# Fabrication of photonic structures

### Photorefractive Crystals

Photorefractivity describes the change of the refractive index as a consequence of an incident intensity distribution that enters a photorefractive medium. Photons excite charge carriers that redistribute due to complex transport mechanisms. The resulting space charge field leads to a change of the refractive index corresponding to the Pockels effect.

For the experiments, we mainly use strontium barium niobate (SBN) crystals, doped with cerium. This birefringent crystal with typical dimensions of 5 x 5 x 20 mm^{3} is installed in the setup with its c-axis perpendicular to the direction of propagation. We apply an external electric field in direction of the c-axis in order to foster charge carrier redistribution. Refractive index modulations are inscribed into the crystal using ordinarily polarized light, since the corresponding electro-optic coefficient is weak and therefore suited for quasi-linear induction. Subsequent probing of the artificial dielectric structure is performed with extraordinarily polarized light, which experiences a strong nonlinear effect due to a high electro-optic coefficient.

By choosing SBN we benefit from a huge flexibility, since inscribed structures can easily be erased with homogeneous white light illumination.

### Optical induction - Setup

As laser source, we use a frequency doubled Nd:YVO_{4} laser that emits cw laser light at a wavelength of 532nm and maximum power of 5W. The linearly polarized beam is expanded and modulated by a full-HD phase-only spatial light modulator (SLM) with 8bit in both, amplitude an phase. Therefore, an adequate Fourier filter is necessary. The spatially modulated light field induces a refractive index change into the biased photorefractive SBN crystal. A set of camera and microscope objective movable in direction of light propagation is capable to scan the light field as well as image entrance and output intensity distribution. In order to obtain the complete information of the light field, we elaborated a phase recording mode of the camera that yields additionally the spatial phase distribution. Similar to the described setup for the structure beam, a second part of the beam is modulated and can – extraordinarily polarized – be used as probe beam.

### Optical induction – Techniques

During the recent years, we have improved and professionalized techniques that allow an arbitrary structuring of photorefractive materials.

By means of parallelization, huge effort has been directed to the research of nondiffracting beams, capable to maintain their transverse intensity distribution and propagate transversely invariant for thousands of diffraction orders – enough to transfer this intensity distribution to the complete length of the photosensitive medium. The resulting two-dimensional photonic structures are suited to demonstrate and study a manifold of effects in dimensionally reduced systems, which are in some cases difficult to access. Especially, the class of nondiffracting beams meanwhile covers a huge variety of different beams. In Cartesian coordinates periodic square and hexagonal patterns as well as quasi-periodic fivefold (i.e. Penrose) structures have been realized, additionally Bessel beams in spherical coordinates, Mathieu beams in elliptical and Weber beams in parabolic coordinates, that all show unique characteristics.

Nevertheless, beneath these relatively ordered structures, light in disordered photonic media is highly appealing. We created random two-dimensional structures and demonstrated a variety of quantum mechanically predicted effects, such as Anderson localization and coherent backscattering.

Furthermore, we created three-dimensional photonic structures. The umbrella configuration as a special interference effect extendes the class of nondiffracting beams. By adding a plane wave propagating in the invariant direction, three-dimensional periodic and also helical structures have been accessed and investigated where we benefitted from a parallel induction process.

Finally, for accessing the class of deterministic aperiodic structures, a new induction technique for the pixel wise approximation of two-dimensional structures that lack both, translational and rotational symmetry, was invented, based on nondiffracting zeroth order Bessel beams as fundamental induction entity. This serial approach covers the possibility to approximate any desired photonic structure.