Masood Samim

Double Stokes Mueller polarimetry of second-harmonic generation in ordered molecular structures

Second-harmonic generation (SHG) is highly sensitive to the structure of ordered aggregates, and therefore, the polarization measurement of SHG can help to elucidate the organization of molecules in crystalline structures. The double Stokes Mueller formalism is developed for the SHG polarimetry and convenient expressions are derived for the double Mueller matrix in terms of the nonlinear susceptibilities. The polarization analysis is presented for cylindrically symmetric structures, providing the method to calculate the characteristic susceptibility component ratios and orientations of molecules in the ordered aggregates. This information, for example, can be used to investigate collagen or myosin structure in biological tissues.

Second harmonic generation double stokes Mueller polarimetric microscopy of myofilaments

The experimental implementation of double Stokes Mueller polarimetric microscopy is presented. This technique enables a model-independent and complete polarimetric characterization of second harmonic generating samples using 36 Stokes parameter measurements at different combinations of incoming and outgoing polarizations. The degree of second harmonic polarization and the molecular nonlinear susceptibility ratio are extracted for individual focal volumes of a fruit fly larva wall muscle.

Differential Polarization Nonlinear Optical Microscopy with Adaptive Optics Controlled Multiplexed Beams

Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red), which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures.

Nonlinear Stokes Mueller Polarimetry

The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional

Second harmonic generation polarization properties of myofilaments

4\times 1

Three-photon Stokes-Mueller polarimetry

Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarimetry.

Experimental demonstration of third-harmonic generation nonlinear Stokes-Mueller polarimetric microscopy

Abstract. 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.

Nonlinear stokes mueller polarimetry for microscopic imaging of ordered biological structures

The generalized theory of Stokes Mueller polarimetry is employed to develop the third-order optical polarimetry framework for third-harmonic generation (THG). The outgoing and incoming radiations are represented by 4-element and 16-element column vectors, respectively, and the intervening medium is represented by a

Nonlinear Stokes Mueller Polarimetric Microscopy

4\times 16

Second-Harmonic Generation Double Stokes Mueller Polarimetric Microscopy

triple Mueller matrix. Expressions for the THG Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, and expanded by four-dimensional