Vortex Phase Plate Research Articles

Direct CW-Laser Writing Sub-Diffraction-Limit Nanopore Array Based on the Low One-Photon Absorption of Polymer

A large area nanopore array with controllable consistency has been fabricated by direct laser writing (DLW) technique with ultralow one-photon absorption (LOPA). In this technique, a doughnut-shape beam generated by 532 nm continuous-wave laser through a vortex phase plate was focused into the thin film of SU8 photoresist by a high numerical aperture objective. The low absorption of the photoresist at the excitation wavelength allowed controllable fabricating structures with sub-diffraction-limit feature size and high aspect ratio. With point-by-point scanning fabrication, nanopore array with the pore's internal diameter, about ten percent of incident laser wavelength, far smaller than Abbe's diffraction limit was achieved. The influences of the exposure intensity and exposure time on the fabricated nanopore size and shape were also investigated by scanning electron microscope (SEM).

Amplitude Modulation of Anomalously Refracted Terahertz Waves with Gated‐Graphene Metasurfaces

AbstractAlthough recent progress in metasurfaces has shown great promise for applications, optical properties in metasurfaces are typically fixed by their structural geometry and dimensions. Here, an electrically controllable amplitude of anomalously‐refracted waves in a hybrid graphene/metasurface system are experimentally demonstrated, which consists of an artificially constructed two‐dimensional metallic apertures array and naturally occurring two‐dimensional carbon atoms (graphene) in the subwavelength‐scale (< λ/10). Based on Pancharatnam–Berry phase and by careful design of a spatially linear phase profile, it is shown that the amplitude of anomalously refracted circularly cross‐polarized terahertz waves can be effectively modulated by an applied gate voltage. The developed electrically tunable graphene metasurfaces may lead to various advanced applications that require dynamical control over electromagnetic waves, such as amplitude tunable active focusing lenses, vortex phase plates and dynamic holography.

Precise characterization of focused vortex beams

Focused vortex beams are characterized in terms of their intensity and phase using an iterative phase retrieval method. The vortex beams generated by a vortex phase plate contain several phase singularities and vortex phase distributions. The wavefields were retrieved using many far-field diffraction profiles obtained by scanning a pinhole along the focal plane. The retrieved intensity and phase distributions agreed well with those predicted using the actual profiles of vortex phase plates, which indicates that the phase retrieval method can be used for the precise characterization of vortex beams. The information obtained is valuable for improving the performance of methods involving vortex beams, such as microscopy and laser processing.

Revealing optical vortices with a small number of photons

AbstractDetecting the optical vortices of darkness hidden in an ultra‐weak background is a difficult task. Here we report an experiment demonstrating that the optical vortices can be directly visualized and identified with a smaller number of photons. Our method is based on the extension of the spiral phase contrast technique to incorporate vortex phase plates (VPP) of high‐order topological charges. In our experiment, we prepare optical vortex arrays of interesting structures such as Arabic numerals and the wings carrying various topological charges. By placing various VPP filters in the Fourier plane of a 4f imaging system, the embedded vortices of an incident ultra‐weak light field can be visualized, revealing both their positions and topological charges. It is found that a higher order vortex generally requires a smaller number of photons to be detected. Our method may find potential application in the fields of astronomical optics and biosensing in an ultra‐weak light environment. image

Spiral phase plate contrast in optical and electron microscopy

The use of phase plates in the back focal plane of a microscope is a well established technique in optical microscopy to increase the contrast of weakly interacting samples and is gaining interest in electron microscopy as well. In this paper we study the spiral phase plate (SPP), also called helical, vortex, or two-dimensional Hilbert phase plate, that adds an angularly dependent phase of the form $e^{i\ell\phi}$ to the exit wave in Fourier space. In the limit of large collection angles, we analytically calculate that the average of a pair of $\ell=\pm1$ SPP images is directly proportional to the gradient squared of the exit wave, explaining the edge contrast previously seen in optical SPP work. The difference between a clockwise-anticlockwise pair of SPP images and conditions where this difference vanishes and the gradient of the exit wave can be seen from one single SPP image, are discussed. Finally, we demonstrate how with three images, one without and one with each of an $\ell=\pm1$ SPP, may give enough information to reconstruct both the amplitude and the phase of the exit wave. This work provides the theoretical background to interpret images obtained with a SPP and can help enable new experiments to study for example magnetic materials in an electron microscope.

Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate

Cylindrical vector (CV) beams have found increasing applications in physics, biology, and chemistry. To generate CV beams, interferometric technique is popularly adopted due to its flexibility. However, most interferometric configurations for the generation of CV beams are faced with system instability arising from external disturbance, limiting their practical applications. A common-path interferometer for the generation of radially and azimuthally polarized beams is proposed to improve the system stability. The optical configuration consists of a vortex phase plate acting to tailor the phase profile and a cube nonpolarizing beamsplitter to split the input beam into two components with mirror-like spiral phase distribution. The generated CV beams show a high quality in polarization and exhibit a better stability of beam profile than those obtained by noncommon-path interferometric configurations.

Focus shaping effect of annular cylindrical vector beam generated by novel polarized convertor

Based on the diffractive vector theory, the focusing properties of annular cylindrical vector beams generated by the novel polarized convertor are investigated. By the combination of the vortex phase plate eimφ and the phase variety parameter cosφ+ihsinφ which exists naturally in the CV beams, the intensity pattern at the focus can be tailored. Flattop spot and light intensity with pure transverse and longitudinal component are formed in the focal region. More interestingly, tunable dark focal spot is also achieved. By changing h, the light intensity in the center of spot can be changed at will while the outer ring of spot remains the same. This works are important for microscope imaging and optical lithography, particle manipulation, electric acceleration etc.

Fabrication of ideal geometric-phase holograms with arbitrary wavefronts

Throughout optics and photonics, phase is normally controlled via an optical path difference. Although much less common, an alternative means for phase control exists: a geometric phase (GP) shift occurring when a light wave is transformed through one parameter space, e.g., polarization, in such a way as to create a change in a second parameter, e.g., phase. In thin films and surfaces where only the GP varies spatially—which may be called GP holograms (GPHs)—the phase profile of nearly any (physical or virtual) object can in principle be embodied as an inhomogeneous anisotropy manifesting exceptional diffraction and polarization behavior. Pure GP elements have had poor efficiency and utility up to now, except in isolated cases, due to the lack of fabrication techniques producing elements with an arbitrary spatially varying GP shift at visible and near-infrared wavelengths. Here, we describe two methods to create high-fidelity GPHs, one interferometric and another direct-write, capable of recording the wavefront of nearly any physical or virtual object. We employ photoaligned liquid crystals to record the patterns as an inhomogeneous optical axis profile in thin films with a few μm thickness. We report on eight representative examples, including a GP lens with F/2.3 (at 633 nm) and 99% diffraction efficiency across visible wavelengths, and several GP vortex phase plates with excellent modal purity and remarkably small central defect size (e.g., 0.7 and 7 μm for topological charges of 1 and 8, respectively). We also report on a GP Fourier hologram, a fan-out grid with dozens of far-field spots, and an elaborate phase profile, which showed excellent fidelity and very low leakage wave transmittance and haze. Together, these techniques are the first practical bases for arbitrary GPHs with essentially no loss, high phase gradients (∼rad/μm), novel polarization functionality, and broadband behavior.

Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms

Based on the quotient of inner products, a simple and rapid algorithm is proposed to retrieve the measured phase from two-frame phase-shifting interferograms with unknown phase shifts. Firstly, we filtered the background of interferograms by a Gaussian high-pass filter. Secondly, we calculated the inner products of the background-filtered interferograms. Thirdly, we extracted the phase shifts by the quotient of the inner products then calculated the measured phase by an arctangent function. Finally, we tested the performance of the proposed algorithm by the simulation calculation and the experimental research for a vortex phase plate. Both the simulation calculation and the experimental result showed that the phase shifts and the measured phase with high accuracy can be obtained by the proposed algorithm rapidly and conveniently.

Ultra-thin optical vortex phase plate based on the L-shaped nanoantenna for both linear and circular polarized incidences

Based on the L-shaped gold nanoantennas, the ultra-thin optical vortex phase plates (VPPs) have been designed to generate the optical vortex beams with different topological charges, which are independent of the incident polarization states and suitable for both X/Y linear and circular polarization incidences simultaneously. The phase and amplitude of transmitted cross-polarization light can be simultaneously manipulated by changing two degrees of freedom (the length and the width) in the L-shaped nanoantenna unit. Evolution properties of the generated vortex beam are demonstrated and analyzed. The different interactions of angular momentums between light and the VPP in the different incident polarization states have also been investigated fully. The designed VPP shows a superior broadband characteristics in near-infrared wavelength ranging from 750nm to 1200nm, which enable a potential implication for integrated optics and vortex optics.

