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Abstract
Optical metasurfaces exhibit unprecedented ability in light field control due to their ability to locally change the phase, amplitude, and polarization of transmitted or reflected light. We propose a multifunctional metalens with dual working modes based on bilayer geometric phase elements consisting of low-loss phase change materials (Sb2Se3) and amorphous silicon (a-Si). In transmission mode, by changing the crystalline state of the Sb2Se3 scatterer, a bifocal metalens with an arbitrary intensity ratio at the telecommunication C-band is realized, and the total focusing efficiency of the bifocal metalens is as high as 78%. Also, at the resonance wavelength of the amorphous Sb2Se3 scatterer, the scatterer can be regarded as a half-wave plate in reflection mode. The multifunctional metalens can reversely converge incident light into a focal point with a focusing efficiency of up to 30%. The high focusing efficiency, dynamic reconfigurability, and dual working modes of the multifunctional metalens contribute to polarization state detection, optical imaging, and optical data storage. In addition, the bilayer geometric phase elements can be easily extended to multilayer, which significantly improves the capability of manipulating the incident light field.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
Li Chen, Yuan Hao, Lin Zhao, Ruihuan Wu, Yue Liu, Zhongchao Wei, Ning Xu, Zhaotang Li, and Hongzhan Liu, "Multifunctional metalens generation using bilayer all-dielectric metasurfaces: erratum," Opt. Express 29, 18304-18304 (2021)https://opg.optica.org/oe/abstract.cfm?uri=oe-29-12-18304
1. Introduction
Optical metasurfaces, a kind of planar artificial nanostructure that composed of compact optical subwavelength dielectric scatterers or metal scatterers, have attracted much attention in manipulating the wavefront of light because the scatterers with specific azimuth and geometric shapes can impose an abrupt phase shift on the incident light. So far, various optical devices based on ultrathin optical metasurfaces have been realized, including polarization converters [1], metalens [2–6], Spin Hall effect [7], holograms [8,9], orbital angular momentum multiplexing and demultiplexing [10], etc. Metalens, a subcategory of metasurfaces, is a reflective (or transmission) device that can focus light into a focal point by adding a parabolic phase on the incident light. All kinds of metalens with complicated functions were implemented owing to the gradual progress of micro-nano processing technology and the flexible control of wavefront achieved by specific scatterers, for example, achromatic metalens based on the principle of phase compensation [11–13], dynamic metalens based on the technology of integration of metalens into Micro-Electro-Mechanical System [14,15], and zoom metalens [16–19]. In recent years, researchers have combined metasurfaces with digital coding [20] and phase change materials [21,22] to provide metasurfaces with dynamic reconfigurability. Non-volatile phase change materials usually refer to materials whose optical properties experience significant changes after phase transition, which are widely used in integrated-photonics devices due to their low loss in the near-infrared region, reconfigurability, and stable intermediate states [23,24]. Sb$_2$Se$_3$ is one of the non-volatile phase change materials [25], and its optical permittivity in both crystalline and amorphous states are much closer to that of amorphous silicon, which conduces to the deposition process compatible with the conventional CMOS manufacturing process. Previous studies have demonstrated that phase change materials can be switched reversibly between crystalline and amorphous states by utilizing voltage control [26], temperature control [27] and laser pulse [28]. The voltage control method is usually to place two indium tin oxide (ITO) electrodes on both ends of the phase change materials, and then apply an appropriate voltage to the two electrodes to achieve phase transition.
