Grating Period Research Articles

Parabolic gratings enhance the X-ray sensitivity of Talbot interferograms

In grating-based X-ray Talbot interferometry, the wave nature of X-ray radiation is exploited to generate phase contrast images of objects that do not generate sufficient contrast in conventional X-ray imaging relying on X-ray absorption. The phase sensitivity of this interferometric technique is proportional to the interferometer length and inversely proportional to the period of gratings. However, the limited spatial coherency of X-rays limits the maximum interferometer length, and the ability to obtain smaller-period gratings is limited by the manufacturing process. Here, we propose a new optical configuration that employs a combination of a converging parabolic micro-lens array and a diverging micro-lens array, instead of a binary phase grating. Without changing the grating period or the interferometer length, the phase signal is enhanced because the beam deflection by a sample is amplified through the array of converging-diverging micro-lens pairs. We demonstrate that the differential phase signal detected by our proposed set-up is twice that of a Talbot interferometer, using the same binary absorption grating, and with the same overall inter-grating distance.

Encrypted optical fiber tag based on encoded fiber Bragg grating array

Optical fibers are typically used in telecommunications services for data transmission, where the use of fiber tags is essential to distinguish between the different transmission fibers or channels and thus ensure the working functionality of the communication system. Traditional physical entity marking methods for fiber labeling are bulky, easily confused, and, most importantly, the label information can be accessed easily by all potential users. This work proposes an encrypted optical fiber tag based on an encoded fiber Bragg grating (FBG) array that is fabricated using a point-by-point femtosecond laser pulse chain inscription method. Gratings with different resonant wavelengths and reflectivities are realized by adjusting the grating period and the refractive index modulations. It is demonstrated that a binary data sequence carried by a fiber tag can be inscribed into the fiber core in the form of an FBG array, and the tag data can be encrypted through appropriate design of the spatial distributions of the FBGs with various reflection wavelengths and reflectivities. The proposed fiber tag technology can be used for applications in port identification, encrypted data storage, and transmission in fiber networks.

Design and Preparation of Anti-Reflection Nanoarray Structure on the Surface of Space Solar Cell Glass Cover

Space solar cell glass covers require high radiation resistance and wide-spectrum high light transmittance. The existing research on the preparation of thin films or special optical structures on the surface of solar cells rarely involves systematic research and the precise control of the high transmittance structural parameters of specific spectral bands by glass covers. Nanoarray structures were designed and constructed on high-purity quartz glass covers, achieving high anti-reflection within the 350–1100 nm range, the high energy part of the solar spectrum on Mars, regardless of the preparation of antireflective film and its radiation resistance. First, G-Solver software package was used to establish a nanoarray structure model according to the equivalent medium theory, and the effects of structural parameters such as the grating period, grating depth, and duty cycle on the glass cover transmittance were investigated. The results show that when the grating period is 50–200 nm, the transmittance ranges from 97.8% to 99.9%. When the grating period further increases from 300 nm, the lowest point of the transmittance spectrum moves to the longwave direction, and the transmittance from 350 nm to the lowest transmittance point significantly reduces. The optimal grating depth is 500 nm for a 300 nm grating period, the transmittance at 350 nm reaches 88.91%, and the average transmittance is 98.23%. When the period is 300 nm and the depth is 500 nm, the optimal duty cycle is 0.67, the transmittance at 350 nm reaches 96.52%, and the average transmittance is 99.23%. Nanoarray structures were constructed on the glass covers with nanoimprint and plasma etching, then modified with atomic layer deposition (ALD) to adjust their depth and duty cycle. The influence rules of the grating period, depth, and duty cycle on the cover transmittance from the experimental results are basically consistent with those from the simulation calculation. The nanoarray structure increases the average transmittance within 350–1100 nm of the glass cover by an average of 2.02% and the peak transmittance by 2.66%. The research results and experimental methods of this study have application value and promotion prospects for improving the photoelectric conversion efficiency of space solar cells and ground solar cells.

