Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon

We propose a new method for transformation of a Laguerre-Gaussian beam of azimuthal index l and radial index n = 0 (LG_l,0) into a vortex, diverging or nondiverging Bessel beam, which can have increased or decreased phase singularity order, or into a zeroth order Bessel beam, by means of a helical axicon. The Bessel beam divergence or nondivergence depends upon the waist position of the input Laguerre-Gaussian beam, regarding the plane where the helical axicon is situated.The expressions for the amplitude and the intensity distribution of the diffracted wave field, in the process of Fresnel diffraction, are deduced using the stationary phase method. The theoretical analysis for the vortex radius and the maximum propagation distance of the Bessel beams obtained is presented.     

Effect of the spiral phase element on the radial-polarization (0, 1) LG beam

Radially-polarized beams can be strongly amplified without significant birefringent-induced aberrations. However, radially-polarized beam is a high-order beam, and therefore has to be transformed into a fundamental Gaussian beam for reduction the beam-propagation factor M². In effort to transform the radially-polarized beam to a nearly-Gaussian beam, we consider effect of a spiral phase element (SPE) on the Laguerre-Gaussian (LG) (0, 1)^∗ beam with radial polarization, and compare this with the case when the input beam is a LG (0, 1)^∗ beam with spiral phase and uniform or random polarization. The LG (0, 1)^∗ beam with radial polarization, despite its identity in intensity profile to the beam with spiral phase, has distinctly different properties when interacting with the SPE. With the SPE and spatial filter, we transformed the radially-polarized (0, 1)^∗ mode with M² = 2.8 to a nearly-Gaussian beam with M² = 1.7. Measured transformation efficiency was 50%, and the beam brightness P/(M²)² was practically unchanged. The SPE affects polarization state of the radially-polarized beam, leading to appearance of spin angular momentum in the beam center at the far-field.     

Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams

We investigate conversion of a linearly-polarized Gaussian beam to a radially- or an azimuthally-polarized doughnut (0, 1)^∗ Laguerre-Gaussian (LG) beams, performed with a spatially-variable retardation (SVR) plate. The SVR plate is composed of eight sectors of a λ/2 retardation plate, each one with different orientation of the to crystal’s slow axis. The analysis reveal that nearly-pure radially- or azimuthally-polarized LG(01)^∗ beam with M² = 2.2 can be obtained, while the transformation efficiency is 89.6%. In the experiments, performed with Nd:YAG laser, we transformed a Gaussian beam with M² = 1.3 to a radially- and azimuthally-polarized (0, 1)^∗ Laguerre-Gaussian beams with M² = 2.5. We carefully characterized the polarization state of the obtained radially- and azimuthally-polarized beams, measuring Stokes parameters. The polarization purity of the obtained beams, calculated from the measured data, was as high as 96%.     

Acoustic scattering of a high-order Bessel beam by an elastic sphere

The exact analytical solution for the scattering of a generalized (or “hollow”) acoustic Bessel beam in water by an elastic sphere centered on the beam is presented. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis and the half-conical angle of the wave vector components of the generalized Bessel beam. The sphere is assumed to have isotropic elastic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The transverse acoustic scattering field is investigated versus the dimensionless parameter ka(k is the wave vector, a radius of the sphere) as well as the polar angle θ for a specific dimensionless frequency and half-cone angle β. For higher-order generalized beams, the acoustic scattering vanishes in the backward (θ = π) and forward (θ = 0) directions along the beam axis. Moreover it is possible to suppress the excitation of certain resonances of an elastic sphere by appropriate selection of the generalized Bessel beam parameters.     

Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Guassian beam

An analytical expression describing the vectorial field distribution of Gaussian light beams diffracted by an axicon is obtained. The theoretical analysis and simulation calculation show that for the linearly x-polarized light incident on an axicon, the y-component of the diffraction field is very small and the x-component dominates. The intensity of the z-component along the propagation direction is related with the open angle and index of axicon. The open angle plays the more important role in determining the polarization than does the index. For a small open angle, the z-polarized effect can be neglected and the scalar method is simple and valid to evaluating the diffraction field distribution of axicon. However, the vectorial method has to be used for great open angle.     

