A Neuro Metasurface Mode-Router for Fiber Mode Demultiplexing and Communications
Yu Zhao
,
Huijiao Wang
,
Zile Li
,
Tian Huang
,
Chao Yang
,
Ying Qiu
,
Yuhan Gong
,
Zhou Zhou
,
Congling Liang
,
Lei Yu
,
Jin Tao
,
Shaohua Yu
,
Guoxing Zheng
aElectronic Information School & School of Microelectronics, Wuhan University, Wuhan 430072, China
bPeng Cheng Laboratory, Shenzhen 518055, China
cState Key Laboratory of Optical Communication Technologies and Networks, China Information Communication Technologies Group Corporation (CICT), Wuhan 430074, China
dWuhan Institute of Quantum Technology, Wuhan 430206, China
Advancements in mode-division multiplexing (MDM) techniques, aimed at surpassing the Shannon limit and augmenting transmission capacity, have garnered significant attention in optical fiber communication, propelling the demand for high-quality multiplexers and demultiplexers. However, the criteria for ideal-mode multiplexers/demultiplexers, such as performance, scalability, compatibility, and ultra-compactness, have only partially been achieved using conventional bulky devices (e.g., waveguides, gratings, and free space optics)—an issue that will substantially restrict the application of MDM techniques. Here, we present a neuro-meta-router (NMR) optimized through deep learning that achieves spatial multi-mode division and supports multi-channel communication, potentially offering scalability, compatibility, and ultra-compactness. An MDM communication system based on an NMR is theoretically designed and experimentally demonstrated to enable simultaneous and independent multi-dataset transmission, showcasing a capacity of up to 100 gigabits per second (Gbps) and a symbol error rate down to the order of 10−4, all achieved without any compensation technologies or correlation devices. Our work presents a paradigm that merges metasurfaces, fiber communications, and deep learning, with potential applications in intelligent metasurface-aided optical interconnection, as well as all-optical pattern recognition and classification.
The pervasive adoption of emerging technologies, such as artificial intelligence, cloud computing, big data, the Internet of Things, and edge computing, has propelled human society into the era of data explosion, which is characterized by an escalating demand for information-transmission capacity [1], [2]. Optical communication technology has been advancing rapidly for several decades, supporting our increasingly information-driven society. However, the swift evolution of diverse coding technologies in modern optical communication has led to a need for the multiplexing of multiple physical dimensions, including amplitude, phase, polarization, time, and frequency, nearly approaching the Shannon limit. To tackle this challenge, space-division multiplexing techniques have been extensively explored as a way of leveraging the degrees of freedom in the transverse spatial domain [3], [4]. These techniques employ multi-mode fibers [5], multi-core fibers [6], and multi-mode multi-core fibers [7], [8] to push communication capacity. Among such technologies, few-mode fibers (FMFs) stand out as a superior choice for high-capacity fiber communication, demonstrating significantly enhanced data throughput while maintaining comparable characteristics in terms of design complexity, energy consumption, integration cost, and utilization scenarios versus single-mode fibers (SMFs). Fiber mode multiplexer and demultiplexer devices are of vital importance to FMF systems and have been extensively studied using diverse methods, including gratings [9], waveguides [10], [11], directional couplers [12], [13], free-space optics [14], [15], and photonic lanterns [16]. Nevertheless, achieving widespread adoption of a mode multiplexer/demultiplexer device with outstanding performance, scalability, and compatibility—all within a simplified design and production—remains a formidable challenge.
