Chemically selective analysis of molecular monolayers by nonlinear optical stokes ellipsometry

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.

Synchronous-digitization for Video Rate Polarization Modulated Beam Scanning Second Harmonic Generation Microscopy

Fast beam-scanning non-linear optical microscopy, coupled with fast (8 MHz) polarization modulation and analytical modeling have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and linear Stokes ellipsometry imaging at video rate (15 Hz). NOSE enables recovery of the complex-valued Jones tensor that describes the polarization-dependent observables, in contrast to polarimetry, in which the polarization stated of the exciting beam is recorded. Each data acquisition consists of 30 images (10 for each detector, with three detectors operating in parallel), each of which corresponds to polarization-dependent results. Processing of this image set by linear fitting contracts down each set of 10 images to a set of 5 parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the fundamental laser beam. Using these parameters, it is possible to recover the Jones tensor elements of the sample at video rate. Video rate imaging is enabled by performing synchronous digitization (SD), in which a PCIe digital oscilloscope card is synchronized to the laser (the laser is the master clock.) Fast polarization modulation was achieved by modulating an electro-optic modulator synchronously with the laser and digitizer, with a simple sine-wave at 1/10th the period of the laser, producing a repeating pattern of 10 polarization states. This approach was validated using Z-cut quartz, and NOSE microscopy was performed for micro-crystals of naproxen.

Polarization-modulated second harmonic generation ellipsometric microscopy at video rate

Fast 8 MHz polarization modulation coupled with analytical modeling, fast beam-scanning, and synchronous digitization (SD) have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and polarized laser transmittance imaging with image acquisition rates up to video rate. In contrast to polarimetry, in which the polarization state of the exiting beam is recorded, NOSE enables recovery of the complex-valued Jones tensor of the sample that describes all polarization-dependent observables of the measurement. Every video-rate scan produces a set of 30 images (10 for each detector with three detectors operating in parallel), each of which corresponds to a different polarization-dependent result. Linear fitting of this image set contracts it down to a set of five parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the incident beam. These parameters can in turn be used to recover the Jones tensor elements of the sample. Following validation of the approach using z-cut quartz, NOSE microscopy was performed for microcrystals of both naproxen and glucose isomerase. When weighted by the measurement time, NOSE microscopy was found to provide a substantial (>7 decades) improvement in the signal-to-noise ratio relative to our previous measurements based on the rotation of optical elements and a 3-fold improvement relative to previous single-point NOSE approaches.

Kinetic trapping of metastable amino acid polymorphs

Second harmonic generation (SHG) microscopy measurements indicate that inkjet-printed racemic solutions of amino acids can produce nanocrystals trapped in metastable polymorph forms upon rapid solvent evaporation. Polymorphism impacts the composition, distribution, and physico-kinetic properties of organic solids, with energetic arguments favoring the most stable polymorph. In this study, unfavored noncentrosymmetric crystal forms were observed by SHG microscopy. Polarization-dependent SHG measurement and synchrotron X-ray microdiffraction analysis of individual printed drops are consistent with formation of homochiral crystal production. Fundamentally, these results provide evidence supporting the ubiquity of Ostwald’s Rule of Stages, describing the hypothesized transitioning of crystals between metastable polymorphic forms in the early stages of crystal formation. Practically, the presence of homochiral metastable forms has implications on chiral resolution and on solid form preparations relying on rapid solvent evaporation.

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.

Second-order nonlinear optical imaging of chiral crystals

Second-order nonlinear optical imaging of chiral crystals (SONICC) is an emerging technique for crystal imaging and characterization. We provide a brief overview of the origin of second harmonic generation signals in SONICC and discuss recent studies using SONICC for biological applications. Given that they provide near-complete suppression of any background, SONICC images can be used to determine the presence or absence of protein crystals through both manual inspection and automated analysis. Because SONICC creates high-resolution images, nucleation and growth kinetics can also be observed. SONICC can detect metastable, homochiral crystalline forms of amino acids crystallizing from racemic solutions, which confirms Ostwald's rule of stages for crystal growth. SONICC's selectivity, based on order, and sensitivity, based on background suppression, make it a promising technique for numerous fields concerned with chiral crystal formation.

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.