Two-dimensional Grating Structures Research Articles

Grating Structures for Silver-Based Surface Plasmon Resonance Sensors with Adjustable Excitation Angle.

Silver-based grating structures offer means for implementing low-cost, efficient grating couplers for use in surface plasmon resonance (SPR) sensors. One-dimensional grating structures with a fixed periodicity are confined to operate effectively within a single planar orientation. However, two-dimensional grating structures as well as grating structures with variable periodicity allow for the plasmon excitation angle to be seamlessly adjusted. This study demonstrates silver-based grating designs that allow for the plasmon excitation angle to be adjusted via rotation or beam position. The flexible angle adjustment opens up the possibility of developing SPR sensor designs with an expanded dynamic range and increased flexibility in sensing applications. The results demonstrate that efficient coupling into two diffraction orders is possible, which ultimately leads to an excitation angle range from 16° to 40° by rotating a single structure. The findings suggest a promising direction for the development of versatile and adaptable SPR sensing platforms with enhanced performance characteristics.

Polarization-independent nonreciprocal thermal radiation by cylindrical grating structure

Due to the significant application value of nonreciprocal thermal radiation in energy collection and conversion, it has always been an active research topic. The current research on polarization-independent nonreciprocal thermal radiation is characterized by low efficiency and a notable disparity in nonreciprocal efficiency between transverse electric (TE) and transverse magnetic (TM) polarizations. To address this issue, a polarization-independent nonreciprocal thermal radiation based on the two-dimensional grating structure is proposed, which is composed of silicon cylindrical grating ridges, magneto-optical materials InAs, and metal Ag. By the rigorous coupled-wave analysis (RCWA), the nonreciprocal efficiency exceeds 90 % at a wavelength of 11.763 μm under both TE and TM polarizations. Meanwhile, the difference in nonreciprocal efficiency between the two polarizations is less than 1 %. Through an examination of the magnetic field and electromagnetic distribution at resonance peaks that are polarization-independent, as well as an analysis of coupling mode theory, we have uncovered the underlying physical mechanisms responsible for this phenomenon. The device is capable of sustaining optimal performance across a wide range of structural parameters, offering a significant role for manufacturing applications. The research proposed in this article provides a novel approach for designing efficient polarization-independent nonreciprocal thermal radiation.

Cost-effective photolithography-based dual liquid crystal alignment for versatile electro-optic applications

Nematic liquid crystals (NLCs) containing rod-shaped molecules exhibit remarkable birefringence and tunability. Therefore, they are of high interest for numerous electro-optic applications. Uniform molecular orientation is of utmost importance for their effective use. Current techniques for LC alignment, such as mechanical rubbing or photo-alignment, have limitations in creating specifically complex LC orientation patterns. To address this issue, we have developed a cost-effective photolithography-based technique for dual LC alignment which combines planar and vertical alignments. Our process involves inexpensive exposure systems and a lift-off process and employs commercially-available alignment materials, thereby reducing production costs. We utilized this process to generate a tunable phase grating with diffraction efficiencies which can be varied through voltage application, thus demonstrating the potential of dual alignment. Furthermore, we investigated smart windows that are insensitive to polarization, utilizing a two-dimensional grating structure, achieving high haze values and dynamic shading without relying on incident polarization.

Optical generation and detection of GHz longitudinal and transverse acoustic waves in solids assisted by two-dimensional metallic grating structure

Absorption of laser pulses with picosecond temporal width in a two-dimensional nano-scale metallic grating deposited on a transparent substrate launches both longitudinal and transverse acoustic waves in to the sample. The periodic metallic structure makes the generated acoustic waves propagate several different directions. The propagating acoustic waves are monitored optically by the delayed light pulses (probe light) as the transient reflectivity change which is known as the Brillouin oscillation. The probe light is also diffracted by the metallic grating, allowing the detection of the acoustic waves propagating in the multiple directions efficiently. The analysis of the Brillouin oscillation frequencies brings the longitudinal and transverse sound velocities and the optical refractive index simultaneously from a single measurement. We verify the above mentioned scheme using a sample with two-dimensional square lattice (period 380 nm) of aluminum square islands of lateral dimension 200 × 200 nm2 and thickness of 50 nm on a fused silica substrate of thickness 1 mm. From the obtained Brillouin oscillation frequencies in several tens GHz, the acoustic and optical properties of the substrate material are successfully retrieved. The technique would be applicable to investigate the acoustic and optical properties of more complicated systems, such as anisotropic and/or inhomogeneous medium.

