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Abstract
A compact, flat lens with dynamically tunable focal length will be an essential component in advanced reconfigurable optical systems. One approach to realize a flat tunable lens is by utilizing metasurfaces, which are two-dimensional nanostructures capable of tailoring the wavefront of incident light. When a metasurface with a hyperboloidal phase profile, i.e., a metalens, is fabricated on a substrate that can be actuated, its focal length can be adjusted dynamically. Here, we design and realize the first reflection type, tunable metalens (i.e., metamirror) operating in the visible regime (670 nm). It is shown that the focal length can be continuously adjusted by up to 45% with a 0% to 20% lateral stretching of the substrate, while maintaining diffraction-limited focusing and high focusing efficiency. Our design as a flat optics element has potential in widespread applications, such as wearable mixed reality systems, biomedical instruments and integrated optics devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Unlike conventional optical components, which often present physical obstructions to the miniaturization of optoelectronic devices, the control of light using flat optics has attracted much recent attention due to unique technological opportunities presented by these devices. For example, optical metasurfaces, which are composed of rationally designed nanostructures, are proposed to replace some of the conventional optical elements given their compact size and more importantly, the ability to produce spatially varying phase change (i.e. wavefront reshaping), amplitude modulation and polarization conversion of incident light over subwavelength dimensions [1–5]. Based on these properties, several compact and flat optical elements have been demonstrated, such as refractive/diffractive gratings [6–8], waveplates [9,10], vortex-beam generators [11,12] and meta-holograms [13–16]. Planar lenses [17–23] based on metasurfaces, also referred to as metalenses, exhibit a number of advantages over their conventional counterparts not only in terms of size and weight, but also in creating cost-effective high numerical aperture [22,23], achromatic [18,24], multifunctional [21,25] and flexible lenses [19,20].
Furthermore, provided the two-dimensional nature of metasurfaces, they may be integrated with dynamic components (e.g. elastomers, semiconductors, graphene, liquid crystal, phase change materials, etc.) for designing active devices, such as frequency-tunable metasurfaces [26–36], electrically tunable modulators [37–39], beam steering devices [40–43] and holograms [44,45]. Among the above active devices, transmissive tunable metalenses based on dynamic components have been demonstrated recently, including electrically-tunable metalenses [46–48], phase-change material based metalens [49], elastic metalenses [50–52] and Alvarez lens [53]. Despite their great success, all reported tunable metalenses work in transmission configuration, except one MEMS-integrated metalens capable of dynamic beam steering at mid-infrared [54]. A reflection type, tunable metalens working in the visible which will find application in wearable augmented reality (AR)/virtual reality (VR) hardware among other applications, has not yet been reported. Here, as a proof of concept, we develop a mechanically tunable, reflection type metalens (i.e., metamirror) working in the visible (i.e. operating at the free-space wavelength of 670 nm), based on an ultrathin (i.e. ~λ/4 thick), gradient metasurface encapsulated in an elastic polymer. The focal length of the metamirror can be continuously changed by stretching the flexible substrate.
2. Structural design
The major challenge in our design is combining the metamirror, which is based on a gradient metasurface, with a stretchable substrate since the gradient metasurface relies on a continuous metallic ground plane. Critical to the success of our implementation is the ground plane sectioning that facilitates stretching without sacrificing the requisite electromagnetic resonance. Here, we utilize the isolated gap surface plasmon (GSP) resonator as the constituent element of our metamirror, which features a high reflective localized plasmonic resonance [55]. The working principle of the metamirror is illustrated in Fig. 1(a). The GSP resonators are carefully positioned and encapsulated in a mechanically stretchable polydimethylsiloxane (PDMS) substrate. By assuming that the neighboring resonators have no (or weak) coupling and their local phase discontinuity does not depend on the substrate deformation, a uniform stretching of the flexible substrate changes the relative position of the GSP resonators; as a result, the wavefront of reflected light can be adjusted locally depending on the position of these resonators, and the focal distance of the device can be tuned accordingly. Specifically, to realize a flat metamirror focusing a normally incident plane wave at a focal length f from the lens plane, one must impart the following hyperboloidal phase shift to each element of the metasurface: φ(r) = k0 , where k0 is the free-space wave vector for a fixed wavelength and r is the radial coordinate of the element [1,56]. Considering a stretching ratio of s applied for the element at a radial location r, the hyperboloidal phase profile changes to the form ; meanwhile, we assume that the local phase response of this element does not change upon the substrate stretching. Under the paraxial approximation [57], the focal length is expected to vary quadratically with the stretching ratio: , demonstrating a large focal length tuning range of the metamirror integrated with a flexible substrate [47,50,51].
