Plasmonic Metalens for Narrowband Dual‐Focus Imaging

A new type of metalens with the capability to selectively focus narrowband light is reported at different focal planes depending on polarization. Two zone planes with two different focal lengths are spatially multiplexed and encoded in the subwavelength regime with arrays of orthogonal silver nanostructures, which are designed to exhibit strong wavelength‐ and polarization‐dependent scattering profiles. Using this principle, imaging under white‐light illumination with independent focal planes is experimentally demonstrated for each polarization at the narrowband resonant wavelength. Furthermore, each focal plane can be dynamically controlled with an output polarizer. In contrast to conventional refractive and diffractive optical elements, functional metalenses allow additional control over wavelength and polarization properties of light for a wide range of applications.

A new type of metalens with the capability to selectively focus narrowband light is reported at different focal planes depending on polarization. Two zone planes with two different focal lengths are spatially multiplexed and encoded in the subwavelength regime with arrays of orthogonal silver nanostructures, which are designed to exhibit strong wavelength-and polarization-dependent scattering profiles. Using this principle, imaging under white-light illumination with independent focal planes is experimentally demonstrated for each polarization at the narrowband resonant wavelength. Furthermore, each focal plane can be dynamically controlled with an output polarizer. In contrast to conventional refractive and diffractive optical elements, functional metalenses allow additional control over wavelength and polarization properties of light for a wide range of applications.

Introduction
Diffractive optical elements (DOEs) are versatile components used to generate arbitrary complex wavefronts. [1,2] DOEs have microstructured surfaces-which can be fabricated with monolithic techniques, as opposed to conventional mechanical lens grinding-and through diffraction, can replicate the performance of their refractive counterparts in a highly reduced form factor. DOEs provide optical functionality beyond that which can be achieved with a single refractive element. This includes aberration correction, beam shaping, and multiplexing multiple optical elements-such as multifocus lensing-in single elements. [1,2] As a result, through the hybridization with refractive optics, or by substitution, DOEs offer a broad optical design The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adom.201700811. on polarization. For each type, two different focal length lenses are encoded with orthogonal anisotropic silver nanostructures, which are designed to exhibit specific scattering spectra (reflection response). The resultant nanostructured optical element controls two orthogonal polarizations at the resonant wavelength, reconstructing the respective polarizations at two independent focal planes. The advantage of this type of lens is that two focal points can be activated independently and onaxis. There are a range of applications in which components exhibiting narrowband wavelength and polarization dependent optical modulation in ultrathin form factors is highly desirable including optical disc technologies, laser-based projector systems, and head mounted displays. [1,2]

