Modeling of CW annular arrays using limited diffraction Bessel beams

Presents a method for characterizing the linear field of any flat, continuous-wave annular array in terms of a set of known limited-diffraction Bessel beams. The technique uses Fourier-Bessel series to model the surface pressure of the transducer surface, with each term in the series giving rise to a Bessel beam with known propagation parameters. The analysis is applied numerically to two different transducers discussed previously in the literature. In both cases, a deeper understanding of the field emitted than was previously available is gained. Brief outlines for extending the technique to pulsed wave and non-annular arrays are also given     

From stationary annular rings to rotating Bessel beams

In this work we use a phase-only spatial light modulator (SLM) to mimic a ring-slit aperture, containing multiple azimuthally varying phases at different radial positions. The optical Fourier transform of such an aperture is currently known and its intensity profile has been shown to rotate along its propagation axis. Here we investigate the near-field of the ring-slit aperture and show, both experimentally and theoretically, that although the near-field possesses similar attributes to its Fourier transform, its intensity profile exhibits no rotation as it propagates.     

Generalized Bessel pulse beams

A generalization of type 3 ultrashort pulses (also known as pulse beams or isodiffracting pulses) is introduced. The Bessel beam form of this generalized beam consists of pulses that propagate in free space, without spreading, with a velocity that can be less than that of light. A model spectral distribution that is zero outside a finite range is investigated.     

Beam steering with segmented annular arrays

Two-dimensional (2-D) arrays of squared matrix have maximum periodicity in their main directions; consequently, they require half wavelength (lambda/2), interelement spacing to avoid grating lobes. This condition gives rise to well-known problems derived from the huge number of array elements and from their small size. In contrast, 2-D arrays with curvilinear configuration produce lower grating lobes and, therefore, allow the element size to be increased beyond lambda/2. Using larger elements, these arrays have the advantage of reducing the number of elements and of increasing the signal-to-noise ratio (SNR). In this paper, the beamforming properties of segmented annular phased arrays are theoretically analyzed and compared with the equivalent squared matrix array. In the first part, point-like elements are considered in order to facilitate the field analysis with respect to the array structure. Afterward, the effect of the element size on the steered beam properties also is presented. In the examples, it is shown that the segmented annular array has notably lower grating lobes than the equivalent squared matrix array and that it is possible to design segmented annular arrays with interelement distance higher than lambda whose beam characteristics are perfectly valid for volumetric imaging applications.     

Propagation of apertured Bessel beams

The propagation features of several apertured Bessel beams are numerically calculated. The calculations show that the relations of axial intensity versus propagation distance are similar to the radial distribution of the aperture functions, which may be helpful in choosing the proper aperture functions in experiments.     

Direct generation of Bessel beams

Two implementations are identified to create a Bessel beam directly, i.e. without the spatial filtering of an initially Gaussian beam. The first implementation is based on a resonator configuration whose lowest-loss transverse mode is a Bessel beam. Numerical simulation to corroborate the geometrical optical arguments is presented. The second implementation is based on the theorem that the angular-plane wave spectrum of a Bessel beam is composed of a cone of wave vectors. This cone is also generated through a phase-matching condition in a four-wave mixing process. This leads to the conclusion that anti-Stokes radiation generated in a nonlinear material will leave the substrate under the form of a Bessel beam.     

Bessel pulse beams and focus wave modes

Free-space propagation of ultrashort pulses is investigated. Space-time couplings are reduced for a particular form of beams that is termed a pulse beam, or a type 3 pulsed beam. General conditions for the formation of pulse beams in the paraxial approximation are presented. The free-space propagation of spatially localized ultrashort laser pulses is investigated. This treatment is based on a particular pulsed form of the well-known Bessel beam, which is termed a Bessel pulse beam. The connections with focus wave modes and X waves are discussed.     

Production of high-order Bessel beams with a Mach-Zehnder interferometer

A new experimental setup is demonstrated to produce high-order Bessel beams. It is based on the field decomposition of the Bessel beam into its even and odd field components. The implementation is performed over the spectral components with a Mach-Zehnder interferometer that synthesizes the components into the desired Bessel beam. The main advantage of our setup is that the required annular transmittances have only discrete phase changes of pi radians instead of a continuous change of phase.     

Free-space delay lines and resonances with ultraslow pulsed Bessel beams

We investigate the ultraslow motion of polychromatic Bessel beams in unbounded, nondispersive media. Control over the group velocity is exercised by means of the angular dispersion of pulsed Bessel beams of invariant transverse spatial frequency, which spontaneously emerge from near-field generators. Temporal dynamics in transients and resonances over homogeneous delay lines (dielectric slabs) are also examined.     

