Phase Modulation Research Articles

Design of short-focus near-eye optical system for virtual reality using polarization-insensitive metasurface

Near-eye optical systems, as an important component of virtual reality displays, have attracted great research interest recently. However, current systems have complex structures and face the design challenge of combining compact, short-focus design with wide field of view and high angular resolution. In this paper, we propose a short-focus near-eye optical system with wide field of view and high angular resolution, referred to as a meta-eyepiece, by patterning a single-layer polarization-insensitive metasurface on a substrate. The metasurface, featuring a quasi-periodic nanopillar arrangement, enables precise phase modulation and enhances design flexibility. The desired metaform phase can be obtained by modeling the light propagation of the meta-eyepiece to determine key design parameters, utilizing metaform phase polynomials, customizing the objective merit function and employing advanced optimization algorithms. Our system achieves a short focal length of approximately 22 mm with an 80° field of view, offering compactness superior to conventional virtual reality optics and a minimum resolvable angle less than 1.25 arcminutes, ensuring high angular resolution. It also exhibits excellent imaging performance with full-field modulation transfer function values exceeding 0.5 at 62.5 lp/mm. Although the initial system utilizes ray optics, the scaled version is validated for its feasibility and scalability through full-wave simulations. Our meta-eyepiece structure and design method show the potential of metasurfaces for applications in virtual reality, offering valuable support for technological development in this field.

Photonic-assisted generation of fast switchable multi-format LFM waveforms with a tuned bandwidth for a joint radar-communication system

A photonic-assisted generation scheme of fast switchable multi-format linearly frequency modulation (LFM) waveforms with a tuned bandwidth for a joint radar-communication (JRC) system is proposed and demonstrated. In this scheme, the up-, down-, dual-chirp LFM waveforms along with zero-value are obtained to form the joint waveform for carrying two bits of information per symbol. The bandwidth of the LFM waveforms can be tuned by adjusting the parabolic signal that drives the phase modulator (PM). The joint waveform can be used not only for radar ranging but also for the wireless communication. Simulation results show the 9–11 GHz up-, down- and dual-chirp waveform as well as the zero-value signal can switch at a rate of 64 MHz. The bandwidths of the LFM waveforms are tunable. The communication rate is up to 128 Mbit/s and the radar ranging resolution can reach up to 1.875 cm. The proposed scheme has a simple structure and can get good communication and range detection performance based on a joint waveform, and is expected to be used in the multifunctional JRC system.

A high‐precision timing and frequency synchronization algorithm for multi‐h CPM signals

AbstractIn the context of certain specific digital communication systems, where there are limitations such as spectral resources and energy availability, continuous phase modulation (CPM) emerges as an appealing choice among various modulation methods. Among CPM signals, multi‐h CPM is particularly noteworthy for its ability to address these constraints within the realm of single‐carrier and constant‐envelope waveforms. At the physical layer, the design of a multi‐h CPM receiver necessitates the efficient implementation of timing and frequency synchronization algorithm within a high dynamic environment. So this paper presents an innovative approach for achieving timing and frequency synchronization. To rectify timing offset and mitigate the adverse effects of noise in received signals, a re‐configurable local filter generation method is integrated into the timing synchronization algorithm. Simultaneously, an enhanced least mean square adaptive filter algorithm is applied to address frequency synchronization. A comprehensive series of simulations rigorously evaluates the outcomes of proposed novel synchronization methodology. These analyses demonstrate a notable proximity between the synchronization errors of proposed algorithm in this paper and the performance benchmark set by the modified Cramer–Rao bound. The proposed synchronization technology also exhibits the capability to substantially reduce the bit error rate, thereby effectively enhancing demodulation performance in multi‐h CPM receivers.

