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Abstract
Metalenses can potentially reduce the size and complexity of existing cameras, displays, and other optical devices, owing to their capability of flexible manipulation of the polarization, amplitude, and phase of light. However, metalenses capable of maintaining polarization and broadband wavefront shaping under arbitrarily polarized excitation have not been studied. In this study, we present the first demonstration of a biomimetic moth-eye-shaped metalens for polarization-maintaining, broadband and angle-insensitive focusing under an arbitrarily polarized excitation in the mid-infrared waveband (3.1–8.0 µm). Modulation and focusing efficiencies of 92% and 90%, respectively, were achieved. Moreover, a bifocal moth-eye-shaped metalens operating at normal and oblique incidences was realized. Compared to previously reported metalenses, the one proposed in this study exhibited a better focusing under oblique incidence, ensuring light transmission as effectively as a traditional lens. This study paves the way for the development of polarization-maintaining, broadband, and angle-insensitive microscale optical devices and imaging systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces are a promising platform for integrated optical devices owing to their planarized structures and unprecedented capabilities to manipulate polarization, amplitude, and phase of light [1–4]. Metalenses are microscale imaging devices based on metasurfaces [5–11]. Compared to the bulky traditional optical lenses, metalenses have the advantages of planarized structures, small size, cost efficiency, and easy integration. Therefore, metalenses can reduce the size and complexity of existing cameras, displays, and other optical devices. They also have broad application prospects in augmented reality, virtual reality, medicine, and others [12–16]. The working mechanism of a metalens is based on three types of phase control schemes and their combinations, i.e., the Pancharatnam–Berry (PB) phase [17–19], resonant phase [20,21], and propagation phase [22,23]. The PB phase scheme is simple and robust against fabrication errors; however, this scheme only works on circularly polarized light and outputs light with opposite circular polarization [19,24]. The resonant phase scheme can modulate the multi-dimensional phase and amplitude; however, it works only on linearly polarized light and outputs cross-polarized light [25,26]. The propagation phase scheme has the potential for broadband modulation owing to the dependence of phase on optical path difference; however, the polarization property of its output has not been studied [27–29]. Polarization is crucial for several optical applications, i.e. nanograting fabrication and molecular alignment, owing to the polarization sensitivity of the material [30–32]. Therefore, exploring polarization-maintaining and broadband wavefront shaping under arbitrarily polarized excitation is of significant interest.
Mid-infrared (MIR) waveband (3.1–8.0 µm) covers the transparent area of the atmospheric window and the characteristic fingerprint spectroscopy of most molecules of the chemical compounds [33]. It exhibits considerable application potential in biosensing [34], high-precision thermal imaging [35], and molecular detection [36]. However, there are relatively few microstructures used for constructing MIR broadband metalenses [37–39]. Hence, exploring new microstructures for building MIR metalenses is of significant interest. In nature, moth eyes have a very fine micro/nanostructure with an anti-reflection function [40]. Inspired by the moth-eye structure, researchers have developed various anti-reflective coatings, sensors, and microlenses [41–45]. In the MIR region, dielectric As2Se3 has high transmittance and refractive index (2.88) and relatively low material hardness [46,47]; thus, dielectric As2Se3 film is suitable for constructing MIR metalenses. Therefore, we designed a MIR moth-eye-shaped polarization-maintaining and broadband focusing As2Se3 metalens using the propagation phase scheme.
This study, for the first time, demonstrates MIR biomimetic moth-eye-shaped metalens for polarization maintenance and broadband focusing under excitation with arbitrary polarization such as linear, circular, and elliptical polarizations. The moth-eye antenna arrays function as an efficient phase modulator, exhibiting high modulation and focusing efficiencies of 92% and 90%, respectively, at a wavelength of 5.1 µm. Moreover, a bifocal moth-eye-shaped metalens operating at both normal and oblique incidences is realized. Compared with previously reported metalenses, the moth-eye-shaped metalens exhibits better focusing at oblique incidence. This study investigates the polarization-maintaining, broadband, and angle-insensitive focusing of the proposed metalens in detail. To a significant extent, these properties guarantee that the moth-eye-shaped metalens transmits light as effectively as the traditional lens. This study provides insights into improving metalens technology and paves the way for the development of polarization-maintaining, broadband focusing, and angle-insensitive microscale optical devices and imaging systems.
