Full Spectral Image Encryption in the Infrared using an Electrically Reconfigurable Metasurface and a Matched Detector

The ability of metasurfaces to manipulate optical waves in the spatial and spectral domain provides new avenues for secure data storage. In this work, an encryption system consisting of an electrically tunable metasurface and a matched detector is presented for secure encryption of grayscale images in the 8–12 μm wavelength range. In the proposed scheme, the encrypted image corresponds to the spatially varying thermal intensity of the metasurface as captured by its matched detector. In contrast to previous metasurface‐based encryption schemes, the current approach leverages the full spectral response of the associated photonic devices to achieve secure encryption while circumventing the need for an increased device size. Using examples of single‐ and multi‐image encryption, it is shown that the optical properties of either the metasurface or matched detector alone do not reveal any meaningful information about the encrypted image, thereby validating the security of the proposed scheme. The electrical tunability of the metasurface provides additional security as the image can only be retrieved by operating it at a predefined voltage level. The results presented in this study provide intriguing possibilities for the development of compact and secure object tagging and anti‐counterfeiting applications in the infrared.


Introduction
The past decade has witnessed rapid advances in the field of optical metamaterials and metasurfaces.These are artificially engineered materials that consist of an array of metallic or dielectric elements that can be configured to realize a wide range of optical functionalities within a small form factor. [1] Owing to their ability to manipulate optical waves in the spatial and spectral domain, such devices have benefited a wide variety of DOI: 10.1002/adpr.202300254 The ability of metasurfaces to manipulate optical waves in the spatial and spectral domain provides new avenues for secure data storage.In this work, an encryption system consisting of an electrically tunable metasurface and a matched detector is presented for secure encryption of grayscale images in the 8-12 μm wavelength range.In the proposed scheme, the encrypted image corresponds to the spatially varying thermal intensity of the metasurface as captured by its matched detector.In contrast to previous metasurface-based encryption schemes, the current approach leverages the full spectral response of the associated photonic devices to achieve secure encryption while circumventing the need for an increased device size.Using examples of single-and multi-image encryption, it is shown that the optical properties of either the metasurface or matched detector alone do not reveal any meaningful information about the encrypted image, thereby validating the security of the proposed scheme.The electrical tunability of the metasurface provides additional security as the image can only be retrieved by operating it at a predefined voltage level.The results presented in this study provide intriguing possibilities for the development of compact and secure object tagging and anti-counterfeiting applications in the infrared.
In this work, we propose an encryption system that leverages the full spectral response of its constituent photonic devices to securely encrypt grayscale images in the IR.We refer to this as full spectral image encryption.Owing to the presence of two atmospheric transmission bands (3-5 and 8-12 μm), the IR wavelength range provides opportunities for remote image collection and processing with broad spectral bandwidth.This, combined with the ability of IR metamaterials to achieve simultaneous spatial, spectral, and polarization control of optical waves creates new avenues for the development of secure IR object tagging and anti-counterfeiting technologies.
The working principle of our encryption system is illustrated in Figure 1.A grayscale image (referred to as the plain image) is encrypted on an electrically reconfigurable metasurface modeled as a rectangular grid of microstructured pixels.To retrieve the encrypted image, an authorized recipient tunes the voltage of the metasurface to a predefined level and performs a pixel-wise measurement of its thermally emitted intensity, using a pixelated matched detector.The recorded spatial intensity profile of the metasurface corresponds to the decrypted plain image.Qualitatively, the signal recorded by each pixel of the detector is determined by its own spectral response as well as that of the corresponding metasurface pixel.As this signal can take a continuous range of values between 0 and 1, our approach allows us to encrypt a wide range of grayscale intensity levels without needing to increase the number of pixels of our photonic devices.Moreover, the voltage tunability of our metasurface and the requirement of a hardware, matched detector, for the decryption add extra layers of security to our encryption process.
Below we provide a theoretical investigation of our proposed scheme along with examples illustrating its utility for image encryption in the IR.We begin by describing the design of our metasurface and detector using metal-insulator-metal (MIM) microstructures. [39]We then proceed to discuss the process of encrypting grayscale images on our devices.We demonstrate that measurements of the spectrally averaged intensity or wavelength-dependent emissivity of either the metasurface or its matched detector do not reveal any meaningful information about the encrypted image.Furthermore, tuning the voltage of the metasurface away from its preselected value causes significant data loss in the decrypted image.Therefore, the stored image can only be retrieved by using the metasurface in conjunction with its matched detector while being operated at the correct voltage level.We conclude with a discussion of the theoretical limit on the number of images that can be securely encrypted on the metasurface along with an example of 26-image encryption.
We believe that our proposed encryption system will provide new avenues for the development of next-generation object tagging and anti-counterfeiting technologies in the IR wavelength range.

