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Abstract
Reconfigurable metasurfaces, whose optical responses can be tailored post-fabrication, hold great promise to enable multifunctional and versatile optical components. However, the singularity of adjustment, usually manifested as switching functions or wavelength-tunable features, hinders their further development in practice. Particularly, active polarization-insensitive metasurfaces usually appear to be forced by using the isotropic nanostructure as their constituent elements, rendering them to lose a degree of freedom in the design space and plaguing them in many practical scenarios. In this paper, we report a polarization-insensitive, switchable and dual-mode multifunctional metalens. By using anisotropic Ge2Sb2Se4Te1 nanofins as building blocks, we can accurately impart the phases to each atom in order to realize the full 2π coverage by restricting their rotation angle to either 0 or 90 degrees. This guarantees that the metalens can elegantly focus any incident polarized light at the operation wavelength of λ0 = 4200 nm. Meanwhile, the proposed metalens can also focus the oblique incident light into one spot within the incident angle range of [−2.4°, +2.4°], providing a field of view (FOV) of 4.8°. Moreover, the designed scheme supports a stable focusing efficiency (above 60%), a near-constant focal length (the focal length shifts less than 6%) and diffraction-limited focal spots over λ = 4000–4500 nm. The point to emphasize here is that when the amorphous Ge2Sb2Se4Te1 (aGSST) is converted into the crystalline state (cGSST), the designed metalens can be switched off in terms of focusing features at λ0 = 4200 nm, while the bright focal spot reappears on the focal plane at the wavelength of λ = 4700 nm unexpectedly. The cGSST-based metalens works well both in the reflection and transmission modes simultaneously at the wavelength of λ = 4000 nm owing to phase matching conditions. The generality of our polarization-insensitive, switchable and dual-mode design allows it to be implemented in a plethora of metasurface devices with promising applications, such as: optical imaging, optical encryption, augmented reality and sensing systems.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces engineered by subwavelength meta-unit arrays, 2D counterparts of metamaterials, exhibit an unprecedented capability to manipulate the amplitude, phase and polarization of the electromagnetic (EM) waves, enabling a plethora of novel applications such as Spin-Hall effects [1,2,3], polarization rotators [4,5], optical cloaking/illusion [6,7], holograms [8,9] and so forth. Amongst these devices, the ultrathin planar metalenses have attracted intense interest owing to their ultraflat configuration as well as ease of fabrication and system integration. In addition, compared with the conventional lenses that rely on geometric curvature to mold the propagation phase of light, metalenses can afford on-demand control of an optical wavefront and offer novel/versatile functions that are very challenging or impossible to realize by the conventional ones, not only allowing for the possibility of highly compact and integrated devices, but also extending the focusing/imaging ability of the current optical devices. Inheriting the exotic merits of metasurfaces, a variety of metalenses have been demonstrated either theoretically or experimentally, including broadband achromatic metalenses [10,11], super-resolution metalenses [12,13] and multi-foci lenses [14,15], multifunctional metalenses [16,17] and polarization-dependence metalenses [18,19]. However, these reported metalenses, engineered by the phase profiles of each constructed element, are either endowed with broadband achromatic focusing characteristics, or can only achieve large-field imaging, or can only realize polarization insensitivity, i.e., focus light with arbitrary polarization states. A single-layer metasurface device, especially the transmission type, that simultaneously realizes polarization-independence and broadband achromatic focusing characteristics, to the best of our knowledge, has merely been reported by Ni’s group very recently [20]. However, their design was completed by adopting the inverse design approach accomplished by random-shaped meta-atoms (meta-atoms with unintuitive geometries), which dramatically increases the design complexity and is unfeasible for mass production.
