Diffraction-free Beams Research Articles

Generation of Nondiffracting Electron Bessel Beams

By putting electrons through a phase-modulation hologram, a thin film of silicon nitride with nanoscale grooves of different thicknesses, scientists achieve, for the first time, the generation of diffraction-free electron Bessel beams.

Diffraction-free asymmetric elegant bessel beams with fractional orbital angular momentum

This paper introduces a new family of diffraction-free asymmetric elegant Bessel beams (EB-beams) with fractional orbital angular momentum (OAM). EB-beams are modes of free space and described by the n-th order Bessel function of the first kind with a complex argument. Functions of complex amplitudes of EB-beams are orthogonal by continuous scaling parameter and not orthogonal on a discrete parameter (topological charge). The intensity distribution of EB-beams has a countable number of isolated zeros of intensity, located on the horizontal axis. These zeros are centers of optical vortices with unit topological charge and opposite signs on different sides of the origin. Isolated intensity zero on the optical axis generates an optical vortex with topological charge of n. OAM of the EB-beams is (n + 0,69777)h per photon, where h is the Planck's constant.

Distance of diffraction-free propagation of the bounded airy beam

We obtain explicit equations for the distance at which the Airy beam, limited in initial plane (from the side where amplitude drops slowly), propagates along the parabolic trajectory without changing its amplitude (i.e. almost diffraction-free). Analogical distance for diffraction-free Bessel beam is proportional to the radius of the circular diaphragm which limits the beam and inversely proportional to the tangent of the slope of the conical wave which generates the Bessel beam. This distance is wavelength-independent. For the Airy beam this distance is proportional to the square root of the module coordinate of the diaphragm edge and inversely proportional to the wavelength of light.

Diffraction-free lommel beams

We consider a new family of nonparaxial diffraction-free laser beams with their complex amplitude being proportional to the n-th order Lommel function of two variables. Therefore, these beams are called Lommel beams (L-beams). We obtained explicit analytical expressions for the angular spectrum of plane waves and for the orbital angular momentum of the L-beams. Transverse intensity of the L-beams has a reflective symmetry with respect to both Cartesian coordinate axes. Since transverse intensity distribution of L-beams does not change upon propagation, L-beams are modes of free space (L-modes). Functions of complex amplitudes of even (n = 2p) and odd (n = 2p + 1) L-modes are mutually orthogonal. For certain parameter, L-modes become traditional Bessel modes.

Characterization of a refractive linear axicon with distant depth of field and no central blocking

We report the manufacturing and characterization of a refractive linear axicon producing a linearly increasing axial intensity Bessel-type beam over a predetermined range starting away from the axicon and without central blocking when illuminated by a plane wave. This is in contrast to a classical axicon that generates a diffraction-free beam starting from the axicon tip and extending to a range limited by the input beam aperture. The measured characteristics of the beam produced by the linear axicon, including its intensity distribution and spot size, are in good agreement with the theoretical predictions. Together with logarithmic axicon and exicon, this is another element of the axicon family that can generate a prescribed intensity distribution over a chosen range/depth of field.

Airy beam with a hyperbolic trajectory

The well-known Airy beams are generated when a transparency with a cubic phase put at the focal distance from a spherical lens is illuminated by a Gaussian beam. In this case, a diffraction-free Airy beam that propagates with acceleration on a parabolic path is generated behind the spherical lens's focus. We have shown that directly behind the cubic-phase transparency there is a path section on which the Airy beam is propagating with acceleration on a hyperbolic path. We refer to the Airy beam on the hyperbolic path section as a Hyperbolic Airy (HA) beam. The HA beams notably show the linear divergence, the nonuniform acceleration, rapidly decaying with distance, and the “center of gravity” shifting linearly with distance in the absence of the linear phase in the initial field, with the acceleration being by an order of magnitude higher than that of the Airy beam on the parabolic path section.

Bessel-beam-written nanoslit arrays and characterization of their optical response

Nanoslit arrays are fabricated on thin metal film coated glass slides using femtosecond laser pulses with Bessel beam profiles. The optical properties of the fabricated structures with different periodicities are characterized with transmission spectroscopy. Experimental results reveal the existence of two separate surface plasmon resonance modes occurring at the metal-air and metal-glass interfaces. These two resonance modes cause two minima in the high transmission spectra of the sub-skin depth thick thin films in the visible and near infrared regions. The existence of double surface plasmon resonance modes is verified with additional experiments, theoretical and numerical studies. Due to its relaxed alignment constraints, reduced aberrations, scalability property to shorter wavelengths, and resulting shorter dimensions, nanofabrication with diffraction-free Bessel beams is an easy, cheap, and advantageous alternative to regular lithography techniques to fabricate nanoslit arrays. The shift of the resonance wavelength with a change in the refractive index of the surrounding medium can be exploited for enhanced sensing.

CO2 laser coating of nanodiamond on aluminum using an annular beam

Laser coating of nanodiamond (ND) on aluminum alloy A319 substrate was investigated using a diffraction-free ring beam. A 1000W continuous wave CO2 laser in the ring beam configuration heated the 25–35μm thick electrostatically sprayed ND powder layers on aluminum surface, melted a very thin layer (10μm) of aluminum in a controlled fashion and caused phase transition of ND to form 50–60μm thick ND/diamond-like carbon (DLC) coating. Significant improvements in friction, wear resistance and surface finish were observed in the ring beam method over the traditional Gaussian beam method suggesting that these thick (50–60μm) ND/DLC laser coatings can outperform the currently used thin (<4μm) chemically vapor deposited DLC coatings for aluminum parts in automobiles.

Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials

Metal–dielectric multilayer metamaterials with extreme loss-anisotropy, in which the longitudinal component of the permittivity tensor has an ultra-large imaginary part, are proposed and designed. Diffraction-free deep subwavelength beam propagation and manipulation, due to the nearly flat iso-frequency contour, is demonstrated in such loss-anisotropic metamaterials. It is also shown that deep subwavelength beam propagation can be realized in practical multilayer structures with large multilayer periods, when the nonlocal effect is considered.

Singular diffraction-free surface plasmon beams generated by overlapping phase-shifted sources

We propose and experimentally demonstrate the singular surface plasmon beam that presents a dark channel generated by a point dislocation and a long diffraction-free propagation distance up to 70λ(sp). The singular surface beam is the result of the interference of two surface plasmon polariton (SPP) plane waves, which are launched by two coupling gratings with lateral displacement. An aperture-type near-field scanning optical microscope is used to map the intensity distribution of the singular SPP waves. The propagating point dislocation embedded in the beam is shown by full-wave calculations and is later verified by near-field interference in the experiment.

Generation of diffraction-free plasmonic beams with one-dimensional Bessel profiles

We demonstrate experimentally generation of diffraction-free plasmonic beams with zeroth- and first-order Bessel intensity profiles using axicon-like structures fabricated on gold film surfaces and designed to operate at a wavelength of 700 nm. The central beam features a very low divergence (~8π mrad) for a narrow waist of the order of one wavelength and the ability to self reconstruct, which are the main signatures of diffraction-free beams.

Properties of the barycenter of a diffraction-free light beam

This paper is concerned with an observable effect of an unusual quantal degree of freedom that is compatible with the constraint of the transversality condition. The dependence of the barycenter of a diffraction-free light beam on this degree of freedom is investigated.

Sending femtosecond pulses in circles: highly nonparaxial accelerating beams

We use caustic beam shaping on 100 fs pulses to experimentally generate nonparaxial accelerating beams along a 60° circular arc, moving laterally by 14 µm over a 28 µm propagation length. This is the highest degree of transverse acceleration reported to our knowledge. Using diffraction integral theory and numerical beam propagation simulations, we show that circular acceleration trajectories represent a unique class of nonparaxial diffraction-free beam profile which also preserves the femtosecond temporal structure in the vicinity of the caustic.

Nonparaxial TE and TM vector beams with well-defined orbital angular momentum

A new formalism is developed for diffraction-free vector beams in free space. The solutions of Maxwell's equations are separated into two polarization modes, TE and TM. We discuss the validity of the method by applying it to a particular solution, the vectorial Bessel beam of order m.

Virtual ghost imaging through turbulence and obscurants using Bessel beam illumination

We experimentally demonstrate a single sensor virtual ghost imaging (VGI) configuration that uses the physics of nearly diffraction free light sources to penetrate partially obscuring media or turbulent media and generate images of remote opaque objects. Randomly displaced nearly diffraction free Bessel beams provided improved illumination patterns for VGI and resolving small distant targets. VGI recovered the image of objects even when the coarse illuminating Bessel beam was transmitted through obscuring and turbulent media or through a small transversely displaced aperture. Bessel beam experiments are compared with Gaussian beam experiments under similar conditions.

Microdroplet oscillations during optical pulling

It was recently shown theoretically that it is possible to pull a spherical dielectric body towards the source of a laser beam [Nature Photonics {\bf 5}, 531 (2011)], a result with immediate consequences to optical manipulation of small droplets. Optical pulling can be realised e.g.\ using a diffraction free Bessel beam, and is expected to be of great importance in manipulation of microscopic droplets in micro- and nanofluidics. Compared to conventional optical pushing, however, the radio of optical net force to stress acting on a droplet is much smaller, increasing the importance of oscillations. We describe the time-dependent surface deformations of a water microdroplet under optical pulling to linear order in the deformation. Shape oscillations have a lifetime in the order of microseconds for droplet radii of a few micrometers. The force density acting on the initially spherical droplet is strongly peaked near the poles on the beam axis, causing the deformations to take the form of jet-like protrusions.

Mesoscopic Self-Collimation and Slow Light in All-Positive Index Layered Photonic Crystals

We demonstrate a mesoscopic self-collimation effect in photonic crystal superlattices consisting of a periodic set of all-positive index 2D photonic crystal and homogeneous layers. We develop an electromagnetic theory showing that diffraction-free beams are observed when the curvature of the optical dispersion relation is properly compensated for. This approach allows us to combine slow-light regime together with self-collimation in photonic crystal superlattices presenting an extremely low filling ratio in air.

Superoscillatory diffraction-free beams

It is theoretically shown that by superimposing diffraction-free solutions of the Helmholtz equation, one can construct localized diffraction-free beams that pass through predetermined points on subwavelength distances. These beams are based on the phenomenon of superoscillations and thus do not contain any evanescent waves. The effect of an aperture and noise is examined in specific examples where truncated beams with λ/3 subwavelength features can propagate into the far field.

Characterization of vector diffraction-free beams

It is observed that a constant unit vector denoted by I is needed to characterize a complete orthonormal set of vector diffraction-free beams. The previously found diffraction-free beams are shown to be included as special cases. The I-dependence of the longitudinal component of diffraction-free beams is also discussed.

Analytical expressions for diffraction-free beams through an opaque disk

We establish analytical expressions that demonstrate that the beam produced after diffraction of a gaussian beam by an opaque disk and collimation by a lens can be approached by a diffraction-free J0 Bessel function. We further demonstrate that a similar analytical expression can be established in the case of femtosecond incident pulses.