Abstract

Planar metalenses are regarded as promising functional nanodevices because of their lightweight, nano-resolution properties, and, therefore, they can serve as versatile platforms for imaging and Fourier transforming. Here, we demonstrate a meta-device that functions as an isotropic bifocal all-dielectric Huygens' metalens to realize nanoscale real-time coaxial digital hologram generation. We design an isotropic bifocal metalens for micro/nano hologram recording, and the metalens utilizes the complete region compared to a previously reported interleaved multifocal metalens scheme. In addition, the hologram generation does not depend on complex polarization conversion, thereby improving the practical efficiency. For high-fidelity reconstruction, compressive reconstruction is utilized to remove twin-image and zero-order items and to suppress noise. Such concept would be extended to white-light achromatic meta-holography and three-dimensional micro/nano in vivo incoherent super-resolution imaging under subwavelength modulation.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Metasurfaces can be used to flexibly manipulate the phase, amplitude, polarization, and other properties of light, and they have the characteristics of miniaturization and lightweight [16]. Metasurfaces provide new opportunities to develop ultrathin devices that are easy to integrate into compact platforms. Metasrufaces have broad application in holography, Fourier optics, analog computing and so on [712]. Huygens’ metasurface is an important type of metasurface used to achieve almost uniform transmission efficiency and flexible phase manipulation. For simplicity, Huygens’ metasurface can function as a combination of orthogonal electric and magnetic dipoles with equal intensity. Huygens’s principle states that every point of wavefront can be considered as a second wavelet source and propagation forward under a certain condition, independent on input polarization [13]. As an important branch of metasurface, ultrathin metalens has received significant attention because of their planar, achromatic advantages. Metalenses can reduce the bulk size of diffractive lenses, and they can spatially modulate the phase discontinuities within ultrashort distances. Therefore, metalenses are used for white-light focusing and full-color imaging [1418]. Specially, metalenses can be used to perform multi-foci/tunable focusing, spectral tomography, among others by applying different mechanisms [1927]. In addition, such metalenses have wide applications to improve performance and open new avenues in imaging systems, optical tomography, information optics, and optical communications [2833].

Digital holography (DH) refers to the technique for the acquisition of holograms using a digital sensor (CCD/CMOS). Usually, the object wave and reference wave interfere with each other to generate a hologram, which is recorded using an optical system. Subsequently, the hologram is processed and reconstructed using a computer [34]. Compared with computer-generated hologram, DH records in situ hologram of a real object by using an optical system in real time; therefore, the DH is generally used for microscopy, 3D holographic storage, and dynamic samples capture. The conventional coaxial holographic recording method (Fresnel incoherent correlation holography, FINCH) utilizes diffractive optical components and/or spatial light modulators (SLMs) to record digital holograms [3542]. In the FINCH optical configuration, the object wave is split into two by using an encoding diffractive lens displayed on an SLM, and two images are created. An image sensor is placed between both the images, and the self-interference hologram is recorded. Because of the twin-image generated from coaxial hologram, many methods are used to eliminate it and enhance the reconstruction quality. In addition, three- or four-step phase-shifting technology, in which phase-shifting holograms are restored and superposed to produce a complex hologram and also reconstructed, is widely used as an effective approach to eliminating twin images, and these technologies are used for DH reconstruction. However, the commercial spatial light modulator has characteristic micrometer pixel size, and there exists dead zone that reflect or transmit light without modulation, which can cause zero background noise. Hence such method has some limitations for achieving micro-nano size holographic imaging. In addition, multi-holograms need more recording operations, thereby consuming significant amount of time. Moreover, the phase-shifting method for multi-holograms recording often faces the challenge of phase mismatch during the instances of mechanical movement or phase noise due to disturbances in system components [4345], especially in meta-optical experimental systems.

Here, we demonstrate a high-efficiency isotropic bifocal Huygens’ metalens, which is used for polarization-insensitive nanoscale coaxial digital hologram generation and imaging-system minimization. Such an optimal all-dielectric bifocal metalens has two foci along the optical axis in the forward transmission space. Therefore, the real object will form two on-axis focused images along the forward direction. The coaxial hologram is generated because of the interference of two identical defocused images on a fixed position between two focused planes. Compared with the traditional hologram recording process that uses diffractive optical elements or chemical films, such real time generation provides a significantly simpler and more efficient method. In addition, such bifocal metalenses can minimize the imaging system, improve the resolution, and provide an easy approach for micro/nano scale high resolution DH. In addition, we adopt the compressive sensing (CS) algorithm to reconstruct the coaxial hologram to eliminate the twin-image and zero-order items. Compressive sensing is a method that can retrieval the original signal through less sampling points than the Nyquist sampling theorem [46]. Because there is larger difference between the reconstructed image and the twin image in the coaxial holographic reconstruction. CS can greatly suppress the twin image and obtain a high-quality image through sparse sampling and reconstruction methods. Such holographic metalens configuration enables flexible and non-mismatched hologram recording, in contrast to a previously reported static metasurface hologram based on preparatory calculation. Furthermore, through delicate design and fabrication, such a bifocal metalens can even be expanded to broadband achromatic range applied for 3D phase or biomedical object recording and reconstruction under incoherent source/fluorescence illumination or in vivo imaging [1516,4748].

2. Methods and results

We demonstrated the real-time holographic recording performed using a bifocal isotropic metalens. Such a meta-device minimizes the holographic imaging system. In addition, the reconstruction is realized on the basis of the CS algorithm, as depicted in Fig. 1. To obtain a high-quality hologram, arbitrary linearly polarized light is used as the illumination. When linearly polarized light passes through the object (USAF1951, negative resolution test chart) and impinges on the bifocal metalens, two images with different magnifications are generated on two focused axial planes. While in the overlap region between the two focal planes, there always exists one fixed plane (maximum section of overlap) with approximately same magnification and intensity, and the plane can be used for recording the interference hologram by camera. Because the recorded hologram is attributed to the coaxial interference, the real image and its twin image will simultaneously appear at the center of the reconstructed plane and become indistinguishable. An effective and time-saving CS algorithm is used for removing the twin-image in the reconstruction process. Consequently, high-quality reconstruction results are obtained.

 figure: Fig. 1.

Fig. 1. Coaxial holography and CS reconstruction using a bifocal metalens.

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The principle of the real-time hologram generation by using a bifocal metalens is based on two sphere wave interference along the coaxial propagation direction, as depicted in Fig. 2. One on-axis point of the object is propagated to the bifocal lens with object distance Ds and is imaged to two different on-axis points, which are located at D1 and D2 planes, respectively. Hence, the two coherent beams can interfere with each other to form a point-source hologram between both the focus planes. Similarly, for the point cloud of the object, all the interference point-sources (hologel) are superimposed to generate the entire hologram. Notably, for simplicity, only the case of on-axis points is considered. However, the principle and results are available for all the off-axis points in the linear space invariant system.

 figure: Fig. 2.

