The orientation dependency of nonlinear optical effects, including the second-harmonic generation (SHG) and third-harmonic generation (THG), as well as two-photon luminescence, in semiconductor nanowires (NW) are described. The mismatch of dielectric constants between nanostructures and their environment governs the rise of optical nonlinearities causing SHG even in materials with a high symmetry crystal lattice that would not generate second harmonic in the bulk state. Due to the depolarization effects, the intensity of the optical electric field inside illuminated NWs depends dramatically on their orientation related to the exciting light polarization. As a result, rotation of the light polarization causes giant angular dependency of all the mentioned optical phenomena, with the maximum relative amplitude at the electric-field polarization oriented along the NWs. Simultaneous measurements of two-photon-induced luminescence, SHG and THG in ZnSe NWs are presented. In accordance with the theory, the angular dependencies of nonlinear phenomena were observed and influence of the environmental dielectric constant on the magnitude of the nonlinear signals was demonstrated. The relative amplitudes of the angular dependencies were also significantly influenced by NW bending and nonuniformity.
The nonlinear optical properties of heterogeneous media are described by an algebraic decomposition of the correlation matrix X(n) of the nth-order nonlinear susceptibility tensor values, obtained from the generalized nonlinear Stokes–Mueller polarimetry measurements. The correlation matrix X(n) forms a square Hermitian semidefinite positive matrix, which can be further decomposed into separate components using projection matrices and calculating eigenvalues and the corresponding eigenvectors for pure states of the heterogeneous media. Up to eight pure states can be deduced for the sum-frequency generation process and up to sixteen states can be presented for a four-wave mixing process. The obtained eigenvalues are used to define the entropy characterizing a heterogeneous media. Filtering and maximum-likelihood estimation approaches are presented to determine the physically realizable values of the nonlinear susceptibility from the X(n) matrix that is obtained by the Stokes–Mueller polarimetry experiments. The Cholesky decomposition is employed for the maximum-likelihood estimation of the correlation matrix X(n). The structural characterization can be used, for example, in nonlinear microscopy for determining the ultrastructure organization of heterogeneous biological samples.
Polarization second harmonic generation (SHG) is described as a label-free, non-invasive and rapid method for the structural analysis of individual starch granules. SHG is a nonlinear optical process that is inherently generated in non-centrosymmetric materials, such as starch granules. SHG microscopy permits intrinsic optical sectioning making it ideally suited for studying structure inside individual granules without physical sectioning. Both the intensity and polarization response of the SHG signal are governed by the structure of the material, and characterized by the nonlinear optical susceptibility tensor. During polarization SHG microscopy, optical measurements of the tensor component values are rapidly performed for each position of the laser focal spot within starch granules by measuring the relation between the laser polarization and the polarization of the SHG signal. Mapping of these tensor components reveals structural features in the sample including crystalline concentration, average orientations of crystals in each pixel as well as a parameter describing quantitatively the structural order. Results from different polarization resolved SHG starch studies are presented including a comparison of starches from potato and maize varieties, followed by the effect of hydration on starch structure. Results from crystalline maltodextrin particles are presented and compared with the results from native starch granules.
Nonlinear optical properties of collagen type-I are investigated in thin tissue sections of pig tendon as a research model using a complete polarimetric second-harmonic generation (P-SHG) microscopy technique called double Stokes-Mueller polarimetry (DSMP). Three complex-valued molecular susceptibility tensor component ratios are extracted. A significant retardance is observed between the chiral susceptibility component and the achiral components, while the achiral components appear to be in phase with each other. The DSMP formalism and microscopy measurements are further used to explain and experimentally validate the conditions required for SHG circular dichroism (SHG-CD) of collagen to occur. The SHG-CD can be observed with the microscope when: (i) the chiral second-order susceptibility tensor component has a non-zero value, (ii) a phase retardance is present between the chiral and achiral components of the second-order susceptibility tensor and (iii) the collagen fibres are tilted out of the image plane. Both positive and negative areas of SHG-CD are observed in microscopy images, which relates to the anti-parallel arrangement of collagen fibres in different fascicles of the tendon. The theoretical formalism and experimental validation of DSMP imaging technique opens new opportunities for ultrastructural characterisation of chiral molecules, in particular collagen, and provides basis for the interpretation of SHG-CD signals. The nonlinear imaging of chiroptical parameters offers new possibilities to further improve the diagnostic sensitivity and/or specificity of nonlinear label-free histopathology.
