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Abstract
Metasurfaces have shown extraordinary light-manipulation abilities, however, most of them deal with free-space waves. It is highly desirable to develop a guided wave-driven metasurface which can extract the in-plane guided modes in the waveguide and mold it into the desired out-of-plane free-space modes. In this paper, an all-dielectric guided wave-driven metasurface, composed of an array of silicon meta-atoms on top of a silicon nitride waveguide, is proposed and simulatively demonstrated. When directly driven by fundamental transverse electric (TE00) and fundamental transverse magnetic (TM00) guided modes at operation wavelength 1.55 µm, the guided wave-driven metasurface converts them into y-polarized and x-polarized free-space light, respectively, and focuses them at different focal points, with polarization extinction ratio over 27 dB, thus simultaneously realizing triple functions of coupling guided modes to free-space waves, bifocal metalens and polarization demultiplexing. Our work offers an alternate way to control light across photonic integrated devices and free-space platforms.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces have drawn increasingly attention due to their remarkable light manipulation ability, low loss and ease of on-chip fabrication thanks to their planar profiles [1–7]. According to whether the excitation wave is a free-space wave or a guided wave, we can roughly divide metasurfaces into three categories. The first type of metasurfaces are driven by incoming free-space waves to realize predesigned manipulation functions, such as beam deflection [6,8], polarization control and wave plates [9], focusing [10], holograms [11], and generation of orbital angular momentum (OAM) beams [12]. In these cases, the input and output waves are both free-space modes. In contrast, the second type of metasurfaces only deal with guided modes, they control guided waves inside waveguides via strong optical scattering at subwavelength intervals. By changing the phase, polarization and amplitude of the guided wave, they can realize mode conversion [13], on-chip second harmonic generation [14], unidirectional transmission of guide waves [15], etc. In these cases, the input and output waves are both guided modes inside waveguides. However, the excellent potentiality to interface between guided waves and free-space waves have not been fully explored in the above two types of metasurfaces. In contrast, the third type of metasurfaces, which combine subwavelength meta-atoms with waveguide structures, can bridge the gap between free-space modes and waveguide modes, and realize desired beam manipulation function as well. Compared with the first two types, the third type of metasurfaces are still in their infancy with relatively few relevant reports [16–19], and most of them are designed to couple the incident free-space wave into guided wave, and further manipulate the guided mode in a desired manner, thus realizing wavelength/polarization (de)multiplexing [16,17], multifunctional mode conversion [18], on-chip generation of orbital angular momentum(OAM) beam [19].
On the other hand, to fully apply the advantages of photonic integrated circuit (PIC) in free space, it is highly necessary to develop an interface, which not only can convert guided waves into free-space ones, but also can conveniently manipulate the extracted waves in a designated way. In 2020, Xingjie Ni's group proposed the concept of guided wave-driven metasurface, which is directly driven by guided waves to realize complex free-space functions [20,21]. It is a hybrid structure consisting of a waveguide and a metasurface composed of subwavelength meta-atoms. When directly driven by guided modes inside the waveguide, the guided wave-driven metasurface extracts and molds them into desired free-space modes to achieve various free-space functions. To some degrees, guided wave-driven metasurfaces are a kind of couplers, however, compared with traditional edge couplers [22] and surface gratings [23], guided wave-driven metasurface not only have the function of coupling, but also can flexibly manipulate the coupled light in a predesigned manner because each meta-atom can be individually designed to completely control the optical beam. Meanwhile, subwavelength meta-atoms with subwavelength interval are beneficial to eliminate diffraction loss and enable denser on-chip integration. Furthermore, multiple guided wave-driven metasurfaces can be conveniently connected via waveguides to achieve different free-space functions simultaneously [20]. Thanks to the advantages of on-chip integration and flexible control of free-space beam, guided wave-driven metasurfaces have excellent application prospects in optical communication, sensing, optical interconnects and optical display [20]. However, as a newly emerging kind of metasurfaces, few relevant works have been reported [20,21,24], and currently realized functions only involve beam deflection [20], focusing [20,21], generation of OAM beams [20,24] and holograph imaging [21,24], therefore, further researches are highly expected, and the functionality also needs to expand. On the other hand, bifocal or multifocal metalenses have important applications in optical communications, multi-imaging systems and optical tomography [25–27], though several bifocal or multifocal metalenses based on the first type of metasurfaces have been realized [25–28], up to now, such metalenses based on guided wave-driven metasurface have not been reported yet.
