Complex Gratings Research Articles

Large‐Scale Multiplexed Azopolymer Gratings with Engineered Diffraction Behavior

AbstractThe diffraction of polychromatic light from periodic superficial structures is often responsible for the structural colors observed in Nature. Similarly, engineered microtextures fabricated on metallic or dielectric surfaces can be used to design diffracted optical patterns with desired shapes and colors. To this aim, advanced diffraction gratings with exceptional design and functionality are continuously proposed, and new fabrication methods follow to stay abreast with the improving design capabilities. Multiplexed surface reliefs, acting as complex gratings with tunable diffraction behavior, can be readily produced on films of azobenzene containing materials by exposing the surface to controlled sequences of holographic interference patterns. This work fully investigates, both theoretically and experimentally, the use of light‐induced surface relief on azopolymers for the realization of large‐scale multiplexed gratings with optimized diffraction performances. The reconfigurable diffraction gratings able to diffract polychromatic light in the same direction with controllable relative color intensities by tuning exposure parameters in a switchable two‐beam interference setup are designed and fabricated. The results can be generalized to more complex diffractive devices, usable in emerging display application areas.

Hemispherical radiative properties of complex gratings near the intrinsic band gap

This work both numerically and experimentally investigates hemispherical radiative properties (absorptance, reflectance, and transmittance) of complex gratings. Crystal silicon is employed to generate samples. One is a double-sided polished 520-μm-thick substrate, and the other is a substrate with complex gratings on its top. The incidence wavelength λ ranges from 0.5 μm to 1.7 μm, containing the intrinsic band gap wavelength λbg = 1.09 μm. Wavelength-selective and polarization-sensitive features are exhibited in spectra of properties for complex gratings. The wavelength-selectivity and polarization-sensitivity are elaborated using near-field electromagnetic patterns at three representative wavelengths (λ < λbg, λ ≈ λbg, and λ > λbg).

Tailoring radiative properties of a complex trapezoidal grating solar absorber by coupling between SPP and multi-order MP for solar energy harvesting

The coupling resonance effect between surface plasmon polariton (SPP) and multi-mode magnetic polariton (MP) is very complicated. In this study, we propose a complex trapezoidal grating solar absorber (CTGSA) with nanoscale structure, which is made of two tungsten trapezoids and a silicon dioxide spacer lying on the tungsten substrate, to study the coupling resonance between SPP and multi-mode MP in detail, not just the fundamental mode. The finite-difference time-domain method is employed to calculate spectral absorptivity and electromagnetic distribution. The coupling between SPP and MP of different modes can be clearly shown through the electromagnetic field, which is conducive to the investigation of the physical mechanisms of the four close-to-unity peaks in the absorptivity curve. The effects of geometric parameters on the resonance conditions are also explored. The coupling between SPP and MP renders the manual control of the absorptance of the structure possible. Calculations of directional absorptance at peak wavelengths for solar radiative intensity show that the absorptance of the proposed CTGSA is stable for a wide range of incident angles. Abnormal behaviors of directional absorptance are observed due to Wood’s anomaly. Besides, for steam generation application, the solar-thermal conversion efficiency is up to 74%, which has a practical significance. By providing a detailed analysis of the coupling of SPP and multi-order MP based on electromagnetic distribution, this paper will fill the gap in the field of MP resonance generated in the space between trapezoidal ridges and present a nanoscale structure with remarkable properties for harvesting broadband solar energy, which can provide a useful reference for optimizing design of solar absorbers.

Complex phase masks for OH suppression filters in astronomy: part I: design.

The design of a complex phase mask (CPM) for inscribing multi-notch fiber Bragg grating filters in optical fibers for OH suppression in astronomy is presented. We demonstrate the steps involved in the design of a complex mask with discrete phase steps, following a detailed analysis of fabrication constraints. The phase and amplitude of the complex grating is derived through inverse modelling from the desired aperiodic filter spectrum, following which the phase alone is encoded into the surface relief of a CPM. Compared to a complicated "running-light" Talbot interferometer based inscription setup where the phase of the inscribing beam is controlled by electro- or acousto-optic modulators and synchronized to a moving fiber translation stage, CPM offers the well-known convenience and reproducibility of the standard phase mask inscription technique. We have fabricated a CPM that can suppress 37 sky emission lines between 1508 nm to 1593 nm, with a potential of increasing to 99 channels for suppressing near-infrared (NIR) OH-emission lines generated in the upper atmosphere and improving the performance of ground-based astronomical telescopes.

