  The nonreciprocal propagation of light typically requires use of materials
like ferrites or magneto-optical media with a strong magnetic bias or methods
based on material nonlinearities which require use of strong electromagnetic
fields. A simpler possibility to produce nonreciprocity is to use
spatio-temporal modulations to produce magnetic fields in synthetic dimensions.
In this paper we show that dissipatively coupled systems can lead to
considerable enhancement of nonreciprocity in synthetic fields. The enhancement
comes about from the existence of nearly nondecaying mode -bound state in
continuum (BIC) in dissipatively coupled systems. The dissipative coupling
occurs in a wide class of systems coupled via transmission lines, waveguides,
or nano fibers. The systems could be optical resonators or microscopic qubits.
Remarkably we find that for specific choice of the modulation amplitudes, the
transmission say in forward direction is completely extinguished whereas in the
backward direction it becomes maximum. The synthetic fields produce
transmission resonances which show significant line narrowing which owe their
origin to existence of BIC's in dissipative systems.
