Free-space Propagation Research Articles

Particle Tracking Using Digital In-Line Holography Coupled With Magnification Lenses

Digital in-line holography (DIH) is a robust volumetric particle tracking technique suitable for the characterization of dilute flows. In a free space propagation setup the accuracy of the particle positioning is directly limited to the sampling conditions which depend on the size of the sensor and its position with respect to the particle field along the optical axis. Therefore, it may be interesting to place a magnification optical system between the particle field and the sensor to improve this accuracy. This work investigates the influence of a beam magnifier on an in-line digital holography setup to measure the size and three-dimensional positions of particles within a flow. First, a physical optical numerical model suitable for the simulation and reconstruction of magnified holograms is proposed. Then, based on a twin numerical and experimental study, the influence of a beam magnifier on the signal collection is evaluated and compared with the usual case of free propagation, especially regarding three relevant parameters: the focusing accuracy, the particles center positioning in space and the diameter measurement. Experimental results on an academic flow of calibrated micrometer beads moving through a particle size analyzer flow cell confirm that it is possible to improve accuracy by more than a factor 3 using a simple afocal system composed of two spherical lenses.

Space squeezing optics: Performance limits and implementation at microwave frequencies

Optical systems often largely consist of empty space as diffraction effects that occur through free-space propagation can be crucial for their function. Contracting these voids offers a path to the miniaturization of a wide range of optical devices. Recently, a new optical element—coined “spaceplate”—has been proposed, which is capable of emulating the effects of diffraction over a specified propagation distance using a thinner non-local metamaterial [Reshef et al., Nat. Commun. 12, 3512 (2021)]. The compression factor of such an element is given by the ratio of the length of free-space that is replaced to the thickness of the spaceplate itself. In this work, we test a prototype spaceplate in the microwave spectral region (20–23 GHz)—the first such demonstration designed to operate in ambient air. Our device consists of a Fabry–Pérot cavity formed from two reflective metasurfaces with a compression factor that can be tuned by varying the size of perforations within each layer. Using a pair of directive horn antennas, we measure a space compression factor of up to ∼6 over a numerical aperture (NA) of 0.34 and a fractional bandwidth of 6%. We also investigate the fundamental trade-offs that exist between the compression factor, transmission efficiency, NA, and bandwidth of this single resonator spaceplate design and highlight that it can reach arbitrarily high compression factors by restricting its NA and bandwidth.

Propagation dynamics of abruptly autofocusing circular Airyprime beam with an optical vortex

Circular Airyprime beam (CAPB) is a new kind of abruptly autofocusing beam introduced recently [Opt. Express, 30, 3804 (2022)], which possesses much stronger autofocusing ability than that of circular Airy beam under the same conditions. In this paper, we investigate the free-space propagation dynamics of such kind of beam embedded with an optical vortex (OV), named circular Airyprime vortex beam (CAPVB) hereafter. The effects of the topological charge and the singularity position of the OV on the abruptly autofocusing ability and the focus position of the CAPVB are examined. Our results reveal that the abruptly autofocusing ability of the CAPVB decreases significantly as the topological charge or the radial position of the OV’s singularity increases, whereas its autofocusing ability keeps invariant against the azimuthal angle of the OV’s singularity if the radial position of the singularity is fixed. In addition, the focus position of the CAPVB elongates with the increase of the topological charge, while this position only has a little changes as the radial position varies. Further, we carry out an experiment for the generation of the CAPVB and demonstrate the autofocusing behaviors experimentally. The experimental results are well consistent with the theoretical results. Although the abruptly autofocusing ability of the CAPVB is weaker than that of the CAPB, the most peculiar properties of the CAPVB is that this beam could produce various special focus intensity patterns by manipulating the topological charge and the singularity position of the OV, and carries the orbital angular momentum, which has promising applications in many fields.

Generation of finite energy Airyprime beams by Airy transformation.

