Introduction to Third-order Processes and Materials
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Gamma is the second hyperpolarizability which is a molecular property. It scales as the cube of the electric field
Nonlinear polarization becomes more important with increasing field strength, since it scales with higher powers of the field. This relates to chi(3), which is a materials property. Chi (3) and gamma can exist in all materials and all molecules, even those which are centrosymmetric materials. (chi(2) can only happen in non centrosymmetric materials).
Under normal conditions, aijE .> ßijk/2 E·E > gijkl /6 E·E·E.
J is the coordinate system for the applied field I is the coordinate system for the induced polarization in the molecule Alpha is 3 x 3 tensor Beta is 3 x 3 x 3 tensor with 27 components Gamma is a 3 x 3 x 3 x 3 tensor with 81 components
Thus, there were few observations of NLO effects before the invention of the laser with its associated large electric fields.
Just as alpha is the linear polarizability, the higher order terms beta and gamma (equation (7)) are called the first and second hyperpolarizabilities respectively.
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