Active Metasurfaces for Non‐Rigid Light Sail Interstellar Optical Communication

The non‐rigidity of the nanophotonic metasail platform and the intense imparted optical force from the terrestrial laser source lead to deformations during the propulsion stage. These deformations must be taken into consideration due to their potential adverse impact on communication performance. Alterations in the shape of the sail body result in varying angles of incidence and polarization components observed by the photonic unit cell, significantly impacting their intended performance. Based on this premise, this paper proposes utilizing a reflective all‐dielectric, low‐power active metasurface that dynamically compensates for the effects of deformation and facilitates beam‐steering for communication purposes among different light sails in interstellar space. Configured as p‐n multi‐junction layers, the constituent elements of the metasurface enable modulation of carrier concentrations through multigate biasing. Through electrostatic simulations, it demonstrates that the required permittivity modulation of Δε=−0.03$\Delta \epsilon = -0.03$ can achieve a wide phase span of 320°. Furthermore, it has investigated the effect of the presence of non‐functional portions in the far‐field radiation pattern of the light sail and highlighted the critical role of tunable elements in mitigating its impact. The obtained results hold great promise for realizing successful interstellar downlink communication between such gram‐scale nano‐crafts and Earth.


Introduction
Human endeavors to explore the universe have always been constrained by the maximum achievable speeds using chemical propellants and the fuel capacity of current spacecraft.Due to these limitations, conventional spacecraft would require thousands of years to reach the nearest habitable exoplanet, Proxima Centauri B, located in the Proxima Centauri star system.

DOI: 10.1002/adts.202300359
This renders such an approach impractical for human space exploration, given our life expectancy.Consequently, the scientific community has initiated a search for new methods to address this challenge. [1]he success of solar sail-based missions, such as the Interplanetary Kite-craft Accelerated by Radiation of the Sun (IKAROS), has sparked significant interest in utilizing gram-scale nanocrafts.These nanocrafts can be accelerated to relativistic velocities within a few minutes through propulsion by Earth-based high-power laser arrays. [2,3]his novel and intricate concept has enabled the Breakthrough Starshot initiative to plan for deploying a swarm of nanoprobes for a flyby mission to the habitable zone of the nearest star system, located approximately 4.2 light years away from Earth (Figure 1).This approach could potentially reduce the travel time from thousands of years to around 20 years. [4]ong-distance optical space communication has recently garnered significant attention due to its high photon efficiency, even in the presence of background space radiation. [5,6]The concept of interstellar communication differs from terrestrial communication scenarios in that the paramount factor is energy efficiency. [7,8]While spectral efficiency holds importance in terrestrial communication scenarios, interstellar communication necessitates the efficient utilization of energy due to the size, power, and mass limitations of the probe.As a result, research in this area is more focused on achieving higher photon efficiencies. [9]Overall, launching a low-mass interstellar probe to Alpha Centauri presents numerous technological challenges.One of the main obstacles is establishment of a robust downlink communication system.The success of the Starshot program hinges primarily on the feasibility of transmitting the acquired data from the interstellar medium and the targeted star system back to Earth. [9]he communication aspect of the light sail can be explored in various ways; however, the primary objective of the current work is to introduce a potential nanophotonic platform for establishing probe-to-probe and probe-to-Earth downlink communication links.Furthermore, the freedom to choose the aperture size of the sail and the power supply for the onboard transmitter can help mitigate the challenges posed by the vast distance between the spacecraft and Earth-based receivers.One of the potential architectures for the Starshot program involves sending swarms Figure 1.The schematic depiction of the proposed gram-scale interstellar probe (not drawn to scale) aims to establish a relaying-based downlink communication channel.Each light sail consists of a multifunctional, all-dielectric nanophotonic platform that provides the required stable beam-riding stability and acts as a reflector antenna for the incident beam radiated by the payload in the front (Starchip).The magnified subfigure also illustrates a small array of communication unit cells that have undergone random geometrical variations during the propulsion stage.
of low-mass nanocrafts equipped with the necessary technology for tasks such as capturing images and sensing the magnetic field, etc. [10] This specific launch configuration can alleviate adverse communication-related consequences stemming from navigational errors, thermal failure, and similar issues in individual probes.Additionally, owing to constraints in power and mass, it is anticipated that each nanocraft will comprise specialized equipment rather than encompassing all required components.The critical enabling factor for the repeated launch of numerous light sails is the comparatively minor cost of additional launches compared to the expenses linked with constructing the propulsion and communication infrastructure. [10]The mentioned requirement necessitates the deployment of an active platform at the aperture of the light sail, capable of beam-steering when required.