Metasurfaces are planar optics patterned with subwavelength-scale nanoscatters [17] that can manipulate various aspects of light, including the phase [18], [19], [20], [21], amplitude [22], [23], [24], polarization [25], [26], [27], [28], and frequency [29], [30]. Thus far, metasurfaces have been extensively applied to realize diverse optical components such as gratings [31], lenses [32], [33], and holograms [34]. In comparison with conventional optics, metasurfaces offer both theoretical exploration and practical application as a novel platform for spatial multiplexing and demultiplexing, especially in high-throughput, site-specific, real-time tasks, delivering the benefits of speed-of-light operation, wide-range integration, and high-density transmission [35], [36], [37]. While current metasurface-based devices have demonstrated success in fundamental mode conversion [38], [39], [40] and mode division [41], [42], obstacles persist for high-speed mode-division multiplexing (MDM) communications. Notably, the existing metasurfaces for mode division are typically integrated into fiber ports and have not been effectively implemented for optical experiments and system-level communication verification due to complex fabrication processes and less-optimized performance indicators for high-speed communications. To date, metasurface-based devices that can efficiently spatially demultiplex mixed modes from an optical fiber while simultaneously transmitting the information carried by each mode at high speed are still rare. Thus, achieving high-speed communications within an ultra-compact framework and with an ultra-simple design for practical applications remains a significant challenge.
Deep learning techniques have gained widespread utility as optimization tools in diverse physical systems; they have been applied to the design of metasurfaces for spatial phase distribution and the geometric structure dimensions of nanoscatters [43], [44]. In contrast to the use of traditional algorithms, such as simulated annealing and gradient search algorithms, the incorporation of a backpropagation algorithm and Adam optimizer within a deep learning framework represents a substantial advancement in both data capacity and system performance [45]. Notably, the backpropagation algorithm introduces performance metrics as components of the loss function, enabling the optimization process to be purposeful and directional rather than random and disordered, which results in higher accuracy [46], [47], [48]. In addition, optimization and evaluation processes across deep learning frameworks typically use training and testing sets obtained by expanding the scales of the datasets, which results in greater robustness of the optimized results [49], [50]. Furthermore, deep learning frameworks can operate in diverse physical systems and handle large model volumes while performing high-speed and high-performance optimizations, thereby delivering system applicability, function scalability, and design flexibility [51], [52], [53].
In this study, we introduce the integration of a metasurface and deep learning with a fiber communication system, presenting the concept of a neuro-meta-router (NMR). Notably, this NMR contains a single metasurface—devoid of any compensation technologies or correlation devices—that enables dual-mode division and dual-channel MDM communication. More specifically, the designed metasurface acts as a Fourier grating, employing phase modulation on the optical fields of two modes transmitted in FMFs. Through the metasurface, two fiber modes can be routed to distinct spatial regions while carrying different sets of digital information. Considering the susceptibility of fibers’ physical properties to environmental disturbances, mode optical fields are vulnerable to transformation along various dimensions, such as position translation, angular rotation, area expansion, and phase divergence. Consequently, our design utilizes a neural network to optimize the phase distribution of the metasurface in order to ensure robustness. This facilitates the division of modes amid the overlay of multidimension transformations and the control of crosstalk, while meeting the requirements for high-capacity communication in practical scenarios. Our experimental validation of the NMR confirms its functionality in dual-mode division, as it spatially routes the two modes of the FMF to designed regions. Systematic integration of the NMR demonstrates its efficacy in dual-channel MDM communications, as it receives dual sets of signals carried by the two modes. Importantly, within the NMR communication system, the transmission capacity reaches 100 gigabits per second (Gbps) for dual channels and 50 Gbps for each channel, and the symbol error rate decreases to the order of 10−4.
2. Design and results
2.1. Mechanism of NMR
In the proposed NMR, fiber modes serve as Internet Protocol (IP) addresses, with each mode carrying a set of information. The algorithmic framework of the neural network aligns with the routing processor, while the modulation capability of the single metasurface corresponds to the routing protocol. The structural distribution of the metasurface, the transmitting modes of the fibers, and their corresponding receiving locations in space collectively constitute the routing table. Consequently, multiple sets of information can be transmitted in independent channels in an organized and efficient manner. Crucially, unlike a switching structure network in the Internet, a single metasurface can fulfill the function of the entire switching organization, demonstrating the high efficiency of the optical Internet of Things.