Add-drop filter with complex waveguide Bragg grating and multimode interferometer operating on arbitrarily spaced channels.

We present a silicon nitride/silicon dioxide add-drop filter operating on arbitrarily spaced channels using multimode interferometers (MMIs) and complex waveguide Bragg gratings (CWBGs). The add-drop filter shows a rejection ratio of >40 dB on all five channels, with a line width of 1.2nm and an on-chip loss of <1 dB. By designing the CWBG with the Layer Peeling/Layer Adding algorithm, this MMI-CWBG add-drop filter platform has the capability for ultrabroadband add-drop operation on arbitrarily spaced channels.

Large range nano alignment for proximity lithography using complex grating

We propose a novel alignment method with nanoscale precision and hundreds of microns detecting range for proximity lithography. With this method, both coarse and final alignments are realized by complex grating based on moiré fringe. For distinguishing the complex gratings in frequency spectrum, there is no interference between the coarse and the final alignment parts. Within only one pattern, modulation of the coarse mark and phase of the final mark can be calculated respectively. Combining the two results, we can do the alignment with nanoscale precision in large measurement range. Furthermore, the structure of our measurement system is simple. Simulation and experiments are carried out to validate the feasibility of the proposed method.

Long period fiber gratings with off-resonance spectral response based on mechanical oscillations.

We present long period fiber gratings with off-resonance spectral response. Our long period fiber gratings are created by the periodic structure of large perturbations in the fiber diameter. These perturbations result in unique spectral response, even in off-resonance frequencies. Writing these long period fiber gratings is based on utilizing the mechanical vibrations of tapered fibers during the tapering process. This writing method is simple and robust; it has high efficiency, high reproducibility, and low polarization dependency; and it enables real-time tunability of the periodicity, efficiency, and length of the grating. We also demonstrate a complex grating by writing multiple gratings one on top of the other. Finally, we utilize the formation of the gratings in different fiber diameters to investigate the Young's modulus of tapered fibers.

Unified fabrication process for complex gratings

A unified fabrication process was developed for four complex gratings. One period of each grating contains multiple pairs of ridges/grooves, and a ridge is usually composed of diversified materials. The process was suitable not only for mass fabrication but also for a large area. Moreover, with only one mold, four gratings could be obtained at once. Two 12×12 mm2 samples were fabricated for demonstration. Profile uniformity of each sample was confirmed with broadband infrared (2.5 to 25 μm) transmittance spectra. A good agreement between measured and modeling results was observed.

Analysis of unidirectional non-paraxial invisibility of purely reflective PT-symmetric volume gratings.

We study the diffraction produced by a slab of purely reflective PT-symmetric volume Bragg grating that combines modulations of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex grating has a directional coupling between the different diffraction orders, which allows us to find an analytic solution for the first three orders of the full Maxwell equations without resorting to the paraxial approximation. This is important, because only with the full equations can the boundary conditions, allowing for the reflections, be properly implemented. Using our solution we analyze unidirectional invisibility of such a grating in a wide variety of configurations.

A technique for mitigating the effect of the writing-beam profile on fibre Bragg grating fabrication.

We propose and demonstrate a pre-compensation mechanism to account for the writing-beam profile which when applied to the design of advanced fibre Bragg gratings helps to achieve a desired design spectral response. We use the example of a complex multi-channel grating as an example to demonstrate the improvement achievable using the pre-compensation and find good agreement between experimental results and numerical calculations.

Analysis of PT-symmetric volume gratings beyond the paraxial approximation.

