Introduction

As a ubiquitous physical phenomenon rooted in fundamental thermodynamics, thermal radiation inherently generates broad-spectrum electromagnetic (EM) waves governed by Planck’s law1. While its applications span from primitive illumination to a variety of modern technologies such as infrared detection2 and passive cooling3, conventional implementations predominantly manipulate photon intensity within the diffusive regime. The inherent spatiotemporal incoherence and polarization randomness of thermal photons set an insurmountable barrier for their integration into phase-critical photonic systems—a realm exclusively served by coherent laser sources. Although bulk optical configurations incorporating spectral filters and polarization modulators can partially enhance thermal light correlation, such approaches inevitably introduce prohibitive energy losses and system complexity4. This persistent challenge underscores the critical scientific question: how to engineer compact thermal emitters that directly generate wavefront-engineered coherent radiation? Resolving this conundrum holds transformative potential for bridging the gap between thermodynamic principles and photonic information technologies, representing an enduring pursuit in the scientific community over the past decades.

Enhancing thermal coherence necessitates simultaneous phase correlation improvement across both spectral and spatial domains. In 1990s, Greffet et al. discovered long-range near-field correlation can be achieved along the emission surface with the aid of resonant surface modes, such as surface-plasmon polaritons (SPPs) or surface-phonon polaritions (SPhPs)5,6. In 2002, they pioneered the experiment to generate and observe this coherent thermal emission over a polar crystal (silicon carbide) surface7. Subsequent advances in metasurfaces spurred the development of resonant architectures—including SPhPs8,9,10,11,12,13, SPPs14,15,16,17,18, coupled resonant cavities19, bound states in the continuum (QBIC)4,20,21 and extended guided modes22,23,24—enabling the engineering of spatiotemporal coherence through tailored dispersion relations.

For these resonant absorptive surfaces, resonant modes rely on collective interactions across a large number of periodic units, rendering their resonant behavior highly sensitive to the structural variations. However, structural complexity is crucial for shaping wavefronts25. While slightly introducing local perturbations can achieve asymmetric unidirectional emission21, band splitting introduces additional lattice modes that severely disrupt the emission wavefronts and degrade the signal-to-noise ratio (SNR), as illustrated in the left panel of Fig. 1a. Further increasing the structural complexity to an aperiodic arrangement necessitates multi-layered nano-fabrications to suppress the local perturbation to the nonlocal resonances, which hinder its experimental developments4. Besides, long range of disorder leads to a higher density of split subbands, approaching a quasi-continuum band (see Supplementary Notes S1.2-1.3 for detailed analysis). This broadened band degrades the coherence of resonances, making it challenging to achieve complex thermal wavefront emission, such as thermal focusing and holography.

Fig. 1: The challenge of thermal wavefront modulation and schematic of meta-emitter.
Fig. 1: The challenge of thermal wavefront modulation and schematic of meta-emitter.
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a Challenges in thermal wavefront shaping. In the resonant lossy surface framework, an inherent trade-off exists between the signal-to-noise ratio (SNR) and the complexity of the thermal wavefront, rendering the emission of intricate thermal wavefronts elusive. In contrast, the lossy and lossless resonant coupling framework suppress the mutual perturbation between resonance and local scatterers, enabling complex thermal wavefront emission with high SNR. b Concept of DF model. Thermal photons generated within the “lossy funnel” are transported to the “lossless funnel” through a bridging resonant “tunnel” while extending their lifetime. c Cross-section of the schematic architecture of DF meta-emitter. The inset enlarges the view of the DF meta-emitter around the central WG. Dispersion relationships \(\omega (k)\) on both sides can be designed by various structures for specific wavefront control requirement. Temporal coherence: cτ; local scatterer: S; WG: waveguide.

Separating the lossy resonance and lossless emitter could significantly suppress the local perturbations to the resonance, thereby theoretically enabling complex emission functionalities26. However, their experimental realization faces challenges, such as position-dependent absorptive-structural fabrication and limited emission power. Due to these limitations, although extensive efforts have been made to enhance the coherence of the thermal radiation, all the experimental demonstrations so far have been confined to planar wavefront emission. More complex wavefront emissions, such as thermal focusing and holography, remain largely theoretical4,13,26. Detailed emission performances and mechanism comparisons between our work and previous studies can be found in Supplementary Note S1.1 and Supplementary Table 1.