Building on MDM technology, we chose an FMF that effectively meets the capacity expansion requirement while maintaining a production cost and application compatibility similar to those of SMFs. This FMF supports LP01 and LP11 modes (linearly polarized modes), each characterized by a distinct complex amplitude distribution and simultaneously loaded with distinct signals (see Section S1 in Appendix A for details on the mode coupling configuration). As illustrated in Fig. 1, the difference between the complex amplitude distribution of the LP01 and LP11 modes enables the NMR to translate the optical field distributions of the fiber modes into distinct spatial routes through an identical phase modulation. The transverse distributions of the two modes serve as complex amplitude inputs to the NMR, and the planar distributions of the target regions represent the intensity outputs from the NMR. The two modes are simultaneously projected to the metasurface and routed to different spatial regions. Moreover, the two sets of information respectively carried by the two modes are transmitted by the metasurface and simultaneously and independently received by fibers at the designed positions.
In the field of MDM technology, as the number of transmittable modes in an FMF increases, the modes being simultaneously transmitted are susceptible to coupling, and the transverse distributions of the modes may change due to environmental perturbations (e.g., bending, twisting, pressing, and moving). While a specially designed ring-core fiber with a cylindrically symmetric structure can mitigate mode coupling between different mode groups to a certain extent, coupling within the same mode group still occurs in weakly guided fibers. At present, systems based on MDM technology often employ multiple-input multiple-output digital signal processing to reduce the influence of mode coupling. However, this approach increases the complexity of the system design while decreasing the flexibility of function regulation. Moreover, imperfect alignments between fiber apertures and metasurface areas—equivalent to changes in the spatial positions of the mode fields in relation to the metasurface—can introduce errors. To address these disturbances, we explore various spatial transformations of the mode fields and incorporate the transformed mode field datasets in the metasurface optimization, as illustrated in Fig. 1. We use a neural network to train the phase distribution of the metasurface, thereby enhancing its anti-jamming capability and alignment tolerance in order to improve the robustness, stability, and anti-interference capability of the system.
2.2. Design of NMR
Deep learning techniques have gained widespread utility as optimization tools in diverse physical systems. As illustrated in Fig. 2(a), we employ a neural network to simulate the actual propagation process of optical signals across the metasurface (see Section S2 in Appendix A for details on the system configuration applied in the training process). Our aim is to optimize the phase distribution of the metasurface, denoted as P, by updating it with a stochastic gradient descent algorithm.
In this problem, the input across the network has two channels, each containing the complex amplitude distribution of the LP01 and LP11 modes from the FMF, which can be expressed as follows:
Here, A(m, n) denotes the amplitude distribution of the mode optical field, and φ(m, n) denotes the phase distribution of the mode optical field. I denote the input distribution across the network, m and n represent the coordinates on the metasurface plane, and i is the imaginary unit. To address the susceptibility of the mode optical field, we consider three types of transformation dimensions for mode configuration: position translation, angular rotation, and phase divergence. Translations along the x and y axes induce shifts in the alignment between the mode field and the metasurface area. Translations and phase divergences along the z-axis result in zooming of the mode field relative to the metasurface area. In-plane angular rotations cause angular shifts of the mode field relative to the central axis of the metasurface. Consequently, there are four possible transformation types for the mode field: transverse axial shifting, longitudinal axial shifting, angular rotation, and areal zooming. Amid the overlay of these four transformation types, we generate input distribution datasets of the two fiber modes as training datasets for use in the optimization architecture, denoted as I01 and I11 in Fig. 2(a) (see Section S3 in Appendix A for details on the data collection of the fiber modes).
The actual output Oactual across the network contains the intensity distributions under the LP01 and LP11 modes, expressed as follows:
Here, Oactual denotes the actual output distributions across the network, and Ϝ represents a Fourier transform. We set the ideal output planes with the target regions at different positions for the two modes used in the optimization architecture, denoted as O01 and O11 in Fig. 2(a). In the ideal output planes, the numerical values of the dark background and light target are set to be 0 and 1, respectively. Our objective is to ensure that the actual outputs, O01actual and O11actual, closely approximate or are even equal to the ideal outputs, O01 and O11, respectively.
As illustrated in Fig. 2(a), we introduce Lossback and Losscorr as loss functions for the backpropagation used in the optimization architecture. Lossback is used to reduce the background noise, and Losscorr is employed to decrease the inter-mode crosstalk (see Section S4 in Appendix A for more details on the loss functions), concentrating the energy of each mode solely on the designed target region. We determine that the light region in the actual output lies within the target region in the ideal output, allowing for the energy of the two modes to be distinctly routed to their respective target regions and the two carried sets of images to be precisely received at the designed positions.
