Sub-wavelength periodic arrays exhibit narrow near-unity reflection bands that arise from guided mode resonances. These resonances have extremely high quality factor (i.e., narrow band features) and are ideal for filtering applications. A high quality factor requires many periods, causing large lateral footprints that limit an imaging system's spatial resolution. We present a 1D ultra-thin (<100 nm) compact finite design of seven periods of amorphous Si slabs with subwavelength periodicity surrounded by Al mirrors, which allow the finite array to approximate an infinite array and enabling a small footprint (∼5 μm), for near-infrared applications (λ = 800–2000 nm). We demonstrate spectral tunability (amplitude, bandwidth, and peak location) via geometric parameter variation and demonstrate the performance of these filters both in experiment and in simulation. This work miniaturizes guided-mode resonance filters, previously limited by extremely large footprints, while being relatively cheap and simple to fabricate compared to many existing designs

Fountaine, Katherine T.

Garcia, Juan C.

Greer, Julia R.

Ng, Ryan C.

English

Caltech Authors - Main

S1 
 
Supplementary Material 
Miniaturization of a-Si guided mode resonance filter arrays for near-IR 
multi-spectral filtering 
 
Ryan C. Ng,1,a) Juan C. Garcia,2 Julia R. Greer,3 and Katherine T. Fountaine2 
 
1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 
91125, USA 
2NG Next, Northrop Grumman Corporation, One Space Park, Redondo Beach, California 90278, USA 
3Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, California 
91125, USA 
 
 
2D nanopillar array 
 
While the design and discussion in this work is restricted to a 1D design, all the ideas here are fully 
applicable to a 2D design should a polarization-independent response be desired at normal 
incidence using an array of pillars or cubes with mirrors on all four sides. To illustrate this idea, in 
Figure S1 we present a proof-of-concept design in 2D that has not been optimized, but still exhibits 
the GMR rapid spectral variation. Figure S1(a) presents a schematic of this design, with Al mirrors 
on only two sides, and Figure S1(b) shows the associated reflection spectrum. This array has 
geometric parameters h = 150 nm, a = 800 nm, f = 0.5, and s = 300 nm for a 7x7 array of a-Si 
nanopillars embedded in SiO2 with Al mirrors. The spectral characteristics can be significantly 
improved through optimization of the geometric parameters. While mirrors are required on all four 
sides for polarization-independence, the ability to miniaturize this design and visualize the GMR 
with mirrors only along one direction further support the GMR mechanism. 
S2 
 
 
 
 
FIG. S1. GMR in compact finite 2D design incorporating mirrors. (a) Schematic of a 2D design 
incorporating mirrors only along two boundaries for an array with geometric parameters h = 150 
nm, a = 800 nm, f = 0.5, and s = 300 nm for a 7x7 array of a-Si nanopillars embedded in SiO2 with 
Al mirrors. (b) Associated reflection spectrum calculated in FDTD demonstrating a non-optimized 
proof-of-concept of the compact finite array design and ability to observe the GMR utilizing a 2D 
array should polarization-independence be desired. 
 
Number of periods required to obtain desired spectral characteristics 
 
For comparison, to quantify the advantage of incorporating a mirror in terms of filter footprint, 
FDTD simulations were done to determine the number of periods required in a finite design that 
does not incorporate any mirrors to match the amplitude of other higher-performance designs 
(Figure S2). Figure S2(a) compares the performance of a 17-period finite mirrorless design with 
the 7-period finite design incorporating mirrors proposed in this work. Figure S2(b) compares the 
performance of a 141-period finite design that does not incorporate mirrors with an infinite design. 
While it is possible to obtain high spectral resolution and high signal-to-noise ratio spectral peaks 
using GMR filter designs that do not incorporate any kind of reflective boundaries, this comes at 
the cost of extremely large lateral footprints. 
S3 
 
 
 
FIG. S2. FDTD simulations comparing spectra between designs that incorporate mirrors and 
designs that do not incorporate mirrors, indicating the number of periods required in a mirrorless 
design to match the performance of other designs in terms of peak amplitude. (a) Comparison 
between the finite 7-period design that incorporates mirrors in this work (green) with a finite 17-
period design that does not incorporate mirrors (pink). (b) Comparison between an infinite design 
(yellow) and a finite 141-period design that does not incorporate mirrors (purple). 
 
