Metasurface-assisted multimodal quantum imaging

Significance

Phase contrast and edge imaging are both commonly used imaging techniques in microscopy systems, but integrating them effectively within the same system remains challenging. In this study, we combine polarization-entangled sources and polarization-multiplexing metasurface to project polarization states onto various basis, enabling phase contrast, edge, and superimposed imaging modes within a single system. Moreover, we utilize the “off” mode of the special basis to achieve self-calibrated edge imaging. Our research provides a different perspective for the synergistic integration of quantum imaging and metasurface optics.

Abstract

Traditional quantum imaging is featured by remarkable sensitivity and signal-to-noise ratio, but limited by bulkiness and static function (either phase contrast imaging or edge detection). Our report synergizes a polarization-entangled source with a metasurface consisting of various sophisticatedly engineered spatial frequency segments. By tuning polarization, we demonstrate multiple “on”-state quantum imaging modes, enabling flexible switching between phase contrast, edge, and arbitrary superimposed imaging mode. Furthermore, the “off”-state, which characterizes the background noise, enables self-calibration of the system by subtracting this noise in “on”-state modes, resulting in self-enhanced edge detection. Our approach performs phase contrast imaging with a phase difference of π/4 present in the target object, and edge imaging capable of detecting tiny (radius about 2 μm) defects, maintaining high image contrast (phase contrast of 0.726, and enhanced edge contrast of 0.902). Our results provide insights into constructive duet between quantum imaging and metaoptics.

Imaging technology has always been at the core of scientific research, providing essential visual data across a wide range of fields from fundamental physics to biomedical sciences, significantly driving scientific innovation and technological breakthroughs. Researchers have consistently been committed to developing new approaches to go beyond traditional imaging, aiming to achieve high-quality imaging in various application scenarios. The quantum properties of light offer a highly promising strategy (1). Quantum imaging techniques that utilize quantum correlations (2–4), including quantum ghost imaging (5, 6), induced coherence imaging (7–9), and quantum holography (10, 11), not only introduce different imaging paradigms (12) but also achieve higher signal-to-noise ratios (SNR) (13, 14), sensitivity (15, 16), and resolution (17–19) compared to traditional imaging. However, current quantum imaging systems, due to their large size and single function, still face challenges with low system integration and limited applicability. Therefore, enhancing the integration and expanding the functionalities of quantum imaging systems are becoming one of the key directions for the further development of quantum imaging technology (20).

Metasurface, artificial arrays of subwavelength unit structures designed for on-chip integration (21), can manipulate multiple degrees of freedom of light (22, 23), including polarization (24, 25), orbital angular momentum (26, 27), and wavelength (28–30), enabling multiplexing across multiple dimensions. Their rich and powerful capability to control light fields and integration characteristics have already empowered various applications in classical optics (31, 32). For example, metasurfaces can facilitate the implementation of edge detection (33–36) and phase imaging (37, 38) with enhanced imaging quality. The combination of metasurfaces with quantum optics offers different prospects for the development of both areas (39, 40). Quantum metasurfaces have already made significant progress in quantum light sources (41, 42), manipulation of quantum states (43, 44), and quantum sensing (45). Notably, all-dielectric metasurfaces have been utilized to achieve nonclassical multiphoton interference and state reconstruction (46). The advanced control capabilities provided by metasurface, when combined with multidimensional entangled photon pairs, further enhance the functionalities (47–49) of quantum imaging and improve the system integration.

Here, we achieve multimodal quantum imaging (phase contrast, edge, superimposed, and “off”) using a polarization-entangled source and polarization-multiplexing metasurface. After passing through the metasurface, the signal photon from the polarization-entangled source transforms the polarization entanglement of twin photons into an entanglement between the heralding photon’s polarization and the imaging modes in the signal arm. Selecting the polarization state of the heralding and signal photons determines the imaging mode in the signal arm. Compared to classical optical imaging, the tuning of modes in quantum remote imaging enhances system integration and stability, expands the application scenarios. Additionally, our approach provides higher image contrast, further demonstrating its advantage.

