We experimentally demonstrate for the first time that a linearly polarized beam is focussed to an asymmetric spot when using a high-numerical aperture focussing system. This asymmetry was predicted by Richards and Wolf [Proc.R.Soc.London A, 253, 358 (1959)] and can only be measured when a polarization insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife edge type set up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focussing theory.
This work focuses on the generation of far-field super-resolved pure-azimuthal focal field based on the fast Fourier transform. A self-designed differential filter is first pioneered to robustly reconfigure a doughnut-shaped azimuthal focal field into a bright one with a sub-wavelength lateral scale (0.392λ), which offers a 27.3% reduction ratio relative to that of tightly focused azimuthal polarization modulated by a spiral phase plate. By further uniting the versatile differential filter with spatially shifted beam approach, in addition to allowing for an extremely sharper focal spot, whose …
The focal field properties of radially/azimuthally polarized Zernike polynomials are studied. A method to design the pupil field in order to shape the focal field of radially or azimuthally polarized phase vortex is introduced. With this method, we are able to obtain a pupil field to achieve a longitudinally polarized hollow spot with a depth of focus up to $12λ$ and $0.14λ$ lateral resolution for a optical system with numerical aperture 0.99; A pupil field to generate 8 circularly polarized focal spots along the optical axis is also obtained with this method.
When focusing a light beam at high numerical aperture, the resulting electric field profile in the focal plane depends on the transverse polarisation profile, as interference between different parts of the beam needs to be taken into account. It is well known that radial polarised light produces a longitudinal polarisation component and can be focused below the conventional diffraction limit for homogeneously polarised light, and azimuthally polarised light that carries one unit of angular momentum can achieve even tighter focal spots. This is of interest for example for enhancing resolution i…
Uncertainty relations for light pulses found in [Phys. Rev. A {\bf 86}, 022118 (2012)] were derived in the three-dimensional case which emphasized the localization in a volume. Here we derive the uncertainty relation for light beams in the two-dimensional plane perpendicular to the direction of the beam propagation which is more interesting for realistic beams. This uncertainty relation connects the area of the focal spot with the spectrum of transverse photon momenta. The shape of the beam that saturates the uncertainty relation is very close to a Gaussian. The directions of the electric and …
An ongoing limitation of terahertz spectroscopy is that the technique is generally limited to the study of relatively large samples of order 4 mm across due to the generally large size of the focal beam spot. We present a nested concentric parabolic reflector design which can reduce the terahertz focal spot size. This parabolic reflector design takes advantage of the feature that reflected rays experience a relative time delay which is the same for all paths. The increase in effective optical path for reflected light is equivalent to the aperture diameter itself. We have shown that the light t…
Thin structured surfaces allow flexible control over propagation of electromagnetic waves. Focusing and polarization state analysis are among functions, required for effective manipulation of radiation. Here a polarization sensitive Fresnel zone plate lens is proposed and experimentally demonstrated for GHz spectral range. Two spatially separated focal spots for orthogonal polarizations are obtained by designing metasurface pattern, made of overlapping tightly packed cross and rod shaped antennas with a strong polarization selectivity. Optimized subwavelength pattern allows multiplexing two di…
This paper reports an experimental demonstration of moiré metalens which shows wide focal length tunability from negative to positive by mutual angle rotation at the wavelength of 900 nm. The moiré metalens was developed using high index contrast transmitarray meta-atoms made of amorphous silicon octagonal pillars, which is designed to have polarization insensitivity and full 2$π$ phase coverage. The fabricated moiré metalens showed focal length tunability at the ranges between $\pm$1.73 -- $\pm$5 mm, which corresponds to the optical power ranges between $\pm$578 -- $\pm$200 m$^{-1}$ at the mu…
We study circular Airy vortex beams (CAVBs) with two same or opposite point vortices symmetrically loaded on x-axis, inside, onside and outside of the main ring (The absolute value of topological charge is one). It is found that the loading position (denoted as dv) can significantly tune the auto-focusing behaviour. For two vortices with same signs, when dv is near zero, the double vortices approximately merge at the focal plane. But as dv increases, the merged vortices will gradually separate along the y-axis. When dv is large, the focal spot becomes Bessel-shaped pattern. For opposite vortic…
Conventional optical lenses have been used to focus light from outside without disturbing the medium. The focused spot size is proportional to the focal distance in a conventional lens, resulting in a tradeoff between depth of penetration in the target medium and spatial resolution. We have shown that virtual ultrasonically sculpted gradient-index (GRIN) optical waveguides can be formed in the target medium to guide and steer light without disturbing the medium. Here, we demonstrate that such virtual waveguides can relay an externally focused beam of light through the medium beyond the focal d…
We report on an experimental comparison on critical intensities of nonlinear self-focusing in air with conventional focusing and spatiotemporal focusing schemes. Our results show that the conventional focusing with the focal lens completely filled with the incident beam allows for the strongest axial intensity confinement against the self-focusing effect. This is because that in the high-numerical-aperture condition, the focal spot will have a compact size which results in a high focal intensity. Meanwhile, the Rayleigh length of the focused beam will be substantially shortened which efficient…
We present a new technique that we have defined as the z-scan confocal method to determine the absolute location and size of the focal spot in a tight focused ultrashort laser pulse. The method permits to accurately position a target in the focal spot with a fast response. The technique is designed to help to automatize the location of an overdense target in focus in a laser plasma experiment. The method allows for a fast localization of the focal position and the relative motion of the target with respect to it. As an example of the capacities we measure the defocusing of a fast rotating disc…
We report the first demonstration of wrinkled membranes as a kind of optical focusing devices, which are low cost, light weight and flexible. Our device consists of concentric wrinkle rings on a gold-PDMS bilayer membrane, which converts collimated illuminations to diffraction-free focused beams. Beam diameters of 300-400 μm have been observed in the visible range. By comparing the theoretically calculated and experimentally measured focal spot profiles, we predict a focal spot size as small as around 50 μm if fabrication eccentricity can be eliminated.