Effect of varying period in finite GMR design 
 
The effect of varying the number of periods in the finite design incorporating mirrors is shown in 
FDTD calculated spectra in Figure S3. With a lower number of periods, the amplitude of the peak 
decreases, the FWHM broadens, and background noise increases. However, depending on the 
specific signal-to-noise that may be desired in the final imaging device, a filter incorporating only 
3 periods still exhibits a GMR that may be useful if the lower signal-to-noise ratio and lower 
spectral resolution is acceptable in a particular application. 
S4 
 
 
FIG. S3. FDTD generated reflection spectra demonstrating the effect of varying the number of 
periods and varying filter footprint in the finite design incorporating mirrors. As the number of 
periods decreases, the amplitude decreases and the bandwidths broaden with increased background 
noise. 
 
Spectral characteristics of arrays 
Table S1 shows the spectral characteristics of the fabricated arrays measured experimentally 
compared to experiment. We observe FWHM values from 140.5 to 205.1 nm in experiment, and 
from 102.7 to 120.6 nm in simulation (overestimation of actual FWHM and underestimation of 
their performance due to defining the FWHM as half of the peak reflection due to the asymmetric 
resonance, defined in the main text). For example, to calculate the FWHM for the 731 nm period 
array in simulation, we find the bandwidth at half of the reflection amplitude (82.6/2), which results 
in a bandwidth of 102.7 nm. This is to avoid ambiguity since the baseline has a slightly different 
amplitude on either side of the asymmetric resonance. Our definition of FWHM causes a 
significant overestimation of the bandwidth of the 881 nm array in experiment. The transmission 
dips are as low as 58.1% experimentally, compared to 17.4% in simulation. We attribute this 
efficiency loss to fabrication imperfections, experimental normalization, and alignment errors in 
fabrication and measurement (angle and polarization). 
 
S5 
 
Table S1. Spectral characteristics for each array in {experiment / simulation} for variable 
periodicity with 7 periods. The color scheme is consistent with that in Figure 3. 
 
Period (nm) Peak Position (nm) Reflection Amplitude FWHM (nm) 
731 1180 / 1176 41.9 / 83.0 140.5 / 103.6 
781 1230 / 1244 39.0 / 79.4 157.5 / 106.2 
831 1300 / 1312 34.0 / 75.4 143.9 / 110.4 
881 1350 / 1381 32.5 / 71.1  205.1 / 116.0 
931 1400 / 1449 23.0 / 66.7 188.6 / 122.7 
 
Top down schematic of filter array and surrounding reflective frame 
 
Rather than patterning and depositing two rectangular blocks for the mirrors as suggested by 
Figure 1(a), we surround the filter with an Al frame. This Al frame now serves two purposes: 1) 
to allow the GMR to reflect back to approximate infinite periodicity and 2) to enable normalization 
during measurements through the array. Transmission through mirror frames matching the area of 
the sample but with no patterned area was measured to properly normalize the power transmitted 
through the patterned sample area, though only reflective mirrors on two sides of the array are 
required to observe the laterally propagating GMR in the finite array. An aerial schematic of this 
layout is shown in Figure S4 and the dimensions of the frame and distances from the filter are 
indicated. The a-Si array is indicated in red and the surrounding Al frame in dark blue. This frame 
is discontinuous with slits in the frame for ease of experimental lift-off. Frames of the same lateral 
dimensions were fabricated without gratings for normalization of the transmission measurements. 
S6 
 
 
 
FIG. S4. Top-down schematic of the 7 period a-Si filter array and surrounding Al mirror/frame. 
The frame is introduced for ease of normalization during measurements. Slits are included in the 
frame for ease of lift-off during fabrication. The array of a-Si slabs has variable periodicity, a, fill 
fraction, f, and spacer region, s. Dimensions for the frame, slits, distance from the array, and lateral 
length of the array slabs are indicated in the figure. This schematic is not to scale. 
 
 
Ellipsometry 
 
Ellipsometry data was obtained (Figure S5) for a 100 nm thick film of a-Si deposited by PECVD 
at 200oC, 800 mTorr, and 10 W with 250 sccm of 5% SiH4 diluted in Ar. This n,k data was used 
in in the FDTD simulations to model a-Si. 
S7 
 
 
 
FIG. S5. Raw n and k data for a-Si determined from ellipsometry. 
 
