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All issues Volume 13 (2026) EPJ Appl. Metamat., 13 (2026) 2 Full HTML
Open Access
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EPJ Appl. Metamat.
Volume 13, 2026
Article Number 2
Number of page(s) 8
DOI https://doi.org/10.1051/epjam/2025013
Published online 22 January 2026

© S. Wu et al., Published by EDP Sciences, 2026

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

Optical metasurfaces are quasi-two-dimensional micro-nano structures that have attracted widespread interest because of their ability to flexibly control the optical wavefront and high level of compactness [1–5]. In recent years, optical metasurfaces have been successfully applied to photon manipulation in linear and classical optics, including focusing [6–10], polarisation detection [11–14], edge-enhanced imaging [15–18] and spectral filtering [19–22]. The next generation of metasurfaces will naturally extend to the fields of nonlinear optics and quantum optics [1,23–33]. As an ultra-thin quasi-planar structure, a metasurface has a unique advantage in optical nonlinear processes in that it has relaxed phase-matching requirements in frequency conversion. Leveraging the potential of metasurfaces combined with optical nonlinear effects could lead to application in “imaging without detection” at wavelengths where cameras are not widely available.

The observation and operation of various optical quantum effects involving complex quantum states rely on nonlinear optical processes. Spontaneous parametric down-conversion (SPDC) is an ideal candidate to generate single photons and quantum-entangled photon pairs because it has high indistinguishability, room-temperature operation, simple signal filtering, coherent emission, and multi degree-of-freedom entanglement [27,34]. In SPDC, a pump photon with a higher frequency (ωp) splits into a signal photon (ωs) and an idler photon (ωi), satisfying energy conservation ωp = ωs + ωi. The key to highly efficient generation of SPDC is to increase vacuum field fluctuations to amplify the spontaneous emission process. Owing to their intrinsic compact nature and their relaxed phase-matching condition requirements, metasurfaces are regarded as suitable candidates for the SPDC process. Another topic that has been reported in a series of works in recent years [24,25,27,29] is resonant metasurfaces as a platform for photon pair generation, where high quality-factor resonances at the signal and idler frequencies are generated by amplifying the vacuum field fluctuations. A classical optical path layout of a resonant metasurface used for photon-pair generation through SPDC is shown in Figure 1a. Light from a continuous-wave (CW) laser at a higher frequency (ωp) propagates through half-wave plates and polarising beam splitter configuration for polarisation control and unidirectional isolation, before being focused by a lens onto the resonant metasurface. The lens is also used to collect the generated photon pairs. The resonance frequency of the resonant metasurface is designed to be equal to the idler or signal frequency to increase the vacuum field fluctuation strength. The rate of this type of spontaneous process depends only on the pump power [26,29], so the improvement from using short-pulse lasers commonly employed in classical nonlinear processes has limited benefits for SPDC generation. Instead, the quality factor of the resonance is a more important factor for efficient photon pair generation via SPDC using resonant metasurfaces.

Bound states in the continuum (BIC) in electromagnetics are regarded as non-radiation eigenstates embedded in the continuum and therefore theoretically yield an infinite quality (Q) factor. Optical metasurfaces are considered a good platform to support and operate BICs [30,35]. In practice, intrinsic material loss/fabrication errors, or deliberately introduced symmetry breaking, can convert a BIC mode with infinite Q into a quasi-BIC (q-BIC) mode with an observable finite high Q factor. Combining q-BICs with SPDC on a metasurface platform has therefore recently begun to call attention. During the collection of generated photons through SPDC, the lens collects photons generated in various directions, so photons in the directions both normal to metasurface plane and with oblique angles are present. However, in previous reports [23,25–29], the resonant frequency of the q-BIC is designed to equal the signal/idler frequency only at the Γ point, while non-zero group-velocity dispersion leads to a mismatch between the mode resonance frequency and ωs/ωi at off-Γ points, as shown in Figure 1b. At the same time, q-BICs originated from symmetry-breaking are commonly designed to have a high Q factor only at the Γ point, which decreases significantly as k∥ increases [36,37]. These two effects greatly reduce the generation efficiency of ωs/ωi photons due to the decreased Q factor. A metasurface structure that supports both low group-velocity dispersion (a flat-band structure) and high-Q factor resonances within a certain range of incidence angles is therefore a more ideal platform. Recent studies have achieved enhancements in properties such as bandwidth and angular range of emission by applying geometric perturbations to the periodic structure of metasurfaces [38,39], while the resonant modes didn't show high Q-factor property. Maintaining a high Q-factor for the mode while enabling wide-angle excitation still needs further research.

