Supplementary Information
Refractometric Biosensing based on Optical Phase
Flips in Sparse and Short-Range-Ordered
Nanoplasmonic Layers
RUNNING TITLE: Biosensing based on Optical Phase Flips
Mikael Svedendahl*, Ruggero Verre, and Mikael Käll*
Department of Applied Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
*Correspondence:
Mikael Svedendahl and Mikael Käll
Applied Physics Department, Chalmers University of Technology
412 96 Göteborg, Sweden.
Phone: +46 (0) 31 772 1000
Fax: +46 (0) 31 772 20 90
Email: mikael.svedendahl@chalmers.se, mikael.kall@chalmers.se
S1. Optical Properties of the Metamaterial Layers
The Hole Mask Colloidal Lithography fabrication process provides samples with robust optical
properties, as indicated by the similar transmission spectra measured from three different samples
in Figure S1. There are, however, small deviations in the exact resonance wavelength and
amplitude, which varies with about 2 nm and 0.2%, respectively. Zero reflection can be achieved
for all samples. However, the small deviations need to be compensated for by slight tuning of the
lasing wavelength of the diode laser and selecting the proper incidence angle, i, in order to
minimize the reflection.
The analytical theory used to calculate the spectra in Figure 3-5 in the main text from Equation
(1) and (2), require  and  as input. We used the same methodology as described in reference
[1] and [2], where a transmission spectrum at normal incidence is used to fit  to experimental
data. The polarizability was modelled using the formulas for an oblate spheroid in the quasistatic
limit together with the modified long wavelength approximation3, 4 and the Drude approximation
for the permittivity of gold.5 We used the size and surface density of the nanoparticles acquired
from the SEM images in Figure 2 to calculate the polarizability and the transmission spectrum for
the layer at a glass/water interface. The ellipsoid model is based on particles in a homogeneous
medium while the actual nanoparticles investigated are situated at a dielectric interface. As seen
in Figure S2, by tuning the effective refractive index surrounding the nanoparticles, we can match
the resonance wavelength to the experimental data. Here, an effective refractive index neff = 1.47
was used, which can be compared to the average refractive index of the two media, which is 1.43
(nglass = 1.52 and nwater = 1.33). Thus, one interpretation might be that the near-fields surrounding
the nanoparticles are not symmetrically distributed, but that more field intensity is located within
the high-index support. For further details regarding the polarizability model, we refer the reader
to reference [1] and [6].
Figure S3 show the phase response of the single particle polarizability together with the phase
difference between p- and s-polarized reflections, , at i = 55°. The rapid response in  is due to
the low reflection associated with the s-polarization. The maximum phase shift per wavelength is
0.8 and 140 °/nm for  and , respectively. Thus, the zero reflection effect leads to a 175 times
steeper phase response in reflection, compared to the intrinsic phase response associated with the
resonance of the individual nanoparticles.
Figure S 1. Optical transmission spectra of the samples shown in Figure 2c in the main text
measured in air.
Figure S 2. Experimental transmission spectrum for a sample in water together with the
analytical approximation, used to calculate the reflection-properties in Figure 3-5 of the main
text.
Figure S 3. A comparison between the phase responses from the polarizability, , and the
reflection at i = 55°, using the modified Fresnel formulas.
S2. Bulk Refractive Index Sensitivity
The bulk refractive index sensitivity is often measured by tracking the plasmon resonance
wavelength through extinction or reflection spectra as the refractive index of the ambient medium
is changed. The extinction (measured in transmission at i = 0°) maxima red shifted about 130
nm/RIU, see Figure S4. However, the shifts in reflection depend on the incidence angle, in
accordance with the modified Fresnel coefficients given in Equation (1)-(2) and the Fano
description of the reflections. Therefore, as an increased refractive index of the ambient can lead
to a decreased refractive index contrast of the boundary, and thus to a lower reflection of the bare
interface, the minimum wavelength in reflection can even blue shift with increasing refractive
index, as seen in Figure S5.
Figure S 4. Bulk refractive index sensitivity measurements in extinction mode. (a) Varying the
bulk refractive index from water to 10% ethylene glycol, (b) the resonance wavelength redshifted 1.3 nm yielding an approximate sensitivity of about +130 nm/RIU.
Figure S 5. Bulk refractive index sensitivity measurements in reflection mode. (a) Varying the
bulk refractive index from water to 10% ethylene glycol, (b) the resonance wavelength blueshifted 0.9 nm yielding an approximate sensitivity of about -90 nm/RIU.
S3. Fringe Tracking Stability
In order to verify the stability (precision) of the measurements and to investigate the possible
signal-to-noise performance of local refractive index measurements, the phase of the fringes were
studied as a function of time. The phase was determined by fitting the experimental data to the
function 𝐼 = (𝐴 + 𝐵𝑥) sin(𝑥𝐶 + 𝐷), where A and B sets the amplitude of the sinusoidal pattern,
C is associated with the frequency of the pattern with respect to the pixel values, x, and D is the
phase.
Figure S 6. Stability of phase measurements. The phase of the sinusoidal fringe pattern (a) was
measured over time (b). The standard deviation during 100 min is below 0.01°
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