Hyperbolic phonon polaritons (HPhPs) are a class of electromagnetic waves that arise from the coupling of photons with optical phonons in anisotropic semiconductors, leading to unique light-matter interactions. These polaritons exhibit hyperbolic dispersion, enabling extreme light confinement and directional propagation, which are absent in isotropic materials. Hexagonal boron nitride (hBN) and silicon carbide (SiC) are two prominent semiconductors that support HPhPs due to their natural hyperbolic responses in specific infrared frequency ranges. Their exceptional properties make them ideal for sub-diffraction imaging, nanophotonic circuits, and thermal management applications.

The dispersion relation of HPhPs is fundamentally different from conventional polaritons in isotropic materials. In hBN and SiC, the crystal anisotropy splits the optical phonon modes into two distinct types: in-plane (transverse optical, TO) and out-of-plane (longitudinal optical, LO) phonons. This anisotropy results in a dielectric permittivity tensor with opposite signs along different crystal directions, creating a hyperbolic dispersion curve. For instance, hBN exhibits type I hyperbolicity in the upper Reststrahlen band (around 1,610–1,700 cm⁻¹) and type II hyperbolicity in the lower Reststrahlen band (around 760–830 cm⁻¹). Type I HPhPs occur when the permittivity components perpendicular to the optical axis are negative, while the parallel component is positive. Conversely, type II HPhPs arise when the parallel component is negative, and the perpendicular components are positive. The hyperbolic dispersion allows for high-momentum wavevectors, enabling sub-wavelength light confinement and enhanced density of optical states.

In SiC, the Reststrahlen band spans 790–970 cm⁻¹, where the permittivity tensor components exhibit similar anisotropy. The dispersion relation for HPhPs in SiC can be described using the effective medium approximation, where the wavevector components satisfy the hyperbolic condition. The propagation of HPhPs is highly directional, with light channeled along specific crystal axes. This directional propagation is quantified by the isofrequency contours, which take the form of hyperboloids in momentum space. The group velocity of HPhPs is perpendicular to these contours, leading to ray-like propagation patterns that can be tuned by adjusting the frequency within the Reststrahlen band.

Confinement effects in HPhPs are remarkable due to their ability to compress light into volumes far below the diffraction limit. In hBN, HPhPs can achieve confinement factors exceeding 100 times smaller than the free-space wavelength, with measured propagation lengths of several micrometers. This tight confinement is facilitated by the large momentum mismatch between HPhPs and free-space photons, preventing radiative losses. The confinement is further enhanced in nanostructured hBN, such as ribbons or disks, where edge effects and localized resonances dominate. For SiC, similar confinement effects are observed, with additional tunability via doping or strain engineering. The quality factor of HPhPs in these materials is determined by the phonon lifetime, which is intrinsically high due to the low damping rates of optical phonons.

Applications of HPhPs in sub-diffraction imaging leverage their ability to resolve features smaller than the wavelength of light. Hyperbolic metamaterials made from hBN or SiC can function as superlenses, capturing evanescent waves that carry sub-diffraction information. Experimental demonstrations have achieved resolutions below 30 nm in the mid-infrared range using hBN slabs. The anisotropic propagation of HPhPs also enables hyperlensing, where objects are magnified along specific directions, breaking the conventional resolution limits of isotropic lenses. These imaging techniques are particularly valuable for nanoscale spectroscopy, enabling chemical fingerprinting of materials with unprecedented spatial detail.

In nanophotonics, HPhPs enable the design of ultra-compact waveguides and resonators. The directional propagation allows for low-loss routing of infrared light along predefined crystal axes, essential for on-chip optical circuits. hBN-based waveguides have demonstrated mode confinement down to 1% of the wavelength, with minimal crosstalk between adjacent channels. Resonators exploiting HPhPs exhibit high quality factors, with Q values exceeding 1,000 in structured hBN cavities. These resonators are pivotal for enhancing light-matter interactions in quantum emitters or molecular vibrations, enabling strong coupling regimes at room temperature.

Thermal applications of HPhPs exploit their ability to mediate near-field heat transfer beyond the blackbody limit. hBN and SiC films can enhance radiative heat transfer by several orders of magnitude due to the tunneling of HPhPs across nanoscale gaps. This effect is critical for thermal management in integrated circuits and energy harvesting devices, where localized heating is a major challenge. The spectral control offered by HPhPs also allows for selective thermal emission, tailoring the radiative properties to match specific absorption bands.

Future advancements in HPhP-based technologies will likely focus on integrating these materials with other photonic platforms, such as plasmonic systems or 2D materials, to achieve hybrid modes with tailored properties. The development of active tuning mechanisms, such as electrostatic gating or optical pumping, will further expand the functionality of HPhP devices. With their unique combination of confinement, directionality, and low losses, hyperbolic phonon polaritons in hBN and SiC represent a transformative platform for next-generation nanophotonic and thermal applications.