Wavelength‐Division Holographic Multiplexing via Cascaded Metasurfaces and THz‐Spaced Microresonator Frequency Combs

ABSTRACT

Achieving high‐density wavelength multiplexing is essential for expanding the capacity of optical information processing. However, traditional optical components lack sufficient dispersion control, hindering high‐efficiency, low‐crosstalk wavefront manipulation across densely spaced channels. Here, we overcome this bottleneck by introducing a double‐layer cascaded metasurface architecture engineered via an end‐to‐end differentiable design framework. Through joint optimization, this cascaded design yields a 25‐fold increase in multiplexing density over single‐layer approaches, theoretically enabling 64‐channel holographic multiplexing with a tight 4.3‐nm spacing in the visible spectrum. Furthermore, we experimentally validate this architecture in the infrared band by utilizing a terahertz‐spaced microresonator frequency comb as a multi‐wavelength coherent source. This first‐of‐its‐kind integration of differentiable cascaded metasurfaces with on‐chip microresonator frequency combs provides a compact, highly efficient pathway for next‐generation wavelength‐division multiplexing, high‐capacity data communications, and integrated photonic systems.

A holographic multiplexing platform is presented using cascaded metasurfaces fabricated via two‐photon polymerization 3D printing and driven by a microresonator frequency comb. The 3D‐printed architecture enables high‐channel‐count holography with densely spaced wavelength channels. The system experimentally demonstrates 12‐wavelength‐channel operation in the near‐infrared band. Numerical simulations project a capacity of 64 wavelength channels across the visible spectrum, showcasing a scalable route to complex multi‐wavelength meta‐optics.

1. Introduction

High‐density multiplexing and independent manipulation of optical wavelengths constitute a core technology for enabling cutting‐edge applications, such as expanding optical communication capacity [1, 2], realizing color holographic displays [3, 4, 5], achieving multispectral imaging [6, 7, 8], and advancing integrated photonic computing [9]. The key to attaining this goal lies in the development of optical components capable of freely controlling the amplitude and phase of each wavelength channel at tightly spaced, nanometer‐scale intervals. Early multiplexing techniques faced limitations due to constrained control over physical dimensions and a scarcity of design degrees of freedom. As a result, channel capacities gradually approached theoretical bottlenecks, making it difficult to meet the explosive demand for information density in future optical communications, displays, and computing.

In recent years, metasurfaces [10, 11, 12] and diffractive optical elements (DOEs) [13, 14, 15] have provided pixel by pixel wavefront manipulation capabilities, offering unprecedented design flexibility. They enable discrete phase jumps at the sub‐wavelength scale, allowing for arbitrary phase modulation within a 2π range [16, 17, 18]. This phase‐stepping capability provides greater localized control than conventional optical designs, enabling the precise shaping of complex wavefronts within a single plane [19, 20]. However, their inherent limited phase accumulation depth and restricted dispersion capabilities impose fundamental limitations on design degrees of freedom when simultaneously handling multiple densely‐spaced wavelengths. Because traditional materials with linear dispersion exhibit nearly linear phase shifts outside their resonance bands, they are inadequate for independent phase modulation across narrow wavelength intervals [21, 22, 23]. This makes it exceptionally challenging to achieve complex phase distributions across multiple target wavelengths concurrently, often forcing difficult trade‐offs among efficiency, bandwidth, and crosstalk [21, 24, 25, 26].

Moreover, the prevailing design paradigm for holographic wavelength multiplexing in metasurfaces and DOEs remains largely confined to the three primary colors (RGB). This corresponds to a large frequency interval (Δf∼100 THz) and, more critically, a relative bandwidth (Δf/f _center) of ∼0.2. Such sparse sampling of the optical spectrum fundamentally underutilizes the available bandwidth and limits channel capacity to merely a handful of discrete wavelengths, leaving vast spectral regions functionally idle. Inverse design has expanded the accessible design space, yet its efficacy in a single‐layer architecture is intrinsically bounded by material properties [24, 26, 27, 28, 29, 30, 31]. Crucially, for a single meta‐atom to achieve decoupled phase control across N distinct wavelength channels, the required number of unique optical responses in the library scales unfavorably, creating a fundamental design bottleneck that restricts multiplexing density. The limited spectral selectivity of single‐layer metasurfaces prevents independent addressing of densely spaced spectrum lines. It is therefore imperative to develop new multiplexing architectures that physically augment the available degrees of freedom, enabling higher spectral density.