Here, we introduce a thermal meta-emitter incorporating separating but synergistic waveguide-coupled lossy and lossless boundaries, enabling arbitrary thermal wavefront manipulation capability without sacrificing SNR or too much emission power, as shown in Fig. 1a. The single connecting waveguide ensures fixed scattering phase relationship on the scattering surface, endowing meta-emitters with arbitrary phase modulation capability. Experimentally, we demonstrate self-focusing thermal emission with near-diffraction-limit performance and quasi-2D high-quality coherent thermal holography with negligible speckle noise, providing the first experimental demonstration of deterministic thermal wavefront control that approaches monochromatic-level performance metrics. Furthermore, we show that the proposed framework can be spatially encoded to realize multiplexed thermal holography. By optimizing the connecting resonance, the spatial coherence of our device can be further extended to 100λ₀ while retaining all these fascinating functionalities (asymmetric emission, focusing and holography). This work establishes a paradigm-shifting platform for coherent thermal radiation control, enabling functional wavefront shaping capabilities that bridge the gap between thermodynamic emission and precision photonic engineering.

Results

Architecture of meta-emitter

The meta-emitter incorporates near-field synergistically coupled lossy and lossless boundaries, which can be aptly conceptualized as a dual-funnel (DF) model, as schematically shown in Fig. 1b. Similar to conventional thermal metasurfaces, the bottom ‘lossy funnel’ engineers the thermally populated electromagnetic mode, and transports it to the “lossless funnel” through a coupling resonant “tunnel” while extending their lifetime. These long lifetime photons correlate the scatterers in the “lossless funnel” with designed phase-delay, thereby efficiently enabling the transformation of the temporal coherence (Wt) to the spatial coherence (Wx) of tailored emission waves. The connecting tunnel serves as an effective coherent source, fixing the scattering phase on the lossless funnel, similar to the point source in ref. 26. The thickness of the design can be suppressed to 1λ0, which is similar to that of conventional thermal metasurfaces.

The corresponding physical architecture is shown in Fig. 1c, comprising two corrugated metallic surfaces with an inner bridging waveguide (WG) tunnel at the center. In this bull’s eye configuration27,28,29,30, thermally populated photons from the lossy bottom surface are efficiently transported to the lossless top surface for devising manipulation, driven by the strong Fabry-Pérot (FP) resonance occurring inside the central WG tunnel. Besides, this narrow WG tunnel effectively mitigates the dispersion-induced “rainbow effect” prevalent in periodic structures7,14,31. The cavity mode’s quality factor (Q-factor) dictates the temporal coherence of transmitted thermal photons, which is transformed into the spatial coherence through the propagation of surface modes. Local scatterers on this radiation surface can be strategically introduced as defect perturbations to contrive phase-correlated thermal emission.

Different from the previous studies usually utilizing band edge standing wave modes with a large Q-factor to enhance spatial coherence, our architecture decouples resonator and scatterers to fully leverage propagating surface wave to efficiently transform the temporal coherence into spatial coherence. The spatial coherence L of meta-emitter characterizes the distance traveled by the wave packet accumulating a specific phase-delay difference, which can be linked to the temporal coherence via the relation \(\Delta \phi=L\Delta \beta=\,\tau \Delta \omega\), where \(\Delta \beta\) and \(\tau\) are respectively the wavevector difference within \(\Delta \omega\) and the photon lifetime. For a high Q resonance (\(\Delta \omega\) → 0) with a specific mode lifetime, the spatial coherence can be expressed by the function of mode lifetime as \(L\approx \tau \frac{d\omega }{d\beta }=\tau {\cdot v}_{{\rm{g}}}\), where vg denotes the group velocity. Supplementary Note S2 showcases an example of the two surface modes with similar lifetime at the same operational frequency could have obviously different spatial coherences along the surface. For the bandedge mode, the band variance can no longer be reflected by the group velocity; the higher-order polynomial expansion term, such as band curvature (\(b\propto {d}^{2}{\rm{\omega }}/d{\beta }^{2}\)), needs to be applied4,21,32 to estimate the spatial coherence.

Physically, this conclusion can be understood as the distance traveled by wave packet within its lifetime. It’s worthy to note that, temporal coherence (Q-factor of the mode) just set an upper boundary of spatial coherence (Lc = cτ, where c is the light speed in free space), different spatial coherence can be obtained with the same temporal coherence by modifying the slope of the operational band, which is not clarified in the previous studies.

