The exponential growth of data traffic in modern communication systems has necessitated the development of high-capacity and energy-efficient interconnect solutions [1,2]. Optical interconnects based on photonic integrated circuits (PICs) have emerged as a pivotal technology to meet these demands, offering superior bandwidth, low latency, and immunity to electromagnetic interference compared to their electronic counterparts [3–5]. By leveraging the properties of light, optical interconnects facilitate high-speed data transmission over short and long distances, making them indispensable in applications ranging from intra-data center communication [6–8] to inter-chip XPU interconnects [9,10].

To further enhance the capacity of optical interconnects, mode-division multiplexing (MDM) has been extensively explored as a promising technique [11–14]. MDM exploits the spatial dimension of light by utilizing multiple orthogonal modes within a single waveguide, thereby significantly increasing the bandwidth density and spectral efficiency [6,10,15]. A central component in MDM systems is the mode multiplexer (MUX), which is responsible for mode conversion and combination. Recent advancements in mode MUXs can be broadly classified into forward-designed and inverse-designed types [16]. Forward-designed MUXs primarily include asymmetric directional couplers (ADCs) [17–19], multi-mode interference (MMI) couplers [20,21], and Y-junctions [22–24]. On the other hand, inverse-designed MUXs can be further divided into those based on analog metamaterials [6,25] and digital metamaterials [26–29]. Analog metamaterial designs often feature irregular shapes and complex boundaries, whereas digital metamaterials are typically composed of regular arrays of circular or square etched holes [30]. While significant progress has been made in increasing mode count and reducing inter-mode crosstalk, the majority of existing MDM implementations operate within a single wavelength band, typically around 1.55 μm. The single-band capability limits the efficient utilization of the optical spectrum, particularly when combined with wavelength-division multiplexing (WDM) technology [10,11,19]. As the demand for higher data rates continues to grow, conventional telecom bands are at risk of resource scarcity, posing a challenge to the scalability of optical interconnects [31–33].

To address this limitation, multi-band MDM schemes have been proposed recently, aiming to exploit the spectral resource of multiple wavelength bands concurrently [34–36]. In 2021, Paredes et al. first proposed a two-mode MUX capable of operating simultaneously in the O and C bands [34], with a device length of 75 μm. Subsequently, in 2022, Wang et al. increased the number of multiplexed modes to four [35], also operating in the O and C bands, with a reduced length of 66 μm. In 2024, we successfully extended the operating bands of mode MUXs (length 84.4 μm) to include the emerging 2 μm band [36], which represents a new communication window enabled by the development of rare-earth-doped amplifiers [37–42]. Transmission experiments demonstrated single-channel data rates of 114 Gb/s and 84 Gb/s at 1.55 μm and 2 μm, respectively. Despite these advances, all current multi-band MDM systems are based on conventional forward design methodologies, specifically ADC structures. To achieve dual-band coupling, the length of the directional coupler needs to be set to the least common multiple of the odd multiples of the coupling lengths required for the target two wavelengths [35]. Moreover, ADC-based MUXs require cascading multiple mode converters to achieve high-order mode multiplexing. These factors result in bulky device architectures, with the physical footprint expanding significantly as the number of supported modes and wavelength bands increases, undermining the compactness and integration density essential for scalable optical interconnects. In terms of operation bandwidth, ADC-based MUXs, with coupling lengths optimized for specific target wavelengths, typically experience significant performance degradation between the target bands due to index mismatches [36]. The escalating demand for scalable, high-density interconnects necessitates a paradigm shift in MUX design, making the development of ultra-compact multi-band MUXs an urgent and transformative priority. In our previous work at ACP 2024 [43], we demonstrated the effectiveness of a pixelated broadband mode MUX through numerical simulations.

