Abstract
In this paper, we present the design, fabrication and optical characterization of computergenerated 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 phaseonly diffractive optical element (PODOE) 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 highorder spiral phase plates (SPPs) has been used. The phase pattern of the designed holographic DOEs has been fabricated using highresolution ElectronBeam 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 computergenerated holograms encoding information for structured light carrying OAM and phase singularities. These optical devices appear promising as highsecurity optical elements for anticounterfeiting applications.
Introduction
The increasing need for ID security and brand protection is driving global adoption of sophisticated technologies to provide considerable and effective barriers to counterfeit through the use of security holograms^{1}. In response to this demand, holographic industries devote a big afford to enhance intrinsic material properties and fabrication complexity^{2}. Likewise, fraud and counterfeiting techniques evolve and the majority of conventional security features are compromised. In order to prevent forgery attempts, the holographic patterns are constantly implemented by increasing the security level, reaching sometimes a degree of sophistication that overwhelms the original intent of fraud prevention. Even if today the development of microad nanoscale fabrication techniques can produce optical and physical features virtually impossible to counterfeit, on the other hand it is important to provide easy detection methods to the examiners^{3}.
Concurrently, optical security and encryption marked significant progress and advancement since the double random phase encoding (DRPE) method was published^{4}. In the last decades, many variations of this technique have been reported^{5,6} and more solutions have been presented and outlined in order to improve the optical security of information^{7,8}. An advantage of optical encryption has been its ability to use multiple degrees of freedom to generate complex multidimensional security keys including wavelength, polarization, 3D coordinates and complex amplitude, both in classical and singlephoton regimes^{9}.
With the intent of engineering novel easytoread security optical elements, in this work we focus on the degree of freedom represented by the decoding illumination and we design a new type of diffractive optical elements (DOEs) which correctly decode visual information only when illuminated with light owning specific spatial distributions of intensity and phase. As numerical analysis and preliminary experimental results suggested^{10}, it is possible to consider these highsecurity optical elements as a further advancement in antifraud technologies.
Traditionally, a hologram is referred to as a physicallyrecorded interference pattern between a coherent reference beam and the wave scattered by an object^{11}. The presence of the actual physical object is nowadays not necessary since the mathematical relations between object and image fields can be implemented numerically. In computergenerated holograms (CGHs), in fact, the hologram pattern is numerically designed and optimized, in terms of signal to noise ratio (SNR) and diffraction efficiency η of the reconstructed image^{12}. The physical process that allows the reconstruction of the image in farfield through a diffraction mechanism occurring in the holographic pattern is mathematically expressed by the FresnelKirchhoff diffraction equation^{13}. In the paraxial approximation, this relation provides the diffraction field O(x, y, z) generated at a distance z from a diffractive optical element, and it is given by:
where U ^{i} (x′, y′) is the complex field incident on the holographic plane, G (x′, y′) is the DOE transmission function, (x′, y′) and (x, y) are the Cartesian coordinates on the holographic plane and on the image plane respectively, and k = 2π / λ is the incident wave vector, being λ the incident wavelength. By developing the two square terms in the exponential contribution inside the integral in eq. (1), we get the following form:
where FT stands for the Fourier Transform operator. Therefore the diffraction field O(x, y, z) is related to the Fourier Transform of a modified hologram transmission function A ^{*}, calculated at the spatial frequencies (x/λz, y/λz). The transmission function A ^{*} is defined as:
and results to be the product between the hologram phase function, the incident field on the hologram plane, and the Fresnel phase factor. Previous equations serve as the basis for the computation of Fresnel computergenerated holograms with specific incident illumination.
Diffractive optics can be designed to work either in transmission or in reflection and can be engineered to manipulate either the phase or the amplitude (or both) of the input wave. Due to their higher efficiency, phaseonly holograms are far more preferable. The phase control of the holographic pattern is expressed by its phase function φ(x, y), which is given below for the two different configurations. For transmission holograms, we have:
being ϑ _{ i } ^{*} the propagation angle inside the hologram medium, n(λ) the refractive index for the given wavelength, d(x, y) the local thickness of the hologram at the position (x, y). In case of holograms working in reflection, we have instead:
defining ϑ _{ i } as the incident angle of illumination and h(x, y) as the depth of the hologram pattern at the coordinates (x, y). A schematic representation of the light path interacting either in transmission or in reflection with a multilevel phaseonly diffractive optical element (PODOE) is shown in Fig. 1.