We study the diffraction produced by a PT -symmetric volume Bragg grating that combines modulation of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex grating has a directional coupling between the different diffraction orders, which allows us to find an analytic solution for the first three orders of the full Maxwell equations without resorting to the paraxial approximation. This is important, because only with the full equations can the boundary conditions, allowing for reflections, be properly implemented. Using our solution we analyze the properties of such a grating in a wide variety of configurations.

Tungsten Complex Gratings as a Thermophotovoltaics Selective Emitter

A kind of concave tungsten complex grating based on superposition of two simple binary tungsten gratings with different groove depths has been proposed for potential application as thermophotovoltaic (TPV) selective emitters. The effect of the simple grating geometric parameters on the spectral emittance is calculated numerically by using the rigorous coupled-wave analysis (RCWA). The emittance of the complex grating shows broadband-directional insensitive peak in the spectral region where the quantum efficiency of TPV cells is high, which is explained by the surface plasmon polariton (SPP). The results show that the complex grating has high emittance value, above 0.8, within the spectral range of 0.8

Control of thermal radiative properties using two-dimensional complex gratings

The present work theoretically investigates the electromagnetic resonance modes on two-dimensional (2-D) complex gratings consisting of a metallic grating, a dielectric film, and a metal substrate. We treat a complex grating as geometrical combination of two square grating elements with different sizes in a single unit cell. In order to identify various resonance modes, such as surface plasmon and magnetic resonance (or magnetic polariton) existing in gratings, the finite-difference time-domain method is employed in solving Maxwell’s equation. Differently from 2-D simple grating structures, we observe the diverse magnetic polariton modes associated with each grating elements in a single unit cell. Furthermore, if two different grating elements are merged together, magnetic polariton will be branched out into multiple modes. These characteristics of 2-D complex grating will be desirable for achieving broad-band absorption, which is critical for energy harvesting applications.

Widely tunable six-section semiconductor laser based on etched slots.

A six section widely tunable laser based on slots etched into the waveguide is presented. This laser is re-growth free which makes it suitable for photonics integration. To improve the laser performance, the front and the back facets are anti- reflection (AR) coated and the laser is integrated with a semiconductor optical amplifier. A tuning range of 55nm covering 12 supermodes with side mode suppression ratio (SMSR) >30dB is reported for the fabricated device using the Vernier tuning effect. This laser platform requires very simple fabrication compared with more complex superstructure gratings.

In-plane scattering patterns from a complex dielectric grating at the normal and oblique incidence

The in-plane scattering patterns from a complex dielectric grating were both numerically and experimentally studied in contrast to those from well-known metallic gratings. The incidence was the transverse electric or transverse magnetic wave of wavelength λ=660 nm. The grating profile was complex with a period Λ=7.0 μm, while the material was lightly doped crystalline silicon. Patterns of the electric field, magnetic field, and spatial intensity distribution were demonstrated at the normal (θ(i)=0°) and oblique (θ(i)=+30°) incidence. Electric and magnetic fields were presented in the near field as well as the far field. The measured power ratio within -90°≤θ(r)≤+90° was plotted. Their major peaks and the numerically obtained diffraction efficiency of 21 orders (-10≤m≤+10 or -15≤m≤+5) of diffracted waves occurred at the same θ(r). Other peaks and stair-like shoulders of major peaks also exhibited in spectra.

P.92: Characterization of Complex Liquid Crystal Polarization Gratings at Oblique Incidence Using Extended Jones Matrix Method

AbstractThe validity of combing extended Jones matrix and vectorial Fourier coefficients to characterize a complex type polarization grating (PG) at oblique incidence was proved. More specifically, the transmitted field of a complex polarization grating at oblique incidence is characterized through the extended Jones matrix. The diffraction properties of the mth order of the grating are determined by the vectorial Fourier coefficients of the transmitted field, under the Fraunhofer approximation. The measured diffraction efficiencies of a complex PG using RGB laser light show very good agreement with the calculated data.

