Phase Gratings Research Articles

Structure of Axial Modes of a Diode Laser with an External Cavity Containing a Volume Phase Grating

Structure of Axial Modes of a Diode Laser with an External Cavity Containing a Volume Phase Grating

Femtosecond laser-induced glass refractive index change in tellurite glass

Tellurite glass has excellent infrared optical properties and is widely used in lasers, optical communications, and sensing. Femtosecond laser direct writing is a preferred method for manufacturing tellurite photonic devices, which requires precise control of the variable of refractive index. However, accurate testing of the refractive index changes induced by femtosecond laser in tellurite glass is challenging due to the small magnitude of change and localized region. In this study, we present a novel approach to measure the refractive index change of tellurite glass through the utilization of volume phase grating (VPG) diffraction. We first investigated the laser-induced damage threshold (LIDT) of tellurite glass and then proceeded to prepare VPGs inside the glass by using femtosecond laser direct writing technology, ensuring that the laser energy remained below the LIDT. By measuring the thickness and diffraction efficiency of VPGs prepared under different laser energies, we determined the associated change in refractive index. In our experiment, when subjected to laser incidence with wavelengths of 632.8 and 808 nm, the maximum values of refractive index change in the laser-modified region are measured to be 1.97 × 10−3 and 1.61 × 10−3, respectively. This method offers a precise means of measuring refractive index change within the microregion of tellurite glass induced by femtosecond laser. This capability holds great significance for the fabrication of high-quality tellurite glass photonic devices using lithography-based techniques.

Fringe projector with submillimeter fringe spacing at a meter-scale field of view.

State-of-the-art fringe projection systems generate fringe patterns using digital light projectors (DLP). The axial uncertainty is limited by the smallest fringe period and is directly related to the pixel count. This results in limited accuracy of current DLP systems that affect applications such as in situ measurements for laser powder bed fusion systems, where a submillimeter fringe period is needed for field-of views larger than 500m m×500m m. This work presents a scalable fringe projection technique that enables the generation of stable fringe patterns over a large field of view spanning several meters while maintaining submillimeter fringe periods. This system uses geometric phase gratings to enable variable fringe spacing and fringe orientation capabilities. The system shears a coherent beam in the Fourier plane using a pair of geometric polarization gratings. The separation between the gratings directly affects the fringe spacing, and the orientation of the gratings affects the fringe orientation. The depth of focus is only limited by the coherence of the light source, enabling high fringe periods even on tilted planes. The system is designed with a single path configuration, making the system more robust to environmental noise. With a rotating linear polarizer, we demonstrate that phase-shifting methods could be employed to acquire phase information about the object. This paper employs a single-shot Fourier transform phase estimation technique to process the intensity maps acquired using projected fringe patterns. Further, we demonstrate the capabilities of the system to produce submillimeter fringe spacing and the ability to project fringes on larger scales for measurements.

Color and luminance processing in V1 complex cells and artificial neural networks.

Object recognition by natural and artificial visual systems benefits from the identification of object boundaries. A useful cue for the detection of object boundaries is the superposition of luminance and color edges. To gain insight into the suitability of this cue for object recognition, we examined convolutional neural network models that had been trained to recognize objects in natural images. We focused specifically on units in the second convolutional layer whose activations are invariant to the spatial phase of a sinusoidal grating. Some of these units were tuned for a nonlinear combination of color and luminance, which is broadly consistent with a role in object boundary detection. Others were tuned for luminance alone, but very few were tuned for color alone. A literature review reveals that V1 complex cells have a similar distribution of tuning. We speculate that this pattern of sensitivity provides an efficient basis for object recognition, perhaps by mitigating the effects of lighting on luminance contrast polarity. The absence of a contrast polarity-invariant representation of chromaticity alone suggests that it is redundant with other representations.

A triple band local oscillator coupling system based on a phase grating for five-meter Dome-A terahertz explorer telescope.

