Measuring Stokes parameters by means of a polarization grating

Lateral spin transport in paraxial beams of light

We investigate the lateral transport of (longitudinal) spin angular momentum in a special polarization tailored light beam composed of a superposition of a y-polarized zero-order and an x-polarized first-order Hermite-Gaussian mode. This phenomenon is linked to the relative Gouy phase shift between the individual modes upon propagation, but can also be interpreted as a geometric phase effect. Experimentally, we demonstrate the implementation of such a mode and measure the spin density upon propagation.

Controllable optical activity with non-chiral plasmonic metasurfaces

Optical activity is the rotation of the plane of linearly polarized light along the propagation direction as the light travels through optically active materials. In existing methods, the strength of the optical activity is determined by the chirality of the materials, which is difficult to control quantitatively. Here we numerically and experimentally investigated an alternative approach to realize and control the optical activity with non-chiral plasmonic metasurfaces. Through judicious design of the structural units of the metasurfaces, the right and left circular polarization components of the linearly polarized light have different phase retardations after transmitting through the metasurfaces, leading to large optical activity. Moreover, the strength of the optical activity can be easily and accurately tuned by directly adjusting the phase difference. The proposed approach based on non-chiral plasmonic metasurfaces exhibits large optical activity with a high controllable degree of freedom, which may provide more possibilities for applications in photonics.

Integrated plasmonic metasurfaces for spectropolarimetry

Plasmonic metasurfaces enable simultaneous control of the phase, momentum, amplitude and polarization of light and hence promise great utility in realization of compact photonic devices. In this paper, we demonstrate a novel chip-scale device suitable for simultaneous polarization and spectral measurements through use of six integrated plasmonic metasurfaces (IPMs), which diffract light with a given polarization state and spectral component into well-defined spatial domains. Full calibration and characterization of our device is presented, whereby good spectral resolution and polarization accuracy over a wavelength range of 500-700 nm is shown. Functionality of our device in a Müller matrix modality is demonstrated through determination of the polarization properties of a commercially available variable waveplate. Our proposed IPM is robust, compact and can be fabricated with a single photolithography step, promising many applications in polarization imaging, quantum communication and quantitative sensing.

Generating and Separating Twisted Light by gradient-rotation Split-Ring Antenna Metasurfaces

Nanoscale compact optical vortex generators promise substantially significant prospects in modern optics and photonics, leading to many advances in sensing, imaging, quantum communication, and optical manipulation. However, conventional vortex generators often suffer from bulky size, low vortex mode purity in the converted beam, or limited operation bandwidth. Here, we design and demonstrate gradient-rotation split-ring antenna metasurfaces as unique spin-to-orbital angular momentum beam converters to simultaneously generate and separate pure optical vortices in a broad wavelength range. Our proposed design has the potential for realizing miniaturized on-chip OAM-multiplexers, as well as enabling new types of metasurface devices for the manipulation of complex structured light beams.

Efficient generation and tight focusing of radially polarized beam from linearly polarized beam with all-dielectric metasurface

We propose a single layer all-dielectric metasurface lens to simultaneously convert and focus an incident linear polarization into a radial beam with high efficiency and high numerical aperture (NA). It shows a better focusing property compared with the linearly polarized metasurface lens for high NA. A tight spot size (0.502λ) is achieved for the NA = 0.94. Additionally, the emergent polarization can in principle be switched flexibly between radially and azimuthally polarized beams by the adjustment of incident polarization direction. It is expected that our scheme may have potential value in microscopy, material processing, medicine, particles accelerating and trapping, and so on.

Diffraction gratings generating orders with selective states of polarization

We propose specially designed double anisotropic polarization diffraction gratings capable of producing a selective number of diffraction orders and with selective different states of polarization. Different polarization diffraction gratings are demonstrated, including linear polarization with horizontal, vertical and ± 45° orientations, and circular R and L polarization outputs. When illuminated with an arbitrary state of polarization, the system acts as a complete polarimeter where the intensities of the diffraction orders allow measurement of the Stokes parameters with a single shot. Experimental proof-of-concept is presented using a parallel-aligned liquid crystal display operating in a double pass architecture.

Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications

This paper reports on an original architecture of microfabricated alkali vapor cell designed for miniature atomic clocks. The cell combines diffraction gratings with anisotropically etched single-crystalline silicon sidewalls to route a normally-incident beam in a cavity oriented along the substrate plane. Gratings have been specifically designed to diffract circularly polarized light in the first order, the latter having an angle of diffraction matching the (111) sidewalls orientation. Then, the length of the cavity where light interacts with alkali atoms can be extended. We demonstrate that a longer cell allows to reduce the beam diameter, while preserving the clock performances. As the cavity depth and the beam diameter are reduced, collimation can be performed in a tighter space. This solution relaxes the constraints on the device packaging and is suitable for wafer-level assembly. Several cells have been fabricated and characterized in a clock setup using coherent population trapping spectroscopy. The measured signals exhibit null power linewidths down to 2.23 kHz and high transmission contrasts up to 17%. A high contrast-to-linewidth ratio is found at a linewidth of 4.17 kHz and a contrast of 5.2% in a 7-mm-long cell despite a beam diameter reduced to 600 μm.

Continuous control of the nonlinearity phase for harmonic generations

The capability of locally engineering the nonlinear optical properties of media is crucial in nonlinear optics. Although poling is the most widely employed technique for achieving locally controlled nonlinearity, it leads only to a binary nonlinear state, which is equivalent to a discrete phase change of π in the nonlinear polarizability. Here, inspired by the concept of spin-rotation coupling, we experimentally demonstrate nonlinear metasurfaces with homogeneous linear optical properties but spatially varying effective nonlinear polarizability with continuously controllable phase. The continuous phase control over the local nonlinearity is demonstrated for second and third harmonic generation by using nonlinear metasurfaces consisting of nanoantennas of C3 and C4 rotational symmetries, respectively. The continuous phase engineering of the effective nonlinear polarizability enables complete control over the propagation of harmonic generation signals. Therefore, this method seamlessly combines the generation and manipulation of harmonic waves, paving the way for highly compact nonlinear nanophotonic devices.

Metasurface for characterization of the polarization state of light

The miniaturization of measurement systems currently used to characterize the polarization state of light is limited by the bulky optical components used such as polarizers and waveplates. We propose and experimentally demonstrate a simple and compact approach to measure the ellipticity and handedness of the polarized light using an ultrathin (40 nm) gradient metasurface. A completely polarized light beam is decomposed into a left circularly polarized beam and a right circularly polarized beam, which are steered in two directions by the metasurface consisting of nanorods with spatially varying orientations. By measuring the intensities of the refracted light spots, the ellipticity and handedness of various incident polarization states are characterized at a range of wavelengths and used to determine the polarization information of the incident beam. To fully characterize the polarization state of light, an extra polarizer can be used to measure the polarization azimuth angle of the incident light.

Metasurface holograms reaching 80% efficiency

Surfaces covered by ultrathin plasmonic structures--so-called metasurfaces--have recently been shown to be capable of completely controlling the phase of light, representing a new paradigm for the design of innovative optical elements such as ultrathin flat lenses, directional couplers for surface plasmon polaritons and wave plate vortex beam generation. Among the various types of metasurfaces, geometric metasurfaces, which consist of an array of plasmonic nanorods with spatially varying orientations, have shown superior phase control due to the geometric nature of their phase profile. Metasurfaces have recently been used to make computer-generated holograms, but the hologram efficiency remained too low at visible wavelengths for practical purposes. Here, we report the design and realization of a geometric metasurface hologram reaching diffraction efficiencies of 80% at 825 nm and a broad bandwidth between 630 nm and 1,050 nm. The 16-level-phase computer-generated hologram demonstrated here combines the advantages of a geometric metasurface for the superior control of the phase profile and of reflectarrays for achieving high polarization conversion efficiency. Specifically, the design of the hologram integrates a ground metal plane with a geometric metasurface that enhances the conversion efficiency between the two circular polarization states, leading to high diffraction efficiency without complicating the fabrication process. Because of these advantages, our strategy could be viable for various practical holographic applications.

Laser beam splitting by polarization encoding

A scheme is proposed to design a polarization grating that splits an incident linearly polarized beam to an array of linearly polarized beams of identical intensity distribution and various azimuth angles of linear polarization. The grating is equivalent to a wave plate with space-variant azimuth angle and space-variant phase retardation. The linear polarization states of all split beams make the grating suitable for coherent beam combining architectures based on Dammann gratings.

