  Radiative losses have traditionally been neglected in the calculation of
thermal noise of transmissive optical elements because for the most commonly
used geometries they are small compared to losses due to thermal conduction. We
explore the use of such transmissive optical elements in extremely
noise-sensitive environments such as the arm cavities of future
gravitational-wave interferometers. This drives us to a geometry regime where
radiative losses are no longer negligible. In this paper we derive the
thermo-refractive noise associated with such radiative losses and compare it to
other known sources of thermal noise.