Once the phase pattern of the diffractive optics has been computed, last equations allow the implementation of the holographic nanostructured surface.
After the seminal paper of Allen and coworkers in 1992^{14}, it is known that light beams characterized by helicoidal phasefronts possess a welldefined orbital angular momentum (OAM). Such beams are characterized by a phase term exp(iℓφ), being ℓ the amount of OAM carried by each single photon in units of ħ. Since then, light beams carrying OAM have gained increasing attention due to the wide range of uses and different possible applications^{15,16,17,18}, such as: particle trapping^{19} and tweezing^{20}, phase contrast microscopy^{21}, STED microscopy^{22}, quantumkey distribution^{23} and telecommunications^{24}. In the paraxial regime, an OAM beam can be described in terms of LaguerreGaussian Modes (LG) characterized by two indices ℓ and p, the azimuthal and radial index respectively. The azimuthal index ℓ, corresponding to the topological charge of the embedded phase singularity, represents the number of intertwined helical wavefronts. The index p represents the number of radial nodes on a plane perpendicular to the direction of propagation and it is related to the distribution of the intensity pattern in p + 1 concentric rings around the central dark zone of the phase singularity.
Different techniques have been presented to tailor the orbital angular momentum of a light beam, such as astigmatic mode converters^{25}, forkholograms^{26} and qplates^{27}. In this work, we use a method based on transmission through spiral phase plates (SPPs). SPPs are phase optical elements looking like spiral staircases, which are able to shape an incident Gaussian beam into an OAM beam, as shown by Beijersbergen et al.^{28}. Common SPPs are transparent optical elements whose thickness h increases as a function of the azimuthal coordinate according to:
where n _{ SPP } is the refractive index of the SPP material, n _{0} is the refractive index of the surrounding medium, usually air, and λ is the impinging wavelength.
Detailed work has been done in order to optimize both design and fabrication procedures for the generation of highorder OAM beams with nonzero radial index^{29}. This is feasible by introducing radial πdiscontinuities on the SPP phase pattern Ω_{SPP}:
where L _{ p } ^{ℓ} is the associated Laguerre polynomial and w _{0} the beam waist of the generated LG beam. In our case, the SPP plays the fundamental keyrole to generate the light beam decoding the specificallydesigned computergenerated hologram, expanding the range of possible application whenever information needs to be stored with increased security and counterfeit prevention. With respect to other optical encryption techniques, a deterministic distribution of intensity and phase is exploited for information encoding into a holographic form. The input light state can be labelled with a set of indices, given arbitrarily, defining the intensity distribution and phase pattern in the selected family of beams. In the specific, we considered beams carrying orbital angular momentum of light and generated with custom spiral phase plates, identified by the OAM content ℓ and the radial index p. Samples have been fabricated by electronbeam lithography on polymethylmethacrylate (PMMA) resist layer, spun over a glass substrate, in highresolution mode, providing highquality phaseonly diffractive optics. In addition, since this fabrication technique, however extremely precise, is slow and expensive, we investigated the possibility to replicate the fabricated optics with faster massproduction techniques, such as nanoimprinting^{30}, which allows higher throughput and much lower production costs. The optical response has been tested on an optical table, showing a correct reconstruction of the encoded information under illumination with the expected OAM field. Conversely, if the computergenerated hologram is illuminated with a common Gaussian beam, the noise is too high to make the image recognizable (Fig. 2). This study refers to a particular case of computergenerated holography, therefore the reader should consider ‘hologram’ standing for ‘computergenerated hologram’ throughout the text.
Results
Holographic design and computation
The realization of a computergenerated hologram can be schematically split into three steps: analysis, implementation and fabrication. The first one consists in the understanding of the physical process governing the formation of the image encoded on the holographic substrate. Therefore, the hologram phase pattern is implemented through the development of a numerical algorithm, which considers both the physics governing the image formation and the restrictions imposed by the selected fabrication process, e.g. limited resolution and spatial mesh. Finally, the designed pattern is realized, with the properly selected fabrication techniques and protocols.