Electrically tunable planar liquid-crystal singlets for simultaneous spectrometry and imaging

Conventional hyperspectral cameras cascade lenses and spectrometers to acquire the spectral datacube, which forms the fundamental framework for hyperspectral imaging. However, this cascading framework involves tradeoffs among spectral and imaging performances when the system is driven toward miniaturization. Here, we propose a spectral singlet lens that unifies optical imaging and computational spectrometry functions, enabling the creation of minimalist, miniaturized and high-performance hyperspectral cameras. As a paradigm, we capitalize on planar liquid crystal optics to implement the proposed framework, with each liquid-crystal unit cell acting as both phase modulator and electrically tunable spectral filter. Experiments with various targets show that the resulting millimeter-scale hyperspectral camera exhibits both high spectral fidelity ( > 95%) and high spatial resolutions ( ~1.7 times the diffraction limit). The proposed “two-in-one” framework can resolve the conflicts between spectral and imaging resolutions, which paves a practical pathway for advancing hyperspectral imaging systems toward miniaturization and portable applications.

Wavelength and spin-decoupled metasurface based on single-parameter modulation.

Metasurfaces provide an unprecedented platform for precise and subwavelength-scale modulation of optical phases, leading to innovative advancements in wavefront shaping and holography devices. This study presents a single-layer umbrella-like metasurface capable of multichannel holography, encoded with both polarization and wavelength. By leveraging a unique chiral-assisted strategy, we achieve simultaneous decoupling of wavelength and spin states through single-parameter modulation. This approach circumvents the complex structure designs and multi-parameter adjustments typically required in previous methods. Numerical simulations confirm the effectiveness of this metasurface, demonstrating wavelength- and spin-decoupled phase modulation at 1550 and 980 nm. Furthermore, we successfully demonstrate a four-channel hologram operable in both transmission and reflection modes, showcasing the potential applications of this metasurface in compact functional integration, information encryption, and 3D displays. This work paves the way for the development of multifunctional optical devices with enhanced integration and performance.

Three-dimensional n-MoSe2/GOx (n= 1T, 1T' and 2H) microsphere: Phase-modulation strategy and microwave absorbing mechanism

MoSe2 was identified as a potential microwave absorber, whereas its practical application was predominantly affected by the ambiguous electromagnetic wave attenuation mechanism and dielectric properties. Here, we developed a novel phase assembly-modulating strategy to prepare n-MoSe2/GOx (n = 1T, 1T' and 2H) composites, wherein phase modulation of MoSe2 exerted a gainful effect on microwave absorption properties. The unique 1T′-MoSe2 phase was first explored in microwave absorption and composited with GOx to afford advanced conductivity loss and dielectric loss. The introduction of additional interface (2H/1T or 2H/1T') and abundant unsaturated defects promote multiple polarization, the semiconductor-metal mixed phase brought in a certain magnetic loss, optimizes the electron transfer ability and adjusts the impedance matching. Consequently, 1T′-MoSe2/GOx provides the minimum reflection loss (RLmin) of −52.08 dB and the effective absorption bandwidth (EAB, RL < -10 dB) of 5.3 GHz at 10 % filler content, which is approximately 9 times that of 2H–MoSe2/GOx and nearly 5 times that of 1T-MoSe2/GOx. This paper specifically explains the reasons for the phase modulation-induced magnetic losses and provides an effective phase modulation paradigm for developing advanced transition metal disulfide (such as MoS2, WS2 and WSe2) microwave absorbers.

Enhancing phase modulation and group delay in reflective Huygens metasurfaces via a Fabry-Perot cavity

