Higher Diffraction Orders Research Articles

Modified transmission line model for grating solar cells.

Due to the wide range of applications of plasmonic diffraction gratings, it has become essential to provide an analytical method for modeling performance of the devices designed based on these structures. An analytical technique, in addition to greatly reducing the simulation time, can become a useful tool for designing these devices and predicting their performance. However, one of the major challenges of the analytical techniques is to improve the accuracy of their results compared to those of the numerical methods. So, here, a modified transmission line model (TLM) has been presented for the one-dimensional grating solar cell considering diffracted reflections in order to improve the accuracy of TLM results. Formulation of this model has been developed for the normal incidence of both TE and TM polarizations taking into account diffraction efficiencies. The modified TLM results for a silicon solar cell consisting of silver gratings considering different grating widths and heights have shown that lower order diffractions have dominant effects on the accuracy improvement in the modified TLM, while the results have been converged considering higher order diffractions. In addition, our proposed model has been verified by comparing its results to those of the finite element method-based full-wave numerical simulations.

Effect of composite vortex beam on a two-dimensional gain assisted atomic grating

We propose an atomic grating based on an electromagnetically induced transparency phenomenon that switches between zeroth-order diffraction to a distinct higher-order diffraction pattern by driving a planar gaseous medium of a four-level tripod () atoms with three laser beams: modulation of standing wave control beam propagating nearly perpendicular to the planar medium, while vortex and weak plane probe beams directed perpendicular to the medium. We numerically investigate the behavior of the amplitude, phase modulations, and probe field diffraction intensities of different orders by the variation of the field detunings and orbital angular momentum number of the composite vortex light beam. Specifically, in the off-resonant case, the interplay between a square lattice of the control and an additional spatial variation of the vortex beam allows the emergence of higher diffraction orders and variable gain due to double transparency windows in this complex optical system. We believe that our proposed scheme might be useful in optical memory devices via the storage of information to diffraction orders of the atomic grating.

Fast measurement of wavefront aberration in double-grating Ronchi lateral shearing interferometry

The accuracy of the shear-phase retrieval method is critical for accurate wavefront aberration measurements in double-grating Ronchi lateral shearing interferometry. Currently, the suppression of the interferences of unwanted diffractions generated by the Ronchi grating at the image plane is eliminated by adding more phase shifts, which increases the measurement time. Here, a stepped phase-shifting algorithm is proposed to suppress the unwanted diffractions and retrieve the shear phase between ±1st orders accurately with fewer phase shifts, and the measurement efficiency can be increased by 25% at least. The minimum number of phase shifts, which depends on the high diffraction orders existing in the interferograms, is analyzed. The proposed method was verified via numerical simulations and experiments. The wavefront measurement was validated via a comparison with the results of point-diffracted interferometry, and the root-mean-square difference was within 2.0 nm.

UTD-PO Solutions for the Analysis of Multiple Diffraction by Trees and Buildings When Assuming Spherical-Wave Incidence

This paper presents two uniform theories of diffraction–physical optics (UTD-PO) formulations to undertake analysis of radiowave multiple diffraction resulting from the presence of both buildings and trees in vegetated urban areas, with the assumption of spherical-wave incidence. The solutions presented consider buildings modeled as knife-edges and rectangular sections (the latter being more complex and realistic) and the effect of the tree canopy (the assumption is that this exceeds the height of the average rooftop) is taken into account by adding proper attenuation factors/phasors to building diffraction phenomena. The validation of these formulations has been undertaken by comparing with other methods and measurements performed at 39 GHz on a scaled-model of the environment under analysis, consisting of an array of bricks and bonsai trees. The chief advantage of the solutions put forward is that because of recursion, the calculations only include single diffractions. This avoids any requirement for higher-order diffraction terms in the diffraction coefficients, which means less computer time/power is demanded. The results of this work may be useful when planning future mobile communication systems, including 6G networks and beyond.

Directional amplified spontaneous emissions from Ag nanohole array with high diffraction orders.

