Beam Propagation Research Articles

A full-space metasurface design for generating multi-mode bessel beams

ABSTRACT To address the challenges of low-quality and single-mode generation of Bessel beams produced by metasurfaces, a full-space metasurface (FS-MS) has been proposed. Based on the polarization and spatial multiplexing principles, the designed unit consists of a polarized reflective grid in the upper layer and a polarization converter in the lower layers. The FS-MS independently controls the phase of co-polarized electromagnetic (EM) waves in reflection mode and both the amplitude and phase of cross-polarized EM waves in transmission mode. Therefore, switching between transmission and reflection modes can be achieved by altering the polarization of incident radiation. The phase distribution of FS-MS is determined based on theories of diffraction-free Bessel beam generation and field superposition. The results indicate that at 12 GHz, in reflection mode, two controllable-power zeroth-order Bessel beams are generated. The diffraction-free ranges of the equal power double beam are 551 mm and 608 mm, respectively, and full widths at half-maximum (FWHM) are 46.44 mm and 52.97 mm. In transmission mode, a Bessel beam with mode l = +2 is produced. The simulation results agree well with the measured results, and the multifunctional FS-MS facilitates the application of Bessel beams in near-field wireless communication and wireless power transmission.

Propagation characteristics of partially coherent twisted off-axis double-vortex beams in atmospheric turbulence

We propose a partially coherent twisted off-axis double vortex (PCTODV) beam and investigate its propagation characteristics in atmospheric turbulence. By employing the extended Huygens–Fresnel principle and the Wigner distribution function, we derive the corresponding analytical expressions and perform numerical simulations to validate our findings. The findings reveal that PCTODV beams possess a wider array of tunable parameters than single vortex beams with central phase singularities, which is beneficial for atmospheric turbulence propagation. The twist factor size notably affects the beam evolution rate in turbulence, with an optimized twist factor enhancing resistance to turbulence. Moreover, factors such as increased wavelength, larger initial beam waist, greater inner turbulence scale, higher refractive index structure constant, and reduced M2 factor contribute to improved transmission stability. These insights advance the understanding of vortex beam propagation in turbulent atmospheric optical communication systems.

Numerical analyses of a mid-IR metasurface spectral beam combiner with high efficiency and low phase distortion

Mid-infrared lasers have been widely used in chem/bio-sensing, medical diagnostics, environmental monitoring, and defense. These applications frequently require broad spectral coverage, high brightness, and compact size. Spectral beam combining (SBC) technology has been proven to be efficient in scaling laser power and broadening spectral range. Although the blazing grating has been successfully applied as the SBC component in mid and far infrared, its performance is limited by strong dispersion and polarization dependence. In this paper, we proposed a spectral beam combiner based on the dual-band anomalous reflective metasurface. The combiner had ultra-high, polarization-independent anomalous reflectivity in two spectral bands (4.0 μm and 4.6 μm). In both bands, the bandwidth with over 95% reflectivity was 100 nm. These properties made both the dense SBC and two-band SBC possible. Moreover, the impacts of the input laser properties on the combining efficiency and beam quality were thoroughly studied. The metasurface beam combiner exhibited high tolerance to the incident angle deviation and input laser spectral linewidth. Even when the laser has a broad linewidth of 70 nm incident on the beam combiner with a large angle deviation of 10°, the beam combiner still showed a higher than 90% efficiency and good reflective beam quality M2<1.5. In addition, in the dense SBC situation, when 7 individual lasers with a central wavelength interval of 25 nm were combined the beam propagation parameter M2 was better than 1.5. We believe that the metasurface spectral beam combiner was an effective alternative to the commercial diffractive gratings and was capable of combining multiple beams from broadband laser sources.

Dual‐Band Metasurface‐Based Structured Light Generations for Futuristic Communication Applications

Structured beams carrying orbital angular momentum carry significant potential for various applications, including optical trapping, manipulations, communications, microscopy, and so on. Among these, perfect vortex (PV) beams are highly attractive due to their immunity to topological charge variations and nondiffracting properties. However, conventional PV beam generation methods typically operate at a single wavelength and rely on bulky components, complicating photonic device integration. To address this, a single‐cell‐driven, dual‐band metasurface platform is experimentally demonstrated to generate nondiffracting PV beams spanning from UV to visible wavelengths (261–405 nm). The proposed metasurfaces, made of rectangular‐shaped silicon nitride nanoantennas, achieve an average transmission efficiency of 65% across dual spectrums. Simulated and experimental results show that the metasurfaces maintain topological charge‐insensitive ring radii. The findings highlight a novel approach for PV beam generations, which can lead to new categories of ultrathin optical devices for diverse applications, including wireless communication, particle trapping, and biomedical imaging.

