Zero-order Diffraction Research Articles

Diffraction efficiency management by complex binary gratings.

The diffraction efficiencies of a complex binary diffraction grating with a rectangular profile are controlled through the steps' phases, amplitudes, and duty cycle, based on analytical expressions. It is demonstrated that the zeroth-diffraction order can be canceled for any arbitrary value of the duty cycle, provided that a π-phase difference is imposed, along with a specific ratio of the steps' amplitudes. This feature is not feasible for separated amplitude-only and phase-only rectangular binary gratings in the context of one-dimensional gratings. In this framework, a key analytic relationship between the duty cycle and the steps' amplitude ratio is derived, allowing the design of such gratings with this desired feature across a wide range of conditions, not limited to a duty cycle of 0.5. Concerning the higher diffraction orders, it is proved that their intensities cancel or maximize for fixed duty cycle no matter the amplitude and phase values of the steps. The intensity of the m-th diffraction order possesses m maxima and m - 1 zeros on the full range of the duty cycle. All these features were corroborated experimentally. The broad insight of such a grating allows the design of gratings with diffraction efficiencies tailored for specific applications.

Electrically tunable third-harmonic generation using intersubband polaritonic metasurfaces

Nonlinear intersubband polaritonic metasurfaces, which integrate giant nonlinear responses derived from intersubband transitions of multiple quantum wells (MQWs) with plasmonic nanoresonators, not only facilitate efficient frequency conversion at pump intensities on the order of few tens of kW cm-2 but also enable electrical modulation of nonlinear responses at the individual meta-atom level and dynamic beam manipulation. The electrical modulation characteristics of the magnitude and phase of the nonlinear optical response are realized through Stark tuning of the resonant intersubband nonlinearity. In this study, we report, for the first time, experimental implementations of electrical modulation characteristics of mid-infrared third-harmonic generation (THG) using an intersubband polaritonic metasurface based on MQW with electrically tunable third-order nonlinear response. Experimentally, we achieved a 450% modulation depth of the THG signal, 86% suppression of zero-order THG diffraction tuning based on local phase tuning exceeding 180 degrees, and THG beam steering using phase gradients. Our work proposes a new route for electrically tunable flat nonlinear optical elements with versatile functionalities.

Second harmonic generation in monolithic gallium phosphide metasurfaces

Abstract Gallium phosphide (GaP) offers unique opportunities for nonlinear and quantum nanophotonics due to its wide optical transparency range, high second-order nonlinear susceptibility, and the possibility to tailor the nonlinear response by a suitable choice of crystal orientation. However, the availability of single crystalline thin films of GaP on low index substrates, as typically required for nonlinear dielectric metasurfaces, is limited. Here we designed and experimentally realized monolithic GaP metasurfaces for enhanced and tailored second harmonic generation (SHG). We fabricated the metasurfaces from bulk (110) GaP wafers using electron-beam lithography and an optimized inductively coupled plasma etching process without a hard mask. SHG measurements showed a high NIR-to-visible conversion efficiency reaching up to 10−5, at the same level as typical values for thin-film-based metasurface designs based on III–V semiconductors. Furthermore, using nonlinear back-focal plane imaging, we showed that a significant fraction of the second harmonic was emitted into the zeroth diffraction order along the optical axis. Our results demonstrate that monolithic GaP metasurfaces are a simple and broadly accessible alternative to corresponding thin film designs for many applications in nonlinear nanophotonics.

Image optimization of a computer-generated hologram by reusing zero-order beams and reflectors vibration.

In computer-generated holography, spatial light modulators are predominantly used for image reconstruction. However, the quality of the reconstructed images is often compromised by laser speckle and zero-order light diffraction. To address these problems, we propose the reuse of the zero-order beam, which not only eliminates the interference caused by zero-order diffraction in the reconstructed images but also considerably enhances image brightness. Moreover, we propose the use of vibrating reflectors in the proposed structure for reusing the zero-order beam to reduce speckle, thereby suppressing the speckle contrast in reconstructed images to less than 4%.

Two-dimensional binary phase gratings for zero-order and high-order diffraction suppression.

A two-dimensional binary phase grating is proposed in this paper. Unlike a conventional transmission grating, in theory, the proposed phase grating can simultaneously eliminate the zero- and high-order diffraction along certain axes on the image plane, forming a pure sinusoidal transmission modulation that leaves only the first-order diffraction. The first-ever, to the best of our knowledge, theoretical model for achieving sinusoidal transmission modulation is suggested in this paper; then the theoretical calculation and experiment results are displayed to investigate the physical mechanism of the proposed grating. Moreover, the manipulation on the arrangement of grating design can disperse or concentrate the diffraction energy at a specific axis. Finally, almost first-order-only diffraction is achieved on a single axis by introducing random changes to certain geometrical parameters of the two-dimensional binary phase grating. Our work provides potential applications in optical science and engineering fields.

