Diffractive Phase Elements Research Articles

Ideal suppression of Bessel beam intensity oscillations with a vortex phase plate.

We propose what we believe to be a new kind of diffractive phase element, i.e., vortex phase plate (VPP) with phase singularities along the azimuth direction. Phase function of the proposed VPP is given analytically. Axial intensity oscillations of propagating Bessel beams are ideally suppressed by using the proposed VPP. Compared with the traditional amplitude mask, the proposed VPP takes such advantages as a simpler fabrication procedure and a lower cost.

Rotation Invariant Parallel Signal Processing Using a Diffractive Phase Element for Image Compression

We propose a new rotation invariant correlator using dimensionality reduction. A diffractive phase element is used to focus image data into a line which serves as input for a conventional correlator. The diffractive element sums information over each radius of the scene image and projects the result onto one point of a line located at a certain distance behind the image. The method is flexible, to a large extent, and might include parallel pattern recognition and classification as well as further geometrical invariance. Although the new technique is inspired from circular harmonic decomposition, it does not suffer from energy loss. A theoretical analysis, as well as examples, are given.

Ion-beam lithography for fabrication of diffractive optical phase elements in silver-ion-exchanged glasses

Ion-beam lithography for fabrication of diffractive optical phase elements in silver-ion-exchanged glasses

Rotationally tunable multi-focal diffractive moiré lenses.

In this work, we show how the combination of cascaded multi-value phase diffractive optical elements can form a multi-focal moiré zone plate with tunable optical power in each diffraction order. The rotationally tunable moiré zone plate is capable of generating an array of equal intensity focal spots with a precisely adjustable axial distance along the propagation direction. Numerical simulations as well as experimental results verify that multiple focal spots are generated, and the distance between the generated uniform foci can be adjusted by a mutual rotation of one multi-value phase diffractive element with respect to the other.

Generation of a variety of Airy beams using a dynamic diffractive optical phase element

We demonstrate theoretically the generation of a variety of dynamic 2D Airy beams. We generate single, 2D dual-, and quad-Airy-like beams using a dynamic optical phase, obtained by the propagation of two crossed standing ultrasonic waves (UWs) in a liquid medium (water). These UWs create sinusoidal variation of the liquid medium refractive index in two dimensions. Using the asymptotic behavior of the sine function near zero, the 2D sinusoidal phase created by the piezoelectric transducer is reduced to a 2D periodic cubic phase. As it is known, the latter converts an input plane wave (Gaussian beam) into an Airy (Airy-like) beam in the far field. By acting on the dynamic optical phase parameters, one can change the characteristics of the obtained Airy beam (trajectory and acceleration). Using combined Gaussian beams, we clearly demonstrate the existence of a variety of combined dynamic Airy beams, such as Airy, dual-Airy, symmetric-Airy, anti-symmetric-Airy, and quad-Airy beams. We believe that the present work is of significant interest in the fields of dynamic focusing, curved manipulation, and transportation of microparticles.

Generation of complex optical fields by double phase modulation in a SLM

We employ a setup, based on a phase spatial light modulator (SLM), for generation of arbitrary optical fields. The process is based on two sequential phase modulations of a laser beam at two different zones of the SLM. The input beam is transformed in the first contact with the SLM by a phase modulation that includes a diffractive phase element (DPE), which encodes the desired complex field, and a Fourier transforming lens. The Fourier transform of the DPE is projected, using a mirror, to the second SLM modulation area, whose transmittance includes a second Fourier transforming lens and a phase spatial filter, used to eliminate non-desired parts of the DPE Fourier spectrum.

Formation of Contour Vortex Fields using Phase Elements Based on Spiral Light Beams

We present the results of the experimental formation of contour vortex fields, based on optics of spiral light beams with diffractive phase elements using binary amplitude—phase masks and phase holograms with symmetric and asymmetric grating line profiles. These methods are compared in diffraction efficiency and quality of obtained light fields.