Operating Principles
A diffractive lens consists of concentric microstructured reliefs in which the principle of diffraction, rather than refraction, is used to focus the light. Two types of structures have shown the capabilities to focus light at a given distance from the diffraction plane: Fresnel zone plates (FZP) and photon sieves (PS). In the case of a FZP, the output corresponds to the constructive interference at the focal point. The diffraction is produced by concentric consecutive rings at the FZP plane. Each ring has a radius given by [23] 4 .
The focal length of the FZP is given by f, n is an integer representing the nth ring boundary from the FZP centre, and λ is the illumination wavelength. Hence a binary FZP uses symmetrical alternating rings (zones), whereby diffraction from the transparent regions interferes, focusing the transmitted light. [1,2] Moreover, ZPs can be simplified with a binary transmittance function-shown in Figure 1a-offering reduced fabrication complexity yet still maintaining a reasonable focusing efficiency. An extension to the FZP is the photon sieve (PS), which is capable of focusing light, through a pinhole modification to the alternating FZP circular rings. [24,25] In practical terms, the transmission regions are replaced with circular apertures located at the same radial distance as the FZP rings. The maximum diameter of a circular aperture, for full packing, is given by The PS has been shown to improve FZP focusing performance and is relatively easier to fabricate than a conventional FZP. [24,25] Nevertheless, in either case, the zones/holes offer no  other functionality other than applying a spatially varying broadband transmittance function to the incident light. By nanostructuring the ZPs, the unique nanoscale light-matter interaction can be utilized to impart customizable scattering profiles over subwavelength dimensions on the lens; specifically, strong wavelength and polarization dependency. This idea is represented by the plasmonic-enhanced metalens in Figure 1b.
Through appropriate design and material choice, the plasmonic resonance-and subsequent scattering spectra-of metallic nanostructures can be tuned. [11] With arrays of tailored scatterers, "surfaces" can be engineered which exhibit a specific spectral and polarization response detectable in the far-field. [5,7,13,26,27] Figure   metallic nanostructure determines the wavelength of operation (scattering cross-section), through localized surface plasmon resonance (LSPR), [12] and its aspect ratio (anisotropy) determines polarization selectivity (spectrally dependent extinction ratio). Figure 2a shows FDTD simulations [22] of the normalized scattering cross-sections for varying length anisotropic nanostructures composed of three different metals (Al/Ag/ Au). Ag is chosen as the material of choice for this work, as a tradeoff between narrow-band optical response in the visible and length required to achieve this output. Specifically, in relation to nanofabrication tolerances, the reproducible resolution of the system means that aspect ratios can be optimized for larger structures, yet a larger structure inevitably induce secondorder LSPRs (such as for Al). [11] Operation in the red (≈650 nm) part of the spectrum is selected for this study. Next, the length of nanostructure identified Figure 2c shows the simulated scattering response, of an anisotropic Ag nanostructure ((50 nm × 50 nm × 160 nm) for different polarization conditions, at a fixed wavelength of 650 nm. Akin to linear polarizers, this response is indicative of a spectrally dependent Malus law, [28] whereby initial intensity is the copolarization state response (LSPR) of the anisotropic structure. Figure 3a,b illustrates the metalens design process. The spatially varying binary transmittance function for each zone plate is calculated, [1,2,24] spatially discretized and sampled with the anisotropic elements. [27,28] For overlapping zone plates, the respective structures are orthogonal and separated by ⪆100 nm to avoid crosstalk. [13] The ZPs are spatially multiplexed, and transverse nanostructures are used as the fundamental scattering element (L = 160 nm) in a 390 nm unit cell, which are designed to give optimal red reflection λ ≈ 650 nm. The two lens types are ≈156 µm in diameter, with designed independent focal lengths of 125 and 250 µm. The fabricated lenses are shown under scanning electron microscope (SEM) in Figure 3c,d at varying magnifications, with indications of varying polarization dependent regions highlighted. A ZP of this nature-composed of functional optical diffractive units (plasmonic scatterers)-has the potential to selectively focus light according to polarization and wavelength. Moreover, spatially multiplexing different ZPs (with varying focal lengths) allows a single ultrathin layer to exhibit multiple focal lengths. It is straightforward to scale these designs for larger focal lengths and operating wavelengths.

Experimental Methodology
80 kV electron beam lithography (EBL) (Nanobeam Ltd., nB-1) is used for the high-resolution patterning of the nanostructures on polished Si-SiO 2 (300 nm). Polymethyl-methacrylate (PMMA) A4 950k positive tone photoresist (baked thickness ≈ 150 nm) is used in combination with EBL exposure conditions: Area dose 20 µC cm −2 and current 5 nA s −1 . Resist development is carried out in a solution of methyl-isobutylketone (MIBK): isopropyl alcohol (IPA) (1:3), for ≈10s. Deposition of Ag(50 nm) is performed using a thermal evaporator at a base pressure ≲1 × 10 −6 mbar. Resist lift-off is carried out in N-methyl-2-pyrrolidone (NMP), at an elevated temperature of 60 °C for 4 h, followed by fresh NMP sonication and IPA rinse. White light optical characterization is performed using an Olympus BX-51 polarizing optical microscope, with halogen bulb light-source, optically attached to an Ocean Optics HR2000+ spectrometer and image sensor on the output arm. A rotating achromatic linear polarizer (analyzer) controls the polarization state reaching the sensor and an aperture stop is used to control the angular distribution of light illuminating the lenses. Alternatively, for single wavelength operation, a red (650 nm) laser diode (5 mW) is used in conjunction with a custom optical cage-mounted set-up, which includes a XYZ translation stage and image sensor. Further details on the optical characterization are included in the Supporting Information. For surface quality inspection, a Carl Zeiss SEM operating at 1-5 keV is used.

Principle Demonstration with Laser Illumination
In order to test the capabilities of the metalens, we simulated the field produced by the different metalenses and then compared with the intensity experimentally measured along the propagation axis. We reduced the complexity of the complete 3D FDTD simulation approach by considering the propagation as a result of interference from an array of spherical scatterers, or Huygens wavelets (each described by exp(ir·K), where r is the position vector and K the wavevector). This simulation only reproduces the propagation of a single polarization, therefore each metalens consisted of two independent simulations for each polarization. Figure 4 shows a comparison between simulated and experimental results of the two metalenses under red laser diode (650 nm) illumination.
The lenses were excited with two orthogonal polarizations and the resultant re-radiated field intensity mapped onto the propagation axis. The mapping was obtained with a microscope focusing at different focal planes; from the lens plane to 300 µm. The two focal planes are ≈125 and ≈250 µm for each orthogonal polarization. The apparent crosstalk shown through simulations in fact arises from further diffraction orders, and not from the unwanted polarization. Experimental measurements also show additional crosstalk, which may arise from fabrication error (reduction of nanostructure anisotropy, hence extinction ratio reduction). Intensity cross-sections through the radial axis are shown in Figure 4a,b(iii). Relatively narrow (≈ 3 µm) FWHMs and large signal-to-noise of the focal point intensity at both polarizations can be observed.

