Showing papers on "Bessel beam published in 2005"

Bessel beams: Diffraction in a new light

Abstract: Diffraction is a cornerstone of optical physics and has implications for the design of all optical systems. The paper discusses the so-called 'non-diffracting' light field, commonly known as the Bessel beam. Approximations to such beams can be experimentally realized using a range of different means. The theoretical foundation of these beams is described and then various experiments that make use of Bessel beams are discussed: these cover a wide range of fields including non-linear optics, where the intense central core of the Bessel beam has attracted interest; short pulse non-diffracting fields; atom optics, where the narrow non-diffracting features of the Bessel beam are able to act as atomic guides and atomic confinement devices and optical manipulation, where the reconstruction properties of the beam enable new effects to be observed that cannot be seen with Gaussian beams. The intensity profile of the Bessel beam may offer routes to investigating statistical physics as well as new techniques for the...

Helmholtz–Gauss waves

Abstract: A detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z=0 is modulated by a Gaussian envelope is presented. We call such a field a Helmholtz–Gauss (HzG) beam. A simple closed-form expression for the paraxial propagation of the HzG beams is written as the product of three factors: a complex amplitude depending on the z coordinate only, a Gaussian beam, and a complex scaled version of the transverse shape of the nondiffracting beam. The general expression for the angular spectrum of the HzG beams is also derived. We introduce for the first time closed-form expressions for the Mathieu–Gauss beams in elliptic coordinates and for the parabolic Gauss beams in parabolic coordinates. The properties of the considered beams are studied both analytically and numerically.

Theory of ``frozen waves'': modeling the shape of stationary wave fields

Abstract: In this work, starting by suitable superpositions of equal-frequency Bessel beams, we develop a theoretical and experimental methodology to obtain localized stationary wave fields (with high transverse localization) whose longitudinal intensity pattern can approximately assume any desired shape within a chosen interval 0⩽z⩽L of the propagation axis z. Their intensity envelope remains static, i.e., with velocity v=0, so we have named “frozen waves” (FWs) these new solutions to the wave equations (and, in particular, to the Maxwell equation). Inside the envelope of a FW, only the carrier wave propagates. The longitudinal shape, within the interval 0⩽z⩽L, can be chosen in such a way that no nonnegligible field exists outside the predetermined region (consisting, e.g., in one or more high-intensity peaks). Our solutions are notable also for the different and interesting applications they can have—especially in electromagnetism and acoustics—such as optical tweezers, atom guides, optical or acoustic bistouries, and various important medical apparatuses.

Stable Spatiotemporal Solitons in Bessel Optical Lattices

Abstract: We investigate the existence and stability of three-dimensional solitons supported by cylindrical Bessel lattices in self-focusing media. If the lattice strength exceeds a threshold value, we show numerically, and using the variational approximation, that the solitons are stable within one or two intervals of values of their norm. In the latter case, the Hamiltonian versus norm diagram has a swallowtail shape with three cuspidal points. The model applies to Bose-Einstein condensates and to optical media with saturable nonlinearity, suggesting new ways of making stable three-dimensional solitons and "light bullets" of an arbitrary size.

Rotating vectorial vortices produced by space-variant subwavelength gratings.

Abstract: A new class of vectorial vortex based on coherent addition of two orthogonal circularly polarized Bessel beams of identical order but with different propagation constants is presented. The transversely space-variant axially symmetric polarization distributions of these vectorial fields rotate as they propagate, while they maintain a propagation-invariant Bessel intensity distribution. These properties were demonstrated by use of discrete space-variant subwavelength gratings for 10.6??mCO2 laser radiation. The polarization properties were verified by both full space-variant polarization analysis and measurements. Rotating intensity patterns are also demonstrated by transmitting the vectorial vortices through a linear polarizer.

Generating Bessel beams by use of localized modes.

