Direct Determination of Effective Interfacial Optical Constants by Nonlinear Optical Null Ellipsometry of Chiral Films

Sum frequency generation as a proxy for ellipsometry: Not just a phase

Infrared refractive indices of organic materials are typically resolved through IR ellipsometry. This technique takes advantage of optical interference effects to solve the optical constants. These are the same effects that complicate the analysis of coherent spectroscopy experiments on thin films. Vibrational sum frequency generation is an interface-specific coherent spectroscopy that requires spectral modeling to account for optical interference effects to uncover interfacial molecular responses. Here, we explore the possibility of leveraging incident beam geometries and sample thicknesses to simultaneously obtain the molecular responses and refractive indices. Globally fitting a higher number of spectra with a single set of refractive indices increases the fidelity of the fitted parameters. Finally, we test our method on samples with a range of thicknesses and compare the results to those obtained by IR ellipsometry.

Dispersion of Complex Refractive Indices for Intense Vibrational Bands. II. Implication to Sum Frequency Generation Spectroscopy

Sharp and intense vibrational bands are characterized with conspicuous dispersion of complex refractive indices. Based on the quantitative data of dispersion in the preceding paper, this paper clarifies the influence of the dispersion on the sum frequency generation (SFG) spectroscopy. As a consequence of the large dispersion, the lineshapes of SFG spectra could be influenced by the frequency dependence of the Fresnel factor as well as the nonlinear susceptibility. This paper argues the relative importance of the two factors in general cases and provides a useful criterion to evaluate their importance. The effect of Fresnel dispersion becomes significant when the SFG spectrum involves a sharp and intense vibrational band as well as a large non-resonant background susceptibility, typically in some solid-liquid interfaces. A possible way to correct the effect of Fresnel dispersion is suggested using the heterodyne measurement.

Imaging the Nonlinear Susceptibility Tensor of Collagen by Nonlinear Optical Stokes Ellipsometry

Nonlinear optical Stokes ellipsometric (NOSE) microscopy was demonstrated for the analysis of collagen-rich biological tissues. NOSE is based on polarization-dependent second harmonic generation imaging. NOSE was used to access the molecular-level distribution of collagen fibril orientation relative to the local fiber axis at every position within the field of view. Fibril tilt-angle distribution was investigated by combining the NOSE measurements with ab initio calculations of the predicted molecular nonlinear optical response of a single collagen triple helix. The results were compared with results obtained previously by scanning electron microscopy, nuclear magnetic resonance imaging, and electron tomography. These results were enabled by first measuring the laboratory-frame Jones nonlinear susceptibility tensor, then extending to the local-frame tensor through pixel-by-pixel corrections based on local orientation.

Sum Frequency Generation of Interfacial Lipid Monolayers Shows Polarization Dependence on Experimental Geometries

Sum frequency generation (SFG) vibrational spectroscopy has been widely employed to investigate molecular structures of biological surfaces and interfaces including model cell membranes. A variety of lipid monolayers or bilayers serving as model cell membranes and their interactions with many different molecules have been extensively studied using SFG. Here, we conducted an in-depth investigation on polarization-dependent SFG signals collected from interfacial lipid monolayers using different experimental geometries, i.e., the prism geometry (total internal reflection) and the window geometry (external reflection). The different SFG spectral features of interfacial lipid monolayers detected using different experimental geometries are due to the interplay between the varied Fresnel coefficients and second-order nonlinear susceptibility tensor terms of different vibrational modes (i.e., ss and as modes of methyl groups), which were analyzed in detail in this study. Therefore, understanding the interplay between the interfacial Fresnel coefficients and χ((2)) tensors is a prerequisite for correctly understanding the SFG spectral features with respect to different experimental geometries. More importantly, the derived information in this paper should not be limited to the methyl groups with a C3v symmetry; valid extension to interfacial functional groups with different molecular symmetries and even chiral interfaces could be expected.