2. Theoretical analysis
The design of moth-eye-shaped polarization-maintaining metalens is illustrated in Fig. 1. As shown in Fig. 1(a) (up), the polarization state of the output light remains consistent with that of the incident light when light with an arbitrary polarization state is incident on the metalens. Meanwhile, the wavefront of the output light is modulated by the metalens and exhibits a focusing effect. Each pixel of the metalens, having dimensions 2.4 µm × 2.4 µm, consists of a moth-eye antenna and a MgF2 substrate, as shown in Fig. 1(a) (bottom). The structural parameters of the moth-eye antenna are as follows: the bottom diameter, D; height, H; and period, P. The parameters are discussed in Section S1 and Fig. S1 (Supporting Information).
Fig. 1. Design of biomimetic moth-eye-shaped polarization-maintaining metalens at a wavelength of 5.1µm. (a) The concept of moth-eye-shaped polarization-maintaining metalens. (Up) Schematic illustration of wavefront focusing that maintains polarization. (Bottom) Each pixel of the metalens consists of a moth-eye antenna and a MgF2 substrate. (b, c) The amplitude and phase of the transmitted electric field versus bottom diameter (D) and height (H) for the x-polarized incident light. The dashed line is the contour line with an amplitude of 1.0. The circles on the contour line indicate the parameters of the antennas providing discrete phases of 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, and 7π/4. (d) Shapes of eight basic moth-eye antennas providing a constant amplitude of 1.0 and discrete phases of 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, and 7π/4. (e) The amplitude and phase of the transmitted electric field as a function of the bottom diameter (D) when the height is 3.7 µm.
Considering the x-polarized incident light at a wavelength of 5.1 µm an example, a full-wave simulation of the transmitted electric field at the top surface of each moth-eye antenna was performed using the finite element method with COMSOL Multiphysics software. Figures 1(b) and 1(c) show the amplitude and phase of the output electric field as a function of bottom diameter (D) and height (H). When the height is 3.7 µm, the amplitude is approximately equal to 1.0, as shown by the dashed line in Fig. 1(b). The dashed line in Fig. 1(c) indicates the antenna parameter that provides a phase modulation in the range 0–2π while keeping the amplitude constant at 1.0. The moth-eyed antennas depicted as circles on the amplitude contour line provide eight discrete phases, namely 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, and 7π/4. The shapes of these eight basic moth-eye antennas are shown in Fig. 1(d), and the detailed structural parameters are listed in Table S1 (Supporting Information). The amplitude and phase of the transmitted electric field as a function of the bottom diameter at the height of 3.7 µm is shown in Fig. 1(e). Phase modulation occurs during light propagation inside the moth-eye antenna due to the phase accumulation arising from the wave-guiding effect. Herein we fixed the height to 3.7 µm; however, the bottom diameter as the critical parameter for designing phase retardation was varied to obtain the full phase modulation from 0 to 2π.
3. Results and discussion
The output electric fields of these eight basic moth-eye antennas are shown in Fig. S2 (Supporting Information). The Stokes parameters (I, Q, U, and V) were calculated to describe the polarization state of the output electric field under an x-polarized excitation at a wavelength of 5.1 µm. The degree of polarization (DOP), P, can be calculated as $P\textrm{ = }{{\sqrt {{Q^2} + {U^2} + {V^2}} } / I}$, where I = 1 is the normalized total electric field intensity, Q is the light component along the x-polarization direction, U is the light component polarized at an angle of 45° to the x-axis, and V is the right circularly polarized light component. The parameters Q, U, V, and P are shown in Fig. 2(a). The DOP value (P = 1) indicates the complete polarization of the output field. Therefore, the total output electric field can be divided into x- and y-polarized components. The averaged amplitude (brown) and phase (blue) of the x- (bold) and y-polarized (thin) components are plotted in Fig. 2(b). The component of y-polarized electric field is zero, as shown by the thin brown line in the figure. The bold blue line shows that these eight basic antennas provide full-phase modulation of the emitted x-polarized (the same polarization as the incident field) electric field. Here, we define the modulation efficiency as the ratio between integral of polarization-maintaining (x-polarized in this case) electric field intensity and the total electric field intensity, i.e.,
Fig. 2. Polarization-maintaining property of the beam deflector constructed with the eight basic moth-eye antennas. (a) The Stokes parameters of the output electric field from the eight basic moth-eye antennas. (b) Comparing the amplitude (brown) and the phase (blue) of the x-(bold) and y-polarized (thin) output electric fields obtained from the eight basic moth-eye antennas. (c) Schematic illustration of the beam deflector composed of the eight basic moth-eye antennas. (d, e) Comparison between the x- (d) and y-polarized (e) output electric fields obtained from the beam deflector under x-polarized excitation.