Fig. 2. Hologram recording diagram, (a)Coaxial holography principle scheme; (b) Bifocal metalens wrap phase profile. Ds: distance between object voxel and bifocal metalens; Dh: recording distance; D1 /D2: two beams converge distance from bifocal metalens.

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The intensity distribution of the on-axis point-hologram E obeys Fresnel paraxial approximation, as follows [49]:

$$E\textrm{ = }{\left|{G\left( {\frac{1}{{{f_{c1}} + {D_h}}}} \right) + G\left( {\frac{1}{{{f_{c2}} + {D_h}}}} \right)} \right|^2}$$
where, for simplicity, we choose the position of the metalens as the original point. The sign of $G(b )= \exp \left[ { - \frac{{i\pi b}}{\lambda }({{x^2} + {y^2}} )} \right]$ represents the Fresnel propagation factor and b the propagation distance away from the metalens. The fc1 distance can be determined using the Gaussian formula ${f_{c1}} = \frac{{{f_1} \times {D_s}}}{{{f_1} - {D_s}}}$, and the other image should be on the position ${f_{c2}} = \frac{{{f_2} \times {f_{c1}}}}{{{f_2} - {f_{c1}}}}$,where f1 and f2 denote both the focal lengths of the bifocal metalens, Ds is distance from object to metalens. The recording plane is fixed at ${D_h} = \frac{{2{f_{c1}} \times {f_{c2}}}}{{{f_{c1}} - {f_{c2}}}}$, where both the magnifications are the same. In addition, the in situ generated hologram at the recording plane is captured using CCD.

The above-mentioned hologram E can also be derived as follows:

$$E^{\prime}\textrm{ = }{I_1}\textrm{ + }G\left[ {\frac{{ - 1}}{{{z_r}}}} \right] + G\left[ {\frac{1}{{{z_r}}}} \right]$$
where I1 denotes the zero-order item, $G[{{1 / {{z_r}}}} ]$ the twin-image item, and zr the reconstruction distance. Therefore, the reconstructed distance of real image $G[{{{ - 1} / {{z_r}}}} ]$ can be expressed as:
$${z_r} = \frac{{({{f_{c1}} + {D_h}} )({{f_{c2}} + {D_h}} )}}{{{f_{c2}} - {f_{c1}}}}$$

For designing the polarization-independent bifocal metalens, cylindrical silicon nanodisks with various diameters based on Huygens’ metasurface principle are arranged according to the bifocal metalens phase distribution:

$${\varphi _L}\textrm{ = arg}\left|\begin{array}{l} \sqrt {{B_1}} \exp \left( { - i\frac{{2\pi }}{\lambda }\left( {\sqrt {({{x^2} + {y^2} + f_\textrm{1}^\textrm{2}} )} - f_\textrm{1}^{}} \right)} \right)\\ \textrm{ + }\sqrt {{B_2}} \exp \left( { - i\frac{{2\pi }}{\lambda }\left( {\sqrt {({{x^2} + {y^2} + f_\textrm{2}^\textrm{2}} )} - f_\textrm{2}^{}} \right)} \right) \end{array} \right|$$
where both the focal lengths are f1 = 1400 µm and f2 = 1600µm. The working wavelength λ is 800 nm. The term $\textrm{arg}|\cdot |$ indicates the phase of the complex-value array. In addition, B1 and B2 denote the focused energies of both the foci, respectively. Here, we set B1 = B2 = 1 to ensure that the interference from the two beam intensity distributions are equal. The phase profile of the bifocal metalens is visualized in Fig. 2(b) according to Eq. (4). We chose an amorphous silicon nanodisk (nsi = 3.693 + 0.006i at 800nm wavelength) of a circular cross-section with 600nm height and 400nm period on a glass substrate (see Fig. 3(a)). The transmit complex-amplitude distribution is recorded by sweeping the diameter of the nanodisk from 120 to 220 nm (in the steps of 10 nm) using the finite difference time domain method. As depicted in Fig. 3(b), eight nanodisks with different diameters are selected, whose transmission phases satisfy equal distribution to cover the complete 2π range, and the energies are fairly uniform. Subsequently, a bifocal metalens (1000 × 1000 pixels) is fabricated via electron beam lithography and reactive ion etching on a silica substrate. The transmission phase map is depicted in Fig. 3(c). Notably, the phase-modulation range can cover the entire 2π range, which can be used to encode the corresponding nanodisks. Huygens’ metasurface can achieve a transmittance with near-unity efficiency. As illustration, we demonstrate the electromagnetic field distribution within one nanodisk (D=190nm, H=600nm, P=400nm) at 800nm wavelength in Fig. 3(d). We found the energy is mainly concentrated within the high refractive index nanodisk. Each meta-atom independently performs complex amplitude modulation for the incident beam. We selected eight specific nanodisks to realize the almost uniform transmittance amplitude, while the phase satisfies the coverage of full 2π range. The experimental setup is depicted in Fig. 3(e). We used a super-continuous laser to illuminate the resolution chart (USAF1951) with the target wavelength of 800 nm. The resolution chart should be located at an appropriate position in front of the metalens until the perfect hologram generation. Subsequently, the light that passes through the metalens is collected and magnified using a commercial Nikon objective (20×, NA = 0.45). In addition, we used a CCD (Thorlabs.co, 1501C-USB, pitch: 6.45 µm) to capture the real-time hologram.

The 45° side views of the scanning electric microscopy images are depicted in Figs. 4(a) and (b). Before performing the imaging experiment, we first characterized both the foci of the metalens. The propagation along the longitudinal direction was simulated according to Fresnel diffraction, as depicted in Fig. 4(c). We observed two foci located at 1400 and 1600 µm respectively, showing consistency with the theoretical design. In addition, clear interference fringes were observed between the two foci. To experimentally measure the focal lengths, a plane wave was directly illuminated on the metalens without using the resolution chart in the setup. We changed the distance between the metalens and objective via the step size of 10 µm by using a precision 3D stage; therefore, different propagation planes could be captured using the CCD. The normalized diffraction intensity along the axial direction is depicted in Fig. 4(d). Both the experimentally characterized foci are located at the distances of 1340 and 1580 µm, respectively, showing satisfactory correspondence to the simulation. Note that there is slightly deviation of the measured foci from the simulation results, which may due to the finite aperture of metalens as well as fabrication accuracy. We provide normalized intensity distribution and its line profile at both foci plane in Fig. 4(e). Note there are some fringes around the focal points, which may result from the diffraction of the bifocal metalens. With the optimization of the metalens and the improvement of the fabrication accuracy, the resolution can be further enhanced. Similarly, we observed a clear interference fringe between both the foci, and this is the precondition for hologram generation. In addition, we performed the Fourier transform infrared spectroscopy (FTIR) of the metalens in the range from 500 to 1100 nm, as depicted in Fig. 4(f). The linear polarization transmission efficiency reached up to 77.6%. Such high efficiency can guarantee the high-quality recording of coaxial holograms.

 figure: Fig. 3.