In this paper, an all-dielectric guided wave-driven metasurface is proposed and simulatively demonstrated, it can couple the in-plane guided modes into the predestinated out-of–plane free-space modes, and achieve bifocal focusing and polarization demultiplexing. When directly driven by fundamental transverse electric (TE00) and fundamental transverse magnetic (TM00) guided modes, the guided wave-driven metasurface converts them into y-polarized and x-polarized free-space waves, respectively, and realize polarization dependent bifocal focusing and polarization demultiplexing. Unlike previously demonstrated multi-foci metalenses [25–28], in which the incoming and output waves are both free-space light, ours bridges the guided modes and free-space waves, and it can simultaneously realize triple functions of extracting guided modes, bifocal focusing and polarization demultiplexing in a single device.
The organization of this paper is as follows, section 2 presents the working principle and device structure of the guided wave-driven metasurface, and section 3 shows the results and discussion. Brief conclusions are given in the final section.
2. Working principle and device structure
2.1. Working principle
To intuitively explain the working principle of the guided wave-driven metasurface, we adopt a simple two-dimensional (2D) model, as shown in Figs. 1(a)–1(b). The metasurface consists of an array of Si cross-shaped meta-atoms (nanoantennas) and a Si3N4 waveguide on the SiO2 substrate. The TE00 and TM00 modes of the waveguide are coupled to free space through resonating with the Si cross-shaped meta-atom array. Specifically, the TE00 mode is converted into y-polarized free-space light, and is further focused to focal point (XTE, fz); while the TM00 mode is extracted as x-polarized free-space light, and is focused to another focal point (XTM, fz). Therefore, from another point of view, the guided wave-driven metasurface has the functions of polarization dependent bifocal focusing and polarization demultiplexing.
Fig. 1. (a) Schematic and working principle of the guided wave-driven metasurface. Driven by TE00 mode and TM00 mode of the waveguide, the metasurface can couple the incident guided wave to the free space and realize polarization-dependent bifocal focusing. (b) Illustration of the wavefront formation of the extracted wave. The total phase shift of the extracted wave consists of the phase accumulation βx in the waveguide and abrupt phase change Δφ induced by the meta-atom. The arrows schematically denote the propagation directions of the electromagnetic waves.
Like the first and second types of metasurfaces, the third type of metasurface also needs to provide proper optical phase profile such that it can control the wavefront of the extracted optical wave in a desired way. Therefore, it is very important to understand the phase changes caused by the guided wave-driven metasurface. As shown in Fig. 1(b), the initial phase of the incident waveguide mode is assumed to be Φ0. After the guided mode is coupled to the free space by the first meta-atom, the phase of the extracted light is Φ0+Δφ1, where Δφ1 represents the abrupt phase change introduced by the first meta-atom [20]. In addition to the abrupt phase change provided by the meta-atom, the waveguide light also accumulates an additional propagation phase. Therefore, after the guide mode travels a distance p in the waveguide to arrive at the second meta-atom and is extracted to the free space, the phase of the extracted wave is Φ0+Δφ2+βp, where Δφ2 is the abrupt phase change induced by the second meta-atom, β is propagation constant, and βp is propagation phase.
If we set the initial phase Φ0 = 0, the phase distribution of the extracted light is written as [20]:
Clearly, the total phase shift of the extracted light has two parts: (1) the abrupt and spatially variant phase shift Δφ(x) caused by each meta-atom; (2) the phase accumulation βx due to the propagation path x in the waveguide.
