Beam shaping of complex amplitude with separate constraints on the output beam

Dynamic iterative correction algorithm for designing diffractive optical elements

When utilizing the Gerchberg-Saxton (GS) algorithm to design diffractive optical elements, correction coefficients are introduced to improve the quality of the design results. The main design idea is to correct the target information dynamically during the iterative calculation process. The effectiveness of the proposed method is demonstrated through the verification of beam shaping and phase-type hologram designs. Compared to the traditional GS algorithm, the results of beam shaping show that the light intensity nonuniformity and the root-mean-square error (RMSE) of the shaped spot are reduced by an order of magnitude. The results of phase-type holograms show that the reconstructed image's peak signal-to-noise ratio (PSNR) is improved by about 12 dB. Finally, the paper also discusses the selection of correction coefficients, providing insights into the selection of optimal design correction coefficients. The simulation and experimental results show that the improved algorithm proposed in this paper is not only simple in design but also highly efficient in obtaining a high-quality phase structure, which is of great help in designing high-quality diffractive optical elements.

Random Silica-Glass Microlens Arrays Based on the Molding Technology of Photocurable Nanocomposites

Random microlens arrays (rMLAs) have been widely applied as a beam-shaping component within an optical system. Silica glass is undoubtedly the best choice for rMLAs because of its wide range of spectra with high transmission and high damage threshold. Yet, machining silica glass with user-defined shapes is still challenging. In this work, novel design and fabrication methods of random silica-glass microlens arrays (rSMLAs) are proposed and a detailed investigation of this technology is presented. Based on the molding technology, the fabricated rSMLAs with tunable divergent angles demonstrate superior physical properties with 1.81 nm roughness, 1074.33 HV hardness, and excellent thermal stability at 1250 °C for 3 h. Meanwhile, their characterized optical performance shows a high transmission of over 90% in the ultraviolet spectrum. The fabricated two types of rSMLAs exhibit excellent effects of beam homogenization with surprising energy utilization (more than 90%) and light spot uniformity (more than 80%). This innovative process paves a new route for fabricating rMLAs on solid silica glass and breaking down the barrier of rMLAs to broader applications.

Generation of arbitrary complex fields with high efficiency and high fidelity by cascaded phase-only modulation method

Independent or joint control over the amplitude and phase of the complex field by phase-only modulation element is crucial in numerous applications. Existing modulation methods can realize high levels of accuracy but are accompanied by noticeable losses in light-usage efficiency. Here a cascaded modulation method is proposed for the generation of arbitrary complex fields with high efficiency and high fidelity. This approach is based on a gradient descent optimization algorithm that minimizes a customized cost function. The major advantage of our approach over existing modulation methods is that the efficiency is significantly enhanced while ensuring high modulation accuracy. For the generation of Laguerre-Gaussian mode (LG₀₁), with similar high accuracy, the efficiency by our approach can reach 79.5%, which is enhanced by 192% compared with the theoretical maximum efficiency of 41.5% [Opt. Express25, 11692 (2017)10.1364/OE.25.011692]. Furthermore, the efficiency of existing modulation methods deteriorates rapidly as the target field turns more intricate, whereas in our approach it maintains at a relatively high level. The field generation fidelity and energy efficiency of the proposed cascaded modulation method are compared with that of several different single-pass modulation methods in generating a series of typical Hermite-Gaussian and Laguerre-Gaussian modes and an amplitude-only "OSA" pattern. Our proposed method features both high efficiency and high accuracy in the simulation and experiment, which may be of growing interest to applications such as optical manipulation or quantum communication.

