Nondiffracting Waves Research Articles

A new non-diffractive wave packet: The Scorer beam

We find the exact solution of the (1+1)-dimensional optical paraxial diffractive system by implementing the self-similarity method, leading to the discovery of a beam solution composed of Scorer functions, which we refer to as the Scorer beam. Through theoretical analysis and numerical simulation, we explore several characteristics of both infinite- and finite-energy Scorer beams, particularly focusing on their non-diffractive and self-accelerating properties. Additionally, we compare the Scorer beam with – and distinguish from – the related Airy beam. This investigation provides both theoretical and numerical insights that may guide the experimental realization of Scorer beams.

Plasmonic Metalens to Generate an Airy Beam.

Airy beams represent an important type of non-diffracting beams-they are the only non-diffracting wave in one dimension, and thus they can be produced with a cylindrical geometry that modifies a wavefront in one dimension. In this paper, we show the design of a cylindrical plasmonic metalens consisting of an array of nanoslits in a gold thin layer that modulates the phase of a Gaussian beam to generate an airy beam propagating in free space. Based on the numerical results, we show that it is possible to generate an airy beam by only matching the phase of wavefronts coming out from the array of gold nanoslits to the airy beam phase at plane z=0. We numerically demonstrate that the airy beam exhibits bending over propagation and self-healing properties. The transmission efficiency is around 60%. The simplicity of the proposed structure open new perspectives in the design of flat metasurfaces for light-focusing applications.

Compact planar meta‐lenses for nondiffracting surface wave deflection

AbstractA novel planar lens structure is proposed by using metasurfaces to convert cylindrical‐like surface wave to inclined nondiffracting wave with a deflection angle. Based on the geometric optics, the refractive index distribution of the surface wave lens is derived. A square metal ring‐shaped metasurface cell is used for realizing small refractive index whilst two opposite E‐shaped metal patches are used to form the meta‐cell with large refractive index. By adjusting the size of meta‐cells, the desired refractive index distribution is obtained after optimization. Measured results show that the inclined nondiffractive surface wave can be achieved with the maximum propagation distance of 99.72 mm at the tilted angle of 26.8°, which are consistent with the full‐wave simulation and numerical calculation results. The proposed meta‐lens achieves compact size, large titled angle, and long nondiffraction propagation distance, therefore could be well utilized in surface wave communication and nondestructive detection of surface defects.

Wideband Airy Beam Generation Using Reflective Metasurfaces with Both Phase and Amplitude Modulation

Airy beams are an intriguing type of non-diffraction wave packet that can exist in one-dimensional (1D) curved orbital plane systems. These beams have gained significant attention due to their unique properties, including non-diffraction, self-healing, and self-bending. In this study, we propose a method for generating high-efficiency and wideband Airy beams in microwave sections with reflective geometry, which is challenging to achieve due to the complexity of the Airy beam’s function and generation structure. Our approach involves both phase modulation and amplitude modulation. The designed metasurfaces were numerically simulated to obtain the most significant features of the microwave Airy beam. In addition, they are well in agreement with those predicted by theory.

OPTICAL SOLITON WAVE SOLUTIONS OF THE FRACTIONAL COMPLEX PARAXIAL WAVE DYNAMICAL MODEL ALONG WITH KERR MEDIA

This paper studies the optical soliton wave solutions of the fractional complex paraxial wave dynamical (FPWD) model with Kerr media. This model investigates the frequency of the beam obeying that reveals non-dispersive and non-diffractive Spatio-temporal localized wave envelopes promulgating in optical Kerr media. This model is equivalently the well-known nonlinear Schrödinger equation. These two models concentrate on the nonlinear visual medium to increase its strength and increase the nonlinear optical operation’s efficiency. Three recent computational schemes are employed to investigate the considered model’s abundant wave solutions; these solutions are then used to evaluate the initial and boundary conditions. The solutions’ accuracy is investigated by calculating the absolute error between solutions exact and approximate solutions. Additionally, the solution’s stability is checked by employing Hamiltonian system properties. The results’ physical interpretation is explained through some different sketches in 2D, 3D, and density plots.

Non-diffracting partially coherent waves with binomial coherence.