Multifocal metalens, with multiple focal points on the horizontal or longitudinal plane, have recently gained many interests in multi-plane imaging [29], polarization state detection [30], optical data storage [31], optical tomography technology [32] and so on. Although the space division multiplexing multifocal metalens [33] has been reported before, its principle is to divide the metalens into multiple concentric ring regions, and each concentric ring modulates the phase required by the corresponding focal point. Multifocal metalens based on this principle inevitably has poor transmission efficiency, low signal-to-noise ratio, and inconvenient control of relative intensity. To solve these limitations, Tian et al. [34] realized a multifocal metalens with controllable relative intensity by combining geometric phase and propagation phase, so the relative intensity of each focal point can be changed by controlling the polarization state of the incident light. This method partly solves the above limitations, but it will significantly increase the complexity of the experiment devices. Lin et al. [35] achieved the generation of coaxial bifocal metalens based on multilayer geometric phase elements structure, and the relative intensity of the two focal points can be adjusted by modifying the size of the geometric phase elements. Subsequently, Zhou et al. [36] designed a helical multiplexed multifocal metalens rely on the compound phase, which can form different focal points under the illumination of left-handed circularly polarized light (LHCP) and right-handed circularly polarized light (RHCP). These devices can improve transmission efficiency and reduce signal-to-noise ratio, however, they usually only work in a single mode (transmission or reflection mode), a single wavelength, and have no reconfigurable characteristics.
In this paper, we design a multifunctional metalens based on bilayer geometric phase elements, which is composed of low-loss phase change materials (Sb$_2$Se$_3$), amorphous silicon (a-Si), ITO, Cr, and silica. Cr, located on the ITO, serves as the electrode pads, an ITO heater is deposited on the bottom of the Sb$_2$Se$_3$ to achieve electrical actuation of Sb$_2$Se$_3$ phase transition. After applying voltage pulses along the ITO, electrical current causes Joule heating and subsequently phase transition of the Sb$_2$Se$_3$ [37]. The Sb$_2$Se$_3$ and a-Si act as the scatterers of the first and second layer, respectively. In transmission mode, for crystalline Sb$_2$Se$_3$ (c-Sb$_2$Se$_3$), the scatterers on both first and second layer can be perceived as a half-wave plate, at this time, the multifunctional metalens can focus the incident light into a focal point and maintain the original polarization state. In contrast, when Sb$_2$Se$_3$ transition from c-Sb$_2$Se$_3$ to amorphous Sb$_2$Se$_3$ (a-Sb$_2$Se$_3$), the scatterer of the first layer can adjust the polarization component of the transmitted light. Thus the transmitted light after passing through the multifunctional metalens includes LHCP and RHCP, and the two beams are focused into specific position to form dual focuses. In addition, we analyzed the influence of Sb$_2$Se$_3$ with different crystalline fractions on the relative intensity of bifocal metalens. Numerical simulations show that Sb$_2$Se$_3$ with various crystalline fractions can change the ratio of LHCP and RHCP in transmitted light to achieve the control of the relative intensity of bifocal metalens. The multifunctional metalens we proposed is able to work not only in transmission mode but also in reflection mode. At the resonance wavelength (975 nm), we use the principle of multipole resonance at a specific wavelength to achieve reverse focusing of the incident light. This multifunctional metalens has potential application in optical imaging, optical tomography technology, optical data storage and other fields.
2. Theoretical analysis and design of the metalens
In order to realize a multifunctional metalens with dual operating modes, we designed bilayer geometric phase elements as shown in Fig. 1(a). A thin layer of ITO [38] is placed on the lower surface of the Sb$_2$Se$_3$ scatterer to realize the phase transition of Sb$_2$Se$_3$. The surroundings of the a-Si scatterer are filled with silica to facilitate the manufacture of the Sb$_2$Se$_3$ scatterer of the first layer. Considering an anisotropic scatterer with short and long axis under normal incidence, as indicated in Fig. 1(b), $t_o$ and $t_e$ represent the complex transmission coefficients of the linearly polarized light (LPL) incident along the short and long axis, respectively. As the scatterer is rotated with an angle $\theta$ relative to the $x$ axis, the transmission coefficients for the scatterer can be obtained by the Jones matrix [39]:
Fig. 1. (a) The schematic of the proposed bilayer geometric phase elements. (b) Rotation of the geometric phase elements, where $x$ and $y$ donate the two principles axis, and $o$ and $e$ are the short and long axis. (c) Schematic of the two geometric phase elements with different rotation angles. Illustration of the operating principle of the multifunctional metalens when Sb$_2$Se$_3$ is in amorphous state (d) and crystalline state (e).
