Two-dimensional photonic structures

The interference of plane waves under appropriate angles results in diffraction-free propagating, transversly periodic waves of various symmetries. Since the periodic intensity profile of such waves does not change during propagation, they enable the optical induction of two-dimensional photonic lattices inside a photorefractive crystal.
Compared to conventionally manufactured photonic crystals, these optically induced lattices offer the advantage of highly reconfigurable, nonlinear photonic structures  achievable at very low power levels (typically in the range of several microwatts). Therefore, they provide an ideal tool for experimental studies of fundamental effects related to wave propagation in periodically modulated matarials.

Besides typical lattice geometries of e.g. square or hexagonal symmetry , the optical induction also allows for more sophisticated structures.
As an example, Fig.1 shows the triangular lattice resulting from the interference of six plane waves inside the crystal.



Abb. 1: Parallel triangular lattice. (a) grating wave, (b) induced refractive index profile, (c) Brillouin-zone-spectroscopy

A very powerful tool for the analysis of the induced refractive index change is given by the so-called Brillouin zone spectroscopy. It enables the visualzation of the characteristic Brillouin zones associated with specific lattice structure by coherent multi-band ecxitation of modes followed by an optical Fourier transformation. The resulting Brillouin zone picture for the triangular lattice is depicted in Fig.1c.

For experimental studies of photonic structures in photorefractive media, it is crucially important to consider the intrinsic anisotropy of such crystals. Due to this anisotropy, the symmetry of the  induced refractive index structure can significantly differ from that of the lattice wave. For example, depending on its orientation, a lattice wave with square symmetry either leads to a two-dimensional pattern of the same symmetry or causes an effectively one-dimensional pattern of reduced symmetry.

The investigation of fundamental linear and nonlinear propagation effects of light in different lattice types under the influence of this anisotropy and especially the formation of nonlinear localized states called lattice solitons are part of our current research activities.