The approach is depicted in Fig. 1, which utilizes a bird-shaped phase object as the target (see SI Appendix, Section S1 for more detail). The bird features color-coded regions that differ by a phase shift of π/4, with the phase increasing progressively from the exterior toward the center. First, using a classical continuous laser illumination imaging system, we briefly illustrate the principles of phase contrast and edge imaging. $|H⟩(|V⟩)$ represents horizontally (vertically) polarized photons. The $|H⟩(|V⟩)$ photons passing through the target object are focused onto the Fourier plane. The metasurface, positioned at the center of the light field, modulates only the mid-to-low frequencies in the angular spectrum. During this process, the polarization of photons $|H⟩(|V⟩)$ passing through the metasurface is converted to $|V⟩(|H⟩)$, and a π phase difference is introduced between mid and low regions in the spatial frequency spectrum. Simultaneously, the high spatial frequency region in the light field, not passing through the metasurface, remains in its original state $|H⟩(|V⟩)$. This leads to emitted photons from the Fourier plane having two orthogonal polarization states: $|H⟩(|V⟩)$, achieving edge imaging by conveying the high-spatial-frequency edge information of the phase object, and $|V⟩(|H⟩)$, realizing phase contrast imaging due to interference in the mid-to-low frequency region (as shown in SI Appendix, Fig. S2). Subsequently, the QHP combination [comprising a quarter-wave plate (QWP), a half-wave plate (HWP), and a polarizing beam splitter (PBS)] is configured to allow only $|H⟩$ to pass through. When the incident polarization state is $|H⟩$, the image exhibits edge effect. Conversely, when the incident polarization state is $|V⟩$, the resulted image is referred to as a phase contrast effect. In the case of incidence with other polarization states, the resulted image is a superposition of both. The metasurface is unable to convert linearly polarized light other than $|H⟩$ and $|V⟩$ polarization. Therefore, if the incident polarization is $|D⟩$ and the polarizer is set to $|A⟩$, no image can be collected, effectively implementing the “off” mode.

Fig. 1.

Multimodal quantum remote imaging scheme and characterization of the metasurface. (A) The signal light from a polarization-entangled source is incident on the metasurface, which realizes different imaging modes. By selecting the polarization state of the heralding and signal photons, the imaging mode in the signal arm is determined, enabling phase contrast, edge, superimposed, or the “off” mode. The arrows represent the projected polarization states. Phase distribution map of the phase object (“bird” in the Upper panel)—the green, white, and yellow regions correspond to a phase of π/4, π/2, and 3π/4, respectively. (B) Perspective view of a metasurface unit. (C) Schematic diagram of the arrangement of metasurface units. (D) Side-view scanning electron microscope (SEM) image of the metasurface. (E) Top-view SEM image of the metasurface. The metasurface measures 350 µm in size with an internal dimension of 14 µm and a structural period of 350 nm, consisting of a silicon nitride nanorod.

Here, this work uses a polarization-entangled source $($state represented as $1/\sqrt{2}(|HV⟩+|VH⟩)$ as the illumination source to achieve remote control over the tuning of phase contrast, edge, superimposed, and “off” modes. In this system, the heralding arm serves as a mode-tuning trigger, jointly determining the imaging mode in the signal arm with the selected polarization basis in the signal arm. When the signal photons and the heralding photons are in a polarization-entangled state, without knowing the polarization state of the heralding and signal photons, the image in the signal arm is a probabilistic superposition of imaging modes. Once the polarization state of the heralding and signal photons are selected, the imaging mode in the signal arm is also determined. Through this approach, we can not only achieve phase contrast imaging with a phase difference of π/4 in the target and edge imaging capable of detecting tiny (radius about 2 μm) defects but also obtain a superimposed image of these two imaging. The “off” mode turns off the image by detecting only noise photons, which consequently eliminates noise and achieves self-enhanced contrast in edge imaging benefitting from the self-calibration with the “off” mode. Furthermore, we can remotely tune between these four imaging modes, thereby enhancing the flexibility and potential applications of optical imaging technology.

1. Metasurface Design for Multimodal Imaging

The key to phase contrast imaging lies in introducing a phase difference in the Fourier plane, while edge imaging relies solely on allowing high-spatial-frequency light to pass through. Based on this, we utilize the polarization multiplexing function of the metasurface to control both the polarization and spatial frequency domain of the incident light.