Abstract: We propose a novel method for generating both propagating and evanescent Bessel beams. To generate propagating Bessel beams we propose using a pair of distributed Bragg reflectors (DBRs) with a resonant point source on one side of the system. Those modes that couple with the localized modes supported by the DBR system will be selectively transmitted. This is used to produce a single narrow band of transmission in κ space that, combined with the circular symmetry of the system, yields a propagating Bessel beam. We present numerical simulations showing that a propagating Bessel beam with central spot size of ∼0.5λ0 can be maintained for a distance in excess of 3000λ0. To generate evanescent Bessel beams we propose using transmission of a resonant point source through a thin film. A transmission resonance is produced as a result of the multiple scattering occurring between the interfaces. This narrow resonance combined with the circular symmetry of the system corresponds to an evanescent Bessel beam. Because propagating modes are also transmitted, although the evanescent transmission resonance is many orders of magnitude greater than the transmission for the propagating modes, within a certain distance the propagating modes swamp the exponentially decaying evanescent ones. Thus there is only a certain regime in which evanescent Bessel beams dominate. However, within this regime the central spot size of the beam can be made significantly smaller than the wavelength of light used. Thus evanescent Bessel beams may have technical application, in high-density recording for example. We present numerical simulations showing that with a simple glass thin film an evanescent Bessel beam with central spot size of ∼0.34λ0 can be maintained for a distance of 0.14λ0. By choice of different material parameters, the central spot size can be made smaller still.

Whispering gallery resonators for studying orbital angular momentum of a photon.

Abstract: We propose a simple method for generation and detection of photons with nonzero angular momentum. The method utilizes high-quality factor ring resonators that transform a plane electromagnetic wave into a wave with nonzero angular momentum, and vice versa. We show that the method is especially promising for studying high-order Bessel beams, unreachable by other techniques.

Vector propagation of radially polarized Gaussian beams diffracted by an axicon

Abstract: On the basis of the vectorial Rayleigh diffraction integrals and stationary-phase method, the analytic expression describing the vectorial field distribution of radially polarized Gaussian beams diffracted by an axicon is derived. The theoretical analysis and simulation calculation show that the radial component of the diffraction field is the propagation-invariant first-order Bessel beam when the radially polarized Gaussian beam illuminates the axicon. However, the longitudinal component possesses no such behavior because of its intrinsic r dependence, and its central intensity is the maximum. The longitudinal component is related to the open angle and index of the axicon, which has to be considered when the open angle and index are large. For a small open angle and index, the longitudinal component can be neglected, and the scalar approximation is valid.

The generation of an array of nondiffracting beams by a single composite computer generated hologram

Abstract: Nondiffracting beams have generated great interest recently owing to their potential applications and unique properties. In this paper, we propose and validate a simple and effective method to generate arrays of various nondiffracting modes using a composite computer-generated hologram, which comprises N × N holograms each generating an individual nondiffracting beam. Employing the composite hologram approach, we can modulate individual nondiffracting beam in an array by varying the location, dimension, and phase information coded on each hologram. We experimentally generated regular arrays of Bessel beams, customized-shaped arrays of Bessel beams, and arrays of self-imaged optical bottle beams. The interference among the beams in the arrays was found to be weak within the nondiffracting distance.

Theory of the unstable Bessel resonator.

Abstract: A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The Huygens–Fresnel self-consistency equation is solved to extract the first eigenmodes and eigenvalues of the cavity, taking into account the finite apertures of the mirrors. Attention was directed to the dependence of the output transverse profiles; the losses; and the modal-frequency changes on the curvature of the output coupler, the cavity length, and the angle of the axicon. Our analysis revealed that while the stable Bessel resonator retains a Gaussian radial modulation on the Bessel rings, the unstable configuration exhibits a more uniform amplitude modulation that produces output profiles more similar to ideal Bessel beams. The unstable cavity also possesses higher-mode discrimination in favor of the fundamental mode than does the stable configuration.

Vector Helmholtz-Gauss and vector Laplace-Gauss beams.