A physical optics formulation of Bloch waves and its application to 4D STEM, 3D ED and inelastic scattering simulations.

Bloch waves are often used in dynamical diffraction calculations, such as simulating electron diffraction intensities for crystal structure refinement. However, this approach relies on matrix diagonalization and is therefore computationally expensive for large unit cell crystals. Here Bloch wave theory is re-formulated using the physical optics concepts underpinning the multislice method. In particular, the multislice phase grating and propagator functions are expressed in matrix form using elements of the Bloch wave structure matrix. The specimen is divided into thin slices, and the evolution of the electron wavefunction through the specimen calculated using the Bloch phase grating and propagator matrices. By decoupling specimen scattering from free space propagation of the electron beam, many computationally demanding simulations, such as 4D STEM imaging modes, 3D ED precession and rotation electron diffraction, phonon and plasmon inelastic scattering, are considerably simplified. The computational cost scales as {\cal O}({N^2} ) per slice, compared with {\cal O}({N^3} ) for a standard Bloch wave calculation, where N is the number of diffracted beams. For perfect crystals the performance can at times be better than multislice, since only the important Bragg reflections in the otherwise sparse diffraction plane are calculated. The physical optics formulation of Bloch waves is therefore an important step towards more routine dynamical diffraction simulation of large data sets.

Temporal evolution, propagation and mutual interaction of cos-gaussian beams in photorefractive crystals exhibiting both the linear and quadratic electro-optic effect

Abstract We investigate for the first time, the temporal evolution, propagation and interaction of cos-gaussian beams in novel photorefractive crystals having both the linear and quadratic electro-optic effect. The dynamical evolution equation is set up as a function of time using the Helmholtz equation in the paraxial approximation using the photorefractive charge transport model. The analysis is performed theoretically using the finite difference method to solve the dyamical evolution equation. Diffraction effects are prominent initially since the photorefractive effect has not built up while at larger values of time, we see self trapping and formation of breather solitons and Y-type solitons. A detailed study is subsequently undertaken for the propagation of cos-gaussian beams of different cosine modulation parameters and at various different values of the external electric field once steady state has been reached. Self trapping and formation of optical spatial solitons including breathing solitons and Y-type breathing solitons are observed as the nonlinearity is strengthened by increasing the external electric field. The characteristics of the solitons are dependent upon the modulation parameter of the cos-gaussian beam. The PMN-0.33PT crystal is taken for illustration of the results. Further, the interplay between the linear and the quadratic electro-optic effect and the ensuing effect on the propagation of the cos-gaussian beams is investigated for various cosine modulation parameters. Finally, the interaction of two cos-gaussian beams is studied for in phase and out of phase beams considering various cosine modulation parameters and various separation distances.

Three-Dimensional Scalar Time-Dependent Photorefractive Beam Propagation Model

This paper presents an open-source time-dependent three-dimensional scalar photorefractive beam propagation model (PRProp3D) based on the well-known split-step method. The angular spectrum method is used for the diffractive steps, and the nonlinearities accumulated at the end of each diffractive step are applied using spatially varying phase screens. Comparisons with previously published experimental results are given for image amplification, photorefractive amplified scattering (fanning) and photorefractive screening solitons. Artifacts can be mitigated by use of step sizes less than 5~10 micrometers and by careful choice of the transverse computation grid size to ensure adequate sampling. Wraparound effects associated with the use of discrete Fourier transforms are mitigated by apodization and beam centering.

3-D semivectorial bidirectional marching solver with fourth-order accuracy for optical waveguides

In this paper, we develop and analyze a new, to the best of our knowledge, semivectorial bidirectional operator marching method with fourth-order accuracy (Bi-OMM4) for three-dimensional optical waveguides. The fourth-order semivector exponential scheme reproduces the exact reformulations for equations with pairs of bidirectional reflection operators based on the Dirichlet-to-Neumann (DtN) mapping. Implementations for large range step sizes in both directions are presented, and exact bidirectional range marching formulas are derived for each range-independent segment. The study compares the results obtained from the Bi-OMM4 with the fourth-order bidirectional beam propagation method based on the finite difference scheme (FD-Bi-BPM4) and the bidirectional operator marching method with second-order accuracy (Bi-OMM2) to validate the accuracy and effectiveness of Bi-OMM4 by analyzing several examples of uniform and longitudinally varying waveguides. The results show that the Bi-OMM4 is numerically faster than the FD-Bi-BPM4 by almost seven times for different transverse grid sampling points, and it offers higher accuracy than Bi-OMM2 without a significant increase in computation resources.