Polarization control of metasurface: The incident light in an arbitrary polarization state is represented as $\left(\begin{array}{c}\cos \left(\phi /2\right)\hfill \\ e^{i\varphi }\sin \left(\phi /2\right)\end{array}\right)$. By selecting appropriate nanopillars on the metasurface, where the propagation phase difference between the polarization along the long and short sides of the pillars is π, and rotating counterclockwise around the z-axis by $\theta$, the Jones matrix of the metasurface is obtained as $\left(\begin{array}{cc}\cos \left(2\theta \right)\hfill & -\sin \left(2\theta \right)\\ -\sin \left(2\theta \right)& -\cos \left(2\theta \right)\end{array}\right)$. The polarization state after passing through the metasurface becomes $\begin{array}{c}\left(\begin{array}{c}\cos \left(2\theta \right)\cos (\phi /2)-e^{i\varphi }\sin \left(2\theta \right)\sin \left(\phi /2\right)\hfill \\ -\sin \left(2\theta \right)\cos \left(\phi /2\right)-e^{i\varphi }\cos \left(2\theta \right)\sin \left(\phi /2\right)\end{array}\right)\hfill \end{array}$. When the angle of pillars is $\theta \pm \pi /2$, the output polarization state is $\begin{array}{c}-\left(\begin{array}{c}\cos \left(2\theta \right)\cos \left(\phi /2\right)-e^{i\varphi }\sin \left(2\theta \right)\sin \left(\phi /2\right)\hfill \\ -\sin \left(2\theta \right)\cos \left(\phi /2\right)-e^{i\varphi }\cos \left(2\theta \right)\sin \left(\phi /2\right)\end{array}\right)\hfill \end{array}$. Both nanopillars yield the same polarization, but with a π phase difference. Furthermore, when the incident polarization state and the rotation angle of the pillars on metasurface satisfy the condition $\cos \left(\varphi \right)·\tan \left(\phi \right)=\cot \left(2\theta \right)$, the output polarization state is orthogonal to the incident state. Therefore, when the above conditions are met, the emitted light is divided into two orthogonally polarization state: high-frequency incident polarization state without passing through the metasurface and mid-to-low frequency orthogonal polarization state that has passed through the metasurface.

In this work, we set the rotation angle $\theta$ of the nanopillars to 45° and 135° in the low- and mid-spatial-frequency region, respectively. Under this condition, we find that the equation is satisfied when $\left(\varphi =\pm \pi /2\right)$ or $\left(\phi =0,\pi \right)$. For linearly polarized light, only the $|H⟩$ $\left(\phi =0\right)$ and $|V⟩$ $\left(\phi =\pi \right)$ polarization states can be converted into orthogonal polarization states. However, $|D⟩=1/\sqrt{2}{\left(1 1\right)}^{\mathrm{T}}$ and $|A⟩=1/\sqrt{2}{\left(1 -1\right)}^T$ polarization states cannot be converted into orthogonal polarizations.

Phase control of the metasurface: The incident light field is $E_0$, and after passing through the pure phase target object, the light field becomes $E_0{e}^{i\phi \left(x,y\right)}$. In the Fourier space, the additional phase added in the internal region (corresponding to low frequency) of the metasurface is denoted as ${\varphi }_l$, and the additional phase added in the external region (corresponding to mid frequency) is denoted as ${\varphi }_m$. The phase difference is $\mathrm{\Delta }\varphi ={\varphi }_m-{\varphi }_l$. After passing through the 4f system, the intensity distribution of the output light field is:

$$\begin{array}{cc}\hfill \mathrm{Intensity}\left(\phi \left(x,y\right),{\varphi }_m-{\varphi }_l\right)=& {\left|\left(E_0{e}^{i\phi (x,y)}-E_0\right)e^{i{\varphi }_m}+E_0{e}^{i{\varphi }_l}\right|}^2\hfill \\ \hfill =& E_0^2\left[3-2\cos \left(\phi \left(x,y\right)\right)+2\cos \left(\phi \left(x,y\right)+\mathrm{\Delta }\varphi \right)-2\cos \left(\mathrm{\Delta }\varphi \right)\right]\hfill \\ \hfill & \end{array},$$ [1]

This introduces a phase difference between the low- and mid-spatial frequency components, achieving phase contrast imaging. Nanopillars with a relative angle difference of $\pi /2$ precisely satisfy the condition $\left(\mathrm{\Delta }\varphi =\pi \right)$. Therefore, these nanopillars are distributed in the internal and external regions of the metasurface, respectively.

Placing a QHP combination after the 4f system, allowing only the unmodulated high-spatial-frequency incident polarization state to pass, results in edge imaging. Allowing only the phase-modulated orthogonal polarization state to pass leads to phase contrast imaging.

