Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.     

Reduction of polarization-induced artifacts in grating-based spectrometers

An optical device that converts unpolarized light into a single polarization state is described. The device is based on a polarizing beam splitter that separates the two polarization directions. The beam splitter is combined with two pairs of equilateral prisms that are used to collimate the two beams in terms of both propagation and polarization directions. When it is used in combination with a blazed diffraction grating, this device is shown to effectively remove the polarization dependence of the first-order diffracted power. The device has an insertion loss of approximately 14% for purely s-polarized light. However, for unpolarized light incident upon the two gratings studied here, the increased throughput of the p-polarized component leads to an average relative gain in overall efficiency of 13%-19%, depending on the grating. In collimating the two polarization directions, the device may cause a reduction in spectral resolution for a rectangular entrance slit. As a result, the device is more likely to find use in spectrometers that have a circular aperture, such as that provided by an optical fiber.     

Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout

The diffraction properties of volume holographic gratings are studied when the gratings are illuminated by an ultrashort pulsed beam with different polarization states. The developed coupled wave theory of Kogelnik is used. Considering the dispersion effect of the grating media, solutions for the diffracted and transmitted intensities, diffraction efficiencies and the bandwidths of the gratings are given in transmission volume holographic gratings and reflection volume holographic gratings. The bandwidths of the gratings are reduced by the dispersion effect of the grating media. They also have different influences on the diffraction of an ultrashort pulsed beam with different polarization states. For different values of the ratio of the spectral bandwidth of the input pulse to that of the grating, the changes of the spectral and temporal distributions of the diffracted intensities, as well as the diffraction efficiencies of the gratings are shown.     

Photopolarimeter based on two gratings recorded in thin organic films

A photopolarimeter based on two different kinds of diffraction gratings (a two-grating photopolarimeter) has been developed for real-time measurements of the four elements of the Stokes vector. The main elements of the device are a pure polarization grating and an ordinary transmission grating, both recorded by means of holographic techniques in thin films of organic materials. The first one consists of a diffraction grating recorded by two interfering opposite circularly polarized beams in a Langmuir-Blodgett film of an azo-compound material. The second component is a grating recorded by two interfering parallel circularly polarized beams in a thin film of a photosensitive polymer. Both gratings offer long time stability and good diffraction efficiency. Four photodiodes collect the first-order diffracted beams from these gratings, the output signals of which are read through an analog-to-digital converter by a PC. The optical alignment of the device is easy and the calibration is realized in a one-step procedure.     

Near-infrared spectropolarimetry based on acousto-optical tunable filters

A new approach to near-infrared (NIR) spectropolarimetry is described, in which the properties of a noncollinear acousto-optical tunable filter (AOTF) made of an anisotropic crystal of TeO2 is employed to produce a novel instrument that precludes or reduces significantly the use of mechanical parts and simplifies the acquisition of optical rotation spectra of absorbing species in the NIR region. In essence, the instrument is based on the measurement of the relative beam intensities produced when a 45 degrees plane polarized beam of radiation passes through a sample cell and is directed to the entrance window of the AOTF. Because of the crystal anisotropy, two planar and orthogonally polarized beams will leave the AOTF, angularly split from the nondiffracted beam, after the acousto-optical interaction has occurred. If an optically nonactive sample is present in the cell, equal intensities for both diffracted beams should be observed. On the other hand, the presence of an optically active sample will cause the polarization plane to rotate and a consequent difference in the intensities of the AOTF diffracted beams will be registered as a function of the optical activity of the sample. The instrument has been evaluated with aqueous solutions of sucrose, glucose, and fructose and for three forms of camphor (d, l, dl).     

Optical grating diffraction method: from strain microscope to strain gauge

The grating diffraction method for direct strain measurement is reviewed. Two systems which use this method are presented. The first system is a compact strain microscope. A Leitz optical transmitting microscope with white light source is reconstructed by developing a loading and recording system. Gratings with median density of between 40 and 200 lines/mm are used. With the help of a Bertrand lens, the Fourier spectrum of the grating is formed with high image quality on the CCD sensor plane. Software is developed to precisely, quickly and automatically determine the diffraction spot centroids. The second system is a new strain sensor based on a high-frequency grating and two Position Sensor Detectors (PSDs). The grating, attached to the surface of the specimen, is illuminated by a focused laser beam, generally with a frequency of 1,200 lines/mm. The centroids of diffracted beam spots from the grating are automatically determined using two PSD sensors connected to a personal computer. The shift of diffracted beam spots due to specimen deformation is detected. Strain sensitivity of one micro-strain can be obtained, as can a 0.4 mm spatial resolution for strain measurement. The system can be used for both static and dynamic tests.     

