  Integrated photonics is a remarkable platform for scalable classical and
quantum light-based information processing. However, polarization manipulation
on a chip despite of its fundamental significance in information processing
remains elusive. Polarization manipulation capabilities have been recently
demonstrated in femtosecond laser-inscribed twisted waveguides, although the
systematic theoretical description of polarization manipulation has not been
established for this architecture. In this work we develop a rigorous theory of
a twisted waveguide unveiling its eigenmodes and transmission matrix in the
closed form. Utilizing the developed theory, we demonstrate that twisted
waveguides can realize virtually arbitrary polarization transformations while
satisfying reasonable design constraints. This fact combined with low cost and
ease of prototyping of laser inscribed photonic integrated circuits allows us
to suggest twisted waveguide as a robust building block for on-chip
polarization-encoded information processing.