Fig. 1B illustrates the schematic of the unit structure in the metasurface. Fig. 1C shows the schematic diagram of the arrangement of nanopillars on the metasurface. The SEM images of the prepared samples are shown in Fig. 1 D and E. The metasurface units have a period of 350 nm, with a silicon dioxide substrate. On the substrate, there are amorphous silicon pillars with a height of 390 nm, a length of 190 nm, and a width of 120 nm, with pillar rotations of 45° and 135°. This work utilized commercial finite difference time domain software to solve the transmission function of the structural unit; periodic boundary conditions were applied along the x and y directions, and perfectly matched layer boundary conditions were set along the z direction. Scanning of length and width allowed for obtaining the phase and transmittance in horizontal and vertical directions of the pillars. Based on this information, we obtained the conversion efficiency for different polarizations of light and measured the actual polarization conversion efficiency (see SI Appendix, Section S2 for details). The size of the low- and mid-spatial-frequency areas directly determines the imaging quality. In phase contrast mode, only photons within the metasurface can pass through, meaning the metasurface’s aperture directly limits the phase contrast imaging quality. While increasing the size of the metasurface improves imaging performance, it simultaneously reduces the number of high-frequency photons needed for edge imaging. Thus, the inner and outer dimensions of the metasurface must strike a balance. By simulating the metasurface with different internal and external areas, the optimal phase contrast and edge imaging effects were achieved with dimensions of 14 μm and 350 μm for the low- and mid- spatial-frequency areas, respectively, both in length and width (see SI Appendix, Section 3 for details). Simulations were also conducted to evaluate the imaging effects of reduced transmission rates due to manufacturing and polarization factors, thereby providing a foundation for our subsequent data processing.

2. Experimental Setup

The experimental setup for remotely controlled multimodal quantum imaging is depicted in Fig. 2A. The experimental device utilizes a focused 390 nm femtosecond laser to excite type-II BBO crystals in a sandwich-like structure. Through the process of spontaneous parametric down-conversion, these BBO crystals generate polarization-entangled photon pairs at a wavelength of 780 nm. The photon pairs are split into heralding and signal arms by prisms. On each arm, ${\mathrm{YVO}}_4$ and ${\mathrm{LiBbO}}_3$ crystals are used to compensate for spatial and temporal walk-off effects, with lenses placed between the crystals for beam collimation. The generated photon state can be represented as $1/\sqrt{2}\left(|H_i{V}_s⟩+|V_i{H}_s⟩\right)$, where the subscripts i and s indicate photons in the heralding and signal arms, respectively.

Fig. 2.

Experimental setup and characterization of the entangled light source. (A) Experimental setup. A 390 nm ultraviolet pulse laser passes through a true zero-order half-wave plate and two beam-like BBO crystals arranged in a sandwich configuration to produce polarization-entangled photon pairs. These photons are split by a prism into heralding and signal arms. A QHP set selectively detects heralding photons. Signal photons are sent to interact with the metasurface (MS) and collected by an ICCD camera, which is gate-controlled by the heralding detection signal. BBO: Beta-Barium Borate crystal; THWP: true zero-order half-wave plate; HWP: half-wave plate; QWP: quarter-wave plate; FC: fiber coupler; PBS: polarizing beam splitter; OL: objective lens; SPAD: single-photon avalanche diode; PO: phase object; BF: bandpass filter. (B) Sinusoidal fitting of the data when the HWP in the signal arm is fixed at 0° (blue) and 22.5° (orange). (C) The real and imaginary parts of the reconstructed density matrix ρ of the two-photon state.

In the heralding arm, photons pass through a set of QHP combinations to project the polarization-entangled state onto a specific polarization basis, and then are detected by a SPAD. The SPAD converts the received photons into electrical signals, triggering an ICCD camera in digital delay and gate (DDG) mode to capture the signal photons. Due to the time delay in this process, to ensure that the photons captured by the ICCD camera are from the same pair as those detected by the SPAD, a 20-m-long optical fiber and the nanosecond-level electronic delay built into the ICCD are used to compensate for the time difference. Considering the polarization dephasing effect of single-mode optical fiber, a set of HWP and QWP is added after the fiber to correct the polarization state of the exiting photons, directing the signal photons emerging from the fiber into the SPAD to test the quality of the quantum state.

After obtaining high-quality quantum states, the signal photons pass through different sets of confocal lenses, which are used to reduce the beam size illuminating the phase object, increase the photon utilization rate, reduce the area that needs to be controlled on the Fourier plane, and magnify the optical field. As a result, the system overall magnifies by 7.5 times. Following polarization selection via the QHP combination, the signal photon is captured by the ICCD camera. The metasurface is positioned at the center of the Fourier plane of the signal arm, modulating the spatial frequency of the phase pattern and the polarization state of the incident light. For more detailed experimental setup, see Section 7.1.

3. Characterization of the Polarization-Entangled Source

High-quality images depend on a bright and high-fidelity polarization-entangled light source. At a pump power of 67 mW, the single-photon counting rate in the heralding (signal) arm is 130 (210) kHz, with a heralding efficiency of approximately 14.9%. Additionally, the lower single-channel counting rate in the heralding arm is advantageous for blocking noise photons.

