Multiwavelength metasurfaces through spatial multiplexing

Metasurfaces are two-dimensional arrangements of optical scatterers rationally arranged to control optical wavefronts. Despite the significant advances made in wavefront engineering through metasurfaces, most of these devices are designed for and operate at a single wavelength. Here we show that spatial multiplexing schemes can be applied to increase the number of operation wavelengths. We use a high contrast dielectric transmittarray platform with amorphous silicon nano-posts to demonstrate polarization insensitive metasurface lenses with a numerical aperture of 0.46, that focus light at 915 and 1550 nm to the same focal distance. We investigate two different methods, one based on large scale segmentation and one on meta-atom interleaving, and compare their performances. An important feature of this method is its simple generalization to adding more wavelengths or new functionalities to a device. Therefore, it provides a relatively straightforward method for achieving multi-functional and multiwavelength metasurface devices.

while maintaining a high transmission amplitude. Since the structure needs to be fabricated with a single step electron beam lithography, the nano-post heights should be the same at both wavelengths (which we have chosen to be 915 and 1550 nm due to availability of laser sources). In addition, since the two wavelengths are relatively far apart, we choose the 1550 nm lattice constant to be twice that of the 915 nm ( Fig. 3a,b). With this choice, the two metasurfaces can be interleaved by simply replacing one out of four 915 nm meta-atoms by a 1550 nm one (Fig. 3c).
Taking these considerations into account, we find that a post height of 718 nm, lattice constants of 360 nm at λ = 915 nm, and 720 nm at λ = 1550 nm, enable full phase coverage with high transmission at both wavelengths. The simulated intensity transmission t ( ) 2 and transmission phase ∠t ( ) for such uniform lattices are plotted in Fig. 2d,e at 915 and 1550 nm, respectively. For simulations, a uniform array of meta-atoms with a given diameter is illuminated with a plane wave at the wavelength of interest (Fig. 2c), and the transmission amplitude and phase are calculated. We have used the rigorous coupled wave analysis 37 to perform the simulations.

