Beam Divergence Research Articles

Butler matrix enabled multi-beam optical phased array for two-dimensional beam-steering and ranging

Based on the wavelength transparency of the Butler matrix (BM) beamforming network, we demonstrate a multi-beam optical phased array (MOPA) with an emitting aperture composed of grating couplers at a 1.55 μm pitch for wavelength-assisted two-dimensional beam-steering. The device is capable of simultaneous multi-beam operation in a field of view (FOV) of 60° × 8° in the phased-array scanning axis and the wavelength-tuning scanning axis, respectively. The typical beam divergence is about 4° on both axes. Using multiple linearly chirped lasers, multi-beam frequency-modulated continuous wave (FMCW) ranging is realized with an average ranging error of 4 cm. A C-shaped target is imaged for proof-of-concept 2D scanning and ranging.

How good are collimated Gaussian beams produced with engineered diffusers?

Collimating a Gaussian beam from an uncollimated laser source has been achieved via the deployment of engineered diffusers (EDs)—also referred to as light shaping diffusers. When compared to conventional pinhole-based optical collimation systems, this method of beam collimation ensures high optical transmission efficiency at the expense of the introduction of additional speckle and a resulting reduction in spatial coherence. Despite a lower collimation quality, these ED-produced collimated beams are attractive and promising in terms of their deployment in various benchtop or tabletop systems that involve shorter beam propagation distances of up to a few meters while requiring a high optical power throughput. This paper aims to further the understanding of collimation quality and propagation properties of ED-produced Gaussian collimated beams via carefully designed experiments and accompanying analysis. We measure and document the beam divergence, Rayleigh distance, and M2 factor, as well as evolution of the wavefront radius of curvature (RoC), of these ED-generated beams over a few meters of propagation—a propagation distance which encapsulates a vast majority of optical systems. We further investigate the changes in the beam profile with the addition of a laser speckle reducer (SR) and compare the ED-produced beams with a near-ideal collimated beam produced with spatial filtering systems.

Tracking bandwidth limitations for strong optical-turbulence conditions.

We derive a modified fundamental tracking frequency that is applicable for beam-control systems that do not employ adaptive-optics compensation. Specifically, we show that there are diminishing returns on tracking faster than the modified fundamental tracking frequency. Furthermore, when D/r0 > 4, where D is the aperture diameter and r0 is the Fried parameter, we show that increasing the track bandwidth alone will not improve system performance. These conclusions result from beam spreading being the dominant driver of decreased system performance, as opposed to beam jitter.

High-accuracy determination of the beam divergence error in free-fall absolute gravimeters

We investigate the bias due to the beam divergence of the collimator in a free-fall absolute gravimeter of type FG5X. First, we measure the beam parameters with a Shack-Hartmann sensor. Then, we use the parameters to simulate the relative gravitational acceleration error of an FG5X gravimeter, which employs an unbalanced Mach-Zehnder laser interferometer. This investigation we do with four different commercial collimators, providing different divergence angles. We compare the results to real gravity measurements using the same collimators. The larger the divergence angle, and the bigger the relative length error, the bigger is the bias in the gravity measurements. A good agreement between theory and experiment is found, resulting in a relative bias of −2.77(24)⋅10−9 ( −2.72(24) μGal) for our standard collimator of type Thorlabs TC25APC, which is usually used for free-fall acceleration determinations. The outcome is also important for the realization of the SI unit kilogram via Kibble balance experiments that, on one side, employ laser interferometers for velocity measurements, and, on the other side, require accurate values of the gravitational acceleration. For example, if this divergence error is not corrected in the Kibble balance, then the mass determination would be biased by 2.77(24) μg kg−1 (numbers are valid only for our gravimeter with our collimator and fiber).