Fully interferometric controllable anomalous refraction efficiency using cross modulation with plasmonic metasurfaces

We present a method of fully interferometric, controllable anomalous refraction efficiency by introducing cross-modulated incident light based on plasmonic metasurfaces. Theoretical analyses and numerical simulations indicate that the anomalous and ordinary refracted beams generated from two opposite-helicity incident beams and following the generalized Snell's law will have a superposition for certain incident angles, and the anomalous refraction efficiency can be dynamically controlled by changing the relative phase of the incident sources. As the incident wavelength nears the resonant wavelength of the plasmonic metasurfaces, two equal-amplitude incident beams with opposite helicity can be used to control the anomalous refraction efficiency. Otherwise, two unequal-amplitude incident beams with opposite helicity can be used to fully control the anomalous refraction efficiency. This Letter may offer a further step in the development of controllable anomalous refraction.

Flexible polarimeter architecture based on a birefringent grating

A polarimeter architecture is presented based on a birefringent grating displayed onto a parallel-aligned liquid crystal (LC) on silicon display (PAL-LCoS). The system is compact and flexible, since the size of the image can be adjusted by means of the period of the grating. The LCoS grating permits simultaneously measuring two orthogonal states of polarization (SOPs). By adding a wave plate, different couples of orthogonal SOPs can be detected. First, a basic proof of concept is presented using one quarter-wave and one half-wave plate with fixed retardances, which permit measuring the six SOPs classically used in polarimetry (linear states at 0°, 45°, 90°, and 135°, and R and L circular states). Next, the system is made fully programmable by incorporating a variable LC retarder (LCR). The LCR orientation and retardance values are optimized by means of the condition number indicator, in order to provide equivalent optimal accuracy. Experimental results of calibration images and test images are presented, showing the potentials of this architecture.

Dielectric multilayer beam splitter with differential phase shift on transmission and reflection for division-of-amplitude photopolarimeter

Dielectric multilayer beam splitter with differential phase shift on transmission and reflection for division-of-amplitude photopolarimeter (DOAP) was presented for the first time to our knowledge. The optimal parameters for the beam splitter are Tp = 78.9%, Ts = 21.1% and Δr - Δt = π/2 at 532nm at an angle of incidence of 45°. Multilayer anti-reflection coating with low phase shift was applied to reduce the backside reflection. Different design strategies that can achieve all optimal targets at the wavelength were tested. Two design methods were presented to optimize the differential phase shift. The samples were prepared by ion beam sputtering (IBS). The experimental results show good agreement with those of the design. The ellipsometric parameters of samples were measured in reflection (ψr, Δr) = (26.5°, 135.1°) and (28.2°, 133.5°), as well as in transmission (ψt, Δt) = (62.5°, 46.1°) and (63.5°, 46°) at 532.6nm. The normalized determinant of instrument matrix to evaluate the performance of samples is respectively 0.998 and 0.991 at 532.6nm.

Triple Wollaston-prism complete-Stokes imaging polarimeter

Imaging polarimetry is emerging as a powerful tool for remote sensing in space science, Earth science, biology, defense, national security, and industry. Polarimetry provides complementary information about a scene in the visible and infrared wavelengths. For example, surface texture, material composition, and molecular structure will affect the polarization state of reflected, scattered, or emitted light. We demonstrate an imaging polarimeter design that uses three Wollaston prisms, addressing several technical challenges associated with moving remote-sensing platforms. This compact design has no moving polarization elements and separates the polarization components in the pupil (or Fourier) plane, analogous to the way a grating spectrometer works. In addition, this concept enables simultaneous characterization of unpolarized, linear, and circular components of optical polarization. The results from a visible-wavelength prototype of this imaging polarimeter are presented, demonstrating remote sensitivity to material properties. This work enables new remote sensing capabilities and provides a viable design concept for extensions into infrared wavelengths.

Diffraction by metallic planar gratings

In this work, a kind of grating that, to our knowledge, has not yet been analyzed for diffractive purposes is proposed. The mentioned grating consists of metallic intercalated slits of two different metals on a glass substrate. The main characteristic and peculiarity of the proposed grating is that it is totally planar, without any slopes or grooves. We analyze the intensity distribution at the near- and far-field produced by the grating. The method used is rigorous-coupled wave analysis. We show how the metallic layer thickness is a crucial parameter to achieve the highest efficiency of the diffraction orders and, therefore, the highest contrast of the diffracted fringes. To conclude, we investigate how parameters such as the period, duty cycle, wavelength, or the used metals affect the diffracted field. Some nonexpected behaviors have been found. As we demonstrate by comparing with other kinds of gratings, the proposed grating would be useful in applications in which fringes are needed in both the front and back sides of the grating.