Design, Fabrication and Validation of Mixed Order Distributed Feed-Back Organic Diode Laser Cavity

In the context of the quest for the organic laser diode, we address a key challenge to design and fabricate high-quality factor cavities compatible with electrical excitation of organic semiconductors. More precisely, we present the design of DFB micro-cavities for integration in organic laser diodes and their validation under optical pumping. To design high-quality factor mixed-order DFB micro-cavities, we consider the half- and quarter-wavelength multilayered system and use the optical waveguide analysis to quantify the effective indices of the high and low indices, and the matrix transfer method to calculate the reflectances. Matrices of DFB micro-cavities made from different doses and different grating periods were fabricated. We then identified those showing laser emission under optical pumping as an indication of optimal matching of their resonance wavelength with respect to the electroluminescence peak of the organic gain material. Potential applications of organic laser diodes deal with light communication, spectroscopy, sensors, and other applications where heterogenous integration is important.

The plasmon–polariton scattering by random-impedance surface defects: The interplay between localization and outflow

We study the scattering of TM-polarized surface plasmon-polariton (SPP) by the finite section of flat metal–vacuum interface with a random impedance. We analyze the solution to the integral equation that connect the scattered field and the incident plasmon–polariton, and is valid for any strength of the scattering and dissipative characteristics of the conducting half-space. We show that the norm of the intermode scattering operator as a measure of scattering strength is not only determined by the parameters of the random impedance (the variance, correlation radius, the length of the heterogeneous section of the interface), but also crucially depends on the metal conductivity. For a small norm of the integral operator, the incident surface plasmon polariton radiates effectively into vacuum, resulting in excitation of quasi-isotropic Norton-type waves above the conducting surface. The intensity of the leaking field is expressed in terms of the pair correlation function of the impedance, whose dependence on wave numbers of incident and scattered waves demonstrates the possibility to observe a phenomenon similar to Wood’s anomalies of wave scattering by periodic gratings. Under strong scattering regime, the radiation into the upper half-space is highly suppressed and the SPP wave is mainly backscattered from the heterogeneous surface segment. For the lossless conducting half-space, the surface plasmon–polariton becomes unstable for arbitrarily small fluctuations of the conductor polarizability. The mirroring should also take place at small norm of the scattering operator, yet in this case it is related to Anderson’s localization of the SPP within the disordered section.

Joint Geometry/Frequency Analyticity of Fields Scattered by Periodic Layered Media

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of high-order perturbation of surfaces/asymptotic waveform evaluation (HOPS/AWE) methods for numerically simulating scattering returns from periodic diffraction gratings. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a periodic two-layer structure. Furthermore, we establish joint analyticity of these solutions with respect to both geometry and frequency perturbations. This result provides hypotheses under which a rigorous numerical analysis could be conducted on our recently developed HOPS/AWE algorithm.

Grating Optimization for Smith–Purcell Radiation: Direct Correlation Between Spatial Growth Rate and Starting Current

Smith–Purcell radiation (SPR) is generated when electrons travel close to a metallic periodic grating. It was found that the starting current of SPR varies by orders of magnitude by simply varying the grating parameters (groove’s heights and widths) while keeping the grating period and the electron beam properties fixed. In this article, we demonstrate that this strong dependence of starting current on the grating parameters is directly related to the spatial growth rate of the SPR. Using the hot-tube dispersion relation, we optimize the grating parameters to minimize the starting current to excite coherent SPR.

Generating an M2 × N2 spot array with a dual-period hybrid Dammann grating fabricated using maskless projection lithography.

The Dammann grating (DG), which redistributes a collimated laser beam into a spot array with a uniform intensity, is a widely adopted approach for profile measurement. Conventional DGs for dense spot projection are binary phase gratings with precisely designed groove structures, which suffer from low efficiency, poor uniformity, and a hard-to-fabricate fine feature size when utilized for a large field of view (FOV). Here, we propose a new, to the best of our knowledge, hybrid DG architecture consisting of two different grating periods which effectively generates an engineering M2 × N2 spot array with a non-complex structural design. As a proof-of-concept, a dual-period hybrid DG with a two-scale grating period ratio of 11.88 μm/95.04 μm (∼1/8) is designed and fabricated as a means to generate a dense 72 × 72 diffraction spot array with a FOV of 17° × 17°. In addition, the DG exhibits superior performance, with a high efficiency (>60%) and a low non-uniformity (<18%) at a wavelength of 532 nm. This kind of hybrid DG constructed from photoresist patterns with a minimum feature size of ∼1.2 μm can be perfectly fabricated by maskless projection lithography for large-scale and low-cost production. The proposed dual-period hybrid DG can pave the way for depth-perception-related applications such as face unlocking and motion sensing.