Robust high-order petal-mode laser with tunable topological charge pumped by an axicon-based annular beam

In this work, we demonstrate a watt-level laser producing high-order, petal-shaped output modes with tunable topological charge, by using an axicon-based divergent annular pump beam. The topological charge of the output beam could be varied in the range of 34–72 by adjusting the position of the Nd:YVO4 crystal relative to the focal plane of the pump beam. The highest order petal-mode beam generated from the system had a topological charge of 72 and a power of 1.3 W. The highest output power up to 2.1 W with a topological charge of 34 was achieved at an absorbed pump power of 5.8 W. The generated output modes were observed to be robust under power scaling and on propagation, with the same spatial profiles being maintained in the near- and far-fields. We anticipate that this system design may find use as a laser source in applications such as 3D optical trapping, fabrication of optical vortex arrays, optical communications, and high-sensitivity spatial measurement.

Topological photonic crystal nanowire array laser with bulk states

A topological photonic crystal InGaAsP/InP core-shell nanowire array laser with bulk states operating in the 1550 nm band is proposed and simulated. By optimizing the structure parameters, high Q factor of 1.2 × 105 and side-mode suppression ratio of 13.2 dB are obtained, which are 28.6 and 4.6 times that of a uniform nanowire array, respectively. The threshold and maximum output are 17% lower and 613% higher than that of the uniform nanowire array laser, respectively, due to the narrower nanowire slits and stronger optical confinement. In addition, a low beam divergence angle of 2° is obtained due to the topological protection. This work may pave the way for the development of high-output, low-threshold, low-beam-divergence nanolasers.

Subarray-based joint source localization in shallow water waveguide via subspace intersection

By the use of an underwater bottom-mounted Horizontal Linear Array (HLA), the two-dimensional joint localization technique and its accuracy are analyzed in this article. The proposed method takes advantage of arrival angles measured by a dual-subarray system consisting of a large-aperture HLA. Then, for the system, expressions for source position estimate and error variation are derived. Analysis of the Geometrical Dilution of Precision, which is a measure of localization error defined in Eq. (4), reveals that the localization error is mainly related to the source bearing, subarray interval and their measurement errors. In order to investigate the impact of the underwater waveguide, numerical simulations were carried out based on the normal mode theory. By using the distribution of acoustic intensity and structure of modal arrival, it is proved that the localization accuracy increases as the grazing angle and the subarray interval increase. However, when the measurement errors of source bearing and subarray interval increase, the localization accuracy will decrease. In addition, the obtained bearing estimation result provides an evident characteristic of beam spreading. When sources are near the end-fire direction of the dual-subarray system, significant bearing estimation error occurs, the negative effect of which is then presented. By applying the Subspace Intersection method, unbiased bearing estimation has been achieved, with relatively reduced computational complexity. Most of all, the improved localization performance is validated by experimental data collected in the South China Sea.

Numerical design and characterization of a novel parallel beam combined lens based on X-ray capillary optics

A novel parallel beam combined lens (PBCL) was designed based on a parabolic monocapillary x-ray lens (PMXRL). The proposed PBCL converted a divergent X-ray beam into a near-solid parallel one, which retains the low divergence characteristics of PMXRL and significantly improves the intensity gain by about one order of magnitude. Compared with the traditional polycapillary parallel x-ray lens (PPXRL), the divergence performance of this lens is improved by an order of magnitude, and the light intensity gain is improved by 3-4 times. In addition, we developed a MATLAB-based visualization tool to simulate X-ray transmission within the PBCL through ray tracing. This tool facilitated the assessment of the PBCL's transmission efficiency and its comparison with conventional PMXRL and the PPXRL. The transport process of the PBCL is systematically investigated under the comprehensive consideration of multiple parameters. This study provided a new idea and theoretical basis for the further development of X-ray modulation technology.

Full wave modeling of radio-frequency beams in tokamaks in the electron cyclotron frequency range

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested.

Laser-to-proton conversion efficiency studies for proton fast ignition

We assess the conversion efficiency from intense picosecond laser pulses to multi-MeV ion beams for a wide range of laser and target parameters, using 2D kinetic particle-in-cell simulations. Scalings are addressed in a quasi-one-dimensional geometry, leaving out beam divergence. Then, we study the conversion efficiency into a narrow spatial band along the laser axis for flat and hemispherical targets in large-scale 2D simulations. Combining these findings allows us to calculate the energy requirements for ignition of a compressed ICF target with an intense proton beam in a fast-ignition scenario.

