Hyper-Selective Plasmonic Color Filters

The subwavelength mode volumes of plasmonic filters are well matched to the small size of state-of-the-art active pixels (~ 1 {\mu}m) in CMOS image sensor arrays used in portable electronic devices. Typical plasmonic filters exhibit broad (>100 nm) transmission bandwidths. Dramatically reducing the peak width of filter transmission spectra would allow for the realization of CMOS hyperspectral imaging arrays, which demand the FWHM of transmission peaks to be less than 30 nm. We find that the design of 5 layer metal-insulator-metal-insulator-metal structures gives rise to multi-mode interference phenomena that suppresses spurious transmission features gives rise to a single narrow transmission band with FWHM as small as 17 nm. The transmission peaks of these multilayer slot-mode plasmonic filters (MSPFs) can be systematically varied throughout the visible and near infrared spectrum, so the same basic structure can serve as a filter over a large range of wavelengths.

In particular, periodic arrays of subwavelength apertures passing through a metal film exhibit enhanced transmission exclusively at conditions corresponding to constructive mutual interference between incident light and SPPs traveling along the surface between adjacent slits. In the case that the metallic layer is thick enough to be substantially opaque to incident photons, the SPP mediated process is the dominant mode of transmission and the surface acts as a band-pass color transmission filters.
Such aperture arrays have been the topic of substantial scientific interest due to these remarkable optical properties and their utility as a testbed for studying fundamental light-matter interactions in plasmonic systems 2,3 . Due to their simplicity, scalability, and durability, plasmonic slit gratings have become an attractive route for development of technological applications including ultra-compact filters suitable for cameras and displays 4,5 .
The dispersion of plasmonic propagating modes can be further engineered using metal-clad slot waveguides, often realized as multilayer stacks with a metal-insulator-metal (MIM) configuration 6 .
Such MIM stacks may support a multitude of polaritonic modes which lie either inside or outside the "light cone," that is, with in-plane momentum either greater or less than that of a photon with equal energy. This additional degree of freedom enables substantially more complex optical transmission filter spectra enabling narrow bandwidth suitable for multispectral and hyperspectral color filtering applications 7 .

Designing Plasmonic Color Filters
Finite difference time domain methods (FDTD) were used to determine the transmission spectra of different filter structures. Figure 1 illustrates the different types of transmission filters and their spectral behavior. MIM have been used to make RGB color filters 7 . These structures can be optimized to have narrowband transmission, but as the structure is optimized to minimize FWHM of the transmission peak, the intensity of the next highest order mode increases. This trade-off can be lifted by introducing a second MIM mode into the structure that couples with the original MIM mode, leading to the suppression of the spurious transmission. The asymmetric nature of the coupled MIM modes plays a role in the suppression of the spurious transmission, as illustrated in Supplemental Figure 1(a). The multilayer slot-mode plasmonic filter (MSPF) investigated demonstrates a narrow transmission bandwidth and spurious peak suppression, as shown in Figure 1(b), and by changing the periodicity of the slits, this filter can be swept across the entire visible spectrum.
The MSPFs were optimized using parameters sweeps that considered both the thicknesses and optical indices of all the insulating and metallic layers, as well as the width and spacing of the milled slits. The initial values for the thicknesses of the metallic layers were determined by considering the skin and penetration depths of various metals. For a successful filter, the top and bottom metallic layers of the structure must be sufficiently thick to be opaque across the visible and near IR parts of the electromagnetic spectrum. Using Rakic data for Ag as an example, the 1/e penetration depth (d p ) of Ag was calculated to range from 12.9 nm -16.8 nm across the visible spectrum. To prevent 98% of light from penetrating the structure, the top and bottom layers must be 4 times d p , so 51.6 nm to 67.2 nm.
Therefore 68 nm was used as the initial parameter sweep value when optimizing the system that utilized Ag.
Likewise, the starting point for the thickness of the insulating layers was approximated by considering the propagating modes guided laterally within the structure. Numerically determined dispersion curves derived from experimental optical constants of Ag and SiO 2 can be used to determine the available modes within an MIM 6 . For SiO 2 thicknesses of less than 100 nm, traditional photonic waveguide modes are cut off in an Ag/SiO 2 /Ag system, so the waveguide only supports highmomentum surface plasmon modes. Therefore, the parameter sweeps used 100 nm as the upper value restriction for the SiO 2 thickness of each waveguide.
Iterating over the parameter sweep led to the final device structure, with alternating layers of Ag and SiO 2 . Both SiO 2 layers were optimized to 70 nm, the top and bottom Ag layers are 70 nm and the spacer layer is 50 nm. The width of the slit is 50 nm for all filters and the slit periodicities investigated vary from 250 nm to 550.
The position of the transmission peak varies linearly with the periodicity of the slits and, as shown in Figure 2(a), peak position can be swept across the visible and near IR spectrum. Therefore, just by varying the inter-slit pitch, a series of MSPFs with the same layer materials and thicknesses can be used as a color filter across a wide range of the spectrum. The FWHM of the transmission spectra are about 20 nm on average with no peak exceeding 28 nm, as shown in Figure 2(b). Additionally, the overall transmission of the side-lobe peak does not exceed 11% of that of the primary peak in the visible portion of the spectrum, and does not exceed 25% of the primary peak intensity in all filters investigated.

