Relief Gratings Research Articles

Diffraction by gratings: from the C-method to the stochastic C-method

The Chandezon, or C-method, is an efficient and versatile numerical method for modeling diffraction problems involving smooth surface relief gratings. For some grating profiles, the C-method is limited when the height-to-period ratio exceeds a factor of three. This is due to the formation of ill-conditioned matrices for inversion. Here, the stochastic C-method (SCM) is introduced as a solution that leverages stochastic differential equations to overcome these numerical difficulties. The SCM is developed by altering the physical model of the grating profile function to include an additive Brownian noise component. The inclusion of noise dramatically expands the applicability of the C-method and enriches the physical model. Numerical experiments show that the SCM achieves a precision on the order of 10−5 for diffracted/transmitted amplitudes on sinusoidal profiles with height-to-period ratios as high as 72. These results are in agreement with those obtained using multi-precision and the rigorous coupled wave analysis (RCWA).

Holographic surface relief diffraction gratings made of hydrogels for direct label-free biosensing of IgGs

This work describes the development of a label-free (LF) biosensing platform for the direct detection of targets based on diffractive structures fabricated with acrylamide-based hydrogels biofunctionalized with proteins and antibodies. Hydrogels containing Bovine Serum Albumin protein (BSA) with different crosslinking degrees were synthesized and characterized to find the optimal conditions for the suitable fabrication of surface relief gratings (SRGs). The bioavailability of BSA-functionalized hydrogels for the specific recognition of anti-BSA antibodies was verified by fluorescence detection. After the hydrogel-based SRG fabrication, diffraction efficiency measures at two different laser wavelengths were used for the direct LF detection of anti-BSA antibodies. The limit of detection in the sub mg L−1 range was read. Additionally, SRGs were prepared with hydrogels biofunctionalized with anti-rabbit antibodies for the direct detection of IgGs from rabbit serum, obtaining similar analytical performance without the necessity of labeling or applying amplification strategies.

3‐1: Invited Paper: Reality Versus Simulations in Diffractive Waveguide Combiners

Dispelix has developed an advanced design toolset capable of optimizing the image quality and performance of augmented reality near‐eye and head‐up displays based on diffractive waveguide technology. The design toolset can solve the unique challenge prevalent in diffractive optical waveguide systems by accurately simulating the operation of nano‐scale diffractive surface relief gratings in an optical waveguide with macro‐scale dimensions. This paper presents simulation results of key performance metrics and compares them to measurement data from samples manufactured by state‐of‐the‐art nanofabrication tools.

95‐1: Augmented Reality Display Based on Surface Relief Grating with Large Area Processing

AR display has been the most promising new technology in the current display market. Among which surface relief grating waveguide has the advantages of large field of view, small volume and light weight. This article adopts the large‐area (370 mm * 470 mm) waveguide prepraration route as a solution to the low‐cost and high‐efficiency waveguide route, showing excellent structural uniformity of more than 95%. The waveguide numbers is 5 to 10 times that of the conventional wafer‐level route, which can further promote the practical application of AR waveguides.

Design and fabrication of polygonal grating waveguide display with full-color 2D eye-box expansion

Over the past few decades, the surface relief grating (SRG) based waveguide display technology has attracted significant interest in the augmented reality community due to its light weight, small form factor and ease of mass production. However, the intuition grating structure restricts the optimization freedom which limits the display quality of full-color SRG waveguide. To address this issue the 2D polygonal grating is presented since it has a higher freedom degree in optimizing color uniformity compared to intuition grating structure. By using the 2D polygonal grating we also proposed a design approach of full-color SRG waveguide with hierarchical optimization method. To validate this design, a 2D polygonal grating-based waveguide composed of double layers waveguide was fabricated by using EBL and nanoimprinting technology. The final experimental results show that the 2D eye-box expansion (EPE) waveguide has a field of view (FOV) of 40°, an eye-box of 15 mm × 12 mm, at an eye relief (ERF) of 25 mm, and the overall luminance uniformity is 60 %.

Photoresponse of new azo pyridine functionalized poly(2-hydroxyethyl methacrylate-co-methyl methacrylate)

A new azo polymer containing photoisomerizable azo pyridine functionalities was synthesized via Mitsunobu reaction of 4-(4-hydroxyphenylazo)pyridine with poly(2-hydroxyethyl methacrylate-co-methyl methacrylate) (p(HEMA-co-MMA)) for creating new photochromic materials. The resulting polymer with azo pyridine side groups was characterized for structural, thermal, and optical properties. UV–vis, 1H NMR and IR spectroscopies confirmed that all hydroxyl groups in p(HEMA-co-MMA) were substituted with azo dye. The obtained azo copolymer exhibited high thermal stability (around 240 °C) and a glass transition temperature (113 °C), promising for applications. The trans-to-cis isomerization upon UV irradiation and the thermal back reaction of the azo chromophore in the copolymer in the solid state was studied. A photostationary state with 50% content of cis-isomers upon 6 min of UV irradiation was reached, and during 48 h dark relaxation at ambient temperature, all cis-isomers converted to the trans form. Additionally, the possibility of efficient photogeneration of surface relief gratings with high amplitude of azo copolymer surface modulation was demonstrated.