Laser Processing of Silicon Suboxide for the Fabrication of Multilevel Fused Silica Diffractive Phase Elements

Laser Processing of Silicon Suboxide for the Fabrication of Multilevel Fused Silica Diffractive Phase Elements

Holographic formation of phase diffractive elements for light beams conversion with photo-induced absorption coefficient changing in PDLCs

A theoretical model of the holographic formation of diffractive optical elements for the Gaussian light beams conversion into Bessel-like ones in polymer-dispersed liquid crystals (PDLCs) is developed. The model is based on the solution of the kinetic equations of photopolymerization-diffusion processes of holograms recording in PDLCs by light beams with inhomogeneous amplitude and phase spatial distributions. The model additionally takes into account the photo-induced changings in the absorption coefficient of the PDLC. It is shown that the absorption changings decreases the rate of the refractive index’s spatial profile decline over the thickness of the material. In this case, when the characteristic time of the absorption changing is much less than the characteristic polymerization time (the absorption changes more rapidly than the photopolymerization takes place), the diffractive element can be characterized by a homogeneous distribution of the refractive index over the thickness.

Generation of vector Bessel beams with diffractive phase elements based on the Jacobi-Anger expansion.

We report the design and optimization of a diffractive phase element whose phase modulation is derived from the Jacobi-Anger relation, which allows the simultaneous generation of multiple scalar Bessel beams of different integer orders. In addition, by the appropriate treatment of a couple of such Bessel beams, we generate a vector Bessel beam of arbitrary order m. This beam is constructed by the collinear superposition of the scalar Bessel beam modes of orders m-1 and m+1, with circular orthogonal polarizations. We demonstrate experimentally both the simultaneous generation of the multiple scalar Bessel beams and the generation of vector Bessel beams of orders m=0 and m=1. These tasks are performed in an optical setup based on a pixelated liquid-crystal spatial light modulator.

Compact Holographic Projection Display Using Liquid-Crystal-on-Silicon Spatial Light Modulator.

This paper presents a holographic projection display in which a phase-only spatial light modulator (SLM) performs three functions: beam shaping, image display, and speckle reduction. The functions of beam shaping and image display are performed by dividing the SLM window into four sub-windows loaded with different diffractive phase elements (DPEs). The DPEs are calculated using a modified iterative Fourier transform algorithm (IFTA). The function of speckle reduction is performed using temporal integration of display images containing speckles. The speckle contrast ratio of the display image is 0.39 due to the integration of eight speckled images. The system can be extended to display full-color images also by using temporal addition of elementary color images. Because the system configuration needs only an SLM, a Fourier transform lens, and two mirrors, the system volume is very small, becoming a potential candidate for micro projectors.

Diffractive control of 3D multifilamentation in fused silica with micrometric resolution

We show that a simple diffractive phase element (DPE) can be used to manipulate at will the positions and energy of multiple filaments generated in fused silica under femtosecond pulsed illumination. The method allows obtaining three-dimensional distributions of controlled filaments whose separations can be in the order of few micrometers. With such small distances we are able to study the mutual coherence among filaments from the resulted interference pattern, without needing a two-arm interferometer. The encoding of the DPE into a phase-only spatial light modulator (SLM) provides an extra degree of freedom to the optical set-up, giving more versatility for implementing different DPEs in real time. Our proposal might be particularly suited for applications at which an accurate manipulation of multiple filaments is required.

Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing

The greatest source of loss in conventional single-junction photovoltaic cells is their inefficient utilization of the energy contained in the full spectrum of sunlight. To overcome this deficiency, we propose a multijunction system that laterally splits the solar spectrum onto a planar array of single-junction cells with different band gaps. As a first demonstration, we designed, fabricated, and characterized dispersive diffractive optics that spatially separated the visible (360–760 nm) and near-infrared (760–1100 nm) bands of sunlight in the far field. Inverse electromagnetic design was used to optimize the surface texture of the thin diffractive phase element. An optimized thin film fabricated by femtosecond two-photon absorption 3D direct laser writing shows an average splitting ratio of 69.5% between the visible and near-infrared light over the 380–970 nm range at normal incidence. The splitting efficiency is predicted to be 80.4% assuming a structure without fabrication errors. Spectral-splitting a...

Diagnostics of the topological charge of optical vortex by a phase-diffractive element

A phase-diffractive optical element is designed to measure the topological charge of optical vortices. We use the scalar diffraction theory to calculate the far-field diffraction patterns. The simulation results show that almost all of the power of the incident beams is diffracted to the same diffraction order, and this approach is also effective for multi-ring optical vortices. We upload this phase-diffractive optical element on the liquid crystal spatial light modulator to do the experiment. The observed far-field diffraction patterns fit well with the simulation results.

