Polarization, mirrors, and reciprocity: Birefringence and its compensation in optical retracing circuits

Birefringence affects all the optical circuits both in free-space and guided-wave optics. It perturbs the state of polarization of the propagating light, causing unwanted detrimental effects in many practical situations. A retracing circuit offers the potentiality of compensating the birefringence, but it is not universal because the birefringence is of different kinds, that is, either linear or circular, as well as either reciprocal or nonreciprocal, and because the common mirror does not hold all the requested symmetries. This paper reviews the compensation techniques suitable for each kind of birefringence, taking into account the introduction of two further generalized mirrors, the mirrored Faraday rotator and the mirrored quarter-wave plate. The main retracing schemes are analyzed and presented with the help of the Poincaré sphere and the Jones matrices. Examples of full compensation of all the main cases of birefringence that occurs in practical optical circuits are given. The different compensation properties of the three mirrors can be interpreted by means of a unified vision in the abstract space related to the Poincaré sphere representation.