Principle and simulation

Based on this hypothesis, we sought to develop photonic resonator interferometric scattering microscopy (PRISM) based upon an all-dielectric nanophotonic surface for the quantitative detection of individual nano-objects such as nanoparticles, viruses, and biomolecules. In place of an ordinary glass slide, a nanostructured PC surface (1 × 1 cm) is directly used as an optically resonant substrate in a transmission laser microscope (Fig. 1a). The PC consists of a TiO₂-coated periodically corrugated polymer surface, fabricated on a coverslip by a low-cost replica molding process (Supplementary Fig. 1). When the incident monochromatic plane wave satisfies the phase-matching condition, the extended PC resonator will efficiently trap light through photonic crystal-guided resonance (PCGR), reshaping the optical near-field interaction and far-field propagation. The advantages of PCs in interferometric microscopy are threefold: (1) For laser excitation, PC functions as a notch filter centered in lieu of the partial reflective mirror. Near-unity back reflection and near-zero transmission can be obtained at resonance via a sharp Fano interference. For the transverse magnetic (TM) polarized plane wave at the wavelength λ₀ = 63 nm, the corresponding modulation transfer function \(H({\mathbf{k}}_{\mathbf{x}},\,{\mathbf{k}}_{\mathbf{y}})\) is obtained as the theoretical PC transmittance in the wavevector domain (Fig. 1b). Specifically, when the PC is illuminated by the collimated beam at normal incidence (Γ-point), <1% of the incident light is allowed to transmit and interferes at the image plane with the light scattered by nano-objects on the surface. As a result, the intensity of the reference beam is substantially reduced in the interferometric system. (2) By effectively trapping light in the resonant substrate, the PC provides nearly two-orders-of-magnitude enhanced excitation for the nanoscale scatterers via near-field coupling²¹ (Fig. 1c). This is achieved by the excitation of a pair of counterpropagating leaky modes in the corrugated TiO₂ guiding layer, from which stationary wave patterns are formed, and a strong evanescent field at the water-TiO₂ interface is induced. (3) The PC redistributes the light scattered from the nanoparticle angularly and thus improves the collection efficiency into the imaging objective lens. In addition to direct out-of-plane scattering, scattered light can be collected into in-plane guided modes, where it temporally recirculates in the PC resonator and eventually radiates into the lower substrate due to the nature of leaky modes (Supplementary Fig. 2). Through a point-dipole approximation for an individual NP, this scattering behavior can be more clearly demonstrated by the radiation power profile of a vertically oriented electric dipole on the PC surface (Fig. 1d). It is noteworthy that the radiated (scattered) light is predominantly (>78%) radiated into the substrate, whose refractive index (n_TiO2 = 2.38) is much larger than that of the superstrate (n_water = 1.33). The PCGR-induced background suppression, enhanced excitation, and improved light extraction simultaneously enable the direct observation of nanoscale scatterers with a non-immersion (NA < 1) objective without significant loss of contrast signal at relatively low luminance. As a result, PRISM enables convenient noncontact-objective imaging and larger field of view.

PC characterization

To experimentally validate the physical principles underlying PRISM, the band structure of the fabricated PC is first obtained via a far-field transmission spectrum measurement (Fig. 2a). We also computed the band structure and derived the modulation transfer function \(H({\mathbf{k}}_{\mathbf{x}},\,{\mathbf{k}}_{\mathbf{y}})\) using both finite-element method (FEM) and finite-difference method in time-domain (FDTD) to cross-validate the calculated results in the prevention of simulation artifacts (Methods and Supplementary Fig. 3). Quantitative agreement between the experimental results and the simulation modeling for the two branches of the PCGR mode (white dashed lines in Fig. 2a) are observed. Here, we focus on the long-wavelength resonance branch for its low transmissivity (0.764%) and high-quality factor (Q = 452.61). The PCGR resonance wavelength at normal incidence can be accurately tuned to match the HeNe laser wavelength (λ₀ = 63 nm) by controlling the thickness of the deposited TiO₂ layer (lower panel, Fig. 2a). To verify the modulation transfer function \(H({\mathbf{k}}_{\mathbf{x}},\,{\mathbf{k}}_{\mathbf{y}})\), the angular diagram of the PC transmissivity at the laser wavelength is obtained through Fourier plane imaging. Figure 2c shows the obtained Fourier space image of a representative PC used in the PRISM system, where the isofrequency contour outlining the dispersive PCGR mode can be clearly observed, in good agreement with the predicted modulation transfer function (Fig. 1b). The measured modulation transfer function \(H({\mathbf{k}}_{\mathbf{x}},\,{\mathbf{k}}_{\mathbf{y}})\) can be understood as a slice on the saddle-shaped photonic band (due to the anisotropic photonic lattice) in the wavevector plane \(({\mathbf{k}}_{\mathbf{x}},\,{\mathbf{k}}_{\mathbf{y}})\) of constant frequency ω₀ (red dotted line in Fig. 2a). For the detuned PCs, the photonic band is slightly shifted in the frequency axis and the corresponding isofrequency contours are therefore also offset from the saddle point (Fig. 2b, d).