Surface plasmon excitations in metallic hole arrays have been extensively studied in the context of light-matter interaction, since the generated Bloch surface plasmon polariton (Bloch-SPP) exhibits unique properties of nanoscale light confinement, near-field enhancements, and long-range metal surface propagation. In this work, we experimentally demonstrate a plasmonic device that exhibits highly directional emission in visible light; using Ag film with a thickness of 100 nm deposited on a subwavelength porous alumina array as a plasmonic cavity, four-level rhodamine 6G (R6G) is selected as the gain material. It is suggested that a Bloch-SPP with high diffraction orders on a Ag nanohole array can generate a strong local electric field and a high Purcell factor at a nanohole edge. Moreover, directional five-fold enhanced amplified spontaneous emission (ASE) with polarization dependence is observed under a low threshold of 199.9 W/cm2 in the visible light region, which comes from the optical feedback provided by the 2D periodic nanohole array. This work opens up a wide range of applications for real-time tunable wavelength, controlled multimode laser, fluorescence detection, etc.

Enhanced EIG in microwave controlled X-type atomic system

A microwave driven five-level X-type atomic system is proposed to diffract weak probe light into higher-order directions via the phenomenon of electromagnetically induced grating. In the proposed scheme, the effect of various system and field parameters on its higher-order diffraction efficiency is studied. The present atomic scheme offers excellent control over higher-order diffraction intensities by utilizing the microwave induced quantum interference effect. It is observed that the desired first-order diffraction efficiency can be attained through optimal selection of microwave field strength and relative phase factor.

Design of single-layer color echelle grating optical waveguide for augmented-reality display.

We proposed a single-layer color echelle grating combined optical waveguide structure for an augmented-reality display. In this structure, we used echelle gratings with super-wavelength periodic scale as in-coupling, relay, and out-coupling elements. The combined propagation of three light beams in the waveguide was realized by overlapping different high diffraction orders of the RGB three primary colors, and deflection of the beam direction between gratings was achieved by conical diffraction generated by the inclined grating. Using the vector diffraction theory, the structural parameters and tolerance ranges of the three types of gratings were optimized, rendering average diffraction efficiencies of the three primary colors of the in-coupling, relay, and out-coupling gratings greater than 74%, 21%, and 35%, respectively. As a result, we obtained dual-channel one-dimensional pupil dilation of the original image and a field-of-view angle of h18.9° × v36.87°.

Enhanced light output from deep ultraviolet light-emitting diodes enabled by high-order modes on a photonic crystal surface.

The authors demonstrate the enhanced light output from 275-nm AlGaN-based deep ultraviolet (DUV) light-emitting diode (LED) structures via the in-plane modulation of shallow photonic crystal (PC) patterns that were fabricated on the p-AlGaN contact layer surface. The employed PC lattice constants are in the range of 270-780 nm, much larger than the fundamental Bragg order lattice constant (∼95 nm). As compared to the unpatterned sample, the intensity of the top (or bottom) emission can be enhanced by up to 331% (or 246%), attributed to the high-order coherent diffraction of the internal trapped light and also the Purcell enhancement of spontaneous emission. The findings in this Letter suggest an easier way for the realization of more energy-efficient DUV LEDs which offer the advantage of high emission for various applications in disinfection and sterilization.