Super-resolution microscopy based on fluorescence emission difference of cylindrical vector beams

We propose a novel fluorescence emission difference microscopy (FED) system based on focusing cylindrical vector beams. In conventional FED, a Gaussian beam and a 0–2π vortex phase plate are used to generate solid and hollow spots. We focus radially polarized and azimuthally polarized cylindrical vector beams to obtain an expanded solid spot and a shrunken hollow spot, taking advantage of the optical properties of cylindrical vector beams to improve the conventional FED performance. Our novel method enhances FED performance because the hollow spot size determines the FED resolution and an expanded solid spot effectively reduces negative side-lobe emergence during image processing. We demonstrate improved performance theoretically and experimentally using an in-house built FED. Our FED achieved resolution of less than λ/4 in test images of 100nm nanoparticles, better than the confocal image resolution by a factor of approximately 1/3. We also discuss detailed simulation analyses and FED imaging of biological cells.

Tight focusing of the azimuthally polarized light beam for a sharper spot

Abstract This paper presents a method to focus azimuthally polarized vortex light beam by the combination of a vortex phase plate, a binary-phase optical element (BOE) and a high-numerical aperture (NA) objective lens. Our proposed method achieves a smaller spot size than other polarized beams under the same condition. Compared to the system with the annular aperture, the minimum of full width at half-maximum is improved to 0.259λ and the energy conversion efficiency is higher in the proposed method when FWHM

Resolution-enhanced surface plasmon-coupled emission microscopy.

A novel fluorescence emission difference technique is proposed for further enhancements of the lateral resolution in surface plasmon-coupled emission microscopy (SPCEM). In the proposed method, the difference between the image with phase modulation by using a 0-2π vortex phase plate (VPP) along with a diaphragm and the original image obtained from SPCEM is used to estimate the spatial distribution of the analyzed sample. By optimizing the size of the diaphragm and the subtractive factor, the lateral resolution can be enhanced by about 20% and 33%, compared with that in SPCEM with a single 0-2π VPP and conventional wide-field fluorescence microscopy, respectively. Related simulation results are presented to verify the capability of the proposed method for improving lateral resolution and reducing imaging distortion. It is believed that the proposed method has potentials to improve the performance of SPCEM, thus facilitating biological observation and research.

Ultra-thin optical vortex phase plate based on the metasurface and the angular momentum transformation

The ultra-thin optical vortex phase plate (VPP) has been designed and investigated based on the metasurface of the metal rectangular split-ring resonators (MRSRRs) array. The circularly polarized incident light can convert into corresponding cross-polarization transmission light, and the phase and the amplitude of cross-polarization transmission light can be simultaneously governed by modulating two arms of the MRSRR. The MRSRR has been arranged in a special order for forming an ultra-thin optical VPP that can covert a plane wave into a vortex beam with a variety of the topological charges, and the transformation between spin angular momentum (SAM) and orbital angular momentum (OAM) has been discussed in detail. The multi-spectral characteristics of the VPP have also been investigated, and the operating bandwidth of the designed VPP is 190 nm (in the range of 710–900 nm), which enable a potential implication for integrated optics and vortex optics.

Fabrication of anisotropically arrayed nano-slots metasurfaces using reflective plasmonic lithography.

Nanofabrication technology with high-resolution, high-throughput and low-cost is essential for the development of nanoplasmonic and nanophotonic devices. At present, most metasurfaces are fabricated in a point by point writing manner with electron beam lithography or a focused ion beam, which imposes a serious cost barrier with respect to practical applications. Near field optical lithography, seemingly providing a high-resolution and low-cost way, however, suffers from the ultra shallow depth and poor fidelity of obtained photoresist patterns due to the exponential decay feature of evanescent waves. Here, we propose a method of surface plasmonic imaging lithography by introducing a reflective plasmonic lens to amplify and compensate evanescent waves, resulting in the production of nano resist patterns with high fidelity, contrast and enhanced depth beyond that usually obtained by near field optical lithography. As examples, a discrete and anisotropically arrayed nano-slots mask pattern with different orientations and a size of 40 nm × 120 nm could be imaged in photoresist and transferred successfully onto a metal layer through an etching process. Evidence for the pattern quality is given by virtue of the fabricated metasurface lens devices showing good focusing performance in experiments. It is believed that this method provides a parallel, low-cost, high-throughput and large-area nanofabrication route for fabricating nanostructures of holograms, vortex phase plates, bio-sensors and solar cells etc.

