Single Phase-only Spatial Light Modulator Research Articles

Experimental optical encryption with full complex modulation

We present, to our knowledge, a novel method to achieve experimental encryption using double random phase encoding with full complex modulation and a single phase-only spatial light modulator. Our approach uses double phase encoding to generate phase-only holograms containing complex-valued input planes for a joint transform correlator (JTC) cryptosystem. This approach enables users to independently manipulate both the phase and amplitude of the cryptographic keys and objects, thereby significantly enhancing the versatility of the optical cryptosystem. We validate the capabilities of our proposed scheme by generating optimized random phase masks and using them to experimentally encrypt various grayscale and binary objects. The experimental complex modulation obtained with the system detailed in this work, in conjunction with optimized random phase masks, results in an enhancement in the quality of the decrypted objects during reconstruction. Both numerical simulations and experimental findings corroborate the effectiveness of our proposal.

Generation of structured light beams by dual phase modulation with a single spatial light modulator

Precise control of amplitude and wavefront of optical fields are prerequisites for many applications, especially in singular optics. This has led to the increasing efforts for developing efficient techniques to control the shape of the light in different dimensions. A spatial light modulator (SLM) can be efficiently used for phase-only or amplitude-only modulation; but offers limitation in complex light field modulation. Hence, shaping the complex amplitude of optical beams is challenging mainly because there are no complex modulators. While there is ongoing research to develop complex amplitude modulating SLMs, a solution is still non-existent. In this study, to achieve complex light modulations, a simple experimental set-up employing single phase-only SLM has been proposed. The SLM has been used as operating in a split-screen-mode. The non-iterative approach of dual-pass modulation has been applied where two cascaded phase value distributions (PVD) are encoded side-by-side onto the SLM. The first PVD is designed to enable amplitude modulation in the second PVD plane which finally helps achieve wavefront shaping. Hence, both amplitude and phase modulation of light beam are possible in this configuration. Commonly known singular beams such as Laguerre–Gaussian and Bessel-Gaussian modes have been generated theoretically as well as experimentally to verify the feasibility of the proposed technique. The method used helps to achieve arbitrary shaped beams as well.

Abruptly Autofocusing Vortex Beams for Rapid Controllable Femtosecond Two-Photon Polymerization.

Micro-fabrication based on structured-beam-assisted Two-Photon Polymerization (2 PP) provides a rapid and flexible method for the manufacture of microstructures with complex morphologies. The tunable Abruptly Autofocusing Vortex (AAFV) beams were designed theoretically and generated experimentally based on a single-phase-only Spatial Light Modulator (SLM). Their specific spatial intensity distributions were further utilized to assist the fabrication of a bowl-shaped Three-Dimensional (3D) micro-trap array via 2 PP with a one-step exposure technique. Finally, the fabricated microstructures act as a novel tool for the trapping and spatial positioning of micro-particles with different diameters, which shows potential applications in fiber optics and cell study.

Compact generation of light beams carrying robust higher-order Poincaré polarization states

We propose a protocol for compact and efficient synthesis of a random vectorial source with a higher-order Poincaré (HOP) polarization state encoded into the spatial coherence structure. The procedure is based on the complex-random-mode representation of the cross-spectral density matrix and employs a single phase-only spatial light modulator (SLM) and a common path interferometric system for the mode construction. The SLM displays a set of elaborated multiplexed holograms, which both encode the HOP polarization state and determine the statistical properties of the source. We demonstrate that the beam from the synthesized source can be highly robust against obstructions in the propagation path in the sense that the encoded HOP polarization state is well reconstructed in the far field (focal plane) even when an obstacle is introduced to largely block the source. The results are useful for the transmission of polarization-encoded information in complex media.

Compact generation of robust Airy beam pattern with spatial coherence engineering.

