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.
In the article it is considered generation of the down-conversion process, which crucially depends on the phase-matching relations between the interacting waves, in geometry of the transverse excitation of an annular periodically poled nonlinear photonic structure by a fundamental Gaussian beam.
It has been investigated the probability and conditions for quasi-phase-matching (QPM) of down-conversion process in annular periodically poled media. Here it is presented in transverse geometry of light propagation, when the fundamental light beam propagates along the axis of the structure; consequently conical beams are formed as a result of the higher-order nonlinear Bragg diffraction. It has been shown strong correlation between the interacting beams polarizations and the type of the nonlinear media for realization of perfect QPM for the process. Besides, it has been calculated the two-photon amplitude of the down-conversion process in the annular nonlinear structure.
We investigate quasi-phase-matching (QPM) and spontaneous parametric down-conversion in randomly poled structures. The novelty is that we consider the disordered structure which involves nonlinear segments separated by domains with linear optical spacers of random lengths. Considering down-conversion, we calculate the probability of production of pair photons by using the procedure of averaging over random positions of domains boundaries. We demonstrate the method of compensation of the dispersive effects in nonlinear segments by appropriately chosen linear dispersive segments of superlattice for realizing effective QPM and preparation of joint states of two photons.
We investigate production of three-photon and four-photon states in cascaded parametric processes of photon splitting
and summing in χ <sup>(2)</sup>nonlinear media, under action of pump field. Generation of photon triplets using simultaneously phase
matched three-photon processes: ω<sub>0</sub>↔ω<sub>1</sub>+ω<sub>2</sub> , ω<sub>2</sub>↔ω<sub>1</sub>+ω<sub>1</sub> , is considered in dual-grating layered structure that involves
nonlinear and linear segments. The production of heralded two-photon entangled states from three-photon states is analyzed
for this configuration by using the method of conditional detection of auxiliary photons. Cascaded four-photon downconversion
based on simultaneously phase matched three-photon processes: ω<sub>0</sub>↔ω<sub>2</sub> +ω<sub>2</sub> , ω<sub>2</sub>↔ω<sub>1</sub>+ω<sub>1</sub> is arranged for
phase-reversed configuration. The effects of correlation between photons in both three-photon and four-photon states is
analyzed in the regimes of amplification of corresponding modes at the frequency of three-photon downconversion
ω<sub>1</sub> = ω<sub>0</sub>/3 and the frequency of four-photon down-conversion ω<sub>1</sub> = ω<sub>0</sub>/4respectively for both cascaded systems.