If one hopes the metasurface to focus the extracted beam to focal point (Xi, fz), the corresponding phase distribution should have a parabolic profile along the x-direction [10]:
From Eqs. (1) and (2), we can derive that the abrupt phase Δφ(x) provided by the guided wave-driven metasurface needs to compensate for the accumulated propagation phase in the waveguide. Taking the TE00 mode as an example, its propagation constant is βTE, we expect the TE00 mode to be focused at the focal point (XTE, fz), then the abrupt phase Δφ(x)TE required by the meta-atoms at different x positions should satisfy:
Similarly, in order to focus the TM00 mode to the focal point (XTM, fz), the abrupt phase Δφ(x)TM provided by the meta-atoms should satisfy:
As can be seen from Eqs. (3) and (4), in order to focus the different polarized light into different points, we need to separately design Δφ(x)TE and Δφ(x)TM. Hence, we choose a cross-shaped dielectric structure as the meta-atom of the metasurface because of the following two factors: first, dielectric meta-atoms suffer from less Ohmic loss than plasmonic (metallic) meta-atoms. Second, a cross-shaped meta-atom is composed of two mutually perpendicularly arranged I-shaped antennas, which are inherently anisotropic and thus have strong polarization dependence. Therefore, one can independently design the lengths of the two I-shaped antennas to separately manipulate Δφ(x)TE and Δφ(x)TM. We just need to find the dependence of the abrupt phase Δφ on the geometrical size of the I-shaped meta-atom, and then select meta-atoms with proper dimensions such that the array of meta-atoms provides the desired phase shift profile required by Eqs. (3) and (4).
2.2. Device structure and design process
2.2.1 Device structure
Figure 2(a) schematically depicts the structure of the guided wave-driven metasurface, which includes an array of silicon (Si) cross-shaped meta-atoms (nanoantennas) on top of a silicon nitride (Si3N4) slab waveguide, and the substrate is silicon dioxide (SiO2). The height and width of the Si3N4 waveguide are set as h1=0.6 µm and w1=0.6 µm, respectively. In this case, it supports fundamental transverse electric (TE00) mode and fundamental transverse magnetic (TM00) mode, whose electric-field distributions are shown in Fig. 2(b). The guided wave-driven metasurface consists of 21 cross-shaped meta-atoms with period p = 0.5 µm and overall length L=10 µm.
Fig. 2. (a) Schematic of the designed guided wave-driven metasurface, the inset shows a meta-atom. (b) Electric-field distributions of TE00 mode and TM00 mode of the Si3N4 waveguide.
As the inset of Fig. 2(a) shows, the cross-shaped meta-atom consists of two orthogonally-arranged I-shaped Si antennas, which have the same width (w2=0.12 µm) but different arm lengths (Lx and Ly). The height h2 of the meta-atom has an important influence on the coupling efficiency when the waveguide mode is coupled to free-space light, which will be discussed in detail later.
2.2.2 Design process
A. Selection of the arm lengths of the cross-shaped antennas
By individually tailoring the arm lengths of the orthogonally cross-shaped antennas, i.e. Lx and Ly, we can independently manipulate the phase profiles of the TE00 mode and TM00 mode, thus realize polarization-controllable bifocal focusing [29]. As mentioned above, a cross-shaped structure can be viewed as the combination of two orthogonally-arranged I-shaped structures. So, the first step is to find out the dependence of abrupt phase shift Δφ on the arm lengths of the I-shaped antennas by carrying out full three-dimensional finite difference time-domain (FDTD) simulations. In the simulation, periodic boundary conditions were applied to the x- and y-directions, and perfectly matched layer condition was used along the z-direction. When calculating abrupt phase shift Δφ induced by the meta-atoms, a plane-wave light source is used.
As shown in Fig. 3(a), the I-shaped meta-atom is composed of two layers: the bottom one is Si3N4 layer and the top one is an I-shaped Si structure (the values of heights h1, h2 and period p are consistent with those in Fig. 2). Figures 3(b) and 3(c) respectively show the simulated phase shift Δφ and transmittance T as functions of length l and width w of the Si antenna for y-polarized incident waves at wavelength λ = 1.55 µm. As the length l and width w change from 0.1 µm to 0.5 µm, the transmission phase shifts of y-polarized incident light can cover the entire 2π phase range, and the transmittance T is larger than 0.5 in most region of Fig. 3(c) except for the small region in the upper-right corner. Similar result holds for x-polarized incident light, too. Due to the system’s two-fold (C2) rotational symmetry of the I-shaped antenna [30], rotating the antenna by 90 degrees can get the same result for x-polarized incident light.
Fig. 3. (a) Schematic of an I-shaped Si antenna. (b) Map of phase shift Δφ and (c) transmittance T for y-polarized incident waves in a parameter space spanned by the antenna width (w) and length (l). The height h2 of antenna is fixed at 1.2 µm. Transmittance T and phase shift Δφ of the transmitted light when w = 0.12 µm for y-polarized incident waves (d) and for x-polarized incident waves (e).