Concurrently, advancements in light‐source technology are reshaping the prospects for high‐density wavelength‐division multiplexing (WDM). The capacity of a WDM system is ultimately governed by both the spectral channel density and the source characteristics. Traditional multi‐wavelength sources, such as discrete laser arrays, are bulky and lack inherent phase coherence, while broadband continuum sources do not provide the discrete, stable spectral lines required for independent channel addressing. Among emerging candidates, microresonator soliton frequency combs have proven to be highly coherent, broadband multi‐wavelength sources. These combs have already enabled important applications in high‐precision ranging [32], coherent optical communications [33], low‐noise microwave generation [34], and optical clocks [35]. However, achieving terahertz (THz)‐repetition‐rate frequency combs on integrated microresonator platforms remains challenging, as it typically requires microresonator radii below 20 µm to obtain a THz‐scale free spectral range (FSR) [36]. However, such tight waveguide bends inevitably introduce significant scattering losses, which compromise the high quality factor (Q‐factor) required for Kerr frequency comb generation.

To overcome these bottlenecks, we propose a dual‐layer cascaded metasurface architecture, designed via an end‐to‐end differentiable framework and global optimization, which combines a THz‐spaced soliton microcomb that serves as a coherent, high‐repetition‐rate light source, as shown in Figure 1. The core of this scheme is the ability to work synergistically to achieve independent spatial encoding of THz‐spaced wavelength channels. This approach transcends isolated component development, paving the way for compact, high‐performance, high‐repetition‐rate nonlinear photonic systems.

FIGURE 1.

Schematic of wavelength‐division holography via THz‐spaced microresonator frequency combs. The double‐layer cascaded optical elements reconstruct distinct holographic images from the multiple closely spaced wavelengths provided by a microresonator frequency comb source.

We first establish the theoretical scalability of our method by designing a 64‐channel holographic multiplexing device operating in the visible band with a relative frequency spacing of 0.01, enabling low‐crosstalk, independent image reconstruction. In addition, through customized device design and advanced nanofabrication, we realize the first THz‐spaced single‐soliton microresonator frequency comb on a thin‐film lithium niobate (TFLN) platform—not as an isolated result, but as an enabling component for the integrated system. Using this chip‐scale light source, we experimentally demonstrate multi‐channel low‐crosstalk holographic display and switchable WDM in the infrared band. Our work establishes an effective route toward compact high‐density WDM systems driven by microresonator frequency combs. More broadly, the ability to independently manipulate densely‐spaced wavelength channels opens new possibilities for next‐generation photonic systems in communications, imaging, and information processing.

2. Result

2.1. Gradient Optimization Framework for Cascaded Metasurfaces

A cascaded system linearly accumulates minuscule inter‐wavelength phase differences through multi‐stage serialization, while leveraging the inherent wavelength dependence of diffraction propagation. Ultimately, it converts these differences into pronounced variations in intensity or spatial distribution, thereby overcoming the insufficient dispersion capability of a single‐layer structure. For a cascaded system composed of multiple optical elements, its modulation on incident light can be expressed as

$$E_{n+1}\left(x,y,\lambda \right)=P_n\left\{E_n\left(x,y,\lambda \right)·T_n\left(x,y,\lambda \right);z\right\}$$ (1)

here, E_n is the incident light of the n‐th propagation layer, T is the complex transmission function, P represents the propagation between optical elements separated by a distance z, and λ is the wavelength. Through iterative computation, the modulation result of light by a multi‐layer cascaded system can be obtained. The light propagation between diffraction layers follows scalar diffraction theory and is modeled using angular spectrum diffraction theory. The propagation can be expressed as

$$P\left\{E_0\left(x,y,\lambda \right);z\right\}={\mathcal{F}}^{-1}\left\{\mathcal{F}\left\{E_0\left(x,y,\lambda \right)\right\}·H\left(f_x,f_y,\lambda ;z\right)\right\}$$ (2)

$$H\left(f_x,f_y,\lambda ;z\right)=\left\{\begin{array}{c}\exp \left(i2\pi \frac{z}{\lambda }\sqrt{1-{\left(\lambda f_x\right)}^2-{\left(\lambda f_y\right)}^2}\right)\\ 0\end{array}\right.\begin{array}{c},if{\left(\lambda f_x\right)}^2+{\left(\lambda f_y\right)}^2\le 1\\ ,if{\left(\lambda f_x\right)}^2+{\left(\lambda f_y\right)}^2>1\end{array}$$ (3)

where E ₀ is the optical field before propagation and H is the angular spectrum transfer function.

