Three-dimensional polarization states of monochromatic light fields

Polarized holographic lithography system for high-uniformity microscale patterning with periodic tunability

Periodic microscale array structures play an important role in diverse applications involving photonic crystals and diffraction gratings. A polarized holographic lithography system is proposed for patterning high-uniformity microscale two-dimensional crossed-grating structures with periodic tunability. Orthogonal two-axis Lloyd's mirror interference and polarization modulation produce three sub-beams, enabling the formation of two-dimensional crossed-grating patterns with wavelength-comparable periods by a single exposure. The two-dimensional-pattern period can also be flexibly tuned by adjusting the interferometer spatial positioning. Polarization states of three sub-beams, defining the uniformity of the interference fringes, are modulated at their initial-polarization states based on a strict full polarization tracing model in a three-dimensional space. A polarization modulation model is established considering two conditions of eliminating the unexpected interference and providing the desired identical interference intensities. The proposed system is a promising approach for fabricating high-uniformity two-dimensional crossed gratings with a relatively large grating period range of 500-1500 nm. Moreover, our rapid and stable approach for patterning period-tunable two-dimensional-array microstructures with high uniformity could be applicable to other multibeam interference lithography techniques.

Optimal polarization modulation for orthogonal two-axis Lloyd's mirror interference lithography

Polarization control is of vital importance in two-axis Lloyd's mirror interference lithography to achieve the preferred interference fringes. In this work, we first establish a three-dimensional polarization ray-tracing model to trace the evolution of polarization states of incident beams through the corner-cube-like interferometer unit of an orthogonal two-axis Lloyd's mirror interferometer. With the established model, we then derive the optimal combination of initial polarization directions of the incident beams according to the orthogonality of polarization states and the contrast of interference fringes. The comparison between the simulated and experimental interference fringes obtained under different combinations of initial polarization states of incident beams verify the feasibility of the established model and the achieved optimal polarization modulation.

Multiple scattering of polarized light in uniaxial turbid media with arbitrarily oriented linear birefringence

The effective scattering Mueller matrices obtained by the simulation were simplified to the reduced matrices and factorized using the Lu–Chipman polar decomposition, which afforded the polarization parameters in two dimensions. In general, the scalar retardance around the illumination point of a pencil beam shows a broad azimuthal dependence with an offset. Photons may behave quite differently under the birefringence according to their polarization state. In contrast, when the birefringence is oriented along the y -axis in the plane parallel to the surface ( x ? y ) plane, for example, the azimuthal dependence of the scalar retardance shows clear maxima along the x - and y -axes and sharp valleys between the maxima. Photons propagating in the medium probably experience the retardance in nearly the same way when they are polarized linearly and circularly. Moreover, the polarization parameters generally become nonsymmetric with respect to the plane perpendicular to both the x - y plane and the plane containing the birefringence axis, which suggests that the pathway of the lateral propagation of photons from the illumination point to the surrounding is slightly oblique upward relative to the x - y plane. These results were also compared with the case in which the birefringence axis is perpendicular to the x - y plane.

Stokes-vector and Mueller-matrix polarimetry [Invited]

This paper reviews the current status of instruments for measuring the full 4×1 Stokes vector S, which describes the state of polarization (SOP) of totally or partially polarized light, and the 4×4 Mueller matrix M, which determines how the SOP is transformed as light interacts with a material sample or an optical element or system. The principle of operation of each instrument is briefly explained by using the Stokes-Mueller calculus. The development of fast, automated, imaging, and spectroscopic instruments over the last 50 years has greatly expanded the range of applications of optical polarimetry and ellipsometry in almost every branch of science and technology. Current challenges and future directions of this important branch of optics are also discussed.

