Nondiffracting Behavior Research Articles

Generating optical vortex needle beams with a flat diffractive lens

We present a novel method for generating optical vortex needle beams (focused optical vortices with extended depth-of-focus) using a compact flat multilevel diffractive lens (MDL). Our experiments demonstrate that the MDL can produce focused optical vortices (FOVs) with topological charges l=1−4 (extendable to other l values), maintaining focus over distances significantly longer than conventional optical vortices. Specifically, FOVs exhibit non-diffracting behavior with a depth-of-focus (DOF) extended beyond 5 cm, compared to conventional optical vortices, which show continuous size increase due to diffraction. When the MDL is illuminated by an optical vortex of 3 mm diameter, it achieves a transmission efficiency of approximately 90% and extends the DOF several times beyond that of traditional lenses. Increasing the size of the input optical vortex further extends the DOF but introduces additional rings, with their number increasing proportionally to the value of l. Our approach, validated by both experimental results and numerical simulations, proves effective for beams such as optical vortex and Hermite-Gaussian modes and holds potential applications in high-resolution imaging, material processing, optical coherence tomography, and three-dimensional optical tweezers, offering a simple and efficient solution for generating non-diffracting beams.

Optical atompilz: Propagation-invariant strongly longitudinally polarized toroidal pulses

Recent advancements in optical, terahertz, and microwave systems have unveiled non-transverse optical toroidal pulses characterized by skyrmionic topologies, fractal-like singularities, space-time nonseparability, and anapole-exciting ability. Despite this, the longitudinally polarized fields of canonical toroidal pulses notably lag behind their transverse counterparts in magnitude. Interestingly, although mushroom-cloud-like toroidal vortices with strong longitudinal fields are common in nature, they remain unexplored in the realm of electromagnetics. Here, we present strongly longitudinally polarized toroidal pulses (SLPTPs), which boast a longitudinal component amplitude exceeding that of the transverse component by over tenfold. This unique polarization property endows SLPTPs with robust propagation characteristics, showcasing nondiffracting behavior. The propagation-invariant strongly longitudinally polarized field holds promise for pioneering light–matter interactions, far-field superresolution microscopy, and high-capacity wireless communication utilizing three polarizations.

Generation of elliptical perfect optical vortex beams and their propagation in free-space.

We investigate the generation of an elliptical perfect optical vortex (EPOV) beam through the optical Fourier transformation of an elliptical Bessel-Gaussian beam and derive an analytical expression for its complex field amplitude. Our analysis includes the examination of the beam's propagation in free-space and the influence of topological charge on its transmission. The EPOV beam's propagation in free-space can be categorized into non-diffracting and diffracting stages. During the non-diffracting stage, the beam intensity and profile size are effectively preserved over a short transmission distance. Subsequently, in the diffracting stage, the beam profile initially contracts and then expands with a change in the beam intensity. Notably, the impact of topological charge on the beam intensity and profile size varies across different stages of propagation. We compare our results with those of the circular perfect optical vortex beam propagating in free-space, observing that the EPOV beam exhibits non-diffracting behavior for short propagation distances compared to its circular counterpart. The signature of the focusing behavior of the EPOV beam is observed at a relatively small propagation distance compared to the circular case.

Extension of Vortex Bessel Beams Generated by Finite-Width Durnin Ring With Helical Phase Modulation

Bessel beams are widely used for different applications due to their attractive non-diffractive behavior. However, the real-world Bessel beams have finite propagation distance, where such behavior can be assumed. In this work we consider the degradation of vortex Bessel beams generated by a finite-width Durnin ring with helical phase modulation. For this purpose, we derive the expression that describes the propagation of rotationally symmetric vortex beams. By using this expression, we show that the axial degradation of the main lobe of Bessel beams is almost independent on their topological charge and decreases by increasing the radius of the Durnin ring and its width. The increase of ring width also yields to the radial degradation (deformation of the secondary lobes) of the Bessel beams. These findings are particularly important for the construction of more sophisticated structured beams described as a linear superposition of vortex Bessel beams.