Fig. 1 The working principle of a reflection type metalens. (a) Schematic illustration of a reflective metasurface encapsulated in a flexible polymer. The metamirror has a lateral size of L along one dimension and it focuses incident light backwards to a focal distance of f from the surface. (b) Illustration of the metamirror’ response after it is stretched by a ratio of s: the focal length of the metamirror under stretching is elongated to f’.
Following the above method, we designed a tunable metamirror using the high-reflective GSP resonators as the building elements for linearly polarized illumination at 670 nm. The schematic of the unit element is shown in Fig. 2(a), which contains an Ag-SiO2-Ag triple layer structure encapsulated in PDMS. The thickness of the top Ag layer, the dielectric layer and the Ag ground plane is 30 nm, 50 nm and 75 nm. The thicknesses for all three layers are determined by optimizing the complex reflection coefficients of the GSP resonator within the parameter space shown in Fig. 2(b). Meanwhile, the total thickness of the GSP resonator is controlled for the ease of pattern transfer during the fabrication process as discussed below. The complex reflection coefficient r = |r|ei∠r of the element unit is evaluated numerically by running a parametric sweep of the lateral dimensions of the stack (ranging from 60 to 300 nm in a step of 4 nm). The lattice pitch is chosen to be 330 nm with no stretching. As shown in Fig. 2(b), a full 2π phase shift is covered within the parameter space (left panel) and except for a narrow region of dimensions (stack width and height <100 nm), a high reflection amplitude (|r| > 80%) of the element unit is maintained (right panel). The unit elements chosen from the parameter space are then arranged periodically to construct a 9.9 × 9.9 μm2 square metamirror with a designed focal length of 3.75 μm (corresponding to a numerical aperture of ~0.8). To mitigate the calculation burden, a moderate-sized metamirror with a large numerical aperture that will yield a shorter focal length was used for the numerical demonstration of focal length tunability. Let us note that the design is scalable for both different pattern sizes and numerical apertures.
Fig. 2 (a) Schematic structure of the unit cell geometry used in our design. The elements are encapsulated in PDMS and are arranged in a square lattice with the pitch fixed at 330 nm. The thickness of the top thin Ag layer, SiO2 spacer and ground Ag layer are 30nm, 50nm and 75 nm, respectively. The top Ag surface is 200 nm below the top PDMS surface. (b) The simulated complex reflection coefficients r = |r|ei∠r for a unit cell under normal incident light (E field along y axis, λ = 670 nm). Left panel: the contour map of reflected phase arg(r) as a function of the nanoantenna lateral dimensions from 60 to 300 nm. Right panel: the contour map of reflectance |r| as a function of the nanoantenna lateral dimensions. (c) Calculated profiles of reflected electric field intensity within the x-z plane. The 0% stretched size of the metamirror is 9.9 × 9.9 μm2. It is located at z = 0 (above the image) and stretched by 0%, 10% and 20% within x-y plane from left to right panels, respectively. The calculated electric field intensity at the focal plane (white dashed lines indicated on the x-z planes) are also shown in the inset of each panel. Scale bar: 1 μm. (d) Electric field intensity distribution along the optical axis under different stretching ratios. (e) Calculated focal lengths of the metamirror (red square) extracted from (d) as a function of the stretching ratio. The predicted focal length is also displayed as the black line. (f) Calculated focusing efficiencies of the metamirror as a function of the stretching ratio.
