Zero-order Diffraction Research Articles

Analysis of Open Grating-Based Fabry–Pérot Resonance Structures With Potential Applications for Ultrasensitive Refractive Index Sensing

We report a theoretical framework to explain the characteristics of Fabry-Perot (FP) resonances excited in a thin film-based grating consisting of a thin gold layer and a rectangular dielectric grating in the sub-wavelength and near-wavelength grating regimes. The zeroth-order diffraction inside the grating layer forms an FP resonant cavity with effective refractive index arising from an averaging effect between the refractive indices of the grating material and the filling material between the grating grooves. A simplified model based on Fresnel equations and phase matching condition is proposed to predict the FP resonant mode for the grating structure, this is compared with rigorous coupled-wave analysis to determine its range of validity. We also compare the performance of the proposed structure with other thin film-based interferometers for refractive index sensing applications, in terms of, sensitivity, full width at half maximum, figure of merit and dynamic range. The proposed structure has a full width at half maximum around 10 times to 60 times narrower than conventional surface plasmon resonance and conventional FP resonators. Thus, the figure of merit is higher than Kretschmann based surface plasmon resonance and FP structures by a factor of 20 and 2 respectively with a wider dynamic range. The total energy stored in the grating resonant cavity is 5 and 20-fold greater than the surface plasmon resonance configuration and the conventional FP structures. Since the resonator discussed here is an open structure, it is far better suited for liquid sensing compared to a closed FP structure.

Design, fabrication, test, and analysis of an out-of-plane plasmonic optical metasurface

Plasmonic metasurfaces with in-plane phase elements have a limit in transmission because they only affect the electric field of incident EM radiation. Recently, a set of out-of-plane plasmonic phase elements was designed using a genetic algorithm to work in the infrared as a Huygens metasurface with significantly improved transmission efficiency. A beam-steering metasurface (i.e., blazed transmissive diffraction grating) was fabricated from this design using membrane projection lithography (MPL) and characterized for its bidirectional transmittance distribution function as a function of scatter angle for normally incident light, and linear incident and transmitted polarizations. Measurements were compared with the designed behavior as predicted by finite element method (FEM) simulations that generated near fields for each phase element and propagated them to the far field as a metasurface using a Stratton–Chu formulation, but measurements showed strong zero-order diffraction not present in the simulation along with the designed +1-diffraction order. We analyze this disagreement between measured and ideal results. Further FEM modeling included the introduction of defects into the phase elements consistent with defects expected from the fabrication process and identified lateral displacement of the plasmonic decoration in the MPL structure as a potential cause for the reduced performance of the fabricated device.

Separation detection and correction of mosaic errors in mosaic gratings based on two detection lights with the same diffraction order and different incident angles

Grating tiling is an important fabrication technology for large-size gratings. However, when using grating tiling technology to form large-size echelle gratings, the interferometer cannot detect the grating's zero-order diffraction wavefront because the zero-order diffraction light of the echelle grating is weak. This prevents use of the zero-order and non-zero-order diffraction light of the grating to realize separation detection and correction of mosaic errors. To solve this problem, a new method for separation detection and correction of mosaic errors in mosaic gratings based on two detection lights with the same diffraction order but different incident angles is proposed and a mosaic error detection system is designed. Then, the correction steps for mosaic errors are summarized and the error in mosaic error detection system is analyzed. Finally, the measurement uncertainty in detecting the wavefront of the mosaic grating and the mosaic accuracy of the grating wavefront are analyzed. The uncertainty is 0.008λ (λ=632.8 nm) and the mosaic accuracy of the peak-to-valley wavefront is 0.069λ, which shows that high-precision measurements of the wavefront and high-precision mosaic of the wavefront were successfully achieved. The proposed method can be used for the mosaic of all blazed gratings.

