Partially coherent waves in nonlinear periodic lattices

H. Buljan
University of Zagreb,Zagreb, Croatia
O. Cohen, T. Schwartz, T. Carmon, O. Manela, G. Bartal, J.W. Fleischer, M. Segev
Technion, Haifa, Israel
Z.H. Musslimani, N.K. Efremidis, D.N. Christodoulides
University of Central Florida, Florida, USA

We present recent developments regarding the problem of propagation of partially coherent waves in nonlinear periodic lattices. In particular, we will discuss Random-phase (incoherent) solitons in nonlinear periodic lattices and the evolution of the (Floquet-Bloch and Fourier) power spectra of partially coherent light in nonlinear lattices. Dynamics here depends mostly on the interplay between the statistical properties of the waves, and the lattice periodicity. The most important characteristic length-scales involved are the spatial correlation distance, which gives a length-scale at which there is still some correlation between the electric field amplitudes, and the lattice spacing. It will be shown that random phase solitons exist in such system when the intensity profiles, statistical (coherence) properties, and power spectra conform to the periodicity of the lattice. Furthermore, we will present a method for nonlinear Brillouin zone spectroscopy, which naturally arises from the specific properties of the nonlinear evolution of the power spectra in this system. While describing the systems mentioned above, we will explain the characteristic length-scales and time-scales involved, briefly explain the derivation of equations of motion from the underlying Maxwell equations, and extract the most interesting features of dynamics. In addition, we will briefly discuss the analogy between these optical systems governed by the Nonlinear Schroedinger type equation(s), and the systems of weakly interacting bosons, at low temperatures, in optically induced lattices.