Optical meta-cage based on phase gradient metagrating

<sec>How to effectively control the refraction, reflection, propagation and wavefront of electromagnetic wave or light is always one of the advanced researches in the field of optics. In recent years, much effort has been devoted to both theoretical and experimental studies of optical phase gradient metagratings (PGMs) due to the fundamental interest and practical importance of PGMs, such as the generalized Snell’s law (GSL). Typically, the PGMs are constructed as periodic gratings consisting of a supercell spatially repeated along an interface, and each supercell consists of <i>m</i> unit cells, with <i>m</i> being an integer. The key idea of PGMs is to introduce an abrupt phase shift covering the range from 0 to <inline-formula><tex-math id="M2">\begin{document}$2\pi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20221696_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20221696_M2.png"/></alternatives></inline-formula> discretely through <i>m</i> unit cells to ensure the complete control of the outgoing waves. The phase gradient provides a new degree of freedom for the manipulation of light propagation, which has allowed a series of ultrathin devices to realize anomalous scattering, the photon spin Hall effect, and many other phenomena.</sec><sec>Intuitively, the number of unit cells <i>m</i> in a supercell does not influence the PGM diffraction characteristics, except that a small value of <i>m</i> will lead to a reduced diffraction efficiency. However, some recent studies have shown that the integer <i>m</i> plays a fundamental role in determining the high-order PGM diffractions when the incident angle is beyond the critical angle predicted by the GSL. In particular, for high-order PGM diffractions, <i>m</i> leads to a new set of diffraction equations expressed as</sec><sec> <inline-formula><tex-math id="M3">\begin{document}$ \left\{ {\begin{aligned} &{{k_x} = k_x^t - nG,{\text{ for odd L,}}} \\ &{{k_x} = k_x^r - nG,{\text{ for even L}}{\text{. }}} \end{aligned}} \right. $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20221696_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20221696_M3.png"/></alternatives></inline-formula></sec><sec>In addition to the phase gradient, the integer number of unit cells <i>m</i> in a supercell is another degree of freedom that can be employed to control the light propagation. By the parity of <i>m</i>, the higher-order outgoing wave can be reversed between the anomalous transmission channel and the anomalous reflection channel.</sec><sec>In this work, according to the concept of abrupt phase and the parity-dependent diffraction law in phase gradient metagrating, we theoretically design and study an optical meta-cage. The meta-cage is a periodic structure with one period that contains <i>m</i> different unit cells. Through numerical simulations and rigorous analytical calculations, we find that the ability of meta-cage to trap light is related to the parity of the number of unit cells <i>m</i> in a supercell. Specifically, when the number of unit cells is odd, the point source placed in the meta-cage can perfectly radiate out of the meta-cage without any reflection. On the contrary, when the number of unit cells is even, the point source can hardly radiate out of the meta-cage, and all the energy is localized within the meta-cage. Moreover, such a phenomenon is robust against the disorder. These results can provide new ideas and theoretical guidance for designing new radar radome and photonic isolation devices.</sec>

A Universal Filter Approximation of Edge Diffraction for Geometrical Acoustics

Sound propagation in urban and indoor environments often involves diffraction at corners, finite objects and openings, resulting in perceptually relevant frequency-dependent attenuation. Geometrical acoustics (GA) have become a de-facto standard for the prediction and simulation of sound propagation and real-time virtual acoustics, including effects of edge diffraction. However, methods to account for edge diffraction often assume infinite edges, such as the uniform theory of diffraction, or are computationally involved, such as the Biot-Tolstoy-Medwin-Svensson (BTMS) method. Particularly for interactive auralization, an efficient approximation of edge diffraction is desirable. Here, an extension of GA to account for diffraction with simple-to-derive parameters and a time-domain recursive filter implementation is suggested. This universal diffraction filter approximation (UDFA) describes diffraction from infinite and finite wedges using a combination of first-order and (fractional) half-order low-pass filters to account for the frequency-dependent attenuation of the diffracted incident and reflected sound field. The physically-based UDFA exactly matches asymptotic solutions for infinite wedges and provides approximations for finite wedges. It is demonstrated that first-order diffraction from flat finite objects like a plate or an aperture can be described by combining the filters for each edge. To account for effects of higher-order diffraction, an additional heuristic filter extension is suggested.

High-efficiency broadband blazed metagrating working in visible light

A simple 1D blazed metagrating is proposed. The metagrating consists of SiO2 film sandwiched by Ag substrate and Ag nanostrips, which can achieve high-efficiency −1st-order diffraction in the range of 550 nm to 700 nm, and the peak efficiency is nearly 98%. The SiO2 dielectric layer in previous designs is used chiefly as a waveguide layer to support a guided mode. In comparison, it is introduced here to suppress the unwanted diffraction order (zero-order), which helps achieve high-efficiency diffraction at a high diffraction order. For analysis, the metagrating is disassembled into two parts, including a flat plate and a grating. By analysing the far-field radiation pattern of scattered waves and the reflection phase of a specific mode for these two parts, we conclude that the cause of high-efficiency blazing draws support from suppressing zero-order based on destructive interference. This work provides an intuitive physical image for this type of metagrating and an idea to design high-efficiency diffraction and beam deflection devices from the perspective of interference.

Flexural wave splitting via elastic metagratings based on high-order diffraction theory

Wave splitting, one of the most valuable applications in wavefront modulation, is of great significance in both practical engineering and academia. However, to date, the available techniques to split waves are scarce aside from using conventional metasurfaces governed by the generalized Snell’s law. To this end, based on the newly proposed high-order diffraction theory, we design a type of simply structured elastic metagrating for the splitting of flexural waves in plate-like structures. Theoretical models are established to characterize wave propagation behavior in metagratings and functional units. Theoretical analysis confirms the validity of our designs, which is also supported by numerical simulations and experiments. The present study provides a general method for the designing of wave splitters.