Designing a Metasurface and Matched Detector for Image Encryption
The first step in designing the metasurface and detector is the construction of a set of possible pixel structures that can be used for encryption.Here, we design pixels based on the MIM structure to allow for the creation of emissive/absorptive features in the IR. [40]The pixels consist of a stack of black phosphorus (BP) and Al 2 O 3 layers sandwiched between a periodic gold stripe grating at the top and a gold back reflector (left panel of Figure 2a).[43] The entire structure is supported on a semi-infinite SiO 2 substrate.The thicknesses of the top gold grating, the Al 2 O 3 spacer and the gold back reflector are taken to be 100 nm each.The periodicity of the structure is 15 μm.
The BP layer thickness is chosen to be different for the metasurface and detector pixels based on the desired functionality of the corresponding device.As illustrated in Figure 1, we require metasurface pixels for which the spectral response can be tuned by applying an external voltage.This is achieved by incorporating a 3 nm thick film of few-layer BP whose optical properties can be tuned via electrical gating. [41]In the chosen device geometry, the top gold grating and the gold back reflector can serve as electrical contacts for this purpose.We note that choosing a BP film with thickness greater than 3 nm for the metasurface pixels is not advantageous, as the electrically induced refractive index change is limited to a thickness of 2-3 nm from the BP-Al 2 O 3 interface. [44]In contrast, we choose a BP layer thickness of 30 nm for the detector pixels so as to use it as the active region.
The middle and right panels of Figure 2a show the spectral responses of the metasurface and detector pixels with a single-metal stripe per unit cell for different values of the stripe length L. The spectra are obtained by simulating the microstructures in Lumerical finite difference time domain (FDTD) (see "Experimental Section" for details of the simulation method).The optical properties of the few-layer BP film used in the metasurface pixels are given by the semiclassical Drude model described in ref. [48].For the results presented in this study,  we use a BP layer charge concentration of 10 11 cm À2 , unless stated otherwise.It can be observed that the spectra for both pixels exhibit a single resonance corresponding to their fundamental cavity mode that redshifts with an increase in the length of their respective metal stripes. [39]ualitatively, the signal recorded by a given detector pixel is proportional to the spectral overlap between its absorptivity and the emissivity of the corresponding metasurface pixel.We define the spectral overlap between the (i, j)th metasurface and detector pixels in the [λ 1 , λ 2 ] wavelength range by the following equation: where α d,(i,j) (λ), ϵ m,(i,j) (λ), and I BB (λ) represent the wavelengthdependent absorptivity of the (i, j)th detector pixel, the emissivity of the (i, j)th metasurface pixel, and the blackbody spectral radiance, respectively.We note that the blackbody spectral radiance incorporates the effect of system temperature on the signal recorded by the detector pixel.For the results presented in this study, we consider our encryption system to be maintained at a constant temperature of 350 K. From Kirchhoff 's law, the absorptivity of the (i, j)th detector pixel is equal to its emissivity.One can thus regard the denominator in Equation ( 1) as a normalization of the signal recorded by the (i, j)th pixel of the detector by its spectrally integrated thermal emittance.
To allow for the existence of a wide range of spectral overlap values between the metasurface and detector pixels, we consider microstructures consisting of three metal stripes per unit cell (left panel of Figure 2b).In such structures, the cavity formed under each of the three metal stripes contributes a single resonance, resulting in a tri-resonant spectral response.We restrict our phase space to only those pixels that generate resonances at 3 of 10 equally spaced wavelength points between 8 and 10 μm.This gives us 120 possible pixel types (number of ways of choosing 3 out of 10 channels) for both the metasurface and detector.The middle and right panels of Figure 2b show the spectral response of one pixel type each for the metasurface and detector.We consider the three metal stripes in each unit cell to be well separated, such that the corresponding cavities are uncoupled.This allows us to write the spectral response of each of the 240 pixels as a sum of the spectral responses of their constituent resonators.The middle and right panels of Figure 2b show that the spectra calculated using this approach are in good agreement with those obtained from simulations of the full three-stripe structure.We note that the spectrum of the metasurface pixel shown in the middle panel of Figure 2b has two emissivity peaks as opposed to the expected three peaks.This is caused by the spectral overlap between the emissivity peaks contributed by the metal stripes with lengths 2.21 and 2.36 μm owing to the small difference in their resonance wavelengths.
We use the 120 metasurface and detector pixels designed before to construct a matrix of overlap values, displayed in the left panel of Figure 2c.The elements of this matrix take continuous values between 0.06 and 0.46.Qualitatively, one can observe that majority of the overlap values correspond to multiple N m -N d pairs.This results in the existence of multiple metasurfacedetector pairs on which a given plain image can be encrypted, thereby introducing a degree of randomness to our encryption scheme.In this study, we discuss the encryption of 4-bit grayscale images that consist of 16 intensity levels, with pixel values ranging from 0 to 15.To encrypt such images, we must first convert the continuous range of overlap values into a discrete number of overlap bins.The histogram in the middle panel of Figure 2c shows the full phase space grouped into 80 overlap bins.Next, we describe the process of selecting 16 out of the 80 overlap bins that would correspond to the 16 intensity levels.
While choosing the 16 overlap bins, it is crucial that the selected N m -N d pixel pairs can be used to construct metasurfaces that do not reveal any information about the encrypted image unless used in conjunction with their matched detectors.To ensure this, we design metasurfaces that have a spatially random emissivity profile in the 8-12 μm wavelength range.We define the emissivity profile of our photonic devices as a 2D array of spectrally integrated emittances of their constituent pixels.For the (i, j)th metasurface pixel, this quantity is given as where ϵ m,(i,j) (λ) and I BB (λ) represent the wavelength-dependent emissivity of the (i, j)th metasurface pixel and the blackbody spectral radiance, respectively.We choose λ 1 = 8 and λ 2 = 12 μm.For a detector pixel, the emissivity in the aforementioned equation is replaced by its absorptivity in accordance with Kirchhoff 's law.
One way to generate metasurfaces with spatially random emissivity profiles is to select only those overlap bins that contain metasurface pixels spanning a wide range of ε int values.Consequently, we select 16 out of the 80 overlap bins corresponding to the 16 largest ranges of ε int values of their constituent metasurface pixels.These are indicated by yellow bars on the histogram.The right panel of Figure 2c shows the truncated overlap matrix obtained by including only the N m -N d pairs corresponding to the 16 chosen overlap bins.The excluded values are indicated by white.Note that here we display the intensity values (ranging from 0 to 15) of the 16 overlap bins such that bin 1 corresponds to intensity level 0, bin 2 corresponds to intensity level 1, and so on.
In the next subsection, we use this overlap matrix to encrypt a grayscale image and subsequently demonstrate the security of our encryption scheme by assessing the spectral responses of the generated metasurface and matched detector.by calculating the overlap values between the metasurface and detector in a pixel-wise manner.We note that in an experimental implementation, any discrepancy in the achieved spectral response of the photonic devices at a given pixel location will only have a minor impact on the intensity value of the output image at that pixel location.In order for the encryption process to be secure, the metasurface and matched detector should not reveal any meaningful information about the plain image in their spatial emissivity profiles.Figure 4a shows the emissivity profiles of the generated metasurface and detector, calculated using Equation ( 2).One can observe that these look completely random, thereby validating our selection criteria for the 16 overlap bins.To evaluate the degree of similarity between the emissivity profiles and the plain image, we calculate their similarity scores.The similarity score S between two images can take a value between 0 for dissimilar images and 1 for identical images (see the "Experimental Section" for a formal definition).The values of S for the metasurface and detector emissivity profiles are 0.063 and 0.026, respectively, thereby showing that these bear little resemblance to the plain image.