An Iterative Fourier Transform Algorithm (IFTA) represents a proper choice for the design of computergenerated holograms, due to the capability of generating an optimized phase pattern by bouncing back and forth the information between two spaces related by a Fourier transform, i.e. the hologram plane and the image plane. In the specific, the developed code implements a modified version of the GerchbergSaxton (GS) algorithm, which since its first publication in 1972^{31} has known many improvements and applications for the calculation of computergenerated holograms^{32,33,34}, with particular attention to phaseonly CGH^{35,36,37}, due to their higher efficiency.
In Fig. 3(d), a scheme of the GS algorithm implemented in MATLAB^{®} environment, is shown. The process begins by collecting the experimental amplitude field generated by the selected SPP. The phase pattern, for given indices p and ℓ of the generating SPP, is assumed to have an azimuthal dependence of the form ℓφ, plus radial jumps equal to π in correspondence of the zeros of the associated Laguerre polynomial L _{ p } ^{ℓ}, as given by eq. (7). Previous interferometric analyses^{38} on the OAM beams generated by the fabricated SPPs confirm the validity of this assumption. The collected intensity distribution and the corresponding azimuthal phase gradient define the complex input field for the computation of the hologram phase pattern.
We chose three different images with increasing complexity for the design of the associated CGHs. The first one exhibits the official Logo of the University of Padua (UniPD logo) and is characterized by having a bitmap format with pure black and white pixels (Fig. 3(a)). The second one shows two intersecting ‘H’ characterized by having grayscale 8 bit/channel (Fig. 3(b)), while the third one represents a wolf portrait with a 8 bit/channel grayscale showing many finer details (Fig. 3(c)). In all cases, the input image is centered in the signal window with a size of 200 × 200 pixels, while the total size of the diffractive optical element is composed of 400 × 400 pixels (Fig. 4(c)).
Starting from the input signal enclosed by a signal window on the image plane, the farfield is brought back to the hologram plane using the inverse Fast Fourier Transform and normalized with respect to the incident illumination, as suggested by eq. (2). The quadratic term in eq. (3) is included in the azimuthal phase of the input field, therefore the image of the computed Fresnel hologram will be at focus on a plane at a distance z from the hologram (fixed at 40 cm). Within this iteration procedure, the numerical algorithm generates a continuous complex spectrum in the holographic plane, denoted with H _{ i } in Fig. 3(d). Since the selected lithographic protocol can reproduce phaseonly patterns with discretized values of phase, this restriction must be considered and properly implemented in the code. For the benefit of the reader we briefly outline the salient points of the algorithm and we refer to Supplementary Information S2 for more details. A quantization operator Q is applied in the hologram plane, within each iteration, performing a direct amplitudeelimination and a direct partial quantization of phase^{39}. This operator can be factorized into two parts Q = P·A, where P and A are the phase and the amplitude operators, acting on the hologram phase and amplitude respectively. During this step, the hologram transmission function H _{ i } is first normalized by its amplitude, obtaining a phaseonly complex spectrum A[H _{ i }] = exp(iΩ), where the phase Ω varies continuously, modulo 2π, in the range [0, 2π). Afterwards, by applying the operator P, a partial discretization is carried out over a discrete finite set of M angles {γ _{ j }} (j = 1, …, M), usually equidistant, being M the number of thickness levels of surfacerelief hologram pattern to be fabricated. This is performed by dividing the range [0, 2π) into M intervals, centered on the values γ _{ j }, and substituting at each point (m, n) of the hologram the phase Ω_{mn}, modulo 2π, with the nearest neighbour in the set {γ _{ j }}. Such phase quantization is partial, since the halfwidth of the intervals is not fixed and increases linearly with the iteration number until the whole unitary circle is covered. Therefore, at each iteration, the phase values falling inside the intervals are substituted as described above, otherwise they are left unchanged until the next iteration.
This quantization process is obviously expected to affect the final quality of the image, introducing noise in the reconstruction plane. However, this noise can be reduced by replacing the amplitude within the signal window with the desired amplitude of the original signal, while leaving both phase and amplitude free outside the signal window, where the noise is substantially relegated. Then, the loop is repeated using the output signal as input field for the next iteration step (see Fig. 4).