The flat metamirror device is constructed by discretizing and sampling its hyperboloidal phase profile φ using the above GSP resonators placed at vertices of a square lattice. The GSP resonator geometry at each lattice site is found by minimizing the reflection error between the desired unity-amplitude phase profile eiφ and complex reflection coefficient of the resonator: ΔR = |eiφ-|r|ei∠r|. According to Fig. 2(b), the phase of reflection coefficient ∠r can always be matched to φ: ΔR = |eiφ-|r|ei∠r| ≈(1-|r|)eiφ, so the reflection error is minimized in our algorithm by first finding a group of resonators having the desired phase value and then selecting one with highest reflection amplitude. The performance of the designed metamirror is tested under different stretching ratios from 0 to 10% and 20%. The lattice pitch is linearly scaled with the stretching ratio in both lateral dimensions. The light source is placed in the -z space, injecting a plane wave on the device (at z = 0) along the z direction. As can be seen from Fig. 2(c), the change of reflected light focusing lengths is clearly identified within the longitudinal electric field intensity map (x-z plane). The intensity profile along the optical axis (x = 0) under different stretching ratios is plotted in Fig. 2(d) and the extracted focal lengths summarized in Fig. 2(e). The focal length increases from z = 3.7 μm (no stretch) to z = 4.7 μm (10% stretching ratio) and z = 5.6 μm (20% stretching ratio), respectively, which agrees well with the predicted values by (black line) and confirms a large focal distance tunability of the device. The focusing efficiencies are calculated by the ratio of the power in focus (integrated within the focal plane) to the power of incident plane wave (integrated over the incident plane), as shown in Fig. 2(f). 52% focusing efficiency is obtained for the relaxed state, and it decreases slightly to 47% and 43% with the stretching ratio of 10% and 20%. The tunable range of the metamirror’s focal length can be lengthened upon further stretching the PDMS substrate. However, there is a stretching limit beyond which the metamirror performance may degrade appreciably. According to Seyedeh et al, for a perfect phase reconstruction and the elimination of higher order diffractions, the lattice constant of a metalens or a metamirror under all stretching ratios should remain non-diffractive and satisfies the Nyquist sampling criterion [50]. For the parameters employed in our work, the metamirror can be stretched up to 30% based on the above criterion.
3. Sample fabrication and optical characterization
To verify the above design for wavefront engineering in applications, we fabricate a 100 × 100 μm2 size metamirror on a flexible substrate with a designed focal length of 245 μm (NA ~0.2). The fabrication process is illustrated schematically in Fig. 3(a). We adopted a “lift-off” method developed by Ee et al to obtain the positive patterns encapsulated in PDMS [51]. For the ease of transfer of positive patterns from a handing wafer to the flexible PDMS, we first create an under-cut bilayer resist stack, i.e., negative hydrogen silsesquioxane (HSQ) resist on top of poly(methylmethacrylate) (PMMA) resist, on a 4-inch Si wafer by electron beam lithography followed by O2 plasma etching of PMMA (step i and ii) [58]. Then we deposited Ag (30 nm), SiO2 (50 nm) and Ag (75 nm) layers successively on the bilayer resist stack by e-beam evaporation (step iii). The corresponding structure on Si wafer under optical microscope and scanning electron microscope (SEM) is shown in Figs. 3(b) and 3(c). Note that the bottom PMMA sacrificial layer should be thicker than the total thickness of the deposited triple layer. The PDMS colloid is cast to the pattern by spin coating and then stripped from the Si wafer after it is cured at 85°C for 2 hours (step iv and v). The deposited triple layer stacks on top of HSQ/PMMA pillars are all transferred to the PDMS film, as shown in Fig. 3(d) (optical image taken on PDMS after stripping and flipped over onto a carrier chip), with the complimentary part of deposited stack stays on the Si wafer, as can be seen from the SEM image shown in Fig. 3(e). The O2 plasma etching performed before Ag deposition increases the adhesion of Ag to the Si wafer, which guarantees the successful transfer of the metamirror from the Si wafer to the PDMS film. Besides its ease of fabrication, the Ag nanoantennas are fully embedded in the PDMS film by this technique, making the fabricated metamirror mechanically and chemically robust. A more detailed fabrication process can be found in the Appendix section.
Fig. 3 (a) Schematic illustration showing the fabrication process of the tunable metamirror encapsulated in PDMS (detailed depicted in the text). (b) Optical image of a 100 × 100 μm2 metamirror fabricated on the Si wafer corresponding to step iii (before PDMS casting). (c) An SEM image taken from the same metamirror on the Si wafer corresponding to step iii (before PDMS casting). (d) Optical image of the same metamirror transferred to PDMS film corresponding to step v. (e) An SEM image taken from the complementary structure of the metamirror on the Si wafer after the transfer process. Scale bar for (d) and (e): 1 μm.