Leveraging this temporal-to-spatial coherence transformation concept, we employ spoof SPPs in our study as energy carriers owing to their low-loss and band-engineerable characteristics across the entire thermal spectrum spanning from terahertz to mid-infrared frequencies. Critically, groove-geometries enabled radiation phase and group velocity manipulation capability makes it easily meet the versatile requirements for complex thermal wavefront shaping. Figure 2a plots the band diagrams of three representative spoof SPP modes explored in our design: a nonradiative bounded mode (BM) below the light cone and two radiative modes: a weakly radiative mode (W-RM) and a strongly radiative mode (S-RM). The W-RM can be viewed as a perturbed version of the BM, where enlarging one of the grooves within a long period folds the band into the light cone. The S-RM represents the extreme case of the W-RM, obtained by removing all the interconnection grooves within the period. The band diagrams of three modes with light lines are shown in Supplementary Fig. 5. The plasma frequency follows the relation ωspoof = πc/2h (where c is the light velocity in vacuum), allowing for broadband adaptability through freely adjustable groove depth h33,34. As shown in Fig. 2b, with realistic material loss, the surface mode lifetime τsurf (defined as τsurf = Qsurf/ω0) and decay length LD (calculated as: \({L}_{D}={\tau }_{{\rm{surf}}}{\cdot v}_{{\rm{g}}}\)) of spoof SPPs can vary in two orders of magnitude, providing the flexibility in accommodating devices in different dimensional scales.

Fig. 2: Design and characteristics of meta-emitter.
Fig. 2: Design and characteristics of meta-emitter.
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a Dispersion diagrams of different spoof SPP modes. The periods of the BM, W-RM and S-RM are 0.13λ0, 0.70λ0, and 0.87λ0, respectively. Groove widths and depths are 0.06λ0 and 0.13λ0 for BM, 0.1λ0 and 0.11λ0 for S-RM. For W-RM, the width of center groove is the same as that in S-RM and other parameters are the same as those in BM. Mode profiles of single unit at frequency ω0 are shown in the right panel. b The mode lifetime (τsurf = Q/ω, τ0 = 2π/ω0, blue bars) and propagation length (\({L}_{D}={\tau }_{{\rm{surf}}}{\cdot v}_{{\rm{g}}},\,{v}_{{\rm{g}}}=\frac{{\rm{d}}{\rm{\omega }}}{{dk}}\)@ω0) along the surface (purple bars) for the above modes. The y-axis is normalized by λ0. c The eigenfrequency and mode lifetime as a function of w1. l1 = 2λ0 is set in the simulation. Inset: the eigenmode profile. d Energy tunneling efficiencies of the hybrid mode with BM on the bottom surface and BM, W-RM and S-RM on the top surface. l1 = 2λ0, w1 = λ0/150 are set in the simulation. e Eigenmode profile of the meta-emitter. The BM is configured as both the bottom and top structures in the simulation. Here, O and r represent the coordinates of the WG and an arbitrary point on the top surface, while ρ denotes the distance between these two points. f Cross-spectral density component Wzz (ρ) of the surface wave as a function of ρ at fixed height z0 = λ0/10 above the surface. g Spatial coherence of different surfaces as a function of w1.

When the propagation loss is small, the spatial coherence of thermal photons is mainly influenced by the finite lifetime τWG of WG mode, which determines the bandwidth (Fig. 2c, inset). This WG mode exhibits a dynamic balance between radiative dissipation and intrinsic damping losses. As shown in Fig. 2c, τWG (Q-factor, τWG = QWG/ω0) peaks at τWG,max = 25τ0 with τ0 = 2π/ω0 for optimal WG width w1, confirming the geometric configuration that minimizes loss. Our theoretical framework (Discussion and Supplementary Note S14) predicts that advanced tunneling cavity designs could suppress loss channels, potentially enhancing τWG,max by two orders of magnitude. The energy transfer efficiency from bottom surface mode to the radiation interface achieves resonant amplification, showing a significant enhancement at matched frequencies compared to off-resonance states (Fig. 2d). This phenomenon arises from near-field coupling between confined surface waves and the WG cavity mode, as visualized by their superimposed electric field distributions (Fig. 2e). The hybrid modes create a photonic “superhighway” that preferentially channels thermal energy while suppressing parasitic dissipation. The lifetime of the hybrid mode is governed by the reciprocal relation 1/τ = 1/τWG + 1/τsurf. Detailed efficiency simulations and comparisons between our design and classical giant transmission schemes27,28,35 are provided in Supplementary Note S3.1. By applying an additional metal board to transform the surface waveguide into a photonic crystal, the bottom surface can be designed as a defect cavity, boosting the emissivity of the device to ~75%. The corresponding design strategies and discussion are also provided in Supplementary Note S3.2.

