Abstract
A method for finding nonzero and linearly independent higher-rank tensor elements by recourse to irreducible spherical tensors, is proposed. A transformation matrix from third-rank tensors, defined in circular-cylindrical coordinates, to irreducible spherical tensors, is derived. Nonzero elements of polar third- and fourth-rank tensors, symmetric in all indices, are determined for all crystallographical classes. The results are applied to the analysis of free as well as electric field- induced second- and third-harmonic generation of laser light.
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