In this paper, the lone generation of a new kind of beam named finite energy Airyprime (FEA) beam through the Airy transformation of the coherent superposition of four different elegant Hermite-Gaussian modes is reported for the first time. Analytical expressions of the centroid, the r.m.s beam width, the divergence angle, and the beam propagation factor of the FEA beam are derived in the output plane of Airy transformation, respectively. The effects of the Airy control parameters on the intensity distribution, the centroid, the r.m.s beam width, and the beam propagation factor are examined in detail through numerical examples. Unlike the Airy beam, the FEA beam upon free space propagation will be associated with an additional Airy mode, and the beam pattern of the FEA beams propagating in free space will evolve into a solid beam spot with two tails along two transverse directions, as well as the the intensity of main lobe of the FEA beam decays much slowly during free space propagation. Further, an experiment setup is established to generate the FEA beam via Airy transformation of four mixed elegant Hermite-Gaussian modes. The propagation characteristics such as the intensity distribution, the r.m.s beam width and the beam propagation factor are measured. The experimental results agree well with the theoretical predictions. Our study affords an effective and novel approach to generate the FEA beam, and is beneficial to expand the potential application of the FEA beam.

Self-healing of multipartite entanglement in optical quantum networks

Multipartite entanglement serves as an essential resource for constructing quantum networks and makes it possible to realize multi-user quantum information protocols outperforming their classical counterparts. Unfortunately, multipartite entanglement is fragile when distributed in complex environments. Therefore, it is urgent to address the issue of multipartite entanglement decoherence caused by complex environments. Here we demonstrate the self-healing of multipartite continuous-variable (CV) entanglement after an obstruction. In our experiment, the tripartite entanglement destroyed by the obstruction-introduced noise and loss can self-heal after free-space propagation of a certain distance due to the self-healing property of a Bessel–Gaussian (BG) beam. We show that the BG beam provides a more robust mode basis for free-space CV quantum entanglement distribution than the widely used fundamental Gaussian beam under similar conditions. In addition, we also demonstrate the self-healing of five sets of tripartite entanglement and 10 sets of bipartite entanglement in orbital-angular-momentum-multiplexed optical quantum networks. Our results pave the way for constructing obstruction-tolerant high-capacity CV optical quantum networks.

Geometric Progression of Optical Vortices

We study coaxial superpositions of Gaussian optical vortices described by a geometric progression. The topological charge (TC) is obtained for all variants of such superpositions. The TC can be either integer or half-integer in the initial plane. However, it always remains integer when the light field propagates in free space. In the general case, the geometric progression of optical vortices (GPOV) has three integer parameters and one real parameter, values which define its TC. The GPOV does not conserve its intensity structure during propagation in free space. However, the beam can have the intensity lobes whose number is equal to one of the family parameters. If the real GPOV parameter is equal to one, then all angular harmonics in the superposition are of the same energy. In this case, the TC of the superposition is equal to the order of the average angular harmonic in the progression. Thus, if the first angular harmonic in the progression has the TC of k and the last harmonic has the TC of n, then the TC of the entire superposition in the initial plane is equal to (n + k)/2, but the TC is equal to n during propagation. The experimental results on generating of the GPOVs by a spatial light modulator are in a good agreement with the simulation results.

First steps into coherent object classification using convolutional deep diffractive neural networks

Abstract As artificial intelligence and deep learning becomes more important, new approaches for photonic neural computing arise. We investigate the concept of deep diffractive neural networks. First proposed in 2018, deep diffractive neural network operate passively, using coherent images and diffractive optics to do image-to-image regression and object classification. In this article we shortly review current approaches, give a brief introduction into the mathematical description of such diffractive networks using the Angular Spectrum method and show the first results of our own developments of convolutional diffractive networks with an experimental accuracy of approximately 84 %. The objective of this article is to give an introduction into the field of optical computing with neural networks using diffraction and free-space propagation of light.

Millimeter-Wave Phased Arrays and Over-the-Air Characterization for 5G and Beyond: Overview on 5G mm-Wave Phased Arrays and OTA Characterization

Millimeter-wave (mm-wave) technology is a viable candidate to address the growing data traffic in 5G wireless communication and beyond. However, challenges related to free-space propagation loss, atmospheric absorption, scattering, and nonline-of-sight propagation must be addressed to benefit from the promised bandwidth available in the mm-wave regime. In this context, phased-array technology is considered vital to provide high-speed and seamless wireless solutions to the industry. A phased array can be defined as a multiple-antenna system that electronically controls the radiated electromagnetic (EM) beam. The official origin of the antenna array concept is attributed to Guglielmo Marconi. A repeated Morse code signal letter “S” from Poldhu, United Kingdom to St. John’s in Canada was successfully demonstrated in December 1901, using a two-element antenna array. In the early 1940s, Luis Walter Alvarez designed the first electronically scanning phased-array radar. Both scientists were awarded the Nobel Prize for their discovery.