Fig. 3. Nanostructure and optical setup: (a) Nanodisk structure; (b) The phase and amplitude of the nanodisks at wavelength 800 nm; (c) Partial phase profile of the double-focal metalens, and it corresponds to nanodisks with various radii; (d) Nanodisk electromagnetic energy distribution; (e) The optical setup of coaxial holography (USAF1951: resolution chart; objective: 20×/0.45; CCD: camera).

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Next, we included the resolution chart to the setup. The real-time in situ hologram was generated on the fixed plane of approximately 1500 µm away from metalens. In addition, we used the CCD to record a point-source hologram and a series of holograms with Arabic numbers holograms 1 − 6 of group 5 (measured linewidth: 4.32, 3.51, 3.24, 2.97, 2.7, and 2.16 µm) in the standard resolution chart(USAF 1951) in Figs. 5(a)–(g). Because these holograms were generated from the coaxial optical setup configuration, twin images and zero-order items were unavoidable during the traditional reconstruction process upon using the Fresnel back-diffraction method, as depicted in Figs. 5(h)–(n). Specifically, the reconstructed point is surrounded by a strong diffraction halo, as depicted in Fig. 5(h). In addition, the reconstructed Arabic numbers (holograms 1 − 6) are disturbed because of twin image diffraction.

 figure: Fig. 4.

Fig. 4. Scanning electric microscopy images and bifocal metalens axial intensity. (a) Top-view and (b) 45°-side-view SEM images. : (c) Simulated and (d) Experimental results of intensity distribution along propagation direction of such bifocal metalens; simulated focal lengths: 1400 and 1600 µm; measured focal lengths: 1340 and 1580 µm; (e) Normalized intensity distribution at the two foci and their line cross-section; (f) FTIR-measurement of different polarization channels.

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To remove the twin images and enhance the reconstruction quality, the CS algorithm was adopted in the reconstruction process [46,4950]. Assuming the measurement intensity Ig and the objective signal f satisfy the relationship as follows:

$${I_g}\textrm{ = }\Phi f$$
where Φ denotes sensing matrix (M × N), and Ig represents the measurement on the detector (reform to a M × 1 column vector; Ig is the hologram). Because natural input signals are not sparse, sparse sampling and transform are needed. While f is the object wave (N × 1 column vector). Using the CS algorithm, the object can be retrieved using a two-step thresholding by solving the following equation:
$$\hat{f} = \mathop {\arg \min }\limits_f \{{||{{I_g} - \Phi f} ||_2^2 + \tau {{||f ||}_{TV}}} \}$$
where $\mathop {\arg \min }\limits_f \{{\cdot} \}$ denotes the minimum operator and $||\cdot ||_2^2$ means the l-2 Euclidean norm. The term τ denotes the relative weight between l-2 Euclidean norm of residual. It is important to improve estimation accuracy by adjusting its value, until obtaining the best reconstruction. In addition, ${||f ||_{TV}}\textrm{ = }\sum\limits_i {\sqrt {{{|{\Delta _i^xf} |}^2} + {{|{\Delta _i^yf} |}^2}} }$, where $\Delta _i^x$ and $\Delta _i^y$ denote the horizontal and vertical first-order local difference operations, respectively. TV-norm is a function of the total variation (TV) regularization, which is adopted as our sparsity function [51]. The sharper edge cause by twin image, the larger TV norm.

 figure: Fig. 5.

Fig. 5. Experimental results: (a-g) Coaxial holograms; (h-n) Fresnel back-propagation reconstructions; (o-u) CS reconstructions of point-source and USAF1951 resolution chart Group 5; scalebar: 16.6 µm.

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Both the twin image and zero-order I1 could be suppressed using the CS algorithm by estimating the correlation between the measured hologram and the reconstructed image at the reconstructed plane. The zero-order item I1 and twin image can result in a strong background and blurry the reconstructed patterns; nevertheless, such blurry speckle has a low correlation with the recorded hologram. In addition, the blurry pattern due to the zero-order item I1 is not sparse. Therefore, most of the estimated error due to zero-order would be eliminated. Regarding the twin image G[1/zr] and other noises, they can be removed using the TV-norm constraint. The TV-norm acts as a sparse filter to suppress the diffused twin image. Finally, high-quality reconstructions of point-source (full width half maximum, Δ = 2.58 µm) and holograms 1 − 6 of group 5 (reconstructed linewidth: 4.83, 4.19, 3.54, 3.87, 3.22, and 2.9 µm) are obtained, as depicted in Figs. 5(i)–(u).

Comparing the two reconstruction methods, i.e., Fresnel diffraction and CS algorithm, for the generation of such an in situ hologram, the latter performs better. For example, the reconstruction image of the point-source hologram possesses a bright circle point with the full width half maximum of 2.58 µm by using the CS algorithm. In addition, the theoretical effective width of the point spread function of such a system ($\Delta = \frac{{0.61\lambda }}{{NA}}$) is 1.08 µm. The experimental obtained image resolution is lower than the theoretical prediction, which may due to the fabrication accuracy and deviation of material property. In addition, because of the inherent twin images resulted from the coaxial hologram recording process, the reconstruction performed using Fresnel back-propagation is not satisfactory. Nevertheless, the reconstructed image qualities can be significantly improved using the CS algorithm. We utilized a single hologram to realize high-quality performance by using such a compressive reconstruction. Compared with the three- or four-step phase-shifting algorithm, the mismatch of multi-hologram recording is avoided, and such method is time efficient as well. In addition, one hologram recording significantly avoids cumulative uncertainty due to system errors and sample fabrication errors.

3. Discussion and conclusions

Notably, our method combined the techniques of FINCH and metasurface elements. FINCH is an enhanced resolution imaging technique that exhibits a non-classical modulation transfer function than that of a regular incoherent imager. Our metalens offered the possibility for continuous 0–2π Huygens’ phase modulation via the spatial arrangement of sub-wavelength meta atoms with constant thickness, unlike classical diffractive elements, which achieve 0–2π phase modulation with thickness variation. Such real-time in situ hologram generation and processing performed using a bifocal metalens can simplify and minimize the traditional double diffractive lenses/SLMs system of FINCH. Because of the integrated compact imaging meta-device, the recording system has higher stability than that of a traditional DH imaging system. In addition, we used the CS algorithm to remove the twin image and bias terms without requiring multiple camera shots or phase shift. Such a technology becomes fast, efficient, and accurate upon integration with the CS algorithm.

