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Optical secret sharing with cascaded metasurface holography
Philip Georgi, Qunshuo Wei, Basudeb Sain, Christian Schlickriede, Yongtian Wang, Lingling Huang, Thomas Zentgraf
TL;DR
The paper addresses how encrypted information can be physically split across shareholders without revealing the secret from individual optical shares. It uses cascaded metasurface holograms whose phase contributions reconstruct a distinct secret image, and demonstrates alignment-based translational multiplexing. The idealized two-phase-pattern case is fully secure, whereas the experimental scheme may contain exploitable correlations from its additional image constraints.
Problem
Existing metasurface multiplexing generally provides multiple channels in one layer but does not physically split information channels across multiple shareholders.
Method
The authors optimize phase-only Fourier holograms on separable metasurfaces so individual layers identify shareholders while stacked layers optically reconstruct a shared image; relative translation adds multiplexing.
Results
The demonstrated stacks reconstruct distinct cascaded holographic images with low apparent cross-talk, and repositioning the layers produces different images; the idealized two-pattern scheme is fully secure.
Takeaways & Limitations
Cascaded metasurface holography provides an optical platform for secret sharing that can scale in stack size and keys and can be adapted to threshold schemes.
Takeaways & Limitations
The experimental security guarantee is not established because simultaneous optimization of single-layer and other-combination images may create exploitable phase-mask correlations.
Abstract
from arXiv · showhide
Secret sharing is a well-established cryptographic primitive for storing highly sensitive information like encryption keys for encoded data. It describes the problem of splitting a secret into different shares, without revealing any information about the secret to its shareholders. Here, we demonstrate an all-optical solution for secret sharing based on metasurface holography. In our concept, metasurface holograms are used as spatially separable shares that carry an encrypted message in form of a holographic image. Two of these shares can be recombined by bringing them close together. Light passing through this stack of metasurfaces accumulates the phase shift of both holograms and can optically reconstruct the secret with high fidelity. On the other hand, the holograms generated by the single metasurfaces can be used for identifying each shareholder. Furthermore, we demonstrate that the inherent translational alignment sensitivity between the two stacked metasurface holograms can be used for spatial multiplexing, which can be further extended to realize optical rulers.
Introduction
The paper introduces cascaded metasurface holography as an optical secret-sharing framework that separates encrypted holographic information across physical shares. Stacked shares reconstruct a distinct secret image, while alignment sensitivity enables translational multiplexing and scalable extensions.
- Motivation: One-layer metasurface multiplexing provides multiple information channels but does not physically split those channels across shareholders.Multilayer layouts provide physically separable layers for distributing information.
- Optical secret sharing: Each metasurface encodes a phase-only Fourier hologram whose single-layer reconstruction identifies its shareholder, while stacking two layers produces a different shared image.The demonstrated stack uses metasurfaces separated by 100 µm and illuminated with circularly polarized light.
- Optical secret sharing: Light through cascaded layers accumulates both phase delays, allowing the secret hologram to be distributed across phase-mask combinations without revealing it from one mask alone.In the ideal zero-distance case, the phase masks add pixelwise, and different single masks can form the same cascaded phase pattern.
- Experimental results: Single-layer images are reconstructed with low background noise, while six cascaded combinations achieve similar quality without apparent single-image cross-talk.The cascaded image quality nevertheless deteriorates under small translational misalignment.
- Design method: The design algorithm simulates single and cascaded image formation, compares outputs with targets, and minimizes total error using automatic differentiation and gradient optimization.The forward pass uses FFT-based image calculation, angular-spectrum propagation with zero padding, and mean squared error.
- Extensions: Relative translation supplies a multiplexing dimension: repositioning the metasurfaces reconstructs different holographic images, and the framework is scalable to more shares, stack sizes, and threshold schemes.The paper also identifies holographic seals and optical rulers as extensions of alignment-sensitive cascaded holography.
Supplementary Information
The supplementary-information section accompanies the paper on optical secret sharing with cascaded metasurface holography and lists its authors and affiliations.
- The paper is titled “Optical secret sharing with cascaded metasurface holography.”
- The author list includes Philip Georgi, Qunshuo Wei, Basudeb Sain, Christian Schlickriede, Yongtian Wang, Lingling Huang, and Thomas Zentgraf.