We employ an optical setup schematically shown in Fig. 4(a) to test the optical response of the fabricated metamirror. A supercontinuum, intensity-tunable fiber laser (WhiteLase-micro 10-1770 by Fianium) combined with a 670 nm bandpass filter and a beam expander is used as the light source, producing a collimated Gaussian beam through a 10 × microscope objective (Mitutoyo, NA = 0.28, achromatic with a focal length of 200 mm) which focuses the laser beam onto the sample. The reflected focusing beam is collected using the same objective and directed through a beam splitter, a focusing lens and mirrors to a CCD camera (WAT-902B by Watec). An additional white light illumination is used for monitoring the pattern size under stretching. As shown in Fig. 4(b), a custom-built sample holder, which has four self-locking tweezers mounted on identical linear translation stages, is used to hold and stretch the PDMS film. The metamirror pattern, which is monitored by the objective, can be isotopically and uniformly stretched by moving carefully the four tweezers holding the four corners of the PDMS film. The sample holder is installed on a XYZ translation stage with standard micrometers.
Fig. 4 (a) Schematic diagram of the experimental setup for testing the optical response of the fabricated metamirror. (b) Side view and top view of a custom-built sample stage holding the stretched PDMS film. The PDMS film is held by four self-locking tweezer clamps mounted on four linear translation stages. The black dashed box indicates the location of the sample. The amount of isotropic stretching of the metamirror can be monitored during the measurement. (c) Optical microscope images of the metamirror isotropically stretched by 0, 10% and 20%, respectively (left to right). The dashed square shows the outline of the metamirror and the scale bar is 20 μm.
4. Results and discussion
By displacing the fabricated device longitudinally from the objective (twice of the designed focal lengths) [59], we observe that the metamirror focuses incident light similarly to a positive lens. Meanwhile, as the PDMS film is stretched gradually, its focal plane is pushed further away from the metamirror, indicating an increased focal distance. Optical images of the focal plane are captured at different focal distances from the metamirror and are shown in Fig. 5(a) (top to bottom: 0, 10% and 20% stretching ratio). The corresponding cross-sectional line profiles are analyzed and presented in Fig. 5(b). As expected, the extracted full width at half maximum (FWHM) of focal spot increases with the stretching ratio due to a decreased NA of the metamirror. However, the extracted FWHM values (red squares) matches with their diffraction limited values (black line) as a function of the designed numerical aperture: 1.22λ/(2NA), where NA ≈D/2f and D is the metamirror diameter, indicating that the device remains at diffraction limited operation under stretching ratios up to 20%.
Fig. 5 (a) Measured beam intensity profiles taken at their respective focal planes (x-y plane) for different stretching ratios of 0 (top), 10% (middle) and 20% (bottom). Scale bar: 5 μm. (b) Measured FWHM values (red dots) extracted from (a) at the focal plane as a function of the numerical aperture (corresponding to different stretching ratios). The error bars are from a Gaussian fit of the FWHM as a function of the NA. The theoretical diffraction limited spot sizes are also plotted as a comparison (black line). (c) Measured longitudinal beam intensity profiles of the metamirror for stretching ratios of 0 (top), 10% (middle) and 20% (bottom). The metamirror is located at z = 0 (left side of images). (d) Measured focal length (red dots) extracted from (c) and predicted focal lengths of the metamirror (black line) as a function of the stretching ratio. The error bars show ranges of focal distance where the intensity is larger than 90% of the peak value. (e) Measured focusing efficiencies of the metamirror as a function of the stretching ratio.
For a more visible change in focal lengths, the longitudinal profiles of the focused light by the metamirror are reconstructed from images captured across the focal point. As shown in Fig. 5(c), the change in focal length along with the stretching ratio is clearly identified: the focal length of the relaxed metamirror is ∼250 μm, and it gradually increases to ∼304 μm and ∼350 μm under a 10% and 20% isotropic, lateral stretching of the metamirror pattern. All extracted focal distances from experiment, as a function of the stretching ratio, are compared to the predicted values as shown in Fig. 5(d), exhibiting good agreement. We find that the focal length can be restored continuously to its original value (relaxed metamirror) as the stretched PDMS film is released gradually. This confirms the tunability of the metamirror and its mechanical robustness which is essential for practical applications of reconfigurable optical components [50,51].