On-Chip Meta-Optics for Engineering Arbitrary Trajectories with Longitudinal Polarization Variation.

On-chip integrated meta-optics promise to achieve high-performance and compact integrated photonic devices. To arbitrarily engineer the optical trajectory along the propagation path in an on-chip integrated scheme is of significance in fundamental physics and various emerging applications. Here, we experimentally demonstrate an on-chip metasurface integrated on a waveguide to enable predefined arbitrary optical trajectories in the visible regime. By transformation of the transverse phase to generate longitudinal mapping, the guided waves are extracted and molded into any different optical trajectories (parabola, hyperbola, and cosine). More intriguingly, predefined polarization states with longitudinal variation are also successfully imparted along the trajectory. Owing to the on-chip propagation scheme, the trajectories are uniquely free from zero-order diffraction interference, naturally having a higher signal-to-noise ratio beyond conventional free-space forms. Overall, such on-chip optical trajectory engineering allows for miniaturized integration and can find paths in potential applications of complex optical manipulation, advanced laser fabrication, and microscopic imaging.

Asymmetric 1D and 2D tunneling induced grating in Quantum Dot system

We propose a tunneling-induced grating based on the phenomenon of tunneling-induced transparency. Our method allows us to alternate between zeroth-order diffraction along with completely different higher-order diffraction patterns. This is accomplished by using four laser beams to drive quantum dots via a planar configuration. Specifically, we modulate a standing waves controlling beam which propagates orthogonal with the planar medium, while weaker planar probing beam, generated signal field, and pumping field are applied adjacent towards the medium. We quantitatively analyzed the dynamics for the phase, amplitude modulations, along with probing fields diffraction strengths of various ordering. By altering the relative phase of fields, we expect asymmetric 1D and 2D tunneling induced grating in quantum dot system. Our suggested approach has significant uses in optical memory systems, notably in the storing of information to diffraction orders via tunneling-induced grating.

2-bit coding metasurface with a double layer random flip structure for wide band diffuse reflection and reciprocity protected transmission.

Coding metasurfaces based on random-flip structures have attracted great attention due to their ability to achieve distortion-free transmission and diffuse reflection simultaneously. However, previous implementation based on 1-bit coding metasurface has a narrow bandwidth and insufficient bandwidth coverage in the near infrared region. Here, we propose a novel vertical 2-bit coding metasurface composed of double-layer random-flip meta-atoms (DLRFM). while the main transmission lobe is unchanged, the zero-order diffraction intensity of DLRFM's reflection direction is less than 10% of the total reflection in the range of 0°∼ 30° incidence angle, which proves its excellent diffuse reflection and distortion-free transmission effect. Such design strategy can be extended to multiple wide band coverage in near-infrared regime by tailoring the geometric parameters, which indicates good application potential in advanced display and lens designs.

Diffractive light-trapping transparent electrodes using zero-order suppression

Abstract A light-trapping transparent electrode design based on sub-surface binary dielectric gratings is introduced and demonstrated experimentally. The structure consists of metallic wires patterned with an array of silicon nanobeams. Optimization of the grating geometry achieves selective suppression of zero-order diffraction, while enabling redirection of incident light to an angle that exceeds critical angle of the local environment. Subsequent total-internal reflection allows recovery of light initially incident on the patterned metal wire. Experiments involving amorphous silicon gratings patterned on gold wires demonstrate a light-trapping efficiency exceeding 41 %. Modeling of crystalline silicon nanobeams on silver wires suggests that a shadowing loss reduction of 82 % is feasible. The achievement of a large shadowing reduction using a coplanar structure with high manufacturing tolerance and a polarization-insensitive optical response makes this design a promising candidate for integration in a wide range of real-world photonic devices.

Impact of unintentional Sb in the tensile InAs layer of strain-balanced type-II InAs/InAsSb superlattices grown on GaSb by molecular beam epitaxy

The impact of unintentional incorporation of Sb in the tensile InAs layer of type-II strain-balanced InAs/InAsSb superlattices is investigated. Several coherently strained midwave and longwave superlattices are grown on (100) GaSb substrates by molecular beam epitaxy and examined using x-ray diffraction and temperature-dependent photoluminescence spectroscopy. The zero-order diffraction angle provides the average Sb mole fraction of the strain-balanced superlattice period. Analysis of the higher order diffraction angles, along with the individual layer growth times and strain, provides the InAs and InAsSb layer thicknesses. Analysis of the photoluminescence measurements provides the ground-state bandgap of the superlattice, which along with simulations of the ground-state energies of the electrons and holes using a Kronig–Penney model, specify how the Sb is distributed between the tensile and compressive layers of the period and ultimately the quantity of unintentional Sb in the InAs layer. The unintentional Sb mole fractions observed in the tensile InAs layers are 1.9% for midwave and 1.2% for longwave. When compared to superlattices with the same period and no Sb in the tensile layer, the presence of unintentional Sb blue-shifts the 77 K temperature cutoff wavelength from 6.3 to 5.3 μm for midwave and from 18.8 to 12.0 μm for longwave.