Significant advancements in computational photonics and nanofabrication have opened up exciting possibilities in the field of optical nanostructures, particularly in the manipulation of nanoparticles using optical forces.[13][14][15][16] The ability to precisely engineer the interaction between the incident beam and the meta-atom forms the foundation of the concept of propelling a photonic membrane to relativistic velocities using a high-power optical beam.19][20][21] A recent study has also demonstrated the potential to control and harness solar radiation pressure using active graphene in plasmonic metasurfaces. [22]Metasails can be seamlessly integrated into a single ultralight platform, minimizing the spacecraft's size, weight, and power (SWaP).The meticulous control of wavefront manipulation, facilitated by the metasurface, allows for precise management of the propulsion laser's reflection direction, achieving self-stabilized beam-riding.A study of the sail's motion trajectory using rigid-body dynamics illustrates that establishing a parabolic or conical phase gradient across the sail and controlling the spacecraft's center of mass distance lead to achieving complete stability throughout the propulsion stage. [17]Nonetheless, ultralight structures like metasails are susceptible to vibrations and deformations during deployment and propulsion scenarios.[25] Nevertheless, the radiation pressure they encounter does not parallel that of laser-propelled metasails.In the latter, a meter-scale ultrathin dielectric membrane must maintain its shape and functionality while being propelled by a high-power laser beam.Research has additionally indicated that augmenting the sail's structural durability can be achieved by increasing its radius of curvature.This enhancement, consequently, opens up possibilities for investigating the potential of employing greater beam power and decreasing the distance needed for acceleration. [26]While accounting for the impact of induced deformation during the propulsion stage is imperative, it is crucial to incorporate regional deformation into the design and evaluation process of the transmitter aperture. [27]Geometrical variations wield significant influence over the performance and functionality of the designed nanophotonic antennas.Moreover, these variations in shape can lead to diverse angles and polarization states being observed across different elements of the metasurface.The resonant behavior exhibited by the metasurface can be markedly affected by the incident beam's polarization and angle, contingent upon the specific supported resonance type.Consequently, the components integrated into the metasail aperture need to be designed to mitigate the impact of these variations on their optimal performance.Given the wavelength's scale, even subtle deformations can noticeably impact the metasurface performance.Therefore, the nanoantennas must possess the capability to restore the phase of the scattered light at the aperture of the deformed sail. [28][31][32][33][34][35][36][37][38][39] This endeavor arises from the challenge encountered by graded-pattern photonic metasurfaces due to their fixed structural parameters.42][43][44][45][46][47][48] Among all these factors, the free carrier effect is particularly intriguing for space-borne applications.[51][52] Electro-refraction, defined as the refractive index alteration due to changes in carrier concentration within the active layer, underpins this modulation mechanism.Individual biasing lines allow for a more pixelated design without introducing extra cross-talk between the elements.Notably, the active region's volume and the electro-refraction strength are two factors reliant on the tuning mechanism, influencing the dynamic phase span of the active metasurface. [53]The intensity of the interaction between light and matter is a pivotal factor in elevating the efficiency of tunability and phase agility in metasurfaces.This attribute can be seen as the exclusive approach to controlling the engineering of tunability in metasurfaces by manipulating the geometry of the meta-atom.A prevalent technique to amplify electro-refractive phase modulation is applying active materials with elevated doping levels, like Transparent Conducting Oxides (TCOs). [46]For instance, indium-tin-oxide has found extensive application in the design of active metasurfaces owing to its elevated doping level (N > 10 19 cm −3 ), which facilitates an epsilon-near-zero transition through bias voltage application in the near-infrared regime.This transition, in turn, enhances the interaction between light and matter.Nevertheless, notable amplitude fluctuations of the metasurface upon phase modulation are unavoidable due to the considerable carrier-induced dissipative loss. [52]One method to mitigate this challenge involves using a low-loss all-dielectric metasurface and arranging the meta-atom into p-i-n or p-n configurations.This strategy enlarges the volume of active regions and mitigates the influence of material loss induced by carriers while maintaining reliance on moderate doping levels.Such an approach effectively tackles the constraint of limited active region volume and the issue of high dissipative loss in tunable metasurfaces.This, in turn, yields a refractive index modulation of approximately Δn ≈ 0.01.Generally, metasurfaces that support lower-order dipolar Mie modes, like electric dipole (ED) or magnetic dipole (MD), lack sufficiently high quality factor (Q-factor) to achieve noteworthy phase spans in response to slight refractive index changes.It is evident that to leverage the aforementioned tuning mechanism with minor permittivity variations, an alldielectric nanophotonic resonator with a high Q-factor becomes essential.Despite the numerous challenges associated with onboard communication technologies, we present a novel solution to address the requirement of an active platform capable of performing beam-steering for communication between the probes.Additionally, our research highlights the crucial role of utilizing a tunable metasail to decouple the optical and scattering properties of the light sail from the physical shape of the aperture.
In this study, we initially introduce the optical responses of the all-dielectric unit cell and the nature of the excited resonant mode.Considering the presence of mechanical stress during the acceleration stage of the mission, we examine the impact of slight variations in the dimensions of the unit cell on the resulting resonance.Subsequently, we present the results of the electrostatic simulation related to the proposed electro-optical tuning mechanism, aiming to achieve slight permittivity variations and enable meta-atom tunability.Following the successful induction of the required refractive index modulation in the proposed nanophotonic structure, we explore the response of the active meta-atom to allowed permittivity variations of Δ < −0.03.Furthermore, we obtain the angular reflection response of the active metasurface to comprehend the behavior of the metasail during deformations.With a comprehensive collection of unit cell responses at our disposal, we analyze the steering performance of a prototype metasail comprised of 100 × 100 unit cells.In this stage, we consider a sample moderate deformation pattern aligned with realistic optomechanical simulations.We investigate the effect of these local deformations on the electromagnetic response of the array and underscore the necessity of employing a dynamically tunable metasurface platform to prevent signal loss.

