Propagation of apertured Bessel beams

Generation of stable propagation Bessel beams and axial multifoci beams with binary amplitude filters

The binary amplitude filter (BAF) is employed to generate stable propagation Bessel beams and axial multifoci beams, rather than the traditional continuous amplitude filter (CAF). We introduce a parameter along the azimuth direction, i.e., angular order of the BAF, to weaken transverse intensity asymmetry. Numerical simulations reveal that the BAF implements the same optical functionalities as the CAF. The BAF holds advantages over the traditional CAF: a simpler fabrication process, a lower cost, and a higher experimental accuracy. It is believed that the BAF should have many practical applications in future optical systems.

Sharp-edge diffraction under Bessel beam illumination: a catastrophe optics perspective

Boundary diffraction wave theory and catastrophe optics have already proved to be a formidable combination in computational optics. In the present paper, a general paraxial theory aimed at dealing paraxial diffraction of Bessel beams by arbitrarily shaped sharp-edge apertures is developed. A key ingredient of our analysis is the δ-like nature of the angular spectrum of nondiffracting beams. This allows the diffracted wavefield to be effectively represented through two-dimensional integrals defined onto rectangular domains, whose numerical evaluation is easily achievable via standard Monte Carlo techniques. As a byproduct of the present analysis, a simple explanation of a recently observed property of some "heart-like" apertures to flatten the axial intensity of apodized Bessel beams is also provided.

Toric lens analysis as a focal ring and Bessel beam generator

We propose an analytical solution of the focal ring generated at the focus of a toric lens. The analytical field of the focal ring is used with a Fourier transform lens to generate a Bessel beam. A comparative analysis between the use of an illuminated annular aperture, an axicon, and a toric lens to generate a Bessel beam is performed, and the benefits and drawbacks of each are discussed. This highlights the advantages of using a toric lens with a Gaussian beam to produce a focal line of increasing intensity, which is advantageous for applications such as high depth-of-field microscopy.

Flattening axial intensity oscillations of a diffracted Bessel beam through a cardioid-like hole

We present a new feasible way to flatten the axial intensity oscillations for diffraction of a finite-sized Bessel beam, through designing a cardioid-like hole. The boundary formula of the cardioid-like hole is given analytically. Numerical results by the complete Rayleigh-Sommerfeld method reveal that the Bessel beam propagates stably in a considerably long axial range, after passing through the cardioid-like hole. Compared with the gradually absorbing apodization technique in previous papers, in this paper a hard truncation of the incident Bessel beam is employed at the cardioid-like hole edges. The proposed hard apodization technique takes two advantages in suppressing the axial intensity oscillations, i.e., easier implementation and higher accuracy. It is expected to have practical applications in laser machining, light sectioning, or optical trapping.

Segmented Bessel beams

We investigate segmented Bessel beams that are created by placing different ring apertures behind an axicon that is illuminated with a plane wave. We find an analytical estimate to determine the shortest possible beam segment by deriving a scale-invariant analytical model using appropriate dimensionless parameters such as the wavelength and the axicon angle. This is verified using simulations and measurements, which are in good agreement. The size of the ring apertures was varied from small aperture sizes in the Frauhofer diffraction limit to larger aperture sizes in the classical limit.

Long-distance Bessel beam propagation through Kolmogorov turbulence

Free-space optical communication has the potential to transmit information with both high speed and security. However, since it is unguided it suffers from losses due to atmospheric turbulence and diffraction. To overcome the diffraction limits the long-distance propagation of Bessel beams is considered and compared against Gaussian beam properties. Bessel beams are shown to have a number of benefits over Gaussian beams when propagating through atmospheric turbulence.

Vector analyses of linearly and circularly polarized Bessel beams using Hertz vector potentials

Using the transverse Hertz vector potentials, vector analyses of linearly and circularly polarized Bessel beams of arbitrary orders are presented in this paper. Expressions for the electric and magnetic fields of vector Bessel beams in free space that are rigorous solutions to the vector Helmholtz equation are derived. Their respective time averaged energy density and Poynting vector are also obtained, in order to exhibit their non-diffracting properties. Polarization patterns and magnitude profiles with different parameters are displayed. Particular emphasis is placed on the cases where the ratio of wave number over its transverse component k/kt approximately equals to one and largely exceeds it, which corresponding to the nonparaxial and paraxial condition, respectively. These results allow us to recognize that the vector Bessel beams exhibit new and important features, compared with the scalar fields.