The refractive index and extinction coefficient of a-Sb$_2$Se$_3$, c-Sb$_2$Se$_3$, and a-Si are provided in Fig. 2 [25,43]. For the Sb$_2$Se$_3$, the refractive index has a significant difference between the a-Sb$_2$Se$_3$ and c-Sb$_2$Se$_3$, which provides the possibility of realizing dynamically adjustable photonic devices. When Sb$_2$Se$_3$ is in crystalline state, the geometry of the c-Sb$_2$Se$_3$ scatterer and a-Si scatterer should be optimized to meet $|{t_o}| = |{t_e}|$, $\arg({t_o}) - \arg ({t_e}) = \pi$, $|t_o^\prime | = |t_e^\prime |$, $\arg(t_o^\prime ) - \arg (t_e^\prime ) = \pi$, so that $T_1^\prime$=0 and $T_1$=0. In this paper, three-dimensional finite difference time domain (FDTD) solver is used to sweep the geometry of the geometric phase elements. The height, length, and width of the Sb$_2$Se$_3$ scatterer are set to 910 nm, 350 nm, and 230 nm, respectively. The height of the ITO layer is 10 nm, and the length and width are equal to the period of the geometric phase elements (650 nm). The a-Si scatterer is located in the middle of the silica layer, and its height, length, and width are 1300 nm, 520 nm, and 190 nm, respectively. The height of the silica layer is 2300 nm, and the length and width are equal to 650 nm.
Fig. 2. The refractive index (a) and extinction coefficient (b) of a-Sb$_2$Se$_3$, c-Sb$_2$Se$_3$, and a-Si.
To make the c-Sb$_2$Se$_3$ scatterer and a-Si scatterer achieve the effect of half-wave plate, we use the $x$-linear polarized light ($x$-LPL) along the long axis of the scatterer, while the $y$-linear polarized light ($y$-LPL) along the short axis of the scatterer. In Fig. 3(a), the phase difference of $x$-LPL and $y$-LPL after passing through the c-Sb$_2$Se$_3$ scatterer is plotted. The discontinuous phase in the transmitted light can be attributed to the optical resonance of the c-Sb$_2$Se$_3$ scatterer, and its resonance wavelengths are 1360 nm, 1392 nm, and 1559 nm. Obviously, the phase difference between the $x$-LPL and $y$-LPL in the transmitted light at the telecommunication C-band (1550 nm) is approximately regarded as $\pi$. It can be seen from Fig. 3(b) that the amplitudes of $x$-LPL and $y$-LPL in the transmitted light at 1550 nm are 0.92 and 0.88, respectively. In the actual design process, it is usually difficult to achieve the same amplitude and phase difference $\pi$ for the $x$-LPL and $y$-LPL in the transmitted light at the same time, which reveals that the scatterer we designed often cannot achieve 100% polarization conversion efficiency. The phase distribution of $x$-LPL and $y$-LPL in the transmitted light at 1550 nm is shown in Fig. 3(c), we find that their phase difference is always $\pi$ in the propagation along the $x$-$z$ plane. Figure 3(d) represents the phase difference of $x$-LPL and $y$-LPL after passing through the a-Si scatterer, and their phase difference is equal to $\pi$ at 1550 nm. For the incidence of $x$-LPL, the phase of transmitted light displays three skips in the spectrum at 1310 nm, 1490 nm, and 1640 nm, which corresponds to multipole modes for the scatterer. In contrast, the phase of $y$-LPL in the spectrum is a smooth curve. And in Fig. 3(e), the amplitude of $x$-LPL and $y$-LPL in the transmitted light is illustrated, and their amplitudes are basically the same at 1550 nm. Figure 3(f) depicts the phase distribution of $x$-LPL and $y$-LPL at 1550 nm along the $x$-$z$ plane. For $x$-LPL and $y$-LPL, the consistent amplitude and the phase difference of $\pi$ not only provide the multifunctional metalens with a high polarization conversion efficiency, but also guarantee only RHCP in the transmitted light passing through the bilayer geometric phase elements. By applying a voltage pulses on ITO layer, the switch from c-Sb$_2$Se$_3$ to a-Sb$_2$Se$_3$ can be realized. The a-Sb$_2$Se$_3$ scatterer no longer serves as a half-wave plate, but it can adjust the components of LHCP and RHCP in transmitted light after passing through the multifunctional metalens.