Here, we propose a flat-band optical metasurface composed of GaAs nano-resonators on a SiO2 substrate, the design of which we optimised through numerical simulations. After careful geometrical optimisation, the device is designed to support an all-band flat band along the Γ − Y direction near the telecommunications band (∼1550 nm), which is commonly used in signal/idler photons generation. The structure supports a band that contains two q-BIC modes whose Q factors are both >109, and owing to the merging of the two BIC modes, the Q factor across the entire band is larger than 105. Such a structure that simultaneously supports a flat band and uniformly high Q factors along the band shows both angle-independent resonance frequency and high Q factor features, supports a much higher density of states, and has the potential to enhance classical and quantum nonlinear processes such as second harmonic generation (SHG) and SPDC.

thumbnail Fig. 1

(a) Conventional optical path for photon pair generation using resonant metasurface. HWP = Half Wave Plate, CW = Continuous Wave, LP filter = Long Pass filter, SNSPD = Superconducting Nanowire Single-Photon Detector. (b) Conceptual illustration of a flatband resonant metasurface versus a dispersive resonant metasurface.

2 Design and results

The proposed metasurface is a periodic array of GaAs nanobricks on a SiO₂ substrate, as shown in Figure 2a. GaAs is chosen because of its excellent second-order nonlinear effects [40,41], while the SiO₂ substrate has a low refractive index (∼1.4), so as to give as small an impact on the system as possible. We propose the use of [110]-cut GaAs as the resonator material to support the BIC modes. Recent studies indicate that [110]- or [111]-cut III-V wafers can support a larger second-order nonlinearity χ (2) and higher overlap integrals of interacting modes compared to the [100]-crystal orientation [25,42,43], particularly for modes possessing out-of-plane components. The high-Q mode supporting BIC-merging investigated in this work is a quasi-TE mode, which features a substantial out-of-plane electric field component, therefore [110]-cut GaAs offers significant advantages. The period in x-direction is P, while the period in y-direction is set to be P multiplied by a scaling factor S (i.e., S × P).

To realise both high-Q over a wide k∥ range and angular dispersion free (flatband) features, we conducted two types of geometry engineering, namely high-Q engineering and flatband engineering, as illustrated in Figures 2b and 2c.

High-Q engineering is achieved by introducing periodic-doubling perturbations (PDPs) to realise a period doubling effect. If we consider a periodic array of nanobrick-like structures with the dimensions W0 × L0 so that it has an effective period of P/2, when a width variation or a length variation is introduced to adjacent elements, the effective period of the array will be doubled to P, as shown in Figure 2b. The metasurface design can therefore be seen as two overlaid periodic structures made up of nanobricks with dimensions W1 × L1 and W2 × L2, where W1 = W0 − δ1, W2 = W0 + δ1, L1 = L0 − δ2, L2 = L0 + δ2. In combination these structures form an effective periodic element consists of two different nano-bricks with a period of P in an array. Such period doubling effects lead to the folding of the bands supported by the metasurface that will be discussed later. Specifically, doubling the effective period along the x-direction in real space can symmetrically fold the bands along the X − M direction in momentum space on to the Γ − Y direction, forming a series of new bands, as illustrated in Figure 3. These new bands exhibit novel physical effects; for example, guided modes originally below the light line are folded above the light line to form quasi-guided modes (QGM), which shows high Q factors while still lying in the radiation continuum. The high-Q modes on these bands and the original modes along the Γ − Y direction undergo mode coupling; new BIC modes can therefore be generated through interference and energy exchange [44]. The width variation δ1 and length variation δ2 that we have introduced makes it possible to have 2-axis (double) PDP instead of single PDP as seen in previous reports [45,46]. We have found that by tuning the magnitudes of both PDPs it can help to merge multiple BICs, maintaining high Q factors over a wider k∥ range. In addition, a scaling factor S has been introduced to modify the duty-cycle along y-direction so as to engineer the angular dispersion of the designed high-Q band, as shown in Figure 2c.