Tunable Building Block Design
In this section, we aim to devise a reflective metasurface with a high Q-factor, an amplitude response approaching unity, and a 2 phase coverage.Additionally, it is imperative to employ materials with ultralow absorptivity to prevent overheating during the propulsion stage, where a high-power laser beam is directed at the sail.The utilization of dielectric metasurfaces in the nearinfrared regime offers a twofold advantage by circumventing the ohmic losses associated with plasmonic structures and enabling the excitation of electric and magnetic resonances within conventional resonator geometries.In this pursuit, it has been demonstrated that traditional all-dielectric Huygens' metasurfaces exhibit low Q-factors for their electric and magnetic dipole modes, resulting in minimal sensitivity to marginal changes in the resonator's refractive index. [52]A higher Q-factor and more localized mode can enhance the interaction between light and matter, primarily due to the extended photon lifetime.Bound states in the continuum (BIC) represent long-lived states confined within the structure.These are often referred to as dark modes in contrast to bright modes, which can radiate away from the resonator. [54,55]hile pure BICs cannot be directly generated from an external source, a quasi-BIC (QBIC) can be induced either by perturbing the structural symmetry or under oblique incidence. [56]This mode displays a highly angle-dependent response and long inplane propagation lengths attributed to its extended QBIC resonance, leading to spatial non-locality.In stark contrast to local resonances, this non-local behavior restricts the use of QBIC resonance-based structures in specific beamforming functionalities where the mutual coupling of unit cells is crucial.Recent developments indicate that by strategically introducing controlled geometric perturbations to symmetry-protected scattering from QBIC resonances, wavefront manipulation capabilities can be realized. [57]An alternative method to attain a high Q-factor mode involves utilizing higher-order Mie resonances. [58]Exciting higher-order modes necessitates expanding the resonator's size within a particular wavelength range, thereby intensifying the interaction of the multipoles among adjacent resonators.This occurrence can significantly diminish the efficiency of beamsteering.Likewise, substantial research has been conducted on reflective metasurfaces with high Q-factors.As can be seen, by decreasing the number of DBR pairs from eight to six, there is minimal degradation in the performance of the metasurface structure.e,f,g,h) The normalized amplitude of the electric and magnetic fields in the x-z and y-z planes, respectively, is illustrated.It should be noted that due to the presence of eight pairs of DBR layers, the structure size is relatively large, making it difficult to display the entire structure in the near-field figures.Additionally, the fields are concentrated in the nanodisk and the buffer layer.Therefore, we have only plotted the region where the disk and the buffer layer are present.
To eliminate sensitivity to incident polarization, we have employed an arrangement involving an array of silicon nanodisks positioned atop a silica buffer.The entire structure is backed by a distributed Bragg reflector (DBR) comprising eight quarterwave stacks of silicon and silica layers, each with a height of  0 ∕4n, where  0 = 1500 nm and n represents the refractive index of the respective materials.Throughout our simulations, we assumed n Si = 3.5 (uniformly within the disk) and n SiO 2 = 1.4,and these simulations were conducted using the commercial software COMSOL Multiphysics.The structure is subjected to the normal incidence of a transverse electric (TE) polarized plane wave, with the electric field oriented towards the e y direction.As shown in Figure 2a, the diameter of the nanodisk and the periodicity of the structure along e x and e y are characterized by D disk and Λ, respectively.In our pursuit of discovering a high-Q resonance while bypassing the reliance on higherorder Mie modes and QBIC resonances, we set the periodicity at Λ = 690 nm.Importantly, this chosen periodicity ensures the unit cell's functionality within the sub-wavelength region, which is crucial for our mission.We will discuss its impact on steering performance in the following section.After conducting a comprehensive parametric examination, we derived the remaining dimensions as D disk = 470 nm, h disk = 500 nm, h si = 107.5 nm, h silica = 260.4nm, and h buffer = 470 nm.Throughout our study, we incorporated eight pairs of DBRs.In general, a metallic substrate is commonly employed to achieve maximal reflectivity within the near-infrared spectrum. [51]However, within the domain of laser-propelled metasails, this approach is not feasible due to the high absorbance of metal within that particular wavelength range, which can bring about thermal collapse and endanger the success of the mission. [59]It is noteworthy that we have only considered the nanodisks in obtaining the results in this section.Nevertheless, we have investigated the performance of the metasurface in the presence of a biasing line in Section S6 (Supporting Information).Next, we plotted the amplitude and phase of reflectance in the wavelength range from 1548 to 1554 nm in Figure 2b,c, respectively, to illustrate the ultrahigh-Q resonance (Q ≈ 9760) within the proposed nanophotonic structure in the unbiased case.Based on the amplitude and phase of the reflectance, it is evident that the resonance exhibits an ultrahigh-Q behavior with a 2 phase agility.As we will discuss, a sharp resonance is crucial to enable the tunability of the structure using our available electro-optical tuning technique.Figure 2d presents an investigation into the influence of the number of DBR pairs on the metasurface's response.The demonstrated trend shows that the Q-factor of the resonance in a reflective metasurface diminishes as the number of DBR pairs decreases.With six pairs of DBR, a high-Q resonance is achieved, providing an advantageous trade-off between total mass and reflectivity assessment.The normalized nearfield distribution of the electric and magnetic fields within the unit cell in the z − x and z − y planes can be observed in Figure 2e-h, respectively.Notably, the normalization in each nearfield plot is independent of the others, as the primary focus is on presenting the electric and magnetic field patterns rather than discussing their relative amplitudes.As depicted in Figure 2e-h, a significant enhancement in the amplitude of the electric and magnetic fields occurs in both the nanodisk and the buffer, indicating a considerably enhanced photon lifetime within the resonator.The nearfield plots suggest that the resonance corresponds to a Fabry-Pérot (FP) resonance.However, due to the nature of the induced ultrahigh-Q resonance, the induced fields predominantly remain within the resonator.This characteristic enhances the sensitivity of the resonance to slight variations in the nanodisk's refractive index, a topic that will be elaborated upon in the following discussion.
