Phase-dependent reversible nonreciprocity in complex metamolecules

Nonreciprocity of complex metamolecules based on the collapse of parity-time symmetry is investigated through an application to an optical waveguide array, demonstrating the strong dependency on the phase of eigenspectra. Contrary to the intuitive expectation, we reveal that more rapid and tunable nonreciprocal dynamics is achieved in the regime where the real and complex phases coexist and, furthermore, with the benefit of significantly reduced gain. It is shown that this paradoxical behavior originates from the effect of ``spatial trapping modes,'' which hinder the energy transfer within the metamolecule due to decreased effective coupling between waveguides. As an application, we demonstrate the novel phenomenon of ``reversible nonreciprocity,'' based on the manipulation of a single trapping mode.