Total angular momentum sorting in the telecom infrared with silicon Pancharatnam-Berry transformation optics

Parallel sorting of orbital angular momentum (OAM) and polarization has recently acquired paramount importance and interest in a wide range of fields ranging from telecommunications to high-dimensional quantum cryptography. Due to their inherently polarization-sensitive optical response, optical elements acting on the geometric phase prove to be useful for processing structured light beams with orthogonal polarization states by means of a single optical platform. In this work, we present the design, fabrication and test of a Pancharatnam-Berry optical element in silicon implementing a log-pol optical transformation at 1310 nm for the realization of an OAM sorter based on the conformal mapping between angular and linear momentum states. The metasurface is realized in the form of continuously-variant subwavelength gratings, providing high-resolution in the definition of the phase pattern. A hybrid device is fabricated assembling the metasurface for the geometric phase control with multi-level diffractive optics for the polarization-independent manipulation of the dynamic phase. The optical characterization confirms the capability to sort orbital angular momentum and circular polarization at the same time.Comment: 15 pages, 10 figure

Holographic generation of highly twisted electron beams

Free electrons can possess an intrinsic orbital angular momentum, similar to those in an electron cloud, upon free-space propagation. The wavefront corresponding to the electron's wavefunction forms a helical structure with a number of twists given by the \emph{angular speed}. Beams with a high number of twists are of particular interest because they carry a high magnetic moment about the propagation axis. Among several different techniques, electron holography seems to be a promising approach to shape a \emph{conventional} electron beam into a helical form with large values of angular momentum. Here, we propose and manufacture a nano-fabricated phase hologram for generating a beam of this kind with an orbital angular momentum up to 200$\hbar$. Based on a novel technique the value of orbital angular momentum of the generated beam are measured, then compared with simulations. Our work, apart from the technological achievements, may lead to a way of generating electron beams with a high quanta of magnetic moment along the propagation direction, and thus may be used in the study of the magnetic properties of materials and for manipulating nano-particles.Comment: 4 pages, 4 figures - Supplementary Material (3 pages and 2 figures) accompanies this manuscrip

Design, fabrication and characterization of Computer Generated Holograms for anti-counterfeiting applications using OAM beams as light decoders

In this paper, we present the design, fabrication and optical characterization of computer-generated holograms (CGH) encoding information for light beams carrying orbital angular momentum (OAM). Through the use of a numerical code, based on an iterative Fourier transform algorithm, a phase-only diffractive optical element (PH-DOE) specifically designed for OAM illumination has been computed, fabricated and tested. In order to shape the incident beam into a helicoidal phase profile and generate light carrying phase singularities, a method based on transmission through high-order spiral phase plates (SPPs) has been used. The phase pattern of the designed holographic DOEs has been fabricated using high-resolution Electron-Beam Lithography (EBL) over glass substrates coated with a positive photoresist layer (polymethylmethacrylate). To the best of our knowledge, the present study is the first attempt, in a comprehensive work, to design, fabricate and characterize computer-generated holograms encoding information for structured light carrying OAM and phase singularities. These optical devices appear promising as high-security optical elements for anti-counterfeiting applications.Comment: 24 pages, 9 figures. Supplementary info: 8 pages, 3 figure

Measuring the orbital angular momentum spectrum of an electron beam

Electron waves that carry orbital angular momentum (OAM) are characterized by a quantized and unbounded magnetic dipole moment parallel to their propagation direction. When interacting with magnetic materials, the wavefunctions of such electrons are inherently modified. Such variations therefore motivate the need to analyse electron wavefunctions, especially their wavefronts, to obtain information regarding the material’s structure. Here, we propose, design and demonstrate the performance of a device based on nanoscale holograms for measuring an electron’s OAM components by spatially separating them. We sort pure and superposed OAM states of electrons with OAM values of between −10 and 10. We employ the device to analyse the OAM spectrum of electrons that have been affected by a micron-scale magnetic dipole, thus establishing that our sorter can be an instrument for nanoscale magnetic spectroscopy

A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams

The design and fabrication of a compact diffractive optical element is presented for the sorting of beams carrying orbital angular momentum (OAM) of light. The sorter combines a conformal mapping transformation with an optical fan-out, performing demultiplexing with unprecedented levels of miniaturization and OAM resolution. Moreover, an innovative configuration is proposed which simplifies alignment procedures and further improves the compactness of the optical device. Samples have been fabricated in the form of phase-only diffractive optics with high-resolution electron-beam lithography (EBL) over a glass substrate. A soft-lithography process has been optimized for fast and cheap replica production of the EBL masters. Optical tests with OAM beams confirm the designed performance, showing excellent efficiency and low cross-talk, with high fidelity even with multiplexed input beams. This work paves the way for practical OAM multiplexing and demultiplexing devices for use in classical and quantum communication

Experiments and Potentialities for the use of Bessel Beam in Superresolution STEM

