Binary Gratings Research Articles

Talbot-effect-based multiplication of Laguerre–Gaussian beams with non-zero radial indices: From theory to experimental realization

We present a Talbot self-imaging inspired method for multiplying Laguerre-Gaussian (LG) beams of non-zero radial indices. We explore theoretically and experimentally the LG beam diffraction from two-dimensional (2D) periodic structures. In particular, we determine near-field LG diffraction patterns from a 2D binary grating of a small opening ratio (OR). We demonstrate that incident LG beam intensity patterns are reproduced as images of individual square apertures of the grating in certain Talbot planes. We also investigate the impact of the number of fractional-Talbot and Talbot planes on the quality of the generated 2D array of multiplexed LG modes. Our theoretical predictions are in good agreement with our experiments. Our method can find applications in optical communication, optical tweezing, multi-particle trapping, screening, and micro-manipulation.

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.

Polarization-Mode Transformation of the Light Field during Diffraction on Amplitude Binary Gratings

In this paper, a comparative analysis and numerical simulation of operation of two types of amplitude binary gratings (conventional and fork), both in the focal plane and near-field diffraction under illumination by mode beams with different polarization states, were performed. The simulation of the field formation in the focal plane was performed using the Richards–Wolf formalism. The diffraction calculation in the near-field diffraction was performed based on the FDTD method, considering the 3D structure of optical elements. The possibility of multiplying the incident beam in different diffraction orders of binary gratings and the polarization transformation associated with spin–orbit interaction at tight focusing were shown. In this case, various polarization transformations were formed in ±1 diffraction orders of the fork grating due to different signs of the introduced vortex-like phase singularity. The obtained results can be useful for the laser processing of materials and surface structuring.

Extending the operational limit of a cooled spatial light modulator exposed to 200 W average power for holographic picosecond laser materials processing

The phase range of a Spatial Light Modulator (SLM) requires full 2π response for accurate phase modulation of the incident laser wavefront to create the desired structured intensity distribution. While cooled SLM’s allow increased power exposures, degradation in performance occurs with average powers P>100 W in a Gaussian beam due to residual absorption and consequent heating of the liquid crystal (LC) layer which seriously limits the phase stroke and diffraction efficiency. By introducing a refractive flat top intensity generator ahead of a cooled SLM, we have extended the phase range to Δφ = 2π at incident power P=210 W with only a small light field depolarisation. The operational limit has therefore been extended significantly, allowing efficient, parallel laser materials processing with a high-power picosecond laser. The calculation and implementation of binary Damman gratings for multi-beam laser processing is also shown to be useful at high power exposure.

Talbot phenomenon in binary optical gratings under Gaussian illumination

Binary optical gratings are used in applications such as optical metrology. Due to the fact, that self-imaging phenomenon depends on the grating fill factor, in present work the effect of fill factor on Talbot image formation has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used to determine the intensity distribution in the near field. Self-images are obtained under different initial beam conditions and it is found several regimes of the effect of Gaussian beam intensity distribution on the self-images are found: (I) decreasing intensity of grating slit at the beam border when Gaussian waist radius is 10 times greater than grating period, (II) transforming binary-like self-image to the cosine-like one in case when Gaussian waist radius ranges from 2 to 5 grating periods, and (III) disappearing regular grating structure when Gaussian waist radius is less than grating period. Additionally it is analyzed transform from Fresnel to Fraunhofer regime in case of Gaussian beam and effect of wavefront curvature radius value on the distance where different regimes appear.

Analysis of Moiré pattern for parallel binary gratings based on AND and OR operators

A method for analyzing the Moiré pattern of a parallel binary grating based on the high-frequency component of the omitted pattern is proposed. The analysis aims to investigate the signal components that influence the dark-light band formation of the Moiré pattern. The analytical technique begins with the consideration that both grating patterns are a set of binary rectangular signals with two signal level values, ‘0’ and ‘1.’ Subsequently, Fourier series expansion of these two sets of signals was performed considering the frequency, initial phase and duty cycle of the signals. The superposition of both input signals relies on algebraic equations equivalent to AND and OR operators. The final step was to eliminate the effect of the high-frequency component, which is analogous to the low-pass filter of the electronic circuit (based on averaging the signal intensity per image length). If the frequencies of the two gratings are equal, the analysis based on both operators provides an output signal depending on the initial phase (placement position) and duty cycle values. If the frequencies of the two gratings are not equal, the analysis results show that the output signal has a frequency equal to the frequency difference between the two signals. Moreover, if the two input gratings had a duty cycle of 0.5, the overlapping resulted in a triangular shape. The results from the computer program to simulate the AND and OR operators were consistently compared to the plots of the analytical equations. In addition, they are compatible with image processing results.

