Grating Period Research Articles

Ultra-high spatial resolutions in photopatterning molecular orientations

Accurately aligning liquid crystal molecules into predetermined spatially variant orientations is crucial for fabricating devices such as flat optical elements, soft actuators and robots. Despite the developments of various photopatterning techniques for this purpose, the limits of their spatial resolutions have been rarely addressed. In this study, we delve into the physical constraints governing the spatial resolutions of two prominent photopatterning methods: single exposure to light fields with structured polarizations and multi-exposures to light fields with structured intensities. Theoretical analyses show that the minimal grating period of the first method is only half of the Abbe limit of an intensity imaging system, and that the minimal grating period for the second system can surpass the Rayleigh limit. Experimental studies demonstrate unprecedent high spatial resolution with minimal grating periods of 1 µm. We further establish that the minimal core size in photopatterned singular topological defects is linearly proportional to the minimal grating period and the topological charge and that these photopatterning techniques can yield less than 1 µm defect cores that are in high demand for applications such as coronagraphs.

Impact of Silicon Dioxide Periodic Grating Structure on Electrical Properties of Graphene

Our study breaks away from the conventional focus on 3D transistor structures, aiming to explore the potential of two-dimensional materials. Graphene, a key player of two-dimensional materials, draws significant attention due to its exceptional electrical properties and chemical stability. Rather than delving into the intrinsic properties of graphene, our research focuses on examining the impact that other materials in contact with graphene have on graphene’s behavior. With a thickness of just one atomic layer, graphene's band structure is easily influenced by materials in contact with it, giving rise to the Surface Charge Transfer Doping (SCTD) effect. Our study involves the utilization of e-beam lithography to define 140 nm gratings and RIE to etch into SiO2 substrates. Subsequently, graphene is transferred onto these SiO2 gratings. Within these grating regions, in other words, graphene is supported by SiO2, while other part of the graphene is suspended. By strategically forming alternatively supported/suspended type of graphene in period of 140 nm through these gratings, our aim is to unravel the impact on the electrical characteristics of graphene along both the vertical and horizontal axes. In vertical direction, we measured contact resistance between graphene and metal; in horizontal, we measured the difference of Id-Vg curve caused by the grating structure under graphene channel. This exploration emerges from the quest to harness novel properties in the face of evolving fabrication methodologies.To have 140 nm grating, we chose e-beam lithography in defining the nano grating pattern. Initially, a clean wafer was coated with chromium, and e-beam resist Zep-520A was spin-coated and soft-baked. Subsequently, using e-beam lithography, we defined the periodic pattern. Following this, ICP-RIE was employed for dry etching of chromium, and the resist was removed. Then, ICP-RIE, with chromium as the hard mask, was utilized for dry etching of SiO2. Finally, the chromium was immersed in a chromium etchant solution, resulting in a periodic grating structure with a depth of 100nm on SiO2. This marks the completion of the first part of the fabrication process. In the second part of fabrication process, we transferred graphene, prepared through CVD, onto the SiO2 substrate with periodic gratings defined through etching. We employed optical lithography to define patterns for transmission line method (TLM) measurements. These patterns were aligned with positions defined by e-beam, ensuring that the graphene-metal contact positions precisely coincided with the underlying grating structure. Utilizing TLM, we measured the contact resistance, enabling the study of the impact of the grating on the electrical properties of graphene in the vertical direction. The fabrication flow can be schematically shown in Fig. 1.By using ELS-7000 (E-beam writer) and Oxford ICP-RIE, we successfully achieved ~140 nm grating structure on silicon dioxide with depth of 100nm, which is observed on SEM as shown in Fig. 2. Then we measured the I-V curve by 4200A-SCS and calculated contact resistance by TLM. The preliminary results of the contact resistance measurement are shown in the Fig. 3. The I-V curve shows that as the channel length increases, the total resistance increases, which is aligned with the assumptions of TLM. We can further calculate the contact resistance through the Y-axis intercept of channel length-resistance curve. With the same process, we can explore the electrical variations of graphene with graphene-metal contact resistance and current-voltage relationship. Figure 1

Dynamic surface gratings for optical encryption: A simple approach based on azobenzene photoisomerization and solvent engineering