a Dispersion diagram measured experimentally from the transmission spectrum, overlaid with numerically obtained photonic band structure (dashed white curves). The laser wavelength λ_L = 633 nm is marked with a red dashed line, and the dotted horizontal line marks the normal incidence angle (Γ point). Lower panel: transmission spectrum (red) at normal incidence along with the normalized laser emission spectrum (blue). b–d Experimentally recorded isofrequency contour by Fourier plane imaging, respectively from PCs with TiO₂ thickness of (b) 90 nm, (c) 97 nm, and (d) 105 nm. e Bright-field reflection image of the border between the PC nanostructure and the glass substrate. Inset: scanning electron microscopy (SEM) image of the corrugated PC surface. f PRISM image of the resonating PC sample used in (c). The majority of the normally incident light is reflected, leaving the PC region appearing black in transmission mode. g PRISM image of the detuned PC used in (d), where the PC region is almost transparent due to resonance wavelength mismatch.

One of the primary benefits of PCs in our microscopy system is that the background can be suppressed under normal incidence by virtue of the PCGR mode, without the need for illumination beyond the critical angle or additional modulation in the Fourier plane, therefore reducing the complexity of the imaging system. To demonstrate this capability, customized transmission illumination was added onto a conventional inverted microscope for the PC to be illuminated by a collimated TM-polarized beam from a 21 mW HeNe laser (Fig. 1a). For bright-field observation, the edge of the representative PC nanostructure was illuminated with 625 nm TM-polarized light from a light-emitting diode (LED), and inspected under reflection mode. Assisted by an oil-immersion objective (NA = 1.46), the horizontally aligned PC gratings (period Λ = 390 nm) are observable, and the brightness validates the high reflectivity of the PC in comparison with the adjacent glass substrate (Fig. 2e). When observed under transmission mode with laser illumination, the same PC region showed significantly lower background intensity than the adjacent glass substrate, as expected from the obtained transfer function in the wavevector domain. A slightly detuned PC, on the other hand, remains highly transmissive owing to the sharp Fano lineshape of the resonance mode.