Huygens metasurfaces exhibit excellent optical properties such as 2π phase modulation and slow light effects. However, they face challenges including wide bandwidth and low group delay due to their high radiation losses. Here, we propose a reflective Huygens metasurface coupled with an F-P cavity. We demonstrate that F-P resonance modes can couple with magnetic-quasi-bound-state (M-QBIC) and electric-quasi-bound-state (E-QBIC) in the Huygens metasurface through constructive interference, significantly enhancing the quality factors of both QBICs. Through structural parameter optimization, our reflective Huygens metasurface achieves 4π phase modulation and a high group delay of up to 166 ps. Compared to the non-coupled Huygens metasurface with the same structural asymmetry, the group delay of the F-P coupled reflective Huygens metasurface is enhanced by up to 30 times. Our design reduces the fabrication precision requirements for Huygens metasurfaces, enabling similar group delays to be achieved in low-symmetry coupling structures as in highly symmetric non-coupling structures. Additionally, the performance of this metasurface shows robustness to changes in incident light polarization. This design highlights the potential for achieving high-quality factors, large phase modulation, and large group delay, offering new avenues for the design of highly sensitive tunable devices, efficient nonlinear optical devices, and narrowband slow light devices.

Enhancing the sensitivity of spin-exchange relaxation-free magnetometers using phase-modulated pump light with external Gaussian noise

An optical pumping scheme is proposed for reducing the gradient of electron spin polarization and suppressing light source noise in a spin-exchange relaxation-free magnetometer. This is achieved by modulating only the phase of a narrow-linewidth pump light field with external Gaussian noise. Compared to the absence of phase modulation, the uniformity of electron spin polarization was improved by over 40%, and the light-frequency noise suppression ratio of the magnetometer was enhanced by 4.3 times. Additionally, the response of the magnetometer was increased by 54%, resulting in a sensitivity of 0.34 fT/Hz1/2 at 30 Hz. The applicability of this scheme can extend to other optical pumping experiments involving large atom ensembles requiring uniform electron spin polarization distribution, which is beneficial for developing ultra-high sensitivity and high stability magnetometers essential for magneto-cardiography and magneto-encephalography research applications.

Performance comparison of various end-to-end learning technologies with a bandwidth-limited OWC system

Recently, end-to-end (E2E) learning methodologies have garnered significant attention as a compelling approach to attain global optimal communication within the domain of 6 G native intelligent systems. Nevertheless, a precise evaluation of the diverse E2E techniques is still lacking, leading to uncertainties regarding their applicable scenarios and effectiveness. In this paper, we present a comprehensive comparison applying three advanced E2E methods including the autoencoder-based geometric shaping (AEGS) model, comprehensive autoencoder (CAE) model, and wave-wise auto-equalization (WWAE) model in a real bandwidth-limited optical wireless communication (OWC) system. A novel attention-based comprehensive noise joint channel estimator (ACNJCE) is proposed to serve as a universal channel model adaptable to the existing E2E methods. Based on traditional carrier-less amplitude and phase modulation (CAP) modulation, AEGS, WWAE, and CAE are compared under the conditions of 2 GBaud and 3 GBaud respectively. The final results demonstrate that the CAE exhibits the capability to autonomously allocate bandwidth and achieves the highest dynamic adjustment range, which is increased by 69% compared with CAP based on neural network (NN) equalization. In contrast, AEGS has obvious advantages in terms of received optical power (ROP) gain. Based on bit-power loading discrete multi-tone modulation (DMT) modulation, WWAE can effectively compensate the signal spectrum after modulation order optimization and finally achieves the highest data rate under the condition that the −3 dB bandwidth of the channel is only close to 1 GHz. The BER of WWAE with DMT at this rate is 25.2% of that using the NN equalization. Furthermore, experimental results under turbulent conditions reveal that AEGS exhibits superior and more stable performance amidst the perturbations caused by turbulence due to its ability to achieve end-to-end autonomous optimization while integrating traditional modulation and bringing additional shaping gain. According to our knowledge, this marks the first comprehensive evaluation and comparison of existing major E2E algorithms and traditional communication algorithms in a real OWC system.