Azobenzene‐containing liquid crystalline poly(methacrylates) with different spacer length as media for holographic grating recording

AbstractLiquid crystalline (LC) poly(methacrylates) with azobenzene moieties in their side chains have been synthesized and their chemical structure has been confirmed with nuclear magnetic resonance spectroscopy and gel permeation chromatography. Azobenzene moieties are linked to polymer backbone via an alkyl spacer with length from 2 to 10 methylene units. Photooptical processes in thin amorphized polymer films are examined through measurements of optical anisotropy and holographic grating recording. Birefringence values induced with a linearly polarized green (532 nm) laser beam has strongly depended from the spacer length. Irradiation with two circularly polarized green laser beams leads to the formation of polarization and surface relief gratings, which have been visualized with polarized optical and atomic force microscopy, respectively. Diffraction efficiency of the recorded gratings is in correlation with the spacer length, namely, the shorter the spacer, the higher diffraction efficiency can be achieved. For polymers with short spacers polarization gratings can be easily erased by circularly polarized light, but only partial erasing of surface relief gratings is observed. The results presented offer the possibility of tailoring the chemical structure of azobenzene‐containing polymers for designing high‐efficiency media for the holographic recording.

Stacked Polarizing Elements for Controlling Parameters of Surface Relief Gratings Written in Photosensitive Materials.

Photosensitive materials are widely used for the direct fabrication of surface relief gratings (SRGs) without the selective etching of the material. It is known that the interferometric approach makes it possible to fabricate SRGs with submicron and even subwavelength periods. However, to change the period of the written SRGs, it is necessary to change the convergence angle, shift a sample, and readjust the interferometric setup. Recently, it was shown that structured laser beams with predetermined, periodically modulated polarization distributions can also be used to fabricate SRGs. A structured laser beam with the desired polarization distribution can be formed with just one polarizing optical element-for example, the so-called depolarizer, a patterned micro-retarder array. The use of such stacked elements makes it possible to directly control the modulation period of the polarization of the generated laser beam. We show that this approach allows one to fabricate SRGs with submicron periods. Moreover, the addition of q-plates, elements effectively used to generate cylindrical vector beams with polarization singularities, allows the efficient formation of fork polarization gratings (FPGs) and the fabrication of higher-order fork-shaped SRGs. Full control of the parameters of the generated FPGs is possible. We demonstrate the formation of FPGs of higher orders (up to 12) by only adding first- and second-order q-plates and half-wave plates to the depolarizers. In this work, we numerically and experimentally study the parameters of various types of SRGs formed using these stacked polarizing elements and show the significant potential of this method for the laser processing of photosensitive materials, which often also serve as polarization sensors.

Guided mode resonances for angular and spectral filtering

The development of devices based on compact waveguides is a rapidly evolving field. A unique variation of such devices is the Fano-like resonance dielectric spectral and spatial filtre, made from a dielectric conformal thin film on a surface relief grating. It can be used in a normal (or oblique) angle-of-incidence configuration. This device facilitates directional selectivity, which is useful for transverse-mode cleaning in short optical cavities. It can also be enhanced by using leaky-mode effects to produce even sharper spectral features. However, a perfect spatial filtre should be as invariant as possible in the spectral and enhanced angular domains. Here, we solved the inverse design problem to produce such an effect. Numerically, we tuned the surface profile of the substrate grating, assuming a conformal layer on top. This resulted in trapezoidal relief patterns followed by narrow flat-top angular features. The combination of leaky mode effect and enhanced device topology will enable efficient and useful devices with a bandwidth of 50 nm and even more in the future.

Creating Supramolecular Functional Materials via Nucleobase Interaction: Investigating Molecular Recognition and the Fabrication of Surface Relief Gratings

Creating Supramolecular Functional Materials via Nucleobase Interaction: Investigating Molecular Recognition and the Fabrication of Surface Relief Gratings

Complex Fourier Surfaces by Superposition of Multiple Gratings on Azobenzene Thin Films

AbstractDiffractive optical elements (DOE) are integral components for lightweight and ultra‐thin optical elements due to their ability to manipulate light efficiently and accurately. However, conventional DOEs are static and cannot be altered after fabrication, which hinders their adaptability to changing requirements. To overcome this limitation, the potential of surface patterning on azobenzene thin films to fabricate reconfigurable DOEs is investigated. Using holographic lithography, surface topographies with sinusoidal surface relief gratings (SRG) are created and the superposition of up to 80 SRGs with high accuracy and minimal information loss in subsequent inscriptions is demonstrated. This is enabled by a surface patterning tool combining holographic lithography and digital holographic microscopy. Reconfigurable and adaptive optical elements can improve the efficiency of optical coupling and increase the sensitivity and selectivity of sensors, especially in applications such as near‐eye displays and plasmonic sensors. These results demonstrate the ability to create complex azobenzene‐based DOEs for advanced photonic applications, where the ability to alter optical elements is of high importance.