Proton acceleration from optically tailored high-density gas jet targets

Laser-driven ion acceleration is well established using solid targets mainly in the target normal sheath acceleration regime. To follow the increasing repetition rate available on high-intensity lasers, the use of high-density gas targets has been explored in the past decade. When interacting with targets reaching densities close to the critical one, the laser pulse can trigger different acceleration mechanisms such as Collisionless Shock Acceleration (CSA) or hole boring. Particle-in-cell simulations using ideal target profiles show that CSA can accelerate a collimated, narrow energy spread and few hundreds of megaelectronvolts ion beam on the laser axis. Nevertheless, in real experiments, the laser will not only interact with an overcritical, thin plasma slab with sharp density gradients, but also with lower density regions surrounding the core of the gas jet, extending to several hundreds of micrometres. The interaction of the laser with these lower density wings will lead to nonlinear effects that will reduce the available energy to drive the shock in the high-density region of the target. Optically tailoring this target could mitigate that issue. Recent experiments conducted on different laser facilities aimed at testing several tailoring configurations. We first tested a scheme with a copropagating picosecond prepulse to create a lower density plasma channel to facilitate the propagation of the main pulse, while the second one was a transverse tailoring driven by nanosecond laser pulses to generate blast waves and form a high-density plasma slab. The main results will be presented here and the methods compared.

Effect of a Weakly Divergent Acoustic Beam on the Spatiotemporal Structure of Pulsed Signals in an Underwater Sound Channel

Effect of a Weakly Divergent Acoustic Beam on the Spatiotemporal Structure of Pulsed Signals in an Underwater Sound Channel

Performance analysis of 2D optical code division multiple access through underwater wireless optical medium

The performance of a two-dimensional optical code division multiple access (2D-OCDMA) system using an underwater wireless optical (UWO) medium is assessed in this work. The optical source is an LED with a working wavelength of 532 nm, and the optical detector is a p–i–n photodiode. When calculating the bit error rate (BER), the phase-induced intensity noise (PIIN), thermal noises, and shot sounds are taken into account. The user code address is set using 2D perfect difference (2D-PD) codes. Link distance, inclination angle, beam divergence angle, transmitter power, and the number of concurrent users are all taken into account when determining the BER performance. For various water media, such as pure sea water (PSW), clear ocean water (CLOW), and coastal ocean water (CSOW), the performance of the suggested system is examined.

Terahertz reflective imaging systems with improved angle compatibility realized by the designed quasi-scattering screen

Active imaging can provide significantly larger signal margins in the terahertz (THz) spectral region than passive imaging. However, the imaging effect of THz active imaging is severely constrained by the orientation requirement of target reflection, which limits the application scenarios of this technique. In view of the shortcomings of existing THz reflective imaging systems, this paper proposes a new system optimization scheme from the aspect of hardware - a compact quasi-scattering screen (QSS) is proposed and designed as a beam-shaping element to eliminate the need for the best direction of specular reflection to the greatest extent. The corresponding relationship between the divergent Gaussian beam and target light field is directly established by using the equal-energy mapping method in non-imaging optics, which rejects the collimation process of the THz source. By customizing the optimization function in ZEMAX® to automatically optimize the surface of the QSS, the direction of incident light propagation can be adjusted. A non-coaxial reflective THz imaging system using a 0.1 THz continuous wave source demonstrates the ability of the QSS to improve the angle compatibility of the traditional THz reflective imaging system. The results show that the imaging angle compatibility range of the system can be increased to more than 5 times without changing the original imaging optical path and its resolution. In addition, it can also improve the imaging quality of the original imaging optical path for the object with a smooth surface or certain structure.