Depolarized FRET (depolFRET) on the cell surface: FRET control by photoselection

Sensitivity of FRET in hetero- and homo-FRET systems on the photoselected orientation distribution of donors has been proven by using polarized and depolarized light for excitation. FRET as well as donor and acceptor anisotropies have been simultaneously measured in a dual emission-polarization scheme realized in a conventional flow cytometer by using single laser excitation and applying fluorophore-conjugated mAbs against the MHCI and MHCII cell surface receptors. Depolarization of the originally polarized light have been achieved by using crystal depolarizers based on Cornu's principle, a quarter-wave plate for circular polarization, and a parallel beam splitter acting as a diagonal-polarizer for dual-polarization excitation. Simultaneous analysis of intensity-based FRET efficiency and acceptor depolarization equivocally report that depolarization of light may increase FRET in an amount depending on the acceptor-to-donor concentration ratio. Acceptor depolarization turned to be more sensitive to FRET than donor hyper-polarization and even than intensity-based FRET efficiency. It can be used as a sensitive tool for monitoring changes in the dynamics of the donor-acceptor pairs. The basic observations of FRET enhancement and increased acceptor depolarization obtained for hetero-FRET are paralleled by analog observations of homo-FRET enhancements under depolarized excitation. In terms of the orientation factor for FRET, the FRET enhancements on depolarization in the condition of the macroscopically isotropic orientation distributions such as those of the cell surface bound fluorophores report on the presence of local orientation mismatches of the donor and acceptor preventing the optimal FRET in the polarized case, which may be eliminated by the excitation depolarization. A theory of fluorescence anisotropy for depolarized excitation is also presented.

Generalized Jones matrix method for homogeneous biaxial samples

The generalized Jones matrix (GJM) is a recently introduced tool to describe linear transformations of three-dimensional light fields. Based on this framework, a specific method for obtaining the GJM of uniaxial anisotropic media was recently presented. However, the GJM of biaxial media had not been tackled so far, as the previous method made use of a simplified rotation matrix that lacks a degree of freedom in the three-dimensional rotation, thus being not suitable for calculating the GJM of biaxial media. In this work we propose a general method to derive the GJM of arbitrarily-oriented homogeneous biaxial media. It is based on the differential generalized Jones matrix (dGJM), which is the three-dimensional counterpart of the conventional differential Jones matrix. We show that the dGJM provides a simple and elegant way to describe uniaxial and biaxial media, with the capacity to model multiple simultaneous optical effects. The practical usefulness of this method is illustrated by the GJM modeling of the polarimetric properties of a negative uniaxial KDP crystal and a biaxial KTP crystal for any three-dimensional sample orientation. The results show that this method constitutes an advantageous and straightforward way to model biaxial media, which show a growing relevance for many interesting applications.

Modeling the tight focusing of beams in absorbing media with Monte Carlo simulations

A severe drawback to the scalar Monte Carlo (MC) method is the difficulty of introducing diffraction when simulating light propagation. This hinders, for instance, the accurate modeling of beams focused through microscope objectives, where the diffraction patterns in the focal plane are of great importance in various applications. Here, we propose to overcome this issue by means of a direct extinction method. In the MC simulations, the photon paths' initial positions are sampled from probability distributions which are calculated with a modified angular spectrum of the plane waves technique. We restricted our study to the two-dimensional case, and investigated the feasibility of our approach for absorbing yet nonscattering materials. We simulated the focusing of collimated beams with uniform profiles through microscope objectives. Our results were compared with those yielded by independent simulations using the finite-difference time-domain method. Very good agreement was achieved between the results of both methods, not only for the power distributions around the focal region including diffraction patterns, but also for the distribution of the energy flow (Poynting vector).

Polarimetric study of birefringent turbid media with three-dimensional optic axis orientation

Recent approaches to the analysis of biological samples with three-dimensional linear birefringence orientation require numerical methods to estimate the best fit parameters from experimental measures. We present a novel analytical method for characterizing the intrinsic retardance and the three-dimensional optic axis orientation of uniform and uniaxial turbid media. It is based on a model that exploits the recently proposed differential generalized Jones calculus, remarkably suppressing the need for numerical procedures. The method is applied to the analysis of samples modeled with polarized sensitive Monte Carlo. The results corroborate its capacity to successfully characterize 3D linear birefringence in a straightforward way.

Generalized Jones matrices for anisotropic media

The interaction of arbitrary three-dimensional light beams with optical elements is described by the generalized Jones calculus, which has been formally proposed recently [Azzam, J. Opt. Soc. Am. A 28, 2279 (2011)]. In this work we obtain the parametric expression of the 3×3 differential generalized Jones matrix (dGJM) for arbitrary optical media assuming transverse light waves. The dGJM is intimately connected to the Gell-Mann matrices, and we show that it provides a versatile method for obtaining the macroscopic GJM of media with either sequential or simultaneous anisotropic effects. Explicit parametric expressions of the GJM for some relevant optical elements are provided.