Abstract: We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG beams are TE and TM Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel-Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz-Gauss beams. The general expression of the vHzG beams can be used straightforwardly to obtain vector Mathieu-Gauss and vector parabolic-Gauss beams, which to our knowledge have not yet been reported.

Soliton spiraling in optically induced rotating Bessel lattices

Abstract: We address soliton spiraling in optical lattices induced by multiple coherent Bessel beams and show that the dynamic nature of such lattices makes it possible for them to drag different soliton structures, setting them into rotation. We can control the rotation rate by varying the topological charges of lattice-inducing Bessel beams.

Vacuum laser-driven acceleration by a slits-truncated Bessel beam

Abstract: An approach of vacuum acceleration by two laser Bessel beams is presented in this letter. With elaborate arrangement, the two Bessel beams are truncated by a set of special annular slits to form consecutive acceleration field in the electron traveling direction. Therefore, the electron of a certain initial energy can be accelerated in the whole interaction region without experiencing deceleration even though the phase-slippage occurs. Furthermore, the Bessel beam can provide a rather long distance for the effective interaction between the electron and the laser field due to its “diffraction-free” property, resulting in improvement of the energy exchange.

Effective magnetic fields induced by EIT in ultra-cold atomic gases

Abstract: We study the influence of two resonant laser beams (to be referred to as the control and probe beams) on the centre-of-mass motion of ultra-cold atoms characterized by three energy levels of the Λ-type. The laser beams being in the electromagnetically induced transparency (EIT) configuration drive the atoms to their dark states. We impose the adiabatic approximation and obtain an effective equation of motion for the dark state atoms. The equation contains a vector potential type interaction as well as an effective trapping potential. We concentrate on the situation where the control and probe beams are co-propagating and have orbital angular momenta (OAM). The effective magnetic field is then oriented along the propagation direction of the control and probe beams. Its spatial profile can be shaped by choosing proper laser beams. We analyse several situations where the effective magnetic field exhibits a radial dependence. In particular, we study effective magnetic fields induced by Bessel beams, and demonstrate how to generate a constant effective magnetic field for a ring geometry of the atomic trap. We also discuss a possibility of creating an effective field of a magnetic monopole.

Microfabricated-composite-hologram-enabled multiple channel longitudinal optical guiding of microparticles in nondiffracting core of a Bessel beam array

Abstract: In this letter, we report multiple-channel longitudinal optical guiding of microparticles using an array of Bessel beams generated from a composite hologram fabricated by ultraviolet lithography. The optical guiding efficiency of each Bessel beam in the optical array is investigated experimentally. The rod-like core of each Bessel beam, with its nondiffracting and self-reconstruction property, has been shown to offer strong capability for optical guiding along the propagation axis possibly even in multiple-microfluidic channels massively.

Trojan States of Electrons Guided by Bessel Beams

Abstract: Our previous work (I. Bialynicki-Birula, Phys. Rev. Lett. 93 , 20402 (2004)) is extended to cover more realistic examples of electromagnetic waves, i.e., the Bessel beams. It is shown that electrons may be guided by a Bessel beam with nonvanishing orbital angular momentum. The mechanism for trapping the elec- trons near the electromagnetic vortex line of such a wave field is the same as for the Trojan states of Rydberg electrons produced by a circularly polarized wave. The main difference is that, in the present case, the transverse motion of electrons in a beam is confined under the action of the electromagnetic wave alone: no additional attraction center is required. We also discuss briefly the motion of electrons in Neumann and Hankel beams.

Method and apparatus for producing stationary intense wave fields of arbitrary shape

Abstract: Method for producing a stationary wave field of arbitrary shape comprising the steps of defining at least one volume being limited in the direction of the axis of propagation of a beam, of the type 0≦z≦L; defining an intensity pattern within the said region 0≦z≦L by a function F(z), describing the said localized and stationary intensity pattern, which is approximated by means of a Fourier expansion or by a similar expansion in terms of (trigonometric) orthogonal functions; providing a generic superposition of Bessel or other beams highly transversally confined; calculating the maximum number of superimposed Bessel beams the amplitudes, the phase velocities and the relative phases of each Bessel beam of the superposition, and the transverse and longitudinal wavenumbers of each Bessel beam of the superposition.