Compact silica dual-band wavelength demultiplexer based on asymmetric-defined multimode interference coupler

Limited refractive index difference of silica waveguide brings great size challenges in wavelength demultiplexing. A silica dual-band wavelength demultiplexer (DBWD) based on an asymmetric multimode interference coupler (MMI) is demonstrated. The selective separation and output of target dual bands can be implemented using the proposed design method based on asymmetric-defined MMI couplers. The beam propagation method is adopted to verify the proposed design principle. Standard CMOS fabrication is used in demultiplexer preparation. At λ=1350 nm, insertion loss (IL) and crosstalk (CT) at port Output1 are 1.94 dB and −24.92 dB, respectively. At λ=1550 nm, IL and CT at port Output2 are 2.44 dB and −29.00 dB, respectively. The 3-dB bandwidth (BW3 dB) for Output1 and Output2 are 82 nm (1297-1379 nm) and 87 nm (1492-1579 nm), respectively. The corresponding CT for Output1 and Output2 are < −7.16 dB and < −12.9 dB, respectively. Due to the introduction of asymmetric MMI coupler, the footprint is reduced to 0.1 mm2 (25 µm × 4000 µm). Because of the periodic characteristic, the wavelength demultiplexing can be extended from O/C bands to E/L bands by a reshaped asymmetric-MMI coupler. Even by combining more asymmetric-MMI couplers with different etched sections, all 18 channels of coarse wavelength division multiplexing (CWDM) transmission (1270-1610 nm) can be covered. The favorable manufacturing tolerance facilitates large-scale integration and mass production.

Improved equivalent optical turbulence method for anisotropic compressible and atmospheric turbulence under different beam transmission distances

The impact of different turbulence on beams can be seen as optical distortions caused by refractive index fluctuations around vortices in turbulence. Therefore, from the perspective of transmission effects, the transmission outcomes of beam in different turbulences can be mutually equivalent. Since the mechanisms of beam propagation in compressible turbulence are not yet fully understood and the relevant theories are not well-established, a preliminary analysis of beam transmission in compressible turbulence is necessary. This analysis will help understand the medium characteristics of compressible turbulence, particularly its similarities and differences with atmospheric turbulence, before the optical effects of compressible turbulence are fully resolved. This paper establishes a connection between anisotropic atmospheric turbulence and compressible turbulence parameters by utilizing the mature solutions of beam in anisotropic atmospheric turbulence. We then employ the optical parameters of anisotropic atmospheric turbulence to represent those in compressible turbulence, leveraging existing solutions to assess beam transmission in compressible turbulence. Building upon the original equivalent method, we extend the dimension of transmission distance, ensuring that beams equivalence is maintained across different turbulence regimes. The results indicate that the equivalent method can effectively adapt to compressible turbulence. By using the equivalent structure function, it is possible to represent compressible turbulence parameters with the atmospheric refractive index structure constant. This method also works across different transmission distances. The method facilitates finding various solutions for beam in compressible turbulence.

Stable laser-acceleration of high-flux proton beams with plasma collimation

Laser-plasma acceleration of protons offers a compact, ultra-fast alternative to conventional acceleration techniques, and is being widely pursued for potential applications in medicine, industry and fundamental science. Creating a stable, collimated beam of protons at high repetition rates presents a key challenge. Here, we demonstrate the generation of multi-MeV proton beams from a fast-replenishing ambient-temperature liquid sheet. The beam has an unprecedentedly low divergence of 1° (≤20 mrad), resulting from magnetic self-guiding of the proton beam during propagation through a low density vapour. The proton beams, generated at a repetition rate of 5 Hz using only 190 mJ of laser energy, exhibit a hundred-fold increase in flux compared to beams from a solid target. Coupled with the high shot-to-shot stability of this source, this represents a crucial step towards applications.

