Dual-parameter chiral detection at the single-particle level enabled by surface cosine waves

Abstract

Accurately probing optical chirality at the single-particle level is essential for chiral molecular sensing, quantum optics, and enantioselective nanophotonic technologies. However, conventional chiroptical techniques rely on ensemble-averaged measurements, obscuring particle-to-particle heterogeneity. Although single-particle circular dichroism spectroscopy has achieved nanoscale resolution, it remains limited to intensity-only detection, omitting essential phase information. Here, we present a dual-parameter chiral sensing platform based on surface cosine waves (SCWs) that simultaneously captures amplitude and phase asymmetries at the single-particle level. SCWs create a polarization-balanced interferometric field comprising equal-amplitude left and right circular components with a built-in π phase offset. When interacting with a chiral scatterer, this symmetry is broken, encoding the structural handedness into two distinct metrics: circular scattering dichroism (CSD) and circular scattering retardance (CSR). Together, these metrics provide a comprehensive electromagnetic characterization of single-particle chirality. This method provides a robust, generalizable framework for high-sensitivity, single-particle chiral sensing, paving the way toward next-generation chiroptical metrology and device development.

Surface cosine waves enable single-particle chiral sensing with simultaneous amplitude and phase readouts.

INTRODUCTION

Optical chirality—the differential interaction of left circularly polarized (LCP) and right circularly polarized (RCP) light with matter—underpins key phenomena in biology (1–3), chemistry (4–6), and photonics (7–10). Resolving chirality at the single-particle scale holds transformative potential for applications such as molecular enantiomer discrimination (11–13), chiral quantum photonics (14–16), and on-chip chiral photonic device design (17–20). Traditional chiroptical methods, such as circular dichroism (CD) and optical rotatory dispersion (ORD), rely on ensemble averaging (21–27), obscuring particle-to-particle heterogeneity and lacking simultaneous access to both amplitude and phase components of the chiral response. Emerging single-particle methods, including dark-field circular differential scattering (CDS) (14, 28–31), photothermal circular dichroism (PT CD) microscopy (32–34), and vortex dichroism spectroscopy (VDS), enable single-particle–resolved measurements but remain blind to the phase signatures essential for a complete chiroptical characterization (35–37). Superchiral light strategies enhance local optical chirality to amplify signals; however, most implementations remain intensity-based and typically lack single-particle resolution (38–43). A promising development introduced magnetic-free chiral eigenmode spectroscopy, enabling simultaneous CD and ORD measurement (44). However, its ensemble nature still fails to resolve nanoscale asymmetries. Thus, a versatile and robust single-particle approach that simultaneously captures both amplitude and phase responses remains a critical unmet need.

Here, we address this challenge by developing a dual-parameter chiral sensing platform based on SCWs. SCWs are structured surface plasmon polariton (SPP) fields (9) that not only offer strong near-field enhancement and nanoscale spatial modulation but also inherently feature equal-amplitude left-handed (LH) and right-handed (RH) circular polarization (LCP and RCP) components with a built-in π-phase offset when launched under a specific excitation geometry ($\mathrm{\theta }=45°$). This configuration establishes an ideal interferometric landscape in which coupling to a chiral scatterer induces measurable asymmetry in both amplitude—quantified as the circular scattering dichroism (CSD)—and phase—quantified as the circular scattering retardance (CSR). By integrating SCW excitation with a polarization-resolved dual-arm detection system, our platform enables rapid, quantitative, and simultaneous retrieval of CSD and CSR at the single-particle level. We validate this approach on electron-beam-lithography-fabricated gammadions and chemically synthesized chiral nanoparticles, demonstrating high sensitivity, robust retrieval of both amplitude and phase components, and excellent agreement with theoretical predictions. This SCW-based dual-parameter method bridges the gap between ensemble chiroptical techniques and intensity-only single-particle techniques, establishing a versatile platform for nanoscale chirality detection.

