  Aims: We present POLARIS (POLArized RadIation Simulator), a newly developed
three-dimensional Monte-Carlo radiative transfer code. POLARIS was designed to
calculate dust temperature, polarization maps, and spectral energy
distributions. It is optimized to handle data that results from sophisticated
magneto-hydrodynamic simulations. The main purpose of the code is to prepare
and analyze multi-wavelength continuum polarization measurements in the context
of magnetic field studies in the interstellar medium. An exemplary application
is the investigation of the role of magnetic fields in star formation
processes.
  Methods: We combine currently discussed state-of-the-art grain alignment
theories with existing dust heating and polarization algorithms. We test the
POLARIS code on multiple scales in complex astrophysical systems that are
associated with different stages of star formation. POLARIS uses the full
spectrum of dust polarization mechanisms to trace the underlying magnetic field
morphology.
  Results: Resulting temperature distributions are consistent with the density
and position of radiation sources resulting from magneto-hydrodynamic (MHD) -
collapse simulations. The calculated layers of aligned dust grains in the
considered cirumstellar disk models are in excellent agreement with theoretical
predictions. Finally, we compute unique patterns in synthetic multi-wavelength
polarization maps that are dependent on applied dust-model and grain-alignment
theory in analytical cloud models.
