Modeling nonlinear optical interactions of focused beams in bulk crystals and thin films: A phenomenological approach

Coherent nonlinear optical micro-spectroscopy is a frequently used tool in modern material science, as it is sensitive to many different local observables, which comprise, among others, crystal symmetry and vibrational properties. The richness in information, however, may come with challenges in data interpretation, as one has to disentangle the many different effects like multiple reflections, phase jumps at interfaces, or the influence of the Guoy-phase. In order to facilitate interpretation, the work presented here proposes an easy-to-use semi-analytical modeling ansatz, that bases upon known analytical solutions using Gaussian beams. Specifically, we apply this ansatz to compute nonlinear optical responses of (thin film) optical materials. We try to conserve the meaning of intuitive parameters like the Gouy-phase and the nonlinear coherent interaction length. In particular, the concept of coherence length is extended, which is a must when using focal beams. The model is subsequently applied to exemplary cases of second-harmonic and third-harmonic generation. We observe a very good agreement with experimental data and furthermore, despite the constraints and limits of the analytical ansatz, our model performs similarly well as when using more rigorous simulations. However, it outperforms the latter in terms of computational power, requiring more than three orders less computational time and less performant computer systems

Hall mobilities and sheet carrier densities in a single LiNbO3_3 conductive ferroelectric domain wall

For the last decade, conductive domain walls (CDWs) in single crystals of the uniaxial model ferroelectric lithium niobate (LiNbO$_3$, LNO) have shown to reach resistances more than 10 orders of magnitude lower as compared to the surrounding bulk, with charge carriers being firmly confined to sheets of a few nanometers in width. LNO thus currently witnesses an increased attention since bearing the potential for variably designing room-temperature nanoelectronic circuits and devices based on such CDWs. In this context, the reliable determination of the fundamental transport parameters of LNO CDWs, in particular the 2D charge carrier density $n_{2D}$ and the Hall mobility $\mu_{H}$ of the majority carriers, are of highest interest. In this contribution, we present and apply a robust and easy-to-prepare Hall-effect measurement setup by adapting the standard 4-probe van-der-Pauw method to contact a single, hexagonally-shaped domain wall that fully penetrates the 200-$\mu$m-thick LNO bulk single crystal. We then determine $n_{2D}$ and $\mu_{H}$ for a set of external magnetic fields $B$ and prove the expected cosine-like angular dependence of the Hall voltage. Lastly, we present photo-Hall measurements of one and the same DW, by determining the impact of super-bandgap illumination on the 2D charge carrier density $n_{2D}$

Comparing Transmission- and Epi-BCARS: A Transnational Round Robin on Solid State Materials

Broadband coherent anti-Stokes Raman scattering (BCARS) is an advanced Raman spectroscopy method that combines the spectral sensitivity of spontaneous Raman scattering (SR) with the increased signal intensity of single-frequency coherent Raman techniques. These two features make BCARS particularly suitable for ultra-fast imaging of heterogeneous samples, as already shown in biomedicine. Recent studies demonstrated that BCARS also shows exceptional spectroscopic capabilities when inspecting crystalline materials like lithium niobate and lithium tantalate, and can be used for fast imaging of ferroelectric domain walls. These results strongly suggest the extension of BCARS towards new imaging applications like mapping defects, strain, or dopant levels, similar to standard SR imaging. Despite these advantages, BCARS suffers from a spurious and chemically unspecific non-resonant background (NRB) that distorts and shifts the Raman peaks. Post-processing numerical algorithms are then used to remove the NRB and to obtain spectra comparable to SR results. Here, we show the reproducibility of BCARS by conducting an internal Round Robin with two different BCARS experimental setups, comparing the results on different crystalline materials of increasing structural complexity: diamond, 6H-SiC, KDP, and KTP. First, we compare the detected and phase-retrieved signals, the setup-specific NRB-removal steps, and the mode assignment. Subsequently, we demonstrate the versatility of BCARS by showcasing how the selection of pump wavelength, pulse width, and detection geometry can be tailored to suit the specific objectives of the experiment. Finally, we compare and optimize measurement parameters for the high-speed, hyperspectral imaging of ferroelectric domain walls in lithium niobate.Comment: 12 pages, 8 figure

Tricyanidoferrates(−IV) and ruthenates(−IV) with non‐innocent cyanido ligands

Exceptionally electron-rich, nearly trigonal-planar tricyanidometalate anions [Fe(CN)(3)](7-) and [Ru(CN)(3)](7-) were stabilized in LiSr3[Fe(CN)(3)] and AE(3.5)[M(CN)(3)] (AE=Sr, Ba; M=Fe, Ru). They are the first examples of group 8 elements with the oxidation state of -IV. Microcrystalline powders were obtained by a solid-state route, single crystals from alkali metal flux. While LiSr3[Fe(CN)(3)] crystallizes in P6(3)/m, the polar space group P6(3) with three-fold cell volume for AE(3.5)[M(CN)(3)] is confirmed by second harmonic generation. X-ray diffraction, IR and Raman spectroscopy reveal longer C-N distances (124-128 pm) and much lower stretching frequencies (1484-1634 cm(-1)) than in classical cyanidometalates. Weak C-N bonds in combination with strong M-C pi-bonding is a scheme also known for carbonylmetalates. Instead of the formal notation [Fe-IV(CN-)(3)](7-), quantum chemical calculations reveal non-innocent intermediate-valent CN1.67- ligands and a closed-shell d(10) configuration for Fe, that is, Fe2-