[62] The initial step involves depositing a DBR structure consisting of 8 pairs of Si/SiO2 quarter-wave layers onto a glass substrate using plasma-enhanced chemical vapor deposition (PECVD).Following this, a SiO2 dielectric spacer is introduced to the sample through PECVD.Subsequently, a layer of silicon can be deposited onto the sample using a PECVD system.To form the sub-wavelength nanodisk, the upper Si layer is then patterned using EBL and subsequently dry etched in a plasma environment.Furthermore, the use of multigate biasing has recently been exhibited in electro-optically tunable metasurfaces featuring vertical gating configurations that rely on mechanisms of free-carrier modulation.Sputtering techniques can be employed, utilizing boron and phosphorous dopants (B+ and P-) to achieve the desired background carrier distribution in the vertical direction through diffusion and ion implementation.The multijunction structure can be biased from the side, with each doped region serving as a gate surface addressable by a gate electrode.To facilitate this, low-resistance contact pads can be established at the periphery of the metasurface, providing access to the p-type and n-type doped regions while being wire-bonded to a biasing module.The experimental demonstration of multigate biasing for multi-junction p-n structures has also been witnessed in the electro-optical modulation of waveguides. [63]66][67][68] It is imperative to acknowledge that the Starshot project is in-herently a long-term endeavor, necessitating substantial advancements across diverse domains of optical and photonic nanofabrication.
Given the challenging operating conditions and mechanical stresses inherent to the considered application, we have conducted a thorough investigation into the susceptibility of the presented nanophotonic meta-atom to variations in its geometric dimensions.The vulnerability in our problem arises due to three critical factors, namely the diameter, height of the disk, and pitch size.Figure 3a illustrates the obtained amplitude and phase of the reflectance as a function of wavelength and disk height.The impact of a minor alteration in the disk height (h disk ) becomes apparent as it results in a subtle spectral shift in the metasurface response.Similar analysis has been carried out for the periodicity (Λ) and disk diameter (D disk ), as depicted in Figure 3b,c, respectively.It should be noted that the incidence beam is considered to be a normal s-polarized beam where the electric field is e y -directed.After discussing the metasurface's performance without any permittivity modulation, we shifted our focus to realizing permittivity variation within the proposed nanophotonic platform using the electro-optical tuning mechanism.The details of the electro-optical simulation are provided in Section S2 (Supporting Information).For this purpose, we divide the meta-atom disk and the biasing lines into three pairs of p-n multi-junctions, each with an identical thickness along the vertical direction.We apply uniform doping of hole and electron carriers, each with a moderate concentration of P = 10 18 cm −3 and N = 10 18 cm −3 , respectively, as shown in Figure 2a.In the absence of an applied bias voltage (V = 0 V), the diffusion of electron and hole carriers across the junctions leads to the creation of a potential barrier zone.As a result, charge-depletion layers are formed on both sides of the junctions, characterized by an absence of free charge.In the case of forward bias, where the p-type region attains a higher positive potential compared to the n-type region, the gradual increment of the bias voltage causes the potential barrier zone to shrink.This contraction facilitates the accumulation of electrons and holes across the volume of the n-type and p-type regions.On the other hand, by employing the reverse biasing technique and rendering the n-type region more positive relative to the p-type region, the length of the depletion region expands with decreasing voltage, leading to an augmented potential barrier.We utilized the Lumerical Device solver, which employs a finiteelement-based method to self-consistently solve the Poisson and drift-diffusion equations for computing the bias-dependent carrier distribution within the p-n multi-junction.Additionally, during our simulations, the n-type layers are grounded, and the bias voltage is applied to the p-type regions through aluminum contacts.The results obtained are depicted in Figure 4, where Figure 4a,b display the spatial distribution of electrons and holes along the z-axis of the nanodisks.This figure reveals the existence of two distinct carrier dynamics patterns that can be distinguished.These patterns are separated by a critical voltage threshold denoted as V T ≈ 1.1 V.When the applied bias voltage is below this threshold (V < V T ), the depletion layer length reduces as the bias voltage increases, and conversely, it expands as the bias voltage decreases.Notably, when the applied bias voltage exceeds the threshold voltage (V T ), a uniform accumulation of carriers occurs in