In summary, a bifocal metalens was designed and fabricated for real-time in situ hologram generation based on Huygens’ metasurface. Because bifocal metalenses have advantages of being ultra-thin and micro/nano scale complex-amplitude manipulation, multi-plane imaging with high efficiency could be achieved. We further demonstrated the minimization of coaxial hologram generation and reconstruction based on such bifocal metalenses, followed by the CS algorithm. High-fidelity reconstruction images were obtained using the CS algorithm rather than Fresnel diffraction or phase-shifting technology. The recording process time was significantly compressed. Simultaneously, such an optical system can improve the efficiency of recording holograms, and is especially appropriate for the imaging of biological tissues or in vivo cells. Furthermore, our design can expand from the narrowband to broadband achromatic metalenses in the visible and near-infrared range. Such techniques might be promising for many practical applications, such as in vivo fluorescence microscopy, 3D dynamic holography, and rainbow holography and so on.

Funding

National Key Research and Development Program of China 2017YFB1002900, Ministry of Science and Technology, China; Fok Ying-Tong Education Foundation of China (161009); Beijing Nova Program (Z171100001117047); Natural Science Foundation of Beijing Municipality (4172057); National Natural Science Foundation of China (61775019); Beijing Outstanding Young Scientist Program (BJJWZYJH01201910007022).

Disclosures

All the authors declare no conflict of interest.

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36. K. Choi, J. Yim, and S. Min, “Optical defocus noise suppressing by using a pinhole-polarizer in Fresnel incoherent correlation holography,” Appl. Opt. 56(13), F121–F127 (2017). [CrossRef]  

37. L. T. Bang, H. Y. Wu, Y. Zhao, E. G. Kim, and N. Kim, “Depth enhancement of 3D microscopic living-cell image using incoherent fluorescent digital holography,” J. Microsc. (Oxford, U. K.) 265(3), 372–385 (2017). [CrossRef]  

38. N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20(18), 19822–19835 (2012). [CrossRef]  

39. Y. Bai, R. Zang, P. Wang, T. Rong, F. Ma, D. Yan-Li, Z. Duan, and Q. Gong, “Single-shot incoherent digital holography based on spatial light modulator,” Acta Phys. Sin. 67, 064202 (2018). [CrossRef]  

40. T. Tahara, T. Kanno, Y. Arai, and T. Ozawa, “T Single-shot phase-shifting incoherent digital holography,” J. Opt. 19(6), 065705 (2017). [CrossRef]  

41. T. Nobukawa, T. Muroi, Y. Katano, N. Kinoshita, and N. Ishii, “Single-shot phase shifting incoherent digital holography with multiplexed checkerboard phase gratings,” Opt. Lett. 43(8), 1698–1701 (2018). [CrossRef]  

42. X. Quan, O. Matoba, and Y. Awatsuji, “Single-shot incoherent digital holography using a dual-focusing lens with diffraction gratings,” Opt. Lett. 42(3), 383–386 (2017). [CrossRef]  

43. Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Laser Eng. 86, 38–43 (2016). [CrossRef]  

44. I. Yamaguchi, “Holography and speckle in phase-shifting digital holography,” Chin. Opt. Lett. 7(12), 1104–1108 (2009). [CrossRef]  

45. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997). [CrossRef]  

46. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009). [CrossRef]  

47. W. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018). [CrossRef]  

48. S. Wang, P. Wu, V. Su, Y. Lai, M. Chen, H. Kuo, B. Chen, Y. Chen, T. Huang, J. Wang, R. Lin, C. Kuan, T. Li, Z. Wang, S. Zhu, and D. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018). [CrossRef]  

49. T. Man, Y. Wan, F. Wu, and D. Wang, “Self-interference compressive digital holography with improved axial resolution and signal-to-noise ratio,” Appl. Opt. 56(13), F91–F96 (2017). [CrossRef]  

50. W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121(9), 093902 (2018). [CrossRef]  

51. J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE T. Image Process 16(12), 2992–3004 (2007). [CrossRef]  

References

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    [Crossref]
  35. J. Rosen and G. Brooker, “Incoherent digital holographic microscopy with coherent and incoherent light,” 87–112 (2011).
  36. K. Choi, J. Yim, and S. Min, “Optical defocus noise suppressing by using a pinhole-polarizer in Fresnel incoherent correlation holography,” Appl. Opt. 56(13), F121–F127 (2017).
    [Crossref]
  37. L. T. Bang, H. Y. Wu, Y. Zhao, E. G. Kim, and N. Kim, “Depth enhancement of 3D microscopic living-cell image using incoherent fluorescent digital holography,” J. Microsc. (Oxford, U. K.) 265(3), 372–385 (2017).
    [Crossref]
  38. N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20(18), 19822–19835 (2012).
    [Crossref]
  39. Y. Bai, R. Zang, P. Wang, T. Rong, F. Ma, D. Yan-Li, Z. Duan, and Q. Gong, “Single-shot incoherent digital holography based on spatial light modulator,” Acta Phys. Sin. 67, 064202 (2018).
    [Crossref]
  40. T. Tahara, T. Kanno, Y. Arai, and T. Ozawa, “T Single-shot phase-shifting incoherent digital holography,” J. Opt. 19(6), 065705 (2017).
    [Crossref]
  41. T. Nobukawa, T. Muroi, Y. Katano, N. Kinoshita, and N. Ishii, “Single-shot phase shifting incoherent digital holography with multiplexed checkerboard phase gratings,” Opt. Lett. 43(8), 1698–1701 (2018).
    [Crossref]
  42. X. Quan, O. Matoba, and Y. Awatsuji, “Single-shot incoherent digital holography using a dual-focusing lens with diffraction gratings,” Opt. Lett. 42(3), 383–386 (2017).
    [Crossref]
  43. Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Laser Eng. 86, 38–43 (2016).
    [Crossref]
  44. I. Yamaguchi, “Holography and speckle in phase-shifting digital holography,” Chin. Opt. Lett. 7(12), 1104–1108 (2009).
    [Crossref]
  45. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
    [Crossref]
  46. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009).
    [Crossref]
  47. W. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018).
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  48. S. Wang, P. Wu, V. Su, Y. Lai, M. Chen, H. Kuo, B. Chen, Y. Chen, T. Huang, J. Wang, R. Lin, C. Kuan, T. Li, Z. Wang, S. Zhu, and D. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
    [Crossref]
  49. T. Man, Y. Wan, F. Wu, and D. Wang, “Self-interference compressive digital holography with improved axial resolution and signal-to-noise ratio,” Appl. Opt. 56(13), F91–F96 (2017).
    [Crossref]
  50. W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121(9), 093902 (2018).
    [Crossref]
  51. J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE T. Image Process 16(12), 2992–3004 (2007).
    [Crossref]

