We examine the properties of interfering high-order Bessel beams. We implement an experimental setup that allows us to realize these interferograms, using interfering Laguerre-Gaussian beams and an axicon. We demonstrate the use of such beams for controlled rotation of microscopic particles in optical tweezers and rotators. The self-healing properties of interfering Bessel beams allow the simultaneous manipulation and rotation of particles in spatially separated sample cells.

Interfering Bessel beams for optical micromanipulation.

Axicons in oblique illumination produce broadened focal lines, a problem, e.g., in scanning applications. A compact mathematical description of the focal segment is presented, for the first time, to our knowledge, and the results are compared with elliptical axicons in normal illumination. In both cases, analytical expressions in the form of asteroid curves are obtained from asymptotic wave theory and caustic surfaces. The results are confirmed by direct diffraction simulations and by experiments. In addition we show that at a fixed angle an elliptical axicon can be used to compensate for the adverse effects of oblique illumination.

Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons

We study numerically the interference resulting from the superposition of two Bessel beams propagating in free space. We discuss how to obtain such beams and show the existence of the self-imaging effect during propagation. The evolution of the superimposed Bessel beams is analyzed on the basis of the evolution of the individual beams. Our exact numerical predictions contradict previous approximated analytical treatments, showing that they can lead to quantitatively wrong results and misleading conclusions.

Interference of traveling nondiffracting beams

A method of generating nondiffracting beams using multimode optical fibers is reported. When a large-core multimode fiber is spliced onto a piece of single-mode fiber, only linearly polarized (LP0,n) modes are excited inside the multimode fiber segment because of mode orthogonality and on-axis excitation. Since the excited LP0,n modes are actually Bessel fields with different transverse wave vectors truncated by the core of the multimode fiber, the beam exiting the multimode fiber facet can form a variety of readily controllable and nearly nondiffracting optical patterns resulting from interference of apertured Bessel fields.

Generation of controllable nondiffracting beams using multimode optical fibers

We propose a new design for fabrication of a highly power-efficient double axicon to generate self-imaged three-dimensional intensity voids along the propagation of a beam. The conventional conical structure of an axicon is modified and shaped like an axiconlike structure with a double-gradient surface profile. The gradient conical surfaces generate Bessel beams with varying radial wave vectors that are superimposed and interfere to generate a sequence of three-dimensional intensity voids. The proposed element was fabricated using electron-beam lithography, and experimental verification of the design is reported.

Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids

A solution for the transmittance of elements forming planar and nonplanar focal curves in the non-paraxial case is proposed in this paper. The treatment is based on the scalar diffraction theory and makes use of the stationary phase method in evaluation of the diffraction integral. The equation of a stationary point enables one to establish mapping relations between the geometrical regions of the element and the corresponding points of the focal curve. These regions turn out to be described by conical curves. The mapping relations can be manipulated by a phase function imposed onto the focal curve. The amplitude factors of the derived transmittances can be omitted and the desired intensity distribution along the focal curve can then be obtained by an appropriate change in the aperture of pure phase elements. The approach is illustrated by examples of elliptical, hyperbolic, conical and circular zone plates. The focus generations for both non-paraxial and paraxial cases of these elements are compa...

Non-paraxial analytical solution for the generation of focal curves

The characteristic dimensions of Bessel beams are fully determined by the corresponding Bessel functions. We consider a way of obtaining a narrower diameter of the central core of a diffractive pattern generated by the Bessel beams. The method relies on superposition of two or more Bessel beams with appropriately chosen amplitudes and widths. The disturbing influence of the aperture's edges can be eliminated by addition of the proper amplitude filter.

Diffractive patterns of small cores generated by interference of Bessel beams.

Spiral zone plates with arbitrary diameter of the dark spot in the centre of their focal point

The central dark line in the focus of the antisymmetric linear zone plate can be used for one-dimensional displacement monitoring. Two crossed wavefronts produced by such a zone plate with added proper phase shift between them enable us to create a focus composed of two perpendicular segments with null intensity in the centre surrounded by a small square-shaped pattern, which is useful for two-dimensional sensing. The characteristic dimensions of the central pattern can be decreased by a phase-only super-resolving filter superposed onto the aperture of the element.

C Gomez-Reino

Papers

Non-paraxial analytical solution for the generation of focal curves

Diffractive patterns of small cores generated by interference of Bessel beams.

Spiral zone plates with arbitrary diameter of the dark spot in the centre of their focal point

Single and crossed antisymmetric focal segments for alignment purposes