Optimization of a customized simultaneous algebraic reconstruction technique algorithm for phase-contrast breast computed tomography

Objective. To introduce the optimization of a customized GPU-based simultaneous algebraic reconstruction technique (cSART) in the field of phase-contrast breast computed tomography (bCT). The presented algorithm features a 3D bilateral regularization filter that can be tuned to yield optimal performance for clinical image visualization and tissues segmentation. Approach. Acquisitions of a dedicated test object and a breast specimen were performed at Elettra, the Italian synchrotron radiation (SR) facility (Trieste, Italy) using a large area CdTe single-photon counting detector. Tomographic images were obtained at 5 mGy of mean glandular dose, with a 32 keV monochromatic x-ray beam in the free-space propagation mode. Three independent algorithms parameters were optimized by using contrast-to-noise ratio (CNR), spatial resolution, and noise texture metrics. The results obtained with the cSART algorithm were compared with conventional SART and filtered back projection (FBP) reconstructions. Image segmentation was performed both with gray scale-based and supervised machine-learning approaches. Main results. Compared to conventional FBP reconstructions, results indicate that the proposed algorithm can yield images with a higher CNR (by 35% or more), retaining a high spatial resolution while preserving their textural properties. Alternatively, at the cost of an increased image ‘patchiness’, the cSART can be tuned to achieve a high-quality tissue segmentation, suggesting the possibility of performing an accurate glandularity estimation potentially of use in the realization of realistic 3D breast models starting from low radiation dose images. Significance. The study indicates that dedicated iterative reconstruction techniques could provide significant advantages in phase-contrast bCT imaging. The proposed algorithm offers great flexibility in terms of image reconstruction optimization, either toward diagnostic evaluation or image segmentation.

Evolution of a fractional-charge optical vortex upon free-space propagation

Previously, it has been demonstrated theoretically (J. Opt. 6, 259 (2004)) and experimentally (Opt Express 19, 5760 (2011)) that upon the free-space propagation, an initial fractional-charge optical vortex acquires an integer topological charge (TС) equal to the nearest smaller integer if the fractional part is less than 0.5, otherwise becoming equal to the nearest larger integer. In this work, we demonstrate by the numerical modeling that as an initial fractional-charge optical vortex propagates in free space, the TC changes to the nearest smaller or larger integer at a fractional part threshold of 0.12. The fact is that an additional singularity center is born on the beam periphery where the field intensity is near-zero (one millionth part of the maximum), meaning that it cannot be experimentally detected but can be numerically simulated.

Modern Energy Optimization Approach for Efficient Data Communication in IoT-Based Wireless Sensor Networks

Many researchers are drawn to mobile wireless sensor networks (WSN) and the Internet of Things (IoT) because of the significant challenges of power consumption and network connectivity. A technique that takes into consideration the characteristics such as network probability, the identified region of individual nodes, and the radius of the whole identified region is presented in this article. Free-space propagation is carried out in the region of interest. This approach assures network connection, long-term communication sustainability, and maximum energy efficiency. It was discovered that a mathematical network model can be built using the probability theory. It has been possible to examine and evaluate the changes in sensor nodes as a function of distance from the detection region using this approach. As a result, a correlation has been established between a network’s communication radius and the identified region. Additionally, a novel method has been developed to reduce energy consumption and sustain connectivity through boosting the connectivity feature. Notably, IoT-based WSN architectures require more energy optimization than any other network, because they have resource-limited nodes. Also, a simulation plot of the proposed approach’s mathematical network scheme is shown to show if it works. The proposed method consumes much less energy averagely 40% compared to the existing methods, which are LEACH, ZTR, and DSR when the radius is 100.

Extraction of Inherent Polarization Modes from an m‐Order Vector Vortex Beam

Superposition of two independent orthogonally polarized beams is a conventional principle of creating a new light beam. Herein, it is intended to achieve the inverse process, namely, extracting inherent polarization modes from a single light beam. However, inherent polarization modes within a light beam are always intertwined so that a stable polarization is maintained during propagation in free space. To overcome this limitation, an approach that breaks the modulation symmetry of an m‐order vector vortex beam is reported, thereby unbinding the inherent polarization modes. Using polarization mode competition along with an optical pen, polarization modes within m‐order vector vortex beam are extracted at will in the focal region of an objective lens. This work treats the light beam as a treasure box, and polarization mode extraction is just like the key of the box. Whatever it is, one can just take it directly from the box. This physical thought conveys an entirely new principle of polarization modulation and paves the way for multidimensional manipulation of light fields.

