Momentum quantization of hyperbolic phonon polaritons in photonic-crystal cavity

Hyperbolic phonon polaritons (HPhPs) in van der Waals crystals enable extreme electromagnetic confinement and access to exceptionally large in-plane momenta, offering a powerful platform for deep-subwavelength nanophotonics. Although the lower Reststrahlen band (RS1) of hexagonal boron nitride (h-BN) is highly attractive for low-loss, strongly volume-confined polaritons, fully exploiting this potential remains challenging because RS1 modes are weakly accessible by conventional near-field detection and require efficient leakage suppression for high-Q confinement. Here, we demonstrate that momentum quantization of RS1 HPhPs enables high-Q, ultrasmall mode volume cavity states in an h-BN photonic-crystal nanocavity architecture. Periodic lateral cavity boundaries impose Fabry-Pérot phase matching, while the surrounding photonic-crystal lattice suppresses in-plane leakage and stabilizes discrete cavity-supported momentum states, transforming the continuous hyperbolic dispersion into a ladder of geometry-defined momentum eigenstates. Using photo-induced force microscopy, we directly visualize the quantized cavity modes in real space and reconstruct their discretized dispersion in momentum space. The resulting hyperbolic polaritonic cavity crystal exhibits quality factors exceeding 340 and ultrasmall mode volumes down to V ¯ m = 4.3 × 10 − 7 ( λ 0 / n ) 3 , corresponding to Purcell enhancements approaching 10 7 . This approach establishes a route to high-Q, ultrasmall-volume RS1 polaritonic nanocavities with geometry-defined momentum states, providing a scalable platform for enhanced light-matter interactions, selective vibrational spectroscopy, and reconfigurable mid-infrared nanophotonic devices.