Spurious Modes in Laterally Excited Bulk Acoustic Resonators (XBARs): Analysis and Suppression

Laterally excited bulk acoustic resonators (XBARs) are plate mode resonators in which one of the higher-order plate modes transforms into the bulk acoustic wave (BAW) due to the very thin plates used in these devices. The propagation of the primary mode is usually accompanied by numerous spurious modes, which deteriorate resonator performances and restrict potential XBARs' applications. This article suggests a combination of different methods for insight into the nature of the spurious modes and their suppression. Analysis of the BAW slowness surface provides optimization of XBARs for single-mode performance in the filter passband and around it. The rigorous simulation of admittance functions in the optimal structures allows for further optimization of electrode thickness and duty factor. Finally, the nature of different plate modes generated in a wide frequency range is clarified via simulation of dispersion curves, which characterize acoustic mode propagation in a thin plate under the periodic metal grating, and visualization of displacements accompanying wave propagation. Application of this analysis to lithium niobate (LN)-based XBARs demonstrated that in LN cuts with Euler angles (0°, 4°-15°, 90°) and plate thickness dependent on orientation and varying between 0.05 and 0.1 wavelengths, the spurious-free response could be achieved. Due to tangential velocities of 18-37 km/s combined with the coupling of 15%-17% and feasible duty factor a/p = 0.5, the found XBAR structures can be applied in high-performance 3-6 GHz filters.

Large Enhancements in Optical and Piezoelectric Properties in Ferroelectric Zn1‐xMgxO Thin Films through Engineering Electronic and Ionic Anharmonicities

AbstractMultifunctionality as a paradigm requires materials exhibiting multiple superior properties. Integrating second‐order optical nonlinearity and large bandgap with piezoelectricity can, for example, enable broadband, strain‐tunable photonics. Though very different phenomena at distinct frequencies, both second‐order optical nonlinearity and piezoelectricity are third‐rank polar tensors present only in acentric crystal structures. However, simultaneously enhancing both phenomena is highly challenging since it involves competing effects with tradeoffs. Recently, a large switchable ferroelectric polarization of ≈80 μC cm−2 was reported in Zn1‐xMgxO films. Here, ferroelectric Zn1‐xMgxO is demonstrated to be a platform that hosts simultaneously a 30% increase in the electronic bandgap, a 50% enhancement in the second harmonic generation (SHG) coefficients, and a near 200% improvement in the piezoelectric coefficients over pure ZnO. These enhancements are shown to be due to a 400% increase in the electronic anharmonicity and a ≈200% decrease in the ionic anharmonicity with Mg substitution. Precisely controllable periodic ferroelectric domain gratings are demonstrated down to 800 nm domain width, enabling ultraviolet quasi‐phase‐matched optical harmonic generation as well as domain‐engineered piezoelectric devices.

CO2 laser-induced long-period fiber grating in the dispersion turning point

A CO2 laser-induced long-period fiber grating (LPFG) in the dispersion turning point (DTP) has been proposed in this work, which has demonstrated the possibility of fabricating LPFG with a shorter period of 115 μm in a thin single-mode fiber (SMF) without etching cladding. The LPFG working near DTP was also induced in a conventional SMF by CO2 laser after etching cladding, whose grating period was 196 μm. Then, the refractive index (RI) sensitivity of LPFG based on thin SMF was optimized by fully combining DTP and cladding reduction. Considering the sensor probe's mechanical strength comprehensively, the thin SMF cladding was etched to 51.03 μm to ensure cladding mode LP1,6 work near DTP, which can result in an average RI sensitivity of 2117.12 nm/RIU in the RI range of 1.33222 to 1.39018. Based on its excellent RI sensing performance, the proposed LPFG is a prospective sensor that can be applied to significant fields such as environmental, chemical, or biological parameters measurement. At the same time, this study provides a low-cost path to fabricate LPFG worked in DTP for most researchers.