The final training result for the phase distribution of the metasurface is depicted in Fig. 2(b), where the enlarged phase distribution (20 × 20 pixels) in the dashed box in the upper-left corner is depicted in Fig. 2(c). The geometric phase, also known as the Pancharatnam–Berry phase, can be utilized to produce a phase delay for the cross-polarized component that is exactly twice the nanostructure orientation angle. To achieve a remarkable transmittance for the cross-polarized component within the infrared communication wavelength at 1550 nm, we used an all-silicon nanostructure for the metasurface (see Section S5 in Appendix A for more details on the design of the nanostructure unit cell).
After training, the robustness of the metasurface was assessed by the Kirchhoff diffraction calculation program using MATLAB (MathWorks, USA). We generated large-scale transformed mode fields in four dimensions as testing datasets beyond the training datasets, thereby ensuring the validity of the assessment, as depicted in Fig. 2(d). More specifically, the length and width of the mode fields were both 860 μm, which was taken as the transformation reference. The scale of the positive and negative x-axial shifting was 50 μm (Δx1,2 = 50 μm), and that of the y-axial shifting was 100 μm (Δy1,2 = 100 μm). The scale of planar rotation was 10° clockwise and counterclockwise (Δθ1,2 = 10). The scales of areal zooming were 0.9 and 1.1 times, corresponding to positive and negative z-axial shifting with a scale of 12.3 mm (Δz1,2 = 12.3 mm), based on a divergency angle of 0.2° (see Section S6 in Appendix A for details on the divergency angle from the actual optical distributions of the modes). Subsequently, we computed the Kirchhoff diffraction distributions of the transformed mode fields through phase modulation by the metasurface, treating them as the actual output planes. As depicted in Fig. 2(d), in each transformation module, the middle column shows the original mode fields and their Kirchhoff diffraction results, with the transformed mode fields and their Kirchhoff diffraction results on either side. The results demonstrate that the metasurface maintains the ability to route large-scale transformed modes to the target regions as accurately as it routes the original modes. Therefore, even when the external environment changes, the two sets of signals carried by the two modes in the FMF can still be smoothly transmitted at high capacity and accurately received at the designed position (see Section S7 in Appendix A for details on the numerical simulation for the robustness assessment).
2.3. Experiment and optical characterization of NMR
To verify the feasibility of our concept, we fabricated a metasurface and established an optical path to characterize its optical response to realize fiber-mode router (see Section S8 in Appendix A for details on the metasurface fabrication). The experimental setup is depicted in Fig. 3(a). A tunable laser source (TLX1, Thorlabs, USA) provided light at an operating wavelength of 1550 nm. A fused-typed fiber mode coupler was used to generate the LP01 and LP11 modes transmitting in the FMF. The mode optical fields of the FMF were collimated by a collimating lens (PAF2-2C, Thorlabs) with a divergence angle of less than 0.2°, which is negligible over short distances. The optical fields from the lens were directed onto the metasurface from a distance of 1 cm. A near infrared (NIR) detector card (VRC4, Thorlabs) was placed at a distance of 1 cm along the optical axes from the metasurface, featuring a black cardstock (with a length and width of 2 mm × 2 mm) stuck in the middle to prevent the detection of zero-order light.
Figs. 3(b) and (c) depict the diffracted spot distributions under the LP01 and LP11 mode incidences in free space, revealing the target and crosstalk spots. As the LP01 and LP11 modes are imperfectly circularly polarized, they contain both left- and right-handed circularly polarized light, resulting in a conjugate spot associated with the zero-order spot for each mode’s target spot. A polarizer and a quarter waveplate were utilized to convert the polarization state of the modes into circular polarization, eliminating these conjugate spots. In the diffracted spot distribution of each mode incidence, we defined the spot at the other mode’s target position as the crosstalk spot. In Figs. 3(b) and (c), dashed lines delineate the edge of the black cardstock in the middle of the detector card. In addition, another infrared detector board (IRDC1-200S-M-SP230614, LBTEK, China) was placed at a distance of 10 cm from the metasurface to capture the diffracted distribution over a greater distance. The measured distances between the target spot and the zero-order spot for the LP01 and LP11 modes were 4.1 and 5.2 cm, corresponding to diffraction angles of 22.3° and 27.5°, respectively. These results agree well with the theoretical simulation values of 4.0 cm, 5.1 cm, 21.9°, and 27.1°.