Another design barrier of metalenses is that they work well in a certain circumstance but become inefficient once the surroundings are altered, which seriously hinders their broader potential applications. “Active metasurfaces” realized by the hybridization of original metasurfaces with mechanical/non-mechanical actuation mechanisms can dynamically tailor the optical response to meet diverse application demands at will, offering a versatile suite of solutions for reconfigurable devices. Nevertheless, mechanical deformation or displacement of metasurfaces usually comes with the price of increased system size and complexity. On the contrary, active metasurfaces that harness non-mechanical actuation mechanisms such as graphene [21,22], phase change materials (PCMs) [6,23] and liquid crystals [24,25] allow for direct control over optical response of meta-atoms, and thus exhibit significant advantages in compactedness, cost of modulation, reliability, as well as design flexibility. Ge2Sb2Se4Te1 (GSST), a novel non-volatile PCM, offers a fascinating platform to induce real “soft” reconfigurability due to the extremely large refractive index contrast between its amorphous (aGSST) and crystalline phases (cGSST) in the mid-infrared region (MIR) [26]. Compared with the classical Ge2Sb2Te5 (GST) phase-change alloy, the exceptionally broadband transparency and low loss in this range enable GSST to afford more degrees of freedom for tunability and flexibility. However, the research on GSST-based metasurfaces is still in infancy due to the relatively complicated and immature preparation process of GSST, let alone manufacturing GSST into patterned and isolated meta-atoms with high aspect ratios. More recently, Gu et al. demonstrated a GSST-nanopillars-based varifocal/active metalens. By defining the target phase maps via the two optical states (aGSST and cGSST), the active metalens features a record large switching contrast ratio, aberration-free and multi-depth imaging, which represents a key experimental demonstration and strong technical supports for achieving the patterned GSST nanostructures [27]. Nevertheless, this design possesses a relative small NA and is limited to a specific wavelength. Besides, the focusing efficiencies of the metalens in the two states were not reported.
In this paper, we propose and design an all-dielectric, low-loss and transmissive metalens consisting of anisotropic Ge2Sb2Se4Te1 nanofins. These anisotropic nanofins allow us to accurately impart the phases to each-atom to realize the full 2π coverage by restricting the rotation angle of each anisotropic element to either 0 or 90 degrees, and thus guaranteeing the metalens can elegantly focus any incident polarized light at an operation wavelength of λ0 = 4200 nm. This is a unique scheme compared with the recent reports on spatial multiplexing and symmetry [28–32]. In addition, the metalens is capable of focusing effectively with a field of view (FOV) up to 4.8° at this wavelength. Moreover, our designed scheme allows for a high NA, a focal length shift of less than 6%, and the diffraction-limited focal spots, while maintaining a high focusing efficiency (above 60%) across λ = 4000∼4500 nm. The point to emphasize here is that the phase transformation of Ge2Sb2Se4Te1 renders the designed metalens to be switched on and off in terms of focusing features at λ0 = 4200 nm as well as to realize dual-mode focusing performance at λ = 4000 nm. Overall, we believe that the polarization-insensitive and switchable/active metasurface design would easily find promising applications, including but not limited to visible imaging, optical information encryption and advanced eyeglass-free 3D stereoscopic displays.
2. Principles and structures
2.1 Design principles of polarization-insensitive focusing
To design a metasurface that functions as a cylindrical lens with a focal length f for the cross-polarized transmission mode, each constituent element of the metasurface is encoded with a spatial phase profiles φ(x) given by [22]:
where f is the preset focal length, λ is the incident wavelength, x is the distance of the meta-atom to the lens center. Almost all previous schemes impart the elements PB phase profiles to construct metalens due to its broadband characteristics of PB phase, i.e., the PB phase is independent of the wavelength of the incidence. However, this approach is accompanied by an awkward polarization sensitivity, where the metalenses can only focus incident light with a particular circular polarization.Our design principle primarily considers the propagation phase due to its independent control over the phase for the left-handed circularly polarized (LCP) light and right-handed circularly polarized (RCP) light, but still involves PB phase. However, we circumvent the routine operations by restricting the rotation angle of each anisotropic element to either 0 or 90 degrees (Fig. 1(a)). Each meta-atom consists of anisotropic GSST nanofins residing on the CaF2 substrate (Fig. 1(b)), which not only affords more geometric parameters to alter for better dispersion control, but also offer more freedom to impose an additional π phase shift without varying their dispersion responses. This is fundamental to fulfill both the desired phase and dispersion. As light transmits through a nanofin, the output electric field can be expressed by the Jones vector [33]:
Fig. 1. Schematic and design principle of the polarization-insensitive metalenses. (a) Schematic of the polarization-insensitive metalenses. It possesses a NA of 0.669 and a diameter of 180 μm. The incident wave of any polarization illuminated from the substrate side can be elegantly focused at one spot. (b) Schematic diagram of the constituent elements of the proposed metalens. Each element is composed of GSST nanofins residing on the CaF2 substrate. These elements with the same height h = 2800 nm are spaced equally with a lattice constant p = 3000 nm. Transmittance (normalized to the incident electric field of 1 V/m) (c) and propagation phase (d) of rectangular GSST nanofins with length a varying from 860 to 2900 nm, while length b maintains the constant of 600 nm.