Optical rotation detection method based on acousto-optic modulation in an atomic spin co-magnetometer

A new concept for probe light intensity stability control and high-frequency modulation based on an acousto-optic modulation in a K-Rb-21Ne co-magnetometer is reported. The structure and optical path are ingeniously designed to avoid the interference of zero-order diffraction light. The average rotation rate sensitivity of is achieved under the light intensity closed-loop control condition and the bias instability calculated by the Allan deviation is improved from 0.13 deg h−1 to 0.06 deg h−1 comparing with open-loop scheme. A square wave modulation with a wide range of frequencies is applied to the probe light intensity and the appropriate modulation frequency for the co-magnetometer is tested to be 10 kHz to 300 kHz and megahertz scale. Finally, the closed-loop control of light intensity has been combined with the high-frequency modulation, which could suppress the low-frequency noise contained in the probe system and improve the long-term stability of the angular velocity measurement.

Phase Retrieval of On-Axis Digital Holography With Modified Coherent Diffraction Imaging

In this paper, a phase retrieval method is proposed to reconstruct the high-quality image free from undesired terms in on-axis digital holography (DH) with modified coherent diffraction imaging (MCDI). A random phase plate (RPP) is applied to generate a modulated diffraction pattern which forms an on-axis digital hologram with a plane reference wave, and a proper iterative algorithm is designed to reconstruct high-quality object information from both on-axis digital hologram and modulated diffraction pattern. Numerical simulations and experiments prove that both modulus and phase distributions can be accurately reconstructed within 100 iterations while the undesired twin image and zero-order diffraction can be effectively removed, thus demonstrating the feasibility of the suggested method.

Processing of 2D Images Using the Bragg Diffraction

Application of the acousto-optic (AO) Bragg diffraction in the processing of 2D images is analyzed. It is shown that conventional Bragg diffraction can be used for 2D processing provided that the zero-order diffraction is supplemented with the diffraction to an additional (side) order. A 2D contour of an optical image is experimentally detected using the first-order diffraction of radiation with a wavelength of 0.63 × 10–4 cm. An AO cell made from ТеО2 single crystal is used as an AO filter of spatial frequencies. Diffraction orders are formed in such an AO cell due to AO interaction with an acoustic wave with a frequency of 26 MHz.

Tunable Polarization Gratings Based on Nematic Liquid Crystal Mixtures Photoaligned with Azo Polymer-Coated Substrates

Liquid crystal polarization gratings are of great interest for optical communications as elements performing beam steering, splitting, multiplexing or beam combining. Material birefringence, cell thickness or a period of the liquid crystal director pattern influence, among other features, spectroscopic and electro-optical characteristics of fabricated devices, determining thus their functionality and applicability. Here, we report on liquid crystal polarization gratings that allow for complete maximization of the first-order diffraction efficiency (resulting in total elimination of the zeroth-order diffraction) for any wavelength of an incident beam from green to the near-infrared spectral region by applying a low electric voltage. The gratings with periods as small as 10 μm were obtained by holographic exposure of the cell substrates coated with light-sensitive azo polymer alignment layers, and then filled with three different liquid crystal mixtures. The influence of gold nanoparticle dopants in the liquid crystalline mixtures on spectroscopic and electro-optical properties of the devices is presented. Moreover, on the basis of the measured transmittance spectra of the fabricated gratings, the unknown birefringence of liquid crystal mixtures as well as their effective birefringence due to molecular reorientation in the electric field in the visible and near IR region were determined.

Hard x-ray phase-contrast microscopy using a Gabor hologram without a zero-order term.

In order to achieve a nanometer-scale resolution in an x-ray microscopy system, a Gabor-type hologram was produced by eliminating the zero-order term of the object diffraction pattern. In this system, a Fresnel zone plate was used for strong illumination of an object, and the zero-order diffraction was physically eliminated by a center stop. An accurate phase plate of π/2 in the Zernike method was numerically created, and the phase-contrast image was realized. The theoretical resolution was 19.8 nm. We proved that a gold nanocube with a size of 50 nm can be reconstructed with the predicted resolution.

Total Emission Time Resolved Decay: a Method for Measurement and Resolution of Broad-Band Emission.