both the n-type and p-type layers, ensuring constant index modulation within the multi-junction.Next, the carrier-induced change in the refractive index and extinction coefficient can be calculated as [69] : where  0 is the permittivity of free space, n 0 is the refractive index of undoped silicon, m * h = 0.39m 0 and m * e = 0.27m 0 are the conductivity effective mass of hole and electron carriers while m 0 being the electron mass, μ e = 80 cm 2 V −1 s −1 and μ h = 60 cm 2 V −1 s −1 .Employing the formalizm mentioned above, we have obtained variations in the refractive index of silicon based on the applied bias voltage.Figure 4c displays the real part of  The amplitude and phase of the reflectance of the proposed unit cell are shown as functions of the induced Δ using the applied bias voltage to the nanodisk.The modestly doped p-n multi-junction structure exhibits a relatively minor change in refractive properties induced by carrier modulation.This results in a dynamic phase shift of 320 degrees in reflection, accompanied by near-unity reflectance amplitude.The obtained large phase span is attributed to the significant enhancement of the electric fields within the active regions.c) Schematic depiction of the p-and s-polarized plane wave illumination.The reflectance amplitude (d) and phase (e) as a function of incident angle and wavelength for a s-polarized beam (TE).f,g) Depict the same for a p-polarized (TM) incident beam.The small magnitude of the spectral shift resulting from variations in the incident angle indicates the localized nature of the resonance, which is an essential characteristic for achieving optimal beam-steering outcomes.h,i) The necessary Δ for adjusting the phase to the ideal case is shown as a function of different incident angles for the TE and TM cases, respectively.It is evident that utilizing the available electro-optically tunable platform makes it feasible to correct for deformations that result in a local incident angle of the refractive index of silicon, depicting bias voltage values ranging from V b = −1.2V to V b = 1.5 V.The imaginary component of the refractive index, along with an additional investigation into the impact of losses on the performance of the proposed active metasurface, is detailed in Section S1 (Supporting Information).In the quest for an electro-optically tunable reflective metasurface, we have adopted an upper limit for the refractive index change of silicon, set at Δn = −0.0045(uniformly across the nanodisk).This value corresponds to a maximum alteration of Δ = −0.03 in the real part of silicon's permittivity.To achieve the utmost phase span in the active scenario, we elevated the height of the unit cell to h disk = 500.5nm, while leaving the other dimen-sions unaltered.Following the guidelines as mentioned earlier, Figure 5a,b illustrates the calculated amplitude and phase of the reflectance of the proposed unit cell as a function of the silicon permittivity variation for the considered operating wavelength of  = 1550.6nm.
As evident in Figure 5a,b, the reflectance amplitude remains close to unity for permittivity variations ranging from Δ = 0 to Δ = −0.03,while achieving a 320 • phase span at the operating wavelength of  = 1550.6nm.Given the substantial distance between the target and Earth, maximizing the reflectivity of the tunable metasurface becomes crucial, a requirement effectively fulfilled by our design.As discussed previously in the introduction section, it is essential to explore the angular sensitivity of the device under various forms of deformation.As depicted in Figure 5c, it is possible to break down the incident field into TE and transverse magnetic (TM) modes in which the magnetic and electric fields are parallel to the plane of incidence, respectively.Figure 5d-g illustrates the amplitude and phase of reflectance for the active unit cell as a function of both wavelength and incident angle for the TE and TM cases, respectively.The depicted figures indicate a spectral shift of less than 3 nm for a 10 • change in the incident angle in both cases, highlighting the localized nature of the supported mode.This shift is notably smaller than the spectral shift observed in non-local guided mode resonance at the same wavelength, which exhibits an almost 130 nm shift for a similar 10 • variation in the incident angle. [58,70]t is important to mention that the interruptions observed in the TE angular response outcomes stem from the induced resonances within the DBR.However, it is worth noting that these resonances have a negligible impact on the overall performance and can be considered during the design process.Moreover, by moving toward the steeper incident angles, the Q-factor increases in both cases, and the resonance becomes sharper.As discussed previously, one of the main reasons that the tunable metasurfaces can become handy is their ability to correct the induced errors in the phase profile of the metasail due to caused geometrical distortion. [71]Thus far, we have studied the effect of oblique incidence on the response of the unbiased metasurface.