Self-standing quasi-random-dots fork gratings for single-order diffraction

Due to the orbital angular momentum it carries, the vortex beam generated by forked gratings is an important way to investigate physics and probe matter. However, unwanted high-order diffractions inherently introduced by traditional fork gratings may be overlaid on useful first-order diffraction, leading to errors in subsequent decomposition of the spectrum. Here, we present a single optical element with a sinusoidal transfer function, termed as quasi-random-dots fork gratings, which can effectively suppress high-order diffractions. The biggest advantage of quasi-random-dots fork gratings is that it can achieve single-order diffraction with a planar structure that can only be achieved by sinusoidal fork gratings with a three-dimensional structure. Therefore, it is a much simpler process to fabricate. Both simulation and experimental results confirm that quasi-random-dots fork gratings can effectively eliminate diffractions of second order and higher orders, and only 0th and ±1st orders are retained. In addition, the helical phase structure of vortex beams with multiple topological charges is also demonstrated. This optical element has potential applications in the field of particle manipulation and imaging.

Generation of phase-only holograms with high-diffraction-order reconstruction by a U-Net-based neural network: A phase grating perspective

Implicit periodic structure in phase-only holograms will result in many diffraction orders in the diffraction field. We analyzed the diffraction pattern from a phase gratings point of view and proved that the diffraction orders were jointly influenced by the phase factor, the single-beam diffraction factor, and the multibeam interference factor. According to the analysis, we proposed the high-diffraction-order angular spectrum method (HDO-ASM) for the numerical reconstruction of high diffraction orders. Different from the conventional methods of removing high diffraction orders, we chose to reconstruct target images in high diffraction orders with HDO-ASM and a U-Net-based neural network. Finally, the 4 K phase-only holograms with high-diffraction-order reconstruction were generated in 0.09s and had a mean reconstruction quality of 34.3 dB (PSNR) in the DIV2K valid dataset. Theoretical and experimental results demonstrated that there are few speckle noises and fringes in the reconstructed images of holograms generated by the proposed method.

Generation of multiple-vortex beams in the process of diffraction of cosine-Laguerre–Gaussian laser beam by the fork-shaped grating

We present the theoretical study about Fraunhofer diffraction of cosine-Laguerre–Gaussian laser beam of mode l,n=0 by the fork-shaped grating with a phase singularity of integer order p. The analytical expressions for the diffracted wave field amplitude and intensity distributions are derived. The transverse intensity and phase profiles of the diffracted beam, in a given diffraction order and for different values of l and p, are calculated. They show that the higher diffraction orders are multiple-vortex beams. In addition, the interference patterns of the diffracted wave field with a slightly inclined plane wave are presented, for confirming the presence of the optical vortices and determining the values and signs of their topological charges. We have shown how an azimuthally shaped, non-vortex beam, consisting of 2l bright lattices, can be transformed into a fan of multiple-vortex beams in the higher diffraction orders.

Ultrafast Continuum IR Generation and Its Application in IR Spectroscopy

The spectral range of femtosecond time-resolved infrared spectroscopy is limited by the bandwidth of mid-IR pulses (100~400 cm-1) generated from the combination of Ti:Sapphire amplifier, Optical Parametric Amplifier (OPA), and Difference Frequency Generation (DFG). To overcome this limitation, we implement a compact continuum mid-IR source producing ultrafast pulses that span the frequency range from 1000 to 4200 cm-1 (from 10 to 2.4 μm), which utilize the mixing of fundamental, second-harmonic, and third-harmonic of 800 nm pulse in the air. After building an IR spectrometer with continuum IR and a monochromator, we found that the distortion of the measured IR spectrum originated from the contamination of higher-order diffraction. We used bandpass filters to eliminate the higher-order contributions and correct the measured IR spectrum. We further characterized the spectral properties of fundamental, second-harmonic, and third-harmonic fields after the plasmonic filamentation process, which helps to improve the efficiency of the continuum IR generation. Using the generated continuum IR pulses, we measured the IR absorption spectrum of a water-benzonitrile mixture, which was found to be consistent with the spectrum obtained with a commercial FT-IR spectrometer. The present work will be useful for the efficient generation of continuum IR pulses for IR pump-probe and two-dimensional IR spectroscopy experiments in the future.