Encryption and Decryption of a Single Grayscale Image
We note that the wavelength-integrated emissivity profiles presented thus far only quantify the spectrally averaged appearance of our devices in the IR.For secure encryption, it is crucial that the plain image information is sufficiently randomized and dispersed uniformly across the entire wavelength range of operation.We evaluate our system for spectral randomness by calculating the wavelength-dependent emissivities of the metasurface and detector at 10 equally spaced wavelengths between 8 and 10 μm (Figure 4b).These are obtained by sampling the emission/absorption spectra of the constituent pixels at the desired wavelengths.It can be observed that the emissivities for both the metasurface and detector look completely random and do not reveal any meaningful information about the plain image.This is validated by the fact that the similarity score of the metasurface emissivity with respect to the plain image attains a maximum value of 0.057 at 8.4 μm while that for the detector has a maximum value of 0.096 at 10 μm.Moreover, the emissivities of the metasurface and detector have a wavelength-independent intensity, thereby qualitatively indicating that plain image data is uniformly distributed across the 10 spectral channels.The emissivity of our devices in the 10-12 μm wavelength range (not shown here) is nearly zero as the constituent pixels were designed to have resonances in the 8-10 μm range.
The electrical reconfigurability of our metasurface introduces an additional layer of security to the encryption process.To illustrate this, we present the images decrypted from the letter "D" metasurface at four different voltage levels in Figure 4c.Each voltage level is characterized by the charge concentration produced by it in the BP layer of the metasurface, ranging from 10 11 to 10 14 cm À2 (from left to right in Figure 4c).One can observe that the output image obtained for n = 10 11 cm À2 resembles the encrypted letter "D" image.This is expected, since the image was originally encrypted at the voltage level corresponding to n = 10 11 cm À2 .With an increase in applied voltage, the difference between the output images and the encrypted plain image increases.For n = 10 14 cm À2 , the output image looks completely random and does not reveal any meaningful information about the encrypted plain image.Therefore, to retrieve the encrypted image, an authorized recipient must know the voltage level at which the image was encrypted, in addition to possessing the matched detector.
Thus far, we have discussed the encryption of a single grayscale image on a metasurface and demonstrated that the encrypted image cannot be retrieved unless decryption is performed using the corresponding matched detector.In the next subsection, we explore the problem of encrypting multiple images on a single metasurface.