DOE-generated laser beams with given orbital angular moment: application for micromanipulation

Abstract: A countable set of linearly independent solutions of the paraxial wave (Schroedinger-type) equation is derived and given the name hyper-geometric modes. These solutions describe pure optical vortices that can be generated when a spiral phase plate is illuminated with a plane wave. The distinction between these modes and the familiar paraxial modes is that in propagation the radius of the former increases as a square root of distance and the phase velocity is the same for all modes. In the present work experimental results on trapping and rotation of 5-10 micron-sized biological objects (yeast cells) and polysty rene beads of diameter 5 P m using various laser beams are discussed. Keywords: diffractive optical elements, pure op tical vortices, orbital angular moment, hyper-geometric modes, optical microparticle manipulation 1. INTRODUCTION The higher-order Bessel and Laguerre-Gaussian (LG) modes contain optical vortices providing screw character and presence of orbital angular moment. A microparticle, trapped in such a beam, receives a rotary movement. The new types of laser beams having orbital angular moment - optical vortices "imbedded" in a plane or a Gaussian beam, are considered. After passing some distance, such fields get rather stable configuration, reminding of LG modes, and are distributed under the similar law. In optics, the Hermite-Gauss (HG) and LG modes, which are partial solutions of the paraxial wave equation (PWE) or Schroedinger equation in the Cartesian or cylindrical coordinates, have long been in wide use [1]. They represent the transverse modes of stable laser resonators. Such modes preserve their structure (cross-section intensity distribution), changing only the scale along the propagation axis. Because these modes form an orthogonal basis it is possible to use their linear combinations for constr ucting other solutions of the PWE. In the cylindrical coordinates, the PWE has other modal solutions that, similar to the HG and LG modes, preserve their structure, changing only in scale. These are referred to as paraxial diffracted Bessel modes [2] and should be distinguished from the paraxial diffraction-free Bessel beams [3 ], which will be reffered to as the Durnin-Bessel modes, to distinguish them from the diffracting Bessel modes. As di stinct from the Gaussian mode s, both Bessel modes possess the infinite energy (their intensity being finite at every space point). The effective diameter of the diffracted Bessel beam increases linearly along the optical axis with increa sing distance from the initial plane. The Durnin-Bessel (DB) beam have a constant diameter. Recently introduced [4-8] new modal solutions of the PWE have been studied theoretically [4-7] and experimentally [8]. These are the Ince-Gaussian modes derived as a solution of the PWE in the elliptic coordinates. In these coordinates, the PWE is solved via separation of variab les, with the solution found as a product of the Gaussian function by the Ince polynomials. Note that the Ince pol ynomials are properly a solution of the Whitteker-Hill equation [2]. The Ince-Gaussian (IG) modes represent an orthogonal basis that generalizes the HG and LG modes. When the elliptic coordinates change to cylindrical (the ellipses change to the circumferences) the IG modes change to the LG modes. With the ellipse eccentric ity tending to infinity (the ellipse changing to a line segment), the IG modes change to the HG modes.

Novel techniques for millimeter wave imaging systems operating at 100GHz

Abstract: In this paper, we report on our investigations of novel imaging techniques such as holography, the generation of limited diffraction beams with large depths of focus and the use of binary optics for millimeter wave systems. Holography, widely used at visible wavelengths is simulated and tested in a simple optical sep-up at 100 GHz using an off-axis lensless configuration. Such a technique can be used to measure absorption characteristics of materials, and can also help classify radiating horns and lens antennas. Gaussian Beam Mode Analysis is used as an efficient computational technique to investigate the propagation of non-diffracting beams, and in particular, Bessel beams, at millimeter wavelengths. Because of the limited throughput of millimeter-wave systems, due to the long wavelength and the need for compact optics for practical applications, modal analysis is a very computationally efficient means for computing propagation characteristics. Typically, the axicon, or conical lens, is the most common optical component used for the generation of such zeroth order Bessel beams, but we show that holographic simulation can be used to design binary holograms for the generation of higher order non-diffracting beams. Furthermore, we describe a practical design for such a simple alternative to the axicon through the manufacture of a binary analogue of this component, which successfully produces diffraction invariant beams.

