Open Access
Add to BibSonomy
Abstract
Structured illumination microscopy (SIM), as a wide-field, rapid, super-resolution imaging technology, is widely employed in the field of biology. In this work, we propose a hyperbolic metamaterial (HMM)-assisted super-resolution structured illumination microscopy technique. By utilizing the HMM, a sub-diffraction illumination pattern of bulk plasmon polariton (BPP) with pure and higher spatial frequency replaces the conventional laser interference fringes, thus the imaging resolution of BPPSIM could surpass that of conventional SIM and reach 65 nm for HMM with 8-layers periodic structure. Moreover, an HMM with 10-layers aperiodic structure designed with particle swarm optimization was obtained, and BPPSIM could bring the imaging resolution down to 60 nm (1/9 of the fluorescence wavelength), which is a 3.3-fold improvement compared with the diffraction-limited image. This BPPSIM would provide a super-resolution, wide field of view, and good bio-compatibility approach in biological imaging.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The invention of optical microscopy plays a significant role in unraveling complex mysteries in the field of biomedical research [1]. When the characteristic size of object is of the order of the wavelength of light, the wave nature becomes particularly significant. Due to the existence of diffraction effects, the imaging system only collects spatial frequencies below its cut-off frequency, and higher spatial frequency information is lost. As a result, the spatial resolution of optical microscope is limited by the diffraction limit of λ/(2NA), where λ is the emission wavelength from sample, NA is the numerical aperture of the objective lens [2]. This indicates that the maximum imaging resolution is approximately 200 nm for visible light [3]. While, most biological processes occur below this limit. Recently, the resolution of optical microscopes has been enhanced by various revolutionary optical super-resolution techniques, such as stimulated emission depletion microscopy (STED) [4,5], photoactivated localization microscopy (PALM) [6,7] and stochastic optical reconstruction microscopy (STORM) [8]. Although these methods can achieve sub-50nm resolution, STED and PALM require a strong power density of light that would cause photodamage for live cells [9], STORM demands thousands of sub-images to reconstruct one super-resolution images, resulting in slow imaging. Although hyperlens composed of alternating metal/dielectric multilayers can realized the real-time super-resolution imaging without image post-processing, its curved surface shape results in the limited field of view and complex fabrication process [10–13]. Alternatively, Due to the high spatiotemporal resolution, low phototoxicity and wide field of view (FOV) [14,15], structured illumination microscopy (SIM) has attracted more and more attentions [16].
SIM realizes sub-diffractive resolution by exploiting patterned illumination, which allows higher spatial frequencies to participate in imaging [17]. The resolution of SIM is mainly determined by the highest attainable spatial frequency fexpand [18].
where fcut and fillum are the cut-off frequency of the optical system and the maximum frequency of illumination patterns, respectively. As the illumination pattern of traditional SIM is also limited by the diffraction limit, the maximum possible improvement of spatial resolution can only be 2 times compared to conventional optical microscopy [19]. In order to further boost the resolution, researchers have explored various methods to expand the spatial frequency of the illumination pattern. One of methods is saturated SIM [20], which obtains high-order spatial illumination frequency fillum through the saturated excitation of fluorescence. Since it requires a stronger laser density, this inevitably brings phototoxicity and photobleaching. Moreover, larger spatial illumination frequencies can also be obtained by utilizing near-field illumination modules, which is friendly to cell. For instance, plasmonic structure illumination microscopy (PSIM) [16,18,21] and localized surface plasmon SIM imaging technology (LPSIM) [22,23]. PSIM, adopting propagating surface plasmon polariton (SPP) to form subwavelength interference patterns, could achieve higher spatial frequency. However, limited metallic materials restrict the further enhancement of the illumination patterns spatial frequency, which is only 2.88k0 for Air/Ag configuration [18], k0 is the light wavevector in vacuum. LPSIM could reach 75 nm imaging resolution with 1.2 NA and 488 nm of the fluorescence wavelength by using the localized surface plasmon modes generated by fine metal disk array [24]. Recently, hyperbolic metamaterials (HMM) has also been introduced into the SIM to further improve the resolution. It consists of a stack of metal and dielectric films, which can theoretically improve the resolution equal to the thickness of metal/dielectric cell [25]. Lee et al. used random speckles launched on the exit surface of the HMM as a illumination pattern with high spatial