2020 (1)

H. Zhou, B. Sain, Y. Wang, C. Schlickriede, R. Zhao, X. Zhang, Q. Wei, X. Li, L. Huang, and T. Zentgraf, “Polarization-encrypted orbital angular momentum multiple metasurface holography,” ACS Nano 14(5), 5553–5559 (2020).
[Crossref]

2019 (6)

Q. Wei, B. Sain, Y. Wang, B. Reineke, X. Li, L. Huang, and T. Zentgraf, “Simultaneous spectral and spatial modulation for color printing and holography using all-dielectric metasurface,” Nano Lett. 19(12), 8964–8971 (2019).
[Crossref]

H. Lv, X. Lu, Y. Han, Z. Mou, and S. Teng, “Multifocal metalens with a controllable intensity ratio,” Opt. Lett. 44(10), 2518–2521 (2019).
[Crossref]

C. Chen, W. Song, J. Chen, J. Wang, Y. H. Chen, B. Xu, M. Chen, H. Li, B. Fang, J. Chen, H. Y. Kuo, S. Wang, D. P. Tsai, S. Zhu, and T. Li, “Spectral tomographic imaging with aplanatic metalens,” Light: Sci. Appl. 8(1), 99 (2019).
[Crossref]

S. Li, C. Zhou, G. Ban, H. Wang, H. Lu, and Y. Wang, “Active all-dielectric bifocal metalens assisted by germanium antimony telluride,” J. Phys. D: Appl. Phys. 52(9), 095106 (2019).
[Crossref]

W. Bai, P. Yang, J. Huang, D. Chen, J. Zhang, Z. Zhang, J. Yang, and B. Xu, “Near-infrared tunable metalens based on phase change material Ge2Se2Te5,” Sci. Rep. 9(1), 5368 (2019).
[Crossref]

S. Tian, H. Guo, J. Hu, and S. Zhuang, “Dielectric longitudinal bifocal metalens with adjustable intensity and high focusing efficiency,” Opt. Express 27(2), 680–688 (2019).
[Crossref]

2018 (8)

Y. Bai, R. Zang, P. Wang, T. Rong, F. Ma, D. Yan-Li, Z. Duan, and Q. Gong, “Single-shot incoherent digital holography based on spatial light modulator,” Acta Phys. Sin. 67, 064202 (2018).
[Crossref]

X. Song, L. Huang, L. Sun, X. Zhang, R. Zhao, X. Li, J. Wang, B. Bai, and Y. Wang, “Near-field plasmonic beam engineering with complex amplitude modulation based on metasurface,” Appl. Phys. Lett. 112(7), 073104 (2018).
[Crossref]

L. Huang, S. Zhang, and T. Zentgraf, “Metasurface holography: from fundamentals to applications,” Nanophotonics 7(6), 1169–1190 (2018).
[Crossref]

R. Paniagua-Dominguez, Y. F. Yu, E. Khaidarov, S. Choi, V. Leong, R. M. Bakker, X. Liang, Y. H. Fu, V. Valuckas, L. A. Krivitsky, and A. I. Kuznetsov, “A metalens with a near-unity numerical aperture,” Nano Lett. 18(3), 2124–2132 (2018).
[Crossref]

T. Nobukawa, T. Muroi, Y. Katano, N. Kinoshita, and N. Ishii, “Single-shot phase shifting incoherent digital holography with multiplexed checkerboard phase gratings,” Opt. Lett. 43(8), 1698–1701 (2018).
[Crossref]

W. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018).
[Crossref]

S. Wang, P. Wu, V. Su, Y. Lai, M. Chen, H. Kuo, B. Chen, Y. Chen, T. Huang, J. Wang, R. Lin, C. Kuan, T. Li, Z. Wang, S. Zhu, and D. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
[Crossref]

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121(9), 093902 (2018).
[Crossref]

2017 (9)

T. Man, Y. Wan, F. Wu, and D. Wang, “Self-interference compressive digital holography with improved axial resolution and signal-to-noise ratio,” Appl. Opt. 56(13), F91–F96 (2017).
[Crossref]

X. Quan, O. Matoba, and Y. Awatsuji, “Single-shot incoherent digital holography using a dual-focusing lens with diffraction gratings,” Opt. Lett. 42(3), 383–386 (2017).
[Crossref]

S. Abdollahramezani, A. Chizari, A. E. Dorch, M. V. Jamali, and J. A. Salehi, “Dielectric metasurfaces solve differential and integro-differential equations,” Opt. Lett. 42(7), 1197–1200 (2017).
[Crossref]

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photonics Rev. 11(3), 1600295 (2017).
[Crossref]

T. Tahara, T. Kanno, Y. Arai, and T. Ozawa, “T Single-shot phase-shifting incoherent digital holography,” J. Opt. 19(6), 065705 (2017).
[Crossref]

K. Choi, J. Yim, and S. Min, “Optical defocus noise suppressing by using a pinhole-polarizer in Fresnel incoherent correlation holography,” Appl. Opt. 56(13), F121–F127 (2017).
[Crossref]

L. T. Bang, H. Y. Wu, Y. Zhao, E. G. Kim, and N. Kim, “Depth enhancement of 3D microscopic living-cell image using incoherent fluorescent digital holography,” J. Microsc. (Oxford, U. K.) 265(3), 372–385 (2017).
[Crossref]

X. Yin, T. Steinle, L. Huang, T. Taubner, M. Wuttig, T. Zentgraf, and H. Giessen, “Beam switching and bifocal zoom lensing using active plasmonic metasurfaces,” Light: Sci. Appl. 6(7), e17016 (2017).
[Crossref]

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alu, and C. Qiu, “A reconfigurable active Huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

2016 (4)

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
[Crossref]

M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodriguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
[Crossref]

S. Abdollahramezani, K. Arik, A. Khavasi, and Z. Kavehvash, “Analog computing using graphene-based metalindes,” Opt. Lett. 41(15), 3451–3454 (2016).
[Crossref]

Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Laser Eng. 86, 38–43 (2016).
[Crossref]

2015 (2)

W. Wang, Z. Guo, K. Zhou, Y. Sun, F. Shen, Y. Li, S. Qu, and S. Liu, “Polarization-independent longitudinal multi-focusing metalens,” Opt. Express 23(23), 29855–29866 (2015).
[Crossref]

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

2013 (6)

P. de Gracia, C. Dorronsoro, and S. Marcos, “Multiple zone multifocal phase designs,” Opt. Lett. 38(18), 3526–3529 (2013).
[Crossref]

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2(4), e72 (2013).
[Crossref]

H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antennas Propag. 61(9), 4615–4623 (2013).
[Crossref]

X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013).
[Crossref]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref]

L. Huang, X. Chen, H. Muehlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

2012 (3)

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref]

X. Chen, L. Huang, H. Muehlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
[Crossref]

N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20(18), 19822–19835 (2012).
[Crossref]

2011 (2)

P. Banerjee, G. Barbastathis, M. Kim, and N. Kukhtarev, “Digital holography and 3-D imaging,” Appl. Opt. 50(34), H1–H2 (2011).
[Crossref]

Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

2009 (3)

2008 (1)

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
[Crossref]

2007 (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE T. Image Process 16(12), 2992–3004 (2007).
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2003 (1)

J. Jia, C. H. Zhou, and L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228(4-6), 271–278 (2003).
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1997 (1)

Abdollahramezani, S.