Design terahertz polarizers and vector polarized vortex terahertz wave generators based on the effective dielectric constant of metal gratings

Polarization and phase devices for terahertz waves have important applications in terahertz detection, imaging, communication, etc. Spatially variable metal gratings can be used for broad-spectrum, miniaturized, and low-cost terahertz polarization and phase modulation devices. Based on the effective dielectric constant and the theory of light propagation in multilayer media, we obtain the relationship between the transmittance and extinction ratio and the parameters such as the duty cycle of the metal grating, the frequency of the incident terahertz wave, the angle of incidence, the thickness of the metal grating, the refractive index of the substrate, and the thickness of the substrate. We propose a method of designing a spatially variable metal grating located on a transparent substrate. The designed spatially variable metal grating is also used to modulate the terahertz spatial polarization and phase to generate terahertz optical fields whose polarization and phase change simultaneously in space, such as azimuthally vector vortex terahertz optical fields, radially vector vortex terahertz optical fields, and so on. This will have important applications in terahertz time-domain spectroscopic detection, terahertz time-domain spectroscopic imaging, terahertz time-domain near-field microscopic imaging, terahertz communication, and so on.

Design of a LiDAR ranging system based on dual‐frequency phase modulation

AbstractPhase‐based light detection and ranging (LiDAR) technology is emerging in the fields of industrial mapping, autonomous driving, and robotics, but the traditional phase‐based ranging technology generally suffers from the problem that the ranging accuracy is inversely proportional to the measurement range under a single measurement frequency, the system structure is complicated, and the performance is unstable, and so forth. In this article, a new type of LiDAR system design based on phase ranging is proposed. The system adopts a 100 + 1 MHz double measuring ruler modulation light source, uses the laser to control the phase difference detection method of the same frequency reference, optimizes the structure of the transceiver optical system, and the design of AD8302 high‐resolution signal phase discriminator circuit, builds a high‐precision laser ranging system, and carries out the experiments on the measurement accuracy of the LiDAR ranging system. The experimental results show that the measurement accuracy of the system is millimeter level, which is simple, practical, and can meet the needs of a wide range of practical applications. This study provides a feasible and innovative solution for LiDAR technology in high‐precision distance measurement.

Advanced GeSe-based thermoelectric materials: Progress and future challenge

GeSe, composed of ecofriendly and earth-abundant elements, presents a promising alternative to conventional toxic lead-chalcogenides and earth-scarce tellurides as mid-temperature thermoelectric applications. This review comprehensively examines recent advancements in GeSe-based thermoelectric materials, focusing on their crystal structure, chemical bond, phase transition, and the correlations between chemical bonding mechanism and crystal structure. Additionally, the band structure and phonon dispersion of these materials are also explored. These unique features of GeSe provide diverse avenues for tuning the transport properties of both electrons and phonons. To optimize electrical transport properties, the strategies of carrier concentration engineering, multi-valence band convergence, and band degeneracy established on the phase modulation are underscored. To reduce the lattice thermal conductivity, emphasis is placed on intrinsic weak chemical bonds and anharmonicity related to chemical bonding mechanisms. Furthermore, extra-phonon scattering mechanisms, such as the point defects, ferroelectric domains, boundaries, nano-precipitates, and the phonon mismatch originating from the composite engineering, are highlighted. Additionally, an analysis of mechanical properties is performed to assess the long-term service of thermoelectric devices based on GeSe-based compounds, and correspondingly, the theoretical energy-conversion efficiency is discussed based on the present zT values of GeSe. This review provides an in-depth insight into GeSe by retrospectively examining the development process and proposing future research directions, which could accelerate the exploitation of GeSe and elucidate the development of broader thermoelectric materials.

Joint waveform design of radar detection, wireless communication and jamming based on chaotic composite modulation

AbstractIn this letter, we address the problem of designing the joint waveform of radar detection, wireless communication and jamming. In the current most powerful filter‐bank multi‐carrier comb spectrum framework, a parameter‐agile time–frequency structure between symbols is elaborated to improve the uncertainty of waveform generation architecture. Furthermore, a novel composite modulation strategy that combines intra‐symbol chaos‐based radar frequency modulation and inter‐symbol chaos‐based phase modulation is proposed for a substantial jamming performance improvement. Simulation results verify that the proposed joint waveform produces a superior jamming performance while satisfying the requirements of radar detection and wireless communication.

