  Black phosphorus (BP) is an emerging two-dimensional semiconducting material
with great potential for nanoelectronic and nanophotonic applications,
especially owing to its unique anisotropic electrical and optical properties.
Many theoretical studies have predicted the anisotropic optical properties of
BP, but the direct experimental quantification remains challenging. The
difficulties stem from the ease of BP's degradation when exposed to air in
ambient conditions, and from the indirect nature of conventional approaches
that are subject to large measurement uncertainties. This work reports a direct
investigation of the birefringent optical constants of micrometer-thick BP
samples with picosecond (ps) interferometry, over the wavelength range from 780
to 890 nm. In this ps-interferometry approach, an ultrathin (5 nm) platinum
layer for launching acoustic waves naturally protects the BP flake from
degradation. The birefringent optical constants of BP for light polarization
along the two primary crystalline orientations, zigzag and armchair, are
directly obtained via fitting the attenuated Brillouin scattering signals. A
bi-exponential model is further proposed to analyze the BS signals for a random
incident light polarization. The BP experimental results and the associated
measurement sensitivity analysis demonstrate the reliability and accuracy of
the ps-interferometry approach for capturing the polarization-dependent optical
properties of birefringent materials.
