We use micro-focused Brillouin light scattering spectroscopy (BLS) to investigate surface acoustic waves (SAWs) in a GaN layer on a Si substrate at GHz frequencies. Furthermore, we discuss the concept of BLS for SAWs and show that the crucial parameters of SAW excitation and propagation can be measured. We investigate a broad range of excitation parameters and observe that Rayleigh and Sezawa waves are excited simultaneously at the same frequency. Spatially resolved measurements of these co-propagating waves show a periodic pattern, which proves their coherent interference. From the periodicity of the spatial phonon patterns, the wavevector difference between the two waves has been identified and compared to the dispersion relation. The appearance of Sezawa waves related to the finite thickness of the piezoelectric substrate leads to acoustic fields with a time-independent spatial variation similar to the situations realized using counter-propagating waves. This periodicity can have an influence on experimental results in angular momentum conversion experiments, for example, via magneto-elastic fields in hybrid-SAW-structures with additional magnetic layers.

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