Here, in this paper, we showcase the first experimental demonstration of the inverse-designed multi-band mode MUX, as well as system-level validation of high-speed dual-band MDM signal transmission. The proposed device achieves an order-of-magnitude reduction in device length while providing an ultra-broadband and ultra-flat spectral response for multiplexing TE0−TE2 modes. The device structure is based on QR-code-like digital metamaterials fabricated on a silicon-on-insulator (SOI) platform, featuring a compact design footprint of 6μm×4.8μm. Numerical simulations indicate that within the 1500–2100 nm range, the broadband MUX exhibits losses below 2.3 dB and crosstalk below −16.3dB across three mode channels. Over the entire 600 nm range, the loss variation for each mode is less than 0.94 dB, demonstrating remarkable spectral flatness. Furthermore, the device performance is experimentally validated in the wavelength ranges of 1525–1585 nm and 1940–2040 nm. In the 1.55 μm band (across the 60 nm range), the MUX exhibits losses below 4.3 dB and crosstalk below −11.6dB for all modes. In the 2 μm band (across the 100 nm range), losses below 4.0 dB and crosstalk below −11.3dB are achieved for all modes. Furthermore, as a proof of concept, dual-band MDM optical interconnect experiments using on-chip MUX/DEMUX circuits demonstrate transmission rates of 3-modes×180Gb/s and 3-modes×114Gb/s in the two bands, respectively, under a 20% soft-decision forward-error-correction (SD-FEC) threshold. To the best of our knowledge, these results set a new benchmark for on-chip multi-band interconnect systems and establish a record-high signal transmission rate for the emerging 2 μm communication band. The ultra-compact and ultra-broadband digital metamaterial-based mode MUX, combined with multi-band MDM signal transmission demonstration, highlights its significant potential for enhancing shoreline density for next-generation high-capacity on-chip interconnects.

A conceptual schematic of the on-chip multi-band MDM optical interconnect system is illustrated in Fig. 1(a). The system comprises a pair of ultra-broadband MUX/DEMUX and a multi-mode bus waveguide. At the input end, incoming light from three single-mode waveguides (arranged from top to bottom) is sequentially converted into TE0, TE1, and TE2 modes within the bus waveguide, thereby achieving broadband, low-crosstalk mode multiplexing. The ultra-broad operational bandwidth of our device is expected to utilize spectral resources ranging from 1.55 μm to 2 μm on each orthogonal mode, enabling high-capacity on-chip optical interconnects. The design is realized on the 220 nm silicon-on-insulator (SOI) platform with a SiO2 cladding layer and buried oxide layer. The structural schematic of the three-mode MUX is depicted in Fig. 1(b), featuring a compact rectangular design region with a footprint of 6μm×4.8μm. This region is divided into a 50×40 grid of square pixels, each with dimensions of 120nm×120nm. Each pixel is composed of either Si or SiO2, enabling local index manipulation. This design is compliant with the design rule checks (DRCs) of mainstream foundries [44], facilitating large-scale manufacturing. To determine the optimal widths for the single-mode waveguide and the multi-mode bus waveguide, we conduct numerical calculations of the effective refractive indices for TE0 to TE2 modes using a finite-difference eigenmode (FDE) solver from ANSYS Lumerical [45], as shown in Fig. 1(c). The single-mode waveguide and multi-mode waveguide widths are set to 650 nm and 1800 nm, respectively, enabling simultaneous accommodation of the first three TE modes in both the 1.55 μm and 2 μm wavelength bands.