frequency and reconstructed one super-resolution image from 500 diffraction-limited sub-images, the resolution could be compressed to 40 nm [26]. Random speckle illumination can obtain finer illumination modes while also introducing a larger spectral gap due to lack of knowledge about precise illumination patterns and the correlation between illumination patterns. To avoid the influence of frequency gaps, dozens or hundreds of sub-images need to be collected, but more sub-images mean the slower imaging speed.In this work, we introduce a periodic bulk plasmon polariton (BPP) illumination pattern based structured illumination microscopy technique (BPPSIM) by employing HMM, which achieves sub-70 nm imaging resolution. The deep subwavelength BPP modes are launched by the HMM [27] composed of Ag/SiO2 alternately stacked multilayers with spatial frequency bandpass property and the two-dimensional grating. Speckle illumination patterns with periodic and high spatial frequency are generated by BPP interference excited by one beam instead of two symmetrical beams for conventional SIM, which would alleviate the complexity of imaging optics. The phase of the period illumination pattern could be changed by adjusting the incident angle of single beam. Subsequently, a super-resolution image is reconstructed by the blind algorithm [28,29] from 15 sub-images. For HMM with 8-layers periodic structure, BPPSIM can resolve two beads with center-to-center distance of 65 nm, that is, the imaging resolution of 65 nm could be achieved. To increase the design freedom of HMM and then the resolution, the HMM is designed as aperiodic structure. The film thickness can be optimized by combining particle swarm algorithm (PSA) [30] with the rigorous coupled wave analysis (RCWA). For HMM with 10-layers aperiodic structure, the imaging resolution could reach 60 nm further. Compared with the diffraction-limited results, the resolution of BPPSIM images of two structures is improved by 3-fold and 3.3-fold, respectively. BPPSIM method has the potential to enhance the resolution of SIM microscopy to the deep subwavelength scale by rationally designing the HMM structure.
2. Method
The designed BPPSIM structure is shown in Fig. 1(a), and a periodic, high-frequency structured illumination pattern is generated by HMM. The HMM can be analyzed by effective medium theory (EMT) [31,32]. Therefore, the equivalent permittivity of the HMM along the x, y, and z directions can be written as,
Fig. 1. BPP based SIM (BPPSIM). (a) Schematic diagram of the BPPSIM structure composed of HMM and grating. (b) Isofrequency curve of air and HMM calculated by EMT. Yellow part and light blue part represent the spatial frequency pass band of light in air and in HMM.(c) OTF of HMM with periodical structures of Ag/SiO2 (20 nm/20 nm) at the wavelength of 532 nm. (d) Cross-sectional view of the three-fold rotationally symmetric grating along the x, y plane. (e) Schematic diagram of BPP extending SIM frequency domain.The purple circle and the green circe represent the frenquency of diffraction-limited system and BPP illumination pattern, respectively. The red line corresponds to the total spatial spectrum region of BPPSIM.
The structured illumination pattern of BPPSIM can be simulated by the finite difference time domain method (FDTD). 3×5 unit cells of grating are selected for illumination field simulation. The boundary conditions of the perfectly matched layer are used in z direction. Periodic boundary conditions are used for normal incidence, while Bloch boundary conditions are used for oblique incidence in x, y direction. The mesh of HMM and grating is 5×5×2 nm3. The default shutoff precision of 1×10−5 is used as the convergence condition. In the simulation, the TM-polarized plane wave with 532 nm wavelength is adopted as the illumination source, the structured illumination patterns could be shifted by changing the incidence angle of single beam. The periodic speckle intensity distributions are obtained at 20 nm away from the exit surface of HMM, as shown in Fig. 2(a)-(c). The in-plane orientation angles of the incident light are 0°, 60°, and 120°, respectively. The period of speckle pattern is 100 nm in the three directions from simulations. For comparison, the case without HMM (yellow bandwidth in Fig. 1(b)) is also simulated, and the light field distribution is shown in Fig. 2(d), which only reach the illumination pattern period of 200 nm. Then, the speckle illumination patterns under the different incident angles were simulated. When the orientation angle of 0°, the period of the speckle illumination pattern are both 100 nm for the incident angles of 9° and 10°, while the position are shifted 25 nm and 35 nm compared with that of the normal incidence, respectively, as depicted in Fig. 2(e). It results from the near electric field amplitudes of ±1 diffraction waves for the incident angle is 9° and 10° from Eq. (7). The cases of incident angles of −9° and −10° are not analyzed detailed because of the symmetry. In one world, the sub-diffraction periodic speckle illumination pattern could be achieved by the HMM.