Comprehensive analysis of non-diffracting optical waves with two-point binomial coherence function (BCF) is presented. This coherence function consists of two terms, each depending on either separation of points or the central point. We establish the necessary and sufficient conditions for nonnegative definiteness of the BCFs. Spectral analysis, including calculations of the eigenvalues and eigenfunctions, for the general BCF case is presented. We consider two simple BCF examples of and analyzed the conditions leading to the maximum irradiance contrast.

Two-photon flow cytometry with laser scanning two-dimensional airy beams

Flow cytometry is an essential technique in biomedical discovery for cell counting, cell sorting, and biomarker detection. In vivo flow cytometers based on one-photon or two-photon excited fluorescence have been developed for over a decade. One drawback of the laser beam scanning two-photon flow cytometer is that the two-photon excitation volume is limited to the focal spot due to the short Rayleigh range of focused Gaussian beams. Hence, the sampling volume is much smaller than in one-photon flow cytometers, making it challenging to count or detect rare circulating cells in vivo. Non-diffracting light waves like Bessel beams and Airy beams have narrow intensity profiles with an effective spot size as small as several wavelengths, making them comparable to Gaussian beams. More significantly, the theoretical depth of field (propagation distance without diffraction) can be infinite, making them an ideal solution as a light source for scanning beam flow cytometry. The trade-off of using Airy beams rather than Gaussian beams is side lobes Airy beams have, which contribute to background noise. Two-photon excitation can reduce this noise, as the excitation efficiency is proportional to intensity squared. Therefore, we developed a two-photon flow cytometer using 2D Airy beams to form a light-sheet that intersects the blood vessel a microfluidic channel, which was used to model a blood vessel. The setup can successfully detect and count flowing fluorescent microspheres in a microchannel.

Optical nondiffractive and nondispersive dark-wave dynamics in hydrodynamic origin

The primary attention of this work focuses on finding rational and generalized rational solutions for the (2 + 1)-dimensional Kadomtsev–Petviashvili equation that can be used to describe nondispersive and nondiffractive localized wave packet in power law nonlinear media. Specifically, the (2 + 1)-dimensional nonlinear Schrödinger equation with power law nonlinearity is first transformed into the Kadomtsev–Petviashvili equation. Then, through the bilinear form and symbolic computation, we derive two hierarchies of multi-lump solitary waves, composing of three, six, and eight lump waves. The obtained solutions observe a specific ‘circularity structure’ that the lump waves sit at the same circular. In addition, we illustrate that these waves are stable during propagation.

Non-Diffracting Light Wave: Fundamentals and Biomedical Applications

The light propagation in the medium normally experiences diffraction, dispersion, and scattering. Studying the light propagation is a century-old problem as the photons may attenuate and wander. We start from the fundamental concepts of the non-diffracting beams, and examples of the non-diffracting beams include but are not limited to the Bessel beam, Airy beam, and Mathieu beam. Then, we discuss the biomedical applications of the non-diffracting beams, focusing on linear and nonlinear imaging, e.g., light-sheet fluorescence microscopy and two-photon fluorescence microscopy. The non-diffracting photons may provide scattering resilient imaging and fast speed in the volumetric two-photon fluorescence microscopy. The non-diffracting Bessel beam and the Airy beam have been successfully used in volumetric imaging applications with faster speed since a single 2D scan provides information in the whole volume that adopted 3D scan in traditional scanning microscopy. This is a significant advancement in imaging applications with sparse sample structures, especially in neuron imaging. Moreover, the fine axial resolution is enabled by the self-accelerating Airy beams combined with deep learning algorithms. These additional features to the existing microscopy directly realize a great advantage over the field, especially for recording the ultrafast neuronal activities, including the calcium voltage signal recording. Nonetheless, with the illumination of dual Bessel beams at non-identical orders, the transverse resolution can also be improved by the concept of image subtraction, which would provide clearer images in neuronal imaging.

