Hybrid Metasurfaces for Simultaneous Focusing and Filtering
Mansoor A. Sultan, Fatih Balli, Daniel L. Lau, J. T. Hastings
HHybrid Metasurfaces for Simultaneous Focusing andFiltering
Mansoor A. Sultan , Fatih Balli , Daniel L. Lau , and J. T. Hastings Department of Electrical and Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA * Corresponding author: [email protected]
ABSTRACT
This work presents the design and fabrication of simple, polymeric, structure-based optical filters thatsimultaneously focus light. These filters represent a novel design at the boundary between diffractiveoptics and metasurfaces that may provide significant advantages for both digital and hyperspectralimaging. The fabrication process for the proposed filters resembles 3D printing, and is based on directlaser writing of a polymeric material using two-photon lithography. In addition, printed structures could beused to create molds for nanoimprint replication and mass production. Filters for visible and near-infraredwavelengths were designed using finite difference time domain (FDTD) simulations.
Color filters are essential for a wide range of applications such as digital cameras, projectors, dis-plays, and spectral imaging systems. However, most of these applications still utilize tri-color dye- orpigment-based filters. These filters transmit the desired spectral region and absorb the rest. The materialcomposition of these filters make them vulnerable to environmental conditions, especially photo- andthermal- degradation . In imaging systems, the integration of these filters with a sensor requires threesteps of aligned lithography. This leads to a protracted and expensive fabrication process. Therefore,structure-based color filters have been of great interest because of their durability, wide tunability, andsimplicity of integration with imaging systems.Several types of structural filters have been investigated as a replacement for color pigments in printingand imaging. These include plasmonic
2, 3 , Metal Insulator Metal (MIM) , Guided-Mode-Resonance(GMR) , Photonic Crystal (PhC) , and color routing structures . However, each of these filter designshave shortcomings. For instance, the plasmonic color filters suffer from ohmic losses associated withthe metallic structure in their design, and GMR filters are very sensitive to angle of incidence. The MIMand PhC filters require multi-step fabrication processes with high fabrication cost related to precisionalignment and gray-scale lithography. Moreover, the transmittance of both plasmonic and MIM filtersare very low which consequently degrades the sensor sensitivity. Finally, color routing devices have highcross-talk between the color pixels.Recently, tremendous effort has been invested in light modulation by thin film materials patternedin quasi-periodic structures called metasurfaces. In contrast to conventional optics, metasurfaces do notdepend on the phase modulation by thick lenses to optimize the light path. Instead, metasurfaces introducesubwavelength nanostructures that allow controllable phase shifting of the propagating light. Metasurfacescan offer precise control over light intensity, phase, and polarization; thus, they have been widely utilizedin the design and fabrication of optical metafilters
8, 9 , metalenses ,and in vortex beam generation .Two-dimensional diffraction gratings composed of sub-wavelength pillars have also been utilized instructural color printing and filtering
18, 19 . These structures lie at the boundary between diffractive opticsand metasurfaces. They exploit waveguiding effects in the pillars to control the coupling of incident light a r X i v : . [ phy s i c s . op ti c s ] S e p o the various diffracted orders, including the transmitted and reflected zero orders. As a result, theycan produce tailored transmission spectra, especially when the transmitted light is angularly filtered by asubsequent lens or spatially filtered by an aperture.In this work, we present a novel approach to creating all-dielectric color filters that also focus light.These hybrid filters exploit a combination of diffraction by periodic structures, phase shifting by a phaseplate, and waveguiding by subwavelength structures to simultaneously focus and filter light in the visibleregion of the spectrum. These filters can be easily fabricated with two-photon lithography (TPL), atechnique that has been widely used in the fabrication of complex, sub-micron, 3D structures. Theflexibility of fabrication by TPL has been proven in different applications with feature size approachingthe diffraction limit such as photonic crystals ,microlenses , and waveguides . The reported filtershave the further advantage that they have no reentrant features and could be replicated by molding forhigh volume production.Here, we implement hybrid metasurface filters based on the structure shown in Fig. 1. The central unitconsists of a phase-plate and pillar with four degrees of freedom: periodicity, phase-plate thickness, pillardiameter, and pillar height. Lim et al. and Balli et al. utilized a similar concept for holographic colorprints and hybrid metalens designs, respectively