Simple phase optical elements for narrowing of a focal spot in high-numerical-aperture conditions

It is shown that a decrease in the size of the focal spot produced by a high numerical aperture focusing system comes as the result of the spatial redistribution of different electric field components in the focal region. The focal distribution of electric field components can be controlled using vortex or binary phase diffractive elements. Situations for differently polarized incident laser beams are discussed and illustrated.

Design of diffractive phase element for modulating the electric field at the out-of-focus plane in a lens system

We demonstrate an efficient method to design the diffractive phase element for modulating the electric field at the out-of-focus plane of a lens system by using an equivalent Fresnel diffraction in free space. In the monochromatic illumination, we show an example to certify the validity of our method experimentally. In the nonmonochromatic illumination, we theoretically display that the spectral beam splitting and highly confined intensity can be obtained simultaneously at the out-of-focus plane, which has the potential in the solar concentrating system and optical encryption.

Fabrication of nickel diffractive phase elements for x-ray microscopy at 8 keV photon energy

The ability to resolve small details using x-ray microscopy is critically dependent on the properties of the optical elements used in the microscope’s setup. Today, Fresnel zone plates (ZPs) are widely used at synchrotron radiation sources, due to their ability to concentrate x-ray beams to spots with diameters in the tens of nanometers range. Unfortunately, fabricating ZPs with high efficiencies and sharp foci proves to be extremely challenging technologically, especially in the range of hard x-rays. A widely recognized fabrication issue is the mechanical instability of narrow and tall features made up of polymeric resists. These features often collapse either during the development or the drying of the structures due to the action of capillary forces, or in the step of electroplating because of the stress applied to them by the growing metal. The authors demonstrate a fabrication strategy that solves such issues by forming high-aspect-ratio templates in materials as hard and mechanically stable as silicon. The strategy is implemented by a combination of high-resolution lithography techniques, electroplating and plasma etching. In the present work, Fresnel zone plates with 200 nm outermost zone widths were demonstrated by electroplating nickel up to 2.1 μm height using 3.5 μm deep template structures.

Double peacock eye optical element for extended focal depth imaging with ophthalmic applications

The aged human eye is commonly affected by presbyopia, and therefore, it gradually loses its capability to form images of objects placed at different distances. Extended depth of focus (EDOF) imaging elements can overcome this inability, despite the introduction of a certain amount of aberration. This paper evaluates the EDOF imaging performance of the so-called peacock eye phase diffractive element, which focuses an incident plane wave into a segment of the optical axis and explores the element's potential use for ophthalmic presbyopia compensation optics. Two designs of the element are analyzed: the single peacock eye, which produces one focal segment along the axis, and the double peacock eye, which is a spatially multiplexed element that produces two focal segments with partial overlapping along the axis. The performances of the peacock eye elements are compared with those of multifocal lenses through numerical simulations as well as optical experiments in the image space. The results demonstrate that the peacock eye elements form sharper images along the focal segment than the multifocal lenses and, therefore, are more suitable for presbyopia compensation. The extreme points of the depth of field in the object space, which represent the remote and the near object points, have been experimentally obtained for both the single and the double peacock eye optical elements. The double peacock eye element has better imaging quality for relatively short and intermediate distances than the single peacock eye, whereas the latter seems better for far distance vision.

Optimization design of diffractive phase elements for beam shaping

An improved approach called the weighted YG algorithm for the design of the diffractive phase element (DPE) that implements beam shaping in the fractional Fourier transform domain and free space is presented. Modeling designs of the DPE are carried out for several fractional orders and different parameters of the beam for optimally converting a Gaussian profile into a uniform beam. We found that our algorithm can improve the beam shaping effect, reduce the error function, and increase uniformity of light intensity.

Energetic Bessel–Gauss pulses from diode-pumped solid-state lasers

We discuss the generation of Bessel–Gauss pulses directly from a diode-pumped solid-state laser. The laser resonator has a plano–concave configuration with the concave end mirror replaced with a diffractive phase element. As the active material, Nd-doped yttrium lithium fluoride (YLF) and GdVO4 crystals have been used. The pulsed operation is obtained by passively Q-switching the laser using Cr4+:yttrium aluminum garnet (YAG) crystals with different unsaturated transmission coefficients. When guiding the pulses out from the resonator through the laser crystal, 5–10 ns long pulses with energies of 40–50 μJ and peak powers on the order of 10 kW are obtained. Even 70 μJ is possible, but this is achieved at the expense of slightly deteriorated beam quality in the far field.