Analysis of Near-Field Patterns generated by Propagating Polaritons

Polaritons are quasi-particles that are excited by the coupling of light and charges within a material. They are closely related to the motion of charges in matter, which gives them a deep connection to material properties. Additionally, in specific low-dimensional materials, they exhibit a high level of light-matter interaction and confinement. Polaritons hold significant value in the field of nanophotonics, and current research is underway in areas such as light absorption, thermal emission, biosensing, and beam deflection. However, directly measuring the complex propagation of polaritons remains a challenging aspect of research due to the difficulty of near-field measurements.<br/>Scattering type scanning near-field optical microscopy (s-SNOM) enables the simultaneous measurement of the amplitude and phase of the near field by utilizing a metallic atomic force microscopy (AFM) tip as a near-field antenna and the interferometric coupling of this signal with the base signal. Typically, s-SNOM excites complex propagating polaritons through the tip and material edges and images them. In the past, Fourier transform (FT) was used on the image profile to extract real momentum, but the damping term was determined through direct fitting or by directly fitting complex momentum from the beginning. This method poses challenges in mixed signal analysis and background removal. Additionally, for edge-launched polaritons, the polariton momentum can shift depending on the edge angle, but this shift has not been considered in recent high-effective-index materials like hBN or MoO₃.<br/>In this study, we first present a standardized method for analyzing the complex momentum of propagating polaritons. To analyze polariton momentum, we fit the FT signal of propagating polaritons with a function obtained by FT of the analysis model. We confirmed a perfect fit and also revealed the relationship between the full-width half-maximum (FWHM) of the FT signal and the damping of propagating polaritons, confirming a specific ratio of . This method using FT makes it easier to analyze comprehensive signals compared to the traditional direct fitting method and offers an advancement in analyzing the loss of polaritons based on the existing Fourier transform approach.<br/>Secondly, we established an analytical model for tip and edge polaritons and experimentally demonstrated edge-oriented momentum shifts that occur during measuring process in edge mode. We measured polaritons on hBN transferred onto crystalline gold. Polaritons launched from the clear atomic gold edge generate modes known as hyperbolic phonon-polaritons (HPP) and hyperbolic image polaritons (HIP) that propagate on both the glass substrate and crystalline gold. We measured the polariton by rotating gold edge at 45-degree angles and confirmed that the degree of shift matched the theoretical model. Furthermore, for HPP, it was observed that HPP exhibited a maximum momentum shift of approximately 8% even at a high effective index of 12.54.