  Optical properties are required for the correct understanding and modelling
of protoplanetary and debris discs. By assuming that comets are the most
pristine bodies in the solar system, our goal is to derive optical constants of
real protoplanetary material. We determine the complex index of refraction of
the near-surface material of comet 67P/Churyumov-Gerasimenko by fitting the
sub-millimetre/millimetre observations of the thermal emission of the comet's
sub-surface made by the Microwave Instrument for the Rosetta Orbiter (MIRO)
with synthetic temperatures derived from a thermophysical model and
radiative-transfer models. According to the two major formation scenarios of
comets, we model the sub-surface layers to consist of pebbles as well as of
homogeneously packed dust grains. In the case of a homogeneous dusty surface
material, we find a solution for the length-absorption coefficient of $\alpha
\approx 0.22~\mathrm{cm^{-1}}$ for a wavelength of 1.594 mm and $\alpha \geq
3.84~\mathrm{cm^{-1}}$ for a wavelength of 0.533 mm and a constant thermal
conductivity of $0.006~\mathrm{Wm^{-1}K^{-1}}$. For the pebble scenario, we
find for the pebbles and a wavelength of 1.594 mm a complex refractive index of
$n = (1.074 - 1.256) + \mathrm{i} \, (2.580 - 7.431)\cdot 10^{-3}$ for pebble
radii between 1 mm and 6 mm. Taking into account other constraints, our results
point towards a pebble makeup of the cometary sub-surface with pebble radii
between 3 mm and 6 mm. The derived real part of the refractive index is used to
constrain the composition of the pebbles and their volume filling factor. The
optical and physical properties are discussed in the context of protoplanetary
and debris disc observations.