3 Color - 3 Dimensional STED Nanoscopy

The stimulated emission depletion microscopy (STED) is a super-resolution technique that enables to overcome the diffraction barrier, allowing to distinguish details of cellular as well as molecular structures, not visible with a conventional confocal microscope [1].Here we present the development of a custom made versatile STED microscope, based on a super-continuum pulsed laser source endowed with 2 high power STED laser beams, at 715 and 745 nm, respectively [2]. In order to obtain three-dimensional super-resolved images, we split the STED beam into two parts. One of the beams passes through a vortex phase plate which creates a donut shape beam for lateral resolution enhancement. For the other beam we introduced a home-made phase plate which introduces a phase delay of π in the center, creating a z-donut to increase resolution in the axial direction [3]. We can tune the microscope PSF adjusting the ratio of the power in the two depletion pathways, to achieve, for example, an isotropic resolution. Additionally in order to perform three color imaging we paid particular attention to chromatic aberrations and we optimized the setup accordingly.Therefore by using proper fluorophores, we are able to do 3 color super-resolved imaging.Thanks to this completely custom made optical architecture, designed for fast scanning, 3D and three color acquisition, we are able to perform multimodal live cell imaging.The achieved 3D resolution discloses morphometric properties at the nano-scale which are completely hidden to the confocal observation.[1] S. W. Hell et al., Opt. Lett., 19, 780-782 (1994).[2] S. Galiani et al., Opt. Express 20, 7362-7374 (2012).[3] B. Harke et al., Nano Letters 8 (5), 1309-1313 (2008).

Highly efficient second harmonic generation of a light carrying orbital angular momentum in an external cavity.

Traditional methods for generating a light carrying orbital angular momentum (OAM) include the use of holographic diffraction gratings, vortex phase plates and spatial light modulators. Here we report a new method for highly efficient second-harmonic generation (SHG) of a light with OAM. By properly aligning an external cavity that contains a quasi-phase matching nonlinear crystal and pumping it with a light carrying OAM, mode matching between the pump light and the cavity's higher order Laguerre-Gaussian (LG) mode is achieved, SHG with a conversion efficiency of up to 10.3% is obtained. We have demonstrated for the first time that the cavity can stably operate at its higher order LG mode similar to that of a Gaussian mode. The second harmonic generated light has an OAM value that is double with respected to the OAM value of the pump light. The parameters that affect the beam quality and conversion efficiency are discussed in detail. Our work opens a brand new field in laser optics and makes the first step toward high efficiency processing using a light carrying OAM.

Influence of retardation between orthogonal components of circularly polarized light in the vortex phase plate on the structure of diffracted beam

The influence of retardation between orthogonal components of circularly polarized light on diffraction pattern generated by the vortex phase plate with a birefringence medium is considered. It is shown that if the ideal retardation π is broken, the pattern diffracted from the phase plate is described by superposition of two components: the vortex beam with the deep hole and the incident beam which preserves its initial characteristics. The computation results characterizing the influence of retardation on the Gaussian and Airy beams transformation in the vortex phase plate are presented. These results point out that vortex beam characteristics are very sensitive to retardation shift from its ideal value. We analyze and present the characteristics of the vortex phase plate that are required for the true vortex pattern generation.

Generation of dark hollow beams used in sub-diffraction-limit imaging in coherent anti-Stokes Raman scattering microscopy

Profile of a dark hollow beam in sub-diffraction -limit imaging is of crucial importance for its spatial resolution when using the coherent anti-Stokes Raman scattering microscopy, as far as the imaging quality is concerned. Therefore, the generation of dark hollow beams through a vortex phase plate will be theoretically analyzed based on the Fresnel diffraction theory. Influences of different incidence conditions on the intensity distribution of the generated dark hollow beams are also investigated. And it is shown that a perfect dark hollow beam could be produced when a Gaussian beam is vertically incident upon a first-order vortex phase plate, with the incident light wavelength equal to that of the phase plate. However, both the circular symmetry of the incident beam's intensity distribution and the alignment between the centers of Gaussian beam and phase plate may affect the intensity distribution of the dark hollow beam, which will almost be in circular symmetry though it may shift some distance from the image center when at a small incident angle. Furthermore, the dark hollow beam's intensity distribution will scarcely change when the central wavelength deviation is very small from the incidence light and the phase plate. These results may be of great value in generation of perfect dark hollow beams in sub-diffraction –limit imaging by coherent anti-Stokes Raman scattering microscopy.

High fidelity detection of the orbital angular momentum of light by time mapping

We demonstrate high-fidelity detection of the orbital angular momentum (OAM) of light using a compact and practical OAM spectrometer that maps the OAM spectrum to time. The spectrometer consists of a single optical delay loop to achieve timing mapping, a vortex phase plate that iteratively decreases the OAM value and a single mode fiber to distinguish zero from non-zero OAM states. Light with arbitrarily OAM compositions can be measured. For light with OAM up to 4ℏ, we measured an average crosstalk of −21.3 dB, which is mainly limited by the purity of the input states and optical alignment.