Fig. 2. Structured illumination patterns for BPPSIM excited by three-fold rotationally symmetric grating. (a)-(c) The periodic speckle illumination pattern of BPP excited by one beam for in-plane orientation angles of 0°, 60°, and 120°. (d) Illumination pattern without HMM (the yellow bandwidth in Fig. 1(b)). (e) The normalized intensity profile of illumination pattern with incident angle 0°, 9°, and 10°.
When reconstructing super-resolution image, Blind algorithm is utilized. The algorithm assumes that the sum of all illumination patterns is uniformly field. The object information and illumination patterns are solved by minimizing the cost function [28,37]. A BPPSIM super-resolution image is reconstructed using 15 sub-images (3 orientations × 5 incident angles). For improving the reconstruction speed, the imaging process of the blind algorithm is changed to the frequency domain calculation. In detain, about 10 minutes was taken to reconstruct a super-resolution image with a pixel size of 500×500 on an NVIDIA Tesla V100s graphic card.
3. Results and discussion
The full width at half maximum (FWHM) of a single particle and the center-to-center distance between two beads are used to assess the resolution of the BPPSIM method. A single fluorescent bead with 40 nm diameter is used as object for imaging. The excitation and emission wavelengths are 532 nm and 560 nm, respectively. A diffraction-limited image was obtained through a conventional imaging system with NA = 1.45, as shown in Fig. 3(a), while Fig. 3(b) displays the greatly reduced spot by employing BPPSIM method. For a more quantitative illustration, the normalized intensity profile of a single bead is shown in Fig. 3(c). The FWHM of the diffraction-limited image is 198 nm, while that of the BPPSIM image is 65 nm. It indicates that 3-fold enhancement in resolution could be achieved compared to the diffraction-limited image. Figure 3(d) and Fig. 3(e) are the diffraction-limited image and BPPSIM super-resolution image of two beads with center-to-center distance of 65 nm, respectively. Two beads can be distinguished clearly through BPPSIM, while it is undistinguishable in the diffraction-limited image. The normalized intensity profile of two beads is illustrated in Fig. 3(e). The center-to-center distance of two beads reconstructed by BPPSIM method is 65 nm, which is consistent with that of two beads.
Fig. 3. BPPSIM super-resolution images of single bead and two beads for HMM with 8-layers periodic structure. (a) Diffraction-limited image and (b) BPPSIM image for a single fluorescent bead. Scale bar: 100 nm. (d) Diffraction-limited image and (e) BPPSIM image for two beads with center-to-center distance of 65 nm. Scale bar: 100 nm. The normalized intensity intercepts along the white dashed line for (c) a single fluorescent bead and (f) two fluorescent beads, respectively.
To verify the resolution of BPPSIM for the dense objects, 18 fluorescent beads are randomly distributed in an area of 2.5×2.5 µm2. Figure 4(a) shows the diffraction-limited image, and Fig. 4(b) shows the recovered image by deconvolution. Although the resolution is improved to a certain extent with deconvolution method, the dense areas are still not indistinguishable. While, through collecting 15 sub-images, a clear and super-resolution image could be reconstructed by BPPSIM, as shown in Fig. 4(c). As one can see, in addition to sharpen the individual bead, the undistinguishable regions of diffraction-limited and the deconvoluted image could be also distinguished after the BPPSIM method. Figure 4(d)-(g) are the spatial frequency spectra of Fig. 4(a)-(c), respectively. The BPPSIM method extends the radius of the spatial frequency spectra ∼3-fold, which is consistent with theoretical value of 3 (Fig. 1(e)).