The entanglement properties of the photon pairs are demonstrated by measuring polarization interference fringes and reconstructing the quantum state density matrix. For measuring the polarization interference fringes, the HWP angle in the signal arm is fixed at ° or 22.5°, while the HWP angle in the heralding arm is varied in 10° increments. As shown in Fig. 2B, the coincidence counts measured within 1 s align well with a sinusoidal function. The visibility of the interference fringes is calculated using the formula $\mathrm{V}=\left(C_{\mathit{max}}-C_{\mathit{min}}\right)/\left(C_{\mathit{max}}+C_{\mathit{min}}\right)$, where ${\mathrm{C}}_{\mathit{max}}$ and ${\mathrm{C}}_{\mathit{min}}$ represent the maximum and minimum coincidence counts, respectively. The interference visibility is $93\pm 0.2\%$ under the $+45°/-45°$ polarization bases and $95\pm 0.1\%$ under the $\mathrm{H}/\mathrm{V}$ bases. Both visibilities exceed the $71\%$ threshold, violating Bell’s inequality limit. For a comprehensive assessment of the prepared quantum state, we performed quantum tomography on the constructed polarization-entangled source. Fig. 2C shows the real and imaginary parts of the reconstructed density matrix, respectively. The fidelity, defined by $F=⟨\mathrm{\Psi }\left|\widehat{\rho }\right|\mathrm{\Psi }⟩$ where $\mathrm{\Psi }$ is the target quantum state and $\widehat{\rho }$ is the density matrix reconstructed from experimental data, is calculated to be $95.63\pm 0.11\%$ for the target state $1/\sqrt{2}\left(|HV⟩+|VH⟩\right)$. The results demonstrate that we have constructed a high-quality source of polarization entanglement.

4. Quantum Remote-Tuning Phase Contrast and Edge Imaging: Contrasting with Classical System

Following the acquisition of high-quality sources of polarization entanglement and the elucidation of the design and imaging principles of the metasurface, this study aims to demonstrate the superiority of integrating quantum imaging with metasurface. As discussed by Zhou et al. (49), one advantage of quantum imaging is its higher image contrast when quantum photon flux is comparable to classical photon flux, due to the correlated nature of photon pairs in quantum imaging.

Leveraging the strong temporal correlation characteristics of energy-time entangled photon pairs generated through spontaneous parametric down-conversion (SPDC) process, second-order correlation imaging can be conducted using an ICCD camera in DDG mode. When the SPAD detects a heralding photon, the signal arm’s ICCD camera briefly activates to capture the twin signal photon, significantly filtering out environmental noise and achieving high SNR imaging. In contrast, classical imaging systems operating in the internally triggered mode accumulate a substantial amount of noise photons, leading to a reduced SNR. To demonstrate the superiority of quantum imaging and the necessity of metasurface, we collected quantum and classical images, including those without metasurface modulation, as well as edge and phase contrast images with metasurface modulation, all within the same system.

As shown in Fig. 3, under the same experimental conditions (including low photon flux, background noise, and Microchannel Plate gain), Fig. 3A displays the SEM image of the target object along with an enlarged view that highlights the defect, where the radius of the tiny defect is approximately 2 μm. Fig. 3B shows the classic image acquired by an internal trigger without metasurface modulation. Fig. 3 C–E respectively represents unmodulated, phase contrast, and edge images collected by the ICCD external trigger under the illumination of a polarization-entangled source. Fig. 3 F–I illustrates the intensity variations along the dashed lines in Fig. 3 B–E, respectively. SI Appendix, Fig. S7 shows the imaging results of the phase contrast and edge images of the ICCD camera in continuous exposure mode and the processed quantum edge-enhanced imaging results. The effective exposure time for classical imaging was set to match that of the corresponding quantum imaging mode (49). In classical imaging, since the number of signal photons per second (~210 k) is much lower than that of noise photons, the signal is overwhelmed by noise, failing to reveal distinct image features. Using the formula $\mathrm{V}=\left({\mathrm{I}}_{\max }-{\mathrm{I}}_{\min }\right)/\left({\mathrm{I}}_{\max }+{\mathrm{I}}_{\min }\right)$, we obtained the average contrast for various images. The contrast values for different imaging results are 0.30, 0.421, 0.726, and 0.783, respectively. The noise images collected by the “off” mode help to obtain self-calibrated edge images with a contrast ratio of 0.902 (see SI Appendix, Section S4 for details). By comparing images with and without metasurface modulation in quantum imaging, it is evident that the modulation effect of the metasurface is crucial for the imaging scheme. Only when the metasurface is involved in modulation can the system achieve high-contrast phase contrast and edge imaging, thereby expanding the functionality and integration level of the system. Classical imaging did not provide any target object information, but the random fluctuations of the noise field still yielded some contrast values through the contrast formula, which can be considered invalid data. The comparison between classical and quantum imaging demonstrates that under the same imaging conditions, quantum imaging offers a higher image contrast and can detect defects with a radius of 2 μm in the target object.