This article reports a time-resolved fluorescence data acquisition technique termed as "Total Emission Time Resolved Decay" (TETRD). TETRD is recorded by using zero-order diffraction of emission grating in TCSPC instrument. TETRD decay curve has entire wavelength dependent decay information buried in it. Cut-off filters are used to avoid scattering contamination. Two existing approaches are used for analysing the interconnected TETRD data. (i) First, global analysis: for discretely decaying multiple components, TETRD dataset is analyzed using global analysis. The normalized pre-exponentials (αi) and relative amplitudes (fi) recovered from global analysis reflect the individual component emission more faithfully and resembles with steady-state spectral data as well. (ii) Second, stretched exponential fitting (StrEF): for continuous lifetime distribution systems, StrEF (I(t) = I0 exp[-(t/τ)1/h]) has been used to analyse TETRD data. The average lifetime (τ) of StrEF matches well with the average lifetime of multi-exponential fitting, the heterogeneity factor (h) of StrEF is an additional parameter, which informs about local heterogeneity in the system. It is shown that the lifetimes obtained with TETRD matches well with the lifetimes obtained using conventional time resolved emission spectra (TRES). TETRD holds advantage in rapid data acquisition and facilitates inclusion of another variable (like concentration, solvent composition, pH, excitation wavelength etc.) into experimental design. Further, with the use of an appropriate data analysis tool, the multi-component decay profiles can be resolved conveniently.

Diffraction of (l,n)th mode Laguerre-Gaussian laser beam by a curved fork-shaped grating

The transformation of (l,n)th mode Laguerre-Gaussian (LG) laser beam, in the process of its diffraction by a curved fork-shaped grating with topological charge p, is theoretically studied. The analytical solutions for the diffracted wave field amplitudes are derived in the Fresnel regime and in the back focal plane of a convergent lens. The zeroth-diffraction order is found as (l,n)th mode LG beam. The higher, th diffraction-order beam is described in the radial direction through a product of the Gauss-doughnut function by the double sum of hypergeometric Kummer functions. Its topological charge can be increased or reduced compared to that of the incident beam, or it can be equal to zero. The radial intensity distributions are plotted and compared to the corresponding ones valid when a fork-shaped grating is used. The results are specialized for the cases of incident LG beams of modes (l, n = 0), (l = 0,n) and (l = 0,n = 0) i.e. Gaussian mode.

Zero-order-free meta-holograms in a broadband visible range

The unwanted zero-order light accompanied by the birth of diffractive optical elements and caused mainly by fabrication errors and wavelength variations is a key factor that deteriorates the performance of diffraction-related optical devices such as holograms, gratings, beam shapers, beam splitters, optical diffusers, and diffractive microlenses. Here, inspired by the unique characteristic of nano-polarizer-based metasurfaces for both positive and negative amplitude modulation of incident light, we propose a general design paradigm to eliminate zero-order diffraction without burdening the metasurface design and fabrication. The experimentally demonstrated meta-hologram, which projects a holographic image with a wide angle of 70 ° × 70 ° in the far field, presents a very low zero-order intensity (only 0.7% of the total energy of the reconstructed image). More importantly, the zero-order-free meta-hologram has a large tolerance limit for wavelength variations (under a broadband illumination from 520 to 660 nm), which brings important technical advances. The strategy proposed could significantly relieve the fabrication difficulty of metasurfaces and be viable for various diffractive-optics-related applications including holography, laser beam shaping, optical data storage, vortex beam generation, and so on.

Consideration of existence of phase information of object shape in zeroth-order diffraction beam using electromagnetic simulation with aperture in front of objective

ABSTRACTIt has been reported that the shape of a measured object can be determined by detecting the change in phase distribution generated by a lateral shift of the object using speckle interferometry. In speckle interferometry technique, it was also reported that the shape of the object beyond the diffraction limit can be measured. In this study, the principle of this method is discussed through experiments and electromagnetic analysis. Accordingly, the results of the experiments and electromagnetic analysis of phase change only under zeroth-order diffraction light through the lateral shift of the object are investigated by shutting out the higher harmonic diffraction lights using an aperture in front of the lens. The results indicate that even if the image of the object cannot be focused upon, three-dimensional shape measurement can be performed by analysing only the zeroth-order diffraction light from the object.