RESULTS

Generation and interferometric properties of SCWs

SCWs arise from the coherent interference of two monochromatic SPP plane waves propagating symmetrically in the transverse plane. These SPPs are excited by transverse magnetic (TM)–polarized beams and travel at angles of $\mathrm{\theta }$ and $\mathrm{\pi }-\mathrm{\theta }$ relative to the x axis, creating an angular separation of $\mathrm{\pi }-2\mathrm{\theta }$ (Fig. 1A). The angle $\mathrm{\theta }$ is defined by the relation: $\mathrm{\theta }={\text{sin}}^{-1}\left[k_x/\text{Re}\left(k_{\text{sp}}\right)\right]$, where $k_x$ is the x component of the in-plane SPP wave vector $k_{\text{sp}}$, and $k_{\text{sp}}=\sqrt{k_x^2+k_y^2}=k_0\sqrt{{\mathrm{\epsilon }}_{\mathrm{d}}{\mathrm{\epsilon }}_{\mathrm{m}}/({\mathrm{\epsilon }}_{\mathrm{d}}+{\mathrm{\epsilon }}_{\mathrm{m}}),}$ where $k_0=\mathrm{\omega }/c$ is the vacuum wave vector, and ${\mathrm{\epsilon }}_{\mathrm{d}}$ and ${\mathrm{\epsilon }}_{\mathrm{m}}$ are the relative permittivity of the dielectric and metal, respectively. The out-of-plane wave vector, $k_z=i\mathrm{\alpha }$, satisfies the SPP dispersion relation $k_{\text{sp}}^2={\mathrm{\alpha }}^2+{\mathrm{\epsilon }}_{\mathrm{d}}{k}_0^2$. Constructive interference between the two SPPs yields a structured SCW field that exhibits a standing-wave pattern (Fig. 1B). The longitudinal electric field component in the dielectric half-space ($z>0$) is given by

$$E(z,t)=2A\text{cos}\left(k_{x}x\right)e^{i{k}_{y}y}{e}^{-\mathrm{\alpha }z}{e}^{-i\mathrm{\omega }t}$$ (1)

other field components can be derived from Maxwell’s equations (Supplementary Materials, text S1). The resulting energy flux, indicated by the Poynting vector, demonstrates y-directional propagation, whereas the x axis exhibits periodic spatial modulation. By tuning the angle $\mathrm{\theta }$, we can tailor both the spatial frequency and phase structure of the SCW (fig. S1).

Fig. 1. Generation and interferometric symmetry of SCWs.

(A) Schematic of SCW generation via the interference of two SPP waves with an angular separation of $\mathrm{\pi }-2\mathrm{\theta }$. (B) Simulated electric field intensity distribution showing a standing-wave pattern characteristic of SCWs. (C) Calculated phase difference ($\mathrm{\Delta \varphi }$; red dots) and amplitude ratios (gray diamonds) between the LCP and RCP components as functions of the excitation angle $\mathrm{\theta }$ ($0°$ to $90°$). At $\mathrm{\theta }=45°$, the phase difference reaches $\mathrm{\pi }$, resulting in (D) complete spatial anti-alignment between the intensity maxima of the LCP (blue) and RCP (red) components.

The unique optical characteristics of SCWs arise from a specific amplitude and phase relation between their circular polarization components. The intensity distributions of the LCP ($I_{\mathrm{l}}$) and RCP ($I_{\mathrm{r}}$) can be analytically derived (Supplementary Materials, text S2) as

$$I_{\mathrm{l}/\mathrm{r}}=\frac{A^2{e}^{-2\text{Re}\left(\mathrm{\alpha }z\right)}\mathrm{\alpha }{\mathrm{\alpha }}^{\ast }}{{\mid k_{\text{sp}}\mid }^2}\left\{1-\text{cos}\left[2(k_{x}x\mp \mathrm{\theta })\right]\right\}$$ (2)

where the minus and plus signs correspond to the LCP and RCP components, respectively. This expression reveals that $I_{\mathrm{l}}$ and $I_{\mathrm{r}}$ have equal amplitudes but exhibit a spatial phase offset of $\mathrm{\Delta \varphi }=4\mathrm{\theta }$, which is directly tunable via the parameter $\mathrm{\theta }$ (Fig. 1C).

At $\mathrm{\theta }=45°$, the phase difference reaches $\mathrm{\pi }$, resulting in perfect anti-alignment: the intensity maxima of the LCP component coincide spatially with the minima of the RCP component (Fig. 1D). This $\mathrm{\pi }$-phase offset establishes an ideal interferometric condition, characterized by equal amplitudes and a built-in phase opposition between the two circular polarization components. Within this symmetric optical background, any imbalance in amplitude or phase, such as that induced by a chiral scatterer, manifests as a measurable perturbation (45), enabling direct and quantitative detection of chiral interactions.

