  Breaking Lorentz reciprocity was believed to be a prerequisite for
nonreciprocal transmissions of light fields, so the possibility of
nonreciprocity by linear optical systems was mostly ignored. We put forward a
structure of three mutually coupled microcavities or optical fiber rings to
realize optical nonreciprocity. Although its couplings with the fields from two
different input ports are constantly equal, such system transmits them
nonreciprocally either under the saturation of an optical gain in one of the
cavities or with the asymmetric couplings of the circulating fields in
different cavities. The structure made up of optical fiber rings can perform
nonreciprocal transmissions as a time-independent linear system without
breaking Lorentz reciprocity. Optical isolation for inputs simultaneously from
two different ports and even approximate optical isolator operations are
implementable with the structure.