Impact of altering phase modulation and geometrical shape of laser beam via a phase-only spatial light modulator on laser-induced fluorescence

This study investigates the impact of modulating and shaping a laser beam via a phase-only spatial light modulator (SLM) on the intensity of the laser-induced fluorescence (LIF) signal. Different phase modulations ranging from 0 to 2π are applied to the SLM window to evaluate the effect of the modulated beam on the emitted LIF signal from extra virgin olive oil EVOO samples. The laser beam is also shaped into circular and square geometries with varying diameters to determine the optimum size for maximizing the LIF signal strength. The results reveal that the highest LIF signal intensity could be obtained after modulating the incident laser beam with phase shifts of 0 and 2π, with an improvement factor of approximately 3 for Avanti olive oil and 1.42 for Al Jouf olive oil. Furthermore, laser beam shaping into a circular aperture with a radius of 2.45 mm or a square aperture with a side length of 2.45 mm yields the highest LIF signal improvement, with enhancement factors of approximately 2.9 for Avanti olive oil and 1.42 for Al Jouf olive oil. This work demonstrates the potential of SLM-based beam shaping techniques to optimize LIF measurements by tailoring the wavefront characteristics of the excitation laser source.

The control for multiple kinds of solitons generated in the nonlinear fractional Schrödinger optical system based on Hermite-Gaussian beams

In this paper, we investigate the control for Hermite-Gaussian (HG) solitons in the nonlinear fractional Schrödinger equation (FSE) by sequentially applying power function modulations, cosine modulations, parabolic potentials, and quadratic phase modulations (QPM). In the photorefractive media, the HG beam forms scattered breathing solitons when the fractional diffraction effect equilibrates with nonlinear effect. Under the power function modulation, the soliton maintains an equidistant linear transmission along the z-axis, and the number of solitons is equal to the mode. In the cosine modulation, the soliton distorts and its energy rapidly decreases after a certain distance of transmission. The time of the distortion varies with the Lévy index, photorefractive coefficient, modulation frequency and order. The freak spots exhibit a “flower” shape pattern. If a parabolic potential is introduced, the HG beam forms crawling soliton pairs or merges into a single bounded breathing soliton by adjusting the correlation among the Lévy index, nonlinear and parabolic coefficients. By increasing the nonlinear coefficient in the negative QPM regime, the defocusing HG beam emits several “filiform” breathing solitons during its propagation, which move in a parallel straight line to each other. The HG beam is transformed into a single fine breathing soliton after being focused under a positive QPM. The time of the formation and breathing rate varies with the Lévy index, QPM and nonlinear coefficients. Moreover, the number of solitons changes irregularly with modes. These results are significant for applications in optical communication, optical device design, and optical signal processing.

Dynamic deformation measurement with 2-frame phase-shifting speckle interferometry based on speckle statistics and wavefront multiplexing.

Phase-shifting speckle interferometry could achieve full-field deformation measurement of rough surfaces. To meet the dynamic requirement and further improve the accuracy, a two-step synchronous phase-shifting measurement system is established based on the polarization-sensitive phase modulation ability of a liquid crystal spatial light modulator; by multiplexing the reference wavefront, an accurate phase shift is generated between two independent recording channels, and a common-path self-reference vortex interference structure is built for precise spatial registration. Meanwhile, according to the speckle statistical principle, a novel two-frame phase-shifting algorithm as well as a two-step spatial registration strategy is presented to strengthen the robustness of intensity and position differences caused by spatial-multiplexing; thereby, accurate transient deformation can be directly obtained from phase-shifting speckle interferograms recorded before and after deformation. The effectiveness and accuracy of the proposal are validated from the out-of-plane deformation measurement experiment by comparing with the traditional two-step and four-step phase-shifting methods. The dynamic ability is exhibited through reconstructing mechanical and thermal deformations across various application scenarios.

