Phase transition to spatial Bloch-like oscillation in squeezed photonic lattices

Abstract

We propose an exactly solvable waveguide lattice incorporating an inhomogeneous coupling coefficient. This structure provides classical analogs to the squeezed number and squeezed coherent intensity distribution in quantum optics where the propagation length plays the role of a squeezed amplitude. The intensity pattern is obtained in a closed form for an arbitrary distribution of the initial beam profile. We have also investigated the phase transition to the spatial Bloch-like oscillations by adding a linear gradient to the propagation constant of each waveguide ($\ensuremath{\alpha}$). Our analytical results show that the Bloch-like oscillations appear above a critical value for the linear gradient of the propagation constant ($\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$). The phase transition (in the propagation properties of the waveguide) is a result of competition between discrete and Bragg diffraction. Moreover, the light intensity decays algebraically along each waveguide at the critical point while it falls off exponentially below the critical point ($\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$).