Wide-field Polarization-resolved Second-Harmonic Generation microscopy is a label-free imaging technique which highlights molecular organization of collagenous tissues, enabling high-throughput quantitative biomedical imaging and cancer diagnostics.
Abstract Nonlinear optical microscopy has become a powerful tool for high‐resolution imaging of cellular and subcellular composition, morphology, and interactions because of its high spatial resolution, deep penetration, and low photo‐damage to tissue. Developing specific harmonic probes is essential for exploiting nonlinear microscopic imaging for biomedical applications. We report an organized aggregate of porphyrins (OAP) that formed within lipidic nanoparticles showing fingerprint spectroscopic properties, structure‐associated second harmonic generation, and superradiant third harmonic generation. The OAP facilitated harmonic microscopic imaging of living cells with significantly enhanced contrast. The structure‐dependent switch between harmonic (OAP‐intact) and fluorescence (OAP‐disrupted) generation enabled real‐time multi‐modality imaging of the cellular fate of nanoparticles. Robustly produced under various conditions and easily incorporated into pre‐formed lipid nanovesicles, OAP provides a biocompatible nanoplatform for harmonic imaging.
The formalism is developed for a tree-dimensional ($3D$) nonlinear Stokes-Mueller polarimetry. The expressions are derived for the generalized $3D$ linear and nonlinear Stokes vectors, and the corresponding nonlinear Mueller matrix. The coherency-like Hermitian square matrix $X$ of susceptibilities is introduced, which is derived from the nonlinear Mueller matrix. The $X$-matrix is characterized by the index of depolarization. Several decompositions of the $X$-matrix are introduced. The $3D$ nonlinear Stokes-Mueller polarimetry formalism can be applied for three and higher wave mixing processes. The $3D$ polarimetric measurements can be used for structural investigations of materials, including heterogeneous biological structures. The $3D$ polarimetry is applicable for nonlinear microscopy with high numerical aperture objectives.
Extracellular matrix (ECM) has important functions in cell proliferation, differentiation, and migration, which influence the development and progression of cancer. ECM in tumor microenvironment experiences changes in composition and structure that can appear early in tumor development and could serve as a biomarker for cancer diagnostics. In addition, some changes in ECM may correlate with the rate of tumor progression or its tendency to form metastases and would allow to predict future tumor development [1]. Collagen is an important structural protein found in ECM. It has a non-centrosymmetric structure, and, thus, can be easily visualized using second harmonic generation (SHG) microscopy. SHG microscopy employs certain polarimetric techniques to gain detailed information about the organization of collagen in various tissues [2]. In this work, polarimetric SHG microscopy is used to acquire collagen images from normal and cancerous regions of human colon and pancreas histological samples. Texture analysis is performed on SHG intensity and polarization images to characterize the distribution of ultrastructure parameters in the tissue. Significant differences are observed in collagen ultrastructure between normal and tumor areas. Further, collagen structures of colon and pancreas tumor microenvironments are compared to investigate relative differences in ECM organization between the tissues. Finally, a machine learning classifier is used to group the acquired images in tumor and normal groups. The results show potential for development of novel cancer diagnostic technique using polarimetric second harmonic generation microscopy and texture analysis. [1] Winkler, J. et al., "Concepts of extracellular matrix remodelling in tumour progression and metastasis", Nat Commun 11, 5120 (2020). [2] Golaraei, A. et al., "Polarimetric second-harmonic generation microscopy of the hierarchical structure of collagen in stage I-III non-small cell lung carcinoma," Biomed. Opt. Express 11, 1851-1863 (2020).
Second harmonic generation (SHG) polarization microscopy was used to investigate the organization of myosin nanomotors in myofilaments of muscle cells. The distribution of the second-order nonlinear susceptibility component ratio χzzz(2)/χzxx(2) along anisotropic bands of sarcomeres revealed differences between the headless and head-containing regions of myofilaments. The polarization-in polarization-out SHG measurements of headless myosin mutants of indirect flight muscle in Drosophila melanogaster confirmed a lower susceptibility component ratio compared to the head-containing myocytes with wild-type myosins. The increase in the ratio is assigned to the change in the deflection angle of the myosin S2 domain and possible contribution of myosin heads. The nonlinear susceptibility component ratio is a sensitive indicator of the myosin structure, and therefore, it can be used for conformational studies of myosin nanomotors. The measured ratio values can also be used as the reference for ab initio calculations of nonlinear optical properties of different parts of myosins.