Directive and coherent thermal emission of hybrid surface plasmon-phonon polaritons in n-GaN gratings of linear and radial shapes

Beaming and coherent thermal emission of the hybrid surface plasmon phonon polaritons (SPPhPs) was numerically and experimentally investigated employing the n-GaN surface relief gratings (SRGs) shaped in a linear and radial geometry. The polariton propagation losses were minimized numerically with the help of a rigorous coupled wave analysis model, while the spatial and temporal quality of selected mode radiation in a normal direction was maximized by fixing the grating period value at 17.5 µm and varying the grating filling factor from 75% to 25%. A set of optimal design linear and radial geometry SRG samples were fabricated in order to validate the emission characteristics of hybrid SPPhPs found by numerical modeling. We demonstrated that both efficient emission and beaming are possible to achieve through the excitation and interference of the same number but opposite sign hybrid polariton modes in n-GaN SRG.

Shaped vibration cutting: A novel fabrication method for mid-infrared relief gratings with controllable profiles

Relief gratings are a particular group of diffractive gratings with a controlled profile, which can precisely modulate the intensity distribution of diffractive lights through its surface structure of depressions and elevations. The mechanical ruling is still one of the most dominant methods for fabricating relief gratings due to its accuracy and capacity to texture free-formed surfaces. However, the ruling has the drawbacks of low material adaptability and inflexible profile adjustability that restrict its wider application. This study invents a novel ruling process, i.e., shaped vibration cutting (SVC), which uses a controllable special-shaped vibration locus of a diamond cutting tool. The tool moves perpendicularly to the cutting plane, enabling the ruling-based fabrication of relief grating on difficult-to-cut materials with flexible control of the grating profile. Slope grooving tests with elliptical and triangular trajectories were performed on aluminum and silicon materials to explore the surface generation and defect formation mechanism comprehensively. The defect-less process window regarding the vibration trajectory, crossfeed, depth of cut, and ruling velocity was identified. Finally, mid-infrared relief gratings were successfully fabricated using the SVC process on aluminum without burrs and silicon in a ductile regime with a maximum depth of 2.3 µm, which outperforms the existing cutting-based texturing technique. To further demonstrate the process capacity of SVC in high material adaptability and flexible profile adjustability, multi-blaze gratings that have spatially varying groove profiles have been fabricated on bulk metallic glass.

Learning from Nature: Fighting Pathogenic Escherichia coli Bacteria Using Nanoplasmonic Metasurfaces

AbstractBioinspired nanoplasmonic 3D crossed surface relief gratings and metasurfaces are fabricated on azobenzene molecular glass thin films to create effective antibacterial surfaces. A synergetic mechanical and photothermal interaction at the interface between the nanostructures and the Escherichia coli (E. coli) bacteria results in a significant decrease in the viable bacterial population. In particular, combined exposure to the interfacial nanospikes as well as the evanescent blue and red electromagnetic fields induced by the nanoplasmonic metasurface, results in a 97% reduction of the viable E. coli in only 25 min, when illuminated with a low‐power white light.

Two-Dimensional Polarization Holographic Gratings in Azopolymer Thin Films: Polarization Properties in the Presence or Absence of Surface Relief

During polarization holographic recording in azopolymer thin films, usually together with the volume anisotropic grating, a surface relief grating (SRG) is also formed. By using two consecutive exposures, it is possible to obtain a two-dimensional (2D) grating. To the best of our knowledge, the polarization properties of such gratings have not been studied yet. To determine the influence of the surface relief on the polarization selectivity of the 2D gratings, we propose two methods to suppress the SRG formation: by varying the recording conditions or varying the sample structure. In these experiments we have used the commercially available azopolymer PAZO, poly[1-4-(3-carboxy-4-hydrophenylazo) benzene sulfonamido]-1,2-ethanediyl, sodium salt] to perform the polarization holographic recording using a 442 nm He-Cd laser. As indicated by our results, when the surface relief is present, it strongly dominates the response of the 2D grating and it behaves almost as a scalar polarization insensitive grating. Conversely, when the SRG formation is suppressed, the polarization properties of the 2D grating in all four diffracted orders are very well pronounced. In this way, we demonstrate that we can easily control SRG formation and, if desired, obtain 2D grating with high surface relief modulation, or alternatively record polarization-selective 2D gratings with virtually no surface relief.

