Complex-amplitude Hologram Research Articles

Metasurfaces enabled dual-channel complex-amplitude hologram designed with neural network

In this work we present a polarization-multiplexing metasurface hologram designed with neural network, which can modulate the amplitude and phase of incident light with four nanopillars comprised unit structures with high efficiency. Then, to improve image quality by minimizing the difference between the complex amplitude field modulated by the structure and that obtained through the network, we developed an end-to-end framework-assisted multifunctional metasurface design method based on the aforementioned neural network, which can directly map geometric parameters of the metasurface to holographic images. The comparative results indicate that for the end-to-end framework, although the optimized distributions of complex amplitudes are limited by the selected finite number of structures, in the simulation results, higher-quality images can still be obtained compared to the forward design method. Full-wave simulation results show our proposed method can obtain higher quality holographic images compared to the GS algorithm. This work may open new possibilities in holographic displays and multifunctional optical devices.

Polarization-independent 3D metasurface with complex amplitude modulation.

Metasurfaces, which possess unprecedented capabilities in manipulating electromagnetic wavefronts, are promising for accurate complex amplitude modulation with a compact device. However, current strategy of complex amplitude modulation based on metasurfaces focuses on anisotropic unit design which is intrinsically constrained of polarization states. In this study, we propose a design methodology of polarization-independent metasurface which comprises an array of nanocylinders with various radii and heights. The effectiveness of the proposed scheme is verified using an optical vortex generator and a complex-amplitude hologram device. The straightforward, cost-effective, and polarization-independent design can provide robust and reliable solutions for wavefronts modulation in various optical applications.

Direct binary search method for high-resolution holographic image projection.

Complex-amplitude modulation of light fields with a digital micromirror device (DMD) has been widely used in holographic image projection. DMD is a binary-amplitude modulator, and its use for complex field modulation in a 4f configuration requires low-pass filtering. However, the reconstructed fields suffer from low resolution due to the limited bandwidth for the existing methods such as the Lee and superpixel methods. Here, we report a direct binary search (DBS) method to design high-resolution complex-amplitude holograms. The method is able to increase the spatial bandwidth up to twice that of the superpixel method. Numerical simulations and experiments are presented to demonstrate the method, which show that the errors are reduced by about 60% and 40% respectively for the test fields compared to the superpixel method. Furthermore, the measured efficiency of laser light can be improved by a maximum of 60%.

End-to-end design of metasurface-based complex-amplitude holograms by physics-driven deep neural networks

Abstract Holograms which reconstruct the transverse profile of light with complex-amplitude information have demonstrated more excellent performances with an improved signal-to-noise ratio compared with those containing amplitude-only and phase-only information. Metasurfaces have been widely utilized for complex-amplitude holograms owing to its capability of arbitrary light modulation at a subwavelength scale which conventional holographic devices cannot achieve. However, existing methods for metasurface-based complex-amplitude hologram design employ single back-diffraction propagation and rely on the artificial blocks which are able to independently and completely control both amplitude and phase. Here, we propose an unsupervised physics-driven deep neural network for the design of metasurface-based complex-amplitude holograms using artificial blocks with incomplete light modulation. This method integrates a neural network module with a forward physical propagation module and directly maps geometric parameters of the blocks to holographic images for end-to-end design. The perfect reconstruction of holographic images verified by numerical simulations has demonstrated that compared with the complete blocks, an efficient utilization, association and cooperation of the limited artificial blocks can achieve reconstruction performance as well. Furthermore, more restricted controls of the incident light are adopted for robustness test. The proposed method offers a real-time and robust way towards large-scale ideal holographic displays with subwavelength resolution.

Arbitrary amplitude and phase control in visible by dielectric metasurface.

Metasurfaces have been widely studied for arbitrary manipulation of the amplitude, phase and polarization of a field at the sub-wavelength scale. However, realizing a high efficiency metasurface with simultaneous and independent control of the amplitude and phase in visible remains a challenge. In this work, an ultrathin single-cell dielectric metasurface which can modulate arbitrary complex amplitude in transmission mode is proposed. The amplitude is controlled by adjusting the dipoles and quadrupoles by tuning the geometric size, while the phase is manipulated based on the Pancharatnam-Berry phase by rotating the meta-atom. Complex amplitude fields for generating holographic images and structure light are utilized to verify the reliability of the proposed structure. It has been experimentally demonstrated that the quality of holographic image of complex-amplitude hologram encoded on the proposed metasurface is better than that of phase-only holograms and verified by simulation that complex structure light can be generated by the proposed structure. Our work expands the superior limits of various applications, including arbitrary beam shaping, 3D biological imaging, optical computing, and optics-on-chip devices.