To verify the phase modulation and the polarization-maintaining properties of moth-eye antennas, arrays of the eight basic moth-eye antennas arranged in a line were constructed using the COMSOL Multiphysics software, as shown in Fig. 2(c). These eight basic moth-eye antennas that provide phases in the range of 0 – 2π were used to construct a beam deflector for beam navigation at an angle of 15.4°. We performed full-wave simulations of the output electric field under x-polarized excitation at normal incidence from the MgF2 substrate using the finite element method. The x-polarized output electric field was extracted and is shown in Fig. 2(d). The numerically calculated external angle is 15°, and this value agrees with the theoretical value, confirming the phase modulation. For comparison, the y-polarized output electric field was also extracted, as shown in Fig. 2(e). Figure 2(e) shows the zero component of y-polarized output electric field. Combining the value of DOP (P = 1) and the zero component of y-polarized output electric field, we conclude that the output electric field is x-polarized, consistent with the polarization state of the incident light. Thus, the apparent polarization-maintaining property and the 100% modulation efficiency were proved.
After verifying the moth-eye antennas’ phase modulation and polarization-maintaining properties, we used these antennas to construct the metalens. To generate the desired focusing, the required phase, φ (x,y), can be written as follows:
Fig. 3. Focusing demonstration under arbitrarily polarized excitation. (a) Phase distribution that produces focusing at a distance of 100 µm. (b) The designed metalens and an expanded view of the moth-eye antenna arrays in the marked area. (c) Output electric field under x-polarized excitation. (Upper left) Output electric field intensity evolution along the z-axis. (Bottom row) The x- and y-polarized electric field intensity distributions at the output surface. (Upper right) The output electric field intensity distribution at the focal plane (z = 100 µm). (d) Output electric field intensity evolution under different polarized excitations, such as linearly polarized lights with polarization angles of 30° (LP_30), 60° (LP_60), and 90° (LP_90) to the x-axis, and right circularly polarized (RCP), left circularly polarized (LCP), right elliptically polarized (REP), and left elliptically polarized (LEP) lights.
The output electric field under the x-polarized excitation was numerically calculated using finite-difference time-domain (FDTD) simulation software. The intensity evolution along the z-axis is shown on the left side of the first row in Fig. 3(c), and the green line represents the intensity distribution at y = 0 µm. The second row in Fig. 3(c) shows the x- and y-polarized electric field intensity distributions at the metalens output surface. Using Eq. (1) and the x- and y-polarized electric field intensity distributions, the modulation efficiency was determined to be 92%, lower than the theoretical value of 100%. This is because of the structural error introduced during the construction of metalens. The electric field intensity distribution at the focal plane (z = 100 µm) is shown on the right side of the first row, where green lines show the intensity distributions at x = 0 µm and y = 0 µm. With the two green lines, we calculated the full width at half maximum (FWHM), approximately 4.8 µm (0.94 λ). We define the focusing efficiency as the ratio of the integral of electric field intensity in the area with diameter D2 at the focal plane and diameter D1 at the output surface, which can be written as follows:
Undifferentiated focusing under arbitrarily polarized excitation is shown in Fig. 3(d). The first three columns represent the output electric field intensity evolution under three different linearly polarized (LP) excitations. The corresponding polarization angles with respect to the x-axis are 30° (LP_30), 60° (LP_60), and 90° (LP_90). The fourth and fifth columns represent the output intensity evolution under right circularly polarized (RCP) and left circularly polarized (LCP) excitations, respectively. The sixth and seventh columns represent the output intensity evolution under right elliptically polarized (REP) and left elliptically polarized (LEP) excitations, respectively. Note that the REP and LEP excitations discussed in this work comprise two vertical waves with an amplitude ratio of 1:2. The insets in Fig. 3(d) show the corresponding electric field intensity distributions at the focal plane. The modulation and the focusing efficiencies are independent of the incident polarization, shown in Fig. S3 (Supporting Information). The polarization properties of the output electric field under different polarized excitations were also studied. The calculated Stokes parameters (I, Q, U, and V) of the output electric field from the eight basic moth-eye antennas under different polarized excitations are presented in Fig. S4 (Supporting Information). We divided the output electric field from the eight basic moth-eye antennas into two components, i.e., the electric field with polarization consistent with the incident polarization and the one with polarization different from the incident polarization. The numerically evaluated amplitudes and phases of these two components are shown in Fig. S5 (Supporting Information). The zero component of output electric field with polarization different from the incident polarization demonstrates that the moth-eye-shaped metalens maintains polarization under arbitrarily polarized excitation.