Effects of evolving surface morphology on yield during focused ion beam milling of carbon

We investigate evolving surface morphology during focused ion beam bombardment of C and determine its effects on sputter yield over a large range of ion dose (10¹⁷-10¹⁹ ions/cm²) and incidence angles (Θ = 0-80°). Carbon bombarded by 20 keV Ga⁺ either retains a smooth sputtered surface or develops one of two rough surface morphologies (sinusoidal ripples or steps/terraces) depending on the angle of ion incidence. For conditions that lead to smooth sputter-eroded surfaces there is no change in yield with ion dose after erosion of the solid commences. However, for all conditions that lead to surface roughening we observe coarsening of morphology with increased ion dose and a concomitant decrease in yield. A decrease in yield occurs as surface ripples increase wavelength and, for large Θ, as step/terrace morphologies evolve. The yield also decreases with dose as rippled surfaces transition to have steps and terraces at Θ = 75°. Similar trends of decreasing yield are found for H₂O-assisted focused ion beam milling. The effects of changing surface morphology on yield are explained by the varying incidence angles exposed to the high-energy beam.     

Nonlinear change of on-axis pressure and intensity maxima positions and its relation with the linear focal shift effect

A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f = 1 MHz, aperture radius a = 1.5 cm and geometrical focal distance R = 11.7 cm, corresponding to a Fresnel number N_F = 1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1 cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.     

Observation of nonstationary effects in saturation spectroscopy

We have studied the nonstationary effects in saturated absorption spectroscopy of the ⁸⁷Rb D₂ line. Varying the size of the σ⁺ polarized pump laser beam, we observed saturated absorption spectra for the σ^± polarized probe beam. For equal polarizations of the pump and probe beams, we found that the resonance signal for the F_g = 1 → F_e = 2 line, and the crossover lines between F_g = 1 → F_e = 2 and F_g = 1 → F_e = 1 (and 0) lines increased to a greater extent than the others. This observation can be understood from the calculated time evolution of the populations of the ground-state sublevels by means of a rate equation model. We also compared experimental data for other conditions with the calculated results. We found good agreement between the calculated results and the data.     

Structure and optical properties of ZnS thin films grown by glancing angle deposition

The glancing angle deposition (GLAD) technique was used to deposit ZnS films by electron beam evaporation method. The cross sectional scanning electron microscopy (SEM) image illustrated a highly orientated microstructure composed of slanted column. The atomic force microscopy (AFM) analysis indicated that incident flux angle had significant effects on the nodule size and surface roughness. Under identical nominal thickness, the actual thickness of the GLAD films is related to the incident flux angle. The refractive index and in-plane birefringence of the GLAD ZnS films were discussed, and the maximum birefringence Δn = 0.036 was obtained at incident flux angle of α = 80°. Therefore, the glancing angle deposition technique is a promising way to create a columnar structure with enhanced birefringent property.     

Generation of diffraction-free vectorial elliptic hollow beams with space-varying inhomogeneous polarizations

Diffraction-free vectorial elliptic hollow beams (vEHBs) are generated by an optical system composed of a short elliptic hollow fiber (EHF) and an axicon. Each beam has a closed elliptic annular intensity profile and space-varying polarization states in its diffraction-free distance of more than 1 m. The generated beams have a counter-clockwise or clockwise periodically-rotated inhomogeneous polarization. And the spin angular momentum (SAM) of the vEHBs is 1ħ or -1ħ which is consistent with the type of dual-mode in the EHF and the periodic polarization rotations of the vEHBs. The vEHBs have potential applications in optically trapping and micromanipulating the micro- or nano-particles, quantum information transmission, and Bose-Einstein condensates, etc.     

Trapping Rayleigh particles using highly focused higher-order radially polarized beams

The optical trapping characteristics of highly focused higher-order radially polarized beams (R-TEM_p1*) acting on a Rayleigh particle are studied theoretically. Numerical results show that as the order p of beam increases and the numerical aperture NA_o of the objective decreases, the axial trap distance increases but the trap depth and maximum restoring force decreases. In a limit of NA_o = 1, three higher-order R-TEM_p1* beams of p = 1, 2, 3, like the fundamental lowest-order radially polarized beam of p = 0, can three-dimensionally trap a particle to the focus but the axial trap stiffness decreases with the increase of p. When NA_o = 0.95, the focus is still a stable trap point for the two beams of p = 0 and 1 but it becomes an unstable trap point for the two beams of p = 2 and 3. The trap stability is also discussed for higher-order radially polarized beam illumination.     