We present a class of partially coherent light sources having Airy-type amplitude and Airy-correlated spatial coherence. We show that the light beam generated by such sources can preserve the Airy beam pattern well during its propagation from source to far field. We demonstrate the robustness of the Airy beam pattern by introducing a hard aperture to largely block the beam source. We find that the coherence-induced Airy beam pattern can still be well reconstructed during propagation. We successfully synthesize such partially coherent source using the principle of complex random modes decomposition by using a single phase-only spatial light modulator. The proposed robust Airy beam pattern may find applications in information transmission through complex media.

The Error Analysis of the Complex Modulation for Flattop Focusing Beam Shaping

In order to obtain a focusing flattop beam with high uniformity, complex modulation is used to modulate the optical pupil function, and the beam shaping algorithm is designed with a single phase-only spatial light modulator (SLM). Actually, the wavefront aberrations introduced by each element reduce the uniformity of the shaped beam. In particular, the wavefront aberrations in different positions have different effects on this complex modulation algorithm. However, there is a lack of the corresponding error data and robustness analysis. Here, the error and robustness of the complex modulation algorithm are analyzed when different types of aberrations (defocus, astigmatism, and coma) exist in different positions of the shaping optical system, and the mixed area magnification-free (MRAF) algorithm is used as a reference for comparison. The results show that coma has the greatest effect on the beam shaping quality. It is also proved that the impact on the beam quality when there are aberrations in the laser and beam expansion system is greater than those in the SLM and the focusing lens for the complex modulation algorithm, which is different from the MRAF case.

Antiferromagnetic spatial photonic Ising machine through optoelectronic correlation computing

Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground-state-search acceleration of an antiferromagnetic model with 40000 spins in number-partitioning problem. Thus such an optoelectronic computing exhibits great programmability and scalability for the practical applications of studying statistical systems and combinatorial optimization problems.

Experimental synthesis of partially coherent beam with controllable twist phase and measuring its orbital angular momentum

Abstract Twist phase is a nontrivial second-order phase that only exists in a partially coherent beam. Such twist phase endows the partially coherent beam with orbital angular momentum (OAM) and has unique applications such as in super-resolution imaging. However, the manipulation and the detection of the twist phase are still far from easy tasks in experiment. In this work, we present a flexible approach to generate a famous class of twisted Gaussian Schell-model (TGSM) beam with controllable twist phase by the superposition of the complex field realizations using a single phase-only spatial light modulator. The precise control of the amplitude and phase of the field realizations allows one to manipulate the strength of the twist phase easily. In addition, we show that the twist factor, a key factor that determines the strength of twist phase and the amount of OAM, can be measured by extracting the real part of the complex degree of coherence of the TGSM beam. The experiment is carried out with the help of the generalized Hanbury Brown and Twiss experiment as the generated TGSM beam obeys Gaussian statistics. The flexible control and detection of the twist phase are expected to find applications in coherence and OAM-based ghost imaging.

Full-color retinal-projection near-eye display using a multiplexing-encoding holographic method.

We propose a novel method to construct an optical see-through retinal-projection near-eye display using the Maxwellian view and a holographic method. To provide a dynamic full-color virtual image, a single phase-only spatial light modulator (SLM) was employed in conjunction with a multiplexing-encoding holographic method. Holographic virtual images can be directly projected onto the retina using an optical see-through eyepiece. The virtual image is sufficiently clear when the crystal lens can focus at different depths; the presented method can resolve convergence and accommodation conflict during the use of near-eye displays. To verify the proposed method, a proof-of-concept prototype was developed to provide vivid virtual images alongside real-world ones.

A crosstalk-reduced method of complex fields encoding using a single phase-only spatial light modulator

Crosstalk is a difficult problem in complex amplitude modulation, which limits the quality of the reconstructed complex amplitude and the practicality of complex amplitude modulation. To alleviate this problem, we propose a crosstalk-reduced method of complex fields encoding using a phase-only spatial light modulator(SLM). In our proposed method, Gaussian low-pass is used to smooth the image to reduce crosstalk. Using our proposal, crosstalk in the reconstructed amplitude and phase is significantly reduced. Moreover, our proposed method is simple, effective, and easy to implement. In order to corroborate our proposal, both simulations and experiment are carried out.

Simultaneous aberration and aperture control using a single spatial light modulator.