With the progress of the iterations, the algorithm converges to an optimized design of the holographic pattern. The convergence can be checked in realtime evaluating the signal to noise ratio (SNR) and the diffraction efficiency η ^{40}. The SNR gives the correlation between input signal and reconstructed signal and is defined as:
where h _{ i,mn } is the signal at the pixel (m, n) at the ith step and h _{ 0,mn } is the corresponding signal in the reference image. The diffraction efficiency η is typically defined as the ratio of the signal energy within the signal window chosen as an active part of the reconstruction plane, and the total energy in the reconstruction (object) plane, given by:
where W stands for the set of pixels inside the signal window.
Fabrication
Phaseonly diffractive optical elements are fabricated as surfacerelief patterns of pixels. This 3D structures can be realized by shaping a layer of transparent material, imposing a direct proportionality between the thickness of the material and the local phase delay. Electron beam lithography is the ideal technique to fabricate 3D high resolution profiles^{41,42}. By modulating the local dose distribution, a different dissolution rate is induced in the exposed polymer, giving rise to different resist thicknesses after the development process. In this work, the SPP and DOE patterns were written on a PMMA resist layer with a JBX6300FS JEOL EBL machine, 5 nm resolution, working at 100 KeV with a current of 100 pA. The substrate used for fabrication is glasscoated ITO with low surface resistivity (8–12 Ω) in order to ensure a good discharge of the sample during electron beam lithography. After the exposure, the resist is developed in a temperaturecontrolled developer bath for 60 s.
At the experimental wavelength of the laser (λ = 632.8 nm), PMMA refractive index results n _{PMMA} = 1.489 from spectroscopic ellipsometry analysis (J.A. Woollam VASE, 0.3 nm spectral resolution, 0.005° angular resolution). The height h _{ k } of the pixels of the kth layer for normal incidence in air is given by
being M the total number of phase levels, k = 1…, M. The fabricated CGHs are 400 × 400 pixels square matrices with M = 16 phase levels. Each pixel is 3.125 × 3.125 μm^{2}, therefore the total area of each sample is 1.250 × 1.250 mm^{2}.
Inserting the given laser wavelength and PMMA refractive index in the previous equation, we get: h _{1} = 0 nm, h _{16} = 1213.2 nm, Δh = 80.9 nm. The quality of the fabricated structures has been assessed using optical microscopy (Fig. 5(a)), Scanning Electron Microscopy (SEM) (Fig. 5(b)) and Atomic Force Microscopy (AFM) (Fig. 5(c,d)). Experimental height values have been compared with the nominal ones exhibiting a remarkable accordance within the experimental errors, estimated considering surface roughness (see Supplementary Figure 1). Spiral phase plates have been fabricated in PMMA on a transparent glass substrate with the same lithographic process, defining the spiral phase ramp with 256 levels^{29}. The total thickness, regarding the given wavelength and PMMA refractive index, is 1294.1 nm.
Optical characterization
The optical characterization setup was mounted on an optical table (see scheme in Fig. 6). The Gaussian beam was emitted by a HeNe laser source (HNR008R, Thorlabs, λ = 632.8 nm, waist w _{0} = 240 μm, power 0.8 mW). The polarized beam (LPVISE100A, Thorlabs) was resized and focused on the selected spiral phase plate. By adjusting the distances from the laser source to the first lens of focal length f _{1} = 25 cm and the SPP, the beamwaist is reduced to w _{1} = 130 μm. Then the transmitted OAM beam was collimated by a second lens of focal length f _{2} = 7.5 cm in ff configuration, and a beamsplitter was used to both collect the intensity profile of the generated OAM beam content and to correctly illuminate the holographic pattern. The field profile was collected with a CCD camera (DCC1545M, Thorlabs, 1280 × 1024 pixels, 5.2 μm pixel size, monochrome, 8bit depth). Farfield images were collected using Nikon D750 camera.
The hologram phase pattern for the same image (Fig. 3(b)) has been computed for three different OAM beams: (p, ℓ) = (1, +1) (Figs. 7(a–d.1)), (p, ℓ) = (2, +1) (Fig. 7(a–d.2)), (p, ℓ) = (0, +2) (Fig. 7(a–d.3)). As expected, the image which correctly appears under the right illumination (Fig. 7(c.1–3)) is not recognizable with standard illumination (Fig. 7(d.1–3)).
