A Multibeam Interference Model for Analyzing Complex Near-Field Images of Polaritons in 2D van der Waals Microstructures

Van der Waals (vdW) materials are among the most promising candidates for photonic integrated circuits because they support a full set of polaritons that can manipulate light at deep subdiffraction nanoscale. It is possible to directly probe the propagating polaritons in vdW materials in real space via scattering-type scanning near-field optical microscopy, such that the wave vector and lifetime of the polaritons can be extracted from as-measured interference fringes by Fourier analysis. However, this method is unsuitable for clutter interference patterns in samples exhibiting inadequate fringes due to small size (less than 10 µm) or complex edges that are often encountered in nanophotonic devices and new material characterization. Here, a multibeam interference model is developed to analyze complex images by disentangling them into periodic patterns and residue. By employing phase stationary approximation, polariton wave vector can be derived from offset ratio of the center point, and the ratio of polariton reflection and scattering rates at the edge is obtained from the ratio of the periodic and aperiodic patterns. This method can be widely used in the optical characterization of new vdW materials that are difficult to synthesize into large crystals, as well as nanophotonic integrated devices with unique boundaries.