Generation of Circularly Polarized Quasi-Non-Diffractive Vortex Wave via a Microwave Holographic Metasurface Integrated with a Monopole

In this paper, a novel method for generating a circularly polarized (CP) quasi-non-diffractive vortex wave carrying orbital angular momentum (OAM), based on the microwave holographic metasurface integrated with a monopole, is proposed. This method is the combination of the non-diffraction theory and the principle of waveguide-fed-based holography and is equivalent to a superposition of two scalar impedance modulation surfaces. To verify the proposed method, a holographic metasurface generating a left-handed circularly polarized (LHCP) quasi-non-diffractive vortex wave carrying −1 mode OAM at the normal direction, was simulated and analyzed. The metasurface consisted of inhomogeneous slot units on a grounded substrate and a monopole excitation. Moreover, the location distribution of slots was determined by a computed interferogram between the reference wave and the object wave with the non-diffractive feature. Compared with an ordinary vortex wave, the quasi-non-diffractive wave obtained by our proposed method possessed a smaller divergence radius and a stronger electric field strength in the 9 times wavelength range. It paved a new path for manipulating the non-diffractive vortex wave in medium distance without using an external feeding source, which holds great potential for the miniaturization devices applied in medium-distance high-capacity secure communication, high-resolution imaging and intelligent detection.

Non-diffraction surface wave with controllable deflection angle by using metasurfaces

A planar metasurface Bessel lens has been proposed for non-diffraction surface wave deflection, which is composed of a planar flat lens and an asymmetric gradient refractive index lens. According to the desired refractive index distribution of the two lenses, a metasurface, consisting of sub-wavelength metallic square rings of different sizes, is constructed to realize the planar Bessel lens. Through the planar Bessel lens, the cylindrical-like surface wave radiated from a point source is converted to an inclined non-diffraction surface wave. The planar Bessel lens is fabricated, and the measurement results show good agreement with the full-wave simulation results, which would verify the correctness of the proposed theory.

Far-field particle manipulation scheme based on X wave

The construction of particle manipulation in the near-field sound field has been extensively studied. In this article, a scheme for far-field particle control through a non-diffracted wave based on the X wave is proposed, which has theoretical completeness and algorithmic simplicity for the construction of far-field acoustic tweezers. The analytical expression of the acoustic radiation force (ARF) acting upon spherical particles of any order X wave is deduced. The spectral pattern of ARF exerted by the X wave in the fluid medium is given. The change law of ARF exerted by the X wave with specific parameters is obtained through calculation. Through the drawn image, the possibility of obtaining a wide range of negative ARFs through X wave is verified. In addition, the far-field invariance of the ARF exerted by the X wave as non-diffraction wave is verified, which provides the possibility of the subsequent construction of far-field acoustic tweezers as well as the basis algorithms for designing acoustic schemes for specific particle manipulation.

Relativistic aberration and null Doppler shift within the framework of superluminal and subluminal nondiffracting waves

We reveal relations between superluminal and subluminal spatiotemporally localized optical pulses and the phenomena of the relativistic aberration of a wavevector and the Doppler shift. It turns out that such waves are Lorentz-transformed versions of simple optical waves generated in another reference frame. The requirement of a null Doppler shift is shown to give rise to a speed associated with the relativistic velocity addition law of a double (two-step) Lorentz transformation. The effects of such a transformation are examined both in terms of four-coordinates and in the spectral domain. It is established that a subluminal pulse reverses its direction. In addition to a change in direction, the propagation term of a superluminal pulse becomes negative. The aberration due to a double Lorentz transformation is examined in detail for propagation invariant superluminal waves (X wave, Bessel X wave), as well as intensity-invariant superluminal and subluminal waves. Detailed symmetry considerations are provided for the superluminal focus X wave and the subluminal MacKinnon wavepacket.

Reactive energy in nondiffracting localized waves

It is well known that although the group velocity of structured light pulses propagating in vacuum can be subluminal or superluminal, the upper limit of the energy flow velocity is $c$, the speed of light in vacuum. This inequality can be explained in terms of the reactive energy left behind by the fields. Energy and reactive energy densities have been calculated for vector-valued two-dimensional (light sheet) superluminal electromagnetic nondiffractive pulses, as well as scalar-valued and transverse magnetic three-dimensional superluminal and subluminal spatiotemporally localized electromagnetic waves. Emphasis is placed on the physical formation of the reactive energy due to interference of the plane-wave constituents of the structured light waves.