Crucially, our DF architecture enables independent modulation of these critical parameters. Figure 2g illustrates the spatial coherence of three modes (BM, W-RM, S-RM) as a function of the geometric parameter w1 at the operational frequency ω0. The WG mode’s finite lifetime fundamentally limits coherence, with measured maxima of 15λ₀, 14λ₀ and 9λ₀ for BM, W-RM, and S-RM, respectively. This discrepancy highlights propagation loss effects under high-Q bridging cavity conditions. For validation, cross-spectral density analysis by the component36,37 \({W}_{{zz}}(\rho,\,z={\lambda }_{0}/10)={\left\langle {{E}_{z}}^{*}\left(O,z\right){E}_{z}(\rho,z)\right\rangle }_{\omega }\) was also performed in simulated data, as plotted in Fig. 2f. The \(1/\sqrt{e}\) correlation lengths of the Wzz are 14λ₀, 13λ₀ and 8λ₀ for BM, W-RM and S-RM, respectively, consistent with the monochromatic model predictions, laying the foundation for the further wavefront manipulation. Detailed derivations are provided in the Method section.

In the following, advanced coherent devices can be obtained through the rational design of local defect scatterers on the emission surface. Due to the narrow width of the designed scatterers (around λ0/10), the emitted phase can be simplified to solely depend on the propagation phase of the spoof SPPs38,39. To streamline the experimental implementation and analysis, our experiments are conducted in the terahertz regime where wavelength-scale phenomena permit precise defect engineering and near-field characterization.

Self-focusing thermal emission

Our first application is to demonstrate diffraction-limited self-focusing thermal emission using a one-dimensional (1D) meta-emitter. As schematically depicted in Fig. 3a, the self-focusing device features a hybrid mode design. The bottom surface is engineered to operate in S-RM, enabling efficient harvesting of ambient thermal energy. Meanwhile, the top surface functions in W-RM and is divided into two distinct functional zones: an outer radiative region (Sr) and an inner coupling region (Sc). Grooves in the coupling region are optimized to match momentum with the WG mode, whereas those in the radiative region are engineered to operate in W-RM. Here, local scatterers are strategically introduced to fulfil the desired emission wavefront. For focusing functionality, it will satisfy a spherical spatial phase profile, i.e.,

$$\varphi (x)={k}_{0}\cdot (\sqrt{{x}^{2}+{f}^{2}}-f)$$
(1)

where x is the coordinate on the surface, f is the focal length and k0 is the free-space wavevector. The position of scatterers is determined by the condition of\(\,\varphi \left(x\right)+\,{k}_{{\rm{sspp}}}x=2m{\rm{\pi }}\), where m is an integer and ksspp is the wavevector of spoof SPP optimized for radiative grooves. Details on parametric optimizations, including ksspp, groove dimensions, and Sc functionality, are provided in Supplementary Note S4 and Supplementary Table 2. For the optimized structure, the eigenmode field analysis (Fig. 3b) reveals a well-defined focusing pattern with a focal length f = 10λ0 (λ0 ≈ 3 mm) and numerical aperture N.A. = 0.7. It achieves a high focusing efficiency of ~95% (defined as the ratio of the integrated energy at the focal line to the energy at the WG exit, details can be found in the Supplementary Note S4 and Supplementary Fig. 10) and a tightly confined focal line of 0.93λ0 (equivalent N.A. = 0.53) realized under the incidence of nonuniform surface wave across the aperture. The focal line width can be further reduced to the ideal limit of 0.72λ0 by engineering the radiative loss of the top surface to achieve a near-uniform scattered amplitude wavefront at the expense of dissipating surface wave energy at the edge of the device. A comprehensive time-domain analysis in Supplementary Note S5 elucidates the transient focusing process initiated by a dipole source positioned near the bottom surface. Supplementary Movie 1 vividly exhibits the dynamic evolution of the hybrid coupling of the spoof SPPs with WG mode, significantly extending the lifetime of thermal photons. In addition, it is important to note that although the FP modes in the central WG exhibit dispersion with respect to the transverse wavevector ky, as shown in Fig. 3c (detailed information can be found in Supplementary Note S6), the leaky groove-based meta-lens employed here features the desired achromatic focusing property (Fig. 3d). Photons of different frequencies converge to form a transverse focal line at the common focal plane z = f, which boost energy utilization efficiency.