White Light Illumination
Similarly, we studied the performance of both types of metalenses with a white light source. Figure 5 shows the experimental measurements under white light illumination (unpolarized incoherent input) using optical microscopy, for the FZP and PS metalenses. Figure 5b shows the optical reflection spectra of the lens array, with collection spot (from multimode fiber) located at the respective focal spots. The optical response peaks at the target red wavelength (650 nm) for both planes, but the 2nd exhibits reduced peak intensity. With the microscope image plane aligned to the lens plane, varying the analyzer (0°, 45°, 90°) reveals an in-plane color change-shown with both FZP (c) and PS (d). For the two focal planes, 2D intensity maps at the different analyzer states are shown in Figure 5c  in the red part of the spectrum, the red-channel pixel data is extracted for this analysis. Polarization dependent focusing at the two different focal planes is observed, yet there is clear crosstalk between the two orthogonal polarization states. Even though the focusing intensity of the unwanted polarization (at the respective focal plane) are similar between planes, the reduced intensity of designed focus means the extinction between planes is reduced. Similarly to the laser illumination in the previous section, it is difficult to distinguish whether the apparent crosstalk arises from the unwanted polarization or from a different diffraction order of the excited polarization. For the respective polarizations (at each focal plane) both metalenses exhibit peak intensity-to-background intensity ratios of up to ≈10 2 ×, and orthogonal polarization selectivity of up to ≈9×-inferred from the data extracted from Figure 5c,d(ii).  A and T (binary transmittance) at a size of ≈2 mm × 2 mm each. The transparency is placed at the imaging plane for the lenses in the optical microscope (input aperture stop location). Imaging with the metalens is achieved by illuminating the transparency with unpolarized white light and a linear polarizer is added between the metalens and the focal plane to discriminate one of the orthogonal polarizations. It can be observed that the letters appear red in color, due to the scattering cross-sections of the NRs peaking at 650 nm-shown in Figure 5b-hence the dominant color at the focal plane is red.

Imaging
The design of the plasmonic enhanced metalenses can be tailored for any wavelength and polarization state. A number of other DOEs (such as blazed gratings, beam splitters, beam shapers, etc.) may be modified with the methodology outlined here to increase optical functionality, i.e., offer specific wavelength and polarization control. Moreover, fabrication via single-step planar lithographic methods rather than a multistep process is commercially attractive. A current limitation in the design is efficiency and narrowband operation, which can be improved through the integration of a metallic back-plane (reflection operation), [7,29] use of a dielectric-based (high-index) nanoresonator approach [9] or multilayer thin-film arrangement. [7,26]

Conclusions
In conclusion, plasmonic-enhanced metalenses which focus light of transverse polarizations at two different focal planes have been experimentally demonstrated. Each lens is composed of two orthogonally polarized, spatially polarized zone plates or photon sieves. The macroscopic patterns are sampled with anisotropic orthogonal Ag nanostructures and then spatially multiplexed. The lens arrays are shown to operate with both laser and white light illumination, showing focusing at two focal depths with reflectance peak at the resonant wavelength, due to the tailored plasmonic resonance of the nanostructures. The lenses-under white light illumination-were used to image letters placed at the image plane and the reconstruction of each letter, at the target wavelength, for each focal plane and polarization, was observed. We envisage that these types of functional metalenses will be expanded to control other characteristics of light such as the phase and wavelength dynamically. Furthermore, lenses of this type are applicable to any wavelength regime and can be of particular interest for wavelengths whereby naturally occurring materials, exhibiting the necessary optical properties for refraction, are difficult to obtain.  . a) Imaging using the plasmonic enhanced metalenses: red light is focused to two different focal planes for orthogonal polarizations. For example, for an input such as the letter "A" (broadband white light), two images are reconstructed. Experimental verification: two binary transmittance transparencies with the letters "A" and "T" are printed and placed in the aperture stop of the microscope. FZP b) and PS c) metalenses are used to image the letters at the two focal planes, at orthogonal polarizations and a the target red (650 nm) wavelength. The scale bars in the images in (b) and (c) are 40 µm.