Fig. 3.

Experimental result of remotely tuned edge and phase contrast imaging. (A) SEM image and magnified view of a portion of the target object. (B) Classical imaging; (C) Quantum imaging without metasurface modulation; (D) Quantum phase contrast imaging; (E) Quantum edge imaging; (F–I) intensity variations along the white dashed lines.

5. Self-Calibration via “Off” Mode and Postcalibration Quantum State Projections

Following the discussion of the high SNR advantage of quantum imaging, this section focuses on another significant advantage of quantum imaging: the remote manipulation of phase contrast and edge imaging modes tuning through quantum entanglement. As shown in SI Appendix, Fig. S9, the images were collected based on different combinations of polarization bases, where the vertical (horizontal) axis represents the polarization bases selected by the QHP in the heralding (signal) arm. To achieve the best imaging results, 900 frames (~1,200 s) were collected in the phase contrast imaging mode, 2,400 frames (~3,240 s) in the edge imaging mode, and 1,800 (~2,400 s) frames in the superimposed image mode, with each frame having a collection time of 1 s.

As previously mentioned, the nanopillars on the metasurface were chosen with rotation angles of 45° and 135°. The polarization states H, V, R, and L all satisfy the equation $\cos \left(\varphi \right)·\tan \left(\phi \right)=0$, allowing these states to be converted into their orthogonal polarizations. The polarization entangled source, $1/\sqrt{2}\left(|HV⟩+|VH⟩\right)$ is equivalent to other forms of polarization basis entanglement: $1/\sqrt{2}\left(|\mathrm{DD}⟩-|AA⟩\right)$, $1/\sqrt{2}i\left(|RR⟩-|LL⟩\right)$. The heralding photons are projected onto H, V, D, A, R, L polarization bases through the QHP combination, thereby triggering the ICCD camera to collect signal photons of different polarization bases. For example, when the polarization in the heralding arm is selected as $|\mathrm{H}⟩$, the photon state in the signal arm collapses to $|\mathrm{V}⟩$. The signal photon is then transformed by the metasurface into an orthogonal polarization state $|\mathrm{H}⟩$, and a phase difference of π is introduced between the mid and low spatial frequencies; the photons that do not pass through the metasurface remain in the $|\mathrm{V}⟩$ state, and no additional phase shift is introduced. Subsequently, after selecting the $|\mathrm{H}⟩$ state through the QHP combination in the signal arm, the collected image is a $|\mathrm{HH}⟩$ phase contrast image. When the polarization in the heralding arm is set to $|\mathrm{V}⟩$, the photon state in the signal arm collapses to $|\mathrm{H}⟩$. The portion that passes through the metasurface changes to $|\mathrm{V}⟩$, while the high-spatial-frequency light that does not pass through remains as $|\mathrm{H}⟩$. The unchanged QHP combination in signal arm results in a $|\mathrm{VH}⟩$ edge image. When the polarization basis of the signal arm is $|\mathrm{H}⟩$, images for other polarization bases in heralding arm are a superposition of phase contrast and edge effects. Similarly, changing only the signal arm’s polarization base without altering the heralding arm’s polarization base yields same imaging results. The imaging principle for R, L bases is the same as for H, V bases. However, the incidence of D, A polarized photons does not alter the polarization state of the photons. Therefore, when the projection polarization basis in the heralding arm is set to D, the quantum state can be described as $1/\sqrt{2}\left(|\mathrm{DD}⟩-|\mathrm{AA}⟩\right)$. Subsequently setting the projection basis in the signal arm to A polarization means that no signal photons should be collected in the signal arm, thereby implementing the “off” mode.

However, in our actual measurements, due to imperfections in the polarization entanglement source, alignment errors of the metasurface, and polarization conversion efficiency (detailed in SI Appendix, Table S1), the images we obtained tend to be overly biased toward either the edge or the phase contrast. This is because if the polarization states are not perfectly aligned, their orthogonal components are also collected. Additionally, since the phase contrast effect primarily occurs in the low- and mid-spatial-frequency regions in our experiment, if the polarization conversion of the metasurface is not ideal, the collected images inevitably exhibit some phase contrast. This explains why the raw edge images we collected are biased toward phase contrast. These defects are particularly noticeable in the DA and AD images. Theoretically, the DA and AD images obtained from the system’s “off” function should only contain noise. This characteristic can be leveraged to perform a system self-calibration process. By using the collected DA and AD raw data (as shown in Fig. 4A), we can mitigate the noise caused by the above factors (see SI Appendix, Section S5 for details), thereby obtaining edge images with enhanced contrast. Similarly, by subtracting the noise from other images, the processed images, as shown in Fig. 4B, demonstrate enhanced contrast in edge images, while the differences in other images compared to the original ones are minimal.