Fig. 3: Self-focusing thermal meta-emitter.
Fig. 3: Self-focusing thermal meta-emitter.
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a The surface wave modulation design. Sc denotes the coupling surface region, which couples the output energy from the WG to the spoof SPPs. Sr represents the radiation surface region, where spoof SPPs are scattered at designed positions to form a focusing profile. b Eigenmode profile of the designed structure. The inset shows an enlarged view of the white dashed region, with the intensity rescaled to clearly display the WG mode pattern. Copper with conductivity of σ = 5.8 × 107 S/m is applied in the simulation. c Out-of-plane wavevector (ky) dispersion of the meta-emitter. d Focal length of eigenmode as a function of ky. The WG length is set to 2.9 mm in the simulation. e–g Ensemble-averaged intensity profiles in the xz, yz, and xy planes under random dipole excitation. h Schematic of the experimental setup. The sample coated with a blackbody layer on the back side is heated using a hot plate. The thermal radiation pattern is collected point by point using a millimeter-wave detector mounted on a 3D translation stage. A foil-wrapped board is employed to block background thermal noise from the hot plate. Upper inset: simulated and measured transmission spectrum of the sample under plane wave excitation at normal incidence. Bottom insets: photographs of the sample images on both sides. Bare and blackbody painted bottom surfaces are presented in the upper panel and bottom panel in the inset. WG: waveguide. The temperature is maintained at 120 °C during the measurement. i–k Measured intensity profile at xz, yz, and xy plane, respectively. Scalar bar: 3 mm. The detailed comparison of intensity profiles in the experiment and simulation can be found in Supplementary Note S9 and Supplementary Fig. 19. Fig. b, e, and i show focal intensity cross-sections in their insets, with FWHM marked on the profiles.

To numerically characterize the stochastic thermal emission behavior of our design, we performed 100 simulations with randomly distributed dipole excitation below the bottom surface with distance of 0.3λ0 to obtain statistical results (detailed simulation methods given in “Method”)26. Averaged intensity profiles across different planes (Fig. 3e–g) demonstrate robust focusing performance: the obtained full-width-at-half-maximum (FWHM) (1.03λ0) of the ensemble-averaged focal line closely approaches the diffraction limit (0.93λ0) observed in eigenmode simulations (Fig. 3b), confirming high spatial coherence across the entire aperture. The slightly broader FWHM in the ensemble-averaged case relative to the eigenmode result (inset, Fig. 3b) arises from contributions of off-resonant frequencies near the eigenfrequency. This effect can be further mitigated by enhancing the Q-factor of the WG mode, such as tunnel geometry optimization analyzed in the Discussion part.

With the optimized design, a copper sample was fabricated using the computer numerical control (CNC) cutting technique. The transmission spectrum under normal incidence (inset, Fig. 3h) shows good agreement with simulations, though the measured transmission peak is slightly broader and blue-shifted, primarily due to fabrication tolerances. The groove fabrication tolerances are within the sculpturing precision of state-of-art CNC techniques. A weak absorptive layer, ~60 μm blackbody paint (BB paint Musou black 2.0, n ≈ 1 + 0.02i @100 GHz), was applied to the bottom surface for thermal photon generation, as shown in the inset of Fig. 3h. This BB layer has minor influence on the lifetime and decay length for S-RM mode in the design, due to its weak localization property. The detailed analysis on the lifetime and decay length degradation for surface modes caused by BB layer is presented in the Supplementary Note S7. The detailed fabrication tolerance analysis is presented in Supplementary Note S8.

The thermal measurement setup and sample photographs are presented in Fig. 3h. The detailed experimental information is given in the Methods section. Using this setup, intensity profiles at different planes were mapped, as shown in Fig. 3i–k. The intensity mapping validation is analyzed in Supplementary Note S9. The FWHM of the measured focal line is ~3.2 mm (1.06λ0), closely matching the statistical numerical result (1.03λ0) plotted in Fig. 3e. Importantly, the near-diffraction-limit focusing performance indicates that all grooves contribute coherently to the focal spot, with a spatial coherence equivalent to the aperture size (11λ₀)— almost an order of magnitude longer than the state-of-the-art reported in ref.21. Other measurements align well with simulations, including intensity distributions in xz and yz planes, as quantitatively compared in Supplementary Fig. 19c–e. The intensity local minima near the center WG is originated from the non-ideal interference of the waves scattered from the left and right sides of lens grooves, due to the depth fabrication error in the coupling region around the slit exit. The detailed analysis can be found in Supplementary Note S8.4.