P‐227: Late‐News Poster: Design Freeform Metagratings for Eye‐glow Attenuation in Diffractive AR Waveguides

We design and integrate free‐form metagratings with irregular nanoscale patterns into diffractive augmented reality (AR) waveguides to achieve simultaneous improvements in eye‐glow attenuation and outcoupling efficiency. The freeform metagrating demonstrates over 40% reduction in eye‐glow while enhancing outcoupling efficiency by 8% compared to the conventional binary grating.

Generation of complex beams using flattening of binary gratings

The generation of complex beams, such as composite vortex beams, using the logical flattening of two or more co-oriented and registered gratings is demonstrated theoretically and experimentally. The geometrical aspects of such gratings were examined to generate composite vortex beams with the desired intensity and orientation. The proposed methodology was extended to produce other complex beams, such as Laguerre Gaussian transformed Hermite Gaussian and composite vortex transformed Airy beams.

Simple strategy for the simulation of axially symmetric large-area metasurfaces

Metalenses are composed of nanostructures for focusing light and have been widely explored in many exciting applications. However, their expanding dimensions pose simulation challenges. We propose a method to simulate metalenses in a timely manner using vectorial wave and ray tracing models. We sample the metalens’s radial phase gradient and locally approximate the phase profile by a linear phase response. Each sampling point is modeled as a binary blazed grating, employing the chosen nanostructure, to build a transfer function set. The metalens transmission or reflection is then obtained by applying the corresponding transfer function to the incoming field on the regions surrounding each sampling point. Fourier optics is used to calculate the scattered fields under arbitrary illumination for the vectorial wave method, and a Monte Carlo algorithm is used in the ray tracing formalism. We validated our method against finite-difference time domain simulations at 632 nm, and we were able to simulate metalenses larger than 3000 wavelengths in diameter on a personal computer.

Design of a Broadband Integrated Mode Converter Based on Non-Uniform Binary Long-Period Grating by Direct Multiparameter Optimization

Design of a Broadband Integrated Mode Converter Based on Non-Uniform Binary Long-Period Grating by Direct Multiparameter Optimization

Wavelength measurement of narrowband terahertz radiation using a diffraction grating

We propose a reflective binary amplitude grating-based setup for determining the frequency of narrowband terahertz radiation. Theoretical analysis was conducted on transmissive and reflective configurations utilizing binary and phase gratings. Simulations were performed to determine the parameters of metallic diffraction gratings with millimeter-scale constants, which were produced using laser cutting techniques. Our implementation consists of a cost effective and easy-to-implement setup that operates within the 0.15–1 THz range. The grating is installed on a rotary stage. The experimental results obtained align closely with the theoretical calculations. By understanding the setup parameters and the angle of the 1st diffraction order, we could calculate the frequency of the unknown radiation. The relative error in determining the frequency was less than 2%.

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.

Wavefront imaging of a biological sample using DMD-based single-pixel phase-shifting interferometric techniques: An experimental comparison

Single-pixel wavefront imaging (SWI) is an innovative technique for simultaneously measuring the amplitude and phase of an unknown field, which is particularly important for wavefront imaging in invisible wavelengths and under low light conditions. However, most of the existing SWI techniques are still in the technical development stage. Here, we provide a comprehensive analysis and comparison of the SWI methods using DMD-based single-pixel multi-step phase-shifting interferometric techniques. Through experimental demonstrations, we first compare the performances of the techniques using the Hadamard basis, Fourier basis, and discrete cosine transform (DCT) basis. Further, the performances of the Hadamard basis-based SWI (HSWI) technique using phase-shifting interferometry with the different reference strategies are investigated while the binary grating, Lee, and super-pixel methods are applied to control the DMD for realizing the necessary complex amplitude modulations there. Experimental results suggest the grating-phase-shifting-based HSWI performs best, in which one can use the checkerboard reference for the maximum field of view or select the peripheral reference for a better imaging resolution; and it can do 2 fps wavefront imaging of the sample at 10 % downsampling rate with a resolution of 128 × 128 pixels. Our work provides researchers with a guideline to choose a suitable SWI technique for their applications.