Fig. 4. BPPSIM super-resolution images of sparse fluorescent beads for HMM with 8-layers periodic structure. (a) Diffraction-limited image. (b) Fourier-based deconvolution image. (c) BPPSIM super-resolution image. Scale bar: 400 nm. (d)-(f) Spatial frequency spectra of images (a)–(c), displayed in logarithmic intensity.
In order to improve the resolution of BPPSIM further, the thickness of HMM is optimized by combining PSA with RCWA. First, the grating period was fixed to 190 nm. Second, the film thickness was obtained by a strategy of minimizing the electric field amplitude difference of the ±1 diffraction waves from grating for achieving the periodic speckle illumination pattern, and then estimated iteratively to minimize the cost functional,
where x1 and x2 are the positions of kx of ±1 diffraction waves under normal incidence, respectively, and x is the range of kx shifted by oblique incidence. In particle swarm algorithm, the number of particles is 100, the learning factor is 2, and the convergence condition is 1e-15. The particle swarm algorithm searches the optimal solution within the range of input HMM film thickness, where the thickness range of metal film is from 5 nm to 20 nm and that of dielectric film is from 10 nm to 50 nm. Subsequently, an HMM with 10-layers aperiodic structure is designed, which enhances the suppression for 0th order diffraction light of the grating compared with the HMM with 8-layers periodic structure [36]. From the entrance to exit surface, HMM is composed of SiO2/Ag sequentially arranged with thicknesses of 34 nm, 13 nm, 20 nm, 17 nm, 28 nm, 18 nm, 24 nm, 12 nm, 37 nm, and 9 nm, respectively. Periodic speckle illumination patterns were also obtained under the incident angle of ±9° and ±10° by FDTD simulation.The object is also made of randomly distributed fluorescent beads in an area of 2.5×2.5 µm2 for testing the resolution. The asymmetry intensity distribution in the diffraction-limited image shown in Fig. 5(a) indicates the presences of multiple beads. The super-resolution image is reconstructed by using blind-SIM from 15 sub-images, as shown in Fig. 5(b). Figure 5(e) shows three of 15 sub-images, which display obvious shift of the peak location, indicating the change of the illumination pattern. Figure 5(c) depicts the zoomed images of the indicated regions for the super-resolution image. Obviously, four beads could be well resolved with the center-to-center distance of ∼90 nm between the closest two beads, and the positions of these beads are in agreement with the marked positions. Figure 5(d) is the intensity profile along the arrow direction in Fig. 5(b), the FWHM of single bead is 63 nm. A diffraction-limited spot consisting of two beads is shown in Fig. 5(f). After the reconstruction, the two merged beads are distinguished, as shown in Fig. 5(g). Moreover, the spatial frequency spectra is also considerably expanded by BPPSIM. The center-to-center space is extracted to be 60 nm, as shown in Fig. 5(h), demonstrating the super-resolution imaging capability of BPPSIM.
Fig. 5. BPPSIM super-resolution images of sparse fluorescent beads for HMM with 10-layers aperiodic structure. (a) Diffraction-limited image and (b) BPPSIM image of multiple beads. Scale bar: 500 nm. (c) Zoom in image of the white dot box in (b). (d) Normalized intensity cross-section of images (b) along indicated direction. (e) Three selected sub-images indicate the change of the illumination pattern. The cross present the position of beads. (f) Diffraction-limited image and (g) BPPSIM super-resolution image of two beads with center-to-center resolution of 60 nm. Inset: the spatial frequency spectra of images. Scale bar: 200 nm. (h) The Normalized intensity profile is plotted along the arrow direction in (g).