Electromagnetically induced grating realization in phaseonium

We propose a method to implement electromagnetically induced grating in a phaseonium medium that has been coherently generated via atomic mechanisms. Phaseonium atoms have a Λ-type structure and three distinct energy levels; such atoms are originally generated in a coherent superposition of two lower levels. The phaseonium system is comprised of three-level atoms with a Λ-type configuration, which are initially prepared in a coherent superposition of two lower levels. To accomplish this spatial modulation based on the susceptibility of phaseonium medium, a standing-wave field is used. By looking at how an optical field diffracts at different relative phases, we find that the zeroth and first order diffraction intensities increase as the relative phase changes. We also investigate the impact of the Rabi frequency of the field on diffraction intensity and notice that an increasing strength of the Rabi frequency leads to amplification in the intensity of both central zeroth order and first-order diffraction. Furthermore, it has been observed that a significant rise in diffraction intensity occurs at longer interaction lengths between external fields and the atomic medium.

Ultra-narrowband, electrically switchable, and high-efficiency absorption in monolayer graphene resulting from lattice plasmon resonance

We propose a novel approach to obtain the ultra-narrowband, electrically switchable, and high-efficiency absorption in the monolayer graphene. The monolayer graphene is sandwiched between the silica substrate and a square array of silver nanospheres, which is covered by a very thick silica layer. The fundamental role of the thick silica cover layer is to homogenize the surrounding medium of the silver nanospheres, and thus efficiently exciting the lattice plasmon resonance. The lattice plasmon resonance arising from the coupling between the dipolar plasmon resonance of silver nanospheres and the zero-order diffraction wave at Wood anomaly can enhance the electromagnetic fields at the graphene surface, and thus greatly improve the near-infrared light absorption of the monolayer graphene with the maximum absorption efficiency up to 45%. Owing to the low radiation loss of the lattice plasmon resonance, the absorption linewidth of the monolayer graphene can be largely compressed to only several nanometers (3.2 nm ∼ 7.4 nm). Moreover, the absorption of the monolayer graphene in our proposed nanostructures has a nearly 100% modulation depth to exhibit an excellent switching property. Our work will be helpful for some graphene-based photoelectric devices.

Multi-spectral snapshot diffraction-based overlay metrology.

Diffraction-based overlay (DBO) metrology has been successfully introduced to deal with the tighter overlay control in modern semiconductor manufacturing. Moreover, DBO metrology typically needs to be performed at multiple wavelengths to achieve accurate and robust measurement in the presence of overlay target deformations. In this Letter, we outline a proposal for multi-spectral DBO metrology based on the linear relation between the overlay errors and the combinations of off-diagonal-block Mueller matrix elements ΔM = Mij - ( - 1)jMji (i = 1, 2; j = 3, 4) associated with the zeroth-order diffraction of overlay target gratings. We propose an approach that can realize snapshot and direct measurement of ΔM over a broad spectral range without any rotating or active polarization component. The simulation results demonstrate the capability of the proposed method for multi-spectral overlay metrology in a single shot.

Zero-order free holographic optical tweezers.

Holographic optical tweezers (HOTs) use spatial light modulators (SLM) to modulate light beams, thereby enabling the dynamic control of optical trap arrays with complex intensity and phase distributions. This has provided exciting new opportunities for cell sorting, microstructure machining, and studying single molecules. However, the pixelated structure of the SLM will inevitably bring up the unmodulated zero-order diffraction possessing an unacceptably large fraction of the incident light beam power. This is harmful to optical trapping because of the bright, highly localized nature of the errant beam. In this paper and to address this issue, we construct a cost-effective, zero-order free HOTs apparatus, thanks to a homemade asymmetric triangle reflector and a digital lens. As there is no zero-order diffraction, the instrument performs excellently in generating complex light fields and manipulating particles.

Highly dispersive liquid crystal diffraction gratings with continuously varying periodicity

By using well-designed anchoring patterns in a liquid crystal (LC) device, novel electro-optic components with enhanced functionality can be designed. We present two types of nematic LC diffraction gratings with varying periodicity, manufactured with patterned photoalignment at the confining substrates. By varying the surface anchoring periodicity, the incident light can be redirected into many different diffraction orders, giving rise to a scattering appearance of the grating. In Type I gratings the anchoring patterns at the top and bottom substrates are aligned in the same direction, whereas in the Type II grating the anchoring patterns at the top and bottom substrates have a relative rotation of 90°. The structural and optical properties of the gratings can be tuned by applying an external voltage. The director configuration in the bulk is revealed with the use of polarizing optical microscopy images and numerical simulations. Experimental results of the diffraction spectra and intensities of different diffraction orders are supported by finite difference time domain (FDTD) simulations. The results specifically aim at tunable LC diffraction gratings which are highly dispersive and have weak zeroth order diffraction. In general, this work is a contribution to the field of LC flat optical components with electric tunability.