High- Q Surface Light Emission from Active Parity-Time-Symmetric Gratings

This work presents a theoretical investigation of an active photonic grating of the parity-time- ($PT$) symmetric architecture. The analytical study of the free-space mode propagation from the grating structure indicates the unique bifurcation property due to the $PT$-symmetry modulation. It is shown that both the gain-loss contrast and the lattice constant parameters are critical factors to modulate the active photonic system in between the $PT$-symmetry to the symmetry-broken phases. Furthermore, numerical simulations via the rigorous coupled-wave analysis (RCWA) method discover the existence of a unique spectral singularity phenomenon in this $PT$ grating structure, which corresponds to a nontrivial single mode and near-zero bandwidth photonic resonant emission. Also, the guiding procedure for fulfilling spectral singularity modes is found to be related to the unique formation of the scattering matrix applied in the $PT$-symmetric photonic gratings. This theoretical work takes a fresh look into the active $PT$-symmetric photonic gratings focusing on the discovery of nontrivial free-space emission modes, which could contribute to the development of high-performance surface-emitting semiconductor devices.

Depolarization of Vector Light Beams on Propagation in Free Space

Nonparaxial propagation of the vector vortex light beams in free space was investigated theoretically. Propagation-induced polarization changes in vector light beams with different spatial intensity distributions were analyzed. It is shown that the hybrid vector Bessel modes with polarization-OAM (orbital angular momentum) entanglement are the exact solutions of the vector Helmholtz equation. Decomposition of arbitrary vector beams in the initial plane z = 0 into these polarization-invariant beams with phase and polarization singularities was used to analyze the evolution of the polarization of light within the framework of the 2 × 2 coherency matrix formalism. It is shown that the 2D degree of polarization decreases with distance if the incident vector beam is not the modal solution. The close relationship of the degree of polarization with the quantum-mechanical purity parameter is emphasized.

Accuracy of peak-power compensation in fiber-guided and free-space acoustic-resolution photoacoustic microscopy.

Acoustic resolution photoacoustic microscopy (AR-PAM) has gained much attention in the past two decades due to its high contrast, scalable resolution, and relatively higher imaging depth. Multimode optical fibers (MMF) are extensively used to transfer light to AR-PAM imaging scan-head from the laser source. Typically, peak-power-compensation (PPC) is used to reduce the effect of pulse-to-pulse peak-power variation in generated photoacoustic (PA) signals. In MMF, the output intensity profile fluctuates due to the coherent nature of light and mode exchange caused by variations in the bending of the fibers during scanning. Therefore, using a photodiode (PD) to capture a portion of the total power of pulses as a measure of illuminated light on the sample may not be appropriate for accurate PPC. In this study, we have investigated the accuracy of PPC in fiber-guided and free-space AR-PAM systems. Experiments were conducted in the transparent and highly scattering medium. Based on obtained results for the MMF-based system, to apply PPC to the generated PA signals, tightly focused light confocal with the acoustic focus in a transparent medium must be used. In the clear medium and highly focused illumination, enhancement of about 45% was obtained in the homogeneity of an optically homogeneous sample image. In addition, it is shown that, as an alternative, free-space propagation of the laser pulses results in more accurate PPC in both transparent and highly scattering mediums. In free-space light transmission, enhancement of 25-75% was obtained in the homogeneity of the optically homogeneous sample image.

Physically-secured high-fidelity free-space optical data transmission through scattering media using dynamic scaling factors.

