Spatial coherence of hybrid surface plasmon-phonon-polaritons in shallow n-GaN surface-relief gratings

Dispersion characteristics of hybrid surface plasmon-phonon-polaritons (SPPhPs) on the air/polar semiconductor interface were investigated by means of shallow surface relief grating using emission spectroscopy methods. A set of grating structures with optimal 1 µm depth and periods from 8 to 22 µm was developed on a heavily-doped GaN crystal. The SPPhPs were excited by thermal heating or electrical biasing of the samples which radiated directive polarized features in an extremely narrowband spectrum range. Detailed analysis of damping factors and propagation losses revealed maximum values of quality factor and spatial coherence of hybrid SPPhPs modes. Highest quality factor was found to be practically independent on the period of the shallow grating, as it was always detected near the frequency of transverse optical phonon, demonstrating values as high as 88 and 200 in experiment and theory, respectively. Meanwhile, the largest values of coherence length strongly depended on the grating as the propagation losses of hybrid SPPhP modes showed a tendency to accumulate with the wavevector increase. The sample with 22 µm grating period demonstrated the highest coherence of hybrid polaritons with the experimental (theoretical) coherence length values as high as 1.6 mm (2.3 mm).