Calibration on contrast signal

To explore the relationship between scattered signal image contrast and the size of the scattering object, we collected PRISM images of spherical gold nanoparticles (AuNPs) ranging in diameter from 5 to 40 nm. For the generality of results as applied to nanoparticles comprised of alternative materials, the laser wavelength is offset from the localized surface plasmon resonance (LSPR) wavelength of the AuNPs by at least 100 nm, preventing the synergistic coupling between the photonic resonator and the plasmonic resonator²². To verify the size of the AuNPs, both scanning electron microscopy (SEM) and dynamic light scattering (DLS) measurements were utilized as AuNP characterization. False-colored SEM images of AuNPs on the PC substrate are shown in Fig. 3a. For PRISM imaging, 20  μL of AuNPs solution (diluted to 1.0 × 10¹⁰ NPS/mL with molecular grade water) was dispensed on the PC substrate and sealed with a Piranha-cleaned coverslip, and individual AuNP binding/unbinding events were recorded at an acquisition rate of 600 frames-per-second (FPS). With the coherence-induced speckle background removed by rolling-window averaging¹, representative images in Fig. 3b, c show the contrast signals from single AuNPs observed respectively with a 40× air objective (NA = 0.95) and a 100× oil immersion objective (NA = 1.46) (see “Methods”, Supplementary Figs. 4–5 and Supplementary Video 1 for details). A Laplacian-of-Gaussian (LoG) filter is applied to localize the center of every AuNP signal within each frame, followed by a single-particle tracking algorithm to obtain the lateral AuNP trajectories²³ (Supplementary Note 1). The averaged contrast signal within each trajectory is considered as a single instance. From over 500 instances for each size of the AuNP recorded by the 100× objective, we constructed contrast histograms reflecting the distribution of interference signal dependent on the AuNP size/mass (Fig. 3d). In addition, the magnitude of the AuNP contrast signal recorded by the non-immersion 40× objective remains largely unchanged (Fig. 3e), indicating the scattering profile is confined to smaller angles, in contrast to the detection of a nanoscopic scatterer/emitter on a glass substrate where an immersion objective (NA ≥ 1.0) is required²⁴. Interestingly, on top of a NA-dependent Airy disk pattern as commonly reported in the conventional interferometric microscopy, the real-space AuNP signal pattern also includes a semi-parabolic pattern (Fig. 3f inset), implying additional k-space information carried by the scattered photons. To extract the directionality as well as the angular distribution of the scattering profile of AuNPs on a resonant PC substrate, we performed Fourier transformation on over 6000 frames of the aforementioned interferometric image and obtained an averaged Fourier plane image (Fig. 3f). Despite the overlay of the shifted patterns caused by the laser-induced interference background, it is observed that a portion of the AuNP-scattered photons radiate into the far-field following the angular distribution described by the isofrequency contour \(H({\mathbf{k}}_{\mathbf{x}},\,{\mathbf{k}}_{\mathbf{y}})\) in Fig. 2c. This result indicates that photons scattered from a NP can preferably couple into PCGR modes, consistent with the cavity-enhanced scattering reported elsewhere^25,26. The isofrequency contours of these wavevectors are largely confined to the low-NA regime (NA ≤ 0.95), which explains the unaffected NP contrast signals by an air objective (Fig. 3e).

a False-colored SEM images of a PC surface with AuNPs of various sizes. Correspondingly, differential interferometric images are recorded using (b) NA = 0.95 and (c) NA = 1.46 objectives for the same AuNPs under PRISM modality. d Contrast histogram of AuNP signal distribution obtained using a NA = 1.46 objective. (n > 500 for each size of AuNP.) The broadening of the contrast distribution for the 40 nm-AuNPs is likely caused by the formation of multiple-particle aggregates. e Scatterplot of the signal contrast as a function of AuNP size. Each dot represents the average of 50 instances of AuNP events. Lower panel: hydrodynamic diameters of the same AuNPs obtained through dynamic light scattering measurement. A clear separation of the hydrodynamic diameter can be except for AuNPs below 10 nm in diameter, where the instability of the laser becomes overwhelming comparing with the weak NP scattering signal. The DLS measurement for each AuNP size was repeated separately five times. f Fourier plane image of the AuNP (d = 40 nm) scattered light obtained by averaging the 2D Fourier-transformed images over 6000 frames. The outer circle is equivalent to NA = 0.95 in air. Inset: a typical real-space signal pattern of a 40-nm AuNP. FOV: 4.5 μm.

Enhancement on scattering cross section

The physical picture of the PC-nanoscatterer interaction can be delineated by temporal coupled-mode theory (TCMT)^22,27 (Supplementary Note 2). The PC is treated as a resonator (resonant frequency ω₀, radiative decay rate γ_r), and allowed to couple with the non-resonant NP antenna (scattering damping rate γ_sc). Here, absorption by the pristine PC resonator is neglected considering the low-loss property of dielectric material. The NP antenna is decoupled from free space radiation as its near-field interaction with the PC resonator is significantly stronger in comparison. Assuming a mirror-symmetry system, we obtain the resonator-mediated NP-scattered light as

where P_sc and P_in are respectively the scattered power and the incident power. From Eq. (1), it is indicated that the scattering signal follows a sharp Lorentzian lineshape centered near the PCGR resonant frequency. The scattering cross-section σ_sc for AuNPs obtained through FEM simulation exhibits good agreement with our analytical prediction, with a broadband background attributed to the onset of the AuNP plasmonic resonance mode (Fig. 4a). It can also be observed from Eq. (1) that the NP scattering efficiency is maximized when the radiative decay rate of the PC resonator matches the effective damping decay rate of NPs (\(\gamma _r = \gamma _{sc}\)). In comparison with a layer of solitary AuNPs, the PC-enabled scattering cross-section enhancement ratio at resonance can be obtained as²⁸

where λ₀ is the resonant wavelength, α is the energy confinement of the PC mode in the NP layer, n is the refractive index of water and d_e is the effective length of the evanescent field. As the intrinsic scattering power of the NP scales with the sixth power of its radius, the scattering damping rate γ_sc approaches the radiative decay rate γ_r with decreasing size; therefore, the PC-enabled scattering cross-section enhancement ratio is also a function of NP size. This volume-dependent relationship is best captured in Fig. 4b, where the amplification of AuNP scattering cross section by the resonating PC substrate is obtained in comparison with that of a glass substrate. In general, AuNPs exhibit at least one-order-of magnitude enhancement in the scattering cross section, but for smaller NPs (d_AuNP = 5 nm) the cross section can be amplified by as much as 287 times.

