Analysis of Effects of Surface Roughness on Sensing Performance of Surface Plasmon Resonance Detection for Refractive Index Sensing Application

Abstract

This paper provides a theoretical framework to analyze and quantify roughness effects on sensing performance parameters of surface plasmon resonance measurements. Rigorous coupled-wave analysis and the Monte Carlo method were applied to compute plasmonic reflectance spectra for different surface roughness profiles. The rough surfaces were generated using the low pass frequency filtering method. Different coating and surface treatments and their reported root-mean-square roughness in the literature were extracted and investigated in this study to calculate the refractive index sensing performance parameters, including sensitivity, full width at half maximum, plasmonic dip intensity, plasmonic dip position, and figure of merit. Here, we propose a figure-of-merit equation considering optical intensity contrast and signal-to-noise ratio. The proposed figure-of-merit equation could predict a similar refractive index sensing performance compared to experimental results reported in the literature. The surface roughness height strongly affected all the performance parameters, resulting in a degraded figure of merit for surface plasmon resonance measurement.

Keywords: instrumentation; refractive index sensing; sensing performance; surface plasmon resonance; surface roughness.

Figure 4

(a) Product of h and a sequence of randomized 0 and 1; (b) magnitude of H(f_x) after Fourier transform (indicated as the blue curve) and a Gaussian distribution plot determined by cl (shown as the red curve); (c) inverse Fourier transform of the product $$H\left(f_x\right)·G\left(f_x\right)$$, resulting in a rough surface structure; and (d) the 10-layer rough gold surface and a single-layer uniform gold surface.

Figure 6

(a) Calculation methods of all quantitative performance parameters of the surface plasmon resonance detection; and (b) normalized optical reflectance and the full width at half maximum (FWHM).

Figure 1

(a) The Otto configuration; and (b) the Kretschmann configuration.

Figure 2

Reflectance spectra of uniform 50 nm gold on BK7 glass substrate when the gold sensor was illuminated by p-polarized coherent light at 633 nm. The blue curve showed the reflectance spectrum when the sample sensing region was water, and the red curve showed the reflectance spectrum when the sample sensing region was BSA protein solution with a sample refractive index of 1.35.

Figure 3

Simulation diagram including roughness parameters required for constructing rough surface profiles.

Figure 5

Flowchart of the simulation and calculation processes, including structure profile construction, RCWA, and sensor-quality computation.

Figure 7

Optical reflectance of the p-polarization for four levels of rough surfaces with the varying number of diffracted orders included in the RCWA calculations. Note that the solid blue curve is for cl of 1 nm and h of 1 nm, the dashed blue curve is for cl of 1 nm and h of 20 nm, the solid black curve is for cl of 50 nm and h of 1 nm, and the dashed blue curve is for cl of 50 nm and h of 20 nm.

Figure 8

(a) Sensitivity calculated using Monte Carlo simulation; (b) SPR dips at h of 1 nm and cl of 50 nm; (c) negative SPR dip movement at h of 9 nm and cl of 15 nm; and (d) reflectance when there was no SPR dip present at h of 15 nm and cl of 5 nm.

Figure 9

(a) The normalized sensitivity based on Equation (8); and (b) the difference between Equation (8) and the RCWA simulation.

Figure 10

(a) The full width at half maximum in rad/μm calculated using Monte Carlo simulation, (b) SPR dips at h of 1 nm and cl of 50 nm with an average FWHM of 0.04 rad/μm; and (c) SPR dips at h of 7 nm and cl of 15 nm with an average FWHM of 0.05 rad/μm.

Figure 11

(a) The normalized full width at half maximum using Equation (9); and (b) the difference between Equation (9) and the RCWA simulation.

Figure 12

(a) The change in intensity calculated using Monte Carlo simulation; (b) SPR dips at h of 1 nm and cl of 50 nm with an average intensity difference of 0.62; and (c) and SPR dips at h of 7 nm and cl of 15 nm with an average intensity difference of 0.004.

Figure 13

(a) The normalized intensity difference using Equation (10); and (b) the difference between Equation (10) and the RCWA simulation.

Figure 14

(a) The dip intensity calculated using Monte Carlo simulation; (b) SPR dips at h of 1 nm and cl of 50 nm with an average dip intensity of 0.01; and (c) SPR reflectance spectrum at h of 5 nm and cl of 10 nm with an average dip intensity of 0.78.

Figure 15

(a) The normalized dip intensity using Equation (11); and (b) the difference between Equation (11) and the simulated output.

Figure 16

(a) The FOM using Monte Carlo simulation; (b) the normalized FOM based on Equation (12); and (c) the difference between Equation (12) and the RCWA simulation.