Reciprocal and unidirectional scattering of parity-time symmetric structures

Abstract

Parity-time symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are intensively studied. Here, we show the reciprocal reflection/transmission in -symmetric system is closely related to the type of symmetry, that is, the axial (reflection) 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 and time-reversal symmetry but keep the parity-time symmetry. The reciprocal reflection (transmission) and unidirectional transmission (reflection) are found in the axial (reflection) -symmetric ring centre. The explorations of symmetry and asymmetry from symmetry may shed light on novel one-way optical devices and application of -symmetric metamaterials.

Unidirectional reflectionless light propagation at exceptional points

“…Unidirectional reflectionlessness can also be attained in optical coupled-resonator systems at EPs [61,62]. Jin et al studied the scattering of rhombic ring form coupled resonators with enclosed synthetic magnetic flux [62].…”

“…Jin et al studied the scattering of rhombic ring form coupled resonators with enclosed synthetic magnetic flux [62]. The scattering center is a two-arm Aharonov-Bohm interferometer.…”

One-way light transport controlled by synthetic magnetic fluxes and ${\mathscr{P}}{\mathscr{T}}$-symmetric resonators

“… symmetry ensures symmetric transmission in  -symmetric non-Hermitian systems [31][32][33][34][35]. The orientation of  -symmetric structures causes symmetric transmission or symmetric reflection [36]. In  -symmetric microcavities, a gain-induced large nonlinearity can break the  symmetry and produce an optical diode [37,38].…”

Incident Direction Independent Wave Propagation and Unidirectional Lasing

“…The topologies of exceptional points are distinct [33][34][35][36][37]. Spectral singularities (SSs) in scattering systems belong to another type of non-Hermitian singularities, at which eigenstate completeness is spoiled [38,39]; incident waves from opposite directions at an appropriate phase match are perfectly absorbed in a coherent perfect absorber [40][41][42][43][44][45][46][47][48].Non-Hermitian character causes unidirectionality [49][50][51][52][53][54], the fundamental mechanism of which differs from that created by chiral light-matter interaction [55][56][57][58][59]. Typical phenomena include unidirectional reflectionlessness [49,50] and unidirectional spectral singularity that allows unidirectional perfect absorption (UPA) and unidirectional lasing (UL) [51,52]; however, the transmissions there protected by symmetry are reciprocal [60][61][62][63].…”

“…Non-Hermitian character causes unidirectionality [49][50][51][52][53][54], the fundamental mechanism of which differs from that created by chiral light-matter interaction [55][56][57][58][59]. Typical phenomena include unidirectional reflectionlessness [49,50] and unidirectional spectral singularity that allows unidirectional perfect absorption (UPA) and unidirectional lasing (UL) [51,52]; however, the transmissions there protected by symmetry are reciprocal [60][61][62][63].…”