Parity-time symmetry in parameter space of polarization

Establishing parity-time (PT) symmetry in non-spatial space is a promising way to simplify the PT-symmetry system structure. In this paper, an implementation of PT symmetry in optical polarization space is reported. By utilizing the polarization multiplexing technology, PT symmetry is formed in overlapping spatial parameter space. The degeneracy of eigenmodes with two distinct PT phases in polarization space is demonstrated. In the PT-symmetric phase, the eigenmodes have real eigenfrequencies that respect PT symmetry, exhibiting broken degeneracy (mode splitting); in the PT-broken phase, the eigenmodes are degenerate with a pair of complex conjugate eigenfrequencies. The sharp-pointed peak filter response in the PT-broken phase due to the strong field localization is characterized, which explains the mode-selection mechanism of PT-symmetry breaking. The polarization-space PT symmetry is applied in a 7-km single-loop optoelectronic oscillator, and a stable single-mode oscillation signal is generated with a phase noise of −138 dBc/Hz at 10 kHz and side-mode suppression ratio of 49 dB. The approach expands the parameter spaces to carry out PT symmetry and could promote the integration of the PT-symmetry photon system.