Then, the fabricated hologram encoding the wolf portrait (Fig. 3(c)), computed for SPP illumination with indices (p, ℓ) = (1, +1), has been tested with several SPPs shaping the incident illumination, in order to test the optical response of the optical element to input OAM beams different from the optimal one. Again, for wrong SPP illumination, noise increases and the image is no longer clearly visible (Fig. 8).
A softlithography replica of a holographic PMMA master has been optimized in order to setup an easy, fast and lowcost fabrication procedure. The optical and morphological characterizations of the generated copies demonstrate exceptional reliability in replicating the hologram 3D structures (see Fig. 9 and supplementary information Figure S3).
Since the CGH phase patterns are computed to be illuminated by a specific intensity and phase spatial distribution, the image reconstruction is expected to be sensitive to misplacements of the decoding beam with respect to the sample position. In order to analyse the farfield image quality as a function of the sample displacement, we selected the computergenerated hologram encoding the UniPD logo decoded for OAM illumination with indices (p, ℓ) = (1, +1) and we collected the farfield image under the correct beam indices and size but for increasing radial and axial shifts of the beam. Specifically, since the input beam is axially symmetric, we moved the hologram along the xaxis positive direction, on a plane perpendicular to the beam axis and located on the beam waist. As Fig. 10(a) shows, the reconstructed image is gradually destroyed for increasing lateral displacement and the details are no longer clearly distinguishable for shift values beyond 90 μm, when the SNR, calculated with respect to the aligned case, drops to values below 10. This threshold value corresponds to 33% of the beam waist radius (w _{0} = 0.275 mm) of the decoding beam and about 14% of the hologram halfsize (0.625 mm). For greater shifts, the zeroorder term becomes dominant and the finest details of the image are not recognizable. However, it is worth noting that this effect is less remarkable than in the case of wrong input illumination, i.e. with wrong radial and azimuthal indices.
The alignment along the beam axis is less critical, as shown in Fig. 10(b), where several farfield images are reported for increasing shift in the z direction up to 2 cm, which corresponds to 26.7% of the focal length f _{2} used for OAMbeam focusing on the sample (f _{2} = 7.5 cm). This tolerance in the hologram position is referable to the amount of the Rayleigh range for the considered beam, which is around 18.8 cm, one order of magnitude greater than the considered zmisplacement. A shift of 2 cm in the zdirection corresponds to an increase in the beam radius around 0.5%, therefore the intensity distribution is roughly the same. However, the incident wavefront is not planar, since the sample is not placed at the beam waist, therefore the image is expected to be focused at a slightly shifted position.
In supplementary information section S3 additional figures are reported regarding the previous analysis. In addition, in order to further enhance the possibility of future applications in Track and Trace using these diffractive optical elements, an image representing a QRcode has been computed and analyzed under OAM illumination (see supplementary information Figure S7) and its tolerance to lateral shifts of the incident beam was checked.
Discussion
In this work, we present the first attempt of a complete design and fabrication procedure of computergenerated holograms encoding information for illumination with structured light beams carrying specific distributions of intensity and phase. In particular, we consider beams carrying orbital angular momentum, generated with highorder spiral phase plates enabling both the transfer of topological charge to the input beam and the generation of a multiring intensity pattern. An iterative Fourier transform algorithm has been implemented for the computation of an optimized phase pattern for the selected input image and incident field. The computation of the hologram pattern for the given input beam imposes a onetoone correspondence between the generated hologram and the SPP and therefore increases the security level of these diffractive optics, so that the encoded information cannot be addressed without the correct illumination key. This result has been demonstrated with the design and optical test of several samples, fabricated with highresolution electronbeam lithography. The optical characterization demonstrates that the encoded image appears, as expected, only when the hologram is illuminated with the correct input illumination, otherwise the information is not recognizable, neither with standard Gaussian illumination nor different OAM beams.
