Diffraction Efficiency Of Gratings Research Articles

The Diffraction Efficiency of Acrylate-Based Holographically Photopolymerized Gratings Enhanced by the Dark Reaction

Photopolymers, especially acrylate-based ones with low cost and simple preparation, are promising materials for high-efficiency holographic gratings. However, it is still challenging to achieve high-performance gratings, due to the influences of many factors. In this work, we found that the dark reaction plays a critical role. The effect of the dark reaction on the optical properties of holographic gratings was investigated. Experimental results reveal that the diffraction efficiency of the gratings can be improved by a factor of three by involving the dark reaction process, and the highest diffraction efficiency for gratings can reach 97.8% after optimization. Therefore, the dark reaction can greatly enhance the optical performance of acrylate-based holographic gratings and other optical elements, thus holding great potential for many applications.

Theoretical efficiency limit of diffractive input couplers in augmented reality waveguides.

Considerable efforts have been devoted to augmented reality (AR) displays to enable the immersive user experience in the wearable glasses form factor. Transparent waveguide combiners offer a compact solution to guide light from the microdisplay to the front of eyes while maintaining the see-through optical path to view the real world simultaneously. To deliver a realistic virtual image with low power consumption, the waveguide combiners need to have high efficiency and good image quality. One important limiting factor for the efficiency of diffractive waveguide combiners is the out-coupling problem in the input couplers, where the guided light interacts with the input gratings again and get partially out-coupled. In this study, we introduce a theoretical model to deterministically find the upper bound of the input efficiency of a uniform input grating, constrained only by Lorentz reciprocity and energy conservation. Our model considers the polarization management at the input coupler and can work for arbitrary input polarization state ensemble. Our model also provides the corresponding characteristics of the input coupler, such as the grating diffraction efficiencies and the Jones matrix of the polarization management components, to achieve the optimal input efficiency. Equipped with this theoretical model, we investigate how the upper bound of input efficiency varies with geometric parameters including the waveguide thickness, the projector pupil size, and the projector pupil relief distance. Our study shines light on the fundamental efficiency limit of input couplers in diffractive waveguide combiners and highlights the benefits of polarization control in improving the input efficiency.

A Study on Length Traceability and Diffraction Efficiency of Chromium Gratings

Measurement traceability is a prerequisite for achieving accurate and reliable results as well as technical standardization. The period of Chromium (Cr) gratings fabricated by atomic lithography can be directly traced back to natural constants. Applying the Cr grating to grating interferometry can achieve nanometer measurement traceability. This research aims to analyze the diffraction efficiency characteristics of self-traceable Cr gratings to provide a theoretical basis for the fabrication and application of Cr gratings. In this regard, we establish the theoretical model of the laser beam incident angle and grating diffraction efficiency using the rigorous coupled-wave method. Then, we analyze the influence of the laser beam incident angle on grating diffraction efficiency by simulation, verify the accuracy of the theoretical model, and finally build a measurement system for grating diffraction efficiency. Through experiments, we find that the diffraction efficiency of the grating shows a rapid increase to reach a stable maximum value followed by a decrease, when a laser beam with a wavelength of 405 nm is incident on the surface of a self-traceable grating in Transverse Magnetic (TM) polarization and the incident angle changes within an effective range. The experimental results are consistent with the trend of theoretical calculation results.

Surface relief coupled grating design for near-eye display

As the most important optical component in a near-eye display system, the performance of a coupling grating directly determines the imaging quality of the final display system. In order to improve the diffraction efficiency and field of view (FOV) of the coupling device, this study proposes a novel surface relief coupling grating. The structural parameters of the surface relief coupled grating are simulated and calculated by using the finite-element analysis method. The simulation results show that the diffraction efficiency of the coupling grating can reach more than 99.5%. Compared with the traditional rectangular tilted grating, the diffraction efficiency has increased by 6.4%, and the full width at half-maximum of the incident angle has increased by 4°, which proves that the structure has higher diffraction efficiency and a larger FOV. Furthermore, the surface relief coupling grating is insensitive to operating conditions and processing errors, fully meeting the processability requirements. Therefore, this new type of surface relief coupling grating can replace traditional coupling gratings and is expected to become a key coupling component in the next generation of near-eye display systems.