14, 24 . Lim et al. used a fixed phase-plate thickness andchanged the pillar height for each holographic color pixel. In contrast, we vary the phase-plate thicknessto obtain focusing behavior, while keeping the pillar height constant to control the filter response.In order to focus specific wavelengths at a focal length of f , the transmitted light must have a parabolicphase profile that satisfies φ ( r , λ ) = − πλ ( (cid:112) r + f − f ) (1)where r is the radial coordinate. The phase delay generated by light propagation in a film with thickness, t ,and refractive index, n , is given by φ ( λ ) = π ( n − ) t λ . (2)Equation (1) represents the required spatial phase shift to focus the light, and Eq. (2) represents the spectralphase shift due to light propagation in a film. From Eqs. (1) and (2), the required phase-plate thicknesscan be obtained from t ( r , λ ) = mod ( φ , π ) πλ ( n − ) . (3)The resulting phase-plate will be a quantized Fresnel lens structure.The 2D grating in combination with the phase-plate works as filter. The filtering process is based ondiffraction and waveguiding effects that introduce phase differences between the light that propagatesinside and outside the pillars
18, 24 . The design process was implemented using the finite-difference time-domain (FDTD) method. First, the pillars were simulated to estimate the dimensions that correspond tothe desired filter function. A unit cell of the 2D grating on a fused silica substrate was simulated withperiodic boundary conditions for x and y and perfectly matched layers on top and bottom. A plane wavelight source was placed inside the substrate and 2 µ m below the pillar, and a frequency domain fieldand power monitor was placed 12 µ m above the pillar to collect transmitted power. For the experimentsdiscussed below, only light with < ◦ diffraction angle will be collected by the objective. The resultswere calculated and plotted for different pillars height and radius as shown in Fig. 2(a). n order to test the simulated structure, pillar arrays were fabricated with different heights and laserpowers to optimize the dimensions. Fig.2(b) shows the transmittance of fabricated pillar arrays when theaverage laser power was set at 37.5 mW for the structure was sliced by 0.2 µ m. The fabrication resultsagree well with the simulations, and the filter function can be predicted based on pillar height and radius.The radius is a function of laser power and pillar height and it is expected that the pillar radius increaseswith height as more voxels overlap in taller pillars. For the wavelength range of interest, shorter andnarrower pillars yield short-pass filters. As the pillars become taller, the filter transitions to a band-passresponse, then to a notch-like response, and finally to oscillatory response.Second, we generated the required phase library for the phase-plate thickness to obtain the requiredphase profile as in Eq. (2). The periodicity of the pillars was fixed at 1.0 µ m , and their height and radiuswere optimized for the desired filter function based on Fig. 2. The filters were designed on a fused silicasubstrate. IP-Dip resist, the two photon lithography resist from Nanoscribe GmbH, was used in simulationprocess for phase-plate and pillars structures. The fused silica refractive index was obtained from andthe exposed IP-Dip resist refractive index was from the Nanoscribe material information database . Thefinal filter design has a focal length of 43 µ m and entrance pupil diameter of 7 µ m . The pillar heightswere 0.9, 1.4 and 1.8 µ m for the three desired colors: blue, green and red respectively.Two-photon lithography was employed to fabricated the hybird metasurface filters. Two photonlithography is a 3D lithography process that generates complex structure in a single step. The processutilizes the absorption of two photons with low energy that cross-link the resist in the focal volume of thelaser beam. The TPL system is a Photonic Professional GT (Nanoscribe GmbH) that uses a femtosecondlaser with 780 nm wavelength. The fabrication process was conducted in dip-in mode with 63x objective(1.4 NA). A laser power sweep was performed for both the pillars and the phase-plate to optimize for thebest filters performance. Scanning electron microscopy (SEM) images of the fabricated hybrid metasurfacefilters are shown in Fig. 3(a-c).Two light sources were used in the test setup (shown in Fig. S1 in