In light optics holographic beam shaping has been largely used to obtain complicated wavefronts [1] and vortex beams. In the last years holograms have been used in the electron vortex beam generation [2]. We have recently improved the technology of hologram fabrication by means of \u201cphase hologram\u201d [3] replacing the amplitude hologram so far used. Phase holograms appropriately change the phase of the incident wavefront by a modulation of thickness in a silicon nitride thin membrane. Beyond vortex generation, holograms can have a large range of applications. As an example in this work we report on the production of a Bessel beam in the Fresnel diffraction regime [4]. Bessel beams have many interesting properties most of which derived from being the Fourier transform of a ring. In this sense they can be considered as the extreme case of hollow cone illumination. However while the production of hollow cone probes requires a strong reduction of the electron beam current by the use of an obstructing aperture, the holographic approach permits to produce high quality Bessel beams with only marginal intensity losses. In particular by the use of phase holograms we could demonstrate up to 40% efficiency. In these conditions the generated beam is competitive with normal aperture limited approaches in terms of intensity. Fig 1a shows the FIB-nanofabricated hologram that has been positioned in the second condenser aperture of a FEI Tecnai F20 operated at 200 kV. Fig 1b is an image of the logarithm of the intensity of the Bessel beam showing the characteristic fringes aside from the central peak. The obtained probe size is in this case 0.5 nm. But we will show that the beam can be potentially scaled to 0.1 nm for larger convergences. In Fig 1c the Fraunhofer diffraction of the hologram is also shown demonstrating that the probe is the Fourier transform of a tiny ring. The calculated convergence is here 1.9 mrad. This beam can be exploited in many applications. One of the main advantages of this is that the probe shape is, to large extent, independent from spherical aberration, chromatic aberration and from defocus; the other is that for the given convergence Bessel beam provide the minimal probe size regardless of spherical aberration. Fig 2a shows the transfer function of a microscope with a conventional probe (with and without aberration) with convergence 15 mrad and with a Bessel probe. Clearly the Bessel probe can produce advantages in the high frequency region. Fig 2b is a simulation of STEM-HAADF images for a Au particle with the two kinds of probes as in fig 2a. Using the Bessel beams in fig 1a we obtained the STEM image in fig 2c that demonstrates that, in spite of the presence of other diffraction peaks, a good quality scan of a sample (a Si-SiO STI structure) can be obtained with a resolution better than 2nm (measured as the blurring of the contrast features). In fact the transmitted and other diffraction beam are completely delocalized and do not contribute significantly to the contrast

Innovative Phase Plates for Beam Shaping

In light optics the use of holographic beam shaping has been largely used to obtain complicated wavefronts [1] and vortex beams but recently holograms have been used in the electron vortex beam generation [2]. We show here our recent improvement in the technology of hologram fabrication by means of “phase hologram” [3] replacing the amplitude hologram so far used. Phase hologram appropriately changes the phase of the wavefront by a modulation of thickness in a Silicon nitride thin membrane. By means of phase hologram we could produce different beam shape in both Fresnel and Fraunhofer regime. Moreover we engineered the hologram shape to obtain high efficiency on the generated wavefunction. Presently we could demonstrate an efficiency of 40% in the generation efficiency for a single beam. This is the best performance ever shown and is much higher than amplitude hologram so far used. The particular holographic technique consists in creating a grating of Si3N4 and modulating the periodicity with the desired wavefront shape. In general many order of diffraction of the grating are generated while only the first order is typically interesting for application with a clear loss of intensity. However if the groove of the grating is a ramp spanning an appropriate thickness corresponding exactly to 2π phase in the electron path (also dubbed “blazed” profile) a single diffraction with the relevant beam can be obtained. Using this principle we generated by FIB a close to ideal hologram. The experimental thickness profile (as calculated by EELS) is shown in fig 1a. In the inset a profile in a line is extracted and compared with the “ideal” blazed pattern. The full pattern for the generation of a Bessel beam is shown in fig 1b while the resulting series of beam in a Fresnel plane is shown in fig 1c. In particular the experimental pattern (up) is compared with the simulated one based Fresnel integral of the hologram in fig 1a [3]. The very good agreement means that the simulated phase is also correct. Therefore the figure in the inset that represents intensity and phase of the simulated beam can be considered as a realistic representation of the actual phase

Engineering of the spin on dopant process on silicon on insulator substrate

We report on a systematic analysis of phosphorus diffusion in silicon on insulator thin film via spin-on-dopant process (SOD). This method is used to provide an impurity source for semiconductor junction fabrication. The dopant is first spread into the substrate via SOD and then diffused by a rapid thermal annealing process. The dopant concentration and electron mobility were characterized at room and low temperature by four-probe and Hall bar electrical measurements. Time-of-flight-secondary ion mass spectroscopy was performed to estimate the diffusion profile of phosphorus for different annealing treatments. We find that a high phosphorous concentration (greater than 1020 atoms cm-3) with a limited diffusion of other chemical species and allowing to tune the electrical properties via annealing at high temperature for short time. The ease of implementation of the process, the low cost of the technique, the possibility to dope selectively and the uniform doping manufactured with statistical process control show that the methodology applied is very promising as an alternative to the conventional doping methods for the implementation of optoelectronic devices. </p