Nonreciprocal surface plasmonic neural network for decoupled bidirectional analogue computing

Abstract

To address the burgeoning demand for computing capacity in artificial intelligence, researchers have explored optical neural networks that show advantages of ultrafast speed, low power consumption, ultra-high bandwidth, and high parallelism. However, most existing optical networks are reciprocal, where forward and backward propagation are intrinsically coupled. This results in the backward pathway remaining largely unexplored, hindering the realization of integrated perception-response systems. Here, we present a nonreciprocal neural network leveraging enhanced magneto-optical effect in spoof surface plasmon polaritons transmission line to decouple forward and backward paths. Moreover, the computing function of the network can be flexibly modulated by the magnetization orientation in ferrites and variations in operating frequency. We demonstrate broadband bidirectional decoupled image processing across various operators, where the operator configuration can be precisely designed by encoding the input signals. This decoupling achieves independent control and signal isolation within the same structure, effectively emulating the unidirectional transmission of biological networks. Furthermore, matrix-solving operations can be facilitated by incorporating feedback waveguides for desired recursion paths. Our findings open pathways to nonreciprocal architectures for independent bidirectional algorithms in analogue computing.

Fig. 1. Nonreciprocal computing network for microwave signals inspired by biological neural systems.

a The unidirectional transmission properties of synapses establish two independent paths between human organs. b Leveraging magneto-optical effects, the microwave computing network achieves effective decoupling of forward and backward processing paths. c Demonstration of three distinct functionalities. Nonreciprocal propagation: FP and BP paths perform different computational tasks. Frequency division multiplexing: signals at different frequencies in the same direction exhibit distinct computational functions. Matrix solving: by incorporating a feedback mechanism, the network is capable of executing matrix operations.

Fig. 2. Nonreciprocal neural network architecture.

a The 8-input, 8-output deep neural network composed of low-reflection nodes and four types of connections. The network features R and NR connections for bidirectional paths, as well as FP and BP connections for unidirectional paths. b Design strategy of the S-matrix. The S-matrix of the multi-port network is derived from the S-matrices of its constituent units. c Physical implementation of the nonreciprocal computing network using SSPP waveguides. The 8-input, 8-output network is constructed by interleaving cells, each comprising a power divider and connections. NR connections are realized by NRPS. d Simulated dispersion curves. Comparisons of the dispersion curves for light, microstrip (MS), and SSPP waveguides, which highlight the near-field properties of SSPP waveguides. Under a magnetic bias, NRPS exhibits asymmetric forward and backward dispersion. e DPS spectrum under magnetic modulation. The DPS of NRPS varies with the magnitude and direction of the bias magnetic field. f Amplitude spectra of three typical S-parameters. The bidirectional amplitude transmission remains symmetric. g Phase spectra characteristics. The first three processed groups (passing through NRPS) exhibit significant forward-backward splitting, while the fourth group (without passing through NRPS) remains overlapped.

Fig. 3. Experimental results of the nonreciprocal computing network.

a Image of the fabricated sample. b Phase spectrum of the S-parameters. The phase response in the forward path (S_11,1) deviates from the backward one (S_1,11) over a broad band. c PD of DCH. The PD can be flexibly tuned from −π to π across a wide frequency band, such as f₁ (10 GHz), f₂ (10.6 GHz), and f₃ (12 GHz). d PD calculation for unidirectional transmission. The PDs for the three DCHs are calculated by subtracting the adjacent rows of the weight matrix. e, f Comparison of PDs in the BP path. The PDs of the three DCHs to ports 1–8 at f₁ and f₂. The simulated (red) and experimental (blue) data are consistent. g S-parameter’s phase of bidirectional propagation. The S-parameter’s phase from ports 9–16 to ports 1–8 at f₂. Processing associated with the NRPS (ports 11, 13, and 15) exhibits a clear difference between forward (blue) and backward (red).

Fig. 4. Image processing results based on a bidirectional decoupled network.

a Image processing results of grayscale images with basic, Robert, and Prewitt operators. The network effectively enhances image contrast and extracts the edge features in the FP and the BP paths, respectively. b Image processing results of binary images. Only the BP path implements edge detection. c Frequency division multiplexing characteristics of the network. In the forward path, the network performs edge detection and image contrast enhanced at f₁ and f₂, respectively. The backward path is exactly the opposite.

Fig. 5. Matrix solver based on a feedback system.

a The closed-loop network for inverse matrix computation. The network consists of three feedback waveguides that connect ports 3 and 11, 5 and 13, 7 and 15, respectively. The feedback waveguides produce recursive wave propagation within the network. Arrows indicate the direction of wave flow through the structure. b Inverse matrix computation results under two spin encoding conditions. The results (nine elements of the 3 × 3 matrix) are extracted from the output port, and the experimental (red) and theoretical (blue) data [real part (boxed) and imaginary part (unboxed)] demonstrate good consistency.