Secure Encryption of Multiple Images on a Single Metasurface
The total number of images that can be encrypted on a single metasurface depends on the difference between their intensity levels.Let us consider a set of M Â N pixel images that collectively assume n i,j distinct intensity values at a pixel location (i, j) (1 ≤ I ≤ M, 1 ≤ j ≤ N).These images can be encrypted on the same metasurface only when there exists at least one metasurface pixel for each (i, j) that can simultaneously take overlap values corresponding to the n i,j intensity levels.In our phase space, each metasurface pixel is capable of producing all 16 overlap levels corresponding to a 4-bit image when used with the appropriate detector pixels.In theory, this allows all possible 16 MN 4-bit images having M Â N pixels to be encrypted on the same metasurface, provided distinct matched detectors are used for their retrieval.We note that in this approach, the difference in intensities between images encrypted on the same metasurface is achieved by having a different detector for each image.This ensures that each image retrieved from the metasurface is free from any remnants of the other images encrypted on it.
As an illustration of multi-image encryption, we consider the encryption of 26 50 Â 50 pixel 4-bit images on a single metasurface (Figure 5).All 26 images have the same background and display one letter of the English alphabet, each with a different intensity value.Figure 5a displays the output images generated by performing decryption on the metasurface with the corresponding matched detectors.One can observe that none of the output images exhibit remnants of the other images encrypted on the metasurface.We present the emissivity profiles of the metasurface in Figure 5b and those of the matched detectors corresponding to the 26 letters in Figure 5c.All profiles look completely random and do not bear any visual resemblance to the encrypted images.This observation is supported by calculations of their similarity scores with respect to the plain images.The emissivity profile of the metasurface is least similar to letter "D" (S = 0.0012) and most similar to letter "R" (S = 0.067).In contrast, of all the matched detectors, the emissivity profile of the letter "B" detector has the lowest S value relative to its plain image (0.0021) while that for the letter "N" has the highest similarity to its plain image (S = 0.064).These results validate the security of multi-image encryption using our approach.

Conclusion
In this study, we proposed an encryption system consisting of an electrically tunable metasurface and a matched detector for encrypting grayscale images in the IR.The photonic devices consisted of an array of microstructured pixels and were designed such that a measurement of the spatially varying thermal intensity of the metasurface using its matched detector revealed the encrypted image.We used our encryption approach to theoretically demonstrate the encryption and decryption of a 4-bit grayscale image.With the help of this example, we showed that the spectral properties of either the metasurface or the matched detector alone do not reveal any meaningful information about the encrypted image.Furthermore, the encrypted image can only be retrieved by operating the metasurface at a preselected voltage level and using a hardware-matched detector.These observations validated the security of our encryption scheme.
We further considered the simultaneous encryption of multiple grayscale images on a single metasurface.Using the definition of our pixel phase space, we argued that it is theoretically possible to design a metasurface that simultaneously encrypts 16 MN 4-bit grayscale images having M Â N pixels each.As an illustration of multi-image encryption, we encrypted 26 images corresponding to the letters of the English alphabet on a single metasurface.Each of these images was retrievable from the metasurface by using its corresponding matched detector.We showed that none of the 26 images obtained by performing decryption on the metasurface had remnants of the other encrypted images.Additionally, the emissivity profiles of the metasurface and the 26 matched detectors revealed no meaningful information about the encrypted images.This demonstrated the utility of our approach for secure encryption of large data volumes.
We note that while this work presented a theoretical investigation of the proposed encryption scheme, recent advances in microstructured photonic devices have paved the way for its experimental realization.For instance, pixelated metasurfaces based on MIM microstructures have been used for encoding images in the mid-wave IR. [45] Additionally, MIM microstructures based on gold and BP have been developed for IR photodetection applications. [43]e believe that the results presented in this study lay the foundation for compact, on-demand data encryption systems.Additionally, the paired metasurface-detector approach for data encryption could pave the way for the development of nextgeneration object tagging and anti-counterfeiting technologies as well as provide new avenues for secure multichannel communication in the IR.