The focusing efficiency of the fabricated metamirror is also evaluated, as shown in Fig. 5(e), as the ratio of focused optical intensity integrated within the focal plane to the incident optical power on the metamirror. A measured efficiency of 34% is obtained for a relaxed device, which decreases slightly to 31% and 29% for the stretching ratio of 10% and 20%, respectively. The slight decrease of focusing efficiency may reside in the small dependence of the reflection coefficient on the stretching ratio (i.e. element pitch changes under stretching) [50]. The measured efficiencies (~30%) are lower than the numerical values (45%) shown in Fig. 2(f). We attribute the difference between the experimental and simulated results to imperfections of both fabrication and testing. First, since the designed minimum separation between adjacent nanoantennae is small (30 nm), the fabrication imperfections may make separations between antennae even smaller. This effect leads to a stronger near field coupling between antennae [60] and thus greater deviation of phase modulation from the imposed phase profile. Second, in the optical setup, four tweezers were employed to stretch the four corners of the flexible substrate. This configuration may cause the device surface to be slightly textured and not perfectly normal to the incident light beam. Meanwhile, the non-perfect uniform mechanical stretching may lead to the deformation and misalignments of elements. The above reasons together contribute to a decreased performance efficiency of the metamirror.
5. Summary
To summarize, based on the highly-reflective GSP resonators, we demonstrated a reflection type, mechanically tunable, ultrathin flat metasurface capable of dynamically modifying the wavefront of the reflected light. As a proof of concept, the focal length of the demonstrated metamirror can be changed significantly and seamlessly by simply stretching the encapsulating polymer film, which also adds the mechanical and chemical robustness to the device. Although the demonstrated metamirror is designed to work at a single wavelength (670 nm), its functioning realm can be extended to a much broader frequency range (telecom or infrared) by scaling the geometry and choosing proper materials for unit elements. Furthermore, improvement of the metamirror such as chromatic aberration corrections can be applied by combining the current platform with dispersive phase compensation strategy [18,24,61,62] or the spatial multiplexing scheme [20,63,64]. This work opens the possibility of designing reflection type, reconfigurable systems for a variety of applications such as flat optics, optical communications and wearable consumer electronics.
6 Appendices
6.1. Metamirror fabrication process
First, a bilayer resist HSQ/PMMA is applied on a 4-inch wafer by spin coating. The thickness of top negative HSQ layer (Dow Corning XR-1541, 6% in methylisobutylketone) is ~80 nm at 5000 rpm for 1 minute and the bottom PMMA layer (MicroChem, 950K molecular weight, 4% in anisole) ~200 nm at 3000 rpm for 1 minute. The designed metamirror pattern is then exposed on the negative HSQ layer using EBL (JEOL-9500, dose ~1100 μC/cm2 at 100 kV accelerating voltage). The HSQ resist is developed in AZ 300 MIF (2.38% TMAH) for 90 s and rinsed in DI water for 60 s. The metamirror pattern is then transferred to the bottom PMMA layer using O2 plasma etching (South Bay Technology, RIE-2000) for 2 minutes with the pressure 50 mTorr and oxygen plasma energy 50 W. The PMMA pillars underneath the HSQ layer serve as a sacrificial layer for the later transfer of the materials on top of HSQ using PDMS. Then we deposit Ag (30 nm), SiO2 (50 nm) and Ag (75 nm) layers successively on the bilayer resist stack by e-beam evaporation (PVD-75 Lesker, the base vacuum is 6 × 10−7 Torr and evaporation rate is kept at 0.3 Å/s for both Ag and SiO2). After that, the PDMS (silicone elastomer base mixed with curing agent with a ratio of 10:1, Dow SYLGARD) is cast to the Si wafer by spin coating (~1000 rpm for 5 minutes) and then stripped from the Si wafer after it is cured at 85°C for 2 hours.
6.2. Numerical simulation
The results presented in Fig. 2 were calculated using a commercial software package FDTD Solutions (version 8.21.1882) by Lumerical Inc. This package is a finite difference time-domain solver, so the simulation is conducted in time domain, and the frequency domain response is obtained by Fourier transformation. The convergence studies are conducted by reducing the mesh step size and quantifying the convergence level by reading the difference of results after the mesh refinement. In the calculation of both Figs. 2(b) and 2(c), the spatial meshing grid size in x, y, z directions are 5 nm, 5 nm and 3 nm, respectively. Periodic boundary conditions were used in lateral boundaries and perfectly matched layers were used in top and bottom boundaries of the simulation domain. The refractive index of PDMS and SiO2 were set to 1.41 and 1.45, and the permittivity of Ag are from Johnson and Christy’s data [65].
Funding
Army Research Office (W911NF-16-1-0162).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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