Nonreciprocal effects in ring lasers

Polarization ring interferometers and their use for studying nonreciprocal optical effects

“…As is known, nonreciprocal optical effects arise if the reciprocity theorem j (1) ext (r, ω)E (2) (r, ω) dr = j (2) ext (r, ω)E (1) …”

“…where E (2) is the field excited on the plane P 1 by the surface current on the plane P 2 , and E (1) is the field excited on the plane P 2 by the surface current on the plane P 1 (Fig. 1).…”

“…Here j (1) ext and j (2) ext are the current densities of external sources of electromagnetic fields and E (1) and E (2) are the corresponding electric fields excited by these sources. To employ this theorem in the Jones matrix method used for analyzing anisotropic systems in the plane-wave approximation, the external sources of electromagnetic fields can be represented as homogeneous surface currents j (1) and j (2) on two parallel planes (P 1 and P 2 ) when discussing nonreciprocal optical effects. In this case from Eq.…”

“…In this case, it is easily seen that, we can write the fields entering Eq. (2) and excited by the currents j (1) and j (2) on the planes P 1 and P 2 , respectively, in the form…”

“…Such effects arise when the time symmetry is violated. This occurs in many cases that are rather interesting from the physical viewpoint [1]. However, we believe that experimental methods for studying such phenomena have not yet been properly developed.…”