In depth Raman analysis of the ferroelectrics KTiOPO4 and LiNbO3 : role of domain boundaries and defects

Die ortsaufgelöste Ramanspektroskopie bietet ein breites Anwendungsspektrum in der Untersuchung von Ferroelektrika, welches von der Analyse der Stöchiometrie oder Defekten bis zur Visualisierung von Domänenstrukturen und Wellenleitern reicht. Vorrausetzung für die Interpretation von gemessenen Spektren ist ein weitreichendes Verständnis der physikalischen Hintergründe und Ursachen. So ist beispielsweise für die weit verbreiteten nichtlinearen Materialien Lithiumniobat und Kaliumtitanylphosphat keine vollständige und eindeutige Zuordnung der Phononenmoden verfügbar, während das Ramanspektrum von Domänenwänden nicht hinreichend verstanden ist. Solche Fragen werden in dieser Arbeit systematisch experimentell in enger Verbindung mit der Dichtefunktionaltheorie untersucht. Hierbei erlaubt die Analyse das Phononenspektrum des Lithiumniobat-Materialsystems in der Gänze zu verstehen. Dies dient als Basis für die Analyse der Spektren der ferroelektrischen Domänenwände. Hier kann das Domänenwandspektrum auf Basis von mikroskopischen Strukturänderungen, wie Verspannung und lokalen elektrischen Feldern, sowie einer makroskopischen Änderung der Ramanauswahlregeln erklärt werden. Diese Effekte zeigen sich zudem auf verschiedenen Längenskalen. Die ersten umfassenden Ramananalysen von Domänenstrukturen und periodische gepolten, Rb-ausgetauschten Wellenleitern zeigen sowohl den Einfluss der Stöchiometrie, aber auch den Einfluss von Verspannungen. Hier erlaubt es die Ramanspektroskopie, den Einfluss dieser Effekten zu analysieren.In the context of ferroelectrics spatially resolved Raman spectroscopy is a powerful tool to investigate stoichiometry, defects or the ferroelectric properties, as well as to visualize domain structures or waveguides. Using Raman spectroscopy for investigations requires a throughout understanding of the spectra and underlying mechanisms. For example, in the context of the common nonlinear materials, lithium niobate and potassium titanyl phosphate, no comprehensive understanding of the Raman spectra of the bulk materials is available, while the underlying mechanism of the domain wall contrast in Raman spectroscopy is not well understood. In this work, questions like these have been addressed in terms of systematic experimental investigations in close cooperation with density functional theory. In particular, it was possible to present a complete assignment of all phonons in the lithium niobate system, which serves as the basis for the understanding of the domain wall spectrum. Here, the domain wall spectrum can be explained with regard to microscopic structural effects, such as strains and electric fields, as well as a macroscopic change of selections rules. Both mechanisms are likewise present in the domain wall spectrum, while being present at different length scales. In the context of potassium titanyl phosphate the first throughout Raman investigations of domain structure, waveguides and periodically poled waveguides are presented. In the context of Rb-exchanged waveguides the change in stoichiometry, but also effects of strain are detected. Here, the Raman analysis provides a method to evaluate these effects.Michael Rüsing ; Supervisor: Prof. Dr. Artur ZrennerTag der Verteidigung: 21.02.2018Universität Paderborn, Dissertation, 201

Tuning the Čerenkov second harmonic contrast from ferroelectric domain walls via anomalous dispersion

Second harmonic (SH) microscopy represents a powerful tool for the investigation of crystalline systems, such as ferroelectrics and their domain walls (DWs). Under the condition of normal dispersion, i.e., the refractive index at the SH wavelength is larger as compared to the refractive index at the fundamental wavelength, n(2ω) . n(ω), bulk crystals will generate no SH signal. Should the bulk, however, contain DWs, an appreciable SH signal will still be detectable at the location of DWs stemming from the Čerenkov mechanism. In this work, we demonstrate both how SH signals are generated in bulk media and how the Čerenkov mechanism can be inhibited by using anomalous dispersion, i.e., n(ω) . n(2ω). This allows us to quantitatively estimate the relative strength of the Čerenkov compared to other SH contrast mechanisms in DWs, such as the interference contrast. The results are in agreement with previous experiments based on the geometric separation of the signals. Due to the observed, strong Čerenkov contrast, such signal contributions may not be neglected in polarimetry studies of ferroelectric DWs in the future

Turn all the lights off: Bright- and dark-field second-harmonic microscopy to select contrast mechanisms for ferroelectric domain walls

Recent analyses by polarization resolved second-harmonic (SH) microscopy have demonstrated that ferroelectric (FE) domain walls (DWs) can possess non-Ising wall characteristics and topological nature. These analyses rely on locally analyzing the properties, directionality, and magnitude of the second-order nonlinear tensor. However, when inspecting FE DWs with SH microscopy, a manifold of different effects may contribute to the observed signal difference between domains and DWs, i.e., far-field interference, Čerenkov-type phase-matching (CSHG), and changes in the aforementioned local nonlinear optical properties. They all might be present at the same time and, therefore, require careful interpretation and separation. In this work, we demonstrate how the particularly strong Čerenkov-type contrast can selectively be blocked using dark- and bright-field SH microscopy. Based on this approach, we show that other contrast mechanisms emerge that were previously overlayed by CSHG but can now be readily selected through the appropriate experimental geometry. Using the methods presented, we show that the strength of the CSHG contrast compared to the other mechanisms is approximately 22 times higher. This work lays the foundation for the in-depth analysis of FE DW topologies by SH microscopy