Optimal binary gratings for multi-wavelength magneto-optical traps.

Grating magneto-optical traps are an enabling quantum technology for portable metrological devices with ultracold atoms. However, beam diffraction efficiency and angle are affected by wavelength, creating a single-optic design challenge for laser cooling in two stages at two distinct wavelengths - as commonly used for loading, e.g., Sr or Yb atoms into optical lattice or tweezer clocks. Here, we optically characterize a wide variety of binary gratings at different wavelengths to find a simple empirical fit to experimental grating diffraction efficiency data in terms of dimensionless etch depth and period for various duty cycles. The model avoids complex 3D light-grating surface calculations, yet still yields results accurate to a few percent across a broad range of parameters. Gratings optimized for two (or more) wavelengths can now be designed in an informed manner suitable for a wide class of atomic species enabling advanced quantum technologies.

Quad-channel waveguide-based near-eye display for metaverse

We present a quad-channel waveguide-based near-eye display as an ultra-wide-angle architecture for the metaverse. The core concept is to divide one field of view into four by placing the couplers within the regions, where only the subsets of field of view are located. Compared to its counterparts, including the single-, double- and triple- channels, our quad-channel waveguide can push the envelope of field of view further. With the aid of k-space diagram, the upper limit of field of view is illustrated and deduced. The design rules of the waveguide, sawtooth grating as the in-coupler, and slanted grating as the out-coupler are expounded. Through the rigorous coupled-wave analysis, the diffraction efficiencies of gratings can be calculated and optimized. As an overall evaluation, its key performance indicators are summarized as follows. Field of view is 100° (diagonal), eye relief is 10 mm, exit pupil is 11.5 × 11.5 mm2, average transmittance is 2.56 %, and average uniformity is 75 %.

Three-dimensional angular deviation and diffraction efficiency of a grating in Littrow-configuration ECDL

We consider in this paper the angular deviation and diffraction efficiency of the reflection gratings in Littrow-configuration for applications of external cavity diode laser using the rigorous coupled-wave analysis method. We consider the three-dimensional diffraction case in general, where the incidence plane is un-parallel with the grating vector, i.e. conical diffraction. The angular tolerance of arbitrary gratings under plane and conical diffraction are thus derived and presented. A typical blazed grating is chosen as an example to calculate its diffraction efficiency using the rigorous coupled-wave analysis method. Furthermore, we point out that the angular tolerance and reflection efficiency can be improved if the appropriate parameter settings are selected for Littrow-configuration devices, including incidence angle, diffraction order, grating period and blazed angle. Otherwise, a tiny slanting angle of the grating vector deviated from the incidence plane will deviate the feedback light away from entering the laser-diode-chip and halt laser oscillation in the external cavity. Finally, a general rule for the parameter settings in Littrow-configuration is provided as a benchmark.

Femtosecond‐laser micromachining fork gratings in LN crystal with different mechanisms

AbstractIn this work, we used femtosecond‐laser direct writing to fabricate two kinds of modified structures with opposite refractive‐index changes to build fork‐grating configurations in z‐cut LiNbO3 (LN) crystals. Experimental and simulation results indicate that the fork grating combined with the modified area of the refractive index increased and refractive index decreased produces a more effective diffraction effect at 532 nm. The diffraction results of these fork gratings have been investigated. Compared with the fork grating only with the refractive‐index‐decreased filaments, when the incident beam is at transverse magnetic, transverse electric, and circular polarizations, the diffraction efficiency is improved by 5.3%, 4.3%, and 9.6%, respectively. Our work provides a new perspective for improving the diffraction efficiency of fork gratings in LN crystals.