Basing on the above results and considering the complexity of design and manufacturing process, we fix the width w of I-shaped antenna as 0.12 µm, and then investigate the polarization dependence of phase shift Δφ on arm length l. As shown in Fig. 3(d), for y-polarized incident wave, the transmission phase changes rapidly from 0 to 2π when varying length l, while the transmittance curve always keeps a relatively high level of 0.6. In contrast, the x-polarized incident wave experiences little phase shift Δφ when varying length l, as shown in Fig. 3(e).
To sum up, varying the arm length l of the I-shaped antenna will significantly change the transmission phase shift of a y-polarized incident wave, however, it has little effect on that of an x-polarized incident wave. Due to the two-fold (C2) rotational symmetry of the I-shaped antenna, one can readily conclude that varying the width w of the I-shaped antenna will notably change the transmission phase shift of the x-polarized incident wave, with little effect on that of the y-polarized incident wave. Therefore, by individually tailoring Lx and Ly values of each cross-shaped antenna, we can independently manipulate the profiles of Δφ(x)TE and Δφ(x)TM to realize polarization-dependent bifocal focusing.
B. Selection of the Si antenna height h2
For the all-dielectric metasurface, the waveguide mode should be coupled to the free space as much as possible. Since Si antenna height h2 has an important influence on the coupling efficiency, it is crucial to determine a suitable height h2 to maximize the spatial modal overlap between the waveguide mode field and the scattering near field from the Si antenna. For a waveguide extended along the x direction, the spatial mode overlap η can be calculated by [19]
According to formula (5), we calculate spatial modal overlap η, and plot η as a function of h2 for TE00 and TM00 modes in Figs. 4(a) and 4(b), respectively.
Figures 4(a) and 4(b) show that, when h2 is 1.2 µm, both modes obtain the maximal value of overlap η, which are 0.036497 for TE00 mode and 0.016052 for TM00 mode. Therefore, in the design of all-dielectric guided wave-driven metasurface, we fix the height h2 of the meta-atom as 1.2 µm.
Our design purpose is as follows: at the operating wavelength of 1.55 µm, the metasurface can convert the TE00 guided mode of the Si3N4 waveguide into y-polarized free-space light, which is focused to focal point (XTE=2.5 µm, fz=5 µm) in free space. While for the TM00 mode, it is coupled to x-polarized free-space mode and is focused to another focal point (XTM=−2.5 µm, fz=5 µm). After analyzing the dependence of transmission phase on the Si antenna arm-length and choose a proper height for the Si antenna, then according to the phase requirement in formulas (3) and (4), we select proper values of Lx and Ly for each cross-shape Si meta-atom. The overall length of the guided wave-driven metasurface is chosen as L=10 µm, the period of the Si meta-atoms is p = 0.5 µm, then the number of meta-atoms is set as 21. It should be mentioned that a larger length and more number of meta-atoms will enable the metasurface to have higher focusing resolution, however, from the focusing performances (presented in Section 3), this length (L=10 µm) and meta-atom number are also suitable for the metasurface to achieve a good focusing ability. In addition, for these Si meta-atoms, their heights are fixed at 1.2 µm, and the values of Lx and Ly vary between 0.1 µm and 0.5 µm, with the aspect ratio in the range of 2.4∼12.0. The proposed metasurface can be fabricated by using electron-beam lithography and inductively coupled plasma (ICP) etching processes [31,32].
3. Results and discussion
Figure 5(a1) shows how the electric field intensity, |E|2, distributes in the free space above the metasurface, when it is only driven by TE00 mode at 1.55 µm wavelength. As can be seen, the TE00 mode is converted into free-space light and is focused into a specific position. In addition, the predominant electric-field component of the free-space light is y-component, Ey. This can be verified by comparing Figs. 5(a2) and 5(a3), which respectively map |E|2 and |Ey|2 distributions at the focal plane. |Ey|2 and |E|2 have nearly the same distributions, while |Ex|2 and |Ez|2 of the free-space mode are several orders of magnitude smaller than |Ey|2 (not shown here). These results indicate that the TE00 guided mode is molded into y-polarized light in free space. Similar results hold for the TM00 mode, it is coupled to x-polarized light and focused to another position in free space, as shown in Figs. 5(b1)–5(b3). By comparing Fig. 5(b3) with Fig. 5(a3), one can find that for the TM00 mode, more light is distributed away from the focal spot, this signifies that the metasurface has better focusing ability for the TE00 mode than it does for the TM00 mode.