Optimizing double-phase method based on gradient descent algorithm with complex spectrum loss function

This study proposes a gradient descent method for enhancing the quality of reconstructed images encoded by double-phase holograms (DPHs). Holographic displays are often noisy because of optical hardware problems. However, owing to the conversion from complex-amplitude holograms to phase-only holograms, the reconstructed images still have noise and cannot be ignored. In this paper, the proposed method uses a spectrum loss function instead of image loss function in the gradient descent optimization process. The spectrum loss function ensures that DPHs can be optimized by gradient descent method, and this method requires only several iterations. The simulations and experimental results have validated the effectiveness of the proposed method.

Tailoring Circular Dichroism in an Isomeric Manner: Complete Control of Amplitude and Phase for High‐Quality Hologram and Beam Forming

AbstractNowadays, the research of metasurfaces has been developed from single‐dimensional toward multi‐dimensional manipulation of electromagnetic (EM) waves, which greatly boosts the practical application of metasurfaces in both microwave and optics regimes. Currently, the demand for new methods to implement effective manipulation of EM waves in multiple dimensions is ever being increased yet it is still a challenging task. Here, a metasurface‐based paradigm is proposed for tailoring both amplitude and phase by isomeric manner in a dichroism level, which reveals a flexible capability of manipulating EM waves within all isotropic, anisotropic and chiral characteristics. Circular dichroism (CD) meta‐atoms are implemented via loading lumped resistors into planar chiral resonators. The cross‐polarization reflection amplitude of the circularly polarized wave is tailored precisely and continuously from 0 to 1 using the diastereomers of CD meta‐atoms, while the phase is independently manipulated by the rotamer counterparts based on Pancharatnam‐Berry (PB) phase. By controlling both amplitude and phase profiles of the metasurfaces with subwavelength spatial resolution, high‐quality complex amplitude hologram and far‐field beam forming are demonstrated. Encouragingly, this approach for achieving simultaneous control of amplitude and phase makes a milestone on multi‐dimensional metasurfaces which may find applications in integrated planar EM functional systems.

Deep learning for hologram generation

This work exploits deep learning to develop real-time hologram generation. We propose an original concept of introducing hologram modulators to allow the use of generative models to interpret complex-valued frequency data directly. This new mechanism enables the pre-trained learning model to generate frequency samples with variations in the underlying generative features. To achieve an object-based hologram generation, we also develop a new generative model, named the channeled variational autoencoder (CVAE). The pre-trained CVAE can then interpret and learn the hidden structure of input holograms. It is thus able to generate holograms through the learning of the disentangled latent representations, which can allow us to specify each disentangled feature for a specific object. Additionally, we propose a new technique called hologram super-resolution (HSR) to super-resolve a low-resolution hologram input to a super-resolution hologram output. Combining the proposed CVAE and HSR, we successfully develop a new approach to generate super-resolved, complex-amplitude holograms for 3D scenes.

Ohmic Dissipation‐Assisted Complex Amplitude Hologram with High Quality

AbstractTailoring the phase and amplitude of electromagnetic waves has drawn great attention in the microwave, terahertz, and even optics domains. However, the existing method for simultaneous control of these two essential properties suffers from inadequate efficiency and narrow bandwidth, especially for microwave devices. Here, a strategy of overcoming this difficulty is proposed by introducing the ohmic sheet into a Fabry–Pérot‐like cavity. The arbitrary phase modulation can be realized by changing the geometric parameters and the orientation of elliptical split resonance ring; via changing the intensity of ohmic dissipation, the amplitude can be continuously adjusted from 0 to 1. Its most significant advantage is arbitrary wide‐band complex‐amplitude modulation without introducing cross‐polarization crosstalk and backward scattering field interference. To verify its feasibility, three phase‐amplitude holographic imaging ​prototypes at 12, 14, and 16 GHz are designed. Both the simulated and measured results manifest the excellent performances of the proposed metasurface, demonstrating the excellent performances with a remarkable signal‐to‐noise ratio and low root‐mean‐square error. This proposed strategy provides an alternative method to control the phase and amplitude arbitrarily, which not only realizes high‐quality holography but also paves a way for random beamforming and so on.

