Complementing Second-Harmonic Generation (SHG) microscopy, a new home-made nonlinear microscope named Pockels Linear Electro-Optical Microscopy (PLEOM) based on the linear electrooptic (Pockels) effect, has been developed and used to map the second-order susceptibility Chi(2) of non-centrosymmetric materials with high sensitivity due to a stabilized interferometric homodyne detection scheme [1, 2]. This enables PLEOM to detect the electrooptic phase retardation of light resulting from the variation of the refractive index of nonlinear materials down to 10-6 radian and to investigate nonlinear materials at the nano-scale [3] towards applications in imaging of biological samples and tracking of labels therein. With PLEOM, a new imaging method allows to access, besides the aplitude, the no less crucial phase response, which is not readily amenable to classical SHG microscopy. In the frame of this dissertation, we have further extended the range of applications of PLEOM to investigate nonlinear materials and structures from nano- to millimeter-scale.

Firstly, we have proposed and demonstrated a new approach towards the full vector determination of the spontaneous polarization of single ferroelectric nano-crystals used as SHG nano-probes. This method allows to remove the ambiguity inherent to earlier polarization-resolved SHG microscopy experiments, and has permitted full determination of the orientation of single domain ferroelectric nano-crystals. The electrooptic phase response obtained in the form of phase images and polarization diagrams yields the full orientation in the laboratory frame of randomly dispersed single nano-crystals, together with their electric polarization dipole. The complete vector determination of the dipole orientation is a prerequisite to important applications including ferroelectric nano-domain orientation, membrane potential imaging and rotation dynamics of single biomolecules, especially by using a new low-cost non-invasive imaging method with a low intensity illumination beam.

The ferroelectric domain pattern of periodically poled KTiOPO4 and of a two-dimensional decagonal quasi-periodic LiNbO3 nonlinear crystal was determined by local measurement of their electro-optically induced phase retardation. Owing to the sign reversal of the electrooptic coefficients upon domain inversion, a 180 degree (pi) phase shift is observed across domain barriers between domains with opposed orientations. PLEOM allows to reveal the nonlinear and electrooptic spatially modulated patterns in ferroelectric crystals in a non-destructive manner and to determine their poling period, duty cycle and short-range order as well as to detect local defects in the domain structure, such due to incomplete poling.

In addition, we have also proposed and demonstrated a new method, based on the voltage dependence of the electrooptic dephasing, to mimic the membrane potential in cells, working at this stage on nonlinear dye containing phospholipidic membranes, grown in a microfluidic set-up.