Design of a single-mode fiber coupling system based on the modified Gerchberg-Saxton algorithm

The efficiency of a hollow beam received by the Cassegrain antenna coupling into a single-mode fiber is low, and converting the hollow beam into a solid beam can remarkably improve the coupling efficiency. In this paper, shaping diffractive optical elements (DOEs) are designed through a modified Gerchberg-Saxton algorithm (MGS) with Fresnel diffraction. Further, the MGS algorithm can be applicable in the issue of circular symmetric beam shaping. The properties of the system with/without shaping DOEs are analyzed and compared. According to the simulation results, in consideration of the energy loss of the antenna, DOEs, and coupling lens, the total transmission efficiency of the receiving antenna system at 1550 nm wavelength can reach 77.81%. In addition, the system with shaping DOEs can better adapt for coupling lenses with different focal lengths, and the variation of the maximum coupling efficiency of the DOEs shaping system at different focal lengths studied in this paper is within 2.00%, which is 6.73% lower than that of the lens shaping system. The research results provide an idea of reverse design for improving a coupling system, which can also provide inspiration for other optical system designs.

Self-healing property of the self-rotating beam

In this study, we demonstrate the self-healing of self-rotating beams with asymmetric intensity profiles. The proposed self-rotating beam exhibits an asymmetric intensity profile and self-healing properties in free-space propagation. In addition, the rotation direction and beam intensity profile of the self-rotating beam can be adjusted using the parameters a and b in the phase function. The effects of the position and size of the obstruction on the self-healing property of a self-rotating beam were studied both experimentally and numerically. The simulation and experimental results demonstrate that a self-rotating beam can overcome a block of obstacles and regenerate itself after a characteristic distance. Transverse energy flows were used to explain the self-healing properties. Moreover, the beam rotates during propagation, which can be used to capture and manipulate microscopic particles in a three-dimensional space. It is expected that these rotating beams with self-healing properties will be useful in penetrating obstacles for optical trapping, transportation, and optical therapy.

Self-rotating beam in the free space propagation

We introduce a class of self-rotating beams whose intensity profile tends to self-rotate and self-bend in the free space propagation. The feature of the self-rotating beams is acceleration in the three-dimensional (3D) space. The acceleration dynamics of the self-rotating beams is controllable. Furthermore, multiple self-rotating beams can be generated by a combined diffractive optical element (DOE) simultaneously. Such a beam can be viewed as evolution of a vortex beam by changing the exponential constant of phase. We have generated this beam successfully in the experiment and observed the expected phenomenon, which is basically consistent with the result of the numerical simulation. Our results may provide new insight into the self-rotating beam and extend potential applications in optical imaging.

Speckleless color dynamic three-dimensional holographic display based on complex amplitude modulation

In this paper, we propose a method to implement a speckleless color dynamic three-dimensional holographic display by modulating amplitude and phase distribution simultaneously. Computer-generated holograms are calculated with an initial uniform phase, and the speckle noise of reconstructed images is suppressed effectively. We perform both numerical simulations and optical experiments to demonstrate the effectiveness of the proposed method. The numerical simulations show that the proposed method can achieve speckleless reconstruction and the optical experiments provide a good color dynamic display effect. It is expected that the proposed method could be widely applied to realize high-quality color dynamic holographic displays in the future.

Integrated Double-Sided Random Microlens Array Used for Laser Beam Homogenization

Double microlens arrays (MLAs) in series can be used to divide and superpose laser beam so as to achieve a homogenized spot. However, for laser beam homogenization with high coherence, the periodic lattice distribution in the homogenized spot will be generated due to the periodicity of the traditional MLA, which greatly reduces the uniformity of the homogenized spot. To solve this problem, a monolithic and highly integrated double-sided random microlens array (D-rMLA) is proposed for the purpose of achieving laser beam homogenization. The periodicity of the MLA is disturbed by the closely arranged microlens structures with random apertures. And the random speckle field is achieved to improve the uniformity of the homogenized spot by the superposition of the divided sub-beams. In addition, the double-sided exposure technique is proposed to prepare the rMLA on both sides of the same substrate with high precision alignment to form an integrated D-rMLA structure, which avoids the strict alignment problem in the installation process of traditional discrete MLAs. Then the laser beam homogenization experiments have been carried out by using the prepared D-rMLA structure. The laser beam homogenized spots of different wavelengths have been tested, including the wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B). The experimental results show that the uniformity of the RGB homogenized spots is about 91%, 89%, and 90%. And the energy utilization rate is about 89%, 87%, 86%, respectively. Hence, the prepared structure has high laser beam homogenization ability and energy utilization rate, which is suitable for wide wavelength regime.