To verify the broadband focusing property, we scanned the transmission spectrum of the moth-eye antennas under x-polarized excitation. The transmission spectra from No. 1, No. 4, and No. 8 basic moth-eye antennas are shown in Fig. 4(a). The sharp drop in amplitude can be attributed to the narrow-band reflection characteristics of the waveguide grating structure. This sharp drop in amplitude can be suppressed by further optimizing the period, D, H, and radius of curvature of the moth-eye antenna. The corresponding reflection spectra are shown in Fig. S6 (Supporting Information). Using the previously constructed metalens shown in Fig. 3(b), we calculated the output electric field intensity evolution under the x-polarized excitation with different wavelengths, such as 3.1, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, and 8.0 µm, as shown in Fig. 4(b). Although the focusing intensities at the short and long wavelengths are smaller than those at the intermediate wavelengths, clear focusing is observed at the MIR waveband at 3.1–8.0 µm. The numerically calculated amplitude transmission spectrum of the moth-eye-shaped metalens is shown in Fig. S7 (Supporting Information). The focal length and FWHM of each focal spot at different wavelengths are shown in Fig. S8 (Supporting Information). The electric field intensity distributions at the output surface of the metalens, and at the focal plane, under different incident wavelengths, can be seen in Visualization 1. We calculated the dependence of modulation and focusing efficiencies on the wavelength to quantify the effect of wavelength on the efficiencies (Fig. 4(c)). The averaged modulation efficiency is approximately 94% at the MIR waveband ranging from 3.1 µm to 8.0 µm. The maximum focusing efficiency at the wavelengths of 5.0 µm and 5.1 µm reaches 90%.
Fig. 4. Broadband focusing property of the moth-eye-shaped metalens. (a) Transmission spectra obtained from moth-eye antennas No. 1, No. 4, and No. 8. (b) Output electric field intensity evolution under the x-polarized excitation with different wavelengths, such as 3.1, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, and 8.0 µm. (c) Dependence of modulation (blue) and focusing (brown) efficiencies on wavelength.
Focusing demonstration of the bifocal moth-eye-shaped metalens under normal and oblique incidences is shown in Fig. 5. The phase distribution of the bifocal metalens (focusing at 100 µm and 200 µm) was calculated using computer-generated holography (CGH) at a wavelength of 5.1 µm, as shown in Fig. 5(a). The calculated output electric field intensity evolution under x-polarized excitation at normal incidence is shown in Fig. 5(b). Two focal spots at 100 µm and 200 µm are clearly visible, consistent with the theoretical design. The green line shows the intensity distribution at y = 0 µm. The intensity ratio of the two focal spots can be controlled by changing the weight of the phase for focusing at different distances through CGH. Figure 5(c) shows the corresponding electric field intensity distribution at the two focal planes (z = 100 µm and z = 200 µm). The green lines represent the intensity distributions at x = 0 µm and y = 0 µm, respectively. The x- and y-polarized electric field intensity distributions at the output surface of the metalens are shown in Fig. 5(d). We calculated the output electric field intensity evolution under the x-polarized excitation at different incident angles to study the influence of incident angle on the focusing. The tilted focusing at the incident angles of 10° and 30° are shown in Figs. 5(e) and 5(f), respectively. The well-focusing under different incident angles demonstrates that the moth-eye-shaped metalens has angle-insensitive property, i.e., focusing is independent of the incident angle.
