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We describe the process of parametric amplification in a directional coupler of quadratically nonlinear and lossy waveguides, which belong to a class of optical systems with spatial parity-time (PT) symmetry in the linear regime. We identify a distinct spectral parity-time anti-symmetry associated with optical parametric interactions, and show that pump-controlled symmetry breaking can facilitate spectrally selective mode amplification in analogy with PT lasers. We also establish a connection between breaking of spectral and spatial mode symmetries, revealing the potential to implement unconventional regimes of spatial light switching through ultrafast control of PT breaking by pump pulses.
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Diana A. Antonosyan, Alexander S. Solntsev, Andrey A. Sukhorukov, "Parity-time anti-symmetric parametric amplification," Proc. SPIE 9546, Active Photonic Materials VII, 95461J (31 August 2015); https://doi.org/10.1117/12.2190266