On the limits of low-numerical-aperture imaging scatterometry.

Although imaging scatterometry has been demonstrated to be a powerful technique for characterization of nano-gratings when high lateral resolution is required, some limits of this novel technique are still undisclosed yet, such as the constraint for the imaging numerical aperture (NA), the number of unit cells for accurate grating reconstruction, and the analyzability of image pixels associated with the grating region. To this end, we establish a vectorial image formation (VIF) model for imaging scatterometry based on the finite-difference time-domain (FDTD) method and vectorial diffraction theory. According to the established VIF model and the simulation results of a Si grating sample with finite numbers of unit cells, we find that accurate grating reconstruction by routine RCWA (rigorous coupled-wave analysis) -based data analysis requires an upper limit for the NA of the employed objective. And enough numbers of unit cells are also required to be covered in the illumination spot. Only in these conditions, the zeroth-order diffraction information of the grating under test can be exclusively and completely collected by the imaging system. Moreover, only the image pixels off the edge of the grating region are analyzable by routine RCWA-based data analysis due to the effect of edge scattering. The required number of grating unit cells and the size of the analyzable region are closely related with the imaging NA and the ratio between the illumination spot size and the size of the grating region D/L. Higher imaging NA or smaller D/L typically requires fewer grating unit cells and meanwhile allows a larger analyzable region. The investigation in this paper promises to provide valuable insights into the application of imaging scatterometry.

Formation of Dynamic and Binocular Three-Dimensional Images in Protective Holograms with Zero Diffraction Order

Variants of implementing trackograms, one of the types of zero-order holograms, for the formation of protective features for non-expert verification of their authenticity are considered. The three-dimensional image in trackograms is formed by glares on the walls of toroidal surfaces-tracks that represent relief stripes with the recording material. Variations in the shape of tracks, their length, and the number of sections of different tracks at one point in the image can provide security features that are convenient for non-expert identification of holograms. Track sizes and depths are compatible with the technology of conventional embossed holograms. Photos of holograms forming images in white light are shown.

Compact vari-focal augmented reality display based on ultrathin, polarization-insensitive, and adaptive liquid crystal lens

Despite the recent advances in augmented reality (AR), which has shown the potential to significantly impact on our daily lives by offering a new way to manipulate and interact with virtual information, minimizing visual discomfort due to the vergence–accommodation conflict remains a challenge. Emerging AR technologies often exploit focus-tunable optics to address this problem. Although they demonstrated improved depth perception by enabling proper focus cues, a bulky form factor of focus–tunable optics prevents their use in the form of a pair of eyeglasses. Here, we propose a novel optical configuration for a compact vari-focal AR display which deliberately utilizes the zeroth and first diffraction orders of the LC lens to produce two foci: one for a real object and the other for a virtual object with addressable focal planes. The prototype AR glasses can adjust the accommodation distance of the virtual image, mitigating the vergence–accommodation conflict without substantially compromising the form factor or image quality. In addition, we describe the design, fabrication, and characterization of an ultrathin, polarization-insensitive focus-tunable liquid crystal (LC) diffractive lens with a large aperture, a low weight, and a low operating voltage. We show that the polarization dependence of the lens, which is an inherent optical property of LC lenses, can be insensitive using the trilayer birefringent materials and by aligning the optical axes of each birefringent material at a specific angle. The polarization insensitivity eliminates the need for a polarizer, thus further reducing the form factor of the optical system. This novel approach offers significantly reduced complexity for designing AR glasses with addressable focal planes. These technologies for ultrathin lens and AR display show promising potential for developing compact optical systems in various applications.