Fig. 4.

Multimodal quantum imaging results with projection onto different polarization bases. (A) The raw DA and AD data collected for the “off” function, which will be used in self-calibration processing. (B) The x axis represents the polarization state projection on the signal arm, while the y axis represents the polarization state projection on the heralding arm. (C) Phase contrast and edge images collected and processed under elliptical polarization states. The images displayed within the coordinate system have been collected and processed for noise after projection onto these different polarization states.

Although the conditions for achieving perfect imaging are relatively stringent, the metasurface is more tolerant to incident polarization light. Combined with the system’s self-calibration function, we are still able to achieve good imaging results. Our designed metasurface can convert elliptically polarized light $\left(\varphi =\pm \pi /2,\phi \in \left[0,2\pi \right]\right)$ into orthogonal elliptically polarized light. We transformed the $1/\sqrt{2}\left(|\mathrm{HV}⟩+|VH⟩\right)$ entangled state into an elliptically polarized entangled state. As shown in SI Appendix, Fig. S10, the optical path has been expanded to include the devices shown in the red dashed line. The $|\mathrm{H}⟩$ was transformed into an elliptical polarization state $\alpha ={\left(1/2 \sqrt{3}i/2\right)}^T$ through a set of wave plates, and the $|\mathrm{V}⟩$ was converted into $\beta ={\left(\sqrt{3}/2 -i/2\right)}^T$. The polarization-entangled state was $1/\sqrt{2}\left(|\alpha \beta ⟩+|\beta \alpha ⟩\right)$, and the QHP combination was similarly selected for the $\alpha$ and $\beta$ bases.

Consistent with previous experimental conditions, we collected phase contrast and edge images illuminated by an elliptically polarized entangled source. After the same noise self-calibration processing, we obtained the processed images as shown in Fig. 4C. The results indicate that the design of the metasurface is not only suitable for conventional linear and circular polarizations but also capable of achieving imaging mode tuning for elliptical polarization, thus reducing the system’s requirements for specific polarization states.

6. Discussion

By leveraging entangled photon pairs, strong image contrast is achieved even under low-light conditions, along with enhanced system stability. Compared to other work (47, 49) utilizing metasurface for quantum imaging, our study features operation in a multimodal manner wherein multiple modes interact synergistically to provide comprehensive quantum imaging results. The phase contrast and edge imaging mode can work as complementation for each other; and the “off” mode detects noise photons, so that self-enhancement can be achieved in the imaging mode. Although the combination of classical pulsed light and time gating can achieve a comparable SNR, it also has inherent limitations. One major constraint is the stringent requirement for external electronic timing control system, which fundamentally differs from the intrinsic time synchronization of SPDC process, achieving femtosecond-level precision (50). Similarly, for the pure state $\left(|\mathrm{HH}⟩\right)$—much like time-gated pulsed imaging, while effectively reducing acquisition time (by approximately half), it also demands precise control of the incident polarization in the imaging path. Both approaches lack polarization entanglement and thus sacrifice the flexibility provided by the heralding arm.

Our imaging approach is particularly well-suited for scenarios requiring low light flux, effectively preventing phototoxicity caused by high light intensities. The remote-control scheme enhances both the mechanical stability and operational convenience of the system. We acknowledge that the primary challenges of this work include prolonged data acquisition times, limited brightness of the quantum light source, and the finite number of polarization-entangled modes, which is a key limitation compared to spatial-mode-based imaging. However, as advancements in high-brightness, high-fidelity quantum entangled sources (51, 52) and more efficient biphoton detection methods (19, 53) continue to progress, the time required for quantum imaging will be significantly reduced. Additionally, with the recent emergence of multimodal polarization-multiplexed metasurfaces (54, 55), the integration of multimode quantum imaging with the latest metasurface technology is expected to unlock more usable imaging modes. This imaging approach is therefore anticipated to extend into broader application areas. Recently, research has focused on combining filtering functions with nonlocal metasurface (36, 38, 56), eliminating the need for 4f systems, and enabling higher integration levels. In the future, this is expected to lead to more compact imaging systems with multimodal quantum imaging.

In summary, our work has demonstrated multimodal quantum imaging that can be remotely tuned by synergizing polarization-entangled photon pairs with a polarization-multiplexed metasurface capable of modulation in the spatial frequency domain and polarization. This constructive duet allows for multiple imaging modes, including phase contrast, edge, and their superposition in phase objects. Additionally, it facilitates self-enhanced contrast (0.902) through the self-calibration with the “off” mode. Our study features operation in a multimodal manner wherein multiple modes interact synergistically to provide comprehensive quantum imaging results. Our results offer insights into the constructive synergy between quantum imaging and metasurface, exploring the potential applications of quantum metasurfaces.