Investigations on OFDM UAV-based free-space optical transmission system with scintillation mitigation for optical wireless communication-to-ground links in atmospheric turbulence

The potential integration of unmanned aerial vehicles (UAVs) with free space optical (FSO) communication systems stands as a promising innovation in the realm of wireless network infrastructures. This study presents a comprehensive investigation into the application of orthogonal frequency division multiplexing (OFDM) in conjunction with UAV-based FSO technology, with a specific focus on establishing robust wireless communication links to ground sites within the evolving landscape of 5G networks. The research introduces a pioneering 4-level quadrature amplitude modulation (4-QAM)-OFDM-FSO framework tailored for UAV-to-ground communication, revolutionizing the prospects for seamless and high-throughput data transmission within dynamic network environments. Through comprehensive simulations and theoretical analyses, we unveil the system's efficacy in mitigating atmospheric turbulence, achieving heightened signal integrity, and ensuring performance adaptability over varying link distances, thus significantly addressing present limitations in traditional wireless communication models. Anchored within the context of modern wireless network infrastructures, this work serves as a crucial stepping stone for the practical application of OFDM-UAV-FSO communication systems, representing a paradigm shift in fostering resilient and agile wireless connectivity in the era of 5G networks. The inception of cutting-edge wireless networks expected to outperform the capabilities of 5G necessitates an infrastructure that can handle vast amounts of data. This infrastructure must be not only cost-effective and simple to deploy but also readily scalable to accommodate the diverse demands of front-haul and backhaul applications. Motivated by the growing interest in harnessing UAVs to extend the reach and enhance the operational efficacy of conventional cellular networks, this work introduces a novel application of UAV-ground station connections. The concept employs FSO to facilitate network traffic within both the segments. To optimize throughput, resilience, and spectral efficiency, the application of OFDM is proposed. The research considers the transmission of a 20 Gbps 4-QAM data signal across various channel conditions. It thoroughly assesses the performance implications of factors such as transmission distance and beam divergence. The study explores the correlation between pointing error, scintillation, beam divergence angle, and average spectral efficiency. A slight increase in pointing error results in a rapid rise in the scintillation index, while a larger beam divergence angle can help minimize the impact of scintillation. Adapting the beam's divergence angle based on the pointing error between the optical transceivers can reduce the effects of scintillation and improve the average spectral efficiency and channel capacity. Additionally, the relationship between pointing error, scintillation, and the determination of the optical beam divergence angle in terms of beam divergence and average spectral efficiency and channel capacity is examined, and theoretical evaluations further confirm the method's effectiveness in reducing scintillation in the presence of pointing errors. Furthermore, the simultaneous use of OFDM adaptive beam divergence control and modulation could significantly enhance the data rate. This approach aims to reduce the impact of scintillation in UAV FSO links, which often experience significant losses due to unpredictable fluctuations in the atmosphere's refractive index. The results of the simulations indicate that the integrated 4-QAM-OFDM-FSO framework can realize high data transmission rates, efficiently serving front-haul and backhaul needs, thereby signifying a significant evolutionary leap for the next generation of wireless technology. The numerical findings demonstrate the significant impact of the coherent FSO OFDM optical wireless communication (OWC) setup in UAV wireless communications to ground links, particularly in mitigating the effects of strong turbulence and pointing errors (PEs). Through the integration of spatial coherence diversity and adaptive modulation OFDM in the coherent OWC, there has been a noticeable enhancement in the average spectral efficiency (ASE). Notably, our results indicate an ASE of 53 bits/s/Hz and 37 bits/s/Hz achieved at an average transmitted optical power of 10 dBm for an aperture diameter of 10 cm, without and with PEs for the coherent OWC-FSO OFDM UAV technique, respectively. The proposed method was validated through simulations, demonstrating both improved average spectral efficiency and effective reduction of the scintillation effect. This approach holds promise for mitigating scintillation effects in UAV-FSO links.

Fast-speed and low-power-consumption optical phased array based on lithium niobate waveguides

Abstract Fast scanning speed and low-power consumption are becoming progressively more and more important in realizing high-performance chiplet optical phased arrays (OPAs). Here, we successfully demonstrated integrated OPAs with multiple waveguides channels based on thin-film lithium niobate-on-insulator (LNOI) platform. Specifically, two lithium niobate (LN) OPA chips have been implemented with 32 and 48 channels LN waveguides, respectively, enabled by electro-optic modulations, which showcases the low power consumption (1.11 nJ/π) and fast operation speed (14.4 ns), showing obvious advantage of the LNOI platform over others. As results, we experimentally achieved a beam steering with a 62.2° × 8.8° field of view (FOV) and a beam divergence of 2.4° × 1.2° for 32 channels, and a FOV of 40° × 8.8° and a beam divergence of 0.33° × 1.8° for 48 channels. This work also demonstrates the feasibility of LNOI platform in scalable OPA chips.