Fig. 5. Electric-field intensity distributions. When the metasurface is driven by TE00 mode, (a1) |E|2 in the x-z plane; (a2) |E|2 in the x-y plane (z=5 µm); (a3) |E y|2 in the x-y plane (z=5 µm). When the metasurface is driven by TM00 mode, (b1) |E|2 in the x-z plane; (b2) |E|2 in the x-y plane (z=5 µm); (b3) |E x|2 in the x-y plane (z=5 µm).
The above is just for the cases when the metasurface is driven by one of the two guided modes. When bothTE00 mode and TM00 mode at 1.55 µm wavelength are simultaneously launched into the metasurface, Fig. 6(a) shows how electric field intensity |E|^2 distributes in the free space above the metasurface. As can be seen, the TE00 mode and TM00 mode are converted into free-space light and focused into two different positions. In order to observe the focus spots more specifically, we also calculate the electric-field intensity distribution in the focal plane, i.e. the position of the white dotted line marked in Fig. 6(a).
Fig. 6. (a) Electric-field intensity distribution in the x-z plane above the metasurface when it is simultaneously driven by TE00 mode and TM00 mode. The white dotted line represents the focal plane. (b) Electric-field intensity distribution of the bifocal points in the focus plane corresponding to the white dashed line in (a).
According to the results in Fig. 6, the TE00 mode is focused at x=2.33 µm, z=5.09 µm; and the TM00 mode is focused at x=−2.33 µm, z=4.80 µm, which match relatively well with the designed focal positions x=± 2.5 µm, z=5 µm. Therefore, it can be concluded that the guided wave-driven metasurface can achieve polarization dependent bifocal focusing.
For a quantitative analysis of the focusing characteristics, we calculate the full width at half maximum (FWHM) of the two focus points and present the results in Fig. 7. The FWHM value of TM00 focus point (FWHMTM) is 1.65 µm (1.06λ), and that of TE00 (FWHMTE) is 1.10 µm (0.71λ), here λ = 1.55µm is the operation wavelength. This suggests that this metasurface has good focusing ability. In addition, TE00 mode has a smaller FWHM value than TM00 mode because less TE00 wave is coupled to the free space by the metasurface, hence smaller coupling provides a smaller FWHM for TE00 mode.
The depth of focus (DOF) is also an important parameter to evaluate focusing characteristics [29]. Figure 8 shows how the electric-field intensity distributes along the optical axis (i.e. the z-axis) of the two focal points. The results show that the depth of focus for TM mode is DOFTM=4.17 µm and that for TE mode is DOFTE=2.77 µm, corresponding to 2.69λ and 1.79λ, respectively. This indicates that the guided wave-driven metasurface has a larger depth of focus. It is also noted that the values of FWHM and DOF are different for the two modes, this is mainly due to their different coupling efficiencies, i.e., different spatial model overlaps.
Fig. 8. Electric-field intensity along the z direction: (a) TM focal point; (b) TE focal point. The DOF for the TM focal point is 4.17 µm and that for the TE is 2.77 µm.
Since the designed guided wave-driven metasurface can focus guided waves of different polarization states at different points in free space, from another point of view, it can also realize the function of polarization demultiplexing. Under the simultaneous incidences of TE00 mode and TM00 mode at wavelength 1.55 µm, we simulate their electric-field intensity at the focal points, and show the result in Fig. 9. As can be seen, the guided waves of different polarization are extracted and separated into different x-positions in free space.
In order to quantitatively analyze the polarization demultiplexing performance of the guided wave-driven metasurfaces, we calculate polarization extinction ratio, which is the ratio of the electric-field intensities of the two orthogonal polarization components at the focus point:
At the focal point x=−2.33 µm for TM00 mode, the electric-field intensity of x component reaches the maximum, and the polarization extinction ratio is 46 dB. At the focal point x=2.33 µm for TE00 mode, the electric field intensity of the y component reaches the maximum, and the polarization extinction ratio is 27 dB.