Determination of longitudinal and transverse shifts of three-dimensional Gaussian beams reflected at a grating near an anomaly

Spatial displacements of three-dimensional Gaussian beams diffracted at a reflection grating are studied theoretically and numerically. The complex diffraction coefficients (amplitudes and phases) of the grating diffracted plane waves calculated by a rigorous method for conical diffraction are the basis for this investigation. The classical analytical formula for the longitudinal shift depending on the gradient of the reflection phase is generalized to the simultaneous analytical treatment of the longitudinal Goos—Hänchen like shift as well as a transverse shift. A second method uses the full integration on the whole spectrum of plane waves of the diffracted beam.     

Polarization holographic gratings in side-chain azobenzene polyesters with linear and circular photoanisotropy

We investigate thin phase polarization holographic gratings recorded with two waves with orthogonal linear polarizations in materials in which illumination with linearly/circularly polarized light gives rise to linear/circular birefringence. The theoretical analysis shows that the presence of circular photoanisot-ropy changes significantly the diffraction characteristics of the gratings. The intensities of the waves diffracted in the +1 and -1 orders of diffraction and their ratio depend substantially on the reconstructing-wave polarization. Experiments with films of side-chain liquid-crystalline azobenzene polyester that is a photoanisotropic material of the considered type confirm the unusual polarization properties. It is shown that polarization holography may be used for real-time simultaneous measurement of photoinduced linear and circular birefringence.     

Slope measurement of bent plates using double grating shearing interferometry

A grating-based shearing interferometeric setup for slope measurement of bent plates has been proposed. The specimen under test is illuminated by a collimated beam from the laser. Light reflected from the specimen passes through two identical holographic gratings placed in tandem. The grating frequency has been so chosen that the diffracted orders from each grating are separated out distinctly. Two first-order beams diffracted from each of the gratings superpose in space. In the resulting interferogram, the fringes due to slope information of the object are visualized. Mathematical formulation for experimental determination of slope values has been undertaken. Validation of the experimental results with theoretical predictions in case of cantilever beam provides good correlation. The main advantage of the technique has been the realization of very compact geometry without the need for spatial filtering arrangement commonly associated with the grating-based techniques used to date.     

Liquid-crystal blazed grating with azimuthally distributed liquid-crystal directors

We propose a novel formation method of arbitrary phase profiles of circular light by controlling azimuthal angles of liquid-crystal directors; its principle is described theoretically. A new liquid-crystal blazed grating is demonstrated by use of the proposed method. It is revealed that the first-order diffraction efficiency reaches the maximum value (theoretically 100%, experimentally approximately 90%) at an optimum applied voltage when the phase difference between the extraordinary and ordinary rays agrees with one-half the wavelength. Furthermore, the polarization states of the diffracted light beams are analyzed by Stokes parameter measurements, and unique polarization-splitting properties are revealed.     

Design and construction of linear laser encoders that possess high tolerance of mechanical runout

A linearly diffracted laser encoder that has high tolerance of head-to-scale misalignment and a high signal-to-noise ratio is described. The preservation of parallelism between the incident and the diffracted beams, which can be attributed to a built-in folded 1x telescope, allows for the high alignment tolerance. It can be shown that, by coupling this newly developed circular polarization interferometer configuration with grating scale geometry optimization, one can eliminate the problems associated with signal distortion that arise from various efficiencies of the p- and the s-polarized light beams and obtain a high signal-to-noise ratio. Both theoretical and experimental results are presented to confirm the improved results and performance.     

High-efficiency diffractive micromachined chopper for infrared wavelength and its application to a pyroelectric infrared sensor

We have developed a diffractive micromachined chopper (DMC) for an IR wavelength of ~10 mum. This device operates mechanically by movable reflection grating beams. It modulates the diffraction efficiency by controlling the displacement of grating beams by an electrostatic force. For a CO(2) laser beam, a high modulation efficiency of 84% with an -0.8-dB small insertion loss was obtained by detecting 0th-order diffracted light. A novel pyroelectric IR microsensor with a DMC and a diffractive multilevel Si microlens was proposed and it demonstrated the detection of human existence.     

Polarization-splitting common-path interferometer based on a zero-twist liquid crystal display

We present a compact optical polarization-splitting common-path interferometer based on a zero-twist liquid crystal display (LCD). The LCD is encoded with a diffraction grating pattern and illuminated with a polarization state with both horizontal and vertical components. The polarization component perpendicular to the director axis of the liquid crystal molecules is not affected by the LCD and forms the reference beam. However, the polarization component parallel to the director axis is diffracted at an angle determined by the period of the grating. By imposing an analyzer polarizer, these two beams create an interferogram that can either display retardance patterns encoded onto the LCD or analyze external birefringent optical elements. The programmability of the system allows new ways of increasing the utility of the interferograms. Experimental results are provided, including the visualization of optical vortices with different and opposite topological charges.     

