An informal survey of some colleagues and students revealed that the notion of reciprocity in optics is not widely appreciated. One colleague even justified the prevailing ignorance by drawing a parallel between reciprocity in optics and complementarity in quantum mechanics: “Both are true statements which have little, if any, practical value in their respective domains.” This chapter is an attempt at explaining the concept of reciprocity, clarifying some associated misconceptions, and pointing out its practical applications.

Non-reciprocity of Faraday rotators

No one disputes that a Faraday rotator is a non-reciprocal element. The usual argument goes as follows. Let a linearly polarized beam of light be fully transmitted through a polarizing beam-splitter (PBS) before being directed through a 45° Faraday rotator, as shown in Figure 17.1. If the beam is reflected back (by an ordinary mirror, for example), it retraces its path through the rotator and emerges with its polarization vector rotated by a full 90°. At the PBS, therefore, the returning beam will be deflected away from its original path. (This, in fact, is a well-known method of isolating laser diodes from spurious reflections within a given system.) Since the reflected light does not return on its original path, and since the PBS is believed to be reciprocal, the argument is taken as proof of the non-reciprocity of the Faraday rotator.

Although it is true that Faraday rotators are non-reciprocal, there is a flaw in the above argument, which will become clear upon inspection of the system of Figure 17.2.