Particularly in multi‐wavelength scenarios, this approach demonstrates greater design potential and energy utilization efficiency. However, the phase modulation capability of a single‐layer metasurface remains limited by its restricted degrees of freedom for dispersion control. When multiple wavelength channels are closely spaced, the high similarity in their phase responses leads to significant inter‐channel crosstalk. The introduction of a double‐layer cascaded metasurfaces effectively adds an independently designable diffraction dimension to the optical system. The coupled diffraction effects and wavelength‐sensitive spatial interference between the two metasurfaces significantly enhances the independent modulation capability across the wavelength dimension, enabling differentiated design of responses for different wavelengths.

To achieve the design objectives under multi‐wavelength conditions, we propose a gradient‐based optimization method for multi‐layer (specifically, double‐layer in this work) cascaded metasurfaces. As illustrated in Figure 2, incident light is sequentially modulated by two or more optical elements to achieve tightly spaced wavelength multiplexing. The method begins by initializing the parameters of all optical elements. For each metasurfaces, parameters such as pixel size, pixel count, element spacing, and the height distribution of each pixel are randomly initialized. By comparing the output with the design target and calculating the loss function, gradients of the loss with respect to the element parameters are obtained via the automatic differentiation module in PyTorch. Here, the loss function is defined as

$$\mathrm{Loss}=\frac{1}{N\times H\times W}\sum _{k=1}^N\sum _{i=1}^H\sum _{j=1}^W{\left(I_k\left(i,j\right)-I_{\mathrm{target}}\left(i,j\right)\right)}^2$$ (4)

where N represents the number of holograms, H and W denote the image height and width, and I denote the image intensity values. Subsequently, the Adam gradient descent algorithm is used to update the geometry parameter distribution of the pixels, completing one optimization iteration. This process is repeated until the loss converges or the maximum preset number of iterations is reached, ultimately outputting the optimized parameter distribution.

FIGURE 2.

Schematic of the joint optimization algorithm for multi‐wavelength cascaded holographic systems. Incident light at multiple wavelengths is modulated by the initial layer, propagates to the second layer (calculated via the angular spectrum diffraction method), and undergoes a second modulation before reaching the target plane. An end‐to‐end optimization is performed iteratively, utilizing gradient information derived from a loss function that compares the simulated optical outputs against the target images.

Through the co‐design of the cascaded metasurfaces via the optimization algorithm, it shortens the independently wavelength multiplexing interval. This enables precise and independent manipulation of the diffraction fields for densely spaced adjacent wavelength channels, thereby simultaneously fulfilling the performance objectives of high diffraction efficiency and low inter‐channel crosstalk in dense wavelength multiplexing scenarios.

2.2. Dense Wavelength Holographic Multiplexing

To validate the capability of the proposed method for handling dense wavelengths, we first design a twelve‐channel holographic multiplexer for the visible band. The design objective is to reconstruct twelve constellation patterns at twelve different wavelengths in the target field, with a central frequency of 547.58 THz and a relative frequency interval of 0.01, corresponding to an average spacing of 6.06 nm ranging from 516.84 to 583.05 nm. The design parameters of the cascaded diffractive optical elements are as follows: the pixel size of a single element is 400 nm, the number of pixels is 500 × 500, the spacing between the two‐stage elements is 200 µm, and the reconstruction plane is located 200 µm behind the second element.