Dynamic diffraction gratings are optical devices that allow for non-mechanical, non-contact and remote on-demand control, and have garnered significant interest in optical encryption. Azobenzene materials are ideal materials for developing dynamic gratings owing to the advantages of fast photo isomerization and good reversibility. It is still challenging to precisely fabricate ordered periodic gratings on the surfaces of azobenzene materials. Here, controllable dynamic grating patterns were successfully fabricated by mask exposure and solvent engineering on azobenzene polyamide acid (PAA-Azo)-solvent system. The movement and mass migration of polymer chains can be regulated by modulating the intermolecular hydrogen bonding and free volume based on different solvents and solvent contents within the system, resulting in the formation of surface gratings with customizable morphology and light-splitting ability. Finally, by regulating the periodicity and amplitude of gratings, colorful dynamic patterns were obtained to monitor the expiration of light-sensitive and short shelf-life products, based on the azobenzene polyamide acid (PAA-Azo)-solvent system. This work provides a new and simple approach for controllable preparation of high-regularity and high-performance dynamic gratings.

A flexible nanostructured multimodal sensor based on surface plasmon resonance

Biosensors are of great significance for human health and safety monitoring, especially the sensor based on Surface Plasmon Resonance (SPR), widely used in biomolecular detection. Improving its sensitivity has always been the focus of research. In this paper, SPR in grating structures was primarily investigated and then a SPR-based nanoscale metal grating sensor was proposed. With Finite Difference Time Domain (FDTD) simulation, optimization of the sensor's duty ratio, thickness of the Gold (Au) layer, and periodic parameters was conducted. Then sensitivity and quality factor of the sensor are analyzed to obtain the optimal sensor parameters. With a grating period of 0.64 μm, Au layer thickness of 30 nm, and sensor's fill factor of 0.625, the sensor achieves a sensitivity of 0.417 μm/refractive index unit (RIU), demonstrating optimal performance. Additionally, Abaqus tensile simulations were performed on the grating imprinting section, validating the uniformity and consistency of strain in the Polydimethylsiloxane (PDMS) substrate-Au film grating structure during stretching. Finally, a combination mold based on acrylic material is designed, effectively addressing the challenging demolding characteristics of cured PDMS material, offering an efficient manufacturing approach for PDMS substrate fabrication. The SPR-based nanoscale grating multimodal sensor designed in this paper exhibits high sensitivity and potential cost-effectiveness in protein molecule detection and flexible stress-strain sensing applications, revealing promising broad prospects for practical utilization.

Talbot phenomenon in binary optical gratings under Gaussian illumination

Binary optical gratings are used in applications such as optical metrology. Due to the fact, that self-imaging phenomenon depends on the grating fill factor, in present work the effect of fill factor on Talbot image formation has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used to determine the intensity distribution in the near field. Self-images are obtained under different initial beam conditions and it is found several regimes of the effect of Gaussian beam intensity distribution on the self-images are found: (I) decreasing intensity of grating slit at the beam border when Gaussian waist radius is 10 times greater than grating period, (II) transforming binary-like self-image to the cosine-like one in case when Gaussian waist radius ranges from 2 to 5 grating periods, and (III) disappearing regular grating structure when Gaussian waist radius is less than grating period. Additionally it is analyzed transform from Fresnel to Fraunhofer regime in case of Gaussian beam and effect of wavefront curvature radius value on the distance where different regimes appear.

Temperature dependence of LiTaO3 refractive index: corrections of Sellmeier equation

We report a new and more precise Sellmeier equation obtained by using the analysis of quasi-phase-matching curves of the optical parametric generation (OPG) in 1D periodically poled LiTaO3 (1D-PPLT) of different grating periods.

Modelling and experimental study of surface morphology evolution during layer growth on nanograting structures

Coating nano/micro-structured elements with a single or multi-layered film can greatly enhance their functionality. The experimental enhancement, however, is significantly limited by the smoothing and distortion of the structural profile after coating. This requires a comprehensive understanding of the layer growth behavior on nanoscale non-isotropic surface with a proper model to analyze and predict the structure evolution. Here, a simplified linear growth model with single free parameter was successfully used for analysis of the smoothening of grating grooves. The model enables a quantitative description of the evolution of surface morphology from substrate to the top surface with sub-nanometer accuracy. Based on this, the smoothing behavior of single-Si layer and W/Si multilayer growth on nanoscale gratings (period ∼ 40 nm) and flat substrates were studied experimentally, for applications in X-ray optics. The smoothing effect of the W/Si multilayer coating is more pronounced than that of the single Si layer for both substrate types. The corrugated nanogratings suppressed the smoothing effect as compared to the flat isotropic surface. These works provide new guidance to predict and control the growth of layers on nanostructures.