Adibi, A.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020)

Aieta, F.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
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Alu, A.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alu, and C. Qiu, “A reconfigurable active Huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
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Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
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S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020)

Arai, Y.

T. Tahara, T. Kanno, Y. Arai, and T. Ozawa, “T Single-shot phase-shifting incoherent digital holography,” J. Opt. 19(6), 065705 (2017).
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Arik, K.

Awatsuji, Y.

Bai, B.

X. Song, L. Huang, L. Sun, X. Zhang, R. Zhao, X. Li, J. Wang, B. Bai, and Y. Wang, “Near-field plasmonic beam engineering with complex amplitude modulation based on metasurface,” Appl. Phys. Lett. 112(7), 073104 (2018).
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L. Huang, X. Chen, H. Muehlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
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X. Chen, L. Huang, H. Muehlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
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Bai, W.

W. Bai, P. Yang, J. Huang, D. Chen, J. Zhang, Z. Zhang, J. Yang, and B. Xu, “Near-infrared tunable metalens based on phase change material Ge2Se2Te5,” Sci. Rep. 9(1), 5368 (2019).
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Bai, Y.

Y. Bai, R. Zang, P. Wang, T. Rong, F. Ma, D. Yan-Li, Z. Duan, and Q. Gong, “Single-shot incoherent digital holography based on spatial light modulator,” Acta Phys. Sin. 67, 064202 (2018).
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Bakker, R. M.

R. Paniagua-Dominguez, Y. F. Yu, E. Khaidarov, S. Choi, V. Leong, R. M. Bakker, X. Liang, Y. H. Fu, V. Valuckas, L. A. Krivitsky, and A. I. Kuznetsov, “A metalens with a near-unity numerical aperture,” Nano Lett. 18(3), 2124–2132 (2018).
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Ban, G.

S. Li, C. Zhou, G. Ban, H. Wang, H. Lu, and Y. Wang, “Active all-dielectric bifocal metalens assisted by germanium antimony telluride,” J. Phys. D: Appl. Phys. 52(9), 095106 (2019).
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Banerjee, P.

Bang, L. T.

L. T. Bang, H. Y. Wu, Y. Zhao, E. G. Kim, and N. Kim, “Depth enhancement of 3D microscopic living-cell image using incoherent fluorescent digital holography,” J. Microsc. (Oxford, U. K.) 265(3), 372–385 (2017).
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Barbastathis, G.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE T. Image Process 16(12), 2992–3004 (2007).
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Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
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Brady, D. J.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121(9), 093902 (2018).
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D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009).
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Cang, J.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121(9), 093902 (2018).
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Cao, L.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121(9), 093902 (2018).
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Capasso, F.

W. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018).
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N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
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P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photonics Rev. 11(3), 1600295 (2017).
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Chen, B.

S. Wang, P. Wu, V. Su, Y. Lai, M. Chen, H. Kuo, B. Chen, Y. Chen, T. Huang, J. Wang, R. Lin, C. Kuan, T. Li, Z. Wang, S. Zhu, and D. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
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C. Chen, W. Song, J. Chen, J. Wang, Y. H. Chen, B. Xu, M. Chen, H. Li, B. Fang, J. Chen, H. Y. Kuo, S. Wang, D. P. Tsai, S. Zhu, and T. Li, “Spectral tomographic imaging with aplanatic metalens,” Light: Sci. Appl. 8(1), 99 (2019).
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Chen, D.

W. Bai, P. Yang, J. Huang, D. Chen, J. Zhang, Z. Zhang, J. Yang, and B. Xu, “Near-infrared tunable metalens based on phase change material Ge2Se2Te5,” Sci. Rep. 9(1), 5368 (2019).
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Chen, J.

C. Chen, W. Song, J. Chen, J. Wang, Y. H. Chen, B. Xu, M. Chen, H. Li, B. Fang, J. Chen, H. Y. Kuo, S. Wang, D. P. Tsai, S. Zhu, and T. Li, “Spectral tomographic imaging with aplanatic metalens,” Light: Sci. Appl. 8(1), 99 (2019).
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C. Chen, W. Song, J. Chen, J. Wang, Y. H. Chen, B. Xu, M. Chen, H. Li, B. Fang, J. Chen, H. Y. Kuo, S. Wang, D. P. Tsai, S. Zhu, and T. Li, “Spectral tomographic imaging with aplanatic metalens,” Light: Sci. Appl. 8(1), 99 (2019).
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Chen, K.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alu, and C. Qiu, “A reconfigurable active Huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
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Chen, M.

C. Chen, W. Song, J. Chen, J. Wang, Y. H. Chen, B. Xu, M. Chen, H. Li, B. Fang, J. Chen, H. Y. Kuo, S. Wang, D. P. Tsai, S. Zhu, and T. Li, “Spectral tomographic imaging with aplanatic metalens,” Light: Sci. Appl. 8(1), 99 (2019).
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S. Wang, P. Wu, V. Su, Y. Lai, M. Chen, H. Kuo, B. Chen, Y. Chen, T. Huang, J. Wang, R. Lin, C. Kuan, T. Li, Z. Wang, S. Zhu, and D. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
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X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
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Chen, S.

L. Huang, X. Chen, H. Muehlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
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Chen, W.

W. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018).
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Chen, X.

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
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L. Huang, X. Chen, H. Muehlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
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X. Chen, L. Huang, H. Muehlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
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Chen, Y.

S. Wang, P. Wu, V. Su, Y. Lai, M. Chen, H. Kuo, B. Chen, Y. Chen, T. Huang, J. Wang, R. Lin, C. Kuan, T. Li, Z. Wang, S. Zhu, and D. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
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Chen, Y. H.