2.2 Structures and methods
Figure 1(a) shows the principle of the polarization-insensitive metalens, from which one can find that the design can efficiently convert the incident circularly-polarized light (LCP or RCP light) to the one of opposite spin state (RCP or LCP light) and focus the light of different spins at the same location. It is well-known that the linearly polarized (abbreviated as LP) light can be regarded as a superposition of LCP and RCP light. Therefore, the focusing spot under LP light also falls in the same position as above. The constituent elements of our design are rectangular GSST nanofins residing on a 2 μm thick CaF2 substrate, as illustrated in Fig. 1(b). The rectangular GSST nanofins with the same height h = 2800 nm have a fixed width b = 600 nm and a varying length a (from 860 to 2900 nm). These constituent elements are arranged with a lattice constant p = 3000 nm to construct the metalens design.
To verify the proposed design, we use the commercial software of COMSOL Multiphysics to simulate the related optical performance. For the simulation of each element, periodic boundary conditions (PBCs) are implemented at both x and y directions, whereas two periodic ports (in which the lower one is the excitation port) are set along the z axis. While for the designed metalens, perfectly matched layers (PML) are set around the model, and the background scattered electric field with the propagation along the z direction acts as the excitation source. The optical constants of GSST films show wavelength-dependent features and can be referenced from the experimental data in ref. 26, While the refractive index of CaF2 is set to 1.47. A prototype of our metalens can be realized by patterning the thermally evaporated GSST films on a CaF2 substrate using electron beam lithography (EBL) and standard plasma etching.
Figures 1(c) and 1(d) illustrate the simulated transmission spectra and propagation phase of light at the operation wavelength of 4200 nm versus the length a varying from 860 to 2900 nm for two constituent elements R0 and R90. Herein, R0 refers to the scenario that the length a is parallel to the x axis, while R90 refers to the scenario that the length a is parallel to the y axis by rotating 90 degrees anticlockwise in the x-y plane. Note that the circularly polarized waves are illuminated from the substrate side and propagate in the z direction, and the transmission spectra and propagation phase are probed for the output light with the opposite spin states from the other side of the structure. From the simulation results, one can see that the unit molecule arranged in either R0 or R90 offers the same phase profile for a given circular polarization, and a 90-degree rotation imparts a π phase shift without affecting the transmission spectra/dispersions. All these confirm the results predicted by Eq. (2). 30 meta-atoms are selected to achieve 2π full-phase coverage while maintaining the efficient transmittance. Notably, about half of the selected 30 meta-atoms are freedodistributed in R0 phase spectrum, and the rest in the R90 phase spectrum, which is fundamental to allow for better implementation of the polarization-insensitive metalens.
3. Results and discussions
With the above strategy, we construct a prototype ultra-thin transmissive metalens using anisotropic nanofins as building blocks and simulate its focusing performance. The designed metalens has a high NA up to 0.669, a focal length of 100 μm and a radius of 90 μm. Figure 2(a) shows the simulated focal spot intensity (|E|2) profiles under normal RCP incidence at x–z plane, verifying that the designed metalens can efficiently focus the transmissive light at the position of z = 102 μm. The negligible discrepancy between the preset focal length (f = 100 μm) and the simulated one (f = 102 μm, shown in Fig. 2(b)) is primarily attributed to the relatively small Fresnel number of the diffractive lens [34]. The corresponding E-field intensity profiles of the focal spot on the focal plane at z = 102 μm is shown in Fig. 2(c). The central lobe possesses a dazzlingly higher intensity than the sidelobes and the full width at half-maximum (FWHM) of the focal spot is about 3000 nm (0.714λ0), indicating a subwavelength focal spot of our designed metalens.