Multidimensional Position And Displacement Estimation Using Periodic Coded Optical Apertures In A Single Camera Imaging System

Accurately estimating multidimensional positions and displacements in fluid dynamic experiments is essential for understanding complex flow phenomena. This paper presents a novel optical measurement setup capable of determining velocity fields using periodic coded optical apertures in a single-camera imaging system. Our method involves placing a periodic transmission grating in front of the optical system and aligning a laser beam along the system’s optical axis. When particles intersect the laser beam, they scatter light, producing out-of-focus images on the imaging sensor resembling the periodic grating. The size and position of these images vary with the distance to the imaging system and the offset from the optical axis, allowing for accurate determination of particle positions. We derive mathematical formulas describing the imaging system and the relationship between image properties and particle positions and verify them through simulations. Additionally, we develop a calibration method enabling arbitrary optical imaging systems to be used with this technique. Finally, we demonstrate the effectiveness of our approach by measuring velocity fields near a ducted ship propeller, a practical application that underscores the real-world impact of our research in fluid dynamics.

Variable Spatial Dynamics of Optical Vortices Produced by a Double Fork‐Shaped Grating

AbstractLight diffraction is studied numerically and experimentally on a double fork‐shaped grating representing a periodic grating containing two spaced dislocations. The spatial dynamics of the phase singularities (optical vortices) has been investigated as a function of dislocation parameters. Produced optical vortices affect each other while propagating in a free space. For dislocations of the same topological charge, the propagation trajectories and their transverse displacement coordinates depend on the dislocation spacing, and the larger the dislocation spacing, the smaller the relative displacement of the optical vortices and the smaller their trajectory curvatures. For oppositely charged dislocations, three types of spatial behavior of optical vortices are found. The numerical results agree well with the experimental data.

Neutron-absorption gratings fabricated by ultrasound-assisted filling method based on gadolinium particles

Neutron differential phase-contrast imaging (DPCI) plays a pivotal role in analyzing magnetic domain structures and field gradients in materials, necessitating high-quality neutron absorption gratings for enhanced fringe contrast. Traditional fabrication techniques, typically filling gadolinium (Gd) or Gd-containing materials into the corresponding grating structures, face challenges in achieving optimal Gd filling ratios and thickness, limiting the neutron DPCI system’s performance. This paper introduces an approach utilizing ultrasound-assisted filling method to introduce Gd particles into grating trenches with dense deposition, achieving an absorption grating period of 42 μm. This method achieves an equivalent Gd thickness of 80.3 μm, corresponding to the filling ratio of 53.53%, as confirmed by scanning electron microscopy and x-ray micro-imaging. The utilization of an ultrasound not only improves the Gd filling ratio, but also suggests potential scalability for large-area grating production, marking a significant advancement in neutron DPCI technology by providing high-quality components.

Versatile femtosecond laser interference patterning applied to high-precision nanostructuring of silicon

We present a high-precision nanostructuring technique based on beam interference from a commercial Ti:Sa femtosecond amplified laser (800 nm, 120 fs, 1 kHz, 1 mJ). Its potential and versatility is illustrated by applying the technique to the nanostructuring of silicon. Employing commercial and ad-hoc laser-fabricated diffractive optical elements together with standard optical components, periodic line gratings and spot arrays with tunable periods down to 650 nm can readily be fabricated. Moreover, fabrication of millimeter-size diffraction gratings via multipulse irradiation at processing speeds up to 0.5 mm/s is demonstrated. The variety of structures written in crystalline silicon feature amorphous fringes and dots with widths down to 300 nm. The corresponding complex topography profiles consist of surface elevations and depressions with sizes down to 120 nm that can be controlled by the laser fluence and fringe width, demonstrating the presence of several competing matter reorganization processes in the molten phase. The exceptional high-contrast ratio of the fringe intensity together with a near-Gaussian intensity envelope of the laser spot enable patterning with well-defined local fluences, paving the way for single-pulse fluence-dependent studies. The high-quality experimental data that can be obtained with this technique can prove critical for modelling attempts aimed at unravelling the underlying formation mechanisms of complex surface topographies in a wide range of materials. Furthermore, the technique presented here has outstanding potential for the rapid and versatile fabrication of high-precision metasurfaces.