4. Conclusion
Guided wave-driven metasurfaces offer compact and versatile platforms to couple guided waves and free-space waves. In this paper, we propose and design an all-dielectric guided wave-driven metasurface which can perform polarization demultiplexing and polarization dependent bifocal focusing in free space when it is driven by the fundamental TE00 and TM00 waveguide modes. It is composed of an array of Si cross-shaped meta-atoms and a Si3N4 waveguide on a SiO2 substrate. The cross-shaped antennas provide independently controlled phase shifts to the orthogonally polarized optical beams, hence the TE00 and TM00 waveguide modes at 1.55 µm wavelength are extracted and focused into free space at two different focus points, (x=2.33 µm, z=5.09 µm) for the TE00 mode and (x=−2.33 µm, z=4.80 µm) for the TM00 mode. In this way, the guided wave-driven metasurface simultaneously realizes the triple functions of coupling guided modes to free-space waves, bifocal metalens and polarization demultiplexing. Such a compact device may find potential applications in polarization-dependent focusing and imaging, polarization-dependent detecting and processing, polarization beam-splitting and polarization demultiplexing in optical communication.
Though the proposed guided wave-driven metasurface works at the 1.55 µm optical communication band, by properly scaling the dimensions of structural units and choosing appropriate meta-atom materials, operation wavelength could be extended to other spectral ranges, such as microwave, terahertz, or even visible range. We believe our work enriches further functions for guided wave-driven metasurfaces and on-chip photonics devices, and also offers an alternate way to control light across photonic integrated devices and free-space platforms.
Funding
National Natural Science Foundation of China (61675074).
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 reasonable request.
References
1. W. Wu, W. Liu, Z. Chun, Y. Ling, J. Ding, X. Wang, L. Huang, and H. Li, “Optical rotation and electromagnetically induced transparency in a chiral metamaterial with C4 symmetry,” Opt. Express 28(20), 29496–29512 (2020). [CrossRef]
2. J. Ding, L. Huang, W. Liu, Y. Ling, W. Wu, and H. Li, “Mechanism and performance analyses of optical beam splitters using all-dielectric oligomer-based metasurfaces,” Opt. Express 28(22), 32721–32737 (2020). [CrossRef]
3. N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012). [CrossRef]
4. Y. Bi, L. Huang, X. Li, and Y. Wang, “Magnetically controllable metasurface and its application,” Front. Optoelectron. 14(2), 154–169 (2021). [CrossRef]
5. C. Ba, L. Huang, W. Liu, S. Li, Y. Ling, and H. Li, “Narrow-band and high-contrast asymmetric transmission based on metal-metal-metal asymmetric gratings,” Opt. Express 27(18), 25107 (2019). [CrossRef]
6. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
7. L. Wan, D. Pan, T. Feng, W. Liu, and A. A. Potapov, “A review of dielectric optical metasurfaces for spatial differentiation and edge detection,” Front. Optoelectron. 14(2), 187–200 (2021). [CrossRef]
8. S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012). [CrossRef]
9. 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]
10. M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016). [CrossRef]
11. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]
12. C. Pfeiffer and A. Grbic, “Controlling vector Bessel beams with metasurfaces,” Phys. Rev. Appl. 2(4), 044012 (2014). [CrossRef]
13. Z. Li, M. H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12(7), 675–683 (2017). [CrossRef]
14. C. Wang, Z. Li, M. H. Kim, X. Xiong, X. F. Ren, G. C. Guo, N. Yu, and M. Lončar, “Metasurface-assisted phase-matching-free second harmonic generation in lithium niobate waveguides,” Nat. Commun. 8(1), 2098 (2017). [CrossRef]