Employing the differentiable optimization framework described, Figure 3a presents the simulated optical intensity distributions for the twelve target wavelengths. The twelve constellation patterns are clearly and independently reconstructed at their designated positions without visually apparent crosstalk. For comparison, holographic reconstructions for a single‐layer case are obtained using the identical optimization framework and parameters while constraining the complex amplitude of the second layer to a uniform distribution. Due to double‐layer transmission and interlayer energy leakage, its diffraction efficiency is approximately 26%. The image quality metrics exhibit a sharp peak response at each target wavelength and are suppressed at adjacent wavelengths (for more details, see Section S3). In this single‐layer configuration, the patterns exhibit extensive overlap, rendering the individual constellation shapes nearly indistinguishable. To quantitatively evaluate the enhanced wavelength‐multiplexing capability of the double‐layer structure over its single‐layer counterpart under conditions of dense wavelength spacing, Figure 3b presents violin plots of the image similarity value—specifically, the diagonal elements of the image similarity matrix (The matrix element M_ij is defined as the coefficient for the non‐negative decomposition of the image reconstructed at the i‐th wavelength with respect to the j‐th target image (used as a basis vector), obtained via non‐negative least squares factorization, see Section S1 for calculation details)—as a function of the relative frequency interval based on the above design. The image similarity for both configurations shows an increasing trend with larger relative frequency intervals, consistent with physical expectations. For the single‐layer, the average image similarity surpasses 0.5 only when the relative frequency interval exceeds 0.1, which approaches the practical limit for available spacing. In contrast, the double‐layer cascade achieves an image similarity of 0.6657 at a significantly smaller relative frequency interval of 0.004, corresponding to a 25‐fold increase in wavelength multiplexing density. Furthermore, the double‐layer structure maintains high reconstruction quality and low crosstalk at relative frequency intervals of 0.008, 0.016, 0.032, and 0.064, with average image similarity values all above 0.8.

FIGURE 3.

Numerical Results of Wavelength‑Multiplexed Multi‑Channel Holography. (a) Comparison of holographic reconstruction results between single‐layer and double‐layer of twelve‐constellation with a relative frequency interval of 0.01. (b) Image similarity of the reconstructed images versus relative frequency interval of 0.001, 0.002, 0.004, 0.008, 0.016, 0.032, 0.064, and 0.128 for both single‐layer and double‐layer cases. (c) Average PSNR of the reconstructed images versus relative frequency interval for both single‐layer and double‐layer cases. (d) Image similarity matrices for reconstructed images with 2, 4, 9, 12, 24, 32, 48, and 64 channels.

The performance advantage is further substantiated by the average peak signal‐to‐noise ratio (PSNR) of the reconstructed images across different relative frequency intervals. The double‐layer configuration demonstrates significantly superior performance, with a maximum PSNR improvement of approximately 5.5 dB (from 17.45 to 22.94 dB) compared to the single‐layer structure. For the specific twelve‐constellation example in Figure 3a, the average value of the diagonal elements in the image similarity matrix is 0.8166, markedly higher than the average off‐diagonal element value of 0.0167, confirming excellent wavelength selectivity. This scalability is tested by reconstructing images with varying channel counts (2, 4, 9, 12, 24, 32, 48, and 64). Even with 64 channels, an average PSNR of 25.31 dB is attained. Figure 3d presents the image similarity matrices for reconstructed images with different numbers of channels. For all channel counts, the main diagonal elements of the image similarity matrix remained substantially higher than the off‐diagonal elements. At 64 channels, the average main diagonal value is 0.3111, compared to an average off‐diagonal value of 0.0109. Additional details are provided in Section S4.

2.3. Near‐Infrared Multi‐Wavelength Holographic Multiplexing

Since off‐the‐shelf optical frequency comb sources are typically limited to repetition rates below 1 GHz, we develop a THz‐spaced microresonator frequency comb designed for metasurface‐based holographic multiplexing. Generating these combs in integrated platforms requires an ultra‐small microresonator with radii below 20 µm. To mitigate the significant scattering losses associated with sharp waveguide bends, we optimize the fabrication process to achieve smooth microresonator sidewalls, as described in Section S6.

We employ the experimental setup shown in Figure 4a to generate the THz‐spaced microresonator frequency comb. Figure 4b presents a scanning electron microscopy (SEM) image of the fabricated TFLN micro‐ring resonator, featuring a compact radius of 19.5 µm and a measured FSR of approximately 1.02 THz (Figure 4c). Furthermore, the device exhibits a high intrinsic Q‐factor of 6.8 × 10⁵ (Figure 4d), corresponding to a low propagation loss of 0.55 dB/cm. The optimized integrated dispersion (D_{i nt}) profile in Figure 4e (see details in Methods) allows us to achieve a broadband soliton comb spectrum (1300–1950 nm) with a line spacing of ∼1.02 THz. Using a customized fiber Bragg grating (FBG), we select three specific comb lines at 1533.65, 1549.83, and 1566.29 nm to serve as the coherent multi‐wavelength source for subsequent encoding and holographic imaging experiments. The detailed characterization of the microresonator frequency combs is provided in Methods.