Imaging the polarization of a light field

We describe and analyze a method by which an optical polarization state is mapped to an image sensor. When placed in a Bayesian framework, the analysis allows a priori information about the polarization state to be introduced into the measurement. We show that when such a measurement is applied to a single photon, it eliminates exactly one fully polarized state, offering an important insight about the information gained from a single photon polarization measurement.

Dynamic polarization grating based on a dye-doped liquid crystal controllable by a single beam in a homeotropic-planar geometry

We present a dynamic polarization grating based on a dye-doped liquid crystal cell that is controllable by a single pump beam in a binary homeotropic-planar configuration produced through selective rubbing. Upon single pump beam irradiation, the azo dyes in the liquid-crystal (LC) layer diffuse and adsorb onto the planar LC-anchoring surface due to trans-cis photo-isomerization. It is found that the dynamic polarization grating effect results mainly from the photo-induced easy axis reorientation by the amount of dye molecules adsorbed on the planar LC-alignment surface in a single-beam control scheme. The initial LC-anchoring conditions and the dynamic behavior of the dye adsorption strongly influence the repetitive writing-erasing processes by the single pump beam.

Longitudinal polarization periodicity of unpolarized light passing through a double wedge depolarizer

The polarization characteristics of unpolarized light passing through a double wedge depolarizer are studied. It is found that the degree of polarization of the radiation propagating after the depolarizer is uniform across transverse planes after the depolarizer, but it changes from one plane to another in a periodic way giving, at different distances, unpolarized, partially polarized, or even perfectly polarized light. An experiment is performed to confirm this result. Measured values of the Stokes parameters and of the degree of polarization are in complete agreement with the theoretical predictions.

Twisted nematic liquid crystal polarization grating with the handedness conservation of a circularly polarized state

We propose a liquid crystal (LC) polarization grating that conserves the polarization state of incident light, wherein the variation range of the twist angle is 2π. The design scheme for theoretically 100% diffraction efficiency of the first-diffraction order is derived, and a prototype LC grating is evaluated. Under zero voltage, the fabricated LC grating exhibits high efficiency of the first-order diffraction, validating the proposed design scheme. The high efficiency of the second-order diffraction can also be achieved under a high voltage so that the LC director in the midplane is vertical to the substrate plane. The circular polarization sense of the second-order diffraction is identical to that of the incident light as in the case of the first-order diffraction. This grating functions as a beam deflector, steering the input beam in three different directions (zeroth-, first-, and second-order diffractions) by adjusting the applied voltage.

Wave front engineering from an array of thin aperture antennas

We propose an ultra-thin metamaterial constructed by an ensemble of the same type of anisotropic aperture antennas with phase discontinuity for wave front manipulation across the metamaterial. A circularly polarized light is completely converted to the cross-polarized light which can either be bent or focused tightly near the diffraction limit. It depends on a precise control of the optical-axis profile of the antennas on a subwavelength scale, in which the rotation angle of the optical axis has a simple linear relationship to the phase discontinuity. Such an approach enables effective wave front engineering within a subwavelength scale.

Simulative method for the optical processor reconfiguration on a dynamically reconfigurable optical platform

With the reconfiguration technique, users can configure the optical processor of a new optical computing platform, the ternary optical computer (TOC), into 42 specific basic operation units, and reconfigure it when the computation is completed. A simulative method of software for this technique is proposed in this paper. Also, an elaborate experiment based on this software is discussed. This simulation of reconfiguration demonstrates that the theory of reconfiguring optical processor in TOC is valid and also lays the foundation for the hardware implementation of the reconfiguration technique.