Second harmonic generation correlation spectroscopy for characterizing translationally diffusing protein nanocrystals

Second harmonic generation correlation spectroscopy (SHG-CS) is demonstrated as a new approach to protein nanocrystal characterization. A novel line-scanning approach was performed to enable autocorrelation analysis without sample damage from the intense incident beam. An analytical model for autocorrelation was developed, which includes a correction for the optical scattering forces arising when focusing intense, infrared beams. SHG-CS was applied to the analysis of BaTiO3 nanoparticles ranging from 200 to ∼500 nm and of photosystem I nanocrystals. A size distribution was recovered for each sample and compared with the size histogram measured by scanning electron microscopy (SEM). Good agreement was observed between the two independent measurements. The intrinsic selectivity of the second-order nonlinear optical process provides SHG-CS with the ability to distinguish well ordered nanocrystals from conglomerates and amorphous aggregates. Combining the recovered distribution of particle diameters with the histogram of measured SHG intensities provides the inherent hyperpolarizability per unit volume of the SHG-active nanoparticles. Simulations suggest that the SHG activity per unit volume is likely to exhibit relatively low sensitivity to the subtle distortions within the lattice that contribute to resolution loss in X-ray diffraction, but high sensitivity to the presence of multi-domain crystals.

Connection of Jones and Mueller Tensors in Second Harmonic Generation and Multi-Photon Fluorescence Measurements

Despite the rapidly growing use of second harmonic generation (SHG) and two-photon excited fluorescence (TPEF) microscopy, opportunities for relating polarization-dependent measurements back to local structure and molecular orientation are often confounded by losses in polarization purity. In this work, connections linking Mueller tensor and Jones tensor descriptions of polarization-dependent SHG and TPEF are shown to substantially simplify partially depolarized microscopy measurements. These connections were facilitated by the derivation of several new tensor identity relations, based on generalization of established transformations of matrices and vectors. Methods are described for integrating local-frame symmetry and azimuthal rotation angle for simplifying the Mueller tensor. Through simple expressions bridging the Mueller and Jones formalisms, mathematical models for partial depolarization can greatly simplify interpretation of SHG and TPEF measurements to reconstruct the more general Mueller tensors using the much more concise Jones descriptions for the purely polarized components. Integrating the Mueller architecture allows polarization-dependent SHG and TPEF measurements to be connected back to a relatively small set of free parameters related to local structure and orientation.

Polarization-resolved second-harmonic generation microscopy as a method to visualize protein-crystal domains

Polarization-resolved second-harmonic generation (PR-SHG) microscopy is described and applied to identify the presence of multiple crystallographic domains within protein-crystal conglomerates, which was confirmed by synchrotron X-ray diffraction. Principal component analysis (PCA) of PR-SHG images resulted in principal component 2 (PC2) images with areas of contrasting negative and positive values for conglomerated crystals and PC2 images exhibiting uniformly positive or uniformly negative values for single crystals. Qualitative assessment of PC2 images allowed the identification of domains of different internal ordering within protein-crystal samples as well as differentiation between multi-domain conglomerated crystals and single crystals. PR-SHG assessments of crystalline domains were in good agreement with spatially resolved synchrotron X-ray diffraction measurements. These results have implications for improving the productive throughput of protein structure determination through early identification of multi-domain crystals.

Elucidation of molecular structures at buried polymer interfaces and biological interfaces using sum frequency generation vibrational spectroscopy

Sum frequency generation (SFG) vibrational spectroscopy has been developed into an important technique to study surfaces and interfaces. It can probe buried interfaces in situ and provide molecular level structural information such as the presence of various chemical moieties, quantitative molecular functional group orientation, and time dependent kinetics or dynamics at such interfaces. This paper focuses on these three most important advantages of SFG and reviews some of the recent progress in SFG studies on interfaces related to polymer materials and biomolecules. The results discussed here demonstrate that SFG can provide important molecular structural information of buried interfaces in situ and in real time, which is difficult to obtain by other surface sensitive analytical techniques.

Hydrogen bonding in the hexagonal ice surface

A recently developed technique in sum frequency generation spectroscopy, polarization angle null (or PAN-SFG), is applied to two orientations of the prism face of hexagonal ice. It is found that the vibrational modes of the surface are similar in different faces. As in the basal face, the prism face of ice contains five dominant resonances: 3096, 3146, 3205, 3253, and 3386 cm(-1). On the basal face, the reddest resonance occurs at 3098 cm(-1); within the bandwidth, the same as the prism face. On both the prism and basal faces, this mode contains a significant quadrupole component and is assigned to the bilayer stitching hydrogen bonds. The bluest of the resonances, 3386 cm(-1), occurs slightly blue-shifted at 3393 cm(-1) in the basal face. The prism face has two orientations: one with the optic or c axis in the input plane (the plane formed by the surface normal and the interrogating beam propagation) and one with the c axis perpendicular to the input plane. The 3386 cm(-1) mode has significant intensity only with the c axis in the input plane. On the basis of these orientation characteristics, the 3386 cm(-1) mode is assigned to double-donor molecules in either the top half bilayer or in the lower half bilayer. On the basis of frequency considerations, it is assigned to double-donor molecules in the top half bilayer. These are water molecules containing a nonbonded lone pair. In addition to identification of the components of the broad hydrogen-bonded region, PAN-SFG measures the tangential vs longitudinal content of the vibrational modes. In accord with previous suggestions, the lower frequency modes are predominantly tangential, whereas the higher frequency modes are mainly longitudinal. On the prism face, the 3386 cm(-1) mode is entirely longitudinal.