High-performance refractive index sensor by nano-cylindrical surface structure

In this work, a two-dimensional grating structure based on the metal assisted guided-mode resonance (MAGMR) effect is proposed, which can be used for near infrared band sensing in an aqueous environment. Following optimization by the finite-difference time-domain method, the structure is able to support MAGMR well, and has an excellent reflection dip. The electromagnetic field shows that the structure not only interacts well with the sensing medium but also has a large penetration depth. Results at different refractive indices of the sensing medium confirm the high sensing performance of the proposed MAGMR sensor, which achieves a sensitivity of 852 nm/RIU. Meanwhile, the sensor has a figure of merit up to 4813 RIU−1 (55 times typical GMR sensors) because of the full width at half maximum is only 0.177 nm. Furthermore, the shape and parameters of the MAGMR sensor have been analyzed in detail in order to gain a comprehensive understanding of its performance. This MAGMR sensor is promising for future applications in biomedicine, chemical measurements and environmental monitoring due to its polarization-independent, non-specific angle of incidence, high penetration depth and high sensing performance.

Mechanically stretchable metamaterial with tunable mid-infrared optical properties.

Over the past decade, tremendous efforts have been devoted to the design of metamaterials with ultrahigh absorption. These perfect absorbers can realize the annihilation of incident electromagnetic waves by eliminating reflection and transmission of microwaves, infrared, visible, and ultraviolet. However, the optical properties are usually unchanged due to a rigid structure. In this work, we propose a mechanically stretchable metamaterial composed of polydimethylsiloxane and gold with tunable optical properties in the mid-infrared region. A large variation of absorptances with different gold filling ratios is demonstrated as well as the corresponding electric field distributions. Under moderate uniaxial and biaxial tensions, the proposed two-dimensional grating structure has achieved a dynamic tuning of infrared thermal properties, including a sharp reflectance-absorptance switch. This mechanically stretchable metamaterial can serve different optical and sensing functions due to its facile tunability.

Millimeter-Long Silicon Photonic Antenna for Optical Phased Arrays at 2-μm Wavelength Band

Silicon photonic optical phased arrays are promising solutions for solid-state LIDAR. But the nonlinear absorption significantly saturates the optical power in the waveguides at 1.5-μm wavelengths. Besides, the high refractive index contrast of silicon grating exhibits a strong diffraction strength of the antenna, which results in a limited aperture of the device. These ultimately place a limit on the detection accuracy and reach. Here, a shallow etched two-dimensional subwavelength grating structure is proposed to improve the efficiency and aperture of the waveguide antenna. A reduction of diffraction strength is achieved via nanohole structure instead of conventional grating lines. Thus, a millimeter-long optical antenna is demonstrated with a peak efficiency of 71%. The far-field diffracted beam width of 0.035° and vertical field-of-view of 17.5° are achieved within 100 nm wavelengths range from 1.95 μm to 2.05 μm. The operation at 2-μm waveband also guarantees better eye-safety and significantly reduces the nonlinear absorption in silicon waveguide compared with conventional 1.5-μm band.