The flat-topped focal line profile arises from the detector’s finite response band (75–120 GHz), which attenuates high-frequency components with large transverse wavevector ky, which is analyzed in Supplementary Note S10 by ray-tracing calculation. Detailed experimental methodologies are given in the Methods section.

Polarization and spatial multiplexed coherent thermal holography

In this section, we demonstrate 1D and quasi-2D coherent thermal holography with more complex light-field manipulation using our DF meta-emitter architecture. Leveraging the design flexibility of S-RM, we introduce polarization multiplexing along orthogonal directions. The shallow grooves (<λ0/5) together with low filling ratio (<10%, defined as groove width w to the period p, F = w/p) of S-RM, ensuring that the cross-polarization-coupling between orthogonal channels can be neglected. By integrating these advantages with a scattering-based holographic design approach39,40,41, we experimentally realize quasi-2D coherent thermal holography through superposition of patterns with distinct polarization states, as exemplified by the digital “8” in Fig. 4a–d. Higher-order diffraction observed in Fig. 4b, d—attributed to fabrication tolerances—can be minimized using precision nano-fabrication techniques. Non-uniform background noise arising from detector zero-point drift is addressable via advanced methods like lock-in amplification42,43. Experimental results for additional holographic numbers (0, 4, 7) are shown in Fig. 4e–g, all achievable through the proposed design framework. To quantitatively evaluate the quality of holographic image44, we calculate the SNR = \(\left\langle I\right\rangle\)/s, in which \(\left\langle I\right\rangle\) and s are the mean and standard deviation of intensity within the blue rectangle box marked in Fig. 4f. Moderate coherence of the engineered thermal light greatly suppresses the speckle noise45, leading to a high image quality (SNR = 22). Detailed design schematics and polarization multiplexing strategies are provided in Supplementary Note S11.

Fig. 4: Measurement of coherent thermal hologram.
Fig. 4: Measurement of coherent thermal hologram.
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a Schematic diagram of the hologram of “8”. b, c Holographic pattern and image of the top side of sample. d The intensity distribution of y-polarized, x-polarized light. e–g Holographic patterns for “0”, “4” and “7”, respectively. h Schematic diagram of spatial multiplexed holography. By exciting different grooves, two holographic states can be switched. i Image of the top side of the spatial multiplexed sample. 5 slits with sequential numbers (1–5) are marked in the figure. Red (1, 3, 5) and blue (2, 3, 4) lines denote the excitation WGs for the hologram of ‘5’ and ‘2’, respectively. The shadow region in the center denotes the spatial multiplexed area. j, k Holographic patterns for ‘5’ and ‘2’, respectively. Corresponding excitation WG numbers are marked below. Scalar bar: 1 cm.

To further showcase the wavefront control versatility of our design, we develop and experimentally realize a spatially multiplexed holographic device, as depicted in Fig. 4h. Grooves within the central shadowed region of the top surface are optimized to simultaneously accommodate two distinct holographic wavefront profiles (Fig. 4i). By leveraging the directional propagation of spoof SPPs along the radiative surface, two unique emission states are achieved through selective excitation of corresponding WGs. Experimental switching between blocked WGs yields separate holographic patterns of ‘5’ and ‘2’ (Fig. 4j–k), with the activated excitation slit WG indicated below each image. Detailed optimization procedures and structural parameters are provided in Supplementary Note S12. Additionally, adjusting the WG width enables tuning of emitted wave coherence: off-axis focusing with multiple diffraction orders demonstrates low coherence, while spatially multiplexed designs with insufficient mode decay highlight excessive spoof SPP spatial coherence (Supplementary Note S13). This demonstration of polarization and spatial multiplexing in thermal holography underscores the design’s feasibility and adaptability for complex wavefront engineering.

Discussion

For our meta-emitter, the spatial coherence is primarily governed by the lifetime of the WG mode, which is fundamentally limited by metallic wall losses (Supplementary Fig. 30a). Through strategic slot geometry optimization–particularly elongating the central WG region–we achieve a 4000-fold enhancement in photon lifetime by enlarging the mode volume, thereby extending spatial coherence to 1000λ₀ (Supplementary Note S14, Fig. 30b–g). This loss suppression strategy effectively redistributes electromagnetic energy density away from lossy interfaces. Limited by the computational capability, highly directional oblique emission, near diffraction-limited thermal self-focusing and holography devices with 100λ₀ spatial coherence are demonstrated in Supplementary Note S14 and Supplementary Fig. 31-35. Furthermore, coherence can be systematically enhanced by engineering the surface mode’s band structure (steep dispersion gradients) and loss characteristics. Tailoring these parameters enables selective suppression of decoherence channels while preserving hybrid mode coupling efficiency.