- The authors are affiliated with Paderborn University in Germany and Beijing Institute of Technology in China.
1. Optical setup for measuring the holographic images
The setup prepares and analyzes light transmitted through cascaded metasurface holograms using polarization control, microscope collection, and Fourier-space imaging. Polarization optics also suppress unwanted single-layer zeroth-order artifacts, while cascaded measurements require co-polarized detection that cannot remove every zeroth-order contribution.
- Optical path: A tunable laser passes through a linear polarizer and quarter-waveplate before illuminating the cascaded metasurfaces, whose transmitted light is collected by a microscope objective.A second quarter-waveplate and linear polarizer filter the polarization state before a CMOS camera images Fourier space.
- Optical path: The experimental setup uses linear polarizers, quarter-waveplates, metasurface holograms, and a microscope objective to measure holographic images.These components are identified in the setup schematic.
- Artifact filtering: Polarization optics partially filter unwanted artifacts in measured Fourier images by removing the zeroth order from single-layer holograms.The transmitted co-polarized light produces the single-layer zeroth order that is filtered out.
- Artifact filtering: Cascaded measurements use co-polarized detection because light ideally changes circular polarization twice while passing through the two metasurfaces.Components that switch polarization only once are filtered out, but unchanged-polarization light produces an unremovable zeroth-order spot.
2. Alignment sensitivity for the cascaded images
Cascaded image quality is strongly dependent on lateral alignment but substantially more tolerant of separation changes. The experiments also show that designed lateral shifts can select distinct reconstructed images, while very small gaps introduce practical near-field concerns.
- In-plane alignment: A 10 µm (2-pixel) x-direction shift makes the cascaded image unrecognizable because pixel matching is required between the phase masks.Propagation between the metasurfaces allows neighboring-pixel interaction, softening the alignment requirement compared with colocated masks.
- Out-of-plane alignment: Out-of-plane movement is more tolerant than in-plane movement: roughly 500 µm of additional separation is needed before image deterioration appears.A minimum experimental separation of 60 µm was achievable, while a 4f system can in principle provide zero separation with aberration-related resolution limits.
- Distance-related effects: Very small metasurface separations can produce unwanted near-field interactions such as Fabry Pérot modes.Without a 4f system, the practical minimum distance is constrained by the experimental setup.
- Distance-related effects: Fabry Pérot effects were not visibly observed when changing the metasurface distance, because the 10 nm incident-light bandwidth averages them out.Transmission-mode design is expected to keep multireflection influence small in the final image.
- Out-of-plane alignment: The cascaded image is sharpest at a 100 µm metasurface distance in the first experimental case.Figure S3 varies the z-separation by moving set A away from the second metasurface.
- Spatial multiplexing: A designed 25 µm (5-pixel) lateral shift separates the sharp reconstructed images ‘3’ and ‘4’.The measured shift agrees with the designed displacement, with a fading noisy pattern between images rather than an organic transition.
3. Optical secret splitting with polarization multiplexed metasurfaces
The polarization-multiplexed framework expands cascaded metasurface encryption by encoding multiple phase masks across polarization-selective holograms. Measurements show visible single-layer images, while cascaded images can retain single-image relics and zeroth-order artifacts from fabrication errors.
- Framework: The framework combines one polarization-independent metasurface in Set A with two polarization-multiplexed metasurfaces in Set B.Set B uses different multiplexing methods, increasing information capacity per hologram but requiring higher-quality fabrication.
- Framework: Each Set B metasurface carries two polarization-selectable phase masks, yielding one Set A hologram, four Set B holograms, five single-layer images, and four cascaded images.Different single letters are encoded and positioned to overlap with their corresponding single-layer images.
- Nanostructure concepts: The polarization-independent metasurface uses symmetric square structures, whereas the birefringent metasurface uses rectangular nanofins to encode separate x- and y-polarization phase masks.The square structures transmit only co-polarized light, while the birefringent nanofins accumulate different phases along the two in-plane directions.
- Nanostructure concepts: The Pancharatnam-Berry metasurface encodes two independent phase masks by combining orientation-dependent geometric phase with a shape-dependent offset phase.The rectangular nanofins act as local half-wave plates for circular input polarization.
- Measurements: All single metasurface holograms are clearly visible, but co-polarized measurements show considerable zeroth-order spots caused by fabrication-design deviations.The cross-polarized zeroth-order spot remains but is removed by polarization filters.