Analytical Analysis
A series of FDTD simulations were executed by sweeping over the visible spectrum using a single frequency plane wave source. Complex vector field data was collected by finely meshed monitors capturing the EM behavior over the span of each of the FDTD simulations. This data contained the Cartesian space variations of the electric and magnetic field information over time, which evolved as the plane wave injected into the simulation interacted with the MSPF. This very large dataset can be compressed by taking a discrete-time Fourier transform at runtime to yield the field data in the frequency domain.
A single electric field component from the compressed data set of a single simulation is plotted in Figure 3(a). The spatial mapping of the electric field superimposed on the MSPF depicts multiple modes that are active in the filter structure. These modes are active along both SiO 2 layers as well as the top and bottom Ag surfaces. The spatial mapping of the electric field indicates that the modes in the two SiO 2 insulators are coupled, because they demonstrate a characteristic beating pattern that indicates that power is being transferred between the two MIMs. This result was expected physically-the spacer layer between the two insulating layers is thinner than the skin depth of Ag at the energies of the generated electric fields.
To better determine the natures of the various modes within the MSPF, a second Fourier Transform was performed. By taking an FFT over the propagation direction of the modes, the phasor direct space dataset can be moved into momentum space (i.e. "k-space"). The results of this FFT can be plotted, as shown in Figure 3(b), to reveal the spatially resolved intensity of the various modes within a structure that was excited by a single frequency source. The profiles of these modes can be determined by spatially mapping the intensity a given spectral frequency. For example, in Figure 3 corresponding to a coupling of the two MIM modes generated within each of the two insulating layers in the structure. This is the mode that was implied in the spatial field map in Figure 3(a) is now clearly depicted in Figure 3(c), which reveals that the two MIM modes within the super-mode are coupled because of strong field overlap within the 50 nm Ag spacer.
The behavior of the energy propagating through the filter can be determined by the FFT analysis, but it does not indicate how these modes contribute to the overall behavior of the filter. By normalizing the transmission curves over the dispersion behavior of each mode and the pitches of the filter gratings, we can reveal the exact ways the modes are contributing to the behavior of the unsuppressed transmission peak.
The dispersion behavior of each plasmon mode can be determined by constructing a dispersion curve for the MSPF. The dispersion curve shown in Figure 4(a) was constructed by using the Fourier Transformed k-space data sets and plotting the power of the modes at each spectral frequency as a function of energy. The two branches on curve correspond to the bottom side SPP and the metalinsulator-metal-insulator-metal (MIMIM) super-mode, and can be mapped to the frequency values that correspond to these modes in Figure 3

