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Group theory description of third harmonic generation in diamond and zincblende lattice

MetadataDetails
Publication Date2019-01-01
JournalJournal of Physics Conference Series
AuthorsB Nurjanati, Husin Alatas, Hendradi Hardhienata
InstitutionsIPB University

We provide a description that shows the importance in finding a susceptibility tensor in nonlinear optics and apply group theory to derive a fourth rank tensor of Oh point group related to the bulk symmetry of monoatomic diamond semiconductor such as Silicon. It is well known that the fourth rank tensor is closely related to the third order nonlinear susceptibility tensor in nonlinear optics through Neumann’s principle and is crucial to understand third harmonic generation (THG) and electric field induced second harmonic generation (EFISH). Using a general Rodriguez rotation, we were able to obtain a three-dimmensional rotation matrix required to perform the symmetry operations, whereas their reflection matrixes are derived using a Householder fromula. We also show how a Td point group corresponding to zincblende can be obtained by breaking the symmetry of the Oh tensor rather than repeating the tedious procedure when obtaining the Oh tensor. Assuming a driven frequency far from the resonance frequency, we can apply Kleinman symmetry and demonstrate that the number of independent components in the Oh and Td fourth rank tensor is reduced from four to just two.