Unified Theory for Polarization Analysis in Second Harmonic and Sum Frequency Microscopy

Ultrafast control over chiral sum-frequency generation

We introduce an ultrafast all-optical approach for efficient chiral recognition that relies on the interference between two low-order nonlinear processes that are ubiquitous in nonlinear optics: sum-frequency generation and third-harmonic generation. In contrast to traditional sum-frequency generation, our approach encodes the medium's handedness in the intensity of the emitted harmonic signal, rather than in its phase, and it enables full control over the enantiosensitive response. We show how, by sculpting the sub-optical-cycle oscillations of the driving laser field, we can force one molecular enantiomer to emit bright light while its mirror twin remains dark, thus reaching the ultimate efficiency limit of chiral sensitivity via low-order nonlinear light-matter interactions. Our work paves the way for ultrafast and highly efficient imaging and control of the chiral electronic clouds of chiral molecules using lasers with moderate intensities, in all states of matter: from gases to liquids to solids, with molecular specificity and on ultrafast time scales.

Fast polarization-sensitive second-harmonic generation microscopy based on off-axis interferometry

We propose polarization-sensitive second-harmonic generation microscopy based on off-axis interferometry (OI-PSHG) by recording the complex field of a wide-field second-harmonic generation (SHG) image and performing polarization measurements. With the ability to record the SHG signals associated with different positions simultaneously, the proposed method exhibits a higher imaging frame rate than raster scanning-based SHG microscopy. The molecular orientation (in terms of their symmetric axis) of tendon collagen fibrils and myosin in muscle is resolved in three dimensions from a subset of polarization-resolved SHG holograms. With the present configuration, it takes approximately 0.01 s to acquire an image with 128 × 128 pixels, which is mainly limited by the excitation power density for wide-field illumination. For the same data throughput using pixel-by-pixel scanning, 0.16-s-long acquisition is required, with the pixel dwell time of 10 µs. Offering the ability to perform wide-field imaging and polarization measurements, the present work lays the foundation for fast SHG microscopy using complex deconvolution and harmonic tomography.

Comparison between Cylindrical, Trigonal, and General Symmetry Models for the Analysis of Polarization-Dependent Second Harmonic Generation Measurements Acquired from Collagen-Rich Equine Pericardium Samples

Polarization-dependent second harmonic generation (PSHG) microscopy is used as an innovative, high-resolution, non-destructive, and label-free diagnostic imaging tool to elucidate biological issues with high significance. In the present study, information on the structure and directionality of collagen fibers in equine pericardium tissue was collected using PSHG imaging measurements. In an effort to acquire precise results, three different mathematical models (cylindrical, trigonal, and general) were applied to the analysis of the recorded PSHG datasets. A factor called the “ratio parameter” was calculated to provide quantitative information. The implementation of the trigonal symmetry model to the recorded data led to the extraction of improved results compared with the application of the widely used cylindrical symmetry model. The best outcome was achieved through the application of the general model that does not include any kind of symmetry for the data processing. Our findings suggest that the trigonal symmetry model is preferable for the analysis of the PSHG datasets acquired from the collagenous tissues compared with the cylindrical model approach although an increased computational time is required.

Monitoring aging-associated structural alterations in Caenorhabditis elegans striated muscles via polarization-dependent second-harmonic generation measurements

The in-vivo elucidation of the molecular mechanisms underlying muscles dysfunction due to aging via non-invasive label free imaging techniques is an important issue with high biological significance. In this study, polarization-dependent second-harmonic generation (PSHG) was used to evaluate structural alterations in the striated muscles during Caenorhabditis elegans lifespan. Young and old wild-type animals were irradiated. The obtained results showed that it was not feasible to detect differences in the structure of myosin that could be correlated with the aging of the worms, via the implementation of the classical, widely used, cylindrical symmetry model and the calculation of the SHG anisotropy values. A trigonal symmetry model improved the extracted results; however, the best outcome was originated from the application of a general model. Myosin structural modifications were monitored via the estimation of the difference in spectral phases derived from discrete Fourier transform analysis. Age classification of the nematodes was achieved by employing both models, proving the usefulness of the usage of PSHG microscopy as a potential diagnostic tool for the investigation of muscle diseases.

Sensitivity of sum frequency generation experimental conditions to thin film interference effects

Sum-frequency generation (SFG) spectroscopy has furthered our understanding of the chemical interfaces that guide key processes in biology, catalysis, environmental science, and energy conversion. However, interpreting SFG spectra of systems containing several internal interfaces, such as thin film electronics, electrochemical cells, and biofilms, is challenging as different interfaces within these structures can produce interfering SFG signals. One potential way to address this issue is to carefully select experimental conditions that amplify the SFG signal of an interface of interest over all others. In this report, we investigate a model two-interface system to assess our ability to isolate the SFG signal from each interface. For SFG experiments performed in a reflective geometry, we find that there are few experimental conditions under which the SFG signal originating from either interface can be amplified and isolated from the other. However, by performing several measurements under conditions that alter their interference, we find that we can reconstruct each signal even in cases where the SFG signal from one interface is more than an order of magnitude smaller than its counterpart. The number of spectra needed for this reconstruction varies depending on the signal-to-noise level of the SFG dataset and the degree to which different experiments in a dataset vary in their sensitivity to each interface. Taken together, our work provides general guidelines for designing experimental protocols that can isolate SFG signals stemming from a particular region of interest within complex samples.