The design and simulations are carried out using the three-dimensional finite-difference time-domain (3D-FDTD) solver [46], which is well-suited for broadband electromagnetic calculations. Figure 2(a) illustrates the overall workflow of our inverse design approach, called the edge-guided analog-and-digital optimization (EG-ADO) method that is proposed in Ref. [10]. This method comprises three primary stages: topology optimization (TO), edge-guided analog-to-digital conversion, and digital optimization (DO). During the TO phase, we employ the adjoint method for gradient-based optimization, where each iteration requires only one forward and one adjoint simulation [47,48]. Starting from an initial continuous permittivity distribution, the Heaviside filter is applied to progressively sharpen the material boundaries. As the iteration count increases, the continuous index profile gradually transitions into a more binary-like structure [see Fig. 2(b)], paving the way for subsequent edge-guided conversion and digital optimization steps. The intermediate step [see Fig. 2(c)], edge-guided analog-to-digital conversion, begins by employing a Canny edge detector to extract clear material boundaries. Subsequently, a max pooling operation is performed to scale up the pixel size from the analog scale (20 nm) to the digital scale (120 nm). The resulting feature map is then subjected to a binarization process, generating a decision map in which all non-zero entries are set to one. Next, we carry out index mapping based on this decision map. In regions devoid of edge pixels (marked in black on the decision map), the local indices can be directly assigned to the value of either Si or SiO2. Conversely, any pixel falling within or adjacent to an edge region is designated as “to be determined” (TBD), deferring its final assignment until a later stage, as shown in the converted pattern in Fig. 2(c). Lastly, the digital optimization (DO) phase refines the structure by determining the final material for each TBD pixel using the direct binary search (DBS) method [49]. In this procedure, every TBD pixel is tested twice: one with its index set to nSi=3.48 and the other with nSiO2=1.44. The material choice that leads to a higher figure of merit (FOM) is then adopted for that pixel. By iteratively applying this procedure to all TBD pixels for one round, the entire optimization concludes. The final digital pattern of the three-mode MUX is shown in Fig. 1(b).

A key rationale underlying our methodology is that while the TO phase steers the design toward a highly efficient direction, it also tends to produce narrow gaps and sharp corners that complicate fabrication. The following two steps gradually eliminate these irregular features, preserving performance while reshaping the entire design region into a fabrication-robust digital metamaterial. To provide greater insight into the optimization process, we present the evolution of FOM and the proportion of edge pixels [i.e., white pixels in the decision map shown in Fig. 2(c)] during the entire optimization in Fig. 2(d). The FOM is defined as FOM=−10·lg(∑i=1n∑j=1qTi,jn·q),(1)where n and q are the number of modes and wavelength points, respectively, and Ti,j is the transmission coefficient of TEi−1 mode at the j-th wavelength point. Eleven equally spaced wavelength points, ranging from 1.5 μm to 2.05 μm, are employed to enable broadband optimization. The transmission coefficient T is calculated based on the modal overlap analysis, which can be expressed as T=|∫dS·(Ee×Ha)+∫dS·(Ea×He)|2Re[∫dS·(Ee×He)],(2)where Ee and He represent the electrical and magnetic field distribution of the ideal eigenmode at the waveguide cross-section S obtained via FDE calculations, while Ea and Ha are the corresponding actual field distribution obtained through FDTD simulations. During the TO phase, the FOM decreases sharply, yet the proportion of edge pixels remains high (>30%). In the following DO stage, the FOM undergoes a slight degradation while the edge pixel ratio steadily falls to 0%, indicating a successful transition to a fully discretized and fabrication-ready pattern. Notably, the complete optimization routine, comprising 338 iterations during the TO phase and 929 iterations during the DO phase, was successfully executed within 36 h on a desktop computer equipped with an Intel i9-10850K, 64 GB RAM, and an NVIDIA RTX 4070, with graphics card acceleration enabled.

Figures 3(a)–3(c) illustrate the simulated transmission spectra of the broadband three-mode MUX, where the TE0 mode is launched from the upper, middle, and bottom ports, as annotated in the insets of each figure. The performance is evaluated over a broad wavelength range of 1500–2100 nm. The minimum insertion losses (ILs) for TE0, TE1, and TE2 modes are 0.49 dB, 1.09 dB, and 1.67 dB, respectively, at their peak wavelengths, with corresponding crosstalk (CT) values of −19.9dB, −25.5dB, and −20.0dB. Across the entire 600 nm range covering the conventional telecom band and the 2 μm waveband, the ILs for the three modes remain below 0.9 dB, 2.0 dB, and 2.3 dB, respectively, while the CT is maintained below −16.3dB, −16.8dB, and −19.6dB, respectively. The insertion loss and crosstalk mainly result from non-ideal mode conversion. Benefiting from the advanced inverse design algorithm for broadband optimization, the transmission spectra demonstrate exceptional flatness, avoiding the spectrum notches commonly observed in multi-band mode MUXs based on the forward-design method. For all the three modes, the IL variations remain within 0.94 dB across the entire 600 nm wavelength range. Figures 3(d)–3(f) illustrate the light propagation process for the three modes at wavelengths of 1550 nm and 2000 nm, confirming that the device effectively converts the TE0 modes from the three separate input waveguides into the TE0, TE1, and TE2 modes in the bus waveguide. This device also exhibits excellent fabrication tolerance due to the broadband optimization method, as shown in Appendix A.

