  We study the electromagnetic response of two- and quasi-two-dimensional
hyperbolic materials, on which a simple dipole source can excite a
well-confined and tunable surface plasmon polariton (SPP). The analysis is
based on the Green's function for an anisotropic two-dimensional surface, which
nominally requires the evaluation of a two-dimensional Sommerfeld integral. We
show that for the SPP contribution this integral can be evaluated efficiently
in a mixed continuous-discrete form as a continuous spectrum contribution
(branch cut integral) of a residue term, in distinction to the isotropic case,
where the SPP is simply given as a discrete residue term. The regime of strong
SPP excitation is discussed, and complex-plane singularities are identified,
leading to physical insight into the excited SPP. We also present a stationary
phase solution valid for large radial distances. Examples are presented using
graphene strips to form a hyperbolic metasurface, and thin-film black
phosphorus. The Green's function and complex-plane analysis developed allows
for the exploration of hyperbolic plasmons in general 2D materials.