A method to simultaneously control aberrations and the aperture of an optical system using a single phase-only spatial light modulator was investigated. The experiment was performed using a liquid-crystal-on-silicon spatial light modulator (LCoS-SLM) within an adaptive optics system used for visual testing, although the method has broader applications in adaptive optics field. The performance of the technique was characterized through the estimation of the system's modulation transfer functions (MTFs) by using a random chart method. MTFs obtained from the phase modulation-based approach were compared with those from using a real aperture (diaphragm). The areas under the MTFs for the two conditions were similar up to 98%, confirming that the low-pass filter effect associated to the size of the entrance pupil was similar for the phase-modulated pupil and the physical pupil. As an example of application, both aberrations and pupil were controlled by a single phase-only modulator to study the through-focus visual performance in real subjects. Limitations and possible enhancements of the presented method were also discussed. The presented technique reduces complexity and cost of adaptive optics systems. It opens the door to new experiments by allowing dynamic modulation of aberrations and apertures of any shape.

Synthesis of ununiformly correlated radially polarized partially coherent beam

Since the unified theory of coherence and polarization for partially coherent vector beams was proposed by Gori and Wolf, the characterization, generation and propagation of partially coherent vector beams have been extensively studied. During the last decade, partially coherent vector beams with non-uniform polarization, also referred to as cylindrical vector partially coherent beams, have gained more and more attention. It was found that the intensity profile of focused azimuthally/radially polarized beam could be shaped by varying its initial spatial coherence. This characteristic may have potential applications in material thermal processing and particle trapping. Until now, there have been several reports concerning the generation of cylindrical vector partially coherent beams. However, in most of these reports a ground-glass diffuser was used, which generally restricts the generation of shell-model sources. In this paper, we theoretically and experimentally investigate the generation of radially polarized partially coherent beams with non-uniform correlation. According to the relation between phase correlation and optical coherence, we theoretically investigate the 2 × 2 cross-spectral density matrix and the coherence distribution of our generated non-uniformly correlated radially polarized partially coherent beams. In experiment, we generate dynamic random phase patterns with uniform distribution in time and inverse Gaussian distribution in space. A complete coherent radially polarized beam is divided into two parts by a polarizing beam splitter, i.e., the transmitted <i>x</i>-polarization component (HG<sub>10</sub> beam) and the reflected <i>y</i>-polarization component (HG<sub>01</sub> beam). The two orthogonally polarized components are respectively modulated with the two halves of a single phase-only liquid crystal spatial light modulator, thus generating a radially polarized partially coherent beam. We measure the correlation distribution of the generated beam in Young’s two-pinhole experiment. It is shown that the experimental observations are in agreement with our theoretical analyses. The generated partially coherent beam has an un-uniform correlation structure, and its coherence degree may be controlled by varying the Gaussian modulation half-width of the random phase. Our experimental results have also shown that the intensity profile of the radially polarized partially coherent beam can be modulated with the Gaussian modulation half-width. With the increase of Gaussian modulation half-widths and the gradual decrease of coherence degree, the intensity profile gradually transforms from a dark hollow beam profile into a flat-topped-like beam profile. The radially polarized partially coherent beams with non-uniform correlation may have some applications in optical manipulation and material thermal processing.

Autostereoscopic three-dimensional display by combining a single spatial light modulator and a zero-order nulled grating

In this paper, an autostereoscopic three-dimensional (3D) display system based on synthetic hologram reconstruction is proposed and implemented. The system uses a single phase-only spatial light modulator to load the synthetic hologram of the left and right stereo images, and the parallax angle between two reconstructed stereo images is enlarged by a grating to meet the split angle requirement of normal stereoscopic vision. To realize the crosstalk-free autostereoscopic 3D display with high light utilization efficiency, the groove parameters of the grating are specifically designed by the rigorous coupled-wave theory for suppressing the zero-order diffraction, and then the zero-order nulled grating is fabricated by the holographic lithography and the ion beam etching. Furthermore, the diffraction efficiency of the fabricated grating is measured under the illumination of a laser beam with a wavelength of 532 nm. Finally, the experimental verification system for the proposed autostereoscopic 3D display is presented. The experimental results prove that the proposed system is able to generate stereoscopic 3D images with good performances.