Excellent energy-storage performance in BNT-BT lead-free ceramics through optimized electromechanical breakdown

Dielectric capacitors with high recoverable energy storage density (Wrec) are in urgent demand for clean energy technologies. However, their lower breakdown strength (Eb) strongly limits their energy storage performance. We, herein, propose a facile method to enhance Eb by enhancing mechanical strength via second phase modulation. The efficiency of this method is validated in the (1-x)(0.94Na0.5Bi0.5TiO3-0.06BaTiO3)-xSr(Ta0.5Sb0.5)O3 ((BNT-BT)-xSTS, x = 0.1, 0.15, 0.2, 0.25, and 0.3) ceramics. The introduction of Sr(Ta0.5Sb0.5)O3 (STS) increases the relaxor degree, refines grain size, and most importantly, creates a second phase of BiSb2O7, which hinders dislocation movement and improves mechanical strength. Our results show that the breakdown strength strongly depends on the mechanical strength. The highest hardness of 7.42 GPa accompanied by the largest Eb of 620 kV/cm was obtained in (BNT-BT)-0.25STS sample. The sample exhibits the best energy storage properties of a large Wrec = 8.3 J/cm3, a high efficiency of 82.3 %, and excellent temperature/frequency stability. Furthermore, the sample also exhibits good charge/discharge stability and ultra-fast transient discharge time (62.26 ns). This work provides a theoretical guidance for developing lead-free dielectrics with superior energy-storage performance.

Real-time in situ phase sensitivity calibration of interferometric fiber-optic ultrasonic sensors.

Output from a fiber-optic interferometric ultrasonic sensor can be affected by the operating point changes and/or the optical power fluctuations. We report a method for real-time and in situ calibration of the responses to ultrasound-induced phase delays for a low-finesse Fabry-Perot (FP) ultrasonic sensor demodulated using a phase-generated carrier. The carrier is produced from an electro-optic phase modulator, and its zero- and fundamental-carrier frequency components yield two quadrature signals. The same phase modulator is employed to generate controllable laser frequency modulations and calibration phase delay modulations. The response to the known calibration phase delays is used to gauge the sensor output in real time and in situ. The experiment has verified the effectiveness of the calibration method against the signal variations from both operating point changes and optical power variations.

Non-interleaved quad-channel metasurfaces for simultaneous nanoprinting and holography enabled by phase and bidirectional intensity modulation

Metasurfaces, with their unparalleled ability to manipulate light-field characteristics, have brought forth numerous advantages in ultra-compact and high-resolution image displays, particularly in multifunctional metadevices for simultaneous nanoprinting and holography. However, current efforts are hindered by challenges such as increased fabrication complexity, low efficiencies, or being confined to classic two/three-channel configurations, limiting their further applications. In this study, we propose a single-cell non-interleaved metasurface platform capable of simultaneously and independently generating two holographic images in the far field and two nanoprinting images in the near field. Through a spin-decoupled phase modulation, the metasurface can produce two far-field holographic images under orthogonal circularly polarized incidences. By fully unlocking the Malus's law-assisted bidirectional intensity modulation, the metasurface enables the reconstruction of two near-field nanoprinting images with two distinct orthogonal polarization optical setups as decoding keys. Moreover, the quad-channel metasurface we proposed exhibits broadband response and on-off binary switching performance enabled by the phase transition of Ge2Sb2Se4Te1. We envision that the proposed design paradigm opens up new possibilities for expanding the functionality and enhancing the capacity of metasurfaces without burdening their design, thereby paving the way for compact multifunctional optical devices in image display, information encoding, anti-counterfeiting, and other related fields.

Electro-optical intensity and phase modulations of racetrack micro-resonator base on LiNbO3-silicon hybrid waveguide covered by electro-optical polymers

Electro-optical intensity and phase modulations of racetrack micro-resonator base on LiNbO3-silicon hybrid waveguide covered by electro-optical polymers