Fig. 5. Focusing demonstration of the bifocal moth-eye-shaped metalens under normal and oblique incidences. (a) Phase distribution for double-focusing at 100 µm and 200 µm. (b–d) Double-focusing under normal incidence. (b) Output electric field intensity evolution. The green line represents the electric field intensity at y = 0 µm. (c) Electric field intensity distributions at the focal planes (100 µm and 200 µm). The green lines represent the intensity distributions at x = 0 µm and y = 0 µm. (d) Distributions of x- and y-polarized electric field intensities at the output surface of metalens. (e, f) Double-focusing under the oblique incidence. Output electric field intensity evolution under x-polarized excitation at the incident angles of (e) 10° and (f) 30°.
The moth-eye-shaped metalens demonstrated in this study was compared with previously reported metalenses [28,29] to evaluate its advantages, and the results are shown in Fig. 6. Three types of metalenses, namely moth-eye-shaped, cylindrical, and cuboidal, were constructed with the phase distribution shown in Fig. 3(a). Considering an oblique incidence of 30° as an example, the output electric field intensity evolutions under the x-polarized excitation at a wavelength of 5.1 µm were calculated using the FDTD simulation software. A schematic diagram of the moth-eye antenna, the structural parameters (D, H) offering eight discrete phases (0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, and 7π/4) and the output electric field intensity evolution from the moth-eye-shaped metalens are presented in Fig. 6(a); the same for the cylindrical and cuboidal metalenses are shown in Figs. 6(b) and 6(c), respectively. To better show the advantages of the proposed moth-eye-shaped metalens, the normalized focusing efficiency and FWHM at the focal plane are presented in Fig. 6(d). Specifically, Fig.6d (Left) presents the intensity distributions on the green dotted lines at the focal plane in Figs. 6(a)–6(c). With the intensity distributions at the focal plane, the normalized focusing efficiency and FWHM of moth-eye-shaped, cylindrical, and cuboidal metalenses are shown in Fig.6d (Right). These focusing results demonstrate that, under oblique incidence, the moth-eye-shaped metalens is superior to other reported metalenses.
Fig. 6. Comparing the moth-eye-shaped metalens designed in this study and the previously reported metalenses [28,29] under an oblique incidence. (a) Structural parameters of eight basic moth-eye antennas providing eight discrete phases, and the focusing result with the moth-eye-shaped metalens. (b) Structural parameters of the eight basic cylindrical antennas providing eight discrete phases and the focusing result with cylindrical metalens. (c) Structural parameters of the eight basic cuboid antennas providing eight discrete phases and the focusing result with cuboidal metalens. (d) Demonstration of focusing efficiency and FWHM.
4. Conclusion
We proposed and demonstrated a biomimetic moth-eye-shaped metalens for polarization-maintaining, broadband focusing, and angle-insensitive focusing under arbitrarily polarized excitation. The proposed metalens comprises moth-eye-shaped As2Se3 antennas and can be operated at the MIR waveband ranging from 3.1 µm to 8.0 µm. Modulation and focusing efficiencies of 92% and 90%, respectively, were achieved by the moth-eye-shaped metalens. Moreover, a bifocal moth-eye-shaped metalens working at normal and oblique incidences was realized. The biomimetic moth-eye-shaped metalens exhibited better focusing under an oblique incidence than previously reported metalenses. The proposed metalens maintaining polarization, shaping broadband, and shaping angle-insensitive wavefront under arbitrarily polarized excitation offers a new possibility for ultracompact optical devices and imaging systems. This metalens has great potential applications in miniaturized night vision, biosensing, and multispectral imaging.
Funding
Joint Funds of the National Natural Science Foundation of China (U21A2056); National Natural Science Foundation of China (62105171); National Natural Science Foundation of China (62105172); the Key R&D program of Zhejiang Province (2021C01025); K. C. Wong Magna Fund in Ningbo University.
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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.
Supplemental document
See Supplement 1 for supporting content.
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