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Implementation of a parity-time (PT) symmetric microwave photonic system inthe optical wavelength space with spatial singularity is proposed. In theproposed PT-symmetric microwave photonic system, the gain and loss modes areconfined in a single spatial resonator, which is different from a conventionalPT-symmetric system in which the two modes are localized in two physicallyseparated resonators to form one-dimensional spatial potential symmetry asrequired by the simplest one-dimensional parity transformation. We show thatPT-symmetry can be implemented between subspaces in non-spatial parameterspaces, in which the gain and loss modes can perfectly overlay spatially butare distinguishable in the designated parameter space. The resultant spatialsingularity enables the possibility in implementing PT-symmetric systems withincreased structural simplicity, integration density and long-term stability.To prove the concept, a PT-symmetric optoelectronic oscillator (OEO) in theoptical wavelength space is implemented. The OEO has a single-looparchitecture, with the gain and loss microwave modes carried by two opticalwavelengths to form two mutually coupled wavelength-space resonators (WSRs).PT-symmetry is achieved by controlling the wavelength spacing and the powercontrast. The operation of PT symmetry in the OEO is verified by the generationof a 10-GHz microwave signal with a low phase noise of 129.3 dBc/Hz at 10-kHzoffset frequency and a high sidemode suppression ratio (SMSR) of 66.22 dB.Compared with a conventional spatial PT-symmetric system, one in the wavelengthspace features a much simpler configuration, better stability and greaterresilience to environmental interferences.

Parity-time symmetry in wavelength space with spatial singularity