For heterodyne receivers, broadband and integrated local oscillator (LO) coupling schemes are crucial. In this paper, we present a novel terahertz broadband receiver system based on a one-pixel phase grating. We designed a phase grating that can simultaneously couple the LO signals at 690, 850, and 1300GHz to a superconducting hot-electron bolometer mixer at the incident angles of 25.7°, 20.6°, and 13.3°, respectively. At these three frequencies, the measured diffraction efficiencies of the phase grating are as high as 70%, 73%, and 65%, and the total power coupling efficiencies of the LO coupling system are 22%, 23%, and 23%, in good agreement with the simulated results. This efficient and highly integrated multiband receiver system has potential applications in the proposed Five-meter Dome-A Terahertz Explorer telescope.

Engineered asymmetric diffractions of diagonal-line odd-symmetric phase gratings

A two-dimensional multi-element phase grating has been designed in terms of the offset refractive index to exhibit the spatially odd symmetry (antisymmetry) along one transparent diagonal line with an even number of rectangular elements while leaving other elements in a unit cell opaque. This grating can be engineered to attain a few intriguing phenomena of asymmetric diffraction, including the elimination of equally spaced oblique diffraction lines, the elimination of alternately crossed oblique diffraction lines, and the selection of equally spaced oblique diffraction lines. These phenomena of engineered asymmetric diffraction are well explained via destructive interference between transmitted field amplitudes from paired, dual-paired, and successive elements along the transparent diagonal line.

Compression of High-Resolution Space Video Using Phase Grating

Compression of High-Resolution Space Video Using Phase Grating

Slightly Off-Axis Digital Holography Using a Transmission Grating and GPU-Accelerated Parallel Phase Reconstruction

Slightly off-axis digital holography is proposed using transmission grating to obtain quantitative phase distribution. The experimental device is based on an improved 4f optical system in which a two-window input plane is used to form the object beam and reference beam. Then, the two beams are diffracted into multiple orders by the transmission grating placed at the Fourier plane. By applying a modified Michelson configuration, the interference patterns can be generated by the object and reference beams from different diffraction orders. After translating the grating, a random phase shift can be introduced to the hologram. To demonstrate the feasibility of our method, both thick and thin phase specimens are retrieved using two carrier phase-shifting holograms. Furthermore, we use the phase reconstruction algorithm based on the NVIDIA CUDA programming model to reduce the retrieval time. Meanwhile, we optimize the discrete cosine transform (DCT)-based least-squares unwrapping algorithm to unwrap the phase. By porting the entire phase reconstruction process to the graphics processing unit (GPU), the phase retrieval acceleration and execution efficiency significantly improve. To demonstrate the feasibility of our method, it is found that our method can measure the surface profiles of standard elements, such as a plano-convex cylinder lens and a microlens array, with a relative error of about 0.5%. For holograms with a different phase shift, the root-mean-square (RMS) value of the phase difference for the main imaging region is about 0.2 rad. By accelerating the phase reconstruction with GPU implementation, a speedup ratio of about 20× for the thick phase specimen and a speedup ratio of about 15× for the thin-phase specimen can be obtained for holograms with a pixel size of 1024 × 1024.

Exploring beam size measurement based on the Talbot effect at BEPCII.

Vertical beam size measurements were carried out at Beijing Electron-Positron Collider II (BEPCII) using a phase grating and an absorption grating based on the Talbot effect. The transverse coherence of synchrotron radiation is closely related to beam size. Due to the partial coherence of the synchrotron radiation source, the coherence length can be calculated by measuring the visibility decay of interferograms recorded at different distances behind the gratings. A vertical beam size of 68.19 ± 2 µm was obtained based on the relationship between the coherence length and beam size at the 3W1 beamline of BEPCII. A comparison of the vertical emittance derived from the grating Talbot method and the synchrotron radiation visible light interferometer method was presented. The vertical emittances from the two methods are 1.41 nm rad and 1.40 nm rad, respectively. The 0.1% difference indicates that the grating Talbot method for beam size measurement is reliable. This technique has great potential for small beam size measurement of fourth-generation synchrotron radiation light sources, considering its small diffraction limitation and simple experimental setups.

Laser beam array spot steering customized trajectories using the acousto-optic effect.