Beyond 1D and quasi-2D thermal wavefront engineering demonstrated above, our meta-emitter platform can also be extended to perform true 2D thermal wavefront shaping. By applying BM with axially symmetric bull’s eye structure on the bottom surface with holographic pattern generation techniques on the top surface, sophisticated emission wavefronts (such as holography, vortex beam) can be obtained39,40. One example of focused radially polarized thermal beam is designed in Supplementary Note S15. The polarization distribution of the focal spot shows good radial polarization property, as shown in Supplementary Fig. S36c–d. While the central hole in the bull’s-eye structure imposes strict transmission constraints, optimizing coupling between bottom-surface spoof SPPs and the hole cavity—combined with critical balancing of radiative and absorption losses—significantly enhances device transmission and overall efficiency.

The top surface, engineered primarily for far-field wavefront control, can also be tailored to manipulate surface wave profiles46,47, enabling applications in on-chip photonic systems. Although the current surface-wave-mediated emission is restricted to p-polarized modes, integrating Pancharatnam-Berry (PB) meta-atoms could extend functionality to arbitrary polarization states46,48. Beyond the terahertz, millimeter-wave, and microwave regimes discussed herein, our SPP-based design strategy could scale naturally to far- and mid-infrared wavelengths—critical for room-temperature thermal radiation studies. The increased absorption loss can be mitigated by employing low-confinement surface mode, such as S-RM mode in Fig. 2a, and compensated by further reducing the size of the radiative perturbations. Supplementary Note S16 demonstrates this scalability with a self-focusing emission device operating at 5.7 μm, achieving single-mode property in a wide band (2–10 μm) and near-diffraction-limited (FWHM ≈ 3.6 μm) focusing performance. The high aspect ratio (>10) of metallic slit and double-sided metal sculpture can be accomplished by the state-of-the-art nano-fabrication and alignment techniques.

In conclusion, we present a straightforward and robust meta-emitter to realize coherent thermal emission with customized wavefronts. Experimental validations, including self-focusing emission and thermal holography in the millimeter-wave band, confirm the efficacy of our design. Beyond serving as a physical demonstration of thermal wavefront engineering, the capability of generating highly coherent light with tailored wavefronts carries substantial practical significance. This innovative approach may pave the way for compact transmitters in next-generation (6 G) communications or mid-infrared anti-counterfeiting displays, promoting system miniaturization and fostering advancements in these domains. We envision that the current work will catalyze the development of advanced thermal devices and unlock potential applications in green-energy communications and display technologies.

Methods

Simulation method of surface mode

The dispersion properties and mode profiles of BM, W-RM and S-RM in Fig. 2a are obtained through 2D simulations using the eigenfrequency solver in COMSOL Multiphysics. The material of the metal is set as copper (σ = 5.8 × 107 S/m) in the simulation. The propagation lengths along the surface for each mode in Fig. 2b are calculated from the Q factors and wavevectors of modes at their designed frequencies. The Q factor indicates how quickly the mode loses energy during one cycle of oscillation and can be directly reflected in the lifetime of the mode:

$$\tau=Q/\omega$$
(2)

where ω0 is the angular frequency of the resonance.

The lifetime \(\tau\) characterizes the decay property in the time domain, defined as the time of the mode energy decay to 1/e of its original value. For its counterpart, the propagation length of the spoof SPPs reveals the spatial distances over which the mode energy decays to 1/e of its original value, which can be expressed as

$$L={v}_{{\rm{g}}}\cdot {\rm{\tau }}$$
(3)

where vg is the group speed of spoof SPP along the surface, given by

$${v}_{{\rm{g}}}=d\omega /d\beta$$
(4)

Substituting for vg and \(\tau\), we can rewrite the expression for L as:

$$L=\frac{d\omega }{d\beta }\cdot {\rm{Q}}/{\rm{\omega }}$$
(5)

where Q factor and \(d\omega /d\beta\) can be obtained from simulation.

The eigenfrequency, Q facor, and eigenmode profile shown in Fig. 2c are obtained by eigenfrequency study in COMSOL Multiphysics. Perfect Matched layers are set as all the boundaries.

