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

Design of freeform phase diffractive optical elements based on the quadratic assignment problem

The design of freeform phase diffractive optical elements is a challenging task, typically necessitating the use of complex differential equations or a large number of iterative calculations. This paper proposes what we believe to be a novel approach to address this problem. In this strategy, we introduce overall comparison optimization (OCO) to ensure the fast convergence of the cost function. The quadratic assignment problem (QAP) is used as the mathematical framework for designing freeform phase diffraction optics. Specifically, the ray mapping calculation problem in geometric optics is simplified as a QAP. To solve this problem, we apply the OCO method, which ensures that the cost function rapidly progresses in the "non-negative" direction, thereby facilitating fast convergence in each optimization iteration. In this manner, the proposed approach alleviates the computational burden associated with repeated evaluations of the cost function and accelerates convergence in the design process. We construct holographic masks using the OCO method and perform simulations to demonstrate the potential of the proposed method in swiftly realizing complex illumination patterns. The results show that the design model has good performance when dealing with complex illumination tasks. The conclusions obtained in this paper can be extended to the realization of phase-only holography and the solution of freeform surfaces illumination design.

Analysis of reconstruction quality for computer-generated holograms using a model free of circular-convolution error

Continuous complex-amplitude computer-generated holograms (CGHs) are converted to discrete amplitude-only or phase-only ones in practical applications to cater for the characteristics of spatial light modulators (SLMs). To describe the influence of the discretization correctly, a refined model that eliminates the circular-convolution error is proposed to emulate the propagation of the wavefront during the formation and reconstruction of a CGH. The effects of several significant factors, including quantized amplitude and phase, zero-padding rate, random phase, resolution, reconstruction distance, wavelength, pixel pitch, phase modulation deviation and pixel-to-pixel interaction, are discussed. Based on evaluations, the optimal quantization for both available and future SLM devices is suggested.

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.

Using an acousto-optic modulator as a fast spatial light modulator

High-speed spatial light modulators (SLM) are crucial components for free-space communication and structured illumination imaging. Current approaches for dynamical spatial mode generation, such as liquid crystal SLMs or digital micromirror devices, are limited to a maximum pattern refresh rate of 10 kHz and have a low damage threshold. We demonstrate that arbitrary spatial profiles in a laser pulse can be generated by mapping the temporal radio-frequency (RF) waveform sent to an acousto-optic modulator (AOM) onto the optical field. We find that the fidelity of the SLM performance can be improved through numerical optimization of the RF waveform to overcome the nonlinear effect of AOM. An AOM can thus be used as a 1-dimensional SLM, a technique we call acousto-optic spatial light modulator (AO-SLM), which has 50 µm pixel pitch, over 1 MHz update rate, and high damage threshold. We simulate the application of AO-SLM to single-pixel imaging, which can reconstruct a 32×32 pixel complex object at a rate of 11.6 kHz with 98% fidelity.

Creating stable trapping force and switchable optical torque with tunable phase of light

Light-induced rotation of microscopic objects is of general interest as the objects may serve as micromotors. Such rotation can be driven by the angular momentum of light or recoil forces arising from special light-matter interactions. However, in the absence of intensity gradient, simultaneously controlling the position and switching the rotation direction is challenging. Here, we report stable optical trapping and switchable optical rotation of nanoparticle (NP)-assembled micromotors with programmed phase of light. We imprint customized phase gradients into a circularly polarized flat-top (i.e., no intensity gradient) laser beam to trap and assemble metal NPs into reconfigurable clusters. Modulating the phase gradients allows direction-switchable and magnitude-tunable optical torque in the same cluster under fixed laser wavelength and handedness. This work provides a valuable method to achieve reversible optical torque in micro/nanomotors, and new insights for optical trapping and manipulation using the phase gradient of a spatially extended light field.

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.

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.

Optimal quantization for amplitude and phase in computer-generated holography

Owing to the characteristics of existing spatial light modulators (SLMs), the computer-generated hologram (CGH) with continuous complex-amplitude is conventionally converted to a quantized amplitude-only or phase-only CGH in practical applications. The quantization of CGH significantly affects the holographic reconstruction quality. In this work, we evaluated the influence of the quantization for both amplitude and phase on the quality of holographic reconstructions by traversing method. Furthermore, we considered several critical CGH parameters, including resolution, zero-padding size, reconstruction distance, wavelength, random phase, pixel pitch, bit depth, phase modulation deviation, and filling factor. Based on evaluations, the optimal quantization for both available and future SLM devices is suggested.

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.

Synergy of Intensity, Phase, and Polarization Enables Versatile Optical Nanomanipulation

Micromanipulation by optical tweezers mainly relies on the trapping force derived from the intensity gradient of light. Here we show that the synergy of intensity, phase, and polarization in structured light allows versatile optical manipulation of nanostructures. When a metal nanoparticle is confined by a linearly polarized laser field, the sign of optical force depends on the particle shape and the laser intensity, phase, and polarization profiles. By tuning these parameters in optical line traps, optical trapping, transporting, and sorting of silver nanostructures have been demonstrated. These findings inspired us to control the motion of nanostructures with designed intensity, phase, and polarization of light using holographic optical tweezers with advanced beam shaping techniques. This work provides a new perspective on active colloidal nanomanipulation in fully controlled optical landscapes, which largely expands the existing optical manipulation toolbox.

Simultaneous optical trapping and imaging in the axial plane: a review of current progress

Optical trapping has become a powerful tool in numerous fields such as biology, physics, chemistry, etc. In conventional optical trapping systems, trapping and imaging share the same objective lens, confining the region of observation to the focal plane. For the capture of optical trapping processes occurring in other planes, especially the axial plane (the one containing the z-axis), many methods have been proposed to achieve this goal. Here, we review the methods of acquiring the axial-plane information from which axial plane trapping is observed and discuss their advantages and limitations. To overcome the limitations existing in these methods, we developed an optical tweezers system that allows for simultaneous optical trapping and imaging in the axial plane. The versatility and usefulness of the system in axial-plane trapping and imaging are demonstrated by investigating its trapping performance with various optical fields, including Bessel, Airy, and snake-like beams. The potential applications of the reported technique are suggested to several research fields, including optical pulling, longitudinal optical binding, tomographic phase microscopy (TPM), and super-resolution microscopy.

Generation of Color Images by Utilizing a Single Composite Diffractive Optical Element

This paper presents an approach that is capable of producing a color image using a single composite diffractive optical element (CDOE). In this approach, the imaging function of a DOE and the spectral deflection characteristics of a grating were combined together to obtain a color image at a certain position. The DOE was designed specially to image the red, green, and blue lights at the same distance along an optical axis, and the grating was designed to overlay the images to an off-axis position. We report the details of the design process of the DOE and the grating, and the relationship between the various parameters of the CDOE. Following the design and numerical simulations, a CDOE was fabricated, and imaging experiments were carried out. Both the numerical simulations and the experimental verifications demonstrated a successful operation of this new approach. As a platform based on coaxial illumination and off-axis imaging, this system is featured with simple structures and no cross-talk of the light fields, which has huge potentials in applications such as holographic imaging.

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.

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.