The fabrication of the broadband three-mode MDM circuit is implemented on an SOI wafer. The device is fabricated at the ShanghaiTech Quantum Device Lab. The device patterns are defined using an Elionix ELS-F125G8 electron-beam lithography (EBL) system, followed by an inductively coupled plasma (ICP) etching process to transfer the pattern onto the silicon core layer. A silicon dioxide cladding layer is subsequently deposited on the silicon layer using plasma-enhanced chemical vapor deposition (PECVD). The silicon core and cladding layer have thicknesses of 0.22 μm and 1 μm, respectively, while the buried oxide layer is 10 μm thick. A microscope image of the fabricated MDM circuit is provided in Fig. 4(a). The SEM image of the circuit and zoomed-in view of the inverse-designed pattern are presented in Fig. 4(b).

Next, we perform experimental testing of the broadband three-mode MUX at the 1.55 μm and 2 μm wavebands, due to the limitation of the experimental equipment. However, it is important to emphasize that the operational bandwidth of our device extends beyond these tested ranges, highlighting its capability for broader applications. To characterize the device at these two wavebands, we replicate the MUX/DEMUX devices with distinct TE-polarized input/output grating couplers. The coupling losses of the grating couplers at 1.55 μm and 2 μm wavebands are approximately 6 dB/facet and 9 dB/facet, respectively. The fiber-to-chip coupling is conducted on a vertical coupling stage (Apico AP-MA-GRT). For transmission spectrum measurements of the circuit, we use polarization-maintaining broadband amplified spontaneous emission (ASE) sources as the input light and employ a polarization controller (PC) to align the input polarization with that of the grating couplers. Specifically, a home-built thulium-doped fiber amplifier (TDFA) is used as the ASE source for the 2 μm band. The output fiber of the chip is connected to the optical spectrum analyzer (OSA, Yokogawa AQ6370D & AQ6375B) to record the broadband response. For the 1.55 μm waveband, the tested wavelength band covers a range of 1525–1585 nm, while for the 2 μm waveband, the available wavelength range is 1940–2040 nm. Measured transmission spectra for the three-mode MUX are shown in Figs. 4(c)–4(e), which have been normalized by subtracting the losses of grating couplers. Insertion losses (ILs) of the mode MUX in the wavelength range of 1525–1585 nm are less than 0.4 dB, 2.7 dB, and 4.3 dB, for TE0 to TE2 modes, respectively, with crosstalk (CT) less than −12.5dB, −14.0dB, and −11.6dB, respectively. In the wavelength range of 1940–2040 nm, ILs of the mode MUX for the three modes are less than 1.26 dB, 2.3 dB, and 4.0 dB, respectively, with CT less than −11.3dB, −11.9dB, and −12.0dB, respectively. Leveraging the advanced inverse design algorithm, the fabricated device demonstrates remarkably flat spectral responses. Across the entire tested 160 nm range, the mode MUX maintains IL and CT below 4.3 dB and −11.3dB, respectively.