Microparticle sorting with a virtual optical chip

We proposed an automatic sorting method based on a virtual optical chip, which was formed by a complex-amplitude beam shaping system. The automatic sorting of different micro-particles was realized by the optical forces of the intensity and phase gradients of the reconstructed optical beam. The method was verified with theoretical analysis and experimental results. Compared with the traditional optical sorting methods, the proposed one does not need high-precision mechanical and/or microfluidic devices. The optical chip is flexible in structure and efficient in optical sorting and can be used in the fields of medical detection and material sensing.

Optimising backscatter from multiple beam interference

Optical sensing applications are usually reliant on the intensity of the measured signal. For remote sensing applications where a target is probed with a laser beam, the sensitivity will be limited by the amount of backscattered light returned from the target to the detector. We demonstrate a method of increasing the signal returned to the detector by illuminating the target with a number of independently controlled beams, where both the position and phase are optimised. We show an improvement in the backscattered signal that is proportional to the number of beams used. The method is demonstrated within a laser microphone, measuring audio signal due to vibrations in surfaces, showing a significant improvement in the signal-to-noise of the measurement.

Robust light beam diffractive shaping based on a kind of compact all-optical neural network

A kind of compact all-optical learning-based neural network has been constructed and characterized for efficiently performing a robust layered diffractive shaping of laser beams. The data-driven control lightwave strategy demonstrates some particular advantages such as smart or intelligent light beam manipulation, optical data statistical inference and incident beam generalization. Based on the proposed method, several typical aberrated light fields can be effectively modulated into the desired fashion including the featured flat-top beams, an arrayed sub-beam arrangement and complex annular fringes compared with conventional GS-based DOEs. An actual THz laser is utilized to evaluate the effectiveness of the method developed.

Rapidly and accurately shaping the intensity and phase of light for optical nano-manipulation

Holographic optical tweezers can be applied to manipulate microscopic particles in various optical patterns, which classical optical tweezers cannot do. This ability relies on accurate computer-generated holography (CGH), yet most CGH techniques can only shape the intensity profiles while the phase distributions remain poor. Here, we introduce a new method for fast generation of holograms that allows for accurately shaping both the intensity and phase distributions of light. The method uses a discrete inverse Fourier transform formula to directly calculate a hologram in one step, in which a random phase factor is introduced into the formula to enable complete control of intensity and phase. Various optical patterns can be created, as demonstrated by the experimentally measured intensity and phase profiles projected from the holograms. The high-quality shaping of intensity and phase of light provides new opportunities for optical trapping and manipulation, such as controllable transportation of nanoparticles in optical trap networks with variable phase profiles.

Fabrication of Random Microlens Array for Laser Beam Homogenization with High Efficiency

The miniaturized and integrated microlens array (MLA) can effectively achieve the beam homogenization, compactness and miniaturization of laser systems. When the high-coherence laser beam is homogenized by means of using the MLA, interference fringes will occur in the homogenized light spot due to the periodicity of the MLA, which seriously affects the uniformity of the homogenized light spot. To solve this problem, a novel random microlens array (rMLA) structure was proposed for the purpose of achieving beam homogenization. The coherence in the homogenization process is suppressed by means of breaking the periodicity of the MLA. The homogenized light spot with a high energy utilization is then obtained accordingly. In the fabrication process, a clever method of combining chemical etching with lithography technology is performed to fabricate a honeycomb rMLA and a rectangular rMLA. The experimental results show that the energy utilization rate of the two types of the rMLAs is about 90%, and the uniformity of the homogenized light spots generated by the honeycomb rMLA and the rectangular rMLA are more than 80% and 85%, respectively. Meanwhile, fully cost-effective fabrication is possible to be realized.