Considering security applications, someone could in principle attempt to brutallyforce the information encoded in the hologram by sequentially generating a varying input illumination by spanning all the values of the indices (p, ℓ) over an arbitrary set until the correct values are guessed, for instance by using a computercontrolled spatial light modulator. A hacking attempt of this kind can be prevented or at least dissuaded by the following considerations. Firstly, a crucial role is represented by the geometrical size of the beam. As theoretically demonstrated in^{43}, the indices p and ℓ define an orthonormal set of modes only for a specific value of the beamwaist parameter, therefore beams with the same ℓ and different p are no more orthogonal if they differ in the beam size as well. As numerically shown in^{10}, for a given set of indices, the image of the encoded hologram clearly forms only in the neighbourhood of the optimal beamwaist. Differently to p and ℓ, which can assume only discrete integer values, the beamwaist is a continuous parameter and the dimensionality of the decoding optical key is therefore remarkably increased. Secondly, the complexity of the decoding optical key can be improved by considering a superposition of two or more OAMbeams with different values of ℓ and p, generating more complex distributions of amplitude and phase^{44}, instead of a symmetric one with integer OAM as presented in this work. Therefore a further parameters set would be represented by the different weights of the several modes constituting the input beam, which are continuous parameters assuming in principle any values in the range (0, 1).
Electronbeam lithography provides a highresolution lithographic technique, allowing the fabrication of concealed security holograms with a resolution far higher than common dotmatrix optical devices^{45,46}, usually fabricated with interferentiallithography systems. One may consider the cost of the EBL as a drawback, but in fact it is the cost of the increased quality and resolution of the holograms. Moreover, we have demonstrated the replica process of one highquality hologram to produce several identical copies by soft lithography methods, which are wellconsidered as a supereconomical technique.
In supplementary information S5, the replica process of a holographic PMMA master is explained in details. Soft lithography technique provides an exceptional reliability in reproducing the exact 3D structures in an easy, fast and low cost process.
The experimental optical bench exploited in this work for the optical characterization of the fabricated diffractive optics, is clearly cumbersome and unhandy in the view of commercial and industrial applications. However, further improvements and integration can be performed. In particular, the SPP can be embodied to the laser source exploited for hologram inspection. The SPP phase pattern will be properly optimized for the size of the beam exiting the laser, and a lens term can be integrated in the SPP phase profile in order to focus the OAM beam at a proper distance, without the need of a further lens as shown in Fig. 6. Misalignment analyses showed a good tolerance in the hologram positioning with respect to the beam focal plane, provided misplacement is one order of magnitude lower than the Rayleigh range of the beam. On the other hand, the alignment of the hologram with respect to the OAM beam singularity is much more critical. A threshold misalignment around 30% of the beam waist radius has been shown in case of OAM beam with indices (p, ℓ) = (1, +1), corresponding to about 90 μm in the considered optical setup. However, this value is far greater than the accuracy of mechanical alignment systems, therefore such security optical elements could be detected and decoded by electronicallycontrolled readers which control the position of the input beam with a micrometric precision. A by hand inspection would require an increase of this tolerance value, for instance increasing the hologram size and the waist of the decoding illumination.
By engineering this new type of diffractive optical elements, which correctly decode visual information only when illuminated with light owning a specific spatial distribution of intensity and phase, we expand the available range of security optical devices and of possible applications of structured light, whenever information needs storing with increased security and counterfeit prevention. The miniaturized size of the fabricated optics allows them to be either integrated or concealed onto greatersize optical elements, such as 2D/3D holograms and other types of overt security devices to be applied on documents and products.
Methods
Numerical simulations
A custom MATLAB code based on IFTA was implemented in order to compute the phaseonly diffractive optical element specifically designed for OAM illumination (see Supplementary Information S2 for details about the algorithm).
Electron beam lithography
All 3D multilevel structures have been fabricated in a 2 µm thick PMMA resist with a molecular weight of 950 k (kg/mol), spincoated on a 1.1 mm thick ITO coated soda lime float glass substrate and prebaked for 10 min at 180 °C on a hot plate. For the greyscale lithography step, a dosedepth correlation (contrast curve) was used. Contact profilometry was performed to determine the remaining resist heights. Dosetoclear value (complete removal of PMMA) was found to be 566 µC/cm^{2}. CGH patterns were written with a JBX6300FS JEOL EBL machine, 12 MHz, 5 nm resolution, working at 100 KeV with a current of 100 pA. The presence of the ITO layer was necessary in order to ensure a good discharge of the sample during electron beam lithography. A dose correction for the compensation of proximity effects has been applied. This compensation is required both to match layout depth with the fabricated relief and to obtain a good shape definition, especially in correspondence of the phase steps. Exposed samples were developed under slight agitation in a temperaturecontrolled developer bath for 60 s. Deionized water: isopropyl alcohol (IPA) 3:7 was found to be the most suitable developer, giving optimized sensitivity and contrast characteristics as well as a minimized pattern surface roughness at 20 °C. After development, the samples were gently rinsed in deionized water and blowdried using nitrogen flux. Different techniques have been used in order to assess sample quality: tappingmode atomic force microscopy, optical microscopy and scanning electron microscopy.