We first show Q-factor engineering achieved through tuning the relative magnitude of the two PDPs. As shown in Figures 4a–4d, a single PDP (taking δ1 = 0, δ2 = 16 nm as an example, i.e. δ1/δ2 = 0.) will introduce a single BIC on the designed band, while a double PDP (non-zero δ1/δ2) will introduce two BICs that can either overlap in k-space or be separated from each other. By finely adjusting the value of δ/δ, the positions of the two BICs in k-space can be tuned. From Figures 4e and 4f   it can be observed that different BIC spacings will have an effect on the Q values of the modes located between the two BICs, and it is no longer the traditional inverse-square decay of Q with respect to k∥. The Q value can therefore be maintained at a relatively high level within a specific range. For the optimised PDP ratio [δ1/δ2 = 3.25 here], as shown in Figures 4h, the corresponding minimum Q-factor (marked with a red dashed line) within the range ky ≤ 0.8 (π/P) exceeds the minimum Q-factors of the eigenmodes associated with other PDP ratios in the same interval. Specifically, the minimum Q-factor achievable here can only be obtained within the range ky ≤ 0.064 in Figure 4e (δ1/δ2 = 0). For the design wavelength of 1550 nm and P = 672 nm, ky = 0.8 and ky = 0.064 respectively, corresponding to approximately 67° and 4° following equation (1):

θ=arcsin(λdesign2Pky).(1)

Consequently, the calculated results show that the designed metasurface has increased high-Q range from 4° to 67°, significantly expanding the availability of high Q through a wider range of angle of incidence.

Next, we show how to control the flatness of the designed high-Q band by tuning the value of the S parameter in Figure 2c (i.e. the duty cycle in the y direction). By increasing the period size in the y direction, the coupling strength between adjacent unit cells can be weakened [47]. The reduction of this nonlocal interaction increases the band flatness. Here we show the change in band flatness for S = 0.9 to S = 1.5. It can be observed in Figures 5a–5d that S = 0.9 has the largest slope, while the band structure corresponding to S = 1.5 is almost a flat band with no slope.

Combining the dual PDPs and duty cycle engineering shown in Figure 2b, we finally obtain the high-Q band structure shown in Figure 6a at δ1/δ2= 2.28 and S = 1.5. The proposed structure simultaneously shows ultra-high Q values (>10⁵) along the whole band and a nearly flat band structure, which can realise enhancement of the SPDC process within a larger range of incidence angles. Any ωs/ωi photon pair that satisfies k∥ values summing to 0 (momentum conservation in k∥ direction) has almost the same wavelength. Figure 6b illustrates the near-field electric field enhancement distribution in the x−z plane (y = 0) for the eigenmode at ky = 0.66. This demonstrates that the proposed device maintains substantial enhancement, even for high deviations from the Γ point. The generation of photon pairs will therefore be significantly enhanced at a certain design wavelength; for example, the 1550 nm photon pairs shown in this case that may be collected using a high-NA lens.

thumbnail Fig. 2

(a) Geometrical layout of the proposed flatband resonant metasurface. Periodic GaAs (made from [110] cut GaAs) metasurface with a period of P in x-direction and S × P in y-direction and thickness of 300 nm. S represents a non-zero scaling factor, which gives a different pitch in x- and y- directions. The substrate SiO2 is not shown for simplicity. (b) & (c) shows the geometry engineering introduced to respectively generate high-Q and flatband features.
thumbnail Fig. 3