For $\mathrm{\theta }$ values other than $45°$, the phase offset deviates from $\mathrm{\pi }$, diminishing the anti-alignment and leading to partial overlap of intensity lobes (fig. S2). The symmetric configuration at $\mathrm{\theta }=45°$ thus provides a uniquely sensitive platform for chiral sensing, in which the SCW’s intrinsic interferometric symmetry maximizes the contrast for detecting even subtle chiroptical perturbations at the nanoscale. In principle, this platform is applicable to most scattering nanoparticles, with performance primarily limited by the scattering cross section, lateral footprint relative to the SCW spatial period, and vertical extent within the SPP decay length (see Supplementary Materials, text S3 and fig. S3).

Theoretical framework for chiral sensing with SCWs

To elucidate the physical mechanism underlying SCW-based chiral sensing at the nanoscale, we conducted finite-difference time-domain (FDTD) simulations to examine the interaction of SCWs with both achiral and chiral nanostructures (simulation details in Supplementary Materials, text S6).

Figure 2A schematically illustrates the sensing concept. Two TM-polarized plane waves are symmetrically incident on a gold film, launching counterpropagating SPPs that interfere to form an SCW. The resulting SCW consists of LCP and RCP components with equal amplitudes and an intrinsic $\mathrm{\pi }$-phase offset. A nanostructure placed atop the surface serves as a near-field scatterer that outcouples the local SCW field into the far field. This interaction perturbs the balance between the LCP and RCP channels. Any symmetry breaking in amplitude or phase introduced by the nanostructure is thus encoded into the polarization-resolved scattering components, providing a direct optical signature of chirality.

Fig. 2. SCW-enabled detection of chirality-induced amplitude and phase asymmetries.

(A) Schematic illustration of the SCW-based chiral sensing configuration. Two symmetrically incident TM-polarized beams excite counterpropagating SPPs on a gold film. Interference between their in-plane wave vector components ($k_{x1}$ and $k_{x2}$) generates an SCW composed of equal-amplitude LCP and RCP components with an intrinsic $\mathrm{\pi }$-phase offset. Upon interacting with a chiral structure, the SCW field is perturbed, leading to amplitude and phase imbalances between the LCP and RCP channels that encode chiral information. (B to D) Simulated LCP (blue) and RCP (red) scattering intensity profiles for (B) NH, (C) LH, and (D) RH. Solid lines denote SCW model fits; dots represent raw FDTD data. Colored arrows mark relative phase shifts, and colored triangles mark peak positions of LCP and RCP components. The black vertical dashed line serves as a spatial phase reference of the unperturbed SCW.

We first analyze an achiral reference structure: a nonhanded (NH) gammadion. Under SCW excitation at $\mathrm{\theta }=45°$, the scattered LCP and RCP intensity profiles (Fig. 2B) exhibit equal amplitudes and retain the expected $\mathrm{\pi }$-phase offset, thus preserving the polarization symmetry inherent to the SCW. Although the finite spatial extent of the nanostructure introduces convolutional smoothing (fig. S4B), this does not change the relative amplitude or phase between the LCP and RCP components (Supplementary Materials, text S4), preserving the polarization-resolved features essential for chiral analysis.

In contrast, when the SCW interacts with a chiral nanostructure, such as an LH or RH gammadion, this symmetry is broken. As shown in Fig. 2 (C and D), the scattered LCP and RCP components exhibit clear amplitude imbalance and spatial phase shifts, indicating polarization-selective coupling. These asymmetries originate from the differential interaction of the chiral structure with the SCW’s circular components, redistributing energy between the LCP and RCP channels (fig. S5).