Experimental study on polarization lens formed by asymmetrical metallic hole array

A polarization bifocal lens based on the polarization effect caused by asymmetrical hole arrays had been designed, fabricated, and characterized experimentally. By considering the fact that the skin depth of an infrared electromagnetic field inside metal is much shorter than the incident wavelength, a polarization bifocal lens composed of high deep-width ratio metallic holes was realized by using a gold-coated silicon structure to replace the one directly formed on a thick metal film. An infrared optical experiment setup is built based on the secondary imagery method for characterizing the focal length of the designed bifocal lens. The measured focal lengths of the fabricated bifocal lens coincide well with the designed values, which proves the validity for realizing the polarization elements with the proposed structure and the feasibility of the fabrication process.

Optical spin-dependent angular shift in structured metamaterials

The physics behind the spin (polarization)-dependent electromagnetic hot-spot phenomenon is due to the presence of the geometric phase resulting from the optical spin-orbit interaction in the interaction of light with the subwavelength microstructures. Unlike the tiny spin-dependent shift of light associated with the usual spin-Hall effect of light, here we present the distinct polarization-dependent angular shift by employing an array of subwavelength metallic apertures. More importantly, this novel electromagnetic precession is accompanied by the extraordinary optical transmission phenomenon and offers the exciting possibilities for novel applications for subwavelength structured metallic systems.

Surface-relief and polarization gratings for solar concentrators

Transmission gratings that combine a large diffraction angle with a high diffraction efficiency and a low angular and wavelength dispersion could be used to collect sunlight in a light guide. In this paper we compare the diffractive properties of polarization gratings and classical surface-relief gratings and explore their possible use in solar concentrators. It is found that polarization gratings and surface-relief gratings have qualitatively comparable diffraction characteristics when their thickness parameters are within the same regime. Relatively large grating periods result in high diffraction efficiencies over a wide range of incident angles. For small grating periods the efficiency and the angular acceptance are decreased. Surface-relief gratings are preferred over polarization gratings as in-couplers for solar concentrators.

Polarization-gratings approach to deformed-helix ferroelectric liquid crystals with subwavelength pitch

Electro-optical properties of deformed helix ferroelectric liquid crystal (DHFLC) cells are studied by using a general theoretical approach to polarization gratings in which the transmission and reflection matrices of diffraction orders are explicitly related to the evolution operator of equations for the Floquet harmonics. In the short-pitch approximation, a DHFLC cell is shown to be optically equivalent to a uniformly anisotropic biaxial layer where one of the optical axes is normal to the bounding surfaces. For in-plane anisotropy, orientation of the optical axes and birefringence are both determined by the voltage applied across the cell and represent the parameters that govern the transmittance of normally incident light passing through crossed polarizers. We calculate the transmittance as a function of the electric field and compare the computed curves with the experimental data. The theoretical and experimental results are found to be in good agreement.

Gaussian-Schell-model beams propagating through rough gratings

In this work we analyze the near-field intensity distribution produced by a rough grating illuminated with a Gaussian-Schell-model beam. This kind of grating is formed by rough and smooth slits. Statistical techniques are used to describe the grating, and the Fresnel approach is used to perform the propagation of light. Two kinds of coherence affect the light propagation. One of them comes from the light beam, since it is not totally coherent. The other one comes from the rough topography of the grating surface. We have found that the Talbot effect is not present just after the grating, but it gradually increases. In addition, the contrast of the self-images decreases from a certain distance due to the coherence properties of the illumination beam. Then, the self-imaging process is only present between two specific distances from the grating. To corroborate the analytical results, we have performed numerical simulations for the mean intensity distribution based on the Sommerfeld-Rayleigh approach, showing their validity.

Jones matrix treatment for optical Fourier processors with structured polarization

We present a Jones matrix method useful to analyze coherent optical Fourier processors employing structured polarization. The proposed method is a generalization of the standard classical optical Fourier transform processor, but considering vectorial spatial functions with two complex components corresponding to two orthogonal linear polarizations. As a result we derive a Jones matrix that describes the polarization output in terms of two vectorial functions defining respectively the structured polarization input and the generalized polarization impulse response. We apply the method to show and analyze an experiment in which a regular scalar diffraction grating is converted into equivalent polarization diffraction gratings by means of an appropriate polarization filtering. The technique is further demonstrated to generate arbitrary structured polarizations. Excellent experimental results are presented.

