Discrete parametric oscillation and nondiffracting beams in a Glauber–Fock oscillator

We consider a Glauber–Fock oscillator and show that diffraction can be managed. We show how to design arrays of waveguides where light beams experience zero diffraction. We find an exact analytical family of nondiffracting localized solution. We predict discrete parametric oscillation in the Glauber–Fock oscillator.