Fig. 2. Simulated focusing responses for the metalens at different linearly and circularly polarized incidence. (a) Simulated E-field intensity profiles for the metalens with a preset focal length f = 100 μm on the x-z plane (at y = 0 μm) upon normally incident RCP light at λ0 = 4200 nm. The simulated focal length is 102 μm. (b) The extracted E-field intensity profiles of the metalens along the z-axis (white lines). (c) The corresponding E-field intensity profiles of the metalens on the focal plane along the x-axis at z = 102 μm (red lines). (d) Peak intensity (red) and FWHM (blue) of the focusing spot on the focal plane at different linearly polarized incident angles in the range of [0°, 180°] with an interval of 5°. The Abbe diffraction limit is denoted by the dashed pink line. The corresponding focusing characteristics of the design under circularly polarized (LCP and RCP) beams are also plotted in (d). (e) Focusing efficiencies of the metalens as a function of linearly polarized incident angles in steps of 5°. The insets shows the focal spot profile of the metalens under the typical linearly and circularly polarized light. The illumination light wavelength is 4200 nm. For all polarizations, the focusing efficiency is maintained at a relatively constant value (around 70%), which is indicative of polarization independence.
To verify the polarization-insensitive performance of the designed metalens, Fig. 2(d) plots the focal spot peak intensity (red) and FWHM (blue) of the focusing spot on the focal plane at different linearly polarized angles in the range of [0°, 180°] with an interval of 5°. The Abbe diffraction limit is also denoted by the dashed pink line for reference. It is seen that for linearly polarized beams with arbitrary polarizations, the peak intensity shows a fluctuation between 12 and 24 corresponding to the cases of x-polarized and y-polarized light, respectively. It is probably due to the relatively higher transmittance of the constituent elements of the metalens under y-polarized incidence. The focal spot FWHM remains almost unchanged with the values about 0.7λ0 at different linearly polarized angles and are all below their corresponding Abbe diffraction limits of 0.747λ0 ($\frac{{{\lambda _0}}}{{2NA}}$), which is very important for high-performance imaging systems. Notably, the corresponding focusing characteristics (the focal spot peak intensity and FWHM) of the metalens under LCP and RCP light are also investigated and can be visualized in Fig. 2(d). The focal spot size is also below the diffraction limit, while the focal spot peak intensity jumps to 36, the sum of the ones under x-polarized and y-polarized light. This is because the electric intensity of any circularly polarized light can be regarded as the algebraic superposition of the electric intensities under the corresponding x- and y-polarized incident component light. Figure 2(e) shows the simulated focusing efficiency versus the polarization angle of linearly polarized incident light in steps of 5° for the designed metalens. Similarly, the corresponding focusing efficiency of the metalens under LCP and RCP light are also investigated. The focusing efficiency is defined as the ratio of the transmitted optical power at the focal spot with a width of three times of the FWHM to the entire incident optical power [35]. It can be seen that at the operation wavelength, the focusing efficiency remains a relatively constant value up to 70% across all polarizations. Moreover, the focal spot profiles for different incident polarizations shown in the insets of Fig. 2(e) confirm again that the metalens can focus incident light of any polarization, which is indicative of polarization independence.
Subsequently, we investigate the broadband characteristics of the designed metalens. Figure 3(a) shows the simulated E-field intensity profiles on the x-z plane (at y = 0 μm) for the metalens upon their respective wavelengths in the MIR. One can witness that our design enables the realization of well-focusing response with a small focal length variation (relative to the preset focal length f = 100 μm labelled by the white dashed line) across the wavelength range from 4000 to 4500 nm. To quantitatively characterize its broadband focusing performance, we show the real focal length extracted from the E-field intensity profiles and the focal length shift at different wavelengths, as shown in Fig. 3(b). It is found that the real focal length decreases as the wavelength increases, in agreement with the focusing behavior of the diffractive lens [36]. The focal length shift, derived by subtracting the preset focal length f = 100 μm from the real focal length, exhibits a fluctuation from 0 to 6 across the MIR of 4000 to 4500 nm, which is all below the depth of focus ($\frac{{{\lambda _0}}}{{N{A^2}}}$, shown in Fig. 3(b)), indicating the designed metalens can maintain the elegant focal spot profiles in this wavelength range. Additionally, the wavelength dependence of the peak intensity, FWHM spot size and focusing efficiency of the metalens at its real focal length are presented in Fig. 3(c). It is intuitive that the peak intensity of the focal spot basically shows a downward trend as the wavelength increases. The FWHM spot sizes keep almost unchanged and show a little bit lower than their corresponding diffraction limits, indicating the diffraction-limited focusing of our design across the wavelength range of 4000 to 4500 nm. The simulations also show that our metalens reveals consistently high focusing efficiency above 60% across the designed wavelength range, which is superior or comparable to other previously reported broadband and polarization-insensitive metalenses that function in the transmission mode [17,37,38]. The small efficiency variation may be due to the interference of the focal spot with the scattered light from the co-polarized component in Eq. (2).