Experimental Results
For experimental demonstration, we have designed and fabricated a multi-sector and an interleaved lens that focus light from single mode fibers at 915 and 1550 nm to a focal point 400 μm away from the lens' surface without spherical aberrations. The lenses are 300 μm in diameter, and the single mode fiber is placed 600 μm away from the backside of the ~500-μm-thick substrate of the lens (resulting in a focal distance of 286 μm, and a numerical aperture of 0.46). The multi-sector lens is formed by dividing two single wavelength lenses designed for 915 and 1550 nm to 8 radial sectors and combining them similar to Fig. 1c and the interleaved lens is formed from combining the two single wavelength lenses in the manner shown in Fig. 3. The single wavelength lenses are designed using the metasurface platforms described above. The smallest nano-post diameter is set to 72 nm in all the designs. For the interleaved lens, a minimum gap of ~50 nm is set between the adjacent nano-posts to facilitate their fabrication. This resulted in the maximum nano-post diameters of 200 and 420 nm for the 915 and 1550 nm lenses, respectively, thus the highest achievable phase delay was ~1.6π at each wavelength. The less than 2π phase coverage leads to small wavefront errors and lowers the focusing efficiencies of the lenses. In the design process, the best nano-post for each lattice site was chosen by minimizing the complex transmission error defined as a b c d , where φ is the desired phase at the lattice site and t is the complex transmission coefficient of the nano-posts. Using this design procedure, and assuming that the lenses require a uniform distribution of nano-posts with various phases from 0 to 2π, we find that the incomplete phase coverage achieved here results in a less than 3% reduction in the lens efficiency.
The devices were fabricated by depositing a 718-nm-thick layer of α-Si on a fused silica substrate using the plasma enhanced chemical vapor deposition method. The device pattern was written on an electron beam resist using e-beam lithography, and was transferred to an aluminum oxide layer using a lift-off process. The aluminum oxide layer served as a hard mask for etching the α-Si layer in a dry etch process, and was removed in a solution of hydrogen peroxide and ammonium hydroxide. Optical and scanning electron microscope images of both the multi-sector and interleaved devices are shown in Fig. 4.
The lenses were characterized by measuring the intensity distributions in the focal plane, and in many planes parallel to the focal plane using custom built microscopes with ~100× magnification. Schematics of measurement setups are shown in Fig. 5. Measured intensities in axial and focal planes at both wavelengths are plotted in Fig. 6a-d for the multi-sector and in Fig. 6i was changed using the polarization controllers shown in Fig. 5, and no polarization dependence was observed. Measured axial plane intensities for the multi-sector lens are plotted in Fig. 6a,c, where a single strong focus is observed at both wavelengths. The intensity distributions in the focal plane are plotted in Fig. 6b,d and show features that are caused by the division of the lens aperture into multiple sectors. The high frequency fluctuations observed in the 1550 nm focal plane measurements are caused by the highly non-uniform responsivity of the phosphorous coated CCD used. To achieve smoother intensity distributions in the axial plane, these high frequency fluctuations are filtered through removing all components with spatial frequencies higher than the free space propagation constant. For comparison, a lens designed with the same method and with the same NA, but with all dimensions and distances four times smaller than the fabricated device was simulated using the finite difference time domain (FDTD) method in MEEP 38 . The smaller size of the simulated device was necessary to make the simulations feasible with the available computational resources. Figure 6e-h show the simulated intensities for this device at both wavelengths in the axial and focal planes. The illumination was linearly polarized in simulations, and the symmetry of the structure ensures the same behavior for other incident polarizations. A very good agreement is observed between simulated and measured focal depths and the focal plane intensities. Focusing efficiency is defined as the ratio of the power focused by the device, to the output power of the fiber, and is measured at 915 and 1550 nm with setups schematically shown in Fig. 5b,c, respectively. The pinhole used at 915 nm has a diameter of 20 μm, and the iris used for 1550 nm is 2 mm in diameter, which translates to a ~20 μm diameter in the object plane. Simulated and measured efficiencies and full width at half maximums (FWHM), in addition to the diffraction limited FWHMs are summarized in Tables 1 and 2  limited FWHMs are found via simulation of a perfect phase mask at each wavelength, with the same optical fiber illuminations that are used to design and measure the lenses. Measurement results for the interleaved lens are plotted in Fig. 6i-l. Unlike 1550 nm, at 915 nm a second focus is observed at z ≈ 220 μm, with the peak intensity approximately 1.8 times, and a power 1.2 times those of the main focus. Similar to the multi-sector lens case, a four times smaller interleaved lens designed using the same platform is simulated for comparison, and the simulated intensities are plotted in Fig. 6m-p. A weak second focus is observed around z ≈ 50 μm in the simulations as well. It is worth noting that these devices are multi-order (similar to multi-order gratings), and have multiple focal points (like a Fresnel zone plate lens). These higher order focal points can be seen in all four axial plane measurements in Fig. 6a,c,i,k. The higher order focal points have low intensities in all cases except for Fig. 6i. If the "blazing" of the lens is perfect (i.e. the phase profile is equal to its ideal case), all of the power will be directed towards the designed focal distance. However, if some error is introduced to the phase profile, a portion of the power will be directed towards higher order focal points. As this error increases, the power in the main focus will decrease. The 1550 nm nano-posts are optically large and support many resonant modes around 915 nm, resulting in some error in the phase of the total transmitted field at 915 nm. Besides, as we will shortly discuss, the coupling between 1550 and 915 nm posts is not negligible at 915 nm. These errors, result in a significant portion of the power going to the higher order focus at 915 nm for the interleaved lens. Measured and simulated efficiencies and FWHMs are summarized in Tables 1 and 2, respectively.
To determine the origin of the focus observed at z ≈ 220 μm, we use paraxial imaging equations by considering the fiber tip as an object and the focal plane intensity as its image. We find that the effective object distance from the lens is 1003 μm using the f 1 = 286 μm focal distance, and the 400 μm image distance. Therefore, the focal distance corresponding to the focus observed at z ≈ 220 μm is f 3 ≈ 180 μm. We represent this focal distance by f 3 , because there is also a secondary focal distance f 2 = 485 μm arising from the 1550 nm nano-posts, as they also form a lens at 915 nm. The focal distance of the lens formed from 1550 nm nano-posts is given by at 915 nm 28 . We note that we have 1/f 3 = 1/f 1 + 1/f 2 . This means that the equivalent transmission mask of the lens contains a term proportional to . This term  is the result of addition of two phase profiles generated by the 915 and 1550 nm nano-posts, and indicates coupling between these nano-posts (this term cannot exist if 915 and 1550 nm posts operate completely independently). Therefore, at 915 nm the coupling between the interleaved nano-posts cannot be completely neglected. For an optimal design, this coupling can be taken into account if unit cells formed from combining the two nano-post groups are analyzed together 28 .