The Complex Charge Paradigm: A New Approach for Designing Electromagnetic Wavepackets.

Singularities in optics famously describe a broad range of intriguing phenomena, from vortices and caustics to field divergences near point charges. The diverging fields created by point charges are conventionally seen as a mathematical peculiarity that is neither needed nor related to the description of electromagnetic beams and pulses, and other effects in modern optics. This work disrupts this viewpoint by shifting point charges into the complex plane, and showing that their singularities then give rise to propagating, divergence‐free wavepackets. Specifically, point charges moving in complex space‐time trajectories are shown to map existing wavepackets to corresponding complex trajectories. Tailoring the complex trajectories in this “complex charge paradigm” leads to the discovery and design of new wavepacket families, as well as unprecedented electromagnetic phenomena, such as the combination of both nondiffracting behavior and abruptly‐varying behavior in a single wavepacket. As an example, the abruptly focusing X‐wave–a propagation‐invariant X‐wave‐like wavepacket with prechosen self‐disruptions that enhance its peak intensity by over 200 times–is presented. This work envisions a unified method that captures all existing wavepackets as corresponding complex trajectories, creating a new design tool in modern optics and paving the way to further discoveries of electromagnetic modes and waveshaping applications.

Planar Antenna Design for Omnidirectional Conical Radiation Through Cylindrical Leaky Waves

An annular periodic leaky-wave antenna (LWA) fed by a simple azimuth-symmetric source is designed to generate a high-gain omnidirectional conical-beam pattern, which scans with frequency over a wide angular range. The proposed structure is defined by a finite metallic radial strip grating printed on a grounded dielectric slab, which supports an $n=0$ cylindrical leaky wave (CLW). The distinctive features of CLWs supported by such a truncated structure are also highlighted and discussed. The directional far-field pattern generated by the proposed LWA, in conjunction with its nondiffracting and wideband behavior in the near field (as previously reported by the authors), defines an original dual-operational LWA. Possible applications include next-generation wireless power transfer systems that provide functionality in both the near and far field, vehicle roof-mounted antennas for base-station data connectivity as well as future short-range near-field communications, and object tracking by ceiling-mounting devices for indoor localization.

Nearly nondiffracting electron lattice beams generated by polygonal slits.

A method for generating electron lattice beams carrying vortices using nanofabricated polygonal slits in a transmission electron microscope is proposed. Experimental and simulation study of the intensity of the beams verified their Bessel beam-like nearly nondiffracting behavior. Phase analysis using a diffractive imaging method found arrays of quantized vortices, forming an electron beam lattice with cylindrical intensity distribution in the propagation direction. Such vortex lattice beams may be used in a variety of applications including nanofabrication, particle manipulation or a new electron imaging method.

Analysis and Design of Bessel Beam Launchers: Longitudinal Polarization

The paper presents the analysis and design of Bessel beam launchers using a finite inward cylindrical traveling wave aperture field distribution. The launcher radiates an electric field whose normal or longitudinal component takes the form of a zeroth-order Bessel function. The nondiffractive behavior of the structure in a well-defined area close to the radiating aperture is analyzed by decomposing the radiated field in its geometrical optics (GO) and diffractive (D) contributions. A closed-form expression is provided for the GO contribution whereas an asymptotic approximation is provided for the diffractive part. Such theoretical analysis allows a precise definition of the nondiffractive region for the generated Bessel beam. At the same time, it also highlights and predicts the oscillating behavior of the longitudinal component of the electric field along the z -axis due to the diffraction from the edges of the aperture. The proposed analysis is validated by a prototype at 30 GHz made by a radial waveguide loaded with metallic gratings and centrally fed by a coaxial probe. Measurement results for the longitudinal component of the electric field are in excellent agreement with full-wave results. In addition, the nondiffractive behavior for the radiated beam is reported over a bandwidth larger than 6.5% around 30 GHz. This behavior is peculiar of the nonresonant first kind Hankel aperture field distribution used for the generation of the Bessel beam.

