  We present a novel, real-time, experimental technique for linear and
nonlinear Brillouin zone spectroscopy of photonic lattices. The method relies
on excitation with random-phase waves and far-field visualization of the
spatial spectrum of the light exiting the lattice. Our technique facilitates
mapping the borders of the extended Brillouin zones and the areas of normal and
anomalous dispersion within each zone. For photonic lattices with defects
(e.g., photonic crystal fibers), our technique enables far-field visualization
of the defect mode overlaid on the extended Brillouin zone structure of the
lattice. The technique is general and can be used for photonic crystal fibers
as well as for periodic structures in areas beyond optics.