Refractive index sensing characteristics of long-period gratings in linearly arranged three-core fiber

We demonstrate the refractive index (RI) sensing characteristics of long-period gratings (LPGs) in linearly arranged three-core fiber (TCF), which are fabricated using arc discharge technique. Due to the asymmetric index modulation during fabrication, the RI sensitivity of TCF-LPGs in the 0° grating inscription direction is greater than that in the 90° grating inscription direction. The spectral and RI sensing characteristics of TCF-LPGs in the 0° grating inscription direction with different grating periods have been investigated experimentally. In the RI range from 1.4538 to 1.4589, the resonance at 1533.3 nm for TCF-LPGs with grating period of 465 μm could achieve the RI sensitivity of 15943.3 nm/RIU, which could be optimized to 18160.7 nm/RIU at 1676.3 nm as the TCF-LPGs with grating period of 600 μm. Moreover, the proposed TCF-LPGs exhibit notably greater RI sensitivity compared to arc-discharged LPGs in conventional single-mode fibre, presenting substantial advantage in RI sensing. And, changing the polarization state of the incident light enhances the RI sensitivity of TCF-LPGs.Additionally, the influence of bending or temperature interference on the RI sensitivity of TCF-LPGs is minimal, ensuring that interference with RI measurements can be neglected. The proposed sensor boasts cost-effectiveness, simplicity in structure, and high sensitivity to RI, showing substantial potential for applications in chemical and biological sensing.

3‐4: Near‐eye Display with Curved Waveguide for Fashionable Form Factor

Various near‐eye displays have been commercialized over the past decade. They are approaching to be a form of ordinary eyeglasses. The majority of researchers use planar waveguides as combiner, which do not distort the image beam while being transferred along the waveguide. However, planar combiners do not look like eyeglasses because they are flat, not curved. In this work an optical architecture with curved waveguide for near eye display is proposed. Two conditions for image transfer through curved waveguide are defined. These conditions have been satisfied using a compensator and grating with a law of variation of the grating period in the optical architecture. It was verified by prototyping to aim for eyeglasses with 150 mm radius of curvature of the curved waveguide with a thickness of 2 mm, which performs RGB full color, 30 degrees of field of view and 12×10 mm of eye box for all day use.

Multi-order orbital angular momentum mode generators based on integrated long-period fiber gratings.

We propose integrated long-period fiber gratings (LPFGs) fabricated by a CO2 laser to realize a multi-channel and multi-order orbital angular momentum (OAM) mode generator. The integrated LPFG is inscribed on multiple surfaces of the few-mode fiber (FMF) by rotating the fiber in the opposite direction at an angle θ. By controlling the rotation angle, the number of integrated LPFGs can be set. The selected rotation angle is 43 ∘, which can integrate up to nine LPFGs, i.e., realizing that the number of channels for first-order orbital angular momentum (OAM) mode conversion is nine. The integrated LPFGs fabricated in this method allow a flexible design of channel spacing. In addition, the flexible selection of the integrated grating period achieves the simultaneous generation of multi-channel second-order and third-order OAM mode conversion. The multi-channel and multi-order OAM mode generators have important application in optical communication multiplexing systems and OAM sensing.

Period measurement of a periodic structure by using a heterodyne grating interferometer

This paper proposes an alternative method for grating period measurement based on heterodyne grating interferometry. The optical configurations for measuring the period of reflection/transmission gratings were demonstrated, and four commercially available gratings were used to evaluate the effectiveness of the proposed method. Based on the phase-lock technique, the grating period could be obtained immediately through the phase wrapped/unwrapped process. Under precise measurement conditions, the grating period measurement error of the proposed method was better than 1 nm, and the grating period difference between product specifications was less than 1%. In addition, the measurement results of the proposed method also exhibited high similarity with optical microscopy measurements.