To determine the insertion loss and crosstalk of the metasurface, we measured the power of the target spots using a photodiode power sensor (S122C, Thorlabs) positioned at a distance of 4 cm from the metasurface, in conjunction with a digital optical power and energy meter (PM100D, Thorlabs). The power of the LP01 mode incident from the collimating lens was measured to be 10.7 dBm, while that of the LP11 mode was 6.8 dBm. As depicted in Figs. 3(b) and (c), the measured powers of the target spot and crosstalk spot were respectively −1.3 and −5.9 dBm under the LP01 mode incidence and −6.6 and −10.6 dBm under the LP11 mode incidence. Therefore, the insertion losses of the metasurface for the LP01 and LP11 modes were respectively calculated to be −12.0 and −13.4 dB—values similar to those typically observed in extremely miniaturized devices. In addition, due to the reflection at the silicon/air interface when the modes were incident onto the metasurface, there was a certain amount of energy loss, which was calculated to be 1.6 dB based on the refractive indices of air and the silicon. As a result, after accounting for the reflections, the insertion losses of the metasurface were −10.4 dB for the LP01 mode and −11.8 dB for the LP11 mode. Moreover, the crosstalk values of the metasurface for the LP01 and LP11 modes were respectively calculated to be −4.6 and −4.0 dBm.
To experimentally assess the robustness of the NMR, we determined the standard state of the optical path corresponding to the spot distributions depicted in Figs. 3(b) and (c). We then conducted translations of the optical path in order to observe the power variations of the target spots (i.e., the differences in the energy of the target spots between the standard and transformed states of the optical path) for both the LP01 and LP11 modes. To carry out translations as axial shifting and areal zooming of the modes, we adjusted the metasurface along the x-axis, y-axis, and z-axis. Alignment in the optical path was necessary, and rotating the modes by rotating the collimating lens was associated with a certain degree of misalignment; therefore, we did not adopt translations in this dimension for experimental verification. The units of translation along the x-axis, y-axis, and z-axis were set at 50 μm, 100 μm, and 1 mm, respectively. As illustrated in Figs. 3(d) and (e), the power of the target spots varied with the three axial translations for the LP01 and LP11 modes, respectively. Within the range of one unit along the positive and negative direction, the power variations of the target spots remained below 0.2 dB for the two modes in the three axial translations. Moreover, within the range of two units, the power variations for both modes were less than 1 dB. Furthermore, the power declinations remained within 3 dB within the range of three units.
The experimental results demonstrate that the metasurface achieves spatial division among the two modes of the FMF with accurate division, minimal crosstalk, and a certain degree of robustness. These results indicate that the metasurface is an ideal and exceptional candidate for a fiber-mode router that can be seamlessly integrated into optical fiber communication systems.
2.4. Implementation of an NMR-based optical communication system
To illustrate the practicality of our concept, we applied the NMR to an MDM communication system and built an information transmission platform in order to verify the NMR-based communication ability. As depicted in Fig. 4(a), the signal transmitting process starts with the generation of in-phase (I) and quadrature (Q) inputs, with a length of 231 − 1 bits, by an arbitrary waveform generator (AWG) with a sample rate of 120 giga samples per second (GSa·s−1). Simultaneously, an external cavity laser (ECL) provides the optical carrier at the infrared communication wavelength of 1550 nm. These inputs then undergo coherent modulation via an IQ modulator to produce a dual-polarization quadrature phase-shift keying (DP-QPSK) signal. Following amplification by an erbium-doped fiber amplifier (EDFA), the signal is divided into two signals through an optical delay line (DL) and then fed into the transmitter fibers, each signal having a separate power of 17.5 dBm. Crucially, the dual-mode channels facilitate simultaneous signal transmission at a capacity of 50 Gbps, enabling MDM communication at a combined capacity of 100 Gbps.