Design of large-deflection-angle high-diffraction-efficiency high-dispersion hybrid gratings

Gratings are key components in many optical systems such as spectrometers. Improving their dispersion is very important for their applications, but improving the single-order diffraction efficiency of an ultrahigh dispersion grating is still very challenging. Here, we propose an analytical approach for the design of a new type of grating named hybrid grating, which consists of a subwavelength grating and a non-subwavelength grating. The proposed analytical approach is based on a physical model in which the non-subwavelength grating acts as an ultrathin reflection grating and the subwavelength grating acts as an antireflection coating. Using the rigorous coupled-wave analysis and the finite-difference time-domain method, we numerically demonstrate that multiple hybrid gratings designed at different wavelengths using the proposed analytical approach show a diffraction efficiency of greater than 95 % in the -1st diffraction order for TE-polarized light, an angular dispersion of greater than 0.8 mrad/nm and a deflection angle of greater than 80°. Furthermore, we numerically demonstrate that by using a combined approach to optimize the parameters of a hybrid grating, the diffraction efficiency in the -1st diffraction order for TE-polarized light can be increased to more than 97 % under the condition that the angular dispersion and the deflection angle of the hybrid grating remain unchanged. Our work provides an avenue for rapid design of gratings with high angular dispersion, large deflection angle and high diffraction efficiency.

Relationship between machining accuracy and optical properties of convex blazed grating in ultra-precision cutting.

For ultra-precision machining of convex blazed grating elements there are inevitable machining errors, surface defects, and surface roughness, all of which can have an impact on their diffraction efficiency. In this paper, we use PCGrate software based on the integration method to establish the machining error model, surface defect model, and surface roughness model of convex spherical blazed grating with a curvature radius of 41.104 mm, a substrate diameter of 14 mm, a grating density of 53.97 line/mm and a blazed angle of 3.86° as the basic specification. To investigate the effect of base curvature radius error, grating period error, blazed angle error, grating ridge and valley passivation radius, Poisson burr height, and blaze surface roughness on their -1 order diffraction efficiency in the 0.95-2.5 µm spectral range. The results show that when the curvature radius error of the spherical base is less than ±80µm, the influence on diffraction efficiency can be ignored. Among the three groups of grating microstructure parameters, the influence of blazed angle on grating diffraction efficiency is the largest, followed by a grating period, and the influence of grating apex angle is the smallest, among which when the error of blazed angle is less than ±0.1° and the error of grating period is less than ±0.1µm, the influence on diffraction efficiency can be ignored. The effect of the passivation radius of the grating valley on the diffraction efficiency is smaller than that of the passivation radius of the grating ridge, and the maximum reduction of diffraction efficiency is 0.096 and 0.144 when the grating ridge and valley passivation radius are 50nm∼650 nm, respectively. The diffraction efficiency decreases significantly in the wavelength range of 1.9-2.5 µm with the increase of Poisson burr height and blaze surface roughness, and its effect on the diffraction efficiency can be neglected when the Poisson burr height is less than 0.5 µm and the blaze surface roughness value is less than RMS 1 nm. The machining error, surface defect, and surface roughness models of the convex blazed grating are optimized to provide a comprehensive machining accuracy basis for ultra-precision cutting of convex grating components.

Study on the influence of surface roughness on the diffraction efficiency of two-dimensional gratings.

This study investigates the effect of surface roughness on the diffraction efficiency of two-dimensional gratings. Firstly, a roughness model was constructed using FDTD, followed by a significant analysis of the ridge roughness, groove roughness, and sidewall roughness on diffraction efficiency. Then, the impact of each roughness type on diffraction efficiency was studied separately. Results indicate that ridge roughness has a negative impact on diffraction efficiency, whereas groove roughness and sidewall roughness have a positive impact on the diffraction efficiency of two-dimensional gratings. When ridge, groove, and sidewall roughness coexist, diffraction efficiency decreases with an increase in roughness, consistent with previous research. However, under conditions of minimal roughness, diffraction efficiency actually increases. Finally, an experiment was conducted to verify the conclusions. The results of this study have significant reference value for the application and development of precision measurement techniques for gratings.

Integrated optical design method for the synchrotron radiation beamlines

In this paper, a new beamline optical system design method is reported in which the calculation of synchrotron radiation source flux distribution, monochromator spectral resolving power, mirror reflectance and grating diffraction efficiency are integrated together in one program to evaluate the whole beamline optical system performance. We demonstrate the advantage of this method by applying it to the Surface Physics beamline at Hefei Light Source to find out better optical system parameters. By using this method, a higher photon flux with the same spectral resolving power than the original design is achieved. The integrated optical system design method provides a great promising application in the beamline optical design and optimization in the future.

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 %.