Spatially encoded polarization-dependent nonlinear optics

A single fixed optic is combined with the sample translation capabilities inherent to most microscopes to achieve precise polarization-dependent second harmonic generation microscopy measurements of thin tissue sections. Although polarization measurements have enabled detailed structural analysis of collagen, challenges in integrating rotation stages or fast electro-optic/photoelastic modulation have complicated the retrofitting of existing systems for precise polarization analysis. Placing a static microretarder array in the rear conjugate plane resulted in spatially encoded polarization modulation across the field of view. A complete set of polarization rotation measurements was acquired at each pixel by sample translation, recovering local-frame tensors relating to structure within collagenous tissue.

In Situ Chemical Analysis of the Gas-Aerosol Particle Interface

The gas-aerosol particle interface is believed to contribute to the growth of secondary organic aerosols in the atmosphere. Despite its importance, the chemical composition of the interface has not been probed directly because of a lack of suitable interface-specific analytical techniques. The preliminary result in our early work has demonstrated direct observations of molecules at the gas-aerosol particle interface with the development of second harmonic scattering (SHS). However, the SHS technique is far away from being an analytical tool of chemical compositions at the gas-aerosol particle interface. In this work, we continued to develop the interface-specific SHS for in situ chemical analysis of molecules at the gas-aerosol particle interface. As an example, we demonstrated coherent SHS signal of a new SHS probe, crystal violet (CV), from interfaces of aerosol particles. The development of the SHS technique includes: (1) Optimization for a more efficient femtosecond laser system in the generation of SHS from aerosol particles. A near 5 MHz repetition rate of a femtosecond laser was found to be optimal for the generation of SHS; (2) exploration of a more effective detector for SHS of aerosol particles. We found that both a CCD detector and a single-photon counter produce similar signal-to-noise ratios of the interfacial SHS signals from aerosol particles. The CCD detector is a more effective option for the detection of SHS and could greatly reduce sampling time of the interfacial responses; (3) combination of the optimal laser system with the CCD detector, which has greatly improved the detection sensitivity of interfacial molecules by more than 2 orders of magnitude and could potentially detect interfacial SHS from a single aerosol particle. These experimental results not only provided a thorough analysis of the SHS technique but also built a solid foundation for further development of a new vibrational sum frequency scattering (SFS) technique for chemical structures at the gas-aerosol particle interface.

Second Harmonic Generation of Unpolarized Light

A Mueller tensor mathematical framework was applied for predicting and interpreting the second harmonic generation (SHG) produced with an unpolarized fundamental beam. In deep tissue imaging through SHG and multiphoton fluorescence, partial or complete depolarization of the incident light complicates polarization analysis. The proposed framework has the distinct advantage of seamlessly merging the purely polarized theory based on the Jones or Cartesian susceptibility tensors with a more general Mueller tensor framework capable of handling partial depolarized fundamental and/or SHG produced. The predictions of the model are in excellent agreement with experimental measurements of z-cut quartz and mouse tail tendon obtained with polarized and depolarized incident light. The polarization-dependent SHG produced with unpolarized fundamental allowed determination of collagen fiber orientation in agreement with orthogonal methods based on image analysis. This method has the distinct advantage of being immune to birefringence or depolarization of the fundamental beam for structural analysis of tissues.

Hyperspectral imaging with laser-scanning sum-frequency generation microscopy

Vibrationally sensitive sum-frequency generation (SFG) microscopy is a chemically selective imaging technique sensitive to non-centrosymmetric molecular arrangements in biological samples. The routine use of SFG microscopy has been hampered by the difficulty of integrating the required mid-infrared excitation light into a conventional, laser-scanning nonlinear optical (NLO) microscope. In this work, we describe minor modifications to a regular laser-scanning microscope to accommodate SFG microscopy as an imaging modality. We achieve vibrationally sensitive SFG imaging of biological samples with sub-μm resolution at image acquisition rates of 1 frame/s, almost two orders of magnitude faster than attained with previous point-scanning SFG microscopes. Using the fast scanning capability, we demonstrate hyperspectral SFG imaging in the CH-stretching vibrational range and point out its use in the study of molecular orientation and arrangement in biologically relevant samples. We also show multimodal imaging by combining SFG microscopy with second-harmonic generation (SHG) and coherent anti-Stokes Raman scattering (CARS) on the same imaging platfrom. This development underlines that SFG microscopy is a unique modality with a spatial resolution and image acquisition time comparable to that of other NLO imaging techniques, making point-scanning SFG microscopy a valuable member of the NLO imaging family.

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.

Three-Dimensional Geometry of Collagenous Tissues by Second Harmonic Polarimetry

Collagen is a biological macromolecule capable of second harmonic generation, allowing label-free detection in tissues; in addition, molecular orientation can be determined from the polarization dependence of the second harmonic signal. Previously we reported that in-plane orientation of collagen fibrils could be determined by modulating the polarization angle of the laser during scanning. We have now extended this method so that out-of-plane orientation angles can be determined at the same time, allowing visualization of the 3-dimensional structure of collagenous tissues. This approach offers advantages compared with other methods for determining out-of-plane orientation. First, the orientation angles are directly calculated from the polarimetry data obtained in a single scan, while other reported methods require data from multiple scans, use of iterative optimization methods, application of fitting algorithms, or extensive post-optical processing. Second, our method does not require highly specialized instrumentation, and thus can be adapted for use in almost any nonlinear optical microscopy setup. It is suitable for both basic and clinical applications. We present three-dimensional images of structurally complex collagenous tissues that illustrate the power of such 3-dimensional analyses to reveal the architecture of biological structures.