Aperiodic nanoplasmonic devices for directional colour filtering and sensing

Exploiting the wave-nature of light in its simplest form, periodic architectures have enabled a panoply of tunable optical devices with the ability to perform useful functions such as filtering, spectroscopy, and multiplexing. Here, we remove the constraint of structural periodicity to enhance, simultaneously, the performance and functionality of passive plasmonic devices operating at optical frequencies. By using a physically intuitive, first-order interference model of plasmon-light interactions, we demonstrate a simple and efficient route towards designing devices with flexible, multi-spectral optical response, fundamentally not achievable using periodic architectures. Leveraging this approach, we experimentally implement ultra-compact directional light-filters and colour-sorters exhibiting angle- or spectrally-tunable optical responses with high contrast, and low spectral or spatial crosstalk. Expanding the potential of aperiodic systems to implement tailored spectral and angular responses, these results hint at promising applications in solar-energy harvesting, optical signal multiplexing, and integrated sensing.

and as a function of both groove-width ( : 50 nm to 400 nm) and free-space wavelength ( 0 : 450 nm to 750 nm), for illumination at = 10° (a and b, respectively) and = 20° (c and d, respectively), and fixed groove-depth ( = 100 nm) at a Ag-air interface. The variation in , , ′ and ′ at = 0° is summarized in Figure 1 of the manuscript and, for consistency, it was verified that ′ and ′ does not vary with . real-space waveform representing the groove locations , and their widths , as projected onto the plane of incidence at each of the three angles of incidence ( = 0°, 10° and 20°), for the aperiodic colour-filter device described in Figure 2 of the manuscript. As the angle of incidence increases, the perceived groove location and width of the aperiodic groove array varies as eff = (1 − sin ) and eff = (1 − sin ) respectively. b, Spatial Fourier-transform of the real-space groove-waveform depicting the associated reciprocal wave-vectors in inverse k-space. As expected, the aperiodic device exhibits dominant spatialfrequency content at wavelengths that agree with the modeled and experimentally measured spectral outputs ( Figure 2c and 2e of the manuscript, respectively). pre-cleaned 20 nm thick ITO-coated fused silica substrate. E-beam lithography (at 100 keV) was used to expose the inverse groove pattern on the resist, and the exposed resist was subsequently developed for 60 s in MIBK followed by 30 s rinse in IPA. Using E-beam evaporation, a 5 nm thick Cr adhesion layer, followed by 100 nm thick Ag was deposited. Following deposition, lift-off was carried out by soaking the sample in Acetone for twelve-hours. The lift-off procedure leaves Ag islands at the location of the exposed regions. A second Ag deposition of thickness 150 nm was performed using electron-beam evaporation in order to elevate the groove pattern by an optically thick layer above the plane of the substrate. Finally, focused-ion-beam milling was used to create a 100 nm-wide, 10 μm-long central through slits (or 150 nmdiameter circular through apertures). The scale bar in the SEM image represents 2 μm.

Supplementary Note 1 | Plasmonic colour pixel analysis:
The optical contrast C of the aperiodic slit-groove device summarized in Figure 2 of the manuscript for the three spectral peaks with FWHM linewidths (Δ 1 2 ) is calculated as: where ON represents the spectral amplitude at the targeted wavelength of interest at corresponding incident angle (for e.g., 690 nm at 0°) and OFF is the residual spectral amplitude at that same wavelength (690 nm) for other incident angles (10° and 20°). The device exhibits an optical contrast of up to 93 % and linewidths as narrow as 60 nm (Supplementary Table 1).
The angle-resolved spectral colour filtering property of the aperiodic plasmonic device has potential for applications as RGB colour pixels. In recent years, several periodic plasmonic colour-pixel designs that include array of apertures, slits or slit-grooves have been proposed for high-quality CMOS digital image sensor applications [1][2][3][4]. Here, we quantitatively measure the spectral crosstalk, or bleed, which is a measure of the performance of a colour-filter, for the aperiodic angle-resolved colour-filters fabricated in this study ( Figure 2 of the manuscript). Spectral crosstalk is a quantitative measurement of the overlap between various spectra in a device with a multi-band spectral response, and is defined as [4,5] where Δ is the integration range extending over the linewidth Δ 1 2 for a relative spectral transmission Γ( , ) peak at . Each integrated spectral range is represented by with i and j =1, 2 or 3 for the threepeaks, respectively and ≠ . The ideal spectral crosstalk for a colour-pixel, given by equation (2), is 0 % indicating that there is no spectral overlap between neighboring spectral peaks. The aperiodic plasmonic device studied here is able to achieve spectral crosstalk values that are comparable to conventional colour filters (Supplementary Table 2). Note here that the performance specifications of the experimentally implemented aperiodic colour-filter structuresincluding spectral linewidth, optical contrast and spectral crosstalk, are all comparable to state-of-the-art plasmonic counterparts that rely on periodic nanostructures [6][7][8]. The optimization algorithm incorporating the interference model allows us to achieve angle resolved full-colour response from a single-pixel device on a micron-scale device footprint.

