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

Magnetization-induced effects in the nonlinear optical response of magnetic media, such as magnetization-induced-second-harmonic generation (MSHG), led to very strong and novel nonlinear magneto-optical effects that appear to be very sensitive to magnetic interface properties. This surface-interface sensitivity of MSHG, in combination with the very large magneto-optical effects, has led to a fast development of this technique over the past decade. On the one hand, an extreme sensitivity of MSHG to the electronic and magnetic structure of clean surfaces has been successfully demonstrated. On the other hand, the penetration depth of light allows one to use this sensitivity to study buried interfaces in multilayer systems. Further experimental developments of the MSHG technique, such as space and time resolution as well as magnetization-sensitive-sum-frequency generation, appear to be promising as well.

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Magnetization-induced-second-harmonic generation from surfaces and interfaces

Optical second-harmonic generation (SHG) studies of a nematic liquid-crystal (NLC) cell have been performed using combined phase and intensity measurements upon variation of the magnitude and sign of an external electric dc field A phase shift of 180° in the harmonic field generated by the bulk NLC molecules was observed upon sign reversal of this field We present here the first demonstration of SHG with electrically controllable phase shift The contributions to the SH signal due to both the bulk NLC molecules and the background of the adjacent cell windows could be identified

Studies of Nematic Liquid-Crystal Cells Using Second-Harmonic Phase Measurements

This paper presents a measurement system for calibrated realtime measurement of differential and common mode signals in differential high-speed data links. In contrast to existing differential coupler measurement systems, a reconstruction of absolute voltage signals in a defined calibration plane is enabled by a frequency domain calibration. The system is verified in simplex and full-duplex data transmission links, showing good performance. A corresponding measurement system is used to perform signal integrity analysis in differential high-speed communication systems, such as automotive Ethernet.

A System for Calibrated Realtime Measurement of Mixed-Mode Waves on High-Speed Data Links

Classification of road users is important for traffic monitoring. The usability of a height estimate based on the two-ray ground-reflection model as a feature for the classification of vehicles is analyzed in this paper. The four-ray ground-reflection model for fast chirp ramp sequence waveforms of FMCW radars is derived and simplified to the well-known two-ray ground-reflection model. A spectrum from which the height of a target can be derived is obtained using the Lomb-Scargle periodogram. Measurements with two vehicle classes illustrate the approach and show that the model could be used as a feature to distinguish vehicles based on their height.

R. Stolle

Papers

Phase measurements in nonlinear optics

Studies of Nematic Liquid-Crystal Cells Using Second-Harmonic Phase Measurements

A System for Calibrated Realtime Measurement of Mixed-Mode Waves on High-Speed Data Links

Radar Classification of Vehicles Using a Ground-Reflection Model

Optical Processes in Organic Materials