(a) Band structure of the proposed metasurface with period of P in both x-/y- directions and the band structure with period of P/2 in x-direction. The colour of the lines indicated the value of quality factor of the modes, while the area above light-lines represents radiation continuum. The green-dashed lines represent the modes that are folded above the lightline. (b) Illustration of Band-folding effect caused by period doubling.
thumbnail Fig. 4

Q factor engineering. (a-d) Band structure of the proposed metasurface with different PDP ratio δ1/δ2. Each mode is coloured based on the Q factor. (e-h) Q factor value in log scale versus ky corresponding to (a-d) respectively.
thumbnail Fig. 5

Flatband engineering. (a-d) Band structure of designed high-Q band with different S parameters.
thumbnail Fig. 6

Optimised high Q flatband design enabled by dual PDPs and duty cycle engineering. (a) Band structure and Q factors of the corresponding eigenmodes. (b) Near field electric field enhancement distribution of the eigenmode with ky = 0.66 and λ = 1548 nm).

3 Conclusion and discussion

A metasurface that supports a high-Q flat-band structure is proposed through simulation, featuring both a flat band along the Γ–Y direction and high-Q modes across the entire band. Using a technique that we refer to as period doubling perturbation (PDP), the guided modes that were originally below the light line were folded to above the light line. By introducing dual, 2- axis, PDPs, the dynamic control two BICs in k-space was achieved, which helped obtain modes with Q factors maintained above 10⁶ along the whole band. The flat band is achieved by tuning the relative period size in the y direction: by reducing the duty cycle of the metasurface unit cell along y, a flat band across the entire Γ–Y direction was obtained. The proposed metasurface has the potential to serve as a platform for efficient spontaneous parametric down-conversion (SPDC) generation of quantum photon pairs, and it supports collection of the photon pairs using a high-NA lens. All the proposed structures are normalised with respect to the period, which means that by changing the period size (and scaling all geometrical parameters accordingly), the design wavelength of this example (1550 nm) can be shifted to any wavelength. In future work, we plan to conduct experiments using the setup illustrated in Figure 1. Recent reports have experimentally highlighted the directionality of photon pair emission [48–50]—a factor that has frequently been overlooked. Consequently, determining whether to employ a transmissive or reflective configuration, or to perform coincidence detection across counter direction (forward-backward directions) will be a critical aspect of our experimental investigation.

Funding

The authors thank UK EPSRC, (Quantic EP/T00097X/1) and Innovate UK, (IUK10058024) for funding the work.

Conflicts of interest

The authors have nothing to disclose.

Data availability statement

Data supporting the findings of this study can be obtained through https://doi.org/10.5525/gla.researchdata.2112.

Author contribution statement

Conceptualization, S.W., V.P., D.C.; Methodology, S.W.; Software, S.W.; Validation S.W.; Formal Analysis, S.W. V.P.; Resources, X.X.; Writing − Original Draft Preparation, S.W.; Writing − Review & Editing, S.W., V.P., D.C.; Visualization, S.W.; Supervision, V.P., D.C.; Funding Acquisition, V.P., D.C.