The ability of curved gratings as sectors of concentric circular gratings to couple linearly polarized light into focused surface plasmons is investigated by theory, simulation and experiment. Curved gratings, as sectors of concentric circular gratings with four different sector angles, are etched into a 30-nm thick gold layer on a glass coverslip and used to couple linearly-polarised free space light at nm into surface plasmons. The experimental and simulation results show that increasing the sector angle of the curved gratings decreases the lateral spotsize of the excited surface plasmons, r…
Almost one and a half centuries ago, Ernst Abbe [1] and shortly after Lord Rayleigh [2] showed that when an optical lens is illuminated by a plane wave, a diffraction-limited spot with a radius 0.61*lambda/sin(alpha) is obtained, where lambda is the wavelength and alpha is the semi-angle of the beam's convergence cone. However, spots with much smaller features can be obtained at the focal plane when the lens is illuminated by an appropriately structured beam. Whereas this concept is known for light beam, here, we show how to realize it for massive-particle wave function of a free electron. We …
The concept of time reversal (TR) of scalar wave is reexamined from basic principles. Five different time reversal mirrors (TRM) are introduced and their relations are analyzed. For the boundary behavior, it is shown that for paraxial wave only the monopole TR scheme satisfies the exact boundary condition while for spherical wave only one of the mixed mode TR scheme, after multiplication by two, satisfies the exact boundary condition. The asymptotic analysis of the near-field focusing property is presented. It is shown that to have a subwavelength focal spot the TRM should involve dipole field…
Materials which possess a high local density of states varying at a subwavelength scale theoretically permit to focus waves onto focal spots much smaller than the free space wavelength. To do so metamaterials -manmade composite media exhibiting properties not available in nature- are usually considered. However this approach is limited to narrow bandwidths due to their resonant nature. Here, we prove that it is possible to use a fractal resonator alongside time reversal to focus microwaves onto $λ/15$ subwavelength focal spots from the far field, on extremely wide bandwidths. We first numerica…
The possibility of focusing light to an ever tighter spot has important implications for many applications and fields of optics research, such as nano-optics and plasmonics, laser-scanning microscopy, optical data storage and many more. The size of lateral features of the field at the focus depends on several parameters, including the numerical aperture of the focusing system, but also the wavelength and polarization, phase and intensity distribution of the input beam. Here, we study the smallest achievable focal feature sizes of coherent superpositions of two co-propagating beams carrying opp…
In the absence of separate apertures, the size and focal length of a lens determines both its resolution and light-collection ability defined by numerical-aperture (NA) and f/#, respectively. We utilize free-form broadband-diffractive-optical elements (BDOEs) to create flat lenses that decouple NA from f#, whereby the resolution of the lens may be chosen independently from its light-collection ability. Specifically, we designed, fabricated and characterized three BDOE lenses operating in the visible band (450nm-750nm), each with f/11.25, but with NAs of 0.00075, 0.0067 and 0.054, respectively.…
Conical refraction occurs when a beam of light travels through an appropriately cut biaxial crystal. By focussing the conically refracted beam through a high numerical aperture microscope objective, conical refraction optical tweezers can be created, allowing for particle manipulation in both Raman spots and in the Lloyd/Poggendorff rings. We present a thorough quantification of the trapping properties of such a beam, focussing on the trap stiffness and how this varies with trap power and trapped particle location. We show that the lower Raman spot can be thought of as a single-beam optical gr…
Drill-bit-inspired dynamic focal fields for augmented laser materials processing
EMPA, Laboratory for Advanced Materials Processing（瑞士联邦材料科技与研究院，先进材料加工实验室）；Institute for Applied Laser, Photonics and Surface technologies ALPS, Bern University of Applied Sciences（伯尔尼应用科学大学，应用激光、光子学与表面技术研究所ALPS）；ESRF – The European Synchrotron（欧洲同步辐射装置）；EMPA, Laboratory for Mechanics of Materials & Nanostructures（瑞士联邦材料科技与研究院，材料与纳米结构力学实验室）
We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak l…
We develop a single-layer waveguide surface grating structure to vertically couple near infrared (NIR) light at ~1.55 um wavelength from a large area (~100 um length scale) Si waveguide on a Silicon-On-Insulator (SOI) substrates to free-space for high-power laser applications. Our design approach is based on the optimization of local emission angles and the out-coupling intensities. Simulation results show that a focal spot with a 1/e2 width of 3.82 um can be achieved at the desired focal position, with 33% (-4.81 dB) simulated source to free-space focusing efficiency, while initial measuremen…
Focusing petawatt-level laser beams to a variety of spot sizes for different applications is expensive in cost, labor and space. In this paper, we propose a plasma lens to flexibly resize the laser beam by utilizing the laser self-focusing effect. Using a fixed conventional focusing system to focus the laser a short distance in front of the plasma, we can adjust the effective laser beam waist within a certain range, as if a variety of focusing systems were used with the plasma lens acting as an adjustable eyepiece in a telescope. Such a setup is a powerful tool for laser wakefield accelerator …