Generation of Propagation-Dependent OAM Self-Torque with Chirped Spiral Gratings

The application of non-uniform spiral gratings to control the structure, topological parameters and propagation of orbital angular momentum (OAM) beams was studied experimentally with coherent near-infrared light. Adapted digital spiral grating structures were programmed into the phase map of a high-resolution liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). It is shown that characteristic spatio-spectral anomalies related to Gouy phase shift can be used as pointers to quantify rotational beam properties. Depending on the sign and gradient of spatially variable periods of chirped spiral gratings (CSGs), variations in rotation angle and angular velocity were measured as a function of the propagation distance. Propagation-dependent self-torque is introduced in analogy to known local self-torque phenomena of OAM beams as obtained by the superposition of temporally chirped or phase-modulated wavepackets. Applications in metrology, nonlinear optics or particle trapping are conceivable.

Polymer-based cascaded waveguide Bragg grating for blood glucose sensing.

Waveguide Bragg grating (WBG) blood glucose sensing, as a biological sensing technology with broad application prospects, plays an important role in the fields of health management and medical treatment. In this work, a polymer-based cascaded WBG is applied to glucose detection. We investigated photonic devices with two different grating structures cascaded-a crossed grating and a bilateral grating-and analyzed the effects of the crossed grating period, bilateral grating period, and number of grating periods on the sensing performance of the glucose sensor. Finally, the spectral reflectance characteristics, response time, and sensing specificity of the cascaded WBG were evaluated. The experimental results showed that the glucose sensor has a sensitivity of 175 nm/RIU in a glucose concentration range of 0-2 mg/ml and has the advantages of high integration, a narrow bandwidth, and low cost.

Free electron emission in vacuum assisted by photonic time crystals

The Cerenkov radiation and Smith–Purcell (SP) effect state that free electron emission occurs exclusively in dielectrics when the velocity of the particles exceeds the speed of light in the medium or in the vicinity of periodic gratings close to each other within a vacuum. We demonstrate that free electrons in a vacuum can also emit highly directional monochromatic waves when they are in close proximity to a medium that is periodically modulated temporally, suggesting the existence of the temporal SP effect. The momentum band gaps of time-varying media, such as photonic time crystals (PTCs), create new pathways for the injection of external energy, allowing the frequency, intensity, and spatial distribution of electromagnetic fields to be controlled. Moreover, the PTC substrate enables the conversion of localized evanescent fields into amplified, highly directional propagating plane waves that are only sensitive to the velocity of particles and the modulation frequency, which allows us to observe and utilize Cerenkov-like radiation in free space. Our work presents significant opportunities for the utilization of time-varying structures in various fields, including particle identification, ultraweak signal detection, and improved radiation source design.

Characterization of a perfect sinusoidal grating profile using an artificial neural network for plasmonic-based sensors

In this paper, we present a system intended to detect a targeted perfect sinusoidal profile of a diffraction grating during its manufactured process. Indeed, the sinusoidal nature of the periodic structure is essential to ensure optimal efficiency of specific applications as plasmonic sensors (surface plasmon resonance -based sensors). A neural network is implemented to characterize the geometrical shape of the structure under testing at the end of the laser interference lithography process. This decision tool operates in classifier mode prior to further processing. Then, the geometrical parameters of the structure can be reliably determined if necessary. Two solutions can be considered: the detection of a fixed geometrical shape operating on a binary mode and the identification of a geometrical shape from a limited number of profiles. These methods are validated in the context of plasmonic sensors on experimental sinusoidal grating structures with a grating period of 627 nm.

Qualitative evaluation of a parabolic mirror with substructured Ronchi gratings

In this work we propose to qualitatively test the quality of a concave parabolic mirror by means of the Ronchi interferometric test using substructured gratings to increase the sharpness of the fringes. The substructured gratings are designed considering that the grating period is divided into several stripes of equal width that can be transparent or opaque; the transmission coefficients of the stripes along the grating period are not periodic, but a previously chosen binary sequence. Equations were derived to obtain the corresponding intensity profiles and an analysis of these profiles was performed for different sequences and positions of the substructured gratings with respect to the test mirror. It was experimentally verified that the fringes are sharper at the Rayleigh distance inside and outside the mirror focus.