In this paper, we propose a method of physically-secured high-fidelity free-space optical data transmission through scattering media using physically- and dynamically-generated scaling factors. Optical channel characteristics are explored, and scaling factors are physically and dynamically generated to serve as security keys in the developed free-space optical data transmission system. The generated dynamic scaling factors provide a security layer for free-space optical data transmission. To the best of our knowledge, it is the first time to physically and dynamically generate scaling factors in free-space optical data transmission system to realize data encryption. The scaling factors existing in free-space optical data transmission channel are physically and dynamically controlled by using two optical devices, i.e., variable beam attenuator (VBA) and amplitude-only spatial light modulator (SLM). Nonlinear and dynamic variation of scaling factors is realized in different free-space wave propagation environments. It is experimentally demonstrated that high security can be guaranteed in the developed physically-secured high-fidelity free-space optical data transmission system, since one random scaling factor is physically and dynamically generated for the transmission of each signal pixel value. In addition, the proposed physically-secured free-space optical data transmission scheme is robust to noise and scattering, and high-fidelity signals are retrieved at the receiving end. The proposed method could open up a new research perspective for the secured free-space optical data transmission.

Propagation-invariant high-dimensional orbital angular momentum states

Photonic states encoded in spatial modes of paraxial light fields provide a promising platform for high-dimensional quantum information protocols and related studies, where several pioneering theoretical and experimental demonstrations have paved the path for future technologies. Crucially, critical issues encountered in free-space propagation still represent a major challenge. This is the case of asynchronous diffraction between spatial modes with different modal orders, which experience variations in their transverse structure upon free-space propagation. Here we address this issue by proposing an encoding method based on the use of Laguerre–Gaussian modes of the same modal order N to define a N + 1 dimensional space. Noteworthy, such modes endowed with orbital angular momentum (OAM) experience the same propagation aberrations featuring an identical Gouy phase and wavefront curvature. We demonstrate our proposal experimentally by using time-correlated-single-photon imaging combined with a digital propagation technique. Importantly, our technique allows to eliminate, without the use of imaging systems, all issues related to asynchronous diffraction, providing an accessible way to generate propagation-invariant OAM qudits for quantum optical protocols.

Ho:LuAG single crystal fiber: growth, spectroscopy and laser characteristics.

Lutetium aluminum garnet single-crystal fiber (SCF, ∼ Φ 0.9 mm - 165 mm) doped with 0.5 at.% Ho3+ has been grown by the micro-pulling-down (µ-PD) technique. The room-temperature absorption and emission spectra exhibit similar features to the bulk crystal. Laser performances of the SCFs with two different pump configurations, i.e., pump guiding and free-space propagation, are studied by employing a 1.9-µm laser diode and a high-brightness fiber laser, respectively. Laser slope efficiencies obtained with both pump configurations can be higher than 50%, and a maximum output power of 6.01 W is achieved at ∼ 2.09 µm with the former pump. The comparable efficiency to the high-brightness pump is an indication of that high laser performance can also be expected through pump-guiding in the SCF even with a low pump beam quality.

Self-rotating beam in the free space propagation.

We introduce a class of self-rotating beams whose intensity profile tends to self-rotate and self-bend in the free space propagation. The feature of the self-rotating beams is acceleration in the three-dimensional (3D) space. The acceleration dynamics of the self-rotating beams is controllable. Furthermore, multiple self-rotating beams can be generated by a combined diffractive optical element (DOE) simultaneously. Such a beam can be viewed as evolution of a vortex beam by changing the exponential constant of phase. We have generated this beam successfully in the experiment and observed the expected phenomenon, which is basically consistent with the result of the numerical simulation. Our results may provide new insight into the self-rotating beam and extend potential applications in optical imaging.

Модели искажений сигналов при распространении в лесных массивах

Models of signal propagation in forests are presented, based on the representation of forests as a continuous quasi-homogeneous medium and characterized by an effective complex permittivity. The values of the effective permittivity are a functional of the total volumetric concentration of the components of vegetation relative to the main medium - the atmosphere, of the frequency of signals, of the electrical and taxometric characteristics of forests. It is shown that when propagating along the lines under consideration, the spectral components of digital signals acquire partial phase and amplitude shifts, which causes distortions of the complex envelopes of signals and energy losses during reception with respect to propagation in free space. Modeling was carried out using models of signal propagation in forests with typical characteristics to estimate the probabilistic characteristics of receiving digital signals with 4-level phase shift keying with frequency band extension. It is shown that for these signals with a frequency band of 10...20 MHz with a center frequency of the P-band with horizontal polarization, the energy loss with respect to propagation in free space with equivalent attenuation exceeds 1.2 dB due to the distortion of the complex envelopes of the signals. A smaller effect on the probabilistic characteristics of receiving signals with vertical polarization is also shown - the energy loss in this case reaches 0.5 dB.