C. Chen, W. Song, J. Chen, J. Wang, Y. H. Chen, B. Xu, M. Chen, H. Li, B. Fang, J. Chen, H. Y. Kuo, S. Wang, D. P. Tsai, S. Zhu, and T. Li, “Spectral tomographic imaging with aplanatic metalens,” Light: Sci. Appl. 8(1), 99 (2019).
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Cheung, S. W.

H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antennas Propag. 61(9), 4615–4623 (2013).
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Chizari, A.

Choi, K.

Choi, S.

R. Paniagua-Dominguez, Y. F. Yu, E. Khaidarov, S. Choi, V. Leong, R. M. Bakker, X. Liang, Y. H. Fu, V. Valuckas, L. A. Krivitsky, and A. I. Kuznetsov, “A metalens with a near-unity numerical aperture,” Nano Lett. 18(3), 2124–2132 (2018).
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Chon, J. W. M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
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Chung, K. L.

H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antennas Propag. 61(9), 4615–4623 (2013).
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Danner, A.

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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de Gracia, P.

Ding, X.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alu, and C. Qiu, “A reconfigurable active Huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
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Dorch, A. E.

Dorronsoro, C.

Duan, Z.

Y. Bai, R. Zang, P. Wang, T. Rong, F. Ma, D. Yan-Li, Z. Duan, and Q. Gong, “Single-shot incoherent digital holography based on spatial light modulator,” Acta Phys. Sin. 67, 064202 (2018).
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Fang, B.

C. Chen, W. Song, J. Chen, J. Wang, Y. H. Chen, B. Xu, M. Chen, H. Li, B. Fang, J. Chen, H. Y. Kuo, S. Wang, D. P. Tsai, S. Zhu, and T. Li, “Spectral tomographic imaging with aplanatic metalens,” Light: Sci. Appl. 8(1), 99 (2019).
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Feng, Y.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alu, and C. Qiu, “A reconfigurable active Huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
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Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE T. Image Process 16(12), 2992–3004 (2007).
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Fu, Y. H.

R. Paniagua-Dominguez, Y. F. Yu, E. Khaidarov, S. Choi, V. Leong, R. M. Bakker, X. Liang, Y. H. Fu, V. Valuckas, L. A. Krivitsky, and A. I. Kuznetsov, “A metalens with a near-unity numerical aperture,” Nano Lett. 18(3), 2124–2132 (2018).
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Gaburro, Z.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref]

Genevet, P.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
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Giessen, H.

X. Yin, T. Steinle, L. Huang, T. Taubner, M. Wuttig, T. Zentgraf, and H. Giessen, “Beam switching and bifocal zoom lensing using active plasmonic metasurfaces,” Light: Sci. Appl. 6(7), e17016 (2017).
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Gong, Q.

Y. Bai, R. Zang, P. Wang, T. Rong, F. Ma, D. Yan-Li, Z. Duan, and Q. Gong, “Single-shot incoherent digital holography based on spatial light modulator,” Acta Phys. Sin. 67, 064202 (2018).
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Gu, M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
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Guo, H.

Guo, Z.

Han, Y.

Hashemi, M.

M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodriguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
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Hemmatyar, O.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020)

Horisaki, R.

Hu, J.

Huang, J.

W. Bai, P. Yang, J. Huang, D. Chen, J. Zhang, Z. Zhang, J. Yang, and B. Xu, “Near-infrared tunable metalens based on phase change material Ge2Se2Te5,” Sci. Rep. 9(1), 5368 (2019).
[Crossref]

Huang, K.

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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Huang, L.

H. Zhou, B. Sain, Y. Wang, C. Schlickriede, R. Zhao, X. Zhang, Q. Wei, X. Li, L. Huang, and T. Zentgraf, “Polarization-encrypted orbital angular momentum multiple metasurface holography,” ACS Nano 14(5), 5553–5559 (2020).
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Q. Wei, B. Sain, Y. Wang, B. Reineke, X. Li, L. Huang, and T. Zentgraf, “Simultaneous spectral and spatial modulation for color printing and holography using all-dielectric metasurface,” Nano Lett. 19(12), 8964–8971 (2019).
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X. Song, L. Huang, L. Sun, X. Zhang, R. Zhao, X. Li, J. Wang, B. Bai, and Y. Wang, “Near-field plasmonic beam engineering with complex amplitude modulation based on metasurface,” Appl. Phys. Lett. 112(7), 073104 (2018).
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L. Huang, S. Zhang, and T. Zentgraf, “Metasurface holography: from fundamentals to applications,” Nanophotonics 7(6), 1169–1190 (2018).
[Crossref]

X. Yin, T. Steinle, L. Huang, T. Taubner, M. Wuttig, T. Zentgraf, and H. Giessen, “Beam switching and bifocal zoom lensing using active plasmonic metasurfaces,” Light: Sci. Appl. 6(7), e17016 (2017).
[Crossref]

L. Huang, X. Chen, H. Muehlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

X. Chen, L. Huang, H. Muehlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
[Crossref]

Huang, T.

S. Wang, P. Wu, V. Su, Y. Lai, M. Chen, H. Kuo, B. Chen, Y. Chen, T. Huang, J. Wang, R. Lin, C. Kuan, T. Li, Z. Wang, S. Zhu, and D. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
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Hussain, S.

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
[Crossref]

Ishii, N.

Ishii, S.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2(4), e72 (2013).
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Jamali, M. V.

Jia, J.

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
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J. Jia, C. H. Zhou, and L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228(4-6), 271–278 (2003).
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Jiang, J.

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
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Jiang, T.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alu, and C. Qiu, “A reconfigurable active Huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Jin, G.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121(9), 093902 (2018).
[Crossref]

L. Huang, X. Chen, H. Muehlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

X. Chen, L. Huang, H. Muehlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
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Kanno, T.

T. Tahara, T. Kanno, Y. Arai, and T. Ozawa, “T Single-shot phase-shifting incoherent digital holography,” J. Opt. 19(6), 065705 (2017).
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Katano, Y.

Kats, M. A.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref]

Kavehvash, Z.

Khaidarov, E.

R. Paniagua-Dominguez, Y. F. Yu, E. Khaidarov, S. Choi, V. Leong, R. M. Bakker, X. Liang, Y. H. Fu, V. Valuckas, L. A. Krivitsky, and A. I. Kuznetsov, “A metalens with a near-unity numerical aperture,” Nano Lett. 18(3), 2124–2132 (2018).
[Crossref]

Khavasi, A.

Khorasaninejad, M.

W. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018).
[Crossref]

Kiarashinejad, Y.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020)

Kildishev, A. V.

X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013).
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A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref]

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2(4), e72 (2013).
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Kim, E. G.