Generation of multiple vortex-cones by direct-phase modulation of annular aperture array

The generation of multiple vortex cones using an annular aperture array and a spatial light modulator (SLM) is studied. The direct downscale imaging of an SLM on the surface of an annular aperture enables the direct-phase modulation of the annular aperture. It is experimentally demonstrated that the direct-phase modulation of an annular aperture array can control both the topological charge and the horizontal positions of multiple vortex cones simultaneously.

Apertured paraxial Bessel beams

The paraxial Bessel beam is obtained by applying an approximation in the wavenumbers. The scattering of the beams by a circular aperture in an absorbing screen is investigated. The scattered fields are expressed in terms of the Fresnel integrals by evaluating the Kirchhoff diffraction integral in the paraxial approximation. The results are examined numerically.

Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture

An electromagnetic nondiffractive Bessel-like beam from a subwavelength aperture is generated by placing a metallic circular gratinglike structure in front of the aperture. When the incident wave is linearly polarized, the beam is axially asymmetric. The beam possesses fluctuating, but approximately uniform, intensity distribution along its longitudinal axis. The full width at half maximum of the beam remains less than two wavelengths over nearly ten wavelengths. Our experimental results are in good agreement with the simulation results and analytical results.

Generation of multiple Bessel beams for a biophotonics workstation

We present a simple method using an axicon and spatial light modulator to create multiple parallel Bessel beams and precisely control their individual positions in three dimensions. This technique is tested as an alternative to classical holographic beam shaping commonly used now in optical tweezers. Various applications of precise control of multiple Bessel beams are demonstrated within a single microscope giving rise to new methods for three-dimensional positional control of trapped particles or active sorting of micro-objects as well as "focus-free" photoporation of living cells. Overall this concept is termed a 'biophotonics workstation' where users may readily trap, sort and porate material using Bessel light modes in a microscope.

Conical optics: the solution to confine light

We compare the performances in terms of confinement and depth of field of spherical and conical optics. It turns out that, if the spherical optics is adapted to the usual parallel imaging, conical optics seems to be the optimized solution for systems based on scanning (sequential imaging). It is shown that the optimized confinement capability of conical optics is due to the ability of conical components to generate a single Bessel beam with high efficiency. The calculations are based on Weyl formulas.

New generalized Bessel-Gaussian beams

Analytical expressions are derived for a new set of optical beams, in which the radial dependence is described by a sum of Bessel distributions of different orders, modified by a flat-topped Gaussian function expressed in the form 1 - [1 - exp(-xi2)]M, where xi is a dimensionless parameter and M(> or = 1) is a scalar quantity. The flat-topped Gaussian function can be readily expanded into a series of the lowest-order Gaussian modes with different parameters; this situation makes it possible to express the optical beam as a series of conventional Bessel-Gaussian beams of different orders. The propagation features of this new set of optical beams are investigated to reveal how a windowed Bessel beam passes progressively from a smooth Gaussian window toward the hard-edge limit.

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.

Marginal phase correction of truncated Bessel beams

Approximate analytic expressions are obtained for evaluating the axial intensity and the central-lobe diameter of J0 Bessel beams transmitted through a finite-aperture phase filter. A reasonable quality factor governing the axial-intensity behavior of a phase-undistorted truncated Bessel beam is found to be the inverse square root of the Fresnel number defined, for a given aperture, from the axial point of geometrical shadow. Additional drastic reduction of axial-intensity oscillations is accomplished by using marginal phase correction of the beam instead of the well-known amplitude apodization. A procedure for analytically calculating an optimal monotonic slowly varying correction phase function is described.

Axially symmetric on-axis flat-top beam

A synthesis method for arbitrary on-axis intensity distributions from axially symmetric fields is developed in the paraxial approximation. As an important consequence, a new pseudo-nondiffracting beam, the axially symmetric on-axis flat-top beam (AFTB), is given by an integral transform form. This AFTB is completely determined by three simple parameters: the central spatial frequency S(c), the on-axis flat-top length L, and the on-axis central position z(c). When LS(c) >> 1, this AFTB can give a nearly flat-top intensity distribution on the propagation axis. In particular, this AFTB approaches the nondiffracting zero-order Bessel J0 beam when L--> infinity. It is revealed that the superposition of multiple AFTB fields can give multiple on-axis flat-top intensity regions when some appropriate conditions are satisfied.