Self-reconstruction property of fractional Bessel beams

We study the self-reconstruction property of a fractional Bessel beam (FBB), where the FBB is described in terms of a Bessel beam of a fractional order for both amplitude and azimuthal phase components. The simulation and experimental results show that the FBB can overcome a block of obstacles and regenerate itself after a characteristic distance. As a comparison, the propagation of a Gaussian beam and an integer-order Bessel beam (IBB) through the same obstacles are also studied.     

Negative propagation of vector Bessel beams

Energy characteristics of the superposition of TE- and TM-polarized electromagnetic Bessel beams are studied. For some phase differences between TE and TM waves the components of the Poynting vector vary in sign. We call this situation "negative propagation," because locally the beam may behave like a wave propagating in the direction opposite to the conventional one. We predict the following phenomena, which should confirm negative beam propagation: reflection of the beam from a circular aperture and unusual movement of microparticles in the beam.     

Scintillations of cos-Gaussian and annular beams

Based on the generalized beam formulation, we derive the scintillation index and selectively evaluate it for cos-Gaussian and annular beams propagating in weak atmospheric turbulence. Dependence of the scintillation index on propagation length, focusing and displacement parameters, wavelength of operation, and source size are individually investigated. From our graphical outputs, it is observed that a cos-Gaussian beam exhibits lower scintillations and thus has a tendency to be advantageous over a pure Gaussian beam particularly at lower propagation lengths. It is also found that at longer propagation lengths, this advantage switches to the side of the annular beam. Furthermore, the scintillation index of a focused annular beam will be below those of both Gaussian and cos-Gaussian beams starting at earlier propagation distances. When analyzed against source sizes, it is seen that cos-Gaussian beams will offer advantages at relatively large source sizes, while the reverse will be applicable for annular beams.     

Double helical laser beams based on interfering first-order Bessel beams

We demonstrate the generation of a nondiffracting double helical beam using axicons and ±1 vortex phase plates in a common-path interferometric system. Using linear diffraction theory, a simple analytical expression describing beam propagation is shown to agree with both experiments and Fresnel-diffraction-based simulations. Experiments are performed using continuous laser light in addition to ultrafast pulses, demonstrating that the common-path arrangement and the diffraction theory work equally well for both cases.     

Rotation of microparticles with Bessel beams generated by diffractive elements

Abstract

We show that imaging a non-diverging Bessel beam by a spherical lens leads to the generation of a diverging Bessel beam. Expressions for the projections of the Umov-Poynting vector for a two-dimensional TE-polarized Bessel beam and a three-dimensional paraxial linearly polarized Bessel beam are derived. A fifth-order Bessel beam is produced using a single optical element-a 16-level phase-only diffractive helical axicon fabricated using electron beam lithography. This beam was successfully used to trap and rotate 5-10 μm diameter yeast particles and polystyrene beads of diameter 5 μm.     

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.     

Generation of Bessel beam arrays through Dammann gratings

In this work we apply the Dammann grating concept to generate an equal-intensity square array of Bessel quasi-free diffraction beams that diverge from a common center. We generate a binary phase mask that combines the axicon phase with the phase of a Dammann grating. The procedure can be extended to include vortex spiral phases that generate an array of optical pipes. Experimental results are provided by means of a twisted nematic liquid crystal display operating as a binary π phase spatial light modulator.     

Generating Bessel beams by use of localized modes

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 kappa 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 approximately 0.5lambda0 can be maintained for a distance in excess of 3000lambda0. 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 approximately 0.34lambda0 can be maintained for a distance of 0.14lambda0. By choice of different material parameters, the central spot size can be made smaller still.     

Experimental study of holographic generation of fractional Bessel beams

We demonstrate the experimental generation of a fractional Bessel beam by holographic means. Such fractional modes of Bessel beams possess an intrinsic opening gap across concentric intensity rings on propagation. We also show that the opening gaps within the fractional modes are diffraction free for a working distance while a fractional helical wave front is maintained.     

A digital beamformer for high-frequency annular arrays

Digital transmit and receive beamformers for a 45-MHz, 7-element annular array are described. The transmit beamformer produces 0- to 80-Vpp monocycle pulses with a timing error of less than +/-125 ps. Up to four adjustable transmit focal zones can be selected. The dynamic receive beamformer uses a variable frequency sampling technique in which the frequency of analog-to-digital conversion on each channel is adjusted as the signals are received. The variable frequency clock signals required to trigger analog-to-digital conversion are obtained using a pair of high-frequency field-programmable gate arrays and a precision quartz oscillator. The gate arrays are also used to sum the digitized signals. A maximum receive beamformer timing error of less than +/-900 ps was obtained on each channel. The performance of the combined transmit and receive beamformer was tested by imaging wire phantoms. Images of CD-1 mice were also generated. The system produced images with a dynamic range of 60 dB.