The propagation behavior of SH surface wave in a semi-infinite magneto-electro-elastic solid with the periodically gold strips

This article theoretically investigates the propagation of shear horizontal (SH) surface wave in the periodically deposited gold strips separated by vacuum on the magneto-electro-elastic (MEE) substrate. Using field analysis theory based on Bloch-Floquet theorem and electromagnetic open boundary conditions, dispersion equations are derived. The MEE composite is comprised of 80% PZT4 and 20% CoFe2O4. The dispersion, wave mode shape, electric and magnetic potentials are being modelled and computed for the SH wave on the MEE substrate. It is observed that the bandgap occurs at resonance when the wavelength of the SH wave matches with periodicity of the grating. The width of the bandgap can be increased or decreased by increasing the strip height to periodicity ratio. It is found that the gold grating on the surface of MEE substrate can traps the SH wave by slowing down the wave when the wave number is less or equal to wave number at the resonance condition. It is observed that above the resonance condition, SH wave shows supersonic behavior where the phase velocity of SH wave is greater than the surface wave velocity. The trapping and supersonic behavior of SH wave are more pronounced as the strip height to grating periodicity ratio increases. As the strip height to periodicity ratio increases, the wave trapping is enhanced and the leakage of wave energy in the substrate is reduced. The results are relevant to design the surface acoustic wave devices.

An Axial Force Sensor Based on a Long-Period Fiber Grating with Dual-Peak Resonance

A high-sensitivity axial force sensor with a large measurement range based on a dual-peak long-period fiber grating (LPFG) is proposed and experimentally demonstrated. Previously, the relationship between the grating period and the dual-peak wavelengths has been investigated based on the coupled-mode theory. In our experiment, the LPFG was fabricated in our laboratory by illuminating the fiber core with the aid of a 213 nm UV laser. The sensitivity of the proposed axial force sensor can reach −14.047 nm/N in the force range from 0.490 N to 4.508 N. Taking the advantages of a compact size, low cost, and large measurement range, our force sensor has more applicable abilities in harsh environments.

Designing Highly Precise Overlay Targets for Asymmetric Sidewall Structures Using Quasi-Periodic Line Widths and Finite-Difference Time-Domain Simulation.

The present study introduces an optimized overlay target design to minimize the overlay error caused by asymmetric sidewall structures in semiconductor manufacturing. To achieve this goal, the overlay error formula was derived by separating the asymmetric bottom grating structure into symmetric and asymmetric parts. Based on this formula, it was found that the overlay target design with the linewidth of the bottom grating closed to the grating period could effectively reduce the overlay error caused by the sidewall asymmetry structure. Simulation results demonstrate that the proposed design can effectively control the measurement error of different wavelengths within ±0.3 nm, even under varying sidewall angles and film thicknesses. Overall, the proposed overlay target design can significantly improve the overlay accuracy in semiconductor manufacturing processes.

Actively tunable nonreciprocal thermal emitter with SiC grating and anisotropy InAs film

Under the external magnetic field, a novel design consisting of SiC grating on a magneto-optical InAs film is proposed to realize tunable nonreciprocal thermal radiation. In combination with low-loss dielectric InAs, the electric field distribution of the guided resonance broke the time-reversal symmetry and reciprocity. The nonreciprocity demonstrates a blue shift with an increased magnetic field and a perfect emission has been achieved at a low magnetic field of 1 T. The influence of the height, period, and width of gratings as well as the thickness and volume fraction of the SiC film on the performance of nonreciprocal emission are fully examined. Finally, tunable emission with different incident angles is investigated. This work may assist the application of nonreciprocal thermal emitters to convert and store energy within a wide frequency band.

FBG-LPFG-Based Sensor to Monitor 3-D Strain in Ice During Freezing–Melting Processes

Three-dimensional strain (3D strain) and the principal strain in ice are very important for glacier movement research and glacier-related disaster prediction. The internal 3D strain of ice is sensitive to temperature, and it is very complex during the whole freezing and melting process including phase transformation. In this study, we present a 3D strain sensor (3D-S Sensor) based on fiber Bragg grating (FBG) and long period fiber grating (LPFG) that can measure the 3D strain in ice. The LPFG (the temperature sensitivity coefficient is 56.3 pm/°C) was fabricated by the laser etching method, which was used for the temperature compensation of FBGs to improve the accuracy of strain measurement. The 3D principal strain can be calculated by the value of 6 direction strains from FBGs. A freeze-melt experiment is designed to verify the performance of 3D-S Sensor. The experimental results show that the sensor can measure the complex 3D deformation of ice from a more precise angle. Among the 6 directions of strain measured by the sensor, the strain value in the Z direction is the largest (ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>z</i></sub> = 6232.9 με). The first principal strain in ice is close to the negative direction of the Z axis (θ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Z</i></sub> = 160.7°), and the maximum value is 6638.2 με. The measured results are consistent with the actual deformation of ice, indicating that the sensor can effectively measure the 3D strain and principal strain inside the ice.