To quantify these chirality-induced deviations, we fit the scattering circular components using a modified SCW expression

$$I_{\text{lcp}/\text{rcp}}^{\text{fit}}=A_{\mathrm{l}/\mathrm{r}}\left\{1-\text{cos}\left[2(k_{x}x\mp \frac{\mathrm{\pi }}{2}+{\mathrm{\delta }}_{\mathrm{\phi l}/\mathrm{r}})\right]\right\}+\text{BG}$$ (3)

where $A_{\mathrm{l}}$ and $A_{\mathrm{r}}$ represent the fitted amplitudes of the LCP and RCP components, ${\mathrm{\delta }}_{\mathrm{\phi l}}$ and ${\mathrm{\delta }}_{\mathrm{\phi r}}$ are the phase shifts induced by the scatterer, and $\text{BG}$ accounts for background signals and convolutional smoothing. In the achiral case, $A_{\mathrm{l}}=A_{\mathrm{r}}$ and ${\mathrm{\delta }}_{\mathrm{\phi l}}={\mathrm{\delta }}_{\mathrm{\phi r}}=0$, yielding perfect interferometric symmetry. In chiral cases, deviations in amplitude and phase directly encode the handedness of the structure.

We define two metrics to quantify these chiral optical signatures.

CSD captures the amplitude asymmetry between LCP and RCP channels

$$\text{CSD} (\%)=\frac{A_{\mathrm{l}}-A_{\mathrm{r}}}{\frac{A_{\mathrm{l}}+A_{\mathrm{r}}}{2}}\times 100$$ (4)

CSR quantifies the relative phase delay between the two polarization components

$$\mathrm{\Delta \phi }=\mid {\mathrm{\delta }}_{\mathrm{\phi l}}\mid -\mid {\mathrm{\delta }}_{\mathrm{\phi r}}\mid$$ (5)

Unlike conventional far-field scattering measurements that are blind to phase, SCWs intrinsically encode both amplitude and phase information into the spatial modulation of the scattered intensity. Consequently, both CSD and CSR can be extracted from spatially resolved intensity profiles of the LCP and RCP channels, where phase information is encoded by the SCW, eliminating the need for conventional interferometric or iterative phase retrieval methods (see Supplementary Materials, text S7 for fitting details).

To assess the robustness of this method, we systematically varied the height ($h$) and linewidth ($w$) of LH, RH, and NH gammadions, keeping the overall footprint fixed at $200 \text{nm} \text{by} 200 \text{nm}$ (Fig. 3G). Figure 3 (A to F) presents the simulated LCP and RCP scattering spectra as a function of height. As expected, the NH gammadions (Fig. 3, C and D) show negligible amplitude and phase asymmetry, whereas the LH and RH gammadions exhibit strong geometry-dependent distortions, including peak shifts and contrast variations, reflecting polarization-dependent scattering.

Fig. 3. Dependence of CSD and CSR on gammadion geometry.

(A to F) Simulated scattering intensity maps for the (A, C, and E) LCP and (B, D, and F) RCP components as a function of structure height ($h$) for LH, NH, and RH gammadions at fixed linewidth $w=20 \text{nm}$. Outlined white circles trace the peak positions; green triangles highlight maximal chirality-induced asymmetry. Data are normalized on a per-set basis for the LCP and RCP data (Supplementary Materials, text S5). (G) Schematic of the gammadion geometry, showing the top view (linewidth $w$) and side view (height $h$), with a fixed footprint of $200 \text{nm} \text{by} 200 \text{nm}$. (H and I) Extracted CSD and CSR as a function of height $h$, peaking at $h=60 \text{nm}$. (J and K) Corresponding CSD and CSR as a function of linewidth $w$, with maxima at $w=20 \text{nm}$. NH gammadions (black) exhibit near-zero values for both parameters, whereas LH (blue) and RH (red) gammadions show mirrored responses, confirming enantiomeric discrimination.

Figure 3 (H and I) summarize the extracted CSD and CSR values as a function of height. NH gammadions yield near-zero values, consistent with their structural symmetry. In contrast, LH and RH gammadions produce mirrored chiral responses, with maximal CSD and CSR observed at $h=60 \text{nm}$. Linewidth dependence (fig. S6) follows similar trends, with extremal values appearing at $w=20 \text{nm}$ (Fig. 3, J and K). At this configuration ($h=60 \text{nm}$; $w=20 \text{nm}$), LH gammadions (Fig. 2C) show enhanced LCP scattering with minimal phase distortion, whereas RCP scattering is suppressed and phase-delayed, yielding $\text{CSD}=+177\%$ and $\text{CSR}=-\mathrm{\pi }/4$. RH gammadions (Fig. 2D) show the opposite trend, with $\text{CSD}=-177\%$ and $\text{CSR}=+\mathrm{\pi }/4$, confirming reciprocal enantiomeric behavior.