Particle analysis based on light extinction method illuminated by a divergent beam

A novel model based on the Monte Carlo principle was put forward to study the phenomenon of particle extinction spectrum under the condition of divergent incident beams and analyze the deviation during particle size inversion. Both the simulation results and experimental results show that the light extinction effect enhances obviously with the increase of divergence angle, accompanied by the distortion of extinction spectrum itself, which is closely related to particle size and optical wavelength. When the divergence angle is up to 20°, the observed relative error during the retrieval of particle size can reach 12.8%, by comparing those obtained by the Lamber-Beer law for particle to the nominal diameter of 0.8 μm. Accordingly, an improved inversion technique was studied, which yielded the particle size measurement error below2% for particles of 0.2 μm, 0.8 μm and 2.88 μm in nominal size.

Coverage extended MMF-based indoor OWC using overfilled launch and diversity reception

Speckle patterns generated as coherent optical beams are reflected by scattering elements. Multimode fibers (MMFs) can modify the transverse intensity distribution of speckle patterns with macro perturbations, i.e., pressures, providing a simple and low-cost way to achieve equivalent beam-steering for indoor optical wireless communications (OWCs) with divergent optical beams. However, the received optical power (ROP) variance severely limits the mobility of user terminals. In this paper, the issue is alleviated by using the overfilled launch of MMFs and the diversity gain of multi-receivers. By adjusting the axial spatial coupling distance between the MMF and the single mode fiber (SMF) emitting coherent laser, the number of excited modes of MMF can be significantly increased at 1550 nm with negligible coupling and bending losses. In addition, the signal-to-noise ratio (SNR) enhancement obtained by applying two receivers is theoretically analyzed for the case when either thermal noise or shot noise is dominant. The experimental results demonstrate that the proposed scheme can efficiently compensate for the ROP inhomogeneity, and at the same time it can extend the achievable full steering angle up to 12° at a 1.5-m free-space distance for bit error rate (BER) values of less than 3.8 × 10−3.

Emission and performance characterization of ionic liquids for an externally wetted electrospray thruster

Ionic liquids are the base for electrospray propulsion, yet few have been explored. The performance of an externally wetted electrospray thruster is characterized for seven different ionic liquids: 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI-BF4), dicyanamide (EMI-DCA), bistrifluoromethylsulfonylimide (EMI-Im), thiocyanate (EMI-SCN), ethylsulphate (EMI-EtOSO3), triflate (EMI-OTf), and trifluoromethanesulfonate (EMI-TFA). This research marks the first time that the latter four liquids are reported for externally wetted emitters. A complete thruster assembly has been tested with each of the propellants. Using time-of-flight mass spectrometry and a Faraday cup for beam divergence, the performance of these ionic liquids has been characterized, assessing thrust, specific impulse and thrust efficiency. EMI-BF4, EMI-DCA and EMI-SCN operated in pure ionic regime while EMI-Im, EMI-EtOSO3, EMI-OTf and EMI-TFA operated in mixed regime.

Smooth motion parallax method for 3D light-field displays with a narrow pitch based on optimizing the light beam divergence angle.

The three-dimensional (3D) light field display (LFD) with dense views can provide smooth motion parallax for the human eye. Increasing the number of views will widen the lens pitch, however, resulting in a decrease in view resolution. In this paper, an approach to smooth motion parallax based on optimizing the divergence angle of the light beam (DALB) for 3D LFD with narrow pitch is proposed. DALB is controlled by lens design. A views-fitting optimization algorithm is established based on a mathematical model between DALB and view distribution. Subsequently, the lens is reversely designed based on the optimization results. A co-designed convolutional neural network (CNN) is used to implement the algorithm. The optical experiment shows that a smooth motion parallax 3D image is achievable through the proposed method.