Fig. 3. Calculated figures of merits for the metalens on broadband focusing responses. (a) Simulated E-field intensity profiles in the x-z plane corresponding to their respective wavelengths in the MIR (labelled to bottom left corner of plots). (b) The focal length, focal length shift and depth of focus at different wavelengths. The shaded domain indicates the valid focusing band where the focal length shift is modestly lower than the depth of focus. (c) Peak intensity (red) and FWHM (blue) of the focusing spot on the focal plane across the MIR from 3950 to 4500 nm. The corresponding Abbe diffraction limit is denoted by the dashed pink line. Focusing efficiencies of the metalens as a function of the incident wavelength are also plotted (orange).
Far-field optical super-resolution imaging is of great importance for superoscillatory optical devices. However, the current superoscillatory optical devices based on the superoscillatory lens [39,40] or the supercritical lens [41,42] are valid for the normal incident case, inevitably leading to a relatively slow imaging acquisition speed when they are utilized for super-resolution imaging. Metasurfaces offer a unique tool for the flexible manipulation of wavefront, and thus can be optimized for super-resolution purposes with a high NA. In order to verify whether our design can support super-resolution focusing of oblique incident light, Fig. 4(a) gives the simulated E-field intensity profiles in the x-z plane corresponding to their respective incident angles at λ0 = 4200 nm. It is intuitive that all focal spots are basically located at the preset focal position (x = 0, z = 100 μm) within the incident angle range of [0, 2.4°], which can be confirmed by Fig. 4(b). Figure 4(b) shows the incident angle-dependence of displacement of hotspot, which refers to the offset of the focus spot center in the x direction relative to x = 0. When the incident angle exceeds 2.8°, the focus displacement will be close to the FWHM, seriously degrading the focus quality. We also investigate the focus spot peak intensity (red) and FWHM (blue) on the focal plane at different incident angles as shown in Fig. 4(c). It is observed that the peak intensity basically maintains a constant within the concerned incident angle range of [0°, 2.4°], essential for scanning imaging applications. Moreover, the focal spot FWHM remains below the diffraction limit in this regime. The focusing efficiency (orange) of the metalens as a function of the incident angles is also plotted. One can find that the focusing efficiencies weakly change with the varied incident angles.
Fig. 4. Simulated results for super-resolution focusing of the metalens under oblique incident light. (a) Simulated E-field intensity profiles in the x-z plane corresponding to their respective incident angles at λ0 = 4200 nm (labelled to top right corner of plots). (b) The incident angle-dependence of displacement of hotspot. The red dashed line denotes the location of the incident angle of 2.8°. (c) The focus spot peak intensity (red) and FWHM (blue) on the focal plane at different incident angles. The corresponding focusing efficiency (orange) of the metalens as a function of the incident angles is also plotted.