Laser-based microprocesses using diffraction-free beams generated by diffractive axicons

Abstract: Diffraction-free beams having a large depth of focus are of great merit in laser-based processes in which light-matter interaction is to occur in an extended region along the beam path. We have investigated two kinds of processes that use a diffraction-free beam known as a zero-order Bessel beam: 1) Laser-drilling metal films coated on a substrate to make pinholes therein using nanosecond laser pulses at 532 nm. Given an uneven surface of the substrate, the beam irradiation point, or the process point, would be displaced from a right position. By using the Bessel beams holes ~2 mm in diameter can be formed despite the displacement of ~2 mm or more. 2) Laser-exposing bulk glass to form modifications inside using femtosecond laser pulses at 800 nm. The pulses must be temporally stretched to save their energy from being used up because of multi-photon absorption. The Bessel pulses can modify through glasses ~3 mm thick in a width of <5 mm. We have developed a new set of formulas to calculate the Bessel fields, which are generated by diffractive optical elements. The elements are designed to convert a Gaussian beam efficiently into an approximate form of the zero-order Bessel beam and are fabricated on fused quartz by direct laser writing and reactive-ion etching.

Trojan states of electrons guided by Bessel beams

Abstract: Previous work [I. Bialynicki-Birula, Phys. Rev. Lett. {\bf 93}, 20402 (2004)] is extended to cover more realistic examples of electromagnetic waves, viz. the Bessel beams. It is shown that electrons may be guided by a Bessel beam with nonvanishing orbital angular momentum. The mechanism for trapping the electrons near the electromagnetic vortex line of such a wave field is the same as for the Trojan states of Rydberg electrons produced by a circularly polarized wave. The main difference is that in the present case the transverse motion of electrons in a beam is confined under the action of the electromagnetic wave alone, no additional attraction center is required. We also discuss briefly the motion of electrons in Neumann and Hankel beams.

Interference of a pair of symmetric Collett–Wolf beams

Abstract: We present a study of the interference of light produced by a pair of mutually correlated Gaussian Schell-model sources. The spatial distributions of the fields produced by these sources are symmetric with respect to a plane through their common center and differ by a phase factor exp(i?). When ?=0, the resulting radiation is a beam with an intensity distribution that displays a narrow bright line at its center. When the sources can be regarded as Collett–Wolf sources, the resulting bright line diverges much more slowly than the beam itself. When ?=? the radiated beam has an intensity distribution with a narrow dark line at its center. The theoretical results are supported by experimental results obtained by use of a modified Michelson interferometer and suggest that the interference of a pair of correlated Collett–Wolf beams can be used to produce a pseudo-nondiffracting beam.

Momentum paradox in a vortex core

Abstract: The identification of angular momentum per photon with optical vortices of charge l appears to require that the field amplitude be zero within a finite distance of the vortex. This, however, is not compatible with the known form of beams such as the Laguerre–Gaussian and Bessel beams. We resolve this paradox by analysing the propagation of a Bessel beam through a small circular aperture, showing that the resulting field has evanescent components.

Reconfigurable directional couplers and junctions optically induced by nondiffracting Bessel beams.

Abstract: We put forward the concept of reconfigurable structures optically induced by mutually incoherent nondiffracting Bessel beams in Kerr-type nonlinear media. We address collinear couplers and X junctions and show how one can tune the switching properties of such structures by varying the intensity of the Bessel beams.