Efficient marching solver for the three-dimensional Helmholtz equation in the cuboid waveguide

In this paper, a marching solver designed for the computation of wave propagation is developed within a class of open three-dimensional waveguides. For the wave propagation model, a three-dimensional scalar and frequency-domain Helmholtz equation is effectively adopted. Specifically, the boundary value problem is converted into an initial value problem by the Dirichlet-to-Neumann (DtN) mapping. Then, with the solving domain restricted to a class of cuboid waveguides, a numerical marching method based on DtN mapping is well established. Besides, when a class of open waveguides is included in the solving domain, the perfectly matched layer (PML) can be used to change the open domain into the bounded form (cuboid waveguide). Finally, the original Helmholtz equation now is equivalent to a complex differential equation with the second order, whose corresponding numerical marching method is also triggered. Numerical comparisons show that the marching method based on the DtN mapping is more efficient and feasible than the one-way method (that is, the beam propagation method (BPM)) when solving the three-dimensional Helmholtz equation.

Establishing and Investigating an Effective Atmosphere‐Ocean Cross‐Medium Propagation Model Based on GSM Beams

AbstractUsing the Gaussian‐Schell model (GSM) beam as the light source, this study creates a blue‐green beam atmosphere‐ocean cross‐medium propagation model (AOCPM) based on the extended Huygens‐Fresnel principle and the linear filtering method. The closed expression of the Cross Spectral Density Function (CSDF) of the GSM beam after propagation through atmospheric turbulence, atmosphere‐ocean interface, and ocean turbulence are derived. And the correctness of the model is verified by simulating the changes in intensity, relative beam width, and speckle normalized intensity autocorrelation function during the propagation of the GSM beam through the atmosphere‐ocean cross‐medium under different parameters. The findings demonstrate that the intensity of the GSM beam after being propagated through the atmosphere‐ocean medium presents a speckle‐like Gaussian distribution, the intensity of the GSM beam gradually attenuates, the relative beam width gradually grows, and the speckle normalized intensity autocorrelation function gradually decreases as the turbulence intensity and propagation distance increase. In addition, the increase in wind speed at rough sea surface mainly leads to the attenuation of intensity. The work of this paper provides a new idea for the study of atmosphere‐ocean cross‐medium propagation of blue‐green beams.

Research on a Low-Loss and Low-Crosstalk Supermode Demultiplexer

ABSTRACT A novel demultiplexer with mode-degenerate output (DMDO) for the six-core supermode fiber (SSF) using finite element method (FEM) and beam propagation method (BPM) is proposed, which can achieve the multiple-input multiple-output free (MIMO-FREE) operations. The DMDO is composed of four directional mode-selective couplers, where the pure silica fiber cores in the couplers significantly minimize fiber attenuation and splicing loss. The main channel with the SSF core (SSFC) supports the supermodes LP01, LP11, LP21, and LP31, where large effective refractive index difference (ERID) between neighboring supermodes enables low crosstalk. The DMDO can achieve mode-degenerate outputs of four supermodes LP01, LP11, LP21, and LP31, which solves the mode rotation issue in the propagation system. In the range of 1530–1565 nm, extinction ratios (ERs) of supermodes LP01, LP11, LP21, and LP31are respectively maintained above 27.48, 29.07, 28.18, and 36.65 dB, while the ER of supermode LP31 is up to a maximum of 39.25 dB. The corresponding coupling efficiencies (CEs) can respectively reach −0.42, −0.22, −0.17, and −0.40 dB. According to principle of light wave reversibility, the DMDO can be used as a multiplexer.

Nonlinear Airy beam propagation in defected photonic lattices.

This work theoretically investigates the interplay of nonlinear Airy beams (AB) propagation and optically induced waveguide arrays in a photorefractive (PR) crystal. By introducing defect guides within the photonic lattice, we control the trajectory and self-bending properties and mostly the complex photoinduced waveguiding structures of these unconventional beams. Positive defects within the lattice induce the formation of solitary-like waves, while negative defects result in strong repulsion effects. In the nonlinear regime, these phenomena are further enhanced, with higher solitonic wave intensity in the case of a positive defect. Our simulations further demonstrate that at a lattice period of 20 µm, a specific defect guide modulation depth, and proper nonlinearity strength, a single laser beam injected in a negatively defected waveguide splits into up to seven distinct output channels. By judiciously adjusting the parameters, we can generate output channels that are spatially separated by up to 19 times the beam waist, thereby offering precise control over both the position and intensity of the output channels.

Characterizing propagation and vortex-splitting dynamics of Bessel-Gaussian beams in short-range atmospheric conditions.