FIGURE 4.

Generation of THz‐spaced soliton microresonator frequency combs. (a) Schematic of the experimental setup. (b) SEM image of the fabricated TFLN microresonator. (c) Measured transmission with an FSR of ∼1.02 THz (8.2 nm). (d) Exemplary resonance curves with extracted Q‐factors. (e) Calculated integrated dispersion (D _int) with the TE₀₀ cavity mode shown in the inset. (f) Measured soliton comb spectrum with a repetition rate of f _rep ≈ 1.02 THz. The labels (I, II, III) indicate selected comb lines at 1533.65, 1549.83, and 1566.29 nm, respectively.

To demonstrate the practical applicability of the cascaded system in the telecommunication band, we design and fabricate a simplified double‐layer cascaded DOE tailored for the THz‐spaced microresonator frequency comb. For this proof‐of‐principle demonstration, we reduce the number of wavelength‐multiplexed channels to three. This configuration independently performs holographic imaging for three specific comb lines (λ₁ = 1533.65 nm, λ₂ = 1549.83 nm, λ₃ = 1566.29 nm), corresponding to an average frequency interval of 2.04 THz and a relative frequency interval of 0.0106). These three channels are used to reconstruct the letters “A”, “B”, and “C” at distinct locations in the target field. The samples are fabricated from IP‐DIP2 photoresist using two‐photon polymerization 3D printing technology (more details can be found in Section S8), with a pixel size of 5 µm arranged in a 200 × 200 array. Both the inter‐layer spacing and the reconstruction distance are fixed at 3.3 mm.

The experimental setup is shown in Figure 5a. The three selected comb lines, delivered through an optical fiber, are converted into collimated beams by a fiber collimator, sequentially modulated by the cascaded metasurface layers, and finally recorded by an infrared CCD at the reconstruction plane. Figure 5b displays the holographic reconstruction images captured when the device is individually illuminated by each of the three target wavelengths. For the double‐layer device, each wavelength generates a bright, well‐defined letter image at its designated position. While some crosstalk is observed due to finite fabrication precision and experimental alignment errors, the intended reconstructed image for each wavelength remains energetically dominant. This is corroborated by the image similarity matrix, whose main diagonal elements are significantly higher than the off‐diagonal elements, representing a distinct improvement over the nearly uniform matrix of the single‐layer device. We have also experimentally verified 12‐channel multi‐wavelength multiplexing at subwavelength periods. In Figure 6, the two cascaded samples have an array size of 500 × 500 with a unit period of 1000 nm. Twelve wavelength channels were selected with equal frequency spacing over 1505 to 1625 nm (184.6 to 199.3 THz) to reconstruct twelve constellation patterns, corresponding to a relative frequency interval of 0.00725. The position of each constellation pattern was shifted to a distinct orientation. Each target pattern is reconstructed as the corresponding image at the correct wavelength, and the reconstruction intensity is notably higher than that of the patterns from other channels. For the experimental results, the average value of the diagonal elements is 0.5077, and the average value of the off‐diagonal elements is 0.0448. The corresponding details are provided in Section S7. The cascaded system imposes relatively stringent requirements on alignment error. Pixel‐level alignment is required to achieve precise dense wavelength multiplexing. According to the analysis in Section S5, our design can reconstruct distinguishable images with a lateral inter‐layer misalignment of less than ±20 µm and a vertical inter‐layer misalignment of less than ±50 µm, simplifying the subsequent precise alignment steps. This level of tolerance is attainable with standard alignment processes. These results confirm that the designed cascaded metasurfaces can accurately resolve and independently manipulate THz‐spaced frequency comb lines for enabling programmable multi‐wavelength routing.

FIGURE 5.