A Seawater Salinity Sensor Based on Optimized Long Period Fiber Grating in the Dispersion Turning Point.

Variations of seawater salinity often cause ocean internal waves, water masses and stratification, which affect the stability of the ocean environment. Therefore, the study of seawater salinity is significant for the prediction of changes in the ocean environment. However, existing methods for measuring seawater salinity generally have the disadvantages of low sensitivity and low accuracy. In this work, we proposed a seawater salinity sensor based on long period fiber grating (LPFG) in the dispersion turning point (DTP), which has demonstrated the possibility to fabricate LPFG with a shorter grating period by CO2 laser in a thin single mode fiber (SMF) of 80 μm cladding diameter without etching. For obtaining higher sensitivity that could meet the measurement requirement in practice, the proposed sensor was optimized by combining etching cladding and DTP. After the LPFG working near DTP was fabricated by a CO2 laser, the cladding diameter was reduced to 57.14 μm for making cladding mode LP1,7 work near DTP by hydrofluoric acid (HF) solutions. The experimental results have demonstrated that a sensitivity of 0.571 nm/‱ can be achieved when the salinity increases from 5.001‱ to 39.996‱, and the sensor shows good repeatability and stability. Based on its excellent performance, the optimized LPFG is a prospective sensor to monitor seawater salinity in real time. Meanwhile, a low-cost way was provided to make LPFG work near DTP instead of ultraviolet exposure and femtosecond laser writing.

Surface-plasmon-enhanced strain-wave-induced optical diffraction changes from a segmented grating

We report on surface-plasmon-polariton-enhanced (SPP-enhanced), strain-wave-induced reflection and diffraction changes on a Au-covered, segmented grating. The segmented grating has a 6020nm period, and its lines are segmented into 7 periods of a 430nm period grating, which allows the excitation of SPPs. This grating has three SPP resonances at different optical wavelengths, for the same incident angle. Pump-pulse-induced strain waves are probed by measuring reflection and diffraction of a tunable probe pulse in a wavelength range that includes all three SPP resonances. Surface Acoustic Waves (SAWs) and Longitudinal Waves (LWs) are identified. When probing close to SPP resonances, the reflection changes from SAWs and LWs are strongly enhanced by factors of 23 and 36, respectively, compared with reflection changes observed when probing at off-resonance wavelengths. The relative SAW- and LW-induced diffraction changes are larger by additional factors of up to 3.3 and 2.6, respectively, compared to the reflection changes.

Dynamics of surface-plasmon lasing in planar metal gratings on semiconductor.

We investigate the dynamics of surface plasmon (SP) lasing in Au gratings fabricated on InGaAs with a period of around 400 nm, which locates the SP resonance near the semiconductor energy gap and facilitates efficient energy transfer. By optically pumping the InGaAs to reach the population inversion required for the amplification and the lasing, we observe SP lasing at specific wavelengths that satisfy the SPR condition depending on the grating period. The carrier dynamics in semiconductor and the photon density in the SP cavity was investigated from the time-resolved pump-probe measurement and the time resolved photoluminescence spectroscopy, respectively. Our results reveal that the photon dynamics is strongly correlated with the carrier dynamics and the lasing build-up is accelerated as the initial gain proportional to the pumping power increases, and this trend is satisfactorily explained using the rate equation model.

High–Efficiency, Widely Tunable MgO: PPLN Optical Parametric Oscillator

We report on the investigation of a high–efficiency, widely tunable femtosecond optical parametric oscillator (OPO) based on a multi–period MgO–doped periodically poled lithium niobite (MgO: PPLN) crystal, pumped by an all–solid–state femtosecond mode–locked Yb: KGW laser at 1030 nm providing 100 fs pulses. With 6 W pump power, the OPO generates 2.68 W of signal power at 1540 nm and 1.2 W of idler power at 3110 nm, which corresponds to the total conversion efficiency adding up to 67.4%. To the best of our knowledge, this is the highest conversion efficiency of a femtosecond OPO. Meanwhile, in order to obtain a broad optical spectrum range, both the grating period and working temperature are tuned, resulting in tunable signals of 1.43–1.78 µm and idlers of 2.44–3.68 µm. This source will be used to generate a femtosecond mid–infrared laser of wavelength range 3.7–6.5 µm and tens milliwatts average power through difference frequency generation (DFG).