Fresnel Correction 
 
This calculation allows for the additional top and bottom interfaces of the glass substrate to be 
accounted for, that are not otherwise accounted for in FDTD simulations. The calculation can be 
done for a fixed number of layers, and then generalized to an arbitrary number of layers. First, we 
assume we have a homogeneous film of a single material in air (i.e. air-film-air with each layer 
numbered as layers 0, 1, and 2, respectively). This stack is schematically shown in Figure S6. RA 
is the amplitude of the wave reflected directly from the top surface of the film, RB is the amplitude 
of the wave reflected from the bottom surface of the film that transmits back through the top 
surface, RC is the wave that reflects from the bottom surface, then internally reflects again off the 
top surface then bottom surface, before transmitting through the top surface, and so on. Then, Rij, 
Tij, rij are the reflectance, transmittance, and reflection coefficients at each interface between each 
layer, respectively. We define: 
𝑅01 =  𝑟01
2 
At normal incidence: 
𝑅01 =  (
𝑛0 −  𝑛1
𝑛0 +  𝑛1
)
2
 
S8 
 
As RA is the reflectance off the top interface, 
𝑅A =  𝑅01 
Then, 
𝑅B =  𝑇01𝑅12𝑇10 
𝑅C =  𝑇01𝑅12𝑅10𝑅12𝑇10 
More generally, to describe the reflectance out of the top surface after m internal reflections off 
the back-side of the film for α ≥ 1: 
𝑅m =  𝑇01𝑇10𝑅12
𝛼𝑅10
𝛼−1 
The total reflectance out of the top surface is the sum of all of these Rm terms that transmit from 
the film to the top surface: 
𝑅tot =  ∑ 𝑅m =  𝑅01 +  𝑇01𝑇10𝑅12 ∑ 𝑅12
𝛼𝑅10
𝛼
∞
𝛼=0
 
This is a geometric series: 
𝑅tot =  𝑅01 +  𝑇01𝑇10𝑅12 (
1
1 − 𝑅12𝑅10
) 
 
For normal incidence, TE and TM polarization are the same, i.e. T = 1 – R for TE, but RTE = RTM. 
We also utilize Rij = -Rji. For a 3-layer air-film-air stack, R02 describes the total reflectance in this 
system considering all interfaces. Simplifying: 
 
𝑅tot =  𝑅02 =  
𝑅01 +  𝑅12
1 + 𝑅12𝑅01
 
 
This result can similarly be generalized to a different number of layers. For a stack of 4 layers: 
S9 
 
 
𝑅tot =  𝑅03 =  
𝑅01 +  (
𝑅12 + 𝑅23
1 +  𝑅23𝑅12
)
1 +  (
𝑅12 + 𝑅23
1 + 𝑅23𝑅12
) 𝑅01
 
 
This is the expression utilized in this work for a 4-layer film of air-glass-glass-air, where the FDTD 
simulated spectrum represents R12, the reflection at the interface between the glass-glass layers.  
 
FIG. S6. Schematic of Fresnel reflection through the interfaces of a single slab of homogeneous 
material. Here, layer 0 and layer 2 are air, though this can be generalized to any cover or substrate. 
RA is the amplitude of the wave reflected directly from the top surface of the film, RB is the 
amplitude of the wave reflected from the bottom surface of the film that transmits back through 
the top surface, RC is the wave that reflects from the bottom surface, then internally reflects again 
off the top surface then bottom surface, before transmitting through the top surface, and so on. 
 
Methods 
Fabrication: The filter arrays were fabricated using a top-down methodology on a glass substrate. 
Approximately 64 nm of a-Si was deposited onto the substrate by PECVD at 200oC, 800 mTorr, 
and 10 W with 250 sccm of 5% SiH4 diluted in Ar for 2 minutes and 18 seconds. The thickness 
deposited in PECVD dictates the height of the a-Si slabs in the array. Prior to all electron beam 
lithography writes in the fabrication process, a sacrificial layer (a solution of poly(4-
styrenesulfonic acid) mixed with 1% by volume of Triton X-100 surfactant) was spin-coated above 
the resist at 3000 rpm and baked at 90oC for 3 minutes, followed by 10 nm of electron beam 
S10 
 