References

  1. W.Y. Ji, J. Chang, H.X. Xu, J.R. Gao, S. Gröblacher, H.P. Urbach, A.J.L. Adam, Light-Sci. Appl. 12, 169 (2023), https://doi.org/10.1038/s41377-023-01218-y [Google Scholar]
  2. A.C. Overvig, S.C. Malek, N.F. Yu, Phys. Rev. Lett. 125, 017402 (2020), https://doi.org/10.1103/PhysRevLett.125. 017402 [Google Scholar]
  3. P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, R. Devlin, Optica 4, 139 (2017), https://doi.org/10.1364/Optica.4.000139 [CrossRef] [Google Scholar]
  4. H.T. Chen, A.J. Taylor, N.F. Yu, Rep. Prog. Phys. 79, 076401 (2016), https://doi.org/10.1088/0034-4885/79/7/076401 [Google Scholar]
  5. A. I. Kuznetsov, M.L. Brongersma, J. Yao, M. K. Chen, U. Levy, D.P. Tsai, N.I. Zheludev, A. Faraon, A. Arbabi, N.F. Yu, D. Chanda, K.B. Crozier, A.V. Kildishev, H. Wang, J.K.W. Yang, J.G. Valentine, P. Genevet, J.A. Fan, O.D. Miller, A. Majumdar, J.E. Fröch, D. Brady, F. Heide, A. Veeraraghavan, N. Engheta, A. Alù, A. Polman, H.A. Atwater, P. Thureja, R. Paniagua-Dominguez, S.T. Ha, A.I. Barreda, J.A. Schuller, I. Staude, G. Grinblat, Y. Kivshar, S. Peana, S.F. Yelin, A. Senichev, V.M. Shalaev, S. Saha, A. Boltasseva, J. Rho, D.K. Oh, J. Kim, J. Park, R. Devlin, R.A. Pala, Acs Photonics 11, 816 (2024), https://doi.org/10.1021/acsphotonics.3c00457 [Google Scholar]
  6. A. Arbabi, A. Faraon, Nat. Photonics 17, 16 (2023), https://doi.org/10.1038/s41566-022-01108-6 [Google Scholar]
  7. S.C. Malek, A.C. Overvig, A. Alu, N.F. Yu, Light-Sci. Appl. 11, 246 (2022), https://doi.org/10.1038/s41377-022-00905-6 [Google Scholar]
  8. W.T. Chen, A.Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z.J. Shi, E. Lee, F. Capasso, Nat. Nanotechnol. 13, 220 (2018), https://doi.org/10.1038/s41565-017-0034-6 [Google Scholar]
  9. S.M. Wang, P.C. Wu, V.C. Su, Y.C. Lai, M.K. Chen, H.Y. Kuo, B.H. Chen, Y.H. Chen, T.T. Huang, J.H. Wang, R.M. Lin, C.H. Kuan, T. Li, Z.L. Wang, S.N. Zhu, D.P. Tsai, Nat. Nanotechnol. 13, 227 (2018), https://doi.org/10.1038/s41565-017-0052-4 [Google Scholar]
  10. B.H. Chen, P.C. Wu, V.C. Su, Y.C. Lai, C.H. Chu, I.C. Lee, J.W. Chen, Y.H. Chen, Y.C. Lan, C.H. Kuan, D.P. Tsai, Nano Lett. 17, 6345 (2017), https://doi.org/10.1021/acs.nanolett.7b03135 [Google Scholar]
  11. S.H. Wu, S.M. Zhu, K.T. Lai, L.P. Hou, V. Pusino, D.R.S. Cumming, Laser Photonics Rev. (2025). https://doi.org/10.1002/lpor.202501360 [Google Scholar]
  12. T.S. Nowack, Y.D. Shah, I. Escorcia, J.P. Grant, M. Kenney, V. Pusino, D. Faccio, E. Wasige, D.R.S. Cumming, Opt. Lett. 47, 4199 (2022), https://doi.org/10.1364/Ol.463143 [Google Scholar]
  13. A.H. Dorrah, N.A. Rubin, A. Zaidi, M. Tamagnone, F. Capasso, Nat. Photonics 15, 287 (2021), https://doi.org/10.1038/s41566-020-00750-2 [Google Scholar]
  14. Y.Q. Hu, X.D. Wang, X.H. Luo, X.N. Ou, L. Li, Y.Q. Chen, P. Yang, S. Wang, H.G. Duan, Nanophotonics-Berlin 9, 3755 (2020), https://doi.org/10.1515/nanoph-2020-0220 [Google Scholar]
  15. J. Sardana, S. Devinder, S. Kaassamani, W.Q. Zhu, A. Agrawal, J. Joseph, Acs Photonics 12, 2380 (2025), https://doi.org/10.1021/acsphotonics.4c01776 [Google Scholar]
