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The terahertz (THz) region of the electromagnetic spectrum, spanning from 0.1 to 30 THz, represents a prospering area in photonics, with transformative applications in imaging, communications, and material analysis. However, the development of efficient and compact THz sources has long been hampered by intrinsic material limitations, inefficient conversion processes, and complex phase-matching requirements. Recent breakthroughs in nonlinear optical mechanisms, resonant metasurface engineering, and advances in the fabrication processes for materials such as lithium niobate (LN) and aluminum gallium arsenide (AlGaAs) have paved the way for innovative THz generation techniques. This review article explores the latest theoretical advances, together with key experimental results and outlines perspectives for future developments.

The boundary integral equation (BIE) method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of the Laplace equation can be used to calculate the full set of eigenvalues and eigenfunctions of the electrostatic operator for shapes and shells described by separable coordinate systems. These results not only unify and generalize many existing studies, but also offer us the opportunity to expand the study of phenomena such as cloaking by anomalous localized resonance. Hence, we calculate the eigenvalues and eigenfunctions of elliptic and circular cylinders. We illustrate the benefits of using the BIE method to interpret recent experiments involving localized surface phonon polariton resonances and the size scaling of plasmon resonances in graphene nanodiscs. Finally, symmetry-based operator analysis can be extended from the electrostatic to the full-wave regime. Thus, bound states of light in the continuum can be studied for shapes beyond spherical configurations.

Particle-dispersed coatings emerged as a promising approach to regulate the apparent radiative properties of underlying substrates in various applications, including but not limited to radiative cooling, thermal management, and infrared stealth. However, most research efforts in this field overlooked the dependent scattering mechanisms between the particles and the substrate, which can impact the optical properties of the particles. In this study, we explored the particle-substrate interactions within the atmospheric radiative window of 8–14 µm. Using the T-matrix method, we calculated the scattering and absorption efficiencies of a dielectric/metallic particle situated above a metallic/dielectric substrate, considering the different gap sizes. Near the small gaps (<0.5a with a the sphere radius), we found that the strong local fields induced by the interaction between the induced and image charges largely enhanced the absorption and scattering efficiencies of the particles. With the increasing gap sizes, the absorption and scattering efficiencies presented a significant oscillation with a period of about 4.5a, which was attributed to the interference (standing wave) between the scattered fields from the sphere and the reflected fields from the substrate. Our findings identify a crucial role of the particle–substrate interactions in the infrared properties of particles, which may guide a comprehensive insight on the apparent radiative properties of the particle composite coatings.