Reducing Computational Complexity and Memory Usage of Iterative Hologram Optimization Using Scaled Diffraction

A complex amplitude hologram can reconstruct perfect light waves. However, as there are no spatial light modulators that are able to display complex amplitudes, we need to use amplitude, binary, or phase-only holograms. The images reconstructed from such holograms will deteriorate; to address this problem, iterative hologram optimization algorithms have been proposed. One of the iterative algorithms utilizes a blank area to help converge the optimization; however, the calculation time and memory usage involved increases. In this study, we propose to reduce the computational complexity and memory usage of the iterative optimization using scaled diffraction, which can calculate light propagation with different sampling pitches on a hologram plane and object plane. Scaled diffraction can introduce a virtual blank area without using physical memory. We further propose a combination of scaled diffraction-based optimization and conventional methods. The combination algorithm improves the quality of a reconstructed complex amplitude while accelerating optimization.

High-performance solar-blind SnO2 nanowire photodetectors assembled using optical tweezers

One-dimensional semiconducting SnO2 nanowires with wide bandgaps are promising candidates to build many important optoelectronic devices. Because building these devices involves the assembly of nanowires into complex structures, manipulation of the active materials needs to be done with high spatial precision. In this paper, an optical tweezer system, comprising a spatial light-modulator, a microscope, and optical elements, is used to individually trap, transfer, and assemble SnO2 nanowires into two-terminal photodetectors in a liquid environment. After the assembly using optical trapping, the two ends of the SnO2 nanowire photodetectors, which are connected with the electrodes, were further stabilized using a focused laser. During exposure to 275 nm deep-ultraviolet light, the as-assembled photodetectors show a high Iph/Idark ratio of 2.99 × 105, a large responsivity of 4.3 × 104 A W-1, an excellent external quantum efficiency of 1.94 × 105, and a high detectivity of 2.32 × 1013 Jones. The photoresponse-speed of the devices could be improved further using passivation with a polymer. The rise and decay times are about 60 ms and 100 ms, respectively. As a result of this study, we can confirm that non-contact optical trapping can enable the construction of nanowire architectures for optoelectronic, bioelectronic, and other devices.

Phase-controlled, speckle-free holographic projection with applications in precision optogenetics

Holographic speckle is a major impediment to computer-generated holographic (CGH) projections in applications ranging from display, optical tweezers, and machining to optogenetic neural control. We present an iterative phase retrieval algorithm that allows the projection of amplitude-controlled speckle-free one-dimensional patterns with a high degree of pattern uniformity. The algorithm, termed the weighted Gerchberg-Saxton with phase-control (GSW-PC), is shown to have the ability to simultaneously control both the phase and amplitude of projected patterns with high diffraction efficiencies. Furthermore, we show that the framework can address the challenge of projecting volumetric phase and amplitude-controlled patterns, by incorporating GSW-PC with the angular spectrum method. The algorithms' performance is numerically and experimentally tested, and further compared with conventional and modern CGH techniques.

Color dynamic holographic display with wide viewing angle by improved complex amplitude modulation

An improved method of complex amplitude modulation (CAM) is proposed for color holographic display with a wide viewing angle. Bandlimited random initial phase is introduced to the CAM method, which overcomes the drawbacks brought by a constant initial phase and maintains the advantages of CAM. Modifications in CAM for color display are also explained. Both simulation and experimental results verify that the proposed method can reconstruct color 3D scenes successfully without the time-consuming process for encoding the computer-generated holograms. Compared with the display via traditional CAM, the results exhibit that the proposed method can reconstruct color 3D scenes with a better viewing effect. Because of the display effect improvement and the high calculation speed, this method can be applied to high performance holographic display.