In line with the spatial optical path described above, the optical signals access the FMF by means of a fused-type fiber mode coupler. The signals from the FMF are first collimated by a lens (denoted here as “Col”) and then distinguished by the metasurface to achieve mode routing from one path to two paths. Consequently, through the NMR, the signals carried by the LP01 and LP11 modes are transferred via different spatial paths and then coupled into the receiver fibers by Col at different spatial locations.
At the signal-receiving end, we conducted tests on the output power of the two receiver fibers to anticipate the achievable transmission capacity of the channels. When both signals were directed to the FMF, the receiver fiber for the LP01 mode exported a power of −2.1 dBm, while the receiver fiber for the LP11 mode measured −6.6 dBm. For the scenario where the signal carried by the LP01 mode accessed the FMF, the output powers of the receiver fibers for the LP01 and LP11 modes were −3.0 and −12.1 dBm, respectively. Conversely, when the signals carried by the LP11 mode accessed the FMF, the output powers of the receiver fibers for the LP01 and LP11 modes were −15.3 and −7.8 dBm, respectively. Due to the imperfection of a fused-type fiber mode coupler within a mode coupling configuration, there was a discrepancy in the exported power between the LP01 and LP11 modes in the receiver fibers. To observe the bit-error-ratio (BER) variation curve, the received optical power was adjusted using a variable optical attenuator (VOA). Ultimately, the received optical signal was demodulated by a coherent receiver and then displayed by a digital storage oscilloscope (DSO) with a sample rate of 256 GSa·s−1.
Figs. 4(b) and (c) show the measured signal BER curves versus the received optical power in dual-channel and single-channel signal transmissions for the LP01 and LP11 modes, respectively. At the received power of −25.5 dBm, the minimum BER is as low as 0.0011 for the LP01 mode under single-channel transmission, and the maximum is 0.0033 for the LP11 mode under dual-channel transmission. As marked by arrows in Figs. 4(b) and (c), the receiver sensitivity penalties of the LP01 and LP11 modes are respectively 0.4 and 2.0 dBm, at a hard-decision forward error correction (HD-FEC) threshold of 0.0038; these values are acceptable for 100 Gbps MDM communications. Moreover, it is evident that the performance of the NMR remains consistent for both modes, exhibiting similar BER variation curves in terms of range and magnitude. It is noteworthy that the communication platform we established contains only the basic signal modulation, demodulation, amplification, and attenuation devices, the necessary transmitter and receiver lines, and the designed NMR. As mentioned earlier, for MDM transmission in multi-mode fibers, where the distinguishable paths have significant spatial overlap and signals are thus susceptible to random coupling among the modes during propagation, equalization via multiple-input multiple-output digital signal-processing techniques is performed at the receiver to mitigate linear impairments. Significantly, simultaneous and independent dual-dataset transmission is accomplished through our platform without any compensation technologies or correlation devices, significantly reducing the complexity of the design while maintaining the performance of the system.
2.5. Application of an NMR-based optical communication system
In order to illustrate the universality and flexibility of the NMR-based MDM communication system, we transmitted images with diverse expression forms to assess the transmission performance (see Section S9 in Appendix A for details on the conversion between the images and the bitstreams). Two sets of images, characterized by different information, were respectively transmitted in the LP01 and LP11 mode channels. As depicted in Fig. 5(a), each set comprised seven images presenting three expression forms: binary, grayscale, and color, numbered sequentially from 1 to 7. The images transmitted in the LP01 channel included a binary image of the Wuhan University badge, a binary image of a quick response (QR) code for the Wuhan University official website, a grayscale image of a cat, and color images of emoji emoticons. The images transmitted in the LP11 channel included a binary image of the Electronic Information School badge, a binary image of a QR code for the Electronic Information School official website, a grayscale image of a dog, and color images of emoji emoticons.