Fig. 3. Optimization of the bilayer geometric phase elements. (a) Phase difference between $x$ and $y$ linear polarization for the first layer c-Sb$_2$Se$_3$ geometric phase elements. (b) Transmission coefficient for $x$ and $y$ linear polarization. (c) The simulated phase distribution for $x$ and $y$ linear polarization. (d) Phase difference between $x$ and $y$ linear polarization for the second layer a-Si geometric phase elements. (e) Transmission coefficient for $x$ and $y$ linear polarization. (f) The simulated phase distribution for $x$ and $y$ linear polarization. The dashed lines in (a), (b), (d) and (e) denote the incident wavelength 1550 nm. The green block in (c) denotes the first layer c-Sb$_2$Se$_3$ geometric phase elements and the red block in (e) denotes the second layer a-Si geometric phase elements.
Now if incident light is focused into a focal point in reflection mode, the Jones matrix of the a-Sb$_2$Se$_3$ scatterer on first layer should obey the following form [41]:
Fig. 4. Reflection spectra and the multipole scattering spectra for the $x$ linear polarization (a) and $y$ linear polarization incidences (b). The electric field of reflected light under $x$ linear polarization (c) and $y$ linear polarization incidences (d). The dashed line box shows the sizes of the scatterer, and the black line depicts the position of the source. The dashed lines in (a) and (b) denote the incident wavelength 975 nm.
Figures 5(a)–5(d) denote the near-field distributions in the scatterer to corroborate the excitation of these resonance modes. With LPL incident along the short axis and long axis of the scatterer, the circular displacement current in the scatterer is excited and forms different near-field distribution, which is mainly caused by the excitation of different resonance modes. For LPL incident along the long axis of the scatterer, the magnetic dipole resonance is barely excited, as plotted in Fig. 5(a). Fig. 5(c) indicates the near electric field distribution on the $x$-$y$ plane, which represents the characteristics of an electric dipole oriented along the $y$ direction, with electric vector in the scatterer pointing in the opposite direction to the incident electric field. In contrast, for LPL incident along the short axis of the scatterer, the excited circular displacement current forms several strong magnetic fields in the scatterer, oriented in the direction of the incident magnetic field, as illustrated in Fig. 5(b). It is a typical feature of magnetic dipole resonance. Fig. 5(d) shows the near electric field distribution on the $x$-$y$ plane. In Fig. 5, the black dotted line represents the size of the scatterer.
Fig. 5. (a) and (b) The displacement currents vectors and magnetic field distribution in the $x$-$z$ plane at 975 nm for $x$ linear polarization and $y$ linear polarization. (c) and (d) The displacement currents vectors and electric field distribution in the $x$-$y$ plane at 975 nm for $x$ linear polarization and $y$ linear polarization. The dashed line box shows the sizes of the scatterer.