We demonstrate a proof of principle of a technique for array laser beam steering according to a generalized elliptical path, using the acousto-optic effect. We explore the dynamic trajectories of the diffraction orders of a Gaussian beam, diffracted by a dynamic 2D sinusoidal phase grating. The latter is generated by two crossed acoustic waves propagating in a transparent medium, giving rise to 2D dynamic sinusoidal refractive index variation. We particularly emphasize the case where the two crossed acoustic waves are modulated in frequency and have a phase difference. In such case, the resulting diffraction orders are dynamic and follow some particular trajectory's shapes, from linear and circular to generalized elliptical shapes. Inspired by Poincaré and Bloch spheres used to represent polarization and quantum states, we suggest the sphere volume trajectory shape to represent all trajectories' shapes of all diffraction orders.

Multiparametric, Label-Free Analysis of Microfluidic Droplets via a Dynamic Phase Grating Approach.

Droplet-based microfluidic systems possess many fundamental advantages as a platform for the analysis of chemical and biological species. However, whereas on-chip operations have rapidly developed over the past decades, approaches for analyzing target molecules within droplets have largely remained limited to methods requiring bulky and expensive instrumentation. In this work, we describe a droplet analysis approach whereby the droplet train itself is the sensing construct. Specifically, the droplet train is interrogated as a transmission phase grating, allowing high-throughput, label-free, solution-phase, and multi-parametric analysis of droplet contents. Importantly, three distinct properties of generated droplets can be simultaneously extracted using this conceptually simple and experimentally straightforward measurement approach. Under constant droplet generation conditions, measurement of droplet viscosity is achieved by monitoring changes in zero order to first order peak separation in the far-field diffraction pattern, with a sensitivity of 2.28 × 10-4 cSt per μm change in peak separation. In parallel, measurement of droplet refractive index (RI) is achieved by measuring changes in the ratio of the zero order to first order peak intensity, with a sensitivity of 2.14 × 10-4 RI units per unit change in a diffracted peak intensity ratio. Finally, droplet generation frequency is determined from the time-varying oscillation of the peak height ratio, yielding comparable results to an expensive high-speed camera commonly used for droplet imaging. Importantly, the experimental strategy for this approach is straightforward and does not require expensive instrumentation; therefore, it may find utility in affordable and portable analysis approaches applied to diverse droplet microfluidic assays.

Electrically Tunable Liquid Crystal Phase Grating with Double Period Based on the VIS Mode

A tunable liquid crystal (LC) phase grating based on vertical-field in-plane electrical switching (VIS) is proposed. The tunable LC phase grating is composed of four parts: an LC layer, the top-plane and bottom-plane electrodes, the polyimide (PI) layer, and the top and bottom periodical strip electrodes. On the one hand, a large period LC phase grating can be obtained by applying voltage to the upper plane electrode and the lower periodic strip electrodes. On the other hand, a small period LC phase grating can be obtained by applying voltage to the lower plane electrode and the upper period electrodes. As a result, two kinds of LC phase grating with different periods can be realized by changing the driving scheme. Naturally, the diffraction angle can be adjusted by controlling different LC phase grating periods. The simulation results show that this tunable LC phase grating based on the VIS mode has a relatively short response time and low operating voltage (5.4 V). These characteristics make the tunable LC phase grating have good application prospects in holographic 3D or augmented reality (AR) display.

Tailored diffractions of asymmetric columns and symmetric rows in two-dimensional multi-element phase gratings.

Two-dimensional multi-element phase gratings can be engineered to show an even symmetry along one direction while an odd symmetry along the other direction in terms of offset refractive indices in each unit cell. The interplay of such even and odd symmetries has been explored to tailor diffraction columns and rows on demand by making offset refractive indices to satisfy specific requirements and hence attain different types of destructive interference. The resultant tailoring effects include the directional column elimination, the grouped column elimination, and the directional column selection as well as the natural row absence, the grouped row elimination, and the central row selection.

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.

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.