However, to conduct a more thorough investigation into the relationship between the induced Δ and various angles of incidence  i , we have generated plots depicting the phase of reflectance for the TE and TM cases, as presented in Figure 5h,i.As can be observed from these figures, in the TE scenario, the sensitivity of the unit cell to angles of incidence below  i < 3 • is predominantly within the −0.03 < Δ < 0 range.Nonetheless, since the spectral shift of resonance is larger for steeper angles of incidence, the tunability of metasurface response necessitates the induction of a positive Δ > 0. Similarly, for the TM case, the wide phase span can be accomplished for incident angles  i < 3 • when −0.03 < Δ < 0. Furthermore, for  i > 3 • , larger Δ is required.By slightly modifying the operation wavelength, the wide phase span should still be achievable for the biased metasurface under oblique light illumination for both polarization.

Performance Assessment of the Metasail
As previously mentioned, the success of the Starshot project hinges primarily on effectively transmitting gathered scientific data from the targeted star system to Earth.In discussions concerning establishing the downlink communication link, a recurring suggestion is to utilize the newly launched probes as relays to convey the information to terrestrial receivers. [10]This concept is appealing as it can harness the network of light sails to allocate otherwise unused power, thereby enhancing the performance of the communication link.Another advantage of deploying a constellation of light sails is the ability to distribute distinct functionalities among various nanocrafts.In this context, individual probes are not obligated to carry the complete sensing and imaging equipment suite, potentially leading to heightened overall system efficiency and versatility. [72]In this work, for the first time to the best of our knowledge, we have examined the impact of local sail deformations on the communication performance of the sail.Given the substantial size difference between the metasail and its unit cells, attempting a full-wave simulation of the entire array (which could encompass trillions of elements) without using simplifications would be unfeasible.Therefore, we have chosen an approximate methodology based on the local periodicity assumption, demonstrating excellent agreement with the results of full-wave simulations. [73]In this method, calculating the local field over the entire array makes it possible to obtain equivalent surface current, acting as a secondary current source that generates the electromagnetic field throughout the surrounding space except within the array itself.More precisely, the equivalent electric and magnetic currents on the surface of a light sail can be written as [74] J s (r where n and ŕ denote the metasurface surface normal vector and position vector, respectively.Also, E(r) and H(r) are the calculated electric and magnetic field at any observation point r which can be expressed as [74] E where μ 0 and  0 are the permeability and permittivity of the free space, k 0 is the free space wave number, |r − r ′ | is the distance between the source and the observation point.
The actual metasail will consist of trillions of unit cells, which renders electromagnetic modeling computationally challenging.In this study, we have employed a prototype containing a 100 × 100 meta-atom array to facilitate our investigation.Moreover, the incident beam is considered to have a Gaussian profile with a spherical phase profile given by exp ( −R 2 w 2 inc ) where w inc = 80 μm is the beam spot size.][77] During our studies, we have adopted a specific deformation pattern for the sample, the equation of which is provided in Section S4 (Supporting Information).In this pattern, the local incident angle  i remains below 3 • .
Our decision to restrict our studies to local incident angles less than  i < 3 • is grounded in the underlying physical mechanism employed for electro-optical tuning within the proposed active unit cell.It is pertinent to mention that our current tuning methodology permits the introduction of a negative Δ in the silicon material constituting the nano disk.Upon a meticulous examination of Figure 5h,i, it becomes evident that for incident angles falling below  i < 3 • , it is feasible to achieve the desired phase modulation in the reflected beam from the active unit cell through the judicious utilization of a negative Δ. Notably, in the instance of TM incidence (Figure 5i), even larger local incident angles  i < 5 • can be effectively compensated for, given the prerequisite of a negative Δ.However, it should be emphasized that, as discerned from the TE incidence results (Figure 5h), the proposed active unit cell exhibits limitations in compensating for phase variations when the incident angle exceeds  i < 3 • .This limitation is attributed to the necessity of a positive Δ, a parameter unattainable via our current methodology.In order to maintain the generality of our findings and ensure their robustness, we have constrained the range of variation in local incident angles of the elements to Figures 6a,b illustrate the considered deformation pattern for a 100 × 100 array and the corresponding local incident angles for each unit cell.It is important to note that our aim here is not to investigate the voltage recalculation process; rather, our primary focus is to examine the effectiveness of using a tunable platform to mitigate the adverse impacts of local deformation on the steering capabilities of the reflective metasail.Furthermore, the practical metasail is expected to be of a considerable scale, reaching meter-scale dimensions, and is composed of numerous segments, each potentially encompassing hundreds of unit cells.Subsequently, during the propulsion phase, the aperture of considered large-scale structure undergoes deformation, which endures beyond the propulsion phase, marking the beginning of the downlink communication scenario.At this stage, the primary objective of the voltage recalculation process is to determine the local deformation angles of each segment constituting the aperture.This task is achieved by employing detectors positioned on the payload. [71]These detectors calculate the deformation amplitude and the local incident angle by comparing the phases of the received signals from various spatial points across the aperture.Once the deformation amplitude (the alteration in the height of metasurface segments concerning their initial flat condition) and local incident angles (the incident angle that each deformed segment senses) are determined, it becomes possible to ameliorate the phase disturbances caused by deformation through the reevaluation of the requisite bias voltage.Finally, using Figure 5h,i the necessary bias voltage for achieving the desired phase gradient across the metasail can be computed.