Band-limited double-phase method for enhancing image sharpness in complex modulated computer-generated holograms.

Herein, we propose a band-limited double-phase method to improve the quality of reconstructed images encoded by double-phase holograms (DPHs) derived from complex-amplitude light waves. Although the quality of images produced by DPHs was improved compared to that of conventional holographic images, it still suffered from degradation because of the spatial shifting noise generated during the conversion from complex-amplitude holograms to phase-only holograms. The proposed method overcomes this shortcoming by defining a band-limiting function according to the spatial distribution of DPHs in the frequency domain to remove the specific spatial frequency components severely affected by the spatial shifting of DPHs. The sharpness of images reconstructed from band-limited DPHs with appropriate optical filtering showed an improvement of 36.84% in simulations and 51.67% in experiments evaluated by 10-90% intensity variation.

Complex-Amplitude Holographic Projection With a Digital Micromirror Device (DMD) and Error Diffusion Algorithm

Conventionally, a digital micromirror device (DMD) can only perform binary amplitude modulation of a light field. Simultaneous amplitude and phase modulation with a DMD is achieved by our proposed error diffusion scheme with a 4f double-lens setup for the first time. The DMD pixels are encoded by adaptive global optimization of binarization errors. In holographic projection, the object image can be optically reconstructed from a complex-amplitude hologram with this scheme. Experimental results show that our proposed error diffusion scheme outperforms the previous superpixel scheme in terms of the image quality and light efficiency of holographic reconstruction results under the same conditions.

Exact design of complex amplitude holograms for producing arbitrary scalar fields.

Typical methods to holographically encode arbitrary wavefronts assume the hologram medium only applies either phase shifts or amplitude attenuation to the wavefront. In many cases, phase cannot be introduced to the wavefront without also affecting the amplitude. Here we show how to encode an arbitrary wavefront into an off-axis transmission hologram that returns the exact desired arbitrary wavefunction in a diffracted beam for phase-only, amplitude-only, or mixed phase and amplitude holograms with any periodic groove profile. We apply this to design thin holograms for electrons in a TEM, but our results are generally applicable to light and X-ray optics. We employ a phase reconstruction from a series of focal plane images to qualitatively show the accuracy of this method to impart the expected amplitude and phase to a specific diffraction order.

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.

Improve the quality of holographic image with complex-amplitude metasurface.

Complex-amplitude hologram can provide a high-quality image that is free of twin image and zero-order noise. Multi-SLMs methods, single SLM with space-division modulations and super pixel methods were striving to meet the requirements of complex amplitude modulation. In this work, we propose an ultra-thin dielectric metasurface to improve the quality of holographic image by loading complex amplitude hologram. This metasurface controls the amplitude and phase simultaneously and independently in transmission mode. The multipole expansion method is applied to analyze the mechanism. The polarization conversion efficiency can be up to 99% and the diffraction efficiency is 71%. The simulations verify that the quality of holographic image could be greatly improved by a complex-amplitude metasurface.

Numerical Reconstruction of Hi-Resolution Microscopic Images for Lens-Less Holographic Microscopy

A new method numerically reconstructing ahigh-resolution microscopic image is developed for lens-less holographic microscopy. Acomplex-amplitude in-line hologram with a large numerical aperture (NA) is extracted from one off-axis hologram recorded with a CCD or CMOS camera by applied one-shot digital holography. The large hologram is divided into a number of small sections, and these sections are superimposed to generate a small complex-amplitude in-line hologram. Focus-free images with high resolving power and no distortion are numerically reconstructed from the generated small hologram using Fast-Fourier-Transforms (FFTs). A resolution higher than 1μm is obtained in the optical experiment, which can be improved up to the wave length. High-resolution microscopic images can also be observed for three-dimensional (3-D) objects with a large depth immersed in dielectric media by using the lens-less holographic microscopy.