Reciprocal and unidirectional scattering of parity-time symmetric structures

Parity-time [Image: see text] symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the [Image: see text] symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are intensively studied. Here, we show the reciprocal reflection/transmission in [Image: see text]-symmetric system is closely related to the type of [Image: see text] symmetry, that is, the axial (reflection) [Image: see text] symmetry leads to reciprocal reflection (transmission). The results are further elucidated by studying the scattering of rhombic ring form coupled resonators with enclosed synthetic magnetic flux. The nonreciprocal phase shift induced by the magnetic flux and gain/loss break the parity [Image: see text] and time-reversal [Image: see text] symmetry but keep the parity-time [Image: see text] symmetry. The reciprocal reflection (transmission) and unidirectional transmission (reflection) are found in the axial (reflection) [Image: see text]-symmetric ring centre. The explorations of symmetry and asymmetry from [Image: see text] symmetry may shed light on novel one-way optical devices and application of [Image: see text]-symmetric metamaterials.