Control method for the optical components of a dynamically reconfigurable optical platform

We propose a control method for the optical components of a dynamically reconfigurable optical platform, the ternary optical computer (TOC). The optical components are made of liquid-crystal cell arrays (LCCAs) and polarizers, so the control method is for generating the pilot signals of the LCCAs to meet user demands. In this work, we first briefly introduce the TOC theory, the modules in the TOC monitor system, and the addressing of these LCCAs. Then we focus on the method for generating the control information (CI) of optical components, i.e., the encoder and the operator in the TOC according to the operands and the information about the basic operating units needed by an operation. In addition, we define data structures, some of which store the information to generate the CI and others that mainly store the generated CI. Finally we provide an example to verify the proposed method and conduct an experiment to generate the LCCA CI. The results demonstrate the correctness and feasibility of the method.

Effects of anisotropic diffractions on holographic polymer-dispersed liquid-crystal gratings

Volume gratings fabricated by interferometric exposure using composite materials composed of nematic liquid crystals (LC) and LC diacrylate monomers are discussed in the effects of diffraction properties on different grating formations, such as varying LC content ratios, film thicknesses, and the surface conditions composed of alignment layers and rubbing directions. Diffraction properties are experimentally investigated in the viewpoints of anisotropic diffraction and LC orientation. The polarization-azimuth dependence of diffraction efficiencies as functions of the incident polarization states shows the controllability of anisotropic diffractions based on the effects of different surface conditions.

Surface-relief polarization gratings for visible light

Polarization gratings are space-variant subwavelength-structured photonic devices that control electromagnetic wave propagation by local modulation of the state of polarization of light. Using electron beam lithography, we have fabricated such devices in the form of dielectric and metallic surface-relief profiles for operation in the visible wavelength region, where structural features with dimensions on the order of 100 nm are required. We provide experimental demonstrations of various laser-beam splitting elements with diffraction efficiencies exceeding values that could be achieved by diffractive elements operating in the framework of scalar optics.

Coupled-wave analysis of vector holograms: effects of modulation depth of anisotropic phase retardation

The diffraction properties of thick vector holograms were analyzed with the use of a simple coupled-wave theory. Two eigenpolarizations in the holograms were determined based on the dielectric perturbation, and diffraction efficiencies for the polarizations were calculated by applying the Kogelnik method. The results were compared with those simulated by the finite-difference time-domain method. As a result, it was demonstrated that the diffraction efficiencies calculated by the two methods are in good agreement for any incident polarization when the modulation depth of the anisotropic phase retardation is substantially smaller than the mean retardation. In addition, we confirmed that coupled-wave analysis provides reasonable accuracy for relatively large modulation in the case of Bragg incidence with eigenpolarization.

Formation of holographic memory for defect tolerance in optically reconfigurable gate arrays

Holographic polymer-dispersed liquid-crystal (HPDLC) memory using liquid-crystal composites is proposed for new optical information processing. Formation of HPDLC memory using a photomask is discussed for parallel programmability to realize fast reconfiguration of optically reconfigurable gate arrays (ORGAs). The defect tolerance of HPDLC memory is investigated to clarify the defect limitation of holographic configurations using ORGAs. Experimental results show that the noise ratio less than 15% applied to HPDLC memory rarely affects its diffraction pattern or a reconfiguration context.

Real-time measurement of unique space-variant polarizations

A configuration for real-time measurement of unique, space-variant, polarizations is presented. The experimental results reveal that the full state of polarization at each location within the beam can be accurately obtained every 10 msec, limited only by the camera frame rate. We also present a more compact configuration which can be modified to determine the real-time wavelength variant polarization measurements.

Polarization-selective diffractive optical elements with a twisted-nematic liquid-crystal display

We propose a method for realizing a polarization-selective diffractive optical element by using of a single twisted-nematic liquid-crystal display (TN-LCD). We have demonstrated that two orthogonal polarization-encoding channels can be formed using a single TN-LCD operated in some special conditions. Based on the two orthogonal encoding channels, two orthogonal polarized components of a field with any complex amplitude can be holographically encoded and reconstructed and, hence, different output images with different polarization states could be obtained, or a vector beam with spatially inhomogeneous polarization distributions, as well as the desired complex amplitude distributions, could be combined.

