Photonic resonator interferometric scattering microscopy

Interferometric scattering microscopy is increasingly employed in biomedical research owing to its extraordinary capability of detecting nano-objects individually through their intrinsic elastic scattering. To significantly improve the signal-to-noise ratio without increasing illumination intensity, we developed photonic resonator interferometric scattering microscopy (PRISM) in which a dielectric photonic crystal (PC) resonator is utilized as the sample substrate. The scattered light is amplified by the PC through resonant near-field enhancement, which then interferes with the <1% transmitted light to create a large intensity contrast. Importantly, the scattered photons assume the wavevectors delineated by PC’s photonic band structure, resulting in the ability to utilize a non-immersion objective without significant loss at illumination density as low as 25 W cm−2. An analytical model of the scattering process is discussed, followed by demonstration of virus and protein detection. The results showcase the promise of nanophotonic surfaces in the development of resonance-enhanced interferometric microscopies.


Supplementary Figure 2. | PC-assisted extraction on the electric dipole radiation. (a)
Normalized radiation power distribution and (c) electric field magnitude of the radiated waves from a dipole place on top of the PC surface (with 0.5 nm separation). It can be observed that due to the match between the radiated photon wavelength (633 nm) and the PC periodicity, a portion of the dipole radiation power is coupled to the PC guiding layer, and subsequently leak into the substrate. The collection efficiency (78%) was obtained by first respectively integrating the radiation power within and below the PC structure, as well as the total radiation within the computation domain, the ratio of which is then obtained as the collection efficiency. In comparison, the conventional glass substrate (b, d) only offers a collection efficiency of 57%.

Supplementary Note 1: Image Processing and Data Analysis
The image processing algorithm used in photonic interferometric scattering microscopy (PRISM) was conducted in Matlab (MathWorks) adapted from previously reported methods 1,2 . All the captured frames obtained from the camera were saved as individual raw images, for a typical observation window of 10 s, more than 6000 raw images were recorded for later analysis.
The image processing procedure contains three major steps: (1) A rolling-window averaging method was applied to remove the background by the virtue of the dynamic measurement. With the window size defined as N, each frame of the raw images was averaged with the following N-1 frames, followed by a ratiometric process where every average image was divided pixelwise by the following average image. For the gold nanoparticle (AuNP) characterization as well as SARS-CoV-2 virion detection, we simply set the rolling window size as 1. Therefore, the ratiometric image is simply the direct division of two consecutive frames, as shown in Fig. S5 (a-c). However, the window size for protein detection is determined as 10 in order to suppress the background noise.
where p is the total pixel number in S. A representative denoised image obtained through this process is shown in Fig. S5 (6) where = √2 erf −1 (1 − 2 ), is the significance level ( < 0.01 in the data analysis), is the uncertainty on ̂[ ] obtained from error propagation, and is the uncertainty on from the standard error of variance. By selecting the pixels whose p-values are lower than , we can obtain the mask of significance highlighting the centers of scattering signals, as shown in Fig. S5 (e). Finally, by overlaying the mask of significance with the local maximum of the Gaussian-of-Laplacian filtered image, the centroid of each scattering signal can be effectively captured, as indicated in Fig. S5 (g).
(3) Following the detection of scattering signals within each frame, a single-particle tracking algorithm ( -track) was utilized to obtain the trajectory information based on the previously obtained centroid coordinates and frame number 4 . Here, we assume that one signal can at most link to one signal in another frame, and no merging or splitting is allowed. A typical image containing AuNP trajectories is shown in Fig. S5 (h).

Supplementary Note 2: Temporal Couple-Mode Theory
As shown in Fig. S8, the photonic crystal (PC) assisted nanoparticle (NP) scattering process can be modelled via a temporal couple-mode theory (TCMT) 5,6 . Considering a PC cavity (resonant frequency 0 , with radiative decay rate ) that exchanges energy with incoming (s(1,2)+) and outgoing (s(1,2)-) waves (s2+ = 0) with coupling constant (1,2) , (1,2) respectively. Additional NP scattering channel is characterized with scattering damping rate ( Supplementary Fig. 1). We first describe the behavior of the resonator S14 = − = (− 0 − − ) + 1+ where A is the amplitude of the PC cavity mode, and is the coupling efficiency between the PC cavity and the external waves. For simplicity, we assume mirror symmetry in the system (which is an approximation for our PC design) therefore 1 2 = 2 2 . From energy conservation and timereversal symmetry, we have = 1 = − 2 = √1/ . From Equation (7) and Equation (8) In general, for a single layer of NPs, the solitary scattered power can be modelled as S15 = ( 0 ) × (14) where 0 is the number density of NPs, is the NP scattering cross section, is the pump power, while d is the NP diameter. From Equation (11) and Equation (14) we can obtain the PC enhancement on the scattered power by where and are respectively the scattered power and the incident power, 0 is the resonant wavelength, is the energy confinement of the PC mode in the NP layer (dependent on the size and material of the particle, ~12% for AuNPs of 20 nm in diameter), n is the refractive index of water and is the effective length of the evanescent field (~ 100 nm). In general, as the NP grows larger in size, the corresponding perturbation in the pristine cavity mode becomes more significant. In other words, the total quality factor QE of the scattering influenced PCGR mode deteriorates with larger NPs, leading to the diminishing scattering enhancement factor as obtained from FEM simulation shown in Fig. 4b.

Supplementary Note 3: Numerical Simulations
The PC transmission/reflection spectrum and the band structure was calculated using both three- The radiated power distribution of a dipole on the PC/glass substrate was obtained using 2D FEM simulation. The extended PC structure was approximated by 9 periods of PC, and the vertically orientated electric dipole was located at the center of the central PC ridge with 0.5 nm separation from the surface.
For FEM simulation of the cavity-enhanced scattering, the AuNP was modelled as a spherical structure with the refractive index provided by Johnson and Christy 8 . The mesh size at the NP was smaller than one tenth of the particle diameter, as shown in Fig. S6a. Further reduction on the mesh size to one twentieth of the particle diameter showed marginal improvement on the accuracy of near-field profile (Fig. S6). Using the wave optics module, the full field solution under Floquet periodic conditions was first calculated to simulate the field profile of a pristine extended PC cavity, which was then used as the background field for AuNP excitation and the previous Floquet periodic boundary conditions were replaced by PML boundary conditions to prevent the back-scattered field from the computational boundary. The scattering cross section can then be calculated as where 0 is the incident intensity, Snp is the closed surface of the AuNP, n is the normal vector on the surface and is the relative Poynting vector. Similarly, the scattering cross section of S17 AuNP on the glass substrate is calculated under the same condition with the PC structure removed.
It is noteworthy that the PC enhancement on the AuNP scattering is dependent on the relative NP location within one PC period. As shown in Fig. S7, the edge of the PC ridge provides more scattering enhancement due to the higher near-field intensity of the PCGR mode at the edge. This location sensitivity explains the slightly broadened PRISM signal distribution for AuNPs in comparison with the DLS measurement results. The scattering enhancement at the center of the PC ridge is close to the averaged enhancement value, and is used for the discussion on the PC-assisted scattering process in the article.