Complex Monte Carlo Light-Driven Dynamics of Monomers in Functionalized Bond Fluctuation Model Polymer Chains.

We study Monte Carlo dynamics of the monomers and center of mass of a model polymer chain functionalized with azobenzene molecules in the presence of an inhomogeneous linearly polarized laser light. The simulations use a generalized Bond Fluctuation Model. The mean squared displacements of the monomers and the center of mass are analyzed in a period of Monte Carlo time typical for a build-up of Surface Relief Grating. Approximate scaling laws for mean squared displacements are found and interpreted in terms of sub- and superdiffusive dynamics for the monomers and center of mass. A counterintuitive effect is observed, where the monomers perform subdiffusive motion but the resulting motion of the center of mass is superdiffusive. This result disparages theoretical approaches based on an assumption that the dynamics of single monomers in a chain can be characterized in terms of independent identically distributed random variables.

Direct magnetic and surface relief patterning using carbazole-based azopolymer

The results on using of carbazole-based azopolymer layers (Polyepoxypropylcarbazole:Methyl Red with magnetic particles of Fe2SO4) for the recording of 1-D and 2-D surface relief gratings are presented in this report. Morphology study using AFM and MFM of obtained structures has shown their good quality. Surface relief gratings with profile height up to 1.2 µm were obtained during the holographic recording using blue laser. Along with surface relief grating it was shown the direct formation of magnetic relief. Possibility of simultaneous direct fabrication of surface and magnetic relief by optical holographic recording using azopolymer thin films as recording media was shown.

Understanding the formation of surface relief gratings in azopolymers: A combined molecular dynamics and experimental study.

The formation of surface relief gratings in thin azopolymeric films is investigated using atomistic molecular dynamics simulations and compared to experimental results for the specific case of poly-disperse-orange3-methyl-methacrylate. For this purpose, the film is illuminated with a light pattern of alternating bright and dark stripes in both cases. The simulations use a molecular mechanics switching potential to explicitly describe the photoisomerization dynamics between the E and Z isomers of the azo-units and take into account the orientation of the transition dipole moment with respect to the light polarization. Local heating and elevation of the illuminated regions with the subsequent movement of molecules into the neighboring dark regions are observed. This leads to the formation of valleys in the bright areas after re-cooling and is independent of the polarization direction. To verify these observations experimentally, the azopolymer film is illuminated with bright stripes of varying width using a spatial light modulator. Atomic force microscopy images confirm that the elevated areas correspond to the previously dark areas. In the experiment, the polarization of the incident light makes only a small difference since tiny grain-like structures form in the valleys only when the polarization is parallel to the stripes.

Viscoplastic Modeling of Surface Relief Grating Growth on Isotropic and Preoriented Azopolymer Films.

We report on solving of two intriguing issues concerning the inscription of surface relief gratings within azopolymer thin films under irradiation with SS, PP and RL interference patterns. For this, we utilize the orientation approach and viscoplastic modeling in combination with experimental results, where the change in surface topography is acquired in situ during irradiation with modulated light. First, the initial orientation state of polymer backbones is proved to be responsible for the contradictory experimental reports on the efficiency of the SS interference pattern. Different orientation states can influence not only the phase of SS grating but also its height, which is experimentally confirmed by using special pretreatments. Second, the faster growth of gratings inscribed by the RL interference pattern is shown to be promoted by a weak photosoftening effect. Overall, the modeled results are in good agreement with the order of relative growth efficiency: RL-PP-SS.

Влияние поля коронного разряда на формирование голографических дифракционных решеток в пленках As-=SUB=-40-=/SUB=-S-=SUB=-60-x-=/SUB=-Se-=SUB=-x-=/SUB=-

The influence of the corona discharge on the holographic recording and the subsequence chemical etching of the recording holographic gratings in the Cr/As40S60-xSex thin film structures was investigated. It was established that applied of the positive corona discharge leads to the increase of the holographic sensitivity during the recording in the As-S-Se films, as well as to the amplification of the diffraction efficiency of the recording gratings and of the relief-phase diffractive gratings obtaining in the result of the consecutive chemical etching. Among the investigated films of the As40S60-xSex system, the best results on the application of the Argon laser irradiation (=488 nm) was obtaining for the composition As40S39Se21. Applied of the corona discharge bring to the increase of the holographic sensitivity more than up two order, and of the diffraction efficiency about three order in the respect of the of the ordinary recording. Reciprocally was reached a amplification of the diffraction efficiency of the relief diffraction gratings formed in the result of the sequent chemical etching up to 30 %.