The phase transformation of special materials, referred to GSST herein, often imparts the reconfigurable metasurface with unprecedented capabilities, rendering it a good platform of multifunctional and versatile optics. Following this thinking, we eventually evaluate the focusing response of our metalens when the amorphous GSST is transformed into the crystalline GSST at three representative wavelengths, as shown in Fig. 5(a). As expected, the focal spot on the focal plane at z = 102 μm becomes completely dimmed when aGSST is transformed into cGSST at the operation wavelength of λ0 = 4200 nm, which is more intuitive by comparing the E-field intensity profiles of the aGSST-based and cGSST-based metalenses on the focal plane along the x axis at z = 102 μm (shown in Fig. 5(c)). We can attribute it to the significant changes of phase dispersion of metasurface units [43]. While at the wavelength of λ = 4700 nm, the bright focal spot reappears on the focal plane, just as the scenario of metalens with aGSST at the operation wavelength of λ0 = 4200 nm. Notably, the focal length becomes shorter, approximately 90 μm. To reveal the underlying mechanism, we investigate the transmission phase spectra of 30 constituent elements that construct our metalens at λ = 4700 nm, as shown in Fig. 5(d), wherein the required phase at each location is calculated by Eq. (1), and the realized one refers to the actually optimized phase. The two phases are for the case of our metalens with a focal length f = 90 μm. It is seen that the two phase spectra almost completely coincide with each other, which is the basis for the design to achieve elegant focusing at λ = 4700 nm. Quite strikingly, at the wavelength of λ = 4000 nm, our metalens can unexpectedly work well (both f = 104 μm) both in the reflection and transmission modes simultaneously, which is reflected in Fig. 5(a). The corresponding reflection phase spectra of 30 constituent elements at λ = 4000 nm in Fig. 5(b) show that the realized phases basically agree with the required ones at all locations, clarifying the reason for perfect reflection focusing. Note that the transmission phase spectra of 30 constituent elements at λ = 4000 nm is not given here, since it is similar to the case in Fig. 5(d). To the best of our knowledge, this is the first single-layer metalens that works well both in the reflection and transmission modes simultaneously at a single wavelength, which undoubtedly expands the flexibility and diversity of the designed functionalities.
Fig. 5. GSST states-dependence focusing responses of the metalenses. (a) Simulated E-field intensity profiles in the x-z plane within the whole simulation domain corresponding to their respective wavelengths of λ = 4000, 4200 and 4700 nm (labelled to bottom left corner of plots) when aGSST is transformed into cGSST, respectively. The white arrow represents the direction of light incidence. The realized (red) and theoretically required phases (blue) for our metalens with cGSST at λ = 4000 nm (b) and λ = 4700 nm (d), respectively. (c) The extracted E-field intensity profile of the cGSST-based metalens on the focal plane at z = 102 μm. The corresponding one of the metalens with the aGSST on the focal plane at z = 102 μm is also provided as comparison.
4. Conclusion
In summary, we have theoretically demonstrated full-polarization, switchable and dual-mode focusing functionalities assisted by Ge2Sb2Se4Te1-based metasurface designs. The design is composed of 30 anisotropic nanostructures, which allow for a more accurate implementation of 2π full-phase coverage by rotating 90 degrees, and thus guarantee the realization of a full-polarization and diffraction-limited metalens. As a demonstration, our metalens based on aGSST is designed with a high NA up to 0.669. We demonstrate that the design can work well in the transmission mode with polarization-independent focusing efficiencies up to 60% as well as continuously support a near-constant focal length (the focal length shift less than 6%) and diffraction-limited focal spots over λ = 4000–4500 nm. Meanwhile, the proposed metalens can focus the oblique incident light at λ0 = 4200 nm within an incident angle range of [−2.4°, +2.4°], providing a FOV of 4.8°. Quite strikingly, a plethora of extraordinary sights occurs as the amorphous Ge2Sb2Se4Te1 is converted into the crystalline state. First, the focal spot on the focal plane at λ0 = 4200 nm becomes completely dimmed due to the significant changes of phase dispersion of metasurface units. Secondly, at the wavelength of λ = 4700 nm, the bright focal spot reappears on the focal plane. Thirdly, our metalens can unexpectedly work well (both f = 104 μm) both in the reflection and transmission modes simultaneously at the wavelength of λ = 4000 nm owing to phase matching conditions. We envision that this work with ease-of-fabrication, low-cost and mass-production advantages will stimulate creation of ultracompact flat photonic elements for vigorous manipulation of structured beams and further boost its potential applications, such as optical imaging, optical encryption and augmented reality.
Funding
National Natural Science Foundation of China (12004347, 61704156); Chinese Aeronautical Establishment (2019ZF055002, 2020Z073055002); Scientific and Technological Project in Henan Province (202102310535, 212102310255); Key Scientific Research Project of Colleges and Universities in Henan Province (20B140017); Natural Science Foundation of Henan Province (212300410414).
Acknowledgments
J. Xu thanks X. Tian and Prof. Z.-Y. Li for their guidance and suggestions for this work.
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.
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