Discussion
The efficiency of the interleaved lens at 915 nm is significantly lower than 1550 nm, both in measurements and simulations. Two factors play important roles in this difference between the efficiencies at the two wavelengths. First, the interleaved lens has an effective lattice constant of 720 nm (Fig. 3c), which is close to λ = = a 727nm n max 2 3 g , the lattice constant above which higher diffraction orders will be propagating in the glass substrate at 915 nm (here n g = 1.452 is the refractive index of glass). Therefore, the non-periodicity of the lens structure results in higher order diffractions propagating inside the substrate. In contrast, this lattice constant is subwavelength enough at 1550 nm such that no higher diffraction orders are present. Second, 915 nm nano-posts are optically small at 1550 nm, whereas 1550 nm nano-posts are optically large and support many resonances around 915 nm. Therefore, while adding the 915 nm nano-posts to the 1550 nm lens results in a relatively small phase error at 1550 nm, introducing the large 1550 nm nano-posts to the 915 nm lens changes the phase profile significantly, and for some nano-post diameters, it also reduces the transmission amplitude. In addition, the measured efficiency for the interleaved lens at 915 nm (10%) is lower than the simulated value of 27%. The transmission phase of the device at 915 nm is more sensitive to errors in the nano-post diameters because of the larger aspect ratio of the nano-posts, and fabrication errors have degraded the phase profile of the lens and its efficiency by directing a significant portion of power to the higher order focus around 220 μm.
Efficiencies of the multi-sector device at the two wavelengths are closer to each other than the interleaved lens. The sum of simulated efficiencies at 915 nm and 1550 nm for these devices is always less than 100%. The interleaved design, in contrary, can have a sum of efficiencies at 915 and 1550 nm higher than 100% as evidenced by the simulation results. This is because the high index nano-posts can have an optical cross-section significantly larger than the geometrical area of the metasurface pixel that they occupy. Besides, the efficiency of the interleaved lens can be increased, and its sensitivity to fabrication errors can be decreased using the meta-molecule concept and a concurrent design of the nano-posts for the two wavelengths 28 . In addition, the division of the aperture to multiple macroscopic sectors changes the shape of the input aperture of the lens and thus the shape of its focal spot. The interleaved design on the other hand, does not cause this issue.
The demonstrated multiwavelength lenses can be used in applications where simultaneous operation at a few discrete wavelengths is required, such as two photon fluorescence microscopy. While conventional refractive achromatic lenses could have a better performance (specifically a higher efficiency) in such applications, they are bulky, more expensive to fabricate, and harder to customize. Besides, multiple metasurfaces can be monolithically integrated in order to correct various aberrations, add functionalities, or be directly integrated with electronics to form compact electro-optical systems 39 . Nevertheless, multiwavelength lenses are demonstrated here only as a proof of concept example for the general method of spatial multiplexing of metasurfaces for implementing multiwavelength multifunctional optical devices. The introduced methods can be directly applied to designing metasurfaces with different functionalities at different wavelengths. For instance, a metasurface can be designed to operate as a lens at one wavelength, and as a grating at the other one. It can also be applied to making metasurfaces that perform multiple functions simultaneously at a single wavelength. It would be very challenging, if at all possible, to fabricate such devices with the conventional refractive optics platform.

Conclusion
We have shown that by spatially multiplexing metasurface lenses that are designed for operation at two different wavelengths, we can realize lenses that simultaneously operate at both wavelengths. We designed, fabricated, and characterized double-wavelength lenses based on macroscopic aperture division (i.e. the multi-sector lens), and meta-atom interleaving. Although here we used this concept to demonstrate double-wavelength lenses, the idea can be readily generalized to devices with more operation wavelengths, or devices that perform different functions at different wavelengths, or even at the same wavelength. Therefore, spatial multiplexing introduces a simple route towards multiwavelength and multi-functional metasurfaces.