This study explores the propagation dynamics of Bessel-Gaussian (BG) beams, focusing on vortex-splitting behavior under short-range atmospheric conditions with varying disturbances. Using the split-step beam propagation method, the research reveals that greater atmospheric turbulence and longer transmission distances enhance both the average vortex splitting distance and its variance while reducing the average topological charge of the received OAM mode. Conversely, laminar conditions promote beam stability. Results highlight the high sensitivity of vortex splitting to beam parameters, with topological charge playing a significant role in phase singularity formation and vortex complexity. Additionally, beam width and shape are critical, as larger widths intensify splitting under atmospheric disturbance. Notably, BG beams exhibit greater stability and less vortex splitting than Laguerre-Gaussian beams, particularly in turbulent environments at short distances. These insights advance the understanding of vortex beam dynamics, with important implications for atmospheric remote sensing applications.

A comparative study of experimental and simulated ultrasound beam propagation through cranial bones

Objective.Transcranial ultrasound is used in a variety of treatments, including neuromodulation, opening the blood-brain barrier, and high intensity focused ultrasound therapies. To ensure safety and efficacy of these treatments, numerical simulations of the ultrasound field within the brain are used for treatment planning and evaluation. This study investigates the accuracy of numerical modelling of the propagation of focused ultrasound through cranial bones.Approach.Holograms of acoustic fields after propagation through four human skull specimens were measured for frequencies ranging from 270 kHz to 1 MHz, using both quasi-continuous and pulsed modes. The open-source k-Wave toolbox was employed for simulations, using an equivalent-source hologram and a uniform bowl source with parameters that best matched the measured free-field pressure distribution.Main results.The average absolute error in k-Wave simulations with sound speed and density derived from CT scans compared to measurements was 15% for the spatial-peak acoustic pressure amplitude, 2.7 mm for the position of the focus, and 35% for the focal volume. Optimised uniform bowl sources achieved calculation accuracy comparable to that of the hologram sources.Significance.This method is demonstrated as a suitable tool for prediction of focal position, size and overall distribution of transcranial ultrasound fields. The accuracy of the shape and position of the focal region demonstrate the suitability of the sound speed and density mapping used here. However, large errors in pressure amplitude and transmission loss in some individual cases show that alternative methods for mapping individual skull attenuation are needed and the possibility of considerable errors in pressure amplitude should be taken into account when planning focused ultrasound studies or interventions in the human brain, and appropriate safety margins should be used.

A metal-only transmission metasurface with dual-layer configuration for generation of orbital angular momentum wave

In this paper, we present a metal-only transmission metasurface adopting dual-layer elements with I-shaped grooves etched on each layer, which is designed for orbital angular momentum (OAM) generation. The special arrangement of the grooves on the elements results in a wider phase compensation range, and by varying the length of the grooves, a full 360° phase coverage with a transmission amplitude of more than −2 dB can be achieved at 10 GHz. As a proof of concept, a metal-only transmission metasurface composed of 400 elements is designed, fabricated, and measured. The simulated and measured results suggest that the OAM transmitted waves with the mode l = −1 can be efficiently generated by a double-layer metal-only metasurface at around 10 GHz. Compared with conventional configurations of OAM transmitted beam generation, this configuration has great potential for high power microwave and space environment applications.

Arbitrary vector beam generation in semiconductor quantum dots

Arbitrary vector beam generation in semiconductor quantum dots

Modeling Femtosecond Beam Propagation in Dielectric Hollow-Core Waveguides

The propagation of femtosecond pulses in guided structures is a matter of both fundamental and practical interest in nonlinear optics. In particular, hollow-core waveguides (HCWs) filled with a gas medium are fabricated and used as devices for the generation of attosecond pulses from high-order harmonics. In this process, the configuration of the laser field (intensity and phase) inside the waveguide is of crucial importance for enhancing the (well-known, low) efficiency of high-order harmonic generation (HHG). Here, we present numerical calculations which demonstrate the main features of the propagation process in fabricated HCWs. We consider a variety of experimental parameters like gas pressure, waveguide size, laser wavelength, and pulse energy and duration. In particular, the beam profile at the fiber input is found to be a sensitive parameter which influences the whole evolution of the laser field along the propagation. Our model is based on a split-step method modified to account for propagation in ionized media and is validated against experimental and theoretical data from the literature. Our results contribute to the description of the main features of beam propagation in HCWs and provide guiding directions for designing efficient configurations for HHG.