Experimental Verification
MSPFs were fabricated by depositing alternating layers of Ag and SiO 2 in an electron beam evaporator and then subsequently milled using a focused ion beam (FIB). The 50 nm slit milled into a 330 nm structure is a prohibitively demanding aspect ratio for a FIB trench mill. For a set of proof-ofconcept filters, these demanding design conditions can be relaxed by considering filters only towards the lower energy portion of the visible spectrum. For a slit width of 120 nm, the suppression of the spurious transmission peak is retained and the FWHM of the primary transmission peak only takes a 25 nm hit.
When Ag is deposited on SiO 2 in an electron beam evaporator, the Ag films grow with a columnar growth mechanism 8 . These films are rough, which increases plasmonic loss, thereby reducing overall transmission intensity of the filter 9 . The roughness of Ag deposited on SiO 2 is even more problematic in a multilayer structure like the MSPF because the roughness of each Ag layer compounds.
A rough substrate increases the roughness of the film deposited on it due to differences in atomic flux received by areas of the film with positive and negative curvatures that are larger than can be compensated for by surface diffusion 10 . Because the SiO 2 conformally deposits on the underlying Ag layer, each Ag layer sees a progressively rougher substrate, leading to a very rough top surface of the MSPF.
By utilizing a seed layer of AgO deposited onto each SiO 2 surface, a much smoother Ag film can be deposited 11 . The AgO is deposited by electron beam evaporating Ag in a chamber with an O2 pressure of 9.5x10 -5 torr. Once 2 nm of AgO are on the surface of the SiO 2 , the deposition is paused and the AgO is held under vacuum. Because AgO is not vacuum stable, the oxygen is pumped out of the film, leaving a thin Ag layer on the surface of the SiO 2 11 . The deposition is then resumed and the rest of the Ag is deposited at in a chamber with pressure 2.3x10 -6 torr and no oxygen flow. The roughness of Ag films deposited with this method was measured to have an RMS of 2.56 nm and the top Ag surface of a multilayer deposited with the AgO growth method has an RMS of 2.92 nm.
To further protect the integrity of the filter, a sacrificial layer was put on the top Ag surface.  Using FDTD simulations, we can compute the transmission behavior of filters with a progressively increasing sidewall taper. The results of these simulations, shown in Figure 5(b) illustrate the importance of the slit sidewalls on the overall behavior of the structure. Using the information gathered from the FDTD simulations, it was determined that to maintain filtering behavior with side lobe suppression, the sidewalls of the slit could not possess greater than a 5⁰ taper. The side lobe in the experimental transmission is due to the 13.7⁰ taper in the fabricated filter.
The FFT analysis indicated that the MSPF super-mode is responsible for the suppression of the spurious transmission peak, and the individual MIM modes are coupled together. As the slits are tapered, the difference between the lengths of the two channels increases, which affects the interference between the two modes, thereby reducing the filtering efficiency of this mode and allowing multiple orders of modes to propagate through the structure.
The polarization response was also experimentally confirmed to match the simulated predications, as shown in Figures 6(a) and (b).

Conclusions
A plasmonic color filter with a single narrowband transmission response was designed using FDTD and fabricated to confirm the simulated response. The filter is readily amenable to device integration, with a size well-matched to state of the art CMOS image sensors. The plasmonic filter utilizes a geometry that flexibly allows for precise selection of the spectral bands of interest, allowing for portable electronic devices to be capable of multi-and hyperspectral imaging. The behavior of this filter was analytically determined to arise from a combination of SPP excitations--the surface SPP mode leads to the enhanced transmission behavior associated with subwavelength plasmonic filters, while the slightly asymmetric MIM super-mode leads to the suppression of the spurious transmission peak that arises in other narrowband plasmonic filter geometries. The MSPF is inherently gated, and this feature will be capitalized on in future work by incorporating transparent conducting oxides into this geometry to create tunable narrowband color filters spanning both the visible and near infrared parts of the spectrum.

Fabrication Methods
A fused silica slide was prepared by 5 minute sonication in acetone followed by a rinse with IPA.
The alternating metal and insulating layers were all deposited via electron beam deposition in the same chamber to maintain the integrity of the Ag/ SiO 2 interfaces. A silver oxide seeding method was used to produce smooth Ag films 11 . 2 nm of Ag is deposited at a rate of 0.1 A/s in a chamber under a pressure of 9.5x10 -5 torr O2. The AgO film is then reduced to an Ag film under vacuum for 10 minutes to yield an Ag film on the surface of the silica substrate. The remaining 68 nm of Ag are deposited at a 0.5 A/s deposition rate followed by a SiO 2 deposition deposited at 1.5 A/s under a pressure of 2.3x10 -6 torr. The remaining Ag and SiO 2 layers are deposited using this method. Once the depositions are completed, 90 nm of PMMA is spun onto the Ag surface before depositing another 70 nm of Ag as a sacrificial layer.
Ga+ ions at 30 kV and 1.5 pA are used to mill 130 nm wide slits into the MSPF and sacrificial layer stack. Multi-pass milling is used to reduce the taper of the slits-first a rectangle is milled, followed by a frame around the perimeter, to better define the edges and clean off redeposition within the slit. After milling the sacrificial layer is removed using first heated remover PG followed by submerging it in acetone and spraying it with an acetone squirt bottle before rinsing in IPA.    This difference leads to a slight difference in the amount of accumulated phase, which allows for enhanced destructive interference that is not possible in the symmetric case, leading to a more highly