  We present a novel Rotational Anisotropy Nonlinear Harmonic Generation
(RA-NHG) apparatus based primarily upon reflective optics. The data acquisition
scheme used here allows for fast accumulation of RA-NHG traces, mitigating low
frequency noise from laser drift, while permitting real-time adjustment of
acquired signals with significantly more data points per unit angle rotation of
the optics than other RA-NHG setups. We discuss the design and construction of
the optical and electronic components of the device and present example data
taken on a GaAs test sample at a variety of wavelengths. The RA-second harmonic
generation data for this sample show the expected four-fold rotational symmetry
across a broad range of wavelengths, while those for RA-third harmonic
generation exhibit evidence of cascaded nonlinear processes possible in
acentric crystal structures.