Supplementary Note 2 | Effective index calculation of a bi-layer dielectric medium:
In order to accurately determine the figure-of-merit (FOM) of the aperiodic plasmonic sensor (studied in Applying these boundary conditions to equations (3), (4) and (5) gives 1, = 2, = , = and: Eliminating the four H-field amplitudes from equations (7a) to (7d) gives the dispersion relation: A similar dispersion relation is obtained in [9], however, in equation (8) no initial assumptions about in the three-regions is made.
Supplementary Table 4 shows the solutions of equation (8) for various medium 2 thicknesses , ranging from = 0 nm to → ∞. For the aperiodic sensing device (in Figure 5 of the manuscript): medium 1 is Ag, medium 2 is Al2O3, and medium 3 is free-space. At the sensor operating wavelength of 540 nm, this corresponds to 1 = −10 7 0 + 0 8 8 , 2 = 1 4, and = 1, using published values of dielectric constant for Ag [10]. For = 0 nm, medium 2 makes no contribution and the values of 1, and , that satisfy equation (8) are complex and represent a bound-mode (Supplementary Table 4). The calculated value for (Supplementary Table 4) also agrees with the theoretical prediction for a bound SPP-mode in a two-layer metallo-dielectric system,   Figure 10a assuming medium 1 to be silver Ag, medium 2 to be Al2O3, and medium 3 to be free-space.

Supplementary Note 3 | Refractive index sensing:
In addition to demonstrating the versatility of the optimization algorithm, incorporating the interference model, to perform linewidth optimization necessary for sensing applications at any arbitrary wavelength and angle of incidence ( Figure 5 of the manuscript), we summarize here the sensing capabilities of the multi-spectral response of an aperiodic device designed on Au-film for operation spanning the visible wavelengths. Simultaneous illumination of the sample at multiple angles of incidence would result in multiple discrete pre-defined spectral peaks in transmission thereby allowing for multiplexed sensing capabilities, which can result in higher-sensitivity than is possible from devices that exhibits only one spectral peak [12]. The aperiodic Au device was designed to fit within the same lateral foot-print as the Ag aperiodic slit-groove device (≤ 10 µm), and is theoretically implemented here to exhibit spectral peaks at

Supplementary Note 4 | SPP propagation length and Ag degradation:
The SPP propagation decay length SPP is experimentally measured (using the method described in ref. 17) to be ≈ 7 μm at λ0 = 690 nm on an evaporated Ag-air interface used in the manuscript (Supplementary Experimentally measured 1/e decay length SPP of SPPs for free-space wavelengths ranging from 500 nm to 800 nm on an evaporated Ag-air interface (blue squares) and a template-stripped Ag-air interface (purple spheres). The theoretical SPP decay length calculated using the bulk effective permittivity of templatestripped Ag (dashed black line).
Note that oxidation of Ag can also have a detrimental issue on device performance when operated under ambient conditions for long periods of time. We have not observed any degradation of Ag films used in our experiments as they were only exposed to air for the duration of the experiments (few minutes to an hour) and stored in a dry-environment. A few-nm thick atomic-layer-deposited protective overcoat of lowloss oxide (Al2O3) or use of doped-Ag films has been shown to dramatically improve the stability of Ag films without any compromise on the optical performance [18,19].