Binary gratings with random heights

We analyze the far-field intensity distribution of binary phase gratings whose strips present certain randomness in their height. A statistical analysis based on the mutual coherence function is done in the plane just after the grating. Then, the mutual coherence function is propagated to the far field and the intensity distribution is obtained. Generally, the intensity of the diffraction orders decreases in comparison to that of the ideal perfect grating. Several important limit cases, such as low- and high-randomness perturbed gratings, are analyzed. In the high-randomness limit, the phase grating is equivalent to an amplitude grating plus a "halo." Although these structures are not purely periodic, they behave approximately as a diffraction grating.

Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude, and phase diffraction gratings

We analyze the performance of a ferroelectric liquid crystal on silicon display (FLCoS) as a binary polarization diffraction grating. We analyze the correspondence between the two polarization states emerging from the displayed grating and the polarization and intensity of the diffracted orders generated at the Fourier diffraction plane. This polarization-diffraction analysis leads, in a simple manner, to configurations yielding binary amplitude or binary phase modulation by incorporating an analyzer on the reflected beam. Based on this analysis, we present two useful variations of the polarization configuration. The first is a simplification using a single polarizer, which provides equivalent results for amplitude or phase modulation as the more general operational mode involving two polarizers. The second variation is proposed to compensate the reduction of the diffraction efficiency when the operating wavelength differs from the design one (for which the FLCoS liquid-crystal layer acts as a half-wave plate). In this situation we show how the ideal grating performance can be recovered in spite of the phase-shift mismatch originated by chromatic dispersion. In all cases, we provide experimental results that verify the theoretical analyses.

Digital polarization holograms with defined magnitude and orientation of each pixel's birefringence

A new form of digital polarization holography is demonstrated that permits both the amplitude and the phase of a diffracted beam to be independently controlled. This permits two independent intensity images to be stored in the same hologram. To fabricate the holograms, a birefringence with defined retardance and orientation of the fast axis is recorded into a photopolymer film. The holograms are selectively read out by choosing the polarization state of the read beam. Polarization holograms of this kind increase the data density in holographic data storage and allow higher quality diffractive optical elements to be written.

Comment on "Can a light beam be considered to be the sum of a completely polarized and a completely unpolarized beam?"

We show that the Stokes theorem is valid for a larger class of partially polarized beams than that given in Opt. Lett.33, 642 (2008).

Self-imaging of gratings with rough strips

We analyze the self-imaging process produced by a transmission grating whose strips present two different roughness levels. This kind of grating periodically modulates the transmitted light owing only to the different microtopographic properties of the strips. In spite of the fact that the grating is not purely periodic, it produces a kind of self-image at Talbot distances. These self-images gradually appear as light propagates, but they are not present just after the grating, as occurs in amplitude or phase gratings. There exists a distance from the grating, which depends on the stochastic properties of roughness, from which the contrast of the self-images becomes stable. Important cases are analyzed in detail, such as low- and high-roughness limits. We assume for the calculations that the grating can be used in a mobile system. Simulations using the Rayleigh-Sommerfeld regime have been performed, which confirm the validity of the theoretical approach proposed in this work.

Control of anisotropic diffraction in liquid-crystal composite volume gratings

Orientation-controlled anisotropic diffraction gratings are realized by interferometric exposure using composite materials of nematic liquid crystals (LCs) and LC diacrylate monomers. The anisotropic diffraction properties in volume gratings, which dominantly diffract p- or s-polarized light, are shown to be controlled by the rubbed directions of the alignment layers under the control of the photopolymerization temperature. Images of the fringe patterns observed by polarization microscopy show the effects of the alignment layers on the LC orientation during grating formation.

Formation of anisotropic diffraction gratings in a polymer-dispersed liquid crystal by polarization modulation using a spatial light modulator

Anisotropic diffraction gratings based on a holographic polymer-dispersed liquid crystal (HPDLC) are realized by interferometric exposure using a spatial light modulator (SLM). The SLM is used in the HPDLC grating formation for anisotropic holographic recordings of two-dimensional polarization states for an incident light beam. The diffraction efficiency for P-polarization and the distinctive ratio of diffraction efficiency in P-polarization to that in S-polarization increases with the signal level applied to the SLM. The resulting volume gratings exhibit diffraction efficiency of more than 60% and a distinctive ratio of diffraction over 100. The microscopic origin of the anisotropic property is investigated by an optical polarizing microscope. The novel characteristics of the anisotropic diffraction properties of HPDLC are applied to an image reconstruction technique.