Analysis on the laser beam pointing instability induced fringe shift and contrast dilution from different interferometers used for writing fiber Bragg grating

This paper presents an analysis on the effect of laser beam pointing instability on the fringe shift and hence the contrast dilution of superposed fringes from two beam interferometers. The interferometers analyzed are those commonly used in writing fiber Bragg grating (FBG) such as phase mask, bi-prism and phase mask based Talbot/Holographic type. The beam pointing instability is incorporated as slight change in the angle between two interfering beams. The relative immunity of different interferometers to laser beam pointing is discussed vs location of FBG writing plane from the beam splitter. The effect of the beam pointing was minimum in proximity FBG writing by phase mask. The effect, in terms of fringes contrast dilution, was worst in case of large length interferometers e.g. phase mask based-Talbot interferometer. For intermediate length prism interferometers, the effect was moderate. For a given length interferometer, the fringe shift was directly proportional to beam pointing angle and inversely proportional to fringe separation. Theoretical analysis is verified experimentally by studying the fringe instability of interference pattern formed by a bi-prism of angle 2^o with the copper vapour laser (CVL, λ = 510 nm) beams of different beam pointing instabilities.     

Generation of a vectorial Mathieu-like hollow beam with a periodically rotated polarization property

We propose a promising and practical scheme to generate a vectorial Mathieu-like hollow beam (vMHB) by using an axicon optical system including a dual-mode elliptic hollow fiber (EHF), and calculate the intensity and polarization distributions of the beam and its fractional orbital angular momentum (OAM). We also fit its intensity profile and obtain suitable theoretical expressions to describe three-dimensional (3D) propagation characteristics of such a Mathieu-like hollow beam. Our study shows that the generated beam is a vMHB within the propagation distance 1.2-2.2 m, which has an unchanged (diffraction-free) intensity profile and periodically rotated polarization properties as well as an unchanged fractional OAM within 1.2-2.2 m.     

Periodic sub-micrometric structures using a 3D laser interference pattern

A method to obtain three-dimensional sub-micrometric periodic structures is presented. The experimental set-up consists in a pulsed UV laser beam source (λ = 355 nm) coming into an interferometer in order to generate four beams converging inside a chamber. According to the directions, to the relative intensities and to the polarizations of these four beams, a 3D interference pattern can be obtained inside the overlapping volume of these four beams; the characteristics of the four laser beams have been optimized in order to obtain a maximal contrast of intensity. In order to visualize the interference pattern, its contrast and its stability at each laser pulse, a video camera coupled to an oil immersion microscope objective has been installed above the interferometer. By suppressing the central beam, it is also possible to generate a bidimensional interference pattern which defines an hexagonal structure in the (1 1 1) plane with a period of 377 nm.This optical set-up has been used to obtain 3D sub-micrometric periodic structures in negative photoresists. Experiments consist in a one- or multi-pulse irradiation of the photoresist followed by a development procedure which leads to a sub-micrometric face-centred cubic structure cut in a (1 1 1) plane with a cell parameter of 650 nm. The optimization of the experimental conditions is presented for two kinds of photoresists; the role of the substrate according to its reflectivity at the laser wavelength and its influence on the interference pattern is also discussed.     

Phase structure of helico-conical optical beams

We examine the phase structures of Helico-Conical (HC) Optical Beams produced via computer-generated holograms (CGH). The CGHs of these beams are made such that the reconstruction will have a phase which is a product of a helical and a conical phase. Interference-based phase measurement technique reveals very distinct differences between the phases of the two types of HC Beams (K = 0 and K = 1). Most obvious is the presence of screw dislocations at the center of the beam for K = 1 while no screw dislocations are found at the center for K = 0. We also compare the experimental interference patterns with numerical interference patterns calculated by superimposing a field containing vortices at different positions and a plane wave. A remarkable similarity is seen between the interferograms, which is a good indication of the phase of these beams. Contour plots are drawn to show the phases of these beams. We observe a string of vortices with equal charge in contrast to the assumption that a string of alternating charges should be seen.     

Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers

Starting from the exact acoustic scattering from a sphere immersed in an ideal fluid and centered along the propagation axis of a standing or quasi-standing zero-order Bessel beam, explicit partial-wave representations for the radiation force are derived. A standing or a quasi-standing acoustic field is the result of propagating two equal or unequal amplitude zero-order Bessel beams, respectively, along the same axis but in opposite sense. The Bessel beam is characterized by the half-cone angle β of its plane wave components, such that β = 0 represents a plane wave. It is assumed here that the half-cone angle β for each of the counter-propagating acoustic Bessel beams is equal. Fluid, elastic and viscoelastic spheres immersed in water are treated as examples. Results indicate the capability of manipulating spherical targets based on their mechanical and acoustical properties. This condition provides an impetus for further designing acoustic tweezers operating with standing or quasi-standing Bessel acoustic waves. Potential applications include particle manipulation in micro-fluidic lab-on-chips as well as in reduced gravity environments.     

