Nonlinear optics is an essential component of modern laser systems and optoelectronic devices. It has also emerged as an important tool in probing the electronic, vibrational, magnetic, and crystallographic structure of materials ranging from oxides and metals, to polymers and biological samples. This review focuses on the specific technique of optical second harmonic generation (SHG), and its application in probing ferroelectric complex oxide crystals and thin films. As the dominant SHG interaction mechanism exists only in materials that lack inversion symmetry, SHG is a sensitive probe of broken inversion symmetry, and thus also of bulk polar phenomena in materials. By performing in-situSHG polarimetry experiments in different experimental conditions such as sample orientation, applied electric field, and temperature, one can probe ferroelectric hysteresis loops and phase transitions. Careful modeling of the polarimetry data allows for the determination of the point group symmetry of the crystal. In epitaxial thin films with a two-dimensional arrangement of well-defined domain orientations, one can extract information about intrinsic material properties such as nonlinear coefficients, as well as microstructural information such as the local statistics of the different domain variants being probed. This review presents several detailed examples of ferroelectric systems where such measurements and modeling are performed. The use of SHG microscopic imaging is discussed, and its ability to reveal domain structures and phases not normally visible with linear optics is illustrated.

Probing Ferroelectrics Using Optical Second Harmonic Generation

We present a new interferometric technique for measuring Coherent Anti-Stokes Raman Scattering (CARS) and Second Harmonic Generation (SHG) signals. Heterodyne detection is employed to increase the sensitivity in both CARS and SHG signal detection, which can also be extended to different coherent processes. The exploitation of the mentioned optical nonlinearities for molecular contrast enhancement in Optical Coherence Tomography (OCT) is presented.

Nonlinear optical contrast enhancement for optical coherence tomography.

Biomolecular structure at solid-liquid interfaces as revealed by nonlinear optical spectroscopy.

Measurement of the phase, and not only the intensity, of the nonlinear optical response of a system is important in many applications which are reviewed here. We demonstrate and compare several techniques for direct measurement of the phase of the nonlinear susceptibilities through nonlinear interferometry. Different ways of imparting a controllable phase shift are discussed. Unless the coherence length is impractically large, the preferred method is to use a variable-pressure gas cell to control the phase difference between the input laser pulse and the nonlinear optical signal.

Phase measurements in nonlinear optics

We report ionic strength-dependent phase shifts in second harmonic generation (SHG) signals from charged interfaces that verify a recent model in which dispersion between the fundamental and second harmonic beams modulates observed signal intensities. We show how phase information can be used to unambiguously separate the χ(2) and interfacial potential-dependent χ(3) terms that contribute to the total signal and provide a path to test primitive ion models and mean field theories for the electrical double layer with experiments to which theory must conform. Finally, we demonstrate the new method on supported lipid bilayers and comment on the ability of our new instrument to identify hyper-Rayleigh scattering contributions to common homodyne SHG measurements in reflection geometries.

Beyond the gouy-chapman model with heterodyne-detected second harmonic generation

Direct measurement of the phase of the surface nonlinear susceptibility is based on the interference of nonlinear optical signals. Up to now, this has not been possible for Second-Harmonic Generation (SHG) in geometries such as Total Internal Reflection (TIR) due to the refractive dispersion of harmonic and fundamental light created in TIR. We demonstrate two schemes which enable us to overcome this dispersion, leading to interference between two second-harmonic signals generated consecutively by the same laser. The advantages and limitations of the two approaches are discussed. We use this technique to check the theoretical predictions for the nonlinear Fresnel factors for SHG in the TIR geometry.

E. Schwarzberg

Papers

Phase measurements in nonlinear optics

Nonlinear interferometry and phase measurements for surface second-harmonic generation in a dispersive geometry

Optical Processes in Organic Materials