Softlithography replica
A suitable amount ofthe elastomer Sylgard 184 polydimethylsiloxane (PDMS)base is mixed with the catalyst in a weight ratio of 10:1 respectively, stirred for a while, and then cast onto the surface of the EBL fabricated master. During the PDMS pouring and mixing, creation of bubbles is inevitable, so the container is placed in a desiccator for30–45 minutes to degas it and remove the trapped air bubbles. The sunken master with PDMS prepolymer is then placed in an oven at the temperature of 100 °C to be cured for 35 minutes, then was left in a freezer for 5 to 10 minutes to cool down. This shrinks the PDMS slightly and helps when peeling the samples out of their molds.
To fabricate the replica of the mold, a UVcurable photopolymer (Norland Optical Adhesive 74) is dropped onto a glass substrate. The PDMS mold is overlaid on it (with the patterned side facing the liquid) and is pushed a bit to form the contact. Finally, the photopolymer is cured under UV light for 30 seconds, after which the PDMS mold is carefully peeled off to get the final replica.
Optical characterization
The characterization setup was designed and assembled on an optical table with gimbal piston isolators (refer to Fig. 6). The Gaussian beam was emitted by a HeNe laser source (HNR008R, Thorlabs, λ = 632.8 nm, waist w _{0} = 240 μm, power 0.8 mW). The polarized beam (LPVISE100A, Thorlabs) impinges on the corresponding spiral phase plates, mounted on a sample holder with micrometric drives (ST1XYS/M, Thorlabs, travel 2.5 mm, resolution 10 μm). By adjusting the distances from the laser source to the first lens of focal length f _{1} = 25 cm and the SPP, the beamwaist was reduced to w _{1} = 130 μm. Then the transmitted beam was collimated by a second lens of focal length f _{2} = 7.5 cm and a 50:50 beamsplitter was used to both collect the intensity profile of the generated OAM beam content and to correctly illuminate the holographic pattern. The field profile was collected with a CCD camera (DCC1545M, Thorlabs, 1280 × 1024 pixels, 5.2 μm pixel size, monochrome, 8bit depth). The holographic sample was fixed on a vertical XY translation mount with micrometric drives (ST1XYS/M, Thorlabs, travel 2.5 mm, resolution 10 μm), and the farfield was projected on a white screen. The projected farfield images were collected using Nikon D750 camera. During misalignment analyses, the farfield was recorded using a second DCC1545M (Thorlabs) CCD camera. The hologram was moved with respect to the beam axis by rotating the ST1XYS/M micrometric screw, providing a shift of 10 μm per graduation. For zmisalignment analysis, both hologram holder and CCD camera were mounted on an optical rail (RLA150/M, Thorlabs) with mm graduation.
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Acknowledgements
This study has been supported by FSE project HOLOAM 21058421212015 funded by Veneto Region. The authors gratefully thank Maurizio Motta of Holo3D Srl for the interesting discussions during this work.
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G.R. developed the numerical codes for computergenerated holograms phasepattern calculation and design for the lithographic process. R.R. performed CGH design and optical characterization and test. G.R. performed misalignment optical tests. M.M. carried out the fabrication with electronbeam lithography and performed microscopy and AFM characterizations. E.M. realized softlithography replica in collaboration with R.R. P.C. performed AFM and SEM analyses. F.R. proposed and supervised the project. All authors contributed to the writing of the manuscript.
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Ruffato, G., Rossi, R., Massari, M. et al. Design, fabrication and characterization of Computer Generated Holograms for anticounterfeiting applications using OAM beams as light decoders. Sci Rep 7, 18011 (2017). https://doi.org/10.1038/s41598017181477
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