Experimental results of wavelength‐multiplexed holography driven by THz‑spaced microresonator frequency combs. (a) Schematic diagram of the experimental setup. (b) Numerical and experimental holographic reconstructions at three selected comb lines (λ₁ = 1533.65 nm, λ₂ = 1549.83 nm, and λ₃ = 1566.29 nm). Image similarity matrices are provided for the single‐layer simulation, double‐layer simulation, and double‐layer experiment, quantifying the cross‑talk among the reconstructed images at each wavelength.

FIGURE 6.

Experimental results of 12‐channel wavelength‐multiplexed metasurface holography. (a) Numerical and experimental holographic reconstructions at target wavelengths (The images have been cropped to zoom in on the corresponding patterns; the original patterns can be found in Figure S12). (b) Schematic diagram of the experimental setup. (c) Image similarity matrices of the double‐layer simulation and double‐layer experiment for 12 channels.

3. Discussion

In summary, we have proposed and validated a novel approach to address the systematic challenges of high‐density wavelength multiplexing. This scheme overcomes the fundamental spectral selectivity limitations inherent in single‐layer metasurfaces or diffractive optical elements. Physically, the dual‐layer cascaded architecture introduces an additional, independently designable spatial dimension. Algorithmically, an end‐to‐end differentiable optimization framework effectively explores this expanded parameter space. This synergy enables the tailored synthesis of complex dispersion profiles, allowing the device to produce the desired phase response at target wavelengths while imposing significantly distinct responses on adjacent channels. As a result, the system achieves precise and independent spatial encoding of densely spaced wavelengths, as evidenced by a 25‐fold increase in designed multiplexing density and the experimental demonstration of low‐crosstalk holography with channel spacings of ∼2 THz (or ∼16 nm) using diffractive elements in the infrared band. The integration of on‐chip combs with cascaded metasurfaces demonstrate a powerful, compact subsystem for high‐density wavelength manipulation. Beyond this specific demonstration, the differentiable optimization framework is general and scalable. Its core strength lies in the deep coupling between the physical model and the optimization algorithm. This allows for the joint optimization of various practical constraints—such as fabrication imperfections and alignment tolerances—within the loss function. It thereby facilitates a shift from pursuing “theoretically optimal” designs toward delivering “manufacturing‐tolerant” solutions. The approach paves the way for next‐generation compact, high‐capacity wavelength‐division multiplexing systems, parallel photonic processing, and advanced spectral imaging, where independent control over numerous closely spaced spectral channels is essential.

4. Methods

4.1. Characterization of THz‐Spaced Microresonator Frequency Combs

We employed the experimental setup shown in Figure 4a for characterizing the microresonator frequency comb. An arbitrary waveform generator (AWG) is used to control a continuous‐wave (CW) tunable laser (Santec TSL‐550C), enabling bidirectional frequency sweeps across the resonator mode at 1549.83 nm with a scanning rate of 5 Hz. The pump power is boosted by an erbium‐doped fiber amplifier (EDFA), and its polarization state is adjusted by a polarization controller (PC) to excite the TE₀₀ mode of the TFLN waveguide. The input light is coupled through a collimator and lens pair, while the output is collected by a lensed fiber and characterized using an optical spectral analyzer (OSA) and a photodetector (PD) connected to an oscilloscope (OSC). An optical isolator (ISO) and FBG are placed before the PD to suppress the intense pump light.

The fiber‐to‐chip insertion loss is measured to be ∼6 dB/facet. A zoom‐in view of the resonance near 1549.83 nm in Figure 4d indicates a full‐width at half‐maximum linewidth of 3.8 pm, corresponding to a loaded Q‐factor of Q_L = 4.1 × 10⁵. The intrinsic Q‐factor is estimated to be Q ₀ = 6.8 × 10⁵ at under‐coupled conditions. The calculated D _int profile in Figure 4e indicates that the microresonator supports dual dispersive wave emission, thereby allowing broadband frequency comb generation.

Author Contributions

L.H. conceived the project and conducted the design. Y.Y. developed the optimization algorithm and performed the numerical simulations. J.L. fabricated the cascaded samples. T.L. designed and fabricated the microresonator. Y.Y. and T.L. conducted experiments and measurements. L.H., X.L., Y.Y., and T.L. carried out data analyses. All authors contributed to manuscript preparation and discussion.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File: adma74054‐sup‐0001‐SuppMat.docx.

Data Availability Statement

The data that support the findings of this study are available from the corresponding authors upon request.