Resonant absorption of light by a two-dimensional imperfect lattice of spherical particles.

The light absorption and scattering by an infinite two-dimensional array with an imperfect lattice of identical spherical particles is considered based on the statistical approach to a description of electromagnetic wave interaction with particulate media. Absorption resonances due to the coherent component of scattered light (zeroth order of diffraction) and resonances arising from the excitation of a flux of incoherently scattered light (higher diffraction orders) propagating at grazing angles to the array plane are studied. The dependence of absorption on the degree of positional ordering of particles is considered. It is shown that with an increase in ordering, the spatial coherence of the light flux along the array plane increases and the absorption resonance becomes more pronounced. Data are presented for silver wavelength-sized particles for s- and p-polarized incident waves. It is shown that at small angles of incidence, the first diffraction order can arise at the wavelength of zeroth-order resonance. In this case, the contributions to absorption created by the coherent and incoherent components of scattered light are summed up. The value of the absorption coefficient can be close to 0.95. A comparison with data for a partially ordered array is carried out.

Electric field driven printing of repeatable random metal meshes for flexible transparent electrodes

Electrohydrodynamic jet printing technology is recognized as one of the most desirable solutions for direct printing of metal meshes. However, electrohydrodynamic jet printing technology makes it difficult to achieve reproducible printing of random metal meshes due to the low stability as well as controllability of the cone jets. Here, a simple and cost-effective printing technique for fabricating flexible transparent electrodes with controlled knot-free random metal meshes was proposed. The simple and green fabrication of transparent electrodes with different random metal meshes was achieved by precisely adjusting the printing process parameters. The sheet resistance variation of the manufactured FTEs with random metal mesh was less than 10 %, showing excellent reliability and stability and environmental adaptability, demonstrating better optoelectronic performance, after 1000 cycles of bending, 180 cycles of adhesion testing, and 72 h of damp heat testing. More importantly, the diffraction experiments show that the fabricated random metal meshes can reduce the negative effects of higher-order diffraction and eliminate the moiré fringe phenomenon. A flexible touch screen application demonstrated the practicality of manufactured FTEs with random metal mesh (area: 80 mm × 130 mm, sheet resistance: 16 Ω/sq, transmittance: 86 %). The proposed method offers a very promising strategy for the efficient and green integrated fabrication of random metal meshes.

Two-Dimension Asymmetric Electromagnetically Induced Grating in Rydberg Atoms

We investigate the realization and manipulation of a two-dimension (2D), asymmetric, electromagnetically induced grating (EIG) in a sample of Rydberg atoms exhibiting the van der Waals (vdW) interactions. The scheme relies on the application of a strong control field and a weak probe field, with the former periodically modulated in a 2D plane and the latter incident perpendicular to the 2D plane. We find that the probe field can be diffracted into an asymmetric intensity distribution depending on the relevant modulation parameters of the control field, as well as the density and length of the atomic sample. In particular, higher-order diffraction intensities can be enhanced in different ways as the vdW interaction, modulation strength, or sample length is increased. It is also of interest that the asymmetric diffraction distribution can be shifted to different quadrants by choosing appropriate modulation phases of the control field. These results may be used to develop new photonic devices with asymmetric diffraction properties required in future all-optical networks.

Polarized induced phase grating in a quantized four-level graphene monolayer system.

We discuss the electromagnetically induced grating (EIG) and electromagnetically induced phase grating (EIPG) in a four-level quantized graphene monolayer system. By using the density matrix technique and perturbation theory, we first obtain the self-Kerr nonlinear susceptibility of the graphene system; afterwards, we study the amplitude and phase modulations of the probe light. We discovered that the EIG and EIPG can be found by controlling the elliptically polarized coupling fields that interact with the monolayer graphene system. Owing to the phase modulation of the transmitted light beam, we recognized that the probe strength can also additionally switch from zeroth-order to high-order diffraction. Moreover, we found that the diffraction performance of the grating may be adjusted through tuning the polarization of the coupling light.