Optimization method of diffraction efficiency of cascade liquid crystal polarization gratings based on polarization compensation

Optimization method of diffraction efficiency of cascade liquid crystal polarization gratings based on polarization compensation

Analysis and study of the diffraction efficiency of self-traceable grating

Analysis and study of the diffraction efficiency of self-traceable grating

Influence of the corona discharge on the formation of the diffractive holographic gratings in the As-=SUB=-40-=/SUB=-S-=SUB=-60-x-=/SUB=-Se-=SUB=-x-=/SUB=- films

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%. Keywords: chalcogenide vitreous semiconductors, holographic diffractive grating, corona discharge, diffraction efficiency, selective etching.

Кремниевые решетки с блеском для мягкого рентгеновского и экстремального ультрафиолетового излучения: влияние формы профиля штриха и случайной шероховатости на дифракционную эффективность

The effect of the groove profile shape and random roughness of the reflecting facet of five silicon diffraction gratings (1°-4° blaze angle, period 0.4, 1.4, 2, and 4 μm, various coatings) operating in the soft X-ray and extreme ultraviolet radiation ranges on the outflow of the diffraction efficiency from working orders is studied. Diffraction gratings were fabricated by wet etching of Si(111) vicinal wafers and characterized by atomic force microscopy to determine the shape of the groove profile and roughness. The diffraction efficiency of gratings operating in classical and conical diffraction mounts was calculated based on realistic groove profiles by computer simulation using the PCGrateTM code and taking into account the scattering intensity using Nevot-Croce or Debye-Waller corrections or using the Monte Carlo method (rigorously). The effect of the groove profile shape and roughness on the diffraction efficiency of the fabricated Si gratings is shown.

Synthesis, characterization, spectral properties and evaluation of the photophysical behavior of novel Congo Red based polymers

New polyazomethines were synthesized by acid-catalyzed polycondensation of Congo Red azo dye with two dialdehydes to form polymers with azo- and azomethine groups in main chain. Polycondensation proceeded at a reflux temperature in DMF solution with formic acid as a catalyst. Copolymers containing azo- and azomethine groups in main chain were characterized by 1H NMR, FT-IR, and UV–Visible spectrometry, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC). The polymers exhibited photoinduced anisotropy as a result of E-Z photoisomerization. Holograms in thin polymeric films for parallel and perpendicular orientation of the object and reference beams polarization have been recorded. In the case of perpendicular polarization, diffraction efficiencies of the hologram gratings are higher comparing to the parallel. This may be due to the polymer matrix structural rearrangement peculiarities.

Effect of sidewall roughness on the diffraction efficiency of EUV high aspect ratio freestanding transmission gratings.

Manufacturing-induced sidewall roughness has a significant impact on the diffraction efficiency of extreme ultraviolet (EUV) gratings and masks, which could be evaluated by a Debye-Waller damping factor. The rough profile models of line structures are always parallel to the surface for the reflective elements. In this manuscript, a model of rough lines along the thickness direction is established, which cannot be ignored for high aspect ratio transmission gratings. Numerical calculations are carried out using both a rigorous model and a Fraunhofer approximation model. The two models agree with each other on the low-order transmission efficiencies, and the fitted Debye-Waller factor indicates a larger roughness value than that of the model due to the absorption of EUV irradiation for 90° sidewall angle. When the sidewall angle is smaller than 88°, an extra degree of freedom is introduced to the traditional Debye-Waller factor-based formula. The +1-order transmission efficiency and absorptivity with smooth and rough sidewalls are also analyzed, as well as the effect of incidence angle, wavelength and grating thickness.

Diffraction characteristics of orthogonal gratings analysis based on a spatial light modulator.

The diffraction characteristics of orthogonal gratings with variable duty cycles and phase modulation depths are analyzed by using a spatial light modulator. The calculation methods of the transmission function, far-field diffraction light field, and diffraction efficiency of orthogonal gratings are deduced in theory. Meanwhile, the influences of the duty cycle and phase modulation depth on the diffraction characteristics of the orthogonal grating are discussed. The simulation and experimental results verify the correctness of the theoretical derivation. This method can be widely used in the fields of an optical vortex array, laser parallel processing, optical computing, optical communication, and optoelectronic hybrid processing.