  Nanofocusing of light offers new technological opportunities for the delivery
and manipulation of electromagnetic fields at sub-diffraction limited length
scales. Here, we show that hyperbolic phonon polarity,HPP, modes in the mid
infrared as supported by a hexagonal boron nitride, h-BN, slab can be
nanofocused (i.e. both field enhanced and wavelength compressed) by propagation
along a vertical taper. Via numerical simulations, we demonstrate that field
enhancement factors of 90, for steep tapers, and wavelength compression of more
than an order of magnitude for adiabatic tapers, can be expected. Employing
scatteringtype scanning near field optical microscopy ,s SNOM, we provide for
the first time proof of principle experimental evidence of a significant HPP
wavelength compression. We expect these functionalities to provide diverse
applications, from biosensing and non-linear optics to optical circuitry.