Self-referenced refractive index sensor based on hybrid mode resonances in 2D metal-dielectric grating

In this paper, we propose a refractive index sensor with self-reference performance based on a two-dimensional grating structure, mainly consisting of periodic arrays of triple layer dielectric nanodisks and a continuous substrate separated by a thin gold film. Three reflection dips are observed and manipulated to realize self-reference and high sensing performance due to the excitation of magnetic dipole mode resonance, substrate mode resonance and metal layer assisted guide mode resonance. These hybrid modes have been explained by the distributions of the electric and magnetic fields in the nanostructure. A detailed analysis of the influences of material thickness on the optical properties of the proposed refractive index sensor is also investigated. Moreover, the proposed refractive index sensor demonstrates a high sensing performance, an important application for future biomedical applications, with a bulk refractive index sensitivity of 672 nm RIU−1 (RIU: refractive index unit) and figure of merit of 1050 RIU−1. Importantly, the function of self-reference is realized simultaneously. Finally, it also shows excellent sensing performance, with the maximum value exceeding 168 000 by measuring the light intensity change in the reflected light at a certain wavelength. This makes it much more suitable for applications in the field of portable detection.

Near-infrared absorption of graphene-metal nanostructure based on magnetic polaritons

As a two-dimensional material with single-layer carbon atoms, the absorptivity of graphene is only about 2.3% in visible and near-infrared region, which restricts its applications in photoelectric detection, modulation and solar cells. A way to enhance the graphene absorption in this wavelength region is to combine graphene with grating nanostructure. The grating nanostructure can generate strong near-field localization by magnetic polaritons (MPs). However, the existing structures based on MPs are facing some problems, such as sensitivity to the polarization direction of the incoming wave and difficulty in processing the deep grating. Moreover, the modulation effect of the hybrid nanostructure based on MPs combining graphene with nano-grating has not been studied. In this work, a hybrid two-dimensional shallow grating nanostructure is proposed to modulate the absorptivity of graphene based on MPs. The finite element simulation is conducted to calculate the absorptive properties. The equivalent circuit model is used to predict the resonance conditions. The current and field distributions further confirm the excitation of magnetic resonance. The influences of structural parameters and the chemical potential on absorption property are studied. The results show that the magnetic polaritons derived from the hybrid two-dimensional shallow grating structure can obviously improve the absorption of graphene in the near-infrared region. Under the specific structure, the overall absorptivity of the structure is 85%, and the absorptivity of graphene in the structure is 55%, which is over 24 times higher than that of free-standing monolayer graphene. The absorption spectra of the hybrid grating nanostructure for different geometric parameters are calculated. The results show that the absorption peak presents an obvious blue-shift as the thickness of the dielectric layer, the grating period or the width of the silver nanoparticles decrease. Numerical simulation results show that by adjusting the chemical potential of graphene, the overall absorptivity of the structure can be tuned dynamically. The reflection modulation depths of hybrid two-dimensional nanostructure under different structural parameters are calculated. By controlling the chemical potential of graphene in a range from 0.1 eV to 1 eV, the reflection modulation depths of 54.8% (1040 nm), 50.3% (890 nm) and 46.8% (750 nm) are obtained, respectively. Compared with the existing structures based on MPs, the present structure is insensitive to the incidence and polarization direction of the incident electromagnetic wave due to the symmetry in two-dimensional directions. Considering the design of shallow silver grating, the structure is easier to implement in the process. The research results provide good theoretical reference for graphene-based photoelectric detection and modulation.

Coherent radiation at the fundamental frequency by a Smith-Purcell free-electron laser with dielectric substrate

This letter reports an approach to realize coherent radiation at the fundamental frequency of the wave that is resonant with the electron beam in a Smith-Purcell (SP) free-electron laser (FEL). We found that a two-dimensional grating structure equipped with a dielectric substrate could provide an electromagnetic mode which shows the property of a surface wave in the vacuum region where the beam-wave interaction occurs, and operates as a radiative wave in the dielectric region. Thus, an electron beam holding medium energy resonant with the mode could radiate at the fundamental frequency, which is different from the typical Smith-Purcell free-electron laser that radiates only at harmonics of the resonant frequency.

Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd's mirror interferometer.