Experimental Section
Simulation Method: The metasurface and detector pixels were simulated using Lumerical FDTD.The optical constants of Au and Al 2 O 3 are taken from ref. [46] while those of the BP layer in the detector pixels were obtained from pseudopotential calculation data published by Morita. [47]The optical properties of the few-layer BP film used in the metasurface pixels were given by the semiclassical Drude model described in ref. [48].We used periodic boundary conditions along the x-direction and perfectly matched layers along the y-direction.The structure was illuminated with a plane wave normally incident along the y-axis, and reflection as a function of wavelength was recorded using a power flux monitor.As there was no transmission through the structure, absorptivity was given as 1 minus reflectivity.From Kirchhoff 's law, the emissivity of the metasurface pixels was equal to their absorptivity.
Definition of Similarity Score: The similarity score S for an image M 0 with respect to an image M was given by S ¼ covðM 0 ,MÞ covðM,MÞ where cov(M 0 ,M) refers to the covariance of M 0 and M. The similarity score took a value between 0 (totally dissimilar images) and 1 (M 0 = M).

Figure 1 .
Figure 1.Schematic depicting the working principle of our encryption system.

Figure 2 .
Figure 2. a) Spectral response of the microstructure with a single-metal stripe per period: (left panel) unit cell, (middle panel) emission spectra for metasurface pixels; and (right panel) absorption spectra for detector pixels.b) Spectral response of the microstructure with three metal stripes per period: (left panel) unit cell, (middle panel) emission spectrum for metasurface pixel with stripe lengths 2.21, 2.36, and 3.06 μm; and (right panel) absorption spectrum for detector pixel with stripe lengths 1.91, 2.64, and 3.1 μm.c) Process of selecting 16 overlap levels from the original phase space.The full overlap matrix (left panel) is grouped into 80 overlap bins (middle panel) out of which 16 bins are selected (highlighted in yellow).The selected N m -N d pairs form the truncated overlap matrix (right panel).

Figure 3 Figure 3 .
Figure3explains the process of encrypting a given 4-bit grayscale image to generate a metasurface and detector.As an example, we consider the encryption of a 50 Â 50 pixel image of the letter "D".The encryption pipeline takes the plain image and the truncated overlap matrix (generated in Figure2) as inputs (left panel).During encryption, the intensity value of each pixel of the plain image (varying between 0 and 15) is used to identify a corresponding N m -N d pair from the truncated overlap matrix.We illustrate this process for the plain image pixel at location(11,3) indicated by the green box.The pixel has an intensity value of 12, which as mentioned in the previous section corresponds to overlap bin no. 13.The middle panel of Figure3displays the N m -N d pixel pairs of the truncated overlap matrix belonging to overlap bin no. 13 (indicated by the blue points).From this set, we choose one N m -N d pair randomly (indicated by the black circle).We assign the microstructures corresponding to the chosen N m and N d to pixel location(11,3) on the generated metasurface and detector, respectively.Repeating this process for all plain image pixels generates the metasurface and detector displayed in the right panel of Figure3.The hidden image can be recovered

2 )Figure 4 .
Figure 4. a) Emissivity profiles of the metasurface and detector generated in Figure 3. b) Wavelength-dependent emissivity profiles of the metasurface and detector at 10 equally spaced wavelengths between 8 and 10 μm.c) Output images obtained by performing decryption using the metasurface and detector for four different applied voltages.In each case, the applied voltage is indicated by the charge concentration produced by it in the black phosphorus layer of the metasurface.

Figure 5 .
Figure 5. a) Output images obtained by performing decryption on the metasurface with the 26 matched detectors.b,c) The emissivity profiles of the metasurface and detectors, respectively.