  16. T.T. Liu, J.M. Qiu, L. Xu, M.B. Qin, L.P. Wan, T.B. Yu, Q.G. Liu, L.J. Huang, S.Y. Xiao, Nano Lett. 24, 14466 (2024), https://doi.org/10.1021/acs.nanolett.4c04543 [Google Scholar]
  17. M. Cotrufo, S. Singh, A. Arora, A. Majewski, A. Alu, Optica 10, 1331 (2023), https://doi.org/10.1364/Optica.500121 [Google Scholar]
  18. T. Badloe, Y. Kim, J. Kim, H. Park, A. Barulin, Y.N. Diep, H.S. Cho, W.S. Kim, Y.K. Kim, I. Kim, J. Rho, Acs Nano 17, 14678 (2023), https://doi.org/10.1021/acsnano.3c02471 [Google Scholar]
  19. S. Rosas, S.K. Biswas, W. Adi, F. Kuruoglu, A. Beisenova, M.S. Patankar, F. Yesilkoy, Adv. Mater. (2025). https://doi.org/10.1002/adma.202504355 [Google Scholar]
  20. M.W. Song, L. Feng, P.C. Huo, M.Z. Liu, C.Y. Huang, F. Yan, Y.Q. Lu, T. Xu, Nat. Nanotechnol. 18, 71 (2023), https://doi.org/10.1038/s41565-022-01256-4 [Google Scholar]
  21. A. John-Herpin, A. Tittl, L. Kühner, F. Richter, S.H. Huang, G. Shvets, S.H. Oh, H. Altug, Adv. Mater. 35, 2110163 (2023), https://doi.org/10.1002/adma.202110163 [Google Scholar]
  22. W.H. Yang, S.M. Xiao, Q.H. Song, Y.L. Liu, Y.K. Wu, S. Wang, J. Yu, J.C. Han, D.P. Tsai, Nat. Commun. 11, 1864 (2020), https://doi.org/10.1038/s41467-020-15773-0 [Google Scholar]
  23. W.H. Jia, G. Saerens, Ü. L. Talts, H. Weigand, R.J. Chapman, L. Li, R. Grange, Y.M. Yang, Sci. Adv. 11, eads3576 (2025), https://doi.org/10.1126/sciadv.ads3576 [Google Scholar]
  24. T.M. Fan, J.H. Zhang, A.A. Sukhorukov, Phys. Rev. A 111, 063519 (2025), https://doi.org/10.1103/p1wr-98wx [Google Scholar]
  25. J. Noh, T. Santiago-Cruz, C.F. Doiron, H. Jung, J.Y. Yu, S.J. Addamane, M.V. Chekhova, I. Brener, Light-Sci. Appl. 14, 371 (2025), https://doi.org/10.1038/s41377-025-01998-5 [Google Scholar]
  26. J. Noh, T. Santiago-Cruz, V. Sultanov, C.F. Doiron, S.D. Gennaro, M.V. Chekhova, I. Brener, Nano Lett. 24, 15356 (2024), https://doi.org/10.1021/acs.nanolett.4c04398 [Google Scholar]
  27. T.T. Liu, M.B. Qin, S.Q. Feng, X. Tu, T.J. Guo, F. Wu, S.Y. Xiao, Phys. Rev. B 109, 155424 (2024), https://doi.org/10.1103/PhysRevB.109.155424 [Google Scholar]
  28. T. Santiago-Cruz, S.D. Gennaro, O. Mitrofanov, S. Addamane, J. Reno, I. Brener, M. Chekhova, Science 377, 991 (2022), https://doi.org/10.1126/science.abq8684 [Google Scholar]
  29. T. Santiago-Cruz, A. Fedotova, V. Sultanov, M.A. Weissflog, D. Arslan, M. Younesi, T. Pertsch, I. Staude, F. Setzpfandt, M. Chekhova, Nano Lett. 21, 4423 (2021), https://doi.org/10.1021/acs.nanolett.1c01125 [CrossRef] [PubMed] [Google Scholar]
  30. J.B. Yu, W.Z. Yao, M. Qiu, Q. Li, Light-Sci. Appl. 14, 174 (2025), https://doi.org/10.1038/s41377-025-01825-x [Google Scholar]
  31. C.U. Hail, L. Michaeli, H.A. Atwater, Nano Lett. 24, 2257 (2024), https://doi.org/10.1021/acs.nanolett.3c04476 [Google Scholar]
  32. Y.J. Zang, R.H. Chai, W.W. Liu, Z.C. Li, H. Cheng, J.G. Tian, S.Q. Chen, Sci. China Phys. Mech. 67, 244212 (2024), https://doi.org/10.1007/s11433-023-2299-9 [Google Scholar]
  33. N. Bernhardt, K. Koshelev, S. J. U. White, K. W. C. Meng, J.E. Fröch, S. Kim, T.T. Tran, D.Y. Choi, Y. Kivshar, A.S. Solntsev, Nano Lett. 20, 5309 (2020), https://doi.org/10.1021/acs.nanolett.0c01603 [Google Scholar]
