  A possible means of optical sensing, based on a porous hyperbolic material
which is infiltrated by a fluid containing an analyte to be sensed, was
investigated theoretically. The sensing mechanism relies on the observation
that extraordinary plane waves propagate in the infiltrated hyperbolic material
only in directions enclosed by a cone aligned with the optic axis of the
infiltrated hyperbolic material. The angle this cone subtends to the plane
perpendicular to the optic axis is $\theta_c$. The sensitivity of $\theta_c$ to
changes in refractive index of the infiltrating fluid, namely $n_b$, was
explored; also considered were the permittivity parameters and porosity of the
hyperbolic material, as well as the shape and size of its pores. Sensitivity
was gauged by the derivative $d \theta_c / d n_b$. In parametric numerical
studies, values of $d \theta_c / d n_b$ in excess of 500 degrees per refractive
index unit were computed, depending upon the constitutive parameters of the
porous hyperbolic material and infiltrating fluid, and the nature of the
porosity. In particular, it was observed that exceeding large values of $d
\theta_c / d n_b$ could be attained as the negative--valued eigenvalue of the
infiltrated hyperbolic material approached zero.