The scatter enhancement by the PC resonator is experimentally validated by the AuNP contrast comparison between the PRISM system and a conventional interferometric system (iSCAT), where coverslips are used as the reference substrate and a partially transmissive (T ≈ 1%) gold disk is placed at the center of the Fourier plane for the attenuation on the reference beam (Fig. 4c). Under the same illumination intensity (25 W cm⁻²) and frame rate (600 FPS), interferometric images of water-suspended AuNPs were recorded and compared to demonstrate the ability of the resonant substrate to amplify the scattering signal (Fig. 4d). The signal contrast, measured at the centroid of the scattering pattern over 400 individual instances, was significantly improved when imaging with the on-resonant PC as the substrate by PRISM (Fig. 4e). Only AuNPs of 30 and 40 nm in diameter are compared here since the contrasts of smaller AuNPs by the partially transmissive disk are overwhelmed by the background noise. In hindsight, the contrast of the interferometric signal can be described as follows⁵

where E_sc and E_r represent the electric field of the scattered light and the reference light, while ϕ is the phase difference between E_sc and E_r. Therefore, the scattering signals from the two microscopy systems can be directly compared as long as the reference beam intensity remains constant. Our FEM calculation results predict that the PCCR offers a 28-fold amplification on σ_sc for AuNPs (d = 30 nm, 40 nm), or a 5.29-fold enhancement in terms of scattered electric field intensity (Fig. 4b), which is in good agreement with the experimentally obtained contrast amplification (Fig. 4e). In addition, it is noteworthy that the PC enhancement on the AuNP scattering is dependent on the relative NP location within one PC period, where the edge of the PC ridge provides more scattering enhancement due to the higher near-field intensity of the PCGR mode at the edge (Supplementary Fig. 7). This location sensitivity explains the broadened PRISM signal distribution for AuNPs in comparison with the DLS measurement results (Fig. 3e) and with the iSCAT measurement (Fig. 4e).

Detection of proteins and virions

As a demonstration of PRISM imaging of a biological nanoparticle, we evaluated the detection of individual SARS-CoV-2 viruses. The gamma (γ)-irradiated SARS-CoV-2 viruses were first imaged using SEM to characterize the virus morphology and physical dimension (d = 50.61 ± 7.97 nm, Fig. 5a). Diluted to 1  × 10⁶ pfu mL⁻¹ with phosphate buffer saline (PBS) solution, the SARS-CoV-2 sample was directly introduced on the PC surface and observed under PRISM (Fig. 5b, Supplementary Video 2). The diffusion of virions was recorded within the field of view (14.6 ×  14.6 μm), and a high SNR contrast signals of ~ −4.55% was obtained from more than 500 virions (Fig. 5c). While the experiment records the presence of virions that transiently encounter the PC surface and their path along the PC surface during Brownian motion (see Supplementary Fig. 9 for the estimation of virion diffusion constant), we anticipate the use of selective capture molecules immobilized on the PC surface that can recognize outer surface features on the virus^29,30, and bind the virus so that it will remain stationary.

Finally, to demonstrate the capability for PRISM to detect individual biological molecules, we exposed the PC surface to a solution containing large proteins. Ferritin (MW = 440 kDa) and fibrinogen (MW = 340 kDa) were prepared in buffer at concentrations of 100 nM and exposed to a bare PC substrate while recording PRISM image sequences at 600 FPS with 10-frame averaging. Representative images show individual protein molecules with contrast ranging from −0.5% to −1% (Fig. 5d). The histogram of signal intensity obtained from over 1000 transient surface scattering events reflects the separation of contrast distribution between the two protein molecules attributed to the mass difference (Fig. 5e). Since the background contrast is measured to be 0.20%, the detection limit of the current PRISM system is estimated to be 185 kDa.