Next, we assume that the voltages across the metasail are adjusted to collimate and direct the incident beam emitted by the Starchip towards  = 10 • and  = 60 • , which can be analytically written as Φ t = −k 0 y sin () cos () − k 0 x sin () sin () where k 0 denotes the wave vector in free-space.We assumed that the incident beam acquires a spherical phase profile given by where R s = 690 μm is a parameter to control the curvature of the wavefront (a surface containing equi-phase points), and R is the distance of a point on the aperture from the center of the sail.It is noteworthy that the selection of R s value will depend on the final architecture of the nanoprobe, and more particularly the distance between the payload and the aperture, which is dictated by the optomechanical requirements. [19]However, to address potential damage to the laser source (attached to the payload) during the propulsion stage, which could result in various aberrations, we introduced random noise in the range of [0,1] to the spherical phase profile of the beam upon arrival at the sail's aperture.To compensate for the curved wavefront of the incident wave, the metasurface should possess a conjugate of that spherical phase profile.As a result the defined phase gradient over the aperture of the metasurface is given by Φ = Φ t − Φ i .Figure 6c,d demonstrates the computed far-field radiation pattern of the active metasail and the real part of the reflected e y -directed electric field (E y ) in the x-z plane, respectively, after undergoing the deformation pattern depicted in Figure 6a.This result indicates that the metasail cannot achieve the necessary beam-steering, leading to the beam diverging toward different angles.This issue holds particular significance in deep space exploration missions, where the distances are considerable.Even slight deviations in the polar plot can result in the beam being directed far from the intended target point.[80][81][82] To assess the impact of metasurface tunability on the beam-steering performance, the defined phase profile across the metasurface has been updated to account for local phase disturbances resulting from structural deformation.In this case, the biasing voltages accross the metasurface are updated to compensate for the induced deformation phase, hence the phase defined accross the elements can be written as Φ = Φ t − Φ i − Φ d .Figure 6e shows the far-field radiation pattern of the metasail after the voltage update process.It is evident that the radiated beam from the sail is precisely steered and collimated toward the targeted direction.Nevertheless, Figure 6f demonstrates the real part of the electric field at the longitudinal x-z plane, which clearly shows the steering to the desired angle as a result of updated bias voltages.
Another important issue in the context of relativistic travel is the interaction of the light sail with the interstellar medium, which consists of dust grains with a diameter of approximately 1 μm.The engagement of dust particles with the aperture of the metasail can destroy a small fraction of the sail. [83]Also, gas bombardment can significantly damage the nanocraft's surface, particularly through track formation caused by heavy elements.Depending on the material composition, the spacecraft's surface can potentially suffer damage after traversing a gas column of a certain density along the path to -Centauri. [84]Another crucial obstacle to laser-driven nanocrafts is the extreme temperatures the sail will experience during the propulsion stage.This problem can worsen if harsh environmental conditions in deep space, such as interstellar dust particles, are taken into consideration.The localized heating caused by a solitary dust particle, which possesses optical absorption properties, can initiate a thermal runaway phenomenon that swiftly propagates and leads to the complete destruction of the sail. [85]One of the proposed techniques to mitigate the aforementioned burn-away process is isolating the absorptive regions of the sail, allowing them to burn away individually, as a means of reducing the overall damage. [85]dditionally, it should be noted that, like any other nanophotonic platforms, the meta-atoms utilized in this context are susceptible to structural perturbations that can malfunction certain components.To account for such complications, we have implemented a segmented design pattern in which each segment consists of 10 × 10 elements.To test the communication performance of the sail after encountering issues in some segments that render them non-functional, we have included plots of the far-field pattern and the real part of the reflected electric field in Figure 6h,i.These figures clarify that the sail continues to work effectively and can steer the reflected beam in the desired direction, despite the significant power spill-over in other directions.Up to this point, our discussion has revolved around the advantages of employing an active metasurface to inhibit the scattering of reflected power in various directions caused by variations in geometrical form.However, the advantages of using tunable elements in situations where specific segments are damaged or non-functional remain uncertain.To better demonstrate the essential nature of recalculating the required bias voltages following any deformation, we investigated a catastrophic scenario in which the sail undergoes both deformation and partial failure of its components.This scenario is detailed in Section S5 (Supporting Information).It is worth noting that the extent of local deformation in each segment can be determined by measuring the distance between different parts of the sail's aperture and the starchip. [86]ith this goal in mind, we have examined the advantages of employing the active metasurface to alleviate the geometrical imperfections that may arise in the sail during different stages.[89][90] Furthermore, active metasurfaces can generate diverse structured light beams, such as vortex beams.[93][94] Dynamic analog signal processing, facilitated by active photonic metasurfaces, can be envisaged in the upcoming generations of relativistic probes due to their low power consumption compared to other signal processing techniques.Moreover, active metasurfaces introduce unprecedented functionalities in the realm of space-time photonic design.This is attributed to their capability to actively manipulate the properties of light across both spatial and temporal domains. [95][98][99] Launching relativistic probes of this nature necessitates advancements in crucial onboard and terrestrial technologies.One such advancement is pulse compression, which has been demonstrated using high-Qfactor time-modulated metasurfaces. [9,100]Notably, many of the applications mentioned, including signal processing, pulse shaping, and optical non-reciprocity, can be readily achieved using the proposed active all-dielectric platform. [101,102]As the number of adjustable components increases, managing the biasing structure becomes exceedingly intricate.However, employing the perimeter-controlled tuning architecture can alleviate this complexity. [103,104]It is important to acknowledge that the Starshot project is a long-term endeavor, allowing ample time to develop the required propulsion and communication technologies.Nonetheless, concerning the necessary communication technologies, finalizing the onboard transmitter technology is imperative prior to the inaugural launch.