Energy-flow velocities of nondiffracting localized waves

A universal relation has been established between the local energy transport velocity along the direction of propagation and the group velocity of scalar and vector-valued propagation-invariant spatiotemporally localized superluminal and subluminal electromagnetic waves in free space. Under specific restrictions, this relationship is very closely valid for physically realizable almost propagation-invariant spatiotemporally confined subluminal and superluminal electromagnetic fields. In both cases, although the group velocity may be either superluminal or subluminal, the universal relation is in accord with the well-established result that the upper limit of the energy transport velocity is c, the speed of light in vacuum.

Zeroth-order continuous vector frozen waves for light scattering: exact multipole expansion in the generalized Lorenz–Mie theory

In this paper we theoretically investigate the exact beam shape coefficients (BSCs) of a specific and promising class of nondiffracting light waves for optical trapping and micro-manipulation known as continuous vector frozen waves (CVFWs). CVFWs are constructed from vector Bessel beams in terms of a continuous superposition (integral) over the longitudinal wavenumber, the final longitudinal intensity pattern being determined through the specification of a given spectrum S(kz). The incorporation of such highly confined and micro-structured fields into the theoretical framework of the generalized Lorenz–Mie theory (GLMT) is a first step toward the integration of such beams with optical tweezers systems as potential laser beams for the multiple manipulation of micro-particles and nano-particles along their optical axis and in multiple transverse planes. Linear, azimuthal, and radial polarizations are considered, the BSCs being calculated using three distinct approaches. The results extend and complete previous works on discrete frozen waves for light scattering problems with the aid of the GLMT.

Multiple self-healing Bloch surface wave beams generated by a two-dimensional fraxicon

Two-dimensional surface waves are a cornerstone for future integrated photonic circuits. They can also be beneficially exploited in sensing devices by offering dark-field illuminations of objects. One major problem in sensing schemes arises from the individual sensing objects: the interaction of surface waves with an object reduces the field amplitude, and the readout of other objects along the propagation path suffers from this reduced signal. Here we show in two experiments that nondiffracting and self-healing Bloch surface waves can be launched using a Fresnel axicon (i.e., fraxicon). First, we visualize the generation of an array of multiple focal spots by scanning near-field optical microscopy in the infrared. With a second device operating in the visible, we demonstrate the self-healing effect directly using a far-field readout method by placing metallic nanoantennas onto the multiple focal spots of the fraxicon. Our study extends the versatile illumination capabilities of surface wave systems.

Temporal dynamics of light-written waveguides in unbiased liquid crystals

The control of light by light is one of the main aims in modern photonics. In this context, a fundamental cornerstone is the realization of light-written waveguides in real time, resulting in all-optical reconfigurability of communication networks. Light-written waveguides are often associated with spatial solitons, that is, non-diffracting waves due to a nonlinear self-focusing effect in the harmonic regime. From an applicative point of view, it is important to establish the temporal dynamics for the formation of such light-written guides. Here we investigate theoretically the temporal dynamics in nematic liquid crystals, a material where spatial solitons can be induced using continuous wave (CW) lasers with few milliWatts power. We fully address the role of the spatial walk-off and the longitudinal nonlocality in the waveguide formation. We show that, for powers large enough to induce light self-steering, the beam undergoes several fluctuations before reaching the stationary regime, in turn leading to a much longer formation time for the light-written waveguide.

Nondiffracting wave beams in non-Hermitian Glauber–Fock lattice

We theoretically study non-Hermitian Glauber–Fock lattice with nonuniform hopping. We show how to engineer this lattice to get nondiffracting wave beams and find an exact analytical solution to nondiffracting localized waves. The exceptional points in the energy spectrum are also analyzed.

Projecting non-diffracting waves with intermediate-plane holography.

We introduce intermediate-plane holography, which substantially improves the ability of holographic trapping systems to project propagation-invariant modes of light using phase-only diffractive optical elements. Translating the mode-forming hologram to an intermediate plane in the optical train can reduce the need to encode amplitude variations in the field, and therefore complements well-established techniques for encoding complex-valued transfer functions into phase-only holograms. Compared to standard holographic trapping implementations, intermediate-plane holograms greatly improve diffraction efficiency and mode purity of propagation-invariant modes, and so increase their useful non-diffracting range. We demonstrate this technique through experimental realizations of accelerating modes and long-range tractor beams.