15. R. Wang, Q. Wu, W. Cai, Q. Zhang, H. Xiong, B. Zhang, J. Qi, J. Yao, and J. Xu, “Broadband on-Chip Terahertz Asymmetric Waveguiding via Phase-Gradient Metasurface,” ACS Photonics 6(7), 1774–1779 (2019). [CrossRef]
16. Y. Guo, M. Pu, X. Li, X. Ma, S. Song, Z. Zhao, and X. Luo, “Chip-Integrated Geometric Metasurface As a Novel Platform for Directional Coupling and Polarization Sorting by Spin-Orbit Interaction,” IEEE J. Sel. Top. Quantum Electron. 24(6), 1–7 (2018). [CrossRef]
17. R. Guo, M. Decker, F. Setzpfandt, X. Gai, D. Y. Choi, R. Kiselev, A. Chipouline, I. Staude, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “High-bit rate ultra-compact light routing with mode-selective on-chip nanoantennas,” Sci. Adv. 3(7), e1700007 (2017). [CrossRef]
18. Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact Graphene-Assisted Tunable Waveguide Couplers with High Directivity and Mode Selectivity,” Sci. Rep. 8(1), 13362 (2018). [CrossRef]
19. Y. Meng, Z. Liu, Z. Xie, R. Wang, T. Qi, F. Hu, H. Kim, Q. Xiao, X. Fu, Q. Wu, S.-H. Bae, M. Gong, and X. Yuan, “Versatile on-chip light coupling and (de)multiplexing from arbitrary polarizations to controlled waveguide modes using an integrated dielectric metasurface,” Photonics Res. 8(4), 564–576 (2020). [CrossRef]
20. X. Guo, Y. Ding, X. Chen, Y. Duan, and X. Ni, “Molding free-space light with guided wave-driven metasurfaces,” Sci. Adv. 6(29), eabb4142 (2020). [CrossRef]
21. Y. Ding, Y. Duan, X. Chen, H. Huang, X. Guo, and X. Ni, “Guided-Wave-Driven Photonic Integrated Metasurface Holograms,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2020), paper JTh2B.23.
22. M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016). [CrossRef]
23. S. A. Masturzo, J. M. Yarrison-Rice, H. E. Jackson, and J. T. Boyd, “Grating couplers fabricated by electron-beam lithography for coupling free-space light into nanophotonic devices,” IEEE Trans. Nanotechnol. 6(6), 622–626 (2007). [CrossRef]
24. Y. Ha, Y. Guo, M. Pu, X. Li, X. Ma, Z. Zhang, and X. Luo, “Monolithic-Integrated Multiplexed Devices Based on Metasurface-Driven Guided Waves,” Adv. Theory Simul. 4(2), 2000239 (2021). [CrossRef]
25. X. F. Zang, H. Z. Ding, Y. Intaravanne, L. Chen, Y. Peng, J. Y. Xie, Q. H. Ke, A. V. Balakin, A. P. Shkurinov, X. Z. Chen, Y. M. Zhu, and S. L. Zhuang, “A multi-foci metalens with polarization-rotated focal points,” Laser & Photon. Rev. 13(12), 1900182 (2019). [CrossRef]
26. 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]
27. Y. Yuan, B. Yao, J. Cao, X. Zang, D. Yu, A. V. Balakin, A. P. Shkurinov, and Y. Zhu, “Geometry phase for generating multiple focal points with different polarization states,” Opt. Express 28(19), 28452–28464 (2020). [CrossRef]
28. R. Wang, J. Han, J. Liu, H. Tian, W. Sun, L. Li, and X. Chen, “Multi-foci metalens for terahertz polarization detection,” Opt. Lett. 45(13), 3506–3509 (2020). [CrossRef]
29. Y. Ling, L. Huang, W. Hong, T. Liu, L. Jing, W. Liu, and Z. Wang, “Polarization-switchable and wavelength-controllable multi-functional metasurface for focusing and surface-plasmon-polariton wave excitation,” Opt. Express 25(24), 29812–29821 (2017). [CrossRef]
30. G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015). [CrossRef]
31. H. Liang, Q. Lin, X. Xie, Q. Sun, Y. Wang, L. Zhou, L. Liu, X. Yu, J. Zhou, T. F. Krauss, and J. Li, “Ultrahigh Numerical Aperture Metalens at Visible Wavelengths,” Nano Lett. 18(7), 4460–4466 (2018). [CrossRef]
32. H. Zhang, X. Zhang, Q. Xu, Q. Wang, Y. Xu, M. Wei, Y. Li, J. Gu, Z. Tian, C. Ouyang, X. Zhang, C. Hu, J. Han, and W. Zhang, “Polarization-independent all-silicon dielectric metasurfaces in the terahertz regime,” Photonics Res. 6(1), 24–29 (2018). [CrossRef]