To validate these findings, we benchmarked the SCW-based chiral parameters against results from conventional dark-field CDS techniques (14, 28, 46). Because of the intensity-only nature of CDS, direct comparison is limited to amplitude asymmetries, i.e., the CSD. Nevertheless, both approaches reveal consistent chirality-dependent trends, particularly in their linewidth dependence (Fig. 3J versus fig. S7C). Minor discrepancies observed in the height dependence (Fig. 3H versus fig. S7F) likely arise from the enhanced vertical sensitivity of SCW-mediated near-field interactions relative to far-field scattering in free space.

These theoretical results validate that SCWs enable simultaneous retrieval of amplitude-based and phase-based chiral signatures through CSD and CSR. By outperforming conventional CDS in information content and near-field sensitivity, SCWs provide a strong basis for experimentally realizing dual-parameter single-particle chiral sensing, as explored in the next section.

SCW-based dual-parameter chiral sensing at the single-particle level

To experimentally validate our SCW-based chiral sensing strategy, we developed a custom-built dark-field scanning near-field optical microscopy (SNOM) system to probe far-field scattering from individual nanostructures coupled to SCWs. As illustrated in Fig. 4A, a 633-nm laser beam is expanded, collimated, and linearly polarized before being phase modulated by a spatial light modulator (SLM). The first-order diffracted beam is Fourier transformed, converted into radially polarized light via a vortex retarder ($m=1$), and relayed through a $4\mathrm{f}$ system into a high-numerical-aperture (NA) oil-immersion objective ($\text{NA}=1.49$) to launch SCWs at the gold-air interface. The back-focal-plane image (Fig. 4B) reveals two reflection lobes at azimuthal angles of ${45}^{°}$ and ${135}^{°}$, corresponding to symmetric TM-mode SPP excitation. The localized darkening within each lobe confirms efficient SCW generation.

Fig. 4. Experimental realization of SCW-based single-particle chiral sensing.

(A) Schematic of the optical setup. A 633-nm laser beam is collimated and expanded (L1 and L2), linearly polarized via a crystal polarizer (P1) and a half-wave plate (HW), and phase modulated by an SLM. The first-order diffracted beam is Fourier transformed (L3), converted to radial polarization using a second HW and a vortex retarder (VR; m = 1), and relayed by a 4f system (L4 and L5) into a high-NA oil-immersion objective (NA = 1.49) to launch SCWs at the gold-air interface. Note: The detection scheme is shown separately in fig. S8. (B) Back-focal-plane image of the reflected 633-nm laser from gold film. (C to E) Far-field scattering intensity profiles (normalized) for LCP (blue) and RCP (red) components as the sample is scanned across the SCW along the x axis: (C) achiral PS sphere (280 nm in diameter, $\text{CSD}=3\%$, $\mathrm{\Delta \phi }=0.007\mathrm{\pi }$), (D) LH gammadion ($w=25 \text{nm}$, $\text{CSD}=49.7\%$, $\mathrm{\Delta \phi }=-0.31\mathrm{\pi }$), and (E) RH gammadion ($w=25 \text{nm}$, $\text{CSD}=-74\%$, $\mathrm{\Delta \phi }=+0.16\mathrm{\pi }$). Light-colored dots: raw data; solid lines: SCW model fits. Insets: SEM images of nanostructures. Scale bars, 100 nm (for LH and RH). (F) Experimental (dots) and simulated (dashed lines) CSD as a function of gammadion linewidth ($w$) for LH (blue) and RH (red) structures. Error bars represent the standard deviation over five measurements.

To ensure stable and accurate acquisition of circularly polarized scattering components, we implemented a dual-arm polarization-resolved detection scheme (Supplementary Materials, text S8 and fig. S8). A rotating polarization wheel alternately switches between LH and RH circular polarization analyzers (CP-L/CP-R), maintaining optical alignment during polarization switching. Simultaneously, a reference arm continuously monitors the LCP channel during both scans. Comparing these reference traces, any temporal drift is quantified and corrected, enabling high-fidelity extraction of both amplitude (CSD) and phase (CSR), together yielding a robust optical fingerprint of structural chirality. The acquisition speed is primarily limited by the scanning stage and detector response, with each polarization-resolved scan completed in ∼0.25 s (see Materials and Methods), demonstrating rapid characterization of individual nanoparticles.