evaporated Au for charge dissipation. The sacrificial layer gold was removed following EBL in 
water and developed as normal. Ti alignment markers (h = 200 nm) were created by first patterning 
in polymethyl methacrylate (PMMA) 950 A8 positive-tone electron beam resist with a Raith 
5000+ electron beam writer at 100 kV, developing in methyl isobutyl ketone:isopropanol 
(MIBK:IPA) in a 1:3 ratio for 90 seconds, and then depositing Ti in electron beam evaporation 
and lifting off. The next EBL write utilized MaN-2403 negative-tone electron beam resist applied 
onto the a-Si. The grating slabs were then exposed in an aligned write to the Ti markers and are 21 
m each in length. Following electron beam exposure, the pattern was developed in MF-319 for 
40 seconds and the pattern was transferred into the a-Si layer with a pseudo-Bosch SF6/C4F8 etch 
with ICP-RIE at 15 oC with 40 W ICP power, 1500 W forward power, 26 sccm of SF6 and 35 sccm 
of C4F8. 
 The MaN-2403 resist mask was removed by cleaning in an oxygen plasma for 10 minutes 
(10 mtorr and 80 W with 20 sccm O2). Finally, the mirrors were aligned and patterned with PMMA 
950 A4 and developed in 1:3 MIBK:IPA for 90 seconds, and a 65 nm thick layer of Al that dictated 
the mirror height was deposited in electron beam evaporation and subsequently lifted-off. Rather 
than patterning and depositing two rectangular blocks for the mirrors as suggested by Figure 1(a), 
we surround the filter with an Al frame. This frame is the length of the filter and spacer regions in 
one lateral direction perpendicular to the grating beams, and 24 m in the other lateral direction 
parallel to the grating beams (Figure S4). It is discontinuous with slits in the frame for ease of 
experimental lift-off. Frames of the same lateral dimensions were fabricated without gratings for 
normalization of the transmission measurements. The resulting filter was in-filled with 500 nm of 
methylsiloxane based spin-on glass solution (Filmtronics 500F).  
Measurement: Measurements were made with a Fianium white light source coupled to a near-IR 
monochromator with Ge photodetectors and a 20X Mitutuyo objective with a range from 480-
S11 
 
1800 nm. This objective allowed focusing of the spot size down to ~10 m. Transmission 
measurements were taken from 1100 to 1600 nm spaced evenly 10 nm apart from one another. To 
properly normalize to the power transmitted through the patterned sample area, transmission 
through mirror frames matching the area of the sample but with no patterned area was measured. 
To account for any power fluctuations between the measurement of the sample and the frame, a 
pair of Ge photodetectors simultaneously recorded the intensity of the beam transmitting through 
the sample, Iref, and the intensity of the incident beam, Iinc, using a beamsplitter prior to the 
objective. The transmissivity of the sample, T, was then calculated by: 
𝑇 =  (
𝐼ref
𝐼inc
)
sample
(
𝐼inc
𝐼ref
)
frame
 
Simulation: Full-field, 2D simulations were computed with Lumerical FDTD, a commercial 
electromagnetics software package. For infinite simulations (Figures 1(b) and 1(c)) and crosstalk 
simulations (Figure 4), periodic boundary conditions were used on the lateral boundaries to reduce 
the simulation region and emulate infinite periodicity. For finite simulations (Figures 1(b), 1(d), 
1(e), 2, and 3), perfectly matched layers were used for the lateral boundaries as an artificial 
absorbing region to emulate infinite space. In all cases, perfectly matched layers were used for the 
axial boundaries. For the polarization, the E-field is parallel to the direction of the length of the 
grating slabs. For the materials in the simulation, Palik data was used for Al and SiO2 and 
ellipsometric data was used for a-Si (Figure S5). A finer override mesh was applied over the a-Si 
slabs with mesh sizes <5% of the height and width of the slabs. The spectra in this work utilized 
single broadband (800-2000 nm) simulations. A Fresnel correction was applied to all simulations 
to account for interfaces that were not included in simulation (Figure S6). 
 
 


Miniaturization of a-Si guided mode resonance filter arrays for near-IR multi-spectral filtering

https://authors.library.caltech.edu/105525/2/compactsi_vf_apl.pdf

Miniaturization of a-Si guided mode resonance filter arrays for near-IR multi-spectral filtering

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