The spatial coherence of the entire device presented in Fig. 2g is calculated by the propagation length of the hybrid mode of slit mode and surface mode on the top side. The Q factor of the hybrid mode can be obtained by:

$${{\rm{Q}}}_{{\rm{hybird}}}={({{{\rm{Q}}}_{{\rm{surf}}}}^{-1}+{{{\rm{Q}}}_{{\rm{WG}}}}^{-1})}^{-1}$$
(6)

Then, the spatial coherence can be obtained by the Equation 5.

Calculation of the cross-spectral density component W zz

To characterize the spatial coherence of the spoof SPPs on the top surface, we calculated the cross-spectral density component of Wzz for the electric field of spoof SPPs (Ez) above the surface at \(z={\lambda }_{0}/10\), with \({\lambda }_{0}=3\,{\rm{mm}}\). The Ez field distribution is obtained by performing 2D frequency domain simulation in COMSOL Multiphysics software. Perfectly matched layers are set as the boundary in the simulation. To attain the Ez fields at different frequencies, an electric dipole with a frequency range from 75–120 GHz is set as the source to excite the spoof SPPs on the bottom side. Three types of top surfaces are simulated. The space-frequency dependent real parts of Ez components are drawn in Supplementary Fig. 5a–c, respectively.

The slit resonance determines the frequency-dependent part, and the same slit results in similar sharp peaks for all the surface modes. The spatial dependence of Ez reflects the energy attenuation of surface modes across the surface, which corresponds to the propagation lengths of modes shown in Fig. 2b. For S-RM, the short propagation length (~10\({\lambda }_{0}\)) leads to obvious attenuation in Ez, as illustrated in Supplementary Fig. 5a. In contrast, the strong EM wave confinement capability of BM and W-RM enables them to exhibit a negligible attenuation of Ez within the range of 20\({\lambda }_{0}\), Supplementary Fig. 5c. Cross-correlation function of Ez for these three modes at a different spatial interval of ρ can be expressed as36,37:

$${w}_{{zz}}\left(\rho,z=\frac{{\lambda }_{0}}{10},\omega \right)={E}_{z}^{*}\left(O,z,\omega \right){E}_{z}\left(\rho,z,\omega \right)$$
(7)

as shown in Supplementary Fig. 5d–f. The spatial attenuation behavior of Ez drawn in Supplementary Fig. 5a–c can also be reflected in the cross-correlation function at each frequency. By taking the ensemble average of \({w}_{{zz}}\), cross-spectral density component Wzz = \({\left\langle {w}_{{zz}}\right\rangle }_{\omega }\) is obtained as described in the main text.

Simulation of the thermal self-focusing performance

We employ Ansys Lumerical FDTD Solutions for the 3D simulation of the entire design. An electric dipole with a random phase, orientation angle, and x, y coordinates is placed on the bottom surface (0.3λ0 away from the bottom surface) as the source to capture the intensity profiles at different frequencies for each plane. This simulation is repeated 100 times, each with a different random dipole source. The average of all simulated intensity profiles is then calculated to obtain the statistical emission profiles for each plane, as shown in Fig. 3e-g. In the simulations, the emission intensities of all random dipoles are set identically. The transmitted energy obtained from each dipole simulation is shown in Supplementary Fig. 11, where the differences originate from the varying coupling efficiencies between individual random dipoles and the bottom surface mode. This excitation-efficiency variation reflects the fundamental process by which thermally populated surface waves are generated, namely that dipoles with near-normal surface polarization possess higher excitation efficiency. Such coupling-induced transmittance fluctuations do not affect the coherence enhancement performance of the designed resonant tunnel.

Measurement and characterization

To characterize the transmission property of the fabricated sample, a vector network analyzer (VNA) with thorn antenna is applied. The transmission spectrum in Fig. 3h is measured under normal incidence.

For the thermal measurement, the sample painted with a blackbody on the bottom side is heated by a hot plate. A 5 mm thick metal spacer is precisely positioned between the sample and the hot plate using thermally conductive adhesive to maintain a fixed separation distance. A foil-wrapped board is applied to block background thermal noise from the hot plate. The thermal radiation pattern generated by the sample on the top side is measured by a polarization-dependent detector on a translation stage point by point. To improve the accuracy of the mapping measurement, a waveguide probe with a sharp tip is designed for the detector. The detailed information of probe design can be found in Supplementary Note S9.