We conduct a high-speed multi-band MDM on-chip optical interconnect experiment utilizing the fabricated three-mode circuits. The experimental setup, along with the offline digital signal processing (DSP) blocks, is illustrated in Fig. 5(a). For signal transmission in the 1.55 μm waveband, a commercial telecom-band Mach-Zehnder modulator (MZM) is employed to modulate continuous-wave light generated by a tunable laser. The MZM is biased at its quadrature point to produce PAM signals. The modulated signal is amplified by an optical amplifier (OA) and then coupled into the MDM chip after polarization alignment using a polarization controller (PC). Specifically, the OA used for the 1.55 μm waveband is the erbium-doped fiber amplifier (EDFA). The output light from the chip is further amplified by a second OA to compensate for on-chip losses, with a variable optical attenuator (VOA) inserted before the photodiode (PD) to sweep the received optical power (ROP). Specifically, the PD used for the 1.55 μm band is a Finisar XPDV4121R, with a responsivity of 0.6 A/W and a 3 dB bandwidth of 100 GHz. For the 2 μm waveband experiment, the system configuration is identical to that of the 1.55 μm experiment, except that the laser, MZM, and PD are replaced with corresponding components operating in the 2 μm band. The employed 2-μm-band PD (Newport 818-BB-51F) features a responsivity of 0.95 A/W and a bandwidth of 12.5 GHz. Additionally, the EDFAs are replaced with TDFAs. The wavelengths of the laser are set to 1530 nm and 1970 nm for the two waveband experiments, respectively. Using Keysight IQtools module [50], the end-to-end system frequency responses (S21) for the two bands are measured, as shown in Fig. 5(b). The system bandwidth of the 2 μm band is primarily limited by the electro-optical bandwidth of the commercial 2 μm MZM and PD used in the experiment.

As for the transmitter-side DSP (Tx-DSP) flow, a pseudo-random binary sequence (PRBS) is first generated and mapped onto PAM symbols. Following re-sampling, the signals are pulse-shaped using a root-raised-cosine (RRC) filter with a roll-off factor of 0.1. Pre-equalization operation is then applied before the signals are uploaded to the arbitrary waveform generator (AWG, Keysight M8194A). For the receiver-side DSP (Rx-DSP) flow, the waveform captured by the oscilloscope (OSC, Keysight UXR0594BP) is first re-sampled and passed through a matched filter. After clock recovery, a third-order Volterra nonlinear equalizer (VNLE) is employed to mitigate nonlinear distortions [51]. Finally, the bit error rate (BER) is determined by comparing the recovered sequence with the originally generated one.

During the signal transmission experiments, the bias voltage of the MZM is first swept to determine the optimal operating point, as shown in Fig. 5(c). The identified optimal bias voltages are 1.4 V for the 1.55 μm MZM (Sumicem T.MXH 1.5-20PD-ADC-LV) and 6.4 V for the 2 μm MZM (iXblue MX2000-LN-10). For the 1.55 μm band experiment, we investigate the BER performance of three mode channels under different received optical powers (ROPs) for transmitting 80 GBaud PAM4 signals [see Fig. 6(a)]. Lower-order mode channels demonstrate better sensitivity due to their reduced on-chip losses. Subsequently, we evaluate the BER performance at varying baudrates for both PAM4 and PAM8 signals to obtain the maximum system capacity. For PAM4 signals, all three mode channels achieve BER values below the SD-FEC threshold (2.4×10−2) at a data rate of 180 Gb/s. For the transmission of 190 Gb/s PAM4 signal, only the TE2 channel exceeds the SD-FEC threshold due to its higher loss. For PAM8 signal transmission, all mode channels maintain BER values below the SD-FEC threshold at 180 Gb/s, while at 210 Gb/s, only the TE2 channel exceeds the SD-FEC threshold. Thus, for the 1.55 μm band, we successfully achieve a total on-chip optical interconnect capacity of 3×180Gb/s under the SD-FEC threshold, corresponding to a net bit rate of 3×150Gb/s. We note that this capacity is limited by the TE2 channel, which can be optimized by modifying the etch hole dimensions and etch depth to further reduce losses.

Similarly, for the 2 μm band experiment, we first analyze the sensitivity differences among the three mode channels by transmitting 40 GBaud PAM4 signals under varying ROPs, as shown in Fig. 7(a). As the ROP decreases, the BER curves of different modes gradually converge due to the dominance of receiver noise, which minimizes the impact of mode-specific losses. For data rate evaluations, all three mode channels meet the SD-FEC threshold for 48 GBaud PAM4 signal transmission. In the case of PAM8 transmission, the BER remains below the threshold for all modes up to 38 GBaud, demonstrating the capability of the 2 μm band to support advanced modulation formats with higher spectral efficiency. Therefore, for the 2 μm band, we successfully achieve a record-setting interconnect capacity of 3×114Gb/s under the SD-FEC threshold, corresponding to a net bit rate of 3×95Gb/s.