Compact, low-cost, and low-crosstalk orbital angular momentum sorter based on binary grating

Compact, low-cost, and low-crosstalk orbital angular momentum sorter based on binary grating

Simulation of the spatial distribution of scattered light under illumination of a resonant diffraction grating with structured light

In this paper, a comparative theoretical analysis and numerical simulation of the operation of various types of diffraction gratings in the far field is carried out using a Fourier transform. In more detail is discussed the spatial spectrum of binary amplitude gratings, including the diffraction patterns in the far field and in the focal plane and while taking into account variations in the fill-factor. When analyzing characteristics of experimentally created halide perovskite resonant gratings, the influence of the illuminating beam type on the formation of the first three diffraction orders is considered.

Full-duplex cylindrical vector beam multiplexing communication using spin-dependent phase modulation metasurfaces

Cylindrical vector beam (CVB) has recently gained attention as a promising carrier for signal multiplexing owing to its mode orthogonality. However, the full-duplex multiplexing communication has not been previously explored for the lack of effective technologies to parallelly couple and separate CVB modes. Herein, we present a full-duplex solution for CVB multiplexing communication that utilizes spin-dependent phase modulation metasurfaces. By independently phase-modulating the two spin eigenstates of CVBs with the metasurface via spin-dependent orbital interactions, and loading two binary Dammann vortex gratings, we enabled an independent and reciprocal wave vector manipulation of CVBs for full-duplex (de)multiplexing operation. To demonstrate this concept, we constructed a 16-channel (including 4 CVB modes and 4 wavelengths) full-duplex CVB multiplexing communication system and achieved the bidirectional transmission of 800 Gbit/s quadrature-phase shift-keying (QPSK) signals over a 5 km few-mode fiber. Our results demonstrate the successful multiplexing and demultiplexing of 2 radial CVB modes and 2 azimuthal CVB modes in full-duplex communication with the bit-error-rates approaching 1.87 × 10−5.

Optimal binary gratings for multi-wavelength magneto-optical traps.

Grating magneto-optical traps are an enabling quantum technology for portable metrological devices with ultracold atoms. However, beam diffraction efficiency and angle are affected by wavelength, creating a single-optic design challenge for laser cooling in two stages at two distinct wavelengths - as commonly used for loading, e.g., Sr or Yb atoms into optical lattice or tweezer clocks. Here, we optically characterize a wide variety of binary gratings at different wavelengths to find a simple empirical fit to experimental grating diffraction efficiency data in terms of dimensionless etch depth and period for various duty cycles. The model avoids complex 3D light-grating surface calculations, yet still yields results accurate to a few percent across a broad range of parameters. Gratings optimized for two (or more) wavelengths can now be designed in an informed manner suitable for a wide class of atomic species enabling advanced quantum technologies.

Partially coherent beam generation with metasurfaces

An optical system for the generation of partially coherent beams with genuine cross-spectral density functions from spatially modulated globally incoherent sources is presented. The spatial intensity modulation of the incoherent source is achieved by quasi-planar metasurfaces based on spatial-frequency modulation of binary Bragg surface-relief diffraction gratings. Two types of beams are demonstrated experimentally: (i) azimuthally periodic, radially quasi-periodic beams and (ii) rotationally symmetric Bessel-correlated beams with annular far-zone radiation patterns.

Pixel-level phase filters for off-axis shifting of sinc envelope in holographic projection.

Off-axis projection is a common practice for reconstructions of Fourier holograms displayed on liquid crystal on silicon (LCoS) spatial light modulators (SLMs), as it spatially separates the image from the undiffracted light. Binary gratings encoded within the holograms enable maximum angular separation. However, as a result, two mirror images of equal intensities are present in the reconstruction. To introduce asymmetry to the intensity distribution and suppress one of those images, we propose a phase mask with a subpixel pattern. Presented results prove the potential of in-built SLM phase-mask layers for optimizing efficiency of the off-axis holographic projection.

Deep learning self-image update procedure in a wavefront sensor based on the Talbot phenomenon under Gaussian illumination

A feature-based image update procedure using machine learning is proposed to use in preprocessing of self-images in a Talbot wavefront sensor. A variant of the recurrent neural network with backpropagation, which is one of most widely applied machine learning tools, is utilized to stabilize intensity distribution in self-images in the case of an optical beam with a Gaussian profile. Once well trained, the neural network can decrease pit image shifts caused by beam intensity distribution in the case of a cosine-like grating. It is shown that based on the proposed recurrent neural network, it is possible to decrease the shift error caused by the Gaussian beam up to nine times depending on the aberration order and value. Despite the decreasing shift error, the value of the error of the restored aberration coefficient does not decrease significantly because of the feature-vector extraction method. It is shown additionally that due to the spatial spectrum wideness, the proposed self-image procedure is not applicable to binary gratings on the example of binary gratings with square pits. Adequate simulations are implemented to demonstrate the effectiveness and accuracy of the proposed approach.