  We propose an exactly solvable waveguide lattice incorporating inhomogeneous
coupling coefficient. This structure provides a classical analogue to the
squeezed number and squeezed coherent intensity distribution in quantum optics
where the propagation length plays the role of 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 waveguides ($ \alpha $). Our analytical results show that the
Bloch-like oscillations appear above a critical value for the linear gradient
of propagation constant ($ \alpha > \alpha_{c} $). The phase transition (in the
propagation properties of the waveguide) is a result of competition between
discrete and Bragg diffraction. Moreover, the light intensity decay
algebraically along each waveguide at the critical point while it falls off
exponentially below the critical point ($ \alpha < \alpha_{c} $).