Conclusion
In conclusion, we have highlighted the necessity for an active metasurface platform capable of recalculating voltage to rectify the phase disturbance induced by geometric deformation.Therefore, we have introduced a low-power, all-dielectric silicon/silica reflective active metasurface platform through numerical analysis that can be integrated into the available metasail aperture.The proposed active element can dynamically provide a broad phase span (320 • ) while maintaining a relatively high reflectance amplitude.However, the significant enhancement in the photon lifetime within the meta-atom results in a notable level of sensitivity.This sensitivity enables a wide range of phase tunability through slight variations in the silicon nanodisk's permittivity.The sensitivity of the obtained nanophotonic response to the variations in the geometrical parameters is investigated.Moreover, the electrostatic simulation results related to the proposed electro-refractive tuning mechanism are obtained and discussed, demonstrating the possibility of achieving the required Δ using only three layers of p-n multi-junction within the disk.To comprehend the behavior of the metasail in deformation cases, we have employed a prototype comprising 10,000 unit cells.This approach aids in reducing computational complexity while facilitating a thorough understanding of the problem.To achieve this, we utilized a random deformation pattern and conducted electromagnetic simulations to compute the far-field radiation pattern.This analysis allowed us to assess the steering performance of the deformed sail.Additionally, we examined the fixed voltage case to demonstrate the effectiveness of utilizing an active platform in the sail's communication devices.

Figure 2 .
Figure 2. a) The geometry of the proposed active all-dielectric metasurface consists of an array of silicon subwavelength nanodisks followed by a silica buffer and silicon/silica DBR layers.The enlarged unit cell of the array shows the nanodisk composed of three pairs of p-n junctions, enabling an individual multigate biasing architecture.b,c) The amplitude and phase of the reflectance of the meta-atom.d) Illustrating the results investigating the effect of the number of DBR pairs on the reflectance amplitude of the all-dielectric unit cell.As can be seen, by decreasing the number of DBR pairs from eight to six, there is minimal degradation in the performance of the metasurface structure.e,f,g,h) The normalized amplitude of the electric and magnetic fields in the x-z and y-z planes, respectively, is illustrated.It should be noted that due to the presence of eight pairs of DBR layers, the structure size is relatively large, making it difficult to display the entire structure in the near-field figures.Additionally, the fields are concentrated in the nanodisk and the buffer layer.Therefore, we have only plotted the region where the disk and the buffer layer are present.

Figure 3 .
Figure 3.The fabrication and damage sensitivity investigation of the proposed unit cell.a,b,c) The calculated amplitude and phase of the reflectance as a result of variations in the geometrical parameters of the unit cell, disk height (h disk ), pitch size (Λ), and disk diameter (D disk ), respectively.It is important to mention that, to account for any imperfection in the fabrication or structural damage during the acceleration, we have considered k (or the imaginary component of the refractive index) as k = 5 × 10 −5 .

Figure 4 .
Figure 4. a,b) The spatial distributions of electron and hole carrier concentrations within the p-n multi-junction configuration are shown as functions of applied bias voltages, respectively.It should be noted that the p-doped layers within the disk are grounded, and the bias voltage is connected to the n-doped segments.The white dashed lines illustrate the boundaries between the n-type and p-type regions.c) The Spatial distribution of the real part of the silicon refractive index within the multi-junction.

Figure 5 .
Figure 5. a,b)The amplitude and phase of the reflectance of the proposed unit cell are shown as functions of the induced Δ using the applied bias voltage to the nanodisk.The modestly doped p-n multi-junction structure exhibits a relatively minor change in refractive properties induced by carrier modulation.This results in a dynamic phase shift of 320 degrees in reflection, accompanied by near-unity reflectance amplitude.The obtained large phase span is attributed to the significant enhancement of the electric fields within the active regions.c) Schematic depiction of the p-and s-polarized plane wave illumination.The reflectance amplitude (d) and phase (e) as a function of incident angle and wavelength for a s-polarized beam (TE).f,g) Depict the same for a p-polarized (TM) incident beam.The small magnitude of the spectral shift resulting from variations in the incident angle indicates the localized nature of the resonance, which is an essential characteristic for achieving optimal beam-steering outcomes.h,i) The necessary Δ for adjusting the phase to the ideal case is shown as a function of different incident angles for the TE and TM cases, respectively.It is evident that utilizing the available electro-optically tunable platform makes it feasible to correct for deformations that result in a local incident angle of  i ≤ 3 • .