High-harmonic-generation-inspired preparation of optical vortex arrays with arbitrary-order topological charges

In the process of high-harmonic generation with a Laguerre-Gaussian (LG) mode, it was well established that the topological charge could be of an N-fold increase due to angular momentum conservation. Here, by mimicking the effect of high-harmonic generation, we devise a simple algorithm to generate optical vortex arrays carrying arbitrary topological charges with a single phase-only spatial light modulator. By initially preparing a coaxial superposition of suitable low-order LG modes, we demonstrate experimentally that the topological charges of the embedded vortices can be multiplied and transformed into arbitrarily high orders on demand, while the array structure remains unchanged. Our algorithm offers a concise way to efficiently manipulate the structured light beams and holds promise in optical micromanipulation and remote sensing.

Controlled generation of mixed spatial qudits with arbitrary degree of purity

We propose a method for preparing mixed quantum states of arbitrary dimension $D$ ($D\geq2$) which are codified in the discretized transverse momentum and position of single photons, once they are sent through an aperture with $D$ slits. Following our previous technique we use a programmable single phase-only spatial light modulator (SLM) to define the aperture and set the complex transmission amplitude of each slit, allowing the independent control of the complex coefficients that define the quantum state. Since these SLMs give us the possibility to dynamically varying the complex coefficients of the state during the measurement time, we can generate not only pure states but also quantum states compatible with a mixture of pure quantum states. Therefore, by using these apertures varying on time according to a probability distribution, we have experimentally obtained $D$-dimensional quantum states with purities that depend on the parameters of the distribution through a clear analytical expression. This fact allows us to easily customize the states to be generated. Moreover, the method offer the possibility of working without changing the optical setup between pure and mixed states, or when the dimensionality of the states is increased. The obtained results show a quite good performance of our method at least up to dimension $D=11$, being the fidelity of the prepared states $F > 0.98$ in every case.

Vector Beam Polarization State Spectrum Analyzer

We present a proof of concept for a vector beam polarization state spectrum analyzer based on the combination of a polarization diffraction grating (PDG) and an encoded harmonic q-plate grating (QPG). As a result, a two-dimensional polarization diffraction grating is formed that generates six different q-plate channels with topological charges from −3 to +3 in the horizontal direction, and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincaré sphere. Consequently, 36 different channels are generated in parallel. This special polarization diffractive element is experimentally demonstrated using a single phase-only spatial light modulator in a reflective optical architecture. Finally, we show that this system can be used as a vector beam polarization state spectrum analyzer, where both the topological charge and the state of polarization of an input vector beam can be simultaneously determined in a single experiment. We expect that these results would be useful for applications in optical communications.

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.

Three-dimensional scene encryption and display based on computer-generated holograms.

An optical encryption and display method for a three-dimensional (3D) scene is proposed based on computer-generated holograms (CGHs) using a single phase-only spatial light modulator. The 3D scene is encoded as one complex Fourier CGH. The Fourier CGH is then decomposed into two phase-only CGHs with random distributions by the vector stochastic decomposition algorithm. Two CGHs are interleaved as one final phase-only CGH for optical encryption and reconstruction. The proposed method can support high-level nonlinear optical 3D scene security and complex amplitude modulation of the optical field. The exclusive phase key offers strong resistances of decryption attacks. Experimental results demonstrate the validity of the novel method.

Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography.

A holographic data storage system using digital holography is proposed to record and retrieve multilevel complex amplitude data pages. Digital holographic techniques are capable of modulating and detecting complex amplitude distribution using current electronic devices. These techniques allow the development of a simple, compact, and stable holographic storage system that mainly consists of a single phase-only spatial light modulator and an image sensor. As a proof-of-principle experiment, complex amplitude data pages with binary amplitude and four-level phase are recorded and retrieved. Experimental results show the feasibility of the proposed holographic data storage system.