This paper presents a detailed analysis on the influence of misalignment errors of optical components in an orthogonal two-axis Lloyd's mirror interferometer, which can fabricate two-dimensional grating structures in a single exposure. In an ideal condition, defect-free two-dimensional grating structures can be fabricated by the interferometer. However, in a real case, visible stripes caused by misalignment errors of the optical components in the interferometer always appear on the fabricated grating structures. In this paper, theoretical analysis and experiments are carried out to analyze the influences of the misalignment errors of the optical components in the orthogonal two-axis Lloyd's mirror interferometer.

Electromagnetic resonance modes on a two-dimensional tandem grating and its application for broadband absorption in the visible spectrum.

In this work, we numerically investigate the electromagnetic resonances on two-dimensional tandem grating structures. The base of a tandem grating consists of an opaque Au substrate, a SiO(2) spacer, and a Au grating (concave type); that is, a well-known fishnet structure forming Au/SiO(2)/Au stack. A convex-type Au grating (i.e., topmost grating) is then attached on top of the base fishnet structure with or without additional SiO(2) spacer, resulting in two types of tandem grating structures. In order to calculate the spectral reflectance and local magnetic field distribution, the finite-difference time-domain method is employed. When the topmost Au grating is directly added onto the base fishnet structure, the surface plasmon and magnetic polariton in the base structure are branched out due to the geometric asymmetry with respect to the SiO(2) spacer. If additional SiO(2) spacer is added between the topmost Au grating and the base fishnet structure, new magnetic resonance modes appear due to coupling between two vertically aligned Au/SiO(2)/Au stacks. With the understanding of multiple electromagnetic resonance modes on the proposed tandem grating structures, we successfully design a broadband absorber made of Au and SiO(2) in the visible spectrum.

Improvement of light trapping in thin-film silicon solar cells by combining periodic and random interfaces

The concept of photonic random textures for application as a light-trapping scheme in thin-film solar cells is introduced. Those textures consist of a randomly textured interface, as commonly applied in thin-film solar cells, which is superimposed with a two-dimensional grating structure. The light-scattering properties of those textures are investigated by scalar scattering theory for transmission into the absorber layer and reflection at the back contact. A quantity to describe the light-trapping efficiency is derived and verified by rigorous diffraction theory. The photonic random textures outperform the random textures and the grating structures significantly.

Highly directional thermal emission from two-dimensional silicon structures

We simulate, fabricate, and characterize near perfectly absorbing two-dimensional grating structures in the thermal infrared using heavily doped silicon (HdSi) that supports long wave infrared surface plasmon polaritons (LWIR SPP's). The devices were designed and optimized using both finite difference time domain (FDTD) and rigorous coupled wave analysis (RCWA) simulation techniques to satisfy stringent requirements for thermal management applications requiring high thermal radiation absorption over a narrow angular range and low visible radiation absorption over a broad angular range. After optimization and fabrication, characterization was performed using reflection spectroscopy and normal incidence emissivity measurements. Excellent agreement between simulation and experiment was obtained.

Design of incident angle-independent color filter based on subwavelength two-dimensional gratings

A novel design of reflective color filters based on a two-dimensional subwavelength grating structure is proposed, which exhibits an incident angle independent property with unpolarized incident light in the visible range. By using rigorous coupled-wave analysis method, the effects of the grating period, the groove depth and the size of the structure on the reflectance spectrum are investigated in detail. The structural parameters of the gratings are optimized, and a color filter with high angular tolerance is achieved. Simulation result shows that the maximal reflectance is 56% at 424 nm with a bandwidth of 45 nm, and that the grating can almost keep its reflectance, bandwidth and the peak position at the incident angle up to about 60° under unpolarized incident light. The peak position of the color filter can be tuned from 400 nm to 520 nm by changing structural parameters of the gratings, and keep its incident angle-independent property.

Fabrication of two-dimensional hard X-ray diffraction gratings

Hard X-ray grating interferometry has shown promising results in phase and scattering imaging, as well as in metrology applications. Recently, the technique has been extended to two dimensions, recording the full phase gradient vector and a directional scattering signal. Here, we present a process for fabricating the key optical elements required for this technique: phase and absorption gratings with periods of few micrometers and high aspect ratios, with a particular focus on two-dimensional grating structures. The fabrication process is based on deep reactive ion etching in silicon and electroplating of gold.