7. Materials and Methods

7.1. Experimental Layout.

The detailed experimental setup is shown in SI Appendix, Fig. S10. Pairs of polarization-entangled photons with a wavelength of 780 nm are generated by pumping light onto BBO crystals with a sandwich-like structure through a spontaneous parametric down-conversion process. The pump light from a femtosecond laser (Coherent, Chameleon Ultra II) has a wavelength of 390 nm and a power of 60 mW and is focused on the center of the BBO crystals by a lens with a focal length of 150 mm. The polarization of the pump light is set to horizontal. Through a prism, the photon pairs are split into the heralding arm and the signal arm and are eventually coupled into single-mode fibers. The optical bin behind the prism collects unused pump light.

In both the heralding and signal arms, lenses with a 150 nm focal length are placed to collimate the beams, and both time compensation and spatial compensation crystals (${\mathrm{YVO}}_4$ and ${\mathrm{LiBbO}}_3$) are installed. A QHP combination (comprising a QWP, a HWP, and a PBS) is used to project the quantum state. To verify the quality of the polarization-entangled source, a flip mirror in the signal arm directs the signal light into the QHP. The entangled photon pairs coupled by the single-mode fiber are directed into a SPAD, and the resulting electrical signals are fed into an FPGA to measure time-coincident photon counting. By adjusting the angles of the BBO and compensation crystals, the contrast of the coincidence in the horizontal(H)/vertical(V) and antidiagonal(A)/diagonal(D) polarization bases is maximized.

After obtaining a high-quality polarization-entangled source, the heralding light is converted into an electrical signal by the SPAD and this electrical signal is fed into the ICCD in the signal arm (iStar A-DH334T-18 U-73) to capture the twin signal photons. The ICCD camera, with a quantum efficiency of 20% at a wavelength of 780 nm, operates in an internal trigger and external trigger DDG mode, offering nanosecond-level electronic delay, with a gate width set at 5 ns. To compensate for the electrical delay between the SPAD collecting signal photons and triggering the ICCD, a 22.5 ns delay is set using a 20-m-long single-mode fiber, and both half-wave and quarter-wave plates are used to compensate for the polarization dephasing issue, with the quantum state being verified again through the QHP.

After acquiring a high-quality polarization-entangled source, the flip mirror is lowered, directing the signal light into the imaging path. A combination of lenses with focal lengths of 200 mm and 100 mm is used to reduce the beam size irradiating the phase target object, enhancing photon utilization. A lens group with focal lengths of 250 mm and 50 mm is used to minimize the area that needs to be controlled on the Fourier plane. Subsequently, a combination of a 20 mm objective lens and a 100 mm lens is used to magnify the light field, enlarging the system by 7.5 times while also avoiding exceeding the camera’s capture range; all lenses in the system are confocal. After polarization selection by the QHP, the signal light is captured by the ICCD camera. The metasurface is placed on the Fourier plane of the imaging arm. Narrowband filters with a bandwidth of 3 nm are added before the QHP in both the heralding and signal arms, as well as in front of the ICCD camera.

In order to prove that the metasurface we designed is also applicable to elliptically polarized light, we add a set of QWP and HWP in the signal path (red box) to change the polarization state so that the orthogonal polarized light entanglement becomes elliptically polarized light entanglement. The rest of the settings are the same as above.

7.2. Metasurface Fabrication.

First, a 500-μm-thick quartz glass substrate is prepared using a cleaning process. Next, a 600 nm thick layer of amorphous silicon (a-Si) is deposited on the cleaned substrate using plasma-enhanced chemical vapor deposition (PECVD) technology. Subsequently, a 120 nm thick layer of conductive electron beam lithography resist, CSAR-6200, is spin-coated. Electron beam lithography (EBL, Elionix, ELS-F125-G8) is then used to pattern the designed metasurface in the CSAR-6200 resist, followed by development processing. Chromium (Cr) layers are evaporated onto the sample using electron beam evaporation (EBE) technology. The sample is then soaked in acetone for stripping, leaving a Cr hard mask on the a-Si layer for subsequent etching. Inductively coupled plasma and reactive ion etching (ICP-RIE) are used to etch the sample. Finally, ammonium cerium nitrate is used to remove the remaining Cr hard mask. The flow chart of fabrication is shown in SI Appendix, Fig. S11.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Code, data, and figures data have been deposited in zenodo (10.5281/zenodo.15063187) (57).