Conventional parity-time (PT) symmetric systems consist of two physically separated resonators to form one-dimensional spatial potential symmetry, with the gain and loss modes localized in respective resonators. We show that PT-symmetry can be implemented between subspaces in non-spatial parameter spaces, in which the gain and loss modes can perfectly overlay spatially but are distinguishable in the designated parameter space. Such optical parameter spaces can be implemented by optical wavelength, wavevector and polarization, etc. The resultant spatial singularity enables the possibility in implementing PT-symmetric systems with increased structural simplicity, integration density and long-term stability. In this talk, PT-symmetric optoelectronic oscillators (OEOs) are implemented in the parameter space of optical wavelength and wavevector; a PT-symmetric laser is implemented in the parameter space of optical polarization. All systems are shown to operate with stable single-mode oscillation and with low structural complexity. We believe that PTsymmetric system in non-spatial parameter spaces can find great applications in optical instrumentation due to its capability for low phase noise signal generation.
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