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The modeling of the near-field interaction in the scattering-type scanning near-field optical microscope (s-SNOM) is rapidly advancing, although an accurate yet versatile modeling framework that can be easily adapted to various complex situations is still lacking. In this work, we propose a time-efficient numerical scheme in the quasi-electrostatic limit to capture the tip-sample interaction in the near field. This method considers an extended tip geometry, which is a significant advantage compared to the previously reported method based on the point-dipole approximation. Using this formalism, we investigate, among others, nontrivial questions such as uniaxial and biaxial anisotropy in the near-field interaction, the relationship between various experimental parameters (e.g. tip radius, tapping amplitude, etc.), and the tip-dependent spatial resolution. The demonstrated method further sheds light on the understanding of the contrast mechanism in s-SNOM imaging and spectroscopy, while also representing a valuable platform for future quantitative analysis of the experimental observations. 

Abstract Phonon polaritons, the hybrid quasiparticles resulting from the coupling of photons and lattice vibrations, have gained significant attention in the field of layered van der Waals heterostructures. Particular interest has been paid to hetero‐bicrystals composed of molybdenum oxide (MoO₃) and hexagonal boron nitride (hBN), which feature polariton dispersion tailorable via avoided polariton mode crossings. In this work, the polariton eigenmodes in MoO₃‐hBN hetero‐bicrystals self‐assembled on ultrasmooth gold are systematically studied using synchrotron infrared nanospectroscopy. It is experimentally demonstrated that the spectral gap in bicrystal dispersion and corresponding regimes of negative refraction can be tuned by material layer thickness, and these results are quantitatively matched with a simple analytic model. Polaritonic cavity modes and polariton propagation along “forbidden” directions are also investigated in microscale bicrystals, which arise from the finite in‐plane dimension of the synthesized MoO₃micro‐ribbons. The findings shed light on the unique dispersion properties of polaritons in van der Waals heterostructures and pave the way for applications leveraging deeply sub‐wavelength mid‐infrared light‐matter interactions. 

Abstract Silicon waveguides have enabled large‐scale manipulation and processing of near‐infrared optical signals on chip. Yet, expanding the bandwidth of guided waves to other frequencies will further increase the functionality of silicon as a photonics platform. Frequency multiplexing by integrating additional architectures is one approach to the problem, but this is challenging to design and integrate within the existing form factor due to scaling with the free‐space wavelength. This paper demonstrates that a hexagonal boron nitride (hBN)/silicon hybrid waveguide can simultaneously enable dual‐band operation at both mid‐infrared (6.5–7.0 µm) and telecom (1.55 µm) frequencies, respectively. The device is realized via the lithography‐free transfer of hBN onto a silicon waveguide, maintaining near‐infrared operation. In addition, mid‐infrared waveguiding of the hyperbolic phonon polaritons (HPhPs) supported in hBN is induced by the index contrast between the silicon waveguide and the surrounding air underneath the hBN, thereby eliminating the need for deleterious etching of the hyperbolic medium. The behavior of HPhP waveguiding in both straight and curved trajectories is validated within an analytical waveguide theoretical framework. This exemplifies a generalizable approach based on integrating hyperbolic media with silicon photonics for realizing frequency multiplexing in on‐chip photonic systems.