Table 1 presents a comparison of state-of-the-art ultra-broadband mode MUXs on the SOI platform, specifically focusing on designs with operation bandwidths exceeding 100 nm [17,21,34–36]. Among dual-band MUXs, all previous designs rely on ADC structures, which typically have large device footprints. In contrast, our inverse-designed MUX achieves a significantly small device length of only 6 μm, representing a dramatic decrease compared to conventional forward-designed structures. The relatively large feature size (120 nm) in our design also holds promise for foundry fabrication using UV lithography [44]. As detailed in Appendix B, reducing the fabrication feature size offers considerable potential for improving device performance, particularly in terms of insertion loss and spectral uniformity. Further process refinements—such as improved sidewall verticality and enhanced accuracy in pixel patterning—are expected to effectively mitigate the discrepancy between experimental and simulated results.Table 1.

Performance Comparison of State-of-the-Art Ultra-broadband Mode MUXs on SOI

In addition, to provide a fair comparison of compactness and mode count, we introduce a metric called mode density, defined as the ratio of mode count to device length. As illustrated in Fig. 8, our device achieves approximately an order-of-magnitude improvement in mode density, benefiting from the high design flexibility of the inverse design method, while maintaining excellent crosstalk suppression. It is important to note that the experimentally measured bandwidth in this work is not limited by the designed devices, and can be further increased by employing ASE sources with a larger available bandwidth. It is also worth noting that there exists a trade-off between mode count and bandwidth, as increasing either introduces larger effective index variations across modes and wavelengths, potentially affecting uniform performance. In future work, this challenge may be mitigated by increasing degrees of design freedom, such as through finer pixelation, enlarged optimization regions, or advanced inverse design methods.

Regarding on-chip multi-band signal transmission, only Ref. [36] has previously conducted experimental demonstrations. Through system optimization, we have achieved a significantly higher single-mode, single-wavelength line rate of 180 Gb/s and 114 Gb/s, along with an enhanced total capacity of 540 Gb/s and 342 Gb/s, at the 1550 nm and 2000 nm wavebands, respectively. To the best of our knowledge, this work realizes the highest reported signal transmission rate to date in the emerging 2 μm communication band. Furthermore, our work can be further optimized by reducing higher-order mode losses through improvements in fabrication processes and by increasing the degrees of freedom in the design of digital metamaterials. Additionally, recent advancements in high-speed PD with bandwidth exceeding 40 GHz [52] and MZM with bandwidth over 25 GHz [32] for the 2 μm band have been reported. These developments could be combined with our ultra-broadband mode MUX to achieve significant breakthroughs in system capacity. Most importantly, our mode MUX is not limited to operation in the demonstrated C-band and 2 μm band. It can be readily adapted to leverage extended wavelength ranges, including the C+L+U bands and the broad 2 μm region, unlocking significant potential for future high-capacity multi-band optical interconnect systems.

In this work, we present the first experimental demonstration of an inverse-designed multi-band three-mode MUX based on digital metamaterial structure, which achieves approximately an order-of-magnitude improvement in mode density compared to the forward-designed counterparts. Leveraging an edge-guided analog-and-digital optimization approach, the proposed MUX is capable of multiplexing TE0−TE2 modes within a compact footprint of 6μm×4.8μm. The device exhibits ultra-broadband performance, with simulation results showing insertion losses below 2.3 dB and crosstalk below −16.3dB across the 1500–2100 nm range, and loss variations under 0.94 dB. Experimental validation in the 1.55 μm and 2 μm bands, covering a total bandwidth of 160 nm, confirms insertion losses below 4.3 dB and 4.0 dB, respectively, with crosstalk below −11.6dB and −11.3dB. Furthermore, system-level optical interconnect experiments achieve single-wavelength transmission rates of 3×180Gb/s and record-high 3×114Gb/s at the 1.55 μm and 2 μm bands, respectively. The successful demonstration of multi-band MDM on-chip interconnect offers significant potential for integration with dense wavelength-division multiplexing within different wavebands, paving the way for a transformative advancement in on-chip optical interconnects.