Transverse (lateral) instantaneous force of an acoustical first-order Bessel vortex beam centered on a rigid sphere

In a recent report [F.G. Mitri, Z.E.A. Fellah, Ultrasonics 51 (2011) 719-724], it has been found that the instantaneous axial force (i.e. acting along the axis of wave propagation) of a Bessel acoustic beam centered on a sphere is only determined for the fundamental order (i.e. m = 0) but vanishes when the beam is of vortex type (i.e. m > 0, where m is the order (or helicity) of the beam). It has also been recognized that for circularly symmetric beams (such as Bessel beams of integer order), the transverse (lateral) instantaneous force should vanish as required by symmetry. Nevertheless, in this commentary, the present analysis unexpectedly reveals the existence of a transverse instantaneous force on a rigid sphere centered on the axis of a Bessel vortex beam of unit magnitude order (i.e. |m| = 1) not reported in [F.G. Mitri, Z.E.A. Fellah, Ultrasonics 51 (2011) 719-724]. The presence of the transverse instantaneous force components of a first-order Bessel vortex beam results from mathematical anti-symmetry in the surface integrals, but vanishes for the fundamental (m = 0) and higher-order Bessel (vortex) beams (i.e. |m| > 1). Here, closed-form solutions for the instantaneous force components are obtained and examples for the transverse components for progressive waves are computed for a fixed and a movable rigid sphere. The results show that only the dipole (n = 1) mode in the scattering contributes to the instantaneous force components, as well as how the transverse instantaneous force per unit cross-sectional surface varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere’s radius), and the half-cone angle β of the beam. Moreover, the velocity of the movable sphere is evaluated based on the concept of mechanical impedance. The proposed analysis may be of interest in the analysis of transverse instantaneous forces on spherical particles for particle manipulation and rotation in drug delivery and other biomedical or industrial applications.     

1 × N add-drop filter structures using one dense wavelength division multiplexing thin-film filter

This paper proposes 1 × N add-drop filter structures in which only one thin-film filter (TF) is used. Our key idea is based on a combination of an angle-multiplexing concept and the flexibility of the optical fiber to allow a multiwavelength optical beam hit the TF several times, each time at a different angle but same position. Due to the TF angle sensitivity, the desired wavelength optical beam corresponding to the incident angle is therefore spatially isolated from the main optical beam. Our first TF-based 1 × N add-drop filter structure is arranged in a reflective design in which N wavelength optical beams can be dropped out from the main channel. For our transmissive architecture, N − 2 channels are directed to their associated output terminals while the remaining λ_N−1 and λ_N wavelength optical beams are sent out at the same port. Experimental proof of concept for our reflective TF-based 1 × 3 add-drop filter using one off-the-shelf TF, a triple fiber-optic collimator, and an optical circulator separates two wavelength optical beams with their channel spacing of 0.8 nm from the main channel. In this case, measured optical losses of 0.67 dB, 1.66 dB, and 2.59 dB are obtained for the first, the second, and the remaining dropped wavelength optical beams, respectively. Optical crosstalk and polarization dependent loss of <−18 dB and <0.08 dB are also investigated, respectively.     

Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon

We show that by focusing ultrashort-pulsed laser beams in air with an axicon, relatively long plasma channels can be generated. The axicon generates Bessel-like beams, where the on-axis intensity stays high over distances much longer compared to focusing with conventional lenses. We developed a scheme to detect the presence of the plasma, based on its screening property. Using this scheme, we detected plasma channels longer than 1 m and 3.5 m generated by 8 mJ and 90 mJ input pulse energies, respectively. Our simulations show that axicon focusing can yield self-guided propagation with or without contribution of plasma, depending on the input pulse power.     

Observation of triangle pits in PbSe grown by molecular beam epitaxy

PbSe thin films on BaF₂ (1 1 1) were grown by molecular beam epitaxy with different selenium beam flux. Evolution of PbSe surface morphologies with Se/PbSe beam flux ratio (R_f) has been studied by atomic force microscopy and high-resolution X-ray diffraction. Growth spirals with monolayer steps on PbSe surface are obtained using high beam flux ratio, R_f ≥ 0.6. As R_f decreases to 0.3, nano-scale triangle pits are formed on the surface and the surface of PbSe film changes to 3D islands when R_f = 0. Glide of threading dislocations in 〈1 1 0〉{1 0 0}-glide system and Pb-rich atom agglomerations are the formation mechanism of spiral steps and triangle pits. The nano-scale triangle pits formed on PbSe surface may render potential applications in nano technology.