -χYXZ, -χYZX). In order for χZXY = -χZYX to hold under this final condition, both terms must be 0. The four independent terms are material dependent properties and can vary as the external conditions change. These four terms give rise to the second harmonic signal, and allow for calculation of material properties such as electronic structure, atomic organization, and molecular orientation.
Read more about this topic: Surface Second Harmonic Generation
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