Observation of non-diffracting behavior at the single-photon level

We demonstrate the generation of non-diffracting heralded single photons, i.e. which are characterized by a single-photon transverse intensity distribution which remains essentially unchanged over a significant propagation distance. For this purpose we have relied on the process of spontaneous parametric downconversion (SPDC) for the generation of signal and idler photon pairs, where our SPDC crystal is pumped by a Bessel-Gauss (BG) beam. Our experiment shows that the well-understood non-diffracting behavior of a BG beam may be directly mapped to the signal-mode, single photons heralded by the detection of a single idler photon. In our experiment, the heralded single photon is thus arranged to be non-diffracting without the need for projecting its single-photon transverse amplitude, post-generation, in any manner.

16O-NUCLEUS ELASTIC SCATTERING IN THE ENERGY RANGE 300 MeV–1.503 GeV

In this work we analyze the elastic angular distribution for the scattering of 16 O from 12 C , 16 O , 28 Si , 40 Ca , 90 Zr , and 208 Pb in the energy range 300 MeV–1.503 GeV within the framework of the Coulomb modified correlation expansion for the Glauber amplitude. Our calculations involve (i) up to the two-body density term in the correlation expansion, (ii) the realistic nuclear form factors, and (iii) the high q-components of the basic (input) NN amplitude. The results are found to provide a satisfactory explanation of the data in all the cases. Moreover, we could assess the energy dependence of the NN amplitude, and the trend of its slope strengthens the need of nondiffractive behavior of the NN amplitude in the energy range under consideration. We also show that the c.m. correlations play an important role in nucleus–nucleus collision.

Few-optical-cycle bessel-gauss pulsed beams in free space

We introduce a new family of nonseparable, pulselike and beamlike solutions of the wave equation in the paraxial approximation with pseudonondiffracting behavior. They are the pulsed versions of the Bessel-Gauss beams by Gori et al., and encompass as particular cases the diffraction-free Bessel-X pulses, isodiffracting pulses, and, in the many-cycle limit, Bessel and Gaussian beams. Unlike Bessel-X waves, these solutions carry finite energy but retain nondiffracting behavior over a finite propagation distance, and could be physically produced with mode-locked toroidal resonators.

Vector meson photoproduction with an effective Lagrangian in the quark model

A quark model approach to the photoproduction of vector mesons off nucleons is proposed. Its starting point is an effective Lagrangian of the interaction between the vector meson and the quarks inside the baryon, which generates the nondiffractive s- and u-channel resonance contributions. Additional t-channel ${\ensuremath{\pi}}^{0}$ and \ensuremath{\sigma} exchanges are included for the \ensuremath{\omega} and ${\ensuremath{\rho}}^{0}$ production, respectively, to account for the large diffractive behavior in the small $t$ region as suggested by Friman and Soyeur. The numerical results are presented for the \ensuremath{\omega} and \ensuremath{\rho} productions in four isospin channels with the same set of parameters, and they are in good agreement with the available data not only in \ensuremath{\omega} and ${\ensuremath{\rho}}^{0}$ productions, but also in the charged \ensuremath{\rho} productions where the additional t-channel \ensuremath{\sigma} exchange does not contribute so that it provides an important test to this approach. The investigation is also extended to the \ensuremath{\varphi} photoproduction, and the initial results show that the nondiffractive behavior of the \ensuremath{\varphi} productions in the large $t$ region can be described by the s- and u-channel contributions with significantly smaller coupling constants, which is consistent with the findings in the similar studies in the QHD framework. The numerical investigation has also shown that polarization observables are essential for identifying so-called ``missing resonances.''

Elastic and inelastic scattering of π± by 208Pb

The elastic and inelastic (3 −, 2.6 MeV) scattering of pions by 208Pb has been measured at 80 MeV ( π + only) and 116 MeV (π + and π −). An optical potential model including quadratic density terms reproduces well the transition from diffractive scattering at the higher energies to the non-diffractive behavior observed at 50 MeV. Good agreement with the inelastic data is obtained with a collective model using the same deformation length βR = 0.85 fm ( β = 0.13) for π + and π −.