Mining the polarization-dependence of nonlinear optical measurements

The electromagnetic field strength present within the focal volume of a pulsed laser is routinely high enough to produce reasonably efficient nonlinear summing and mixing of optical frequencies. The polarization-dependence of the outgoing beam is a sensitive function of the polarization state(s) of the incident beam(s) and the structure, orientation, and symmetry of the sample. Mining this information hinges on two elements: (1) accurate and precise polarization-dependent measurements, and (2) reliable modeling to relate the measured responses back to local structure and orientation. The central focus of this review is on the first step. Experimental strategies for precise and accurate nonlinear optical ellipsometry (NOE) polarization measurements are summarized for the most common and simplest case of second harmonic generation (SHG), or the frequency doubling of light, although extension to higher-order nonlinear optical interactions is straightforward in most cases.

Discrete retardance second harmonic generation ellipsometry

A new instrument was constructed to perform discrete retardance nonlinear optical ellipsometry (DR-NOE). The focus of the design was to perform second harmonic generation NOE while maximizing sample and application flexibility and minimizing data acquisition time. The discrete retardance configuration results in relatively simple computational algorithms for performing nonlinear optical ellipsometric analysis. NOE analysis of a disperse red 19 monolayer yielded results that were consistent with previously reported values for the same surface system, but with significantly reduced acquisition times.

Quantitative measurement and interpretation of optical second harmonic generation from molecular interfaces

Second harmonic generation (SHG) has been proven a uniquely effective technique in the investigation of molecular structure and conformations, as well as dynamics of molecular interfaces. The ability to apply SHG to molecular interface studies depends on the ability to abstract quantitative information from the measurable quantities in the actual SHG experiments. In this review, we try to assess recent developments in the SHG experimental methodologies towards quantitative analysis of the nonlinear optical properties of the achiral molecular interfaces with rotational isotropy along the interface normal. These developments include the methodology for orientational analysis of the SHG experimental data, the experimental approaches for more accurate SHG measurements, and a novel treatment of the symmetry properties of the molecular polarizability tensors in association with the experimentally measurable quantities. In the end, the recent developments on the problem of surface versus bulk contribution in SHG surface studies is discussed. These developments can put SHG on a more solid foundation for molecular interface studies, and to pave the way for better understanding and application of SHG surface studies in general.

Highly Ordered Polymer Films of Amphiphilic, Regioregular Polythiophene Derivatives

The fabrication and characterization of highly ordered thin films made from amphiphilic, regioregular polythiophene derivatives are described. Films of poly(3-(11-(2-tetrahydropyranyloxy)undecyl)thiophene (PTHPUDT) were prepared by the Langmuir-Blodgett technique. The amphiphilic nature of the polymer affords layer-by-layer deposition and the formation of multilayer films of head-to-head and tail-to-tail Y-type structure. X-ray diffraction studies indicate bilayer separations of approximately 30 A. Anisotropic optical absorption in the plane of the film indicates that the thiophene backbones are preferentially oriented along the dipping direction. Further, polarized light microscopy studies indicate that these films are highly birefringent and that the optical retardation is uniform over the entire film. Ellipsometry studies confirm the sizable magnitude of the birefringence. Optical second-harmonic generation studies of multilayer films provide information regarding both the thiophene orientation within the film and the anisotropic distribution of chromophores in the surface plane. Taken together, these data offer strong evidence of highly ordered films in which the hydrophobic polythiophene chains lie parallel to the substrate surface with their alkyl chains oriented normal to the surface, as dictated by the hydrophilic nature of the alkyl chain's terminal tetrahydropyran functional group. As such, these films offer the potential for elucidating the connection between polymer morphology and physical property in materials that are otherwise subject to a sufficiently complex distribution of morphologies that such a correspondence is precluded.