A Side-Absorption Concentrated Module with a Diffractive Optical Element as a Spectral-Beam-Splitter for a Hybrid-Collecting Solar System

In this paper, we propose a side-absorption concentrated module with diffractive grating as a spectral-beam-splitter to divide sunlight into visible and infrared parts. The separate solar energy can be applied to different energy conversion devices or diverse applications, such as hybrid PV/T solar systems and other hybrid-collecting solar systems. Via the optimization of the geometric parameters of the diffractive grating, such as the grating period and height, the visible and the infrared bands can dominate the first and the zeroth diffraction orders, respectively. The designed grating integrated with the lens and the light-guide forms the proposed module, which is able to export visible and infrared light individually. This module is demonstrated in the form of an array consisting of seven units, successfully out-coupling the spectral-split beams by separate planar ports. Considering the whole solar spectrum, the simulated and measured module efficiencies of this module were 45.2% and 34.8%, respectively. Analyses of the efficiency loss indicated that the improvement of the module efficiency lies in the high fill-factor lens array, the high-reflectance coating, and less scattering.

Real-time phase measurement and correction of dynamic multimode beam using a single spatial light modulator

In this Letter, a novel system for adaptively correcting the phase of a dynamic multimode beam is proposed. While using merely one spatial light modulator, the phase measurement of the first-order diffraction pattern and the correction of the zeroth diffraction order are simultaneously realized. The real-time experimental result is obtained at a control rate of 10 Hz. The power-in-the-bucket value is improved from 38.5% to 61.8%, even with fundamental mode content that is consistently below 30%. To the best of our knowledge, this is the first implementation of real-time adaptive correction of the entire multimode beam.

High-precision microdisplacement sensor based on zeroth-order diffraction using a single-layer optical grating.

A high-precision microdisplacement sensor based on zeroth-order diffraction of a single-layer optical grating is reported. Laser grating interference occurs when part of the laser is reflected diffraction by the grating and another part is vertically reflected back by a mirror and diffracted again by the grating, thus generating optical interferometric detection. For the purpose of obtaining the optimal contrast of the optical interferometric detection, the duty cycle of the grating and the orders of diffraction were optimized by the diffraction scalar theory. The microdisplacement sensor demonstrates a sensitivity of 0.40%/nm, a resolution of 0.6 nm, and a full-scale range of up to 100 µm. This work enables a high-performance displacement sensor, and provides a theoretical and technical basis for the design of a displacement sensor with an ultracompact structure.

Lattice-depth measurement using continuous grating atom diffraction

We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, which leads to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally we present a steady-state solution to the finite-temperature system, which in principle makes possible the measurement of both the lattice depth, and initial temperature of the atomic gas simultaneously.

Tunable Diffraction Gratings in Copolymer Network Liquid Crystals Driven with Interdigitated Electrodes

The diffraction behavior of a polymer network liquid crystal (PNLC) was studied in in-plane switching (IPS) test cells and compared to the behavior seen in a neat liquid crystal. Due to the presence of polymer, the diffraction behavior was varied drastically: PNLCs are composites, which possess a specific domain size. The size of such polymer-induced domains was investigated with polarized optical microscopy and scanning electron microscopy. PNLCs are capable of continuous optical-phase modulation. It was found that electrical addressing with nonhomogenous electric fields can be useful to vary the phase modulation profile as compared to a neat LC. The diffraction patterns seen in a nematic LC were influenced by the applied addressing voltage and showed some limited tunability already. However, in the PNLC, the diffraction patterns were drastically varied as compared to a neat nematic LC. These gratings showed responses localized to the electrodes, had higher tuneability, and could also be useful to partially suppress the zeroth-diffraction order. Depending on the applied voltage, the diffraction efficiency could be tuned, efficiently. The presented results are instructive to understand the impact of a polymer network on the field-dependent reorientation of the liquid crystal director: if addressed with the same electric field profile, the responses were much more localized than in a neat nematic LC. In a straightforward numerical approach, domains in the PNLC samples were described by using cuboids. Diffraction patterns were then calculated based on the director reorientations seen and compared to the experimental data.