Elastic continuum analysis of the liquid crystal polarization grating

We apply elastic continuum theory to model critical parameters influencing the free-energy equilibrium configuration and the dynamic performance of a continuous and in-plane liquid crystal profile acting as a polarization grating. We present analytical expressions for the threshold voltage, critical thickness, and the dynamic switching times under strong anchoring conditions, negligible flow, and arbitrary splay, twist, and bend constants. We also study the influence of weak anchoring, and derive expressions describing a dramatic reduction of the critical thickness and voltage threshold, even for modest grating periods and surface anchoring strengths. Good correlation exists with previously reported experimental data, except in the dynamic response; we therefore show that flow effects (backflow and kickback) likely play an essential role in the fall times, presumably due to the prominent splay-bend deformation of the zero-field configuration. We consider the impact of surface pretilt, and validate our entire analysis with numerical simulations. The approximation technique we employ is likely broadly useful for many problems which include nano- or micropatterned surfaces.

Two-dimensional polarization rotator using a twisted-nematic liquid-crystal display

We present a novel configuration for a twisted-nematic liquid-crystal display (TN-LCD) that makes it operate as a controllable polarization rotator. We extend a previously reported polarization rotator configuration using a zero-twist LCD inserted between two quarter-wave plates. We first operate the TN-LCD in the polarization eigenvector configuration and show how this system can act as an equivalent voltage-controlled wave plate. Next we incorporate this wave plate into the optical rotator configuration. We show that the plane of polarization of the transmitted light can be rotated as a function of the phase introduced by the display. Finally, we create a 2D polarization mask where different areas of the TN-LCD form different polarization states. Experimental results are included.

Space-variant polarization manipulation for far-field polarimetry by use of subwavelength dielectric gratings

A method for polarimetric measurement that uses a discrete space-variant subwavelength dielectric grating is presented. One retrieves the polarization state by measuring the far-field intensity of a beam emerging from the grating followed by a polarizer. The analysis for a partially polarized, quasi-monochromatic beam is performed by use of the beam coherence polarization matrix along with an extended van Cittert-Zernike theorem. We experimentally demonstrate polarization measurements of both fully and partially polarized light.

Polarization-invariant grating based on a photoaligned liquid crystal in an oppositely twisted binary configuration

We demonstrate a polarization-invariant liquid-crystal (LC) grating in an oppositely twisted and mutually orthogonal configuration. The polarization-invariant LC grating with high diffraction efficiency is fabricated using a single-masking process with two-step exposure of a linearly polarized ultraviolet light. It is found that the zeroth- and the first-order diffracted beams are linearly polarized and perpendicular to each other irrespective of the incident polarization for the phase retardation of m pi (m=integer).

Fractional Montgomery effect: a self-imaging phenomenon

Self-imaging means image formation without the help of a lens or any other device between object and image. There are three versions of self-imaging: the classical Talbot effect (1836), the fractional Talbot effect, and the Montgomery effect (1967). Talbot required the object to be periodic; Montgomery realized that quasiperiodic suffices. Classical means that the distance from object to image is an integer multiple of the Talbot distance Z(T) = 2p2/lambda, where p is the grating period. Fractional implies a distance that is a simple fraction of Z(T): say, Z(T)/2, Z(T)/4, 3Z(T)/2.... We explore the most general case of the fractional Montgomery effect.

Polarization-multiplexed diffractive optical elements with liquid-crystal displays

We show experimental results for programmable polarization multiplexing of diffractive optical elements (DOEs) onto two liquid-crystal displays (LCDs). The first LCD encodes the two multiplexed phase-only diffractive optical elements. The second LCD acts as a pixelated polarization rotator to change the polarization state for each of these two DOEs. Although the system requires precise alignment, the DOE's and polarization angles are fully programmable.

Polarization-selective beam splitter based on a highly efficient simple binary diffraction grating

A polarization beam splitter (PBS) based on a giant-reflection to zero-order (GIRO) grating is presented. The GIRO grating is a simple binary diffraction grating with parameters chosen such that the excited optical modes in the grating interfere constructively and destructively at the respective interfaces. This interference results in high-zero-order reflection (>99%) with a high polarization-selective extinction ratio (+/-30 dB). The grating shows a low aspect ratio. The GIRO PBS is theoretically and experimentally shown to be an adequate PBS for use as an optical isolator in combination with a quarter-wave plate in a CO2-laser system.