Silicon complex grating with different groove depths as an absorber for solar cells

A kind of concave silicon complex grating based on the superposition of multiple simple silicon gratings with different groove depths (ridge heights) is proposed for a potential application as an absorber for solar cells in the visible and near-infrared wavelength regions. For simple binary gratings, the associated absorptance peak is narrowband and direction sensitive. This study demonstrates that these drawbacks can be remedied by using this kind of concave complex grating with different groove depths, which can tailor radiative properties in the whole of the interested spectral range by making full use of the microcavity resonance effect to enhance absorption. A parametric study is carried out to evaluate the influences of filling ratio, incident angle and groove depth on the spectral absorptance of a silicon grating. And an efficient way of searching for the optimal profiles for the complex gratings is employed. The orthogonal array from the Taguchi method benefits the optimization of structure depths, periods, and filling ratios among thousands of combinations. The average spectral absorptance of the optimized structure is above 0.94 within wavelength region from 0.3 to 1.1μm for the silicon complex grating with two groove depths, which suggests that the proposed structure can be well suitable for solar absorber applications. All numerical results are obtained from validated programs based on the rigorous coupled-wave analysis (RCWA) method.

Widening Absorption Band of Grating Structure With Complex Dual-Groove Grating

The wavelength-selective radiative property is becoming a noticeable requirement in various technological fields. There are many researches that have been focused on the radiative properties of metal periodic microstructure surface. However, the spectral bandwidth of high absorptance is often too narrow if excited by the conventional grating structures. In order to solve this problem, two novel periodic grating structures are proposed in this paper, which can increase the effective bandwidth of high absorption peaks. One of the new periodic grating structures, called dual-groove grating, is constructed by adding a rectangular groove at the bottom of the simple grating's groove through a secondary microscale processing. The other grating structure, which is called complex dual-groove grating, is constructed by superposing a dual-groove grating with a simple grating within one period. Aluminum grating structure is taken as an example to show the advantage of proposed structures on increasing effective bandwidth of high absorption peaks within mid-infrared and far-infrared spectra. The rigorous coupled-wave analysis (RCWA) is used to calculate the absorptance of periodic grating structures. The results shows that, two close absorption peaks and three connecting absorption peaks are obtained respectively for the two periodic grating structures. The effective bandwidth of high absorption peaks within interested wavelength band is improved obviously by these two microscale grating structures.

Design and fabrication of tunable laser with digital concatenated grating

A novel tunable laser with digital concatenated grating reflectors, which has a flatter envelope of reflection peaks, is designed and fabricated. The key concept of the approach is to utilize multi-sampled gratings which have different Bragg wavelengths and the same sampling period. The difference of each Bragg wavelength is integer multiple of the space between the peaks of sampled gratings. Here, nanoimprint lithographic technology is used to fabricate the complex gratings. The typical threshold current of the tunable laser is 34 mA, and the tuning range is larger than 32 nm. The non-uniformity of the output power is less than 2 dB.

Contrast and stimulus complexity moderate the relationship between spatial frequency and perceived speed: Implications for MT models of speed perception

Area MT in extrastriate visual cortex is widely believed to be responsible for the perception of object speed. Recent physiological data show that many cells in macaque visual area MT change their speed preferences with a change in stimulus spatial frequency (N. J. Priebe, C. R. Cassanello, & S. G. Lisberger, 2003) and that this effect can accurately predict the dependence of perceived speed on spatial frequency demonstrated in a related psychophysical study (N. J. Priebe & S. G. Lisberger, 2004). For more complex compound gratings and high contrast stimuli, MT cell speed preferences show sharper tuning and less dependence on spatial frequency (Priebe et al., 2003), allowing us to predict that such stimuli should produce speed percepts that are less vulnerable to spatial frequency variations. We investigated the perceived speed of simple sine wave gratings and more complex compound gratings (formed from 2 sine wave components) in response to changes in contrast and spatial frequency. In all cases, high contrast stimuli appeared to translate more rapidly. In addition, high spatial frequencies appeared faster-the opposite effect to that predicted by changes in MT cell spatial frequency preferences. Complex grating stimuli were somewhat "protected" from the effect of spatial frequency (compared to simple gratings), as predicted. However, contrary to predictions, the effect of spatial frequency was larger in high (compared to low) contrast gratings. Our data demonstrate that the previously established links between changes in MT cells' speed preferences and human speed perception are more complex than first thought.