Among HMM assisted structured illumination microscopy methods, BPPSIM has its own advantages. Benefited from the spatial frequency bandpass filtering effect of the HMM, single periodic speckle illumination pattern can be obtained. From an information-theoretical point of view, BPPSIM utilizes the known periodic illumination patterns rather than unknown ones to reduce of the required sub-images for reconstructing. Therefore, compared to random speckle illumination [26], the BPPSIM method improves the speed of reconstructing super-resolution images obviously. Furthermore, compared with the interference of two symmetrical beams of traditional SIM, BPPSIM is more convenient to shift the illumination pattern only by changing the incident angle of single beam.
4. Conclusion
In conclusion, we propose and demonstrate a BPPSIM method with periodic sub-diffraction speckle illumination. The deep subwavelength BPP modes are launched by utilizing the HMM with bandpass properties, and the periodic sub-diffraction speckle illumination patterns are generated after BPP interference. Subsequenctly, one super-resolution image was reconstructed by blind algorithm from 15 sub-images. For HMM with 8-layers periodic structure, the resolution of BPPSIM can reach 65 nm. While for an HMM with 10-layers aperiodic structure optimized by combining PSA with RCWA, the resolution of BPPSIM image could be compressed down to 60 nm, which is a 3.3-fold improvement. In contrast to traditional SIM, the BPPSIM method greatly extends spatial resolution. Therefore, this technique would play an important role in the field of super-resolution biomedical imaging.
Funding
West Light Foundation of the Chinese Academy of Sciences; National Natural Science Foundation of China (62192773); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2021379).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon request.
References
1. E. P. Canovi, D. T. Seidl, S. R. Polio, A. A. Oberai, and M. L. Smith, “Biomechanical imaging of cell stiffness and prestress with subcellular resolution,” Biomechanics & Modeling in Mechanobiol. 13(3), 665–678 (2014). [CrossRef]
2. K. Kaniecki, L. De Tullio, and E. C. Greene, “A change of view: homologous recombination at single-molecule resolution,” Nat. Rev. Genet. 19(4), 191–207 (2018). [CrossRef]
3. B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010). [CrossRef]
4. T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. 97(15), 8206–8210 (2000). [CrossRef]
5. C. Wang, M. Taki, K. Kajiwara, J. Wang, and S. Yamaguchi, “Phosphole-oxide-based fluorescent probe for super-resolution stimulated emission depletion live imaging of the lysosome membrane,” ACS Mater. Lett. 2(7), 705–711 (2020). [CrossRef]
6. S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006). [CrossRef]
7. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006). [CrossRef]
8. S. van de Linde, A. Loschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, and M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6(7), 991–1009 (2011). [CrossRef]
9. S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5(2), 155–157 (2008). [CrossRef]
10. H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007). [CrossRef]
11. L. Chen and G. P. Wang, “Pyramid-shaped hyperlenses for three-dimensional subdiffraction optical imaging,” Opt. Express 17(5), 3903–3912 (2009). [CrossRef]
12. D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat Commun 3(1), 1205 (2012). [CrossRef]
13. T. Zhang, L. Chen, and X. Li, “Graphene-based tunable broadband hyperlens for far-field subdiffraction imaging at mid-infrared frequencies,” Opt. Express 21(18), 20888–20899 (2013). [CrossRef]
14. B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer 3rd, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014). [CrossRef]
15. D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer 3rd, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Advanced imaging: extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015). [CrossRef]