supplementary material): a broadbandlight source (tungsten-halogen lamp) for focusing efficiency and pillar transmittance measurements over thevisible range and a super-continuum laser source (SuperK Extreme with SuperK Select, NKT Photonics)to measure the full-width at half maximum (FWHM) at center wavelengths of 450 nm, 550 nm, and650 nm. A collimating lens was add during FWHM measurement and removed for pillar characterizationand focusing efficiency measurement. Focusing efficiency and pillar transmittance were measured by afiber-coupled spectrophotometer (Ocean Optics HR4000CG-UV-NIR). The collection area of the fiberwas adjusted to ensure that light was collected only from the focused spot. The FWHM was measured bya high resolution Ximea grey scale camera and the image were post-processed with MATLAB.The wavelength dependent focusing efficiency matched well with the design as shown in Fig. 3. Thefabricated filters have focusing efficiency of 50-55% as shown in Fig. 3(d-f). In comparison to plasmoniccolor filters
27, 28 , these filters offer higher transmittance by virtue of the the dielectric material from whichthey are made.The FWHM of the focused spots shows excellent agreement with simulation, as shown in Fig. 4(a-f).The finite bandwidth of the source does not contribute significantly to the spot size. Likewise, the FWHMvaries with wavelength as expected. The spot sizes themselves are well matched to common digital camerasensor pixel sizes regardless of wavelength. Thus, with refinement, similar filters might ultimately beintegrated with CCD or CMOS image sensors . As mentioned earlier, hybrid filters are based on bothdiffraction and waveguiding. However, the results presented in Fig. 4 do not show the higher diffractedorders because these waves are beyond the numerical aperture of the objective (NA = 0.50). However,higher order diffraction is visible in the simulated optical power distributions shown in Fig. 5. Thesesimulations confirm that higher orders will not be collected with numerical aperture that we employed. For more detail, see the far-field angular distributions in Fig. S2.) Thus, unlike non-focusing filters ofsimilar design, either spatial or angular separation of the diffracted light can be used with the focusingfilters. In addition, changing the angle of incidence reduces the integrated transmission of the filters, butdoes not dramatically change the shape of the filter spectrum as shown in the supplementary Figs. S3 andS4. Thus, the filters maintain their color performance even off axis.In conclusion, we have demonstrated the design and fabrication of novel structure-based color filtersthat also focus light. The filters have focusing efficiency of 50-55%. These filters overcome some of theshortcomings of other filters such as plasmonic, GMR, PhC, MIM and metafilters, as long as higher orderdiffraction can be separated. They offer zero ohmic losses, a simpler fabrication process, and their spectralresponse does not strongly depend on incident angle. The focused spot size is smaller than both the filteritself and common image sensor pixel sizes. The focusing characteristic of these hybrid metasurface filtersoffers another appealing property that could make refined designs a potential replacement for the filter andmicrolens layers in modern camera sensors.
Funding.
Intel Corporation; National Science Foundation (IIS-1539157).
Acknowledgement.
The authors thank the UK Center for Nanoscale Science and Engineering, a memberof the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the NationalScience Foundation (ECCS-1542164). This work used equipment supported by National Science Founda-tion Grant No. CMMI-1125998.
Disclosures.
The authors declare no conflicts of interest.
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3D model of a hybrid metasurface filter and its central unit cell with the variable dimensionslabeled. a) ( b) Figure 2.
Transmittance of pillars arrays (non-focussing) as a function of wavelength, pillar radius, andpillar height. (a)
Simulated transmittance (b)
Measured transmittance. The periodicity was fixed at 1.1 µ m. a) ( b) ( c) F o c u s i ng e ff i c i en cy MeasuredSimulation1525354555 F o c u s i ng e ff i c i en cy
450 550 650 750wavelength(nm)10305070 F o c u s i ng e ff i c i en cy ( d) ( e) ( f) Figure 3. (a-c)
SEM images for 3D printed hybrid metasurface filters with peaks in the blue, green andred respectively. The scale bar for all images is 5 µ m (d-f) Simulated (red) and measured (blue)transmittance for the fabricated filters over the visible spectrum for the three filters (blue, green and redrespectively). - P o s iti on ( μ m ) MeasuredSimulated - - P o s iti on ( μ m ) - - P o s iti on ( μ m ) ( a) ( b) ( c) λ= 450nmλ= 550nmλ= 650nm ( d) ( e) ( f) Figure 4.
