William Angerer - Department of Physics and Astronomy - University ...

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6.2 Nonlinear Rotational Symmetry of GaN
In section 2.3 we discussed the relationship between the allowed second-order susceptibility
elements and the symmetry of the media. In this section we discuss our
investigations of the symmetry of GaN by second-harmonic generation. By measuring
second-harmonic intensity as a function of the angle between the incident beam and
crystal a.'{es for a variety of polarizations, we probed the symmetry of our Ga.\" thin
films. Fig. 6.1 displays the geometry of the sample and the fundamental and secondharmonic
beams. Because SHG is mediated by a third rank tensor, second-harmonic
generation is a more sensitive probe of crystal symmetry than linear spectroscopies,
which are mediated by second rank tensors.
The second-harmonic response of GaN is determined by transforming the dipole
allowed second-order nonlinearities in the crystal frame of reference to the lab frame
of reference. i.e.
(2),lab _ R(A.). R( '). R( .) (2),crystal
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