Non-iterative phase-only Fourier hologram generation with high image quality

We report a novel and non-iterative method for the generation of phase-only Fourier hologram for image projection. Briefly, target image is first added with a special quadratic phase and then padded with zeros. A complex Fourier hologram is generated via the simple fast Fourier transform. Subsequently, the error diffusion algorithm is applied to convert the complex hologram into a phase-only hologram. The numerical, as well as the optical reconstructed images with the proposed method are of higher visual quality and contain less speckle noise compared to the original random phase method, which add the random phase to the target image and then preserve the phase component of the complex hologram. The influences of quadratic phase and zero-padding on the image quality are also discussed in detail.

High-fidelity phase and amplitude control of phase-only computer generated holograms using conjugate gradient minimisation

We demonstrate simultaneous control of both the phase and amplitude of light using a conjugate gradient minimisation-based hologram calculation technique and a single phase-only spatial light modulator (SLM). A cost function, which incorporates the inner product of the light field with a chosen target field within a defined measure region, is efficiently minimised to create high fidelity patterns in the Fourier plane of the SLM. A fidelity of F = 0.999997 is achieved for a pattern resembling an LG10 mode with a calculated light-usage efficiency of 41.5%. Possible applications of our method in optical trapping and ultracold atoms are presented and we show uncorrected experimental realisation of our patterns with F = 0.97 and 7.8% light efficiency.

Speckleless holographic display by complex modulation based on double-phase method

The purpose of this study is to implement speckle reduced three-dimensional (3-D) holographic display by single phase-only spatial light modulator (SLM). The complex amplitude of hologram is transformed to pure phase value based on double-phase method. To suppress noises and higher order diffractions, we introduced a 4-f system with a filter at the frequency plane. A blazing grating is proposed to separate the complex amplitude on the frequency plane. Due to the complex modulation, the speckle noise is reduced. Both computer simulation and optical experiment have been conducted to verify the effectiveness of the method. The results indicate that this method can effectively reduce the speckle in the reconstruction in 3-D holographic display. Furthermore, the method is free of iteration which allows improving the image quality and the calculation speed at the same time.

High-accuracy method for holographic image projection with suppressed speckle noise

Iterative Fourier transform algorithms are widely used for creating holograms in holographic image projection. However, the reconstructed image always suffers from the speckle noise severely due to the uncontrolled phase distribution of the image. In this paper, a new iterative method is proposed to eliminate the speckle noise. In the iteration, the amplitude and phase in the signal window in the output plane are constrained to the desired distribution and a special object-dependent quadratic phase distribution, respectively. Since the phase of the reconstructed image is assigned artificially, the speckle noise came from the destructive interference between the sampling points with random and erratic phase distribution can be eliminated. To verify the method, simulations and experiments are performed. And the result shows that high quality, low noise images can be achieved.

Composite Thue-Morse zone plates

We present a new family of diffractive lenses, composite Thue-Morse zone plates (CTMZPs), formed by multiple orders of Thue-Morse zone plates (TMZPs). The typical structure of a CTMZP is a composite of two concentric TMZPs. The focusing properties of the CTMZPs with different parameters have been investigated both theoretically and experimentally. Compared with the TMZPs, the CTMZPs have higher performance in axial intensity and imaging resolution. The CTMZP beams are also found to possess the self-reconstruction property, and would be useful for three-dimensional optical tweezers, laser machining, and optical imaging.

Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram

An iterative beam shaping algorithm is proposed to simultaneously shape the amplitude and phase of an optical beam. The proposed algorithm consists of one input plane and two completely overlapped output planes which refer to the output plane in real space. The two output planes are imposed with both amplitude and phase constraints, and the constrained areas in the two output planes are complementary. As a result, both the amplitude and phase in the entire output plane are controllable and arbitrary target complex amplitudes can be achieved with the proposed algorithm. The computing result of the proposed algorithm is a phase-only distribution which can be conveniently realized with a spatial light modulator or a fabricated diffractive optical element. Both simulations and experiments have verified the high performance of the proposed algorithm.