FWHM characterization for the fabricated filter. (a-c)
Intensity distribution in the focal planefor Blue, Green, and Red respectively. (d-f) are comparison between the simulated and measured relativeintensity in(a.u) at the focal plane for Blue, Green, and Red respectively. z ( µ m ) x(µm) x(µm) x(µm)(a) (b) (c) Figure 5.
Simulated optical power distribution of hybrid filters showing the higher diffracted orders ofthe blue filter at RGB wavelengths (a) (b) (c) upplementary Material : Hybrid Metasurfaces forSimultaneous Focusing and Filtering
The optical setup for filter characterization is shown in Fig. S1. The light source is halogen-deuterium fibercoupled source from Ocean Optics. Two types of camera were used: a colored camera (Amscope MU100)and gray-scale camera (Ximea - xiQ). The spectrophotometer is a UV-NIR model (HR4000CG-UV-NIR)from Ocean Optics.
The filters were fabricated on fused silica substrates of 0.7mm thickness with IP-DIP resist (NanoscribeGmbH). After exposure the sample was developed for 20 min with 2-Methoxy-1-methylethyl acetate(PGMEA from J.T. Baker) then rinsed for 3 min in IPA and 30 seconds in Engineering fluid.
As noted in the main text, the diffracted light from the filter is removed by angular or spatial filtering.Figure S2 shows the simulated far-field projections of a green filter alongside the NA of the objective. Inall cases the higher diffracted orders fall outside the NA of the objective
The simulation model of the focusing filters was based on single pixel filter with perfect matching layer(PML) in all boundaries (x = y = − µ m : + µ m , z = − µ m : + µ m ) and total scattering field source(TSFS). The lower boundary of the source was placed 2 µ m below the filter pixel inside the substrate. Afrequency domain power monitor was placed in the focal plane of the filter. The focusing efficiency wascalculated by normalizing poynting vector integration through a circular area of5 µ m radius to the sourcepower. The area was chosen with this size to match the experiments. Figures (S4 & S5 ) show the incidentangle effect on the optical power profile and focusing efficiency. In addition to the complete pixel fabrication (phase-plate + pillars), We fabricated the phase-plate onlyand measured the focusing efficiency to study the effect of phase-plate on the filtering process. The resultsare shown in figure(S5). ight source Sample
NA 0.50
SpectrophotometerInverted microscopeCamera Objective PCBeam splitterCollimator [H]
Figure S1.
Experimental setup for filter characterization (a)(b)(c)
Objective NAlog ( E /min( E )) Figure S2.
Far-field profiles (log scale) for the green filter normalized to the minimum field at 450nmwavelength. The wavelengths are (a)
450 nm, (b)
550 nm, and (c)
650 nm. The acceptance angle of theobjective is shown in orange, and all diffracted orders but zero fall beyond the objective’s NA. z ( µ m ) z ( µ m ) z ( µ m ) x(µm)
20 -20 0 x(µm)
20 -20 0 x(µm)
20 -20 0 x(µm)
20 -20 0 x(µm) n m n m n m
0° 2.5° 5.0° 7.5° 10.0°
Figure S3.
Optical power profile of a green filter in the xz-plane at different angles of incidence anddifferent wavelengths as labeled on the figure. A change in the angle of incidence moves the focused spotas expected, and reduces the overall transmission, but has little effect on the relative transmitted poweramong the three wavelengths.
00 500 600 700 800Wavelength(nm)0102030405060 F o c u s i ng e ff i c i en cy ° ° ° ° ° Figure S4.
Simulated focusing efficiency of green filter at different angles of incidence. Although theoverall transmission changes, the shift in the filter spectrum, and thus the color, is negligible
00 450 500 550 600 650 700 750 800 wavelength(nm) F o c u s i ng E ff i c i en cy BlueGreenRed
Figure S5.