16. F. Ströhl and C. F. Kaminski, “Frontiers in structured illumination microscopy,” Optica 3(6), 667 (2016). [CrossRef]
17. K. Zhanghao, X. Chen, W. Liu, M. Li, Y. Liu, Y. Wang, S. Luo, X. Wang, C. Shan, H. Xie, J. Gao, X. Chen, D. Jin, X. Li, Y. Zhang, Q. Dai, and P. Xi, “Super-resolution imaging of fluorescent dipoles via polarized structured illumination microscopy,” Nat. Commun. 10(1), 4694 (2019). [CrossRef]
18. F. Wei and Z. Liu, “Plasmonic structured illumination microscopy,” Nano Lett. 10(7), 2531–2536 (2010). [CrossRef]
19. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000). [CrossRef]
20. M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. 102(37), 13081–13086 (2005). [CrossRef]
21. S. Wei, T. Lei, L. Du, C. Zhang, H. Chen, Y. Yang, S. W. Zhu, and X. C. Yuan, “Sub-100 nm resolution PSIM by utilizing modified optical vortices with fractional topological charges for precise phase shifting,” Opt. Express 23(23), 30143–30148 (2015). [CrossRef]
22. A. Bezryadina, J. Zhao, Y. Xia, Y. U. Lee, X. Zhang, and Z. Liu, “Localized plasmonic structured illumination microscopy with gaps in spatial frequencies,” Opt. Lett. 44(11), 2915–2918 (2019). [CrossRef]
23. A. Bezryadina, J. Zhao, Y. Xia, X. Zhang, and Z. Liu, “High spatiotemporal resolution imaging with localized plasmonic structured illumination microscopy,” ACS Nano 12(8), 8248–8254 (2018). [CrossRef]
24. J. L. Ponsetto, A. Bezryadina, F. Wei, K. Onishi, H. Shen, E. Huang, L. Ferrari, Q. Ma, Y. Zou, and Z. Liu, “Experimental demonstration of localized plasmonic structured illumination microscopy,” ACS Nano 11(6), 5344–5350 (2017). [CrossRef]
25. Q. Ma and Z. Liu, “Metamaterial-assisted illumination nanoscopy,” Natl. Sci. Rev. 5(2), 141–143 (2018). [CrossRef]
26. Y. U. Lee, J. Zhao, Q. Ma, L. K. Khorashad, C. Posner, G. Li, G. B. M. Wisna, Z. Burns, J. Zhang, and Z. Liu, “Metamaterial assisted illumination nanoscopy via random super-resolution speckles,” Nat Commun 12(1), 1559 (2021). [CrossRef]
27. E. Narimanov, “Hyperstructured Illumination,” ACS Photonics 3(6), 1090–1094 (2016). [CrossRef]
28. E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012). [CrossRef]
29. J. L. Ponsetto, F. Wei, and Z. Liu, “Localized plasmon assisted structured illumination microscopy for wide-field high-speed dispersion-independent super resolution imaging,” Nanoscale 6(11), 5807–5812 (2014). [CrossRef]
30. J. Hong, H. Son, C. Kim, S. E. Mun, J. Sung, and B. Lee, “Absorptive metasurface color filters based on hyperbolic metamaterials for a CMOS image sensor,” Opt. Express 29(3), 3643–3658 (2021). [CrossRef]
31. D. Lee, S. So, G. Hu, M. Kim, T. Badloe, H. Cho, J. Kim, H. Kim, C.-W. Qiu, and J. Rho, “Hyperbolic metamaterials: fusing artificial structures to natural 2D materials,” eLight 2(1), 1 (2022). [CrossRef]
32. L. Y. Beliaev, O. Takayama, P. N. Melentiev, and A. V. Lavrinenko, “Photoluminescence control by hyperbolic metamaterials and metasurfaces: a review,” Opto-Electron. Adv. 4(8), 210031 (2021). [CrossRef]
33. X. Chen, C. Zhang, F. Yang, G. Liang, Q. Li, and L. J. Guo, “Plasmonic lithography utilizing epsilon near zero hyperbolic metamaterial,” ACS Nano 11(10), 9863–9868 (2017). [CrossRef]
34. P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
35. Y. U. Lee, O. P. M. Gaudin, K. Lee, E. Choi, V. Placide, K. Takaishi, T. Muto, P. André, A. Muranaka, M. Uchiyama, F. Mathevet, T. Aoyama, J. Wu, A. D’Aléo, and J.-C. Ribierre, “Organic Monolithic Natural Hyperbolic Material,” ACS Photonics 6(7), 1681–1689 (2019). [CrossRef]
36. B. Wood, J. Pendry, and D. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006). [CrossRef]
37. A. Jost, E. Tolstik, P. Feldmann, K. Wicker, A. Sentenac, and R. Heintzmann, “Optical sectioning and high resolution in single-slice structured illumination microscopy by thick slice blind-SIM reconstruction,” PLoS One 10(7), e0132174 (2015). [CrossRef]