- Measurements: Cascaded images contain their corresponding single letters because systematic errors create superpositions of target and constant phase masks.The first cascaded case shows a weaker A than S, while the second excludes A through polarization filtering.
4. Nanostructure design
The metasurfaces are designed with RCWA-based nanostructure maps tailored to polarization response, geometric phase, and isotropic phase coverage. The selected geometries provide high transmission, multiplexed phase control, or broad 2π phase coverage depending on the design.
- Simulation framework: RCWA optimizes cuboid silicon nanofins on ITO glass in a square lattice, while periodic simulations approximate each isolated nanostructure.The simulations use a fixed height of 600 nm, a 500 nm period, and sweep length and width from 70 nm to 300 nm in 5 nm steps.
- Pancharatnam-Berry design: The Pancharatnam-Berry design selects nanofins with high cross-circular transmission and low co-circular transmission at 800 nm.A 190 nm length and 130 nm width balance fabrication accuracy and broadband behavior; multiplexing geometries cover the full 2π offset-phase range.
- Birefringent design: The birefringent design smoothly covers 0 to 2π phase modulation for both x- and y-polarization channels while maintaining high amplitude.This enables simultaneous selection of structures for the two polarization channels.
- Isotropic design: The isotropic design covers the full 2π phase range with average amplitude above 95% across the selected side-length range.Efficiency decreases considerably only at the 155 nm resonance dip.
5. Spectral efficiency measurement
Spectral efficiency measurements were used to compensate systematic fabrication deviations from the design. The fabricated Pancharatnam-Berry metasurface reached its measured efficiency maximum at a shorter wavelength than predicted.
- Wavelength selection: The measurement wavelength was set to 740 nm because the measured relative conversion-efficiency maximum shifted shorter than the calculated spectrum.Figure S9 compares measured and RCWA-simulated relative conversion efficiency, with design and measurement wavelengths marked at 800 nm and 740 nm.
- Fabrication deviations: A 5% deviation in nanostructure dimensions can produce a 30 nm shift toward shorter wavelengths in numerical simulations.Possible contributors include refractive-index deviations and structure-dimension errors, especially nanofin height.
6. The gradient optimization scheme
The hologram design uses explicit forward simulation with adaptive gradient optimization to generate high-quality single-layer and cascaded images across experimental cases.
- Optimization approach: The scheme combines an explicit forward calculation with a gradient optimizer for designing metasurface phase masks.The forward model calculates image formation and the optimizer minimizes differences between target and calculated images.
- Optimization approach: The adaptive optimizer evaluates two candidate steps and the starting point, then changes the learning rate according to the lowest associated error.This compares points along the gradient or momentum direction to speed convergence.
- Experimental cases: The translational case modifies the forward pass by periodically expanding the quadratic phase mask and cropping the propagated field according to relative translation.The polarization case instead treats the multiplexed metasurfaces as two independent phase masks.
- Optimization performance: Around 200 iterations were sufficient for convergence, with roughly 0.4 s required per iteration on an Intel i5-7500 PC.The reported calculation time is linked to the hologram's low pixel count.
- Image-quality metric: Correlation coefficients quantify reconstructed-image quality by comparing reconstructed and target images using covariance and variances.The coefficient is defined from COV(T, R) and the variances of T and R.
- Reconstruction results: All first-case simulated correlation coefficients exceeded 0.95, while translational results were similar and polarization results mostly exceeded 0.95.In the polarization case, the single hologram for letter A reached 0.82, attributed to its use in more reconstructions.
7. Discussion on cryptographic security strength
The two-pattern, zero-distance case is fully secure because one phase mask reveals no information about the cascaded image or the other mask. This guarantee does not extend to the experimental scheme, where joint optimization may create exploitable correlations, although no known attack currently breaks it.
- The simplest two-pattern, zero-distance scheme is fully secure: knowing one phase mask provides no information about the cascaded image.Every cascaded phase pattern can still be created for any known phase mask.
- Revealing one phase mask does not change the Shannon entropy of the second phase mask.
- The experimental scheme lacks this formal guarantee because optimizing additional single-layer and combination images imposes boundary conditions that might create exploitable correlations.
- The authors do not conclude that the method is insecure and report no currently known method that breaks the encryption scheme.