3. Results and discussion
3.1 Switching between single focus and dual focuses
We propose a multifunctional metalens with radii of 20 $\mu$m, focal lengths of $f_1$=15 $\mu$m and $f_2$=30 $\mu$m. The corresponding numerical aperture of these two focal points is 0.8, 0.555, and the numerical aperture is calculated by $NA = \sin [{\tan ^{- 1}}(D/2f)]$. According to the theoretical analysis section, when Sb$_2$Se$_3$ is in crystalline state, both c-Sb$_2$Se$_3$ and a-Si scatterers can be regarded as a half-wave plate, which reveals that Eq. (6) can be simplified to Eq. (10). To reduce the simulation time and ensure accuracy, we established a 3D FDTD simulation model with simulation region of $40\;\mu\textrm {m}\times 40\;\mu \textrm {m}\times 8\;\mu \textrm {m}$, and a mesh size of $30\;\textrm {nm}\times 30\textrm {nm}\times 50\textrm {nm}$ was used in the multifunctional metalens. Here, by projecting the near-field data to the far-field, we obtained the required far-field data such as electric field and magnetic field. Figure 6(a) illustrates that the multifunctional metalens focuses the incident light into a focal point and the polarization state of the transmitted light is the same as the incident light. Obviously, a focal point appears at $z$=15.2 $\mu$m, which is close to our design focal length $f_1$. The normalized intensity at the focal plane $y$=0 is illustrated in Fig. 6(b). The full widths at half-maximum (FWHM) at the focal point is 1088 nm, which is an essential parameter to the evaluation the focusing effect of the metalens. Figure 6(c) displays the intensity distribution on the $z$-axis, we find that there are three peaks. Because $|{t_o}| = |{t_e}|$, $\arg({t_o}) - \arg ({t_e}) = \pi$, $|t_o^\prime | = |t_e^\prime |$, $\arg(t_o^\prime ) - \arg (t_e^\prime ) = \pi$ cannot be strictly satisfied, a small part of $\frac {1}{4}{T_2}T_1^\prime {e^{ - j2{\theta _1}}}{e_L}$, $\frac {1}{4}{T_1}T_2^\prime {e^{ - j2{\theta _1}}}{e_L}$ still exists in the transmitted field. To confirm the the multifunctional metalens has good focusing performance at other wavelengths. In Fig. 6(d), the intensity distribution in the $x$-$z$ plane of the multifunctional metalens at different wavelengths ranging from 1520 nm to 1580 nm is plotted, it is obvious that the multifunctional metalens can work well for the broadband focusing of single focus when Sb$_2$Se$_3$ is in crystalline state. When Sb$_2$Se$_3$ transition from c-Sb$_2$Se$_3$ to a-Sb$_2$Se$_3$, the multifunctional metalens will converge RHCP and LHCP into the designed focal length, respectively. Figure 6(e) denotes the intensity distribution in the $x$-$z$ plane. Obviously, two focal points appear in the transmitted field, and their focal lengths are $z$=14.45 $\mu$m and $z$=31.5 $\mu$m, respectively. The small difference between the designed and simulated focal length for the second focal point can be ascribed to the 3.22 $\mu$m thickness of multifunctional metalens as well as the discrete phase of the geometric phase elements. Generally, the deviation can be reduced by increasing the size of device. Fig. 6(f) shows the normalized intensity distribution at the two focal planes ($y$=0), the corresponding FWHM size of these two focal points are 1026 nm, 1472 nm, which are very close to their corresponding theoretical FWHM size of 969 nm, 1397 nm. Thus the multifunctional metalens has a good focusing performance. The intensity distribution on the $z$-axis is plotted in Fig. 6(g). Here the focusing efficiency is calculated by the following equation [45]:
Fig. 6. (a) The intensity distribution in the $x$-$z$ plane of the multifunctional metalens when Sb$_2$Se$_3$ is in crystalline state and (b) Corresponding horizontal cuts of the focal point. (c) The intensity distribution along the negative $z$-axis. (d) The intensity distribution in the $x$-$z$ plane of the multifunctional metalens at different wavelengths ranging from 1520 nm to 1580 nm. (e) The intensity distribution in the $x$-$z$ plane of the multifunctional metalens when Sb$_2$Se$_3$ is in amorphous state and (f) Corresponding horizontal cuts of the dual focuses. (g) The intensity distribution along the negative $z$-axis.