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously.     

Observation of self-diffraction effect in acid blue 7 dye soaked gelatin films

Abstract

Permanent self-diffraction gratings are formed in red sensitive Acid blue 7 dye soaked gelatin films under illumination of an interference pattern by two linearly polarized beams from a He-Ne laser at 632.8 nm. Growth of the self-diffraction grating is monitored by measuring intensities of various diffraction orders. Systematic studies are carried out to investigate the influence of various parameters involved in diffraction efficiency of the grating such as time of exposure, concentration of dye in the gelatin-coated plate, intensity of interfering beams and intensity ratio of interfering beams. Efficient gratings with ten diffracted orders are formed. Several interesting observations are made by blocking one of the writing beams and an attempt is made to analyse these results.     

Three-dimensional converging-diverging Gaussian beam diffraction by a volume grating

The diffraction characteristics of a volume grating (VG) illuminated by a three-dimensional (3-D) converging-diverging Gaussian beam at conical incidence are investigated by applying 3-D finite-beam (FB) rigorous coupled-wave analysis (RCWA) based on the conventional 3-D RCWA in conjunction with two-dimensional plane-wave decomposition. The Gaussian beam is assumed to have an arbitrary incidence angle, an arbitrary azimuthal angle, and any linear polarization. The two cases with linear polarizations of the central beam of the Gaussian (E perpendicular K and H perpendicular K) are investigated. The diffraction efficiencies and the diffracted beam profiles for both unslanted VGs and slanted VGs (designed for substrate-mode optical interconnects) are presented. In general, the diffraction efficiencies of a converging-diverging spherical Gaussian beam diffracted by both unslanted VGs and slanted VGs increase and approach the central-beam results as the refractive-index modulation increases.     

Effect of reconstruction beam polarization on the kinetics of anisotropic gratings in bacteriorhodopsin

Anisotropic gratings are recorded on bacteriorhodopsin films by two parallelly polarized beams, and the effect of the polarization orientation of the reconstructing beam on the diffraction efficiency kinetics is studied. A theoretical model for the diffraction efficiency kinetics of the anisotropic grating is developed by combining Jones-matrix and photochromic two-state theory. It is found that the polarization azimuth of the reconstructing beam produces a cosine modulation on the kinetics of the diffraction efficiency, being positive at the peak efficiency and negative for steady state. By adding auxiliary violet light during grating formation, the saturation of the grating can be restrained. As a result, the negative cosine modulation for the steady-state diffraction efficiency changes to a positive one. In addition, the steady-state diffraction efficiency is increased appreciably for all reconstructing polarization orientations.     

Polarization of holographic grating diffraction. I. General theory

The full polarization property of volume holographic grating diffraction is investigated theoretically. With a simple volume grating model, the diffracted fields and Mueller matrices are first derived from Maxwell's equations by using the Green's function algorithms. The formalism is derived for the general case that the diffraction beam and the grating wave vector are not in the plane of incidence, where s waves and p waves are not decoupled. The derived photon-momentum relations determine the Bragg angle selectivity. The parameters of diffraction strength related to the hologram-writing process and material are defined and are not necessarily small in general. The diffracted-beam profiles are analytically calculated by using the known grating shape function. This theory has provided a fundamental understanding of the polarization phenomena of a real holographic diffraction grating device. The derived algorithm would provide a simulation-analysis tool for the engineering design of real holographic beam combiner/splitter devices.     

Induced and form birefringence in high-frequency polarization gratings

High-frequency phase polarization gratings are fabricated holographically in dichromated gelatin dyed with malachite green. It is observed that the intensity of the -1 diffracted beam is a sinusoidal function of the incident polarization angle. In addition, we analyze the dependence of the diffracted order polarization on grating frequency. It is evident from our results that form birefringence becomes significant when the grating period is smaller than the illumination wavelength, thus modifying the optically induced birefringence. Then, in polarization hologram reconstruction, it is not possible to obtain the polarization distribution at the recording step for high-frequency objects.     

光栅分振幅光偏振测量系统的研制

使用一个既能产生反射光衍射又能产生透射光衍射的特殊金属光栅作为分光器,研制一种新颖的高速光波偏振态测量系统。它没有使用转动光学部件或调制器,而是将金属光栅产生的四条1级衍射光的光强线性地转换为电信号,通过定标方法得到系统的非奇异的仪器矩阵,然后通过线性运算得到入射光的待测Stokes矢量。该系统结构紧凑、安装方便,可用作实时偏振测量术和椭偏测量术中的偏振态探测器。