  34. J.W. Wang, F. Sciarrino, A. Laing, M.G. Thompson, Nat. Photonics 14, 273 (2020), https://doi.org/10.1038/s41566-019-0532-1 [CrossRef] [Google Scholar]
  35. W.J. Zhou, G.C. Sun, Y.Y. Yuan, Y.X. Wang, S.N. Burokur, Y. Wang, K. Zhang, Ann. Phys. −Berlin 537, 2400250 (2025), https://doi.org/10.1002/andp.202400250 [Google Scholar]
  36. C.B. Zhou, L.J. Huang, R. Jin, L. Xu, G.H. Li, M. Rahmani, X.S. Chen, W. Lu, A.E. Miroshnichenko, Laser Photonics Rev. 17, 2200564 (2023), https://doi.org/10.1002/lpor.202200564 [Google Scholar]
  37. K. Koshelev, S. Lepeshov, M.K. Liu, A. Bogdanov, Y. Kivshar, Phys. Rev. Lett. 121, 193903 (2018), https://doi.org/10.1103/PhysRevLett.121.193903 [Google Scholar]
  38. Y. Jiang, J. Zhang, J. Ma, D.N. Neshev, A.A. Sukhorukov, APL Quantum. 2, 026115 (2025), https://doi.org/10.1063/5.0247669 [Google Scholar]
  39. J. Zhang, C. Shi, J. Ma, F. Setzpfandt, T. Pertsch, C. Bao, J. Zhang, A.A. Sukhorukov, arXiv:2502.08990 [physics.optics] (2025) [Google Scholar]
  40. Z. Wang, R. Lin, J. Yao, D.P. Tsai, npj Nanophoton. 2, 4 (2025), https://doi.org/10.1038/s44310-024-00050-5 [Google Scholar]
  41. P.P. Vabishchevich, S. Liu, M.B. Sinclair, G.A. Keeler, G.M. Peake, I. Brener, Acs Photonics 5, 1685 (2018), https://doi.org/10.1021/acsphotonics.7b01478 [Google Scholar]
  42. J.Y. Ma, T.M. Fan, T. Haggren, L.V. Molina, M. Parry, S. Shinde, C. McManus-Barrett, J.H. Zhang, R.C. Morales, F. Setzpfandt, H.H. Tan, C. Jagadish, D.N. Neshev, A.A. Sukhorukov, Sci. Adv. 11, eadu4133 (2025), https://doi.org/10.1126/sciadv.adu4133 [Google Scholar]
  43. S. Liu, P.P. Vabishchevich, A. Vaskin, J.L. Reno, G.A. Keeler, M.B. Sinclair, I. Staude, I. Brener, Nat. Commun. 9, 2507 (2018), https://doi.org/10.1038/s41467-018-04944-9 [Google Scholar]
  44. N.D. Le, P. Bouteyre, A. Kheir-Aldine, F. Dubois, L. Berguiga, X. Letartre, P. Viktorovitch, T. Benyattou, H.S. Nguyen, Phys. Rev. Lett. 132, 173802 (2024), https://doi.org/10.1103/PhysRevLett.132.173802 [Google Scholar]
  45. W.H. Wang, Y.K. Srivastava, T.C. Tan, Z.M. Wang, R. Singh, Nat. Commun. 14, 2811 (2023), https://doi.org/10.1038/s41467-023-38367-y [Google Scholar]
  46. W. Adi, S. Rosas, A. Beisenova, S.K. Biswas, H.Y. Mei, D.A. Czaplewski, F. Yesilkoy, Nat. Commun. 15, 10049 (2024), https://doi.org/10.1038/s41467-024-54284-0 [Google Scholar]
  47. X.Y. Zhang, Q. Li, F.F. Liu, M. Qiu, S.L. Sun, Q. He, L. Zhou, Light-Sci. Appl. 9, 76 (2020), https://doi.org/10.1038/s41377-020-0313-0 [Google Scholar]
  48. C. Son, V. Sultanov, T. Santiago-Cruz, A.P. Anthur, H.Z. Zhang, R. Paniagua-Dominguez, L. Krivitsky, A.I. Kuznetsov, M.V. Chekhova, Nanoscale 15, 2567 (2023), https://doi.org/10.1039/d2nr05499j [Google Scholar]
  49. M.A. Weissflog, J.Y. Ma, J.H. Zhang, T.M. Fan, S. Lung, T. Pertsch, D.N. Neshev, S. Saravi, F. Setzpfandt, A.A. Sukhorukov, Nanophotonics-Berlin 13, 3563 (2024), https://doi.org/10.1515/nanoph-2024-0122 [Google Scholar]
  50. Z.Y. Lu, J. Janousek, S.M. Assad, S.Y. Qiu, M. Joshi, Y.C. Hu, A.Y. Song, C.Y. Wang, M. Suriyage, J. Zhao, P.K. Lam, Y.R. Lu, Nat. Commun. 16, 9616 (2025), https://doi.org/10.1038/s41467-025-64620-7 [Google Scholar]

