# Modulated Χ^{(2)} materials

For efficient frequency doubling the fundamental and SHG waves have to fulfill the phase matching condition. Phase matching can be realized for instance by using the birefringence of the crystal. A more flexible approach is the periodic structuring of the Χ^{(2)}-nonlinearity, which can be realized in ferroelectric crystals by periodically poling of the domains. A two-dimensional structure of the Χ^{(2)}-nonlinearity represents an extension of the concept of quasi-phase matching leading to new phase matching conditions. In comparison with photonic lattices or photonic crystals these nonlinear structures possess a homogeneous refractive index but a modulated nonlinearity. Due to their discrete nature periodic nonlinear photonic structures can only be used for an effective frequency conversion of discrete wavelengths. However, for frequency conversion of ultrashort laser pulses with a large spectral bandwidth nonlinear photonic structures with a broad bandwidth are desired. For this purpose the period of the alternating nonlinearity can be linearly increased (chirp) or one can use so called quasi gratings. A rather simple kind of structure is a random orientation of the nonlinearity. Domains are already randomly oriented when the ferroelectric crystal is not homogeneously poled. We take advantage of this situation for our work on an effective and tunable frequency conversion of ultrashort laser pulses: we examine frequency conversion of ultrashort laser pulses in strontium barium niobate (SBN), where the order of the nonlinearity is specifically molded [Zitat]. We have demonstrated all kinds of parametric three-wave mixing processes in unpoled SBN: second harmonic generation, sum-frequency generation, and difference-frequency generation. Cascaded processes to generate the third and fourth harmonic are also possible. As the nonlinearity is modulated in two dimensions, the phase-matching process is non-collinear which leads to a spatial distribution of the higher harmonics. The frequency converted light is emitted either in a plane or on a cone. We examine the influence of the degree of disorder and the size, shape and orientation of the ferroelectric domains on the intensity, polarization and spatial distribution of the second harmonic. We have developed a new technique called Cerenkov-SHG-spectroscopy [Zitat] to analyse the domain distribution and for the three dimensional visualization of the domains we are using Cerenkov-SHG-microscopy.