3.2 Reverse focus
At the resonance wavelength of the a-Sb$_2$Se$_3$ scatterer, the multifunctional metalens works in the reflection mode. The a-Sb$_2$Se$_3$ scatterer can control the phase and amplitude of the reflected light based on the characteristic of high reflectivity and half-wave plate. As mentioned above, the phase distribution of the reflected light satisfies $\varphi _{3} (x_{i},y_{i},\lambda _1,f_1,f_2)$, so the incident light will be focused into a focal point in the reverse direction and maintain the same polarization state as the incident light. The intensity distribution of the reflected light on the $x$-$z$ plane is shown in Fig. 7(a). We see that the focal point appears at $z$=15.6 $\mu$m, which is consistent with our expected focal length. Fig. 7(b) illustrates the normalized intensity at the focal plane $y$=0. The simulated focusing efficiency and FWHM of the multifunctional metalens are 30% and 658 nm, respectively. The FWHM size acquired from numerical simulations is close to corresponding diffraction-limited FWHM size of 607 nm. The main reason for the low focusing efficiency is that the relatively small designed focal lengths $f_1$ and $f_2$, resulting in discontinuous phase of the multifunctional metalens. The focusing efficiency in reflection mode can improved by properly increasing $f_1$ and $f_2$. The intensity distribution in the $z$-axis is demonstrated in Fig. 7(c). Here, the relationship among focal length ($f_3$) in reflection mode and focal lengths ($f_1$, $f_2$) in transmission mode will be analyzed, the phase distribution to focus reflected light focus at desired focal length ($f_3$) satisfies the following relationship:
Fig. 7. The intensity distribution in the $x$-$z$ plane of the multifunctional metalens when Sb$_2$Se$_3$ is in amorphous state and (b) Corresponding horizontal cuts of the focal point. (c) The intensity distribution along the positive $z$-axis. (d) The intensity distribution in the $x$-$z$ plane of the multifunctional metalens at different wavelengths ranging from 970 nm to 980 nm.
3.3 Dual focus with controllable intensity ratio
Above we only discussed the Sb$_2$Se$_3$ is in crystalline and amorphous states. In general, different crystalline states of Sb$_2$Se$_3$ are stable and can be realized [46]. These intermediate states can be formed when the time for completion of crystallization is insufficient. Here, we assume that the intermediate state of the Sb$_2$Se$_3$ scatterer is composed of different crystalline and amorphous molecules, the Lorentz-Lorenz relationship is used to analyze the optical permittivity of Sb$_2$Se$_3$ with different crystalline states [47]:
Fig. 8. The intensity distribution in the $x$-$z$ plane of the multifunctional metalens (design 1) for four different levels of the crystalline fraction. (b) The intensity distribution along the negative $z$-axis of design 1 for four different levels of the crystalline fraction. (c) Total focusing efficiency, corresponding focusing efficiency and FWHM for design 1 with four different levels of the crystalline fraction. (d) Total focusing efficiency, corresponding focusing efficiency and relatively intensity ratio for design 2 with different levels of the crystalline fraction. (e) The intensity distribution in the $x$-$z$ plane of the multifunctional metalens (design 2) for four different levels of the crystalline fraction.
4. Conclusion
In this paper, a multifunctional metalens with dual working modes based on bilayer geometric phase elements is proposed. In transmission mode, the multifunctional metalens can converge the incident light into specific position to generate dual focuses when Sb$_2$Se$_3$ is in amorphous state. For the first focal point, the numerical simulation shows that the FWHM and focusing efficiency are 1026 nm and 31%, respectively. For the second focal point, the FWHM and focusing efficiency are 1472 nm and 47%. Therefore, the total focusing efficiency is as high as 78%. However, when Sb$_2$Se$_3$ changes from a-Sb$_2$Se$_3$ to c-Sb$_2$Se$_3$, the multifunctional metalens can converge normal incident light into a focal point, the focusing efficiency and FWHM are 59% and 1088 nm, respectively. Meanwhile, the effect of Sb$_2$Se$_3$ with the partially crystalline state on bifocal performance is also analyzed, and we find that when the crystallization fraction changes from 5% to 20%, the focusing performance of the first focal point will be significantly improved, while the focusing performance of the second focal point will decrease. In addition, in reflection mode, the multifunctional metalens can reversely focus the incident light into a focal point, and the corresponding focusing efficiency and FWHM are 30% and 658 nm, respectively. Owing to the multiple operating wavelengths, dual operating modes, and dynamic reconfigurability, our devices can be applied in multiple imaging systems, particle capture and other fields.
Funding
National Natural Science Foundation of China (61875057, 61475049, 61774062); Science and Technology Program of Guangzhou (2019050001).
Disclosures
The authors declare no conflicts of interest.
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