Experimental and numerical polarization analysis of the 3D transfer behavior in microsphere-assisted interferometry for 1D phase gratings

Enhancing the lateral resolution in optical microscopy and interferometry is of great interest in recent research. In order to laterally resolve structures including feature dimensions below the Abbe resolution limit, microspheres in the optical near-field of the specimen are shown to locally improve the resolution of the imaging system. Experimental and simulated results following this approach are obtained by a high NA Linnik interferometer and analyzed in this contribution. They show the reconstructed surface of a 1D phase grating below the resolution limit. For further understanding of the transfer characteristics, measured interference data are compared with FEM (finite element method) based simulations with respect to the polarization dependency of the relevant image information for 1D phase gratings. Therefore, the implemented Koehler illumination as well as the experimental setup utilize polarized light.

The Interplay of Processing-Related Influences on the Formation of Volume Holographic Gratings in a Free-Surface Epoxy-Based Recording Material

Understanding the formation processes of holographic gratings in polymers as a function of material composition and processing is important for the development of new materials for holography and its associated applications. Among the processing-related factors that affect grating formation in volume holographic recording material, pre-exposure, prebaking and dark storage, as well as the associated variations in layer thickness and composition, are usually underestimated. This study highlights the influence and interaction of these factors and shows that they should not be neglected. This is of particular importance for samples with a free surface. Here, one such epoxy-based free-surface material is investigated. To determine the influence of prebaking on the holographic grating formation, as well as on the achieved refractive index contrast, angular resolved analysis of volume holographic phase gratings is applied through point-by-point scanning of the local material response. Grating characteristics are determined by comparison with simulations based on rigorous coupled wave theory. Thus, the optimal dose for prebaking can be determined, as well as the optimal exposure time, depending on the dose. The influence of dark storage on the material response is investigated over a period of 12 weeks and shows a strong dependence on the deposited energy density.

Toward Arbitrary Spin‐Orbit Flat Optics Via Structured Geometric Phase Gratings (Laser Photonics Rev. 17(5)/2023)

Toward Arbitrary Spin-Orbit Flat Optics via Structured Geometric Phase Gratings In article number 2200800, Peng Chen, Zhi-Han Zhu, Yan-Qing Lu, and colleagues demonstrate a new type of flat-optics elements, termed structured geometric phase gratings, capable of complex-amplitude control with polarization switchable behavior. Such an advanced spin-orbit device, compared with the present elements, unlocks the control of paraxial structured light in all spatial dimensions and paves the way towards arbitrary SOC conversion via flat optics.

High-order OAM states unwrapping in multiplexed optical links

To accurately unwrap the high-order orbital angular momentum (OAM) for multiplexed vortex beams is a challenge. In this work, over ±160 order OAM topological charges have been unwrapped in multiplexed optical links. Optical imaging based discrepancy identification enables the multiplexed OAM modes separating in physics, and the intelligent pattern recognition further promotes its unwrapping in numerical domain. Particularly, the combination of annular phase grating and auxiliary beams features compound spiral stripes, which paves the way for optical intensity recognition with low-complexity and high-commonality. Moreover, the spiral direction characterizes the symbol of the OAM states, which dramatically broadens the amount of multiplexed links. Here, optical separating means assisted by intelligent pattern recognition opens up a new route to high-speed and large-capacity optical communication, which may shed new light on 6G application.

Multi-functional liquid crystal devices based on random binary matrix algorithm

ABSTRACT Multi-functional diffraction gratings have found broad applications in laser processing, medicine, beam manipulation, etc. However, based on the existing schemes there are still some challenges in fabricating the diffraction gratings with the controllable and arbitrary diffraction intensity of each order, multiple phase distribution, and polarisation of the output. Here, we propose a new phase mixing algorithm based on the random binary matrix and describe the theoretical foundation and experimental realisation of the proposed scheme. Using the new algorithm, several phase-mixing devices were fabricated, and the experiment verified the relationship of the light intensity, polarisation, phase and the algorithm. Our approach is practical to mix the phases of several diffraction gratings to realise the controllable diffraction orders, offering an innovative idea for the research of the liquid crystal phase mixing devices.