L. T. Bang, H. Y. Wu, Y. Zhao, E. G. Kim, and N. Kim, “Depth enhancement of 3D microscopic living-cell image using incoherent fluorescent digital holography,” J. Microsc. (Oxford, U. K.) 265(3), 372–385 (2017).
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Kim, M.

Kim, M. K.

Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Laser Eng. 86, 38–43 (2016).
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Kim, N.

L. T. Bang, H. Y. Wu, Y. Zhao, E. G. Kim, and N. Kim, “Depth enhancement of 3D microscopic living-cell image using incoherent fluorescent digital holography,” J. Microsc. (Oxford, U. K.) 265(3), 372–385 (2017).
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Q. Wei, B. Sain, Y. Wang, B. Reineke, X. Li, L. Huang, and T. Zentgraf, “Simultaneous spectral and spatial modulation for color printing and holography using all-dielectric metasurface,” Nano Lett. 19(12), 8964–8971 (2019).
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Q. Wei, B. Sain, Y. Wang, B. Reineke, X. Li, L. Huang, and T. Zentgraf, “Simultaneous spectral and spatial modulation for color printing and holography using all-dielectric metasurface,” Nano Lett. 19(12), 8964–8971 (2019).
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Q. Wei, B. Sain, Y. Wang, B. Reineke, X. Li, L. Huang, and T. Zentgraf, “Simultaneous spectral and spatial modulation for color printing and holography using all-dielectric metasurface,” Nano Lett. 19(12), 8964–8971 (2019).
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X. Song, L. Huang, L. Sun, X. Zhang, R. Zhao, X. Li, J. Wang, B. Bai, and Y. Wang, “Near-field plasmonic beam engineering with complex amplitude modulation based on metasurface,” Appl. Phys. Lett. 112(7), 073104 (2018).
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W. Bai, P. Yang, J. Huang, D. Chen, J. Zhang, Z. Zhang, J. Yang, and B. Xu, “Near-infrared tunable metalens based on phase change material Ge2Se2Te5,” Sci. Rep. 9(1), 5368 (2019).
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ACS Nano (1)

H. Zhou, B. Sain, Y. Wang, C. Schlickriede, R. Zhao, X. Zhang, Q. Wei, X. Li, L. Huang, and T. Zentgraf, “Polarization-encrypted orbital angular momentum multiple metasurface holography,” ACS Nano 14(5), 5553–5559 (2020).
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Acta Phys. Sin. (1)

Y. Bai, R. Zang, P. Wang, T. Rong, F. Ma, D. Yan-Li, Z. Duan, and Q. Gong, “Single-shot incoherent digital holography based on spatial light modulator,” Acta Phys. Sin. 67, 064202 (2018).
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Adv. Mater. (2)

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alu, and C. Qiu, “A reconfigurable active Huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
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M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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Adv. Opt. Mater. (1)

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Appl. Opt. (3)

Appl. Phys. Lett. (1)

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J. Microsc. (Oxford, U. K.) (1)

L. T. Bang, H. Y. Wu, Y. Zhao, E. G. Kim, and N. Kim, “Depth enhancement of 3D microscopic living-cell image using incoherent fluorescent digital holography,” J. Microsc. (Oxford, U. K.) 265(3), 372–385 (2017).
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Nano Lett. (3)

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Q. Wei, B. Sain, Y. Wang, B. Reineke, X. Li, L. Huang, and T. Zentgraf, “Simultaneous spectral and spatial modulation for color printing and holography using all-dielectric metasurface,” Nano Lett. 19(12), 8964–8971 (2019).
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Nanophotonics (1)

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Nature (1)

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M. Hashemi, A. Moazami, M. Naserpour, and C. J. Zapata-Rodriguez, “A broadband multifocal metalens in the terahertz frequency range,” Opt. Commun. 370, 306–310 (2016).
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Phys. Rev. B (1)

Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

Phys. Rev. Lett. (1)

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121(9), 093902 (2018).
[Crossref]

Sci. Rep. (1)

W. Bai, P. Yang, J. Huang, D. Chen, J. Zhang, Z. Zhang, J. Yang, and B. Xu, “Near-infrared tunable metalens based on phase change material Ge2Se2Te5,” Sci. Rep. 9(1), 5368 (2019).
[Crossref]

Science (1)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref]

Other (3)

H. Tang and P. Liu, “Long-distance enhanced fourier transform by hyperbolic gradient-Index metalens,” 40th International Conference on Infrared Millimeter and Terahertz Waves, 7327447 (2015).

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020)

J. Rosen and G. Brooker, “Incoherent digital holographic microscopy with coherent and incoherent light,” 87–112 (2011).

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Figures (5)

Fig. 1.
Fig. 1. Coaxial holography and CS reconstruction using a bifocal metalens.
Fig. 2.
Fig. 2. Hologram recording diagram, (a)Coaxial holography principle scheme; (b) Bifocal metalens wrap phase profile. Ds: distance between object voxel and bifocal metalens; Dh: recording distance; D1 /D2: two beams converge distance from bifocal metalens.
Fig. 3.
Fig. 3. Nanostructure and optical setup: (a) Nanodisk structure; (b) The phase and amplitude of the nanodisks at wavelength 800 nm; (c) Partial phase profile of the double-focal metalens, and it corresponds to nanodisks with various radii; (d) Nanodisk electromagnetic energy distribution; (e) The optical setup of coaxial holography (USAF1951: resolution chart; objective: 20×/0.45; CCD: camera).
Fig. 4.
Fig. 4. Scanning electric microscopy images and bifocal metalens axial intensity. (a) Top-view and (b) 45°-side-view SEM images. : (c) Simulated and (d) Experimental results of intensity distribution along propagation direction of such bifocal metalens; simulated focal lengths: 1400 and 1600 µm; measured focal lengths: 1340 and 1580 µm; (e) Normalized intensity distribution at the two foci and their line cross-section; (f) FTIR-measurement of different polarization channels.
Fig. 5.
Fig. 5. Experimental results: (a-g) Coaxial holograms; (h-n) Fresnel back-propagation reconstructions; (o-u) CS reconstructions of point-source and USAF1951 resolution chart Group 5; scalebar: 16.6 µm.

Equations (6)

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E  =  | G ( 1 f c 1 + D h ) + G ( 1 f c 2 + D h ) | 2
E  =  I 1  +  G [ 1 z r ] + G [ 1 z r ]
z r = ( f c 1 + D h ) ( f c 2 + D h ) f c 2 f c 1
φ L  = arg | B 1 exp ( i 2 π λ ( ( x 2 + y 2 + f 1 2 ) f 1 ) )  +  B 2 exp ( i 2 π λ ( ( x 2 + y 2 + f 2 2 ) f 2 ) ) |
I g  =  Φ f
f ^ = arg min f { | | I g Φ f | | 2 2 + τ | | f | | T V }

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