As illustrated in Fig. 5(a), from a subjective perspective, a comparison of the transmitted images and the originals reveals that there are only few pixel distortions in the received images. Objective metrics were employed to assess the quality of the received images. We measured the signal BER values and computed the pixel errors in the received images, as illustrated in Figs. 5(b) and (c) (see Section S10 in Appendix A for details on the image evaluation). The minimum BER measured was 0.000156 and the maximum was 0.0068, even under external environmental perturbations and transmission power fluctuations. These results demonstrate that the two sets of images were successfully transmitted from the transmitting module to the receiving module by the FMF and NMR, simultaneously and independently.
The experimental results show that the NMR system successfully achieves MDM communication within the two mode channels in the FMF. The proposed NMR system possesses a trifecta of critical attributes: precision in signal transmission with a low BER, efficiency in system operation with a high capacity, and excellence in device integration with a simplified design.
3. Discussion
We have theoretically designed and experimentally demonstrated a fiber-mode routing framework using a neural-network-trained metasurface, which offers the advantages of device compatibility, performance enhancement, function scalability, and ultra-compactness. The scalability of the functional channels of the NMR for a larger number of modes can theoretically be achieved under the computation capacity of the neural network architecture and the modulation ability of the metasurface within a single layer. For example, the optimization process was replicated for four modes (the LP01, LP11, LP02, and LP21 modes). As shown in Figs. 6(a) and (b), the four-mode NMR enables spatial division for all four modes while maintaining the same size as the dual-mode NMR. In essence, aside from the optimization process, the nanostructure design, fabrication process, and system configuration can be generally replicated for a multi-mode NMR.
In contrast to conventional optoelectronic demultiplexing devices, our NMR operates entirely in optics and integrates seamlessly with systems, enabling speed-of-light and yet-to-be data transmitting while maintaining an ultra-compact framework and ultra-simple design. Note that the system is not augmented by any compensation technologies or correlation devices and contains only the basic signal modulation, amplification, and attenuation devices, the necessary transmitter and receiver lines, and the proposed NMR. Moreover, our approach results in a superior performance of mode division and signal transmission, with a high transmission capacity and low signal error. It is notable that the finitely transformed modes remain efficiently separable, ensuring robustness and simplicity. We have supplied a comparison of our work to previous similar systems across multiple perspectives, such as functionality, scalability, construction, and implementation (see Section S11 in Appendix A for details on the work comparison).
Furthermore, it is feasible to extend the functional channels in various directions by considering the modulated dimensions through the metasurface, transmitted modes in the fiber, and integrated devices across the communication. In particular, polarization-sensitive metasurfaces enable phase modulations for the optical fields of modes in two orthogonal polarization directions independently and simultaneously, achieving the division of polarized fiber modes and the integration of a polarization multiplexing scheme. Moreover, due to the optical response and modulation of the metasurface within its bandwidth, there is potential to incorporate a wavelength division multiplexing scheme into the proposed system, which will greatly enhance the transmission capacity. This can be achieved by adjusting the wavelength of the incident light at regular intervals and transmitting diverse information in different wavelength channels.
4. Conclusions
Our proposed framework amalgamates metasurfaces, deep learning, and optical fiber communication, establishing a practical pathway for high-quality routers in diverse emerging applications, including object classification, image display, and information encryption. The capabilities of metasurface devices can be readily broadened in various directions. Firstly, the diversity of the transmitted modes in the FMFs can be increased, based on the intensity distribution, phase distribution, and polarization direction. Secondly, metasurfaces can be empowered by multiple degrees of freedom, including amplitude, phase, frequency, spectra, polarization, and orbital angular momentum. Thirdly, metasurfaces can be integrated into existing communication devices, such as fibers and waveguides. Thus, we anticipate the development of ultra-compact, high-quality, multi-functional neural metasurface platforms that can replace a variety of traditional data-processing and information-transmission devices.
Acknowledgments
This research was supported by the National Key Research and Development Program of China (2023YFB2804704) and the National Natural Science Foundation of China (12174292, 12374278, and 62105250).
Compliance with ethics guidelines
Yu Zhao, Huijiao Wang, Zile Li, Tian Huang, Chao Yang, Ying Qiu, Yuhan Gong, Zhou Zhou, Congling Liang, Lei Yu, Jin Tao, Shaohua Yu, and Guoxing Zheng declare that they have no conflict of interest or financial conflicts to disclose.
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