Bridging the Gap Between Nanophotonic Waveguide Circuits and Single Mode Optical Fibers Using Diffractive Grating Structures

In this paper, the use of diffractive grating structures to efficiently interface between a single mode fiber and a high index contrast waveguide circuit is outlined. We show that high index contrast grating structures allow for broadband and high efficiency coupling. Since no polished facet is required on the photonic integrated circuit to interface with the optical fiber, fiber-to-chip grating couplers enable wafer-scale testing, reducing the cost for testing large scale integrated optical circuits. We show that two-dimensional grating structures can solve the problem of the huge polarization dependence of high index contrast photonic integrated circuits. Finally, an optical probe is presented, which allows testing individual components of a photonic integrated circuit, analogous to the electrical probes used in micro-electronics.

Broadening the angular tolerance in two-dimensional grating resonance structures at oblique incidence

Broadening of the angular response of two-dimensional (2D) guided mode resonant spectral filters at oblique incidence is investigated. Coupling into multiple fundamental guided resonant modes having the same propagation constant but propagating in different planes (inherent multiple-plane diffraction by 2D gratings) is shown to significantly broaden the angular tolerance while maintaining narrow linewidth. Resonances have symmetric and broad angular responses when the incident wave is coupled to four resonant modes in a structure with a hexagonal grating pattern. Further broadening is implemented by enhancing the second Bragg diffraction of the 2D grating structure. Resonance with a narrow spectral linewidth (Dlambda(FWHM) approximately 1.6 x 10(-4)lambda(0)) and angularly tolerant to an ~6 mum beam diameter is obtained. A second approach utilizing a dual 2D grating configuration with a second grating on the substrate side is shown to increase the lateral confinement, causing the merging of two successive resonant bands. This results in further improvement of the angular/spectral linewidth ratio by ~80%.

Silicon-on-insulator ultra-compact duplexer based on a diffractive grating structure

The use of a silicon-on-insulator diffractive grating structure is proposed to achieve ultra-compact duplexing operation. One-dimensional grating structures are proposed to spatially separate two wavelength bands. This device can become a key component in the fabrication of integrated optical transceivers for fiber-to-the-home applications, where a 1310nm wavelength channel and a 1490nm wavelength channel need to be duplexed. A 10mum x 10mum one-dimensional grating structure allows to spatially separate both wavelength bands on the photonic integrated circuit, with an average coupling efficiency of 55% and an optical bandwidth of 55-60nm. While these one-dimensional grating structures are strongly polarization dependent, a two-dimensional grating structure is presented to achieve polarization independent operation.

Mathematical modelling of indirect measurements in scatterometry

In this work, we illustrate the benefits and problems of mathematical modelling and effective numerical algorithms to determine the diffraction of light by periodic grating structures. Such models are required for reconstruction of the grating structure from the light diffraction patterns. With decreasing structure dimensions on lithography masks, increasing demands on suitable metrology techniques arise. Methods like scatterometry as a non-imaging indirect optical method offer access to the geometrical parameters of periodic structures including pitch, side-wall angles, line heights, top and bottom widths. The mathematical model for scatterometry is based on the Helmholtz equation derived as a time-harmonic solution of the Maxwell equations. It determines the incident and scattered electric and magnetic fields, which fully specify the light propagation in a periodic two-dimensional grating structure. For numerical simulations of the diffraction patterns, a standard finite element method (FEM) or a generalized finite element method (GFEM) is used for solving the elliptic Helmholtz equation. In a first step, we performed systematic forward calculations for different varying structure parameters to evaluate the applicability and sensitivity of different scatterometric measurement methods. Furthermore our programs include several iterative optimization methods for reconstructing the geometric parameters of the grating structure by the minimization of a functional. First reconstruction results for different test data sets are presented.