Cite this article as: Shuhao Wu, Vincenzo Pusino, David R.S. Cumming, An angular dispersion-free resonant metasurface for quantum photon pair generation, EPJ Appl. Metamat. 13, 2 (2026), https://doi.org/10.1051/epjam/2025013

All Figures

thumbnail Fig. 1

(a) Conventional optical path for photon pair generation using resonant metasurface. HWP = Half Wave Plate, CW = Continuous Wave, LP filter = Long Pass filter, SNSPD = Superconducting Nanowire Single-Photon Detector. (b) Conceptual illustration of a flatband resonant metasurface versus a dispersive resonant metasurface.
In the text
thumbnail Fig. 2

(a) Geometrical layout of the proposed flatband resonant metasurface. Periodic GaAs (made from [110] cut GaAs) metasurface with a period of P in x-direction and S × P in y-direction and thickness of 300 nm. S represents a non-zero scaling factor, which gives a different pitch in x- and y- directions. The substrate SiO2 is not shown for simplicity. (b) & (c) shows the geometry engineering introduced to respectively generate high-Q and flatband features.
In the text
thumbnail Fig. 3

(a) Band structure of the proposed metasurface with period of P in both x-/y- directions and the band structure with period of P/2 in x-direction. The colour of the lines indicated the value of quality factor of the modes, while the area above light-lines represents radiation continuum. The green-dashed lines represent the modes that are folded above the lightline. (b) Illustration of Band-folding effect caused by period doubling.
In the text
thumbnail Fig. 4

Q factor engineering. (a-d) Band structure of the proposed metasurface with different PDP ratio δ1/δ2. Each mode is coloured based on the Q factor. (e-h) Q factor value in log scale versus ky corresponding to (a-d) respectively.
In the text
thumbnail Fig. 5

Flatband engineering. (a-d) Band structure of designed high-Q band with different S parameters.
In the text
thumbnail Fig. 6

Optimised high Q flatband design enabled by dual PDPs and duty cycle engineering. (a) Band structure and Q factors of the corresponding eigenmodes. (b) Near field electric field enhancement distribution of the eigenmode with ky = 0.66 and λ = 1548 nm).
In the text

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