Wavefront single-pixel imaging using a flexible SLM-based common-path interferometer

Wavefront single-pixel imaging (WSPI) is an important tool for simultaneously measuring the amplitude and phase of an unknown field, especially suitable for wavefront detecting in some special wavelengths where array detectors are immature or even unavailable. Here, a passive-detection-based WSPI method using a flexible SLM-based common-path interferometer is proposed, in which by detecting the zero-order diffraction of the SLM directly, the common-path phase-shift or off-axis technique can be flexibly realized by a “sandwich” structure consisting of a half-wave plate, a SLM, and a polarizer. The reference light can be conveniently chosen as the direct reflected light from the SLM, the unmodulated light from the pixels of the SLM, or the light from both of them. We experimentally verify the feasibility and advantages of the proposed method. We further demonstrate the method for wavefront measurement of a dragonfly wing, which suggests it can be used for quantitative phase imaging. It provides a high-resolution spatial wavefront passive detection technique, with a compact, stable, and flexible setup, which has lots of applications involving three-dimensional imaging, aberration correction, digital holographic measurement, and digital microscopy.

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.

CTIS-GAN: computed tomography imaging spectrometry based on a generative adversarial network.

Computed tomography imaging spectrometry (CTIS) is a snapshot hyperspectral imaging technique that can obtain a three-dimensional (2D spatial+1D spectral) data cube of the scene captured within a single exposure. The CTIS inversion problem is typically highly ill-posed and is usually solved by time-consuming iterative algorithms. This work aims to take the full advantage of the recent advances in deep-learning algorithms to dramatically reduce the computational cost. For this purpose, a generative adversarial network is developed and integrated with self-attention, which cleverly exploits the clearly utilizable features of zero-order diffraction of CTIS. The proposed network is able to reconstruct a CTIS data cube (containing 31 spectral bands) in milliseconds with a higher quality than traditional methods and the state-of-the-art (SOTA). Simulation studies based on real image data sets confirmed the robustness and efficiency of the method. In numerical experiments with 1000 samples, the average reconstruction time for a single data cube was ∼16m s. The robustness of the method against noise is also confirmed by numerical experiments with different levels of Gaussian noise. The CTIS generative adversarial network framework can be easily extended to solve CTIS problems with larger spatial and spectral dimensions, or migrated to other compressed spectral imaging modalities.

Super-resolution computed tomography imaging spectrometry

Computed tomography imaging spectrometry (CTIS) is a snapshot spectral imaging technique that relies on a limited number of projections of the target data cube (2D spatial and 1D spectral), which can be reconstructed via a delicate tomographic reconstruction algorithm. However, the restricted angle difference between the projections and the space division multiplexing of the projections make the reconstruction suffer from severe artifacts as well as a low spatial resolution. In this paper, we demonstrate super-resolution computed tomography imaging spectrometry (SRCTIS) by assimilating the information obtained by a conventional CTIS system and a regular RGB camera, which has a higher pixel resolution. To improve the reconstruction accuracy of CTIS, the unique information provided by the zero-order diffraction of the target scene is used as a guidance image for filtering to better preserve the edges and reduce artifacts. The recovered multispectral image is then mapped onto the RGB image according to camera calibration. Finally, based on the spectral and the spatial continuities of the target scene, the multispectral information obtained from CTIS is propagated to each pixel of the RGB image to enhance its spectral resolution, resulting in SRCTIS. Both stimulative studies and proof-of-concept experiments were then conducted, and the results quantified by key metrics, such as structural similarity index measurement and spectral angle mapping have suggested that the developed method cannot only suppress the reconstruction artifacts, but also simultaneously achieve high spatial and spectral resolutions.

Coaxial dual-beam wavefront shaping using nonlocal diffractive metasurfaces in terahertz frequencies.

Metasurfaces for wavefront shaping rely on local phase modulation in subwavelength unit cells, which show limited degree of freedom in dealing with complex and multiple beam transformation. Here, we assign multiple beams into different diffraction orders coaxially located along the same direction, whose wavefronts are tailored by optimizing the diffraction coefficients in two orders and two polarization states of a supercell. By evenly splitting the energy into two orders and adjusting the zeroth-order diffraction phase, a Bessel beam and a vortex beam are simultaneously generated in the near field and far field along a coaxial direction. The effectiveness of the method is validated by the excellent agreement between the simulation and experimental characterization of the two beams.