Electrically tunable epsilon-near-zero–hyperbolic canalization in a hybrid plasmonic waveguide with black phosphorus ribbons

Hybrid plasmonic waveguides, non-Hermitian exceptional points (EPs), and anisotropic 2D materials have so far been exploited mostly in isolation, each providing only one of the following: deep-subwavelength confinement, enhanced sensitivity, or dispersion control. Hyperbolic plasmon polaritons in black phosphorus (BP) further promise field localization but, in practice, are highly lossy, yielding strongly damped, short-range modes that limit device-level utility. Here, we present a single, electrically reconfigurable platform that combines these capabilities while recovering long-range, strongly confined hyperbolic fields: BP ribbons embedded in a hybrid-plasmonic slot waveguide. Electrostatic gating of BP tunes its anisotropic permittivity and drives the structure through four operation regimes at a fixed wavelength and geometry: (i) a delocalized regime in which index mismatch expels the slot mode, (ii) an index-matched EP where hybrid-plasmonic and waveguide eigenmodes coalesce and maximize responsivity, (iii) an epsilon-near-zero regime with deep-subwavelength confinement in the BP ribbons, and (iv) a hyperbolic regime that supports edge-guided canalization of high-$k$ fields with extended propagation lengths. This bias-programmable architecture overcomes the usual ``one-phenomenon-per-platform'' constraint and enables compact, CMOS-compatible modulators, sensors, and switches that cointegrate EP-enhanced sensitivity, ENZ localization, and hyperbolic light--matter interactions.