We first validated the system using achiral 280-nm polystyrene (PS) spheres. As expected, the LCP and RCP scattering intensities were nearly identical, with a $\mathrm{\pi }$ phase difference (Fig. 4C), yielding negligible CSD (∼3%) and CSR (∼0.007$\mathrm{\pi }$). These results confirm the intrinsic symmetry of the SCW background and establish a baseline for chiral sensing.

Subsequently, we investigated LH and RH gammadions fabricated via electron beam lithography (EBL). At a linewidth of 25 nm, the LH gammadion exhibited a positive CSD and a negative CSR ($\text{CSD}=50\%$; $\text{CSR}=-0.31\mathrm{\pi }$), whereas its RH counterpart displayed the opposite response ($\text{CSD}=-74\%$; $\text{CSR}=+0.16\mathrm{\pi }$), in close agreement with simulation results (Fig. 4, D and E; and see Fig. 2, C and D). As the linewidth increased to 35 and 45 nm, the magnitude of the CSD progressively decreased (Fig. 4F and fig. S9, A to D), indicating reduced structural chirality.

Quantitatively, the measured CSD values were approximately half those predicted by simulations, whereas the CSR (fig. S9E) exhibited greater fluctuations, likely arising from fabrication-induced imperfections [see scanning electron microscopy (SEM) insets]. Notably, the chiroptical responses of LH and RH gammadions were not strictly reciprocal, deviating from ideal enantiomeric symmetry. This asymmetry reflects the system’s high sensitivity to nanoscale structural deviations, including imperfections introduced during nanofabrication. Despite these imperfections, both CSD and CSR retained their expected signs and geometric trends, underscoring the robustness and precision of the SCW-based dual-parameter sensing platform.

To further demonstrate the broad applicability of our SCW-based dual-parameter sensing platform, we extended the technique to chemically synthesized chiral gold nanoparticles. These nanostructures inherently exhibit morphological heterogeneity, which often obscures the individual chiral responses in ensemble-averaged chiroptical spectroscopy. We selected two distinct morphological subtypes, denoted Morphology-I (M-I) and Morphology-II (M-II), each comprising both LH and RH enantiomers (Fig. 5, A, E, I, and M). CD spectroscopy of these particles in solution revealed pronounced differences in optical activity at 633 nm—the excitation wavelength used in our SCW-based single-particle measurements. M-I displayed strong chiroptical responses, with LH and RH particles exhibiting negative and positive g-factors, respectively [$\mathit{\text{g}}\text{-factor}=2(A_{\mathrm{L}}-A_{\mathrm{R}})/(A_{\mathrm{L}}+A_{\mathrm{R}})$], indicating preferential coupling of LH particles to RCP light and RH particles to LCP light (fig. S10, A). In contrast, M-II showed much weaker g-factors with reversed handedness preference, suggesting diminished and inverted chiral interactions at the ensemble level (fig. S10, B).

Fig. 5. SCW-based single-particle chiral sensing of chemically synthesized gold helicoids.

(A, E, I, and M) SEM images of LH (A and I; false-colored blue) and RH (E and M; false-colored pink) gold helicoids with two distinct morphologies: M-I (A and E) and M-II (I and M). (B to D, F to H, J to L, and N to P) Normalized far-field scattering intensities for LCP (blue) and RCP (red) components as a function of lateral position x, measured from three spatially isolated single particles for each enantiomer. Dots represent raw experimental data; solid lines are cosine fits. The extracted CSD (CSD%) and CSR ($\mathrm{\Delta \phi }$) are labeled in each plot.

To resolve these chiral characteristics at the single-particle level, we performed SCW-based dual-parameter measurements on three spatially isolated LH and RH nanoparticles from each morphology. All particles exhibited distinct and quantifiable CSD and CSR, with noticeable interparticle variability (Fig. 5, B to D, F to H, J to L, and N to P). Notably, M-I consistently yielded larger CSD values than M-II, in agreement with ensemble-level g-factor trends. Moreover, the sign of CSD—negative for LH and positive for RH in M-I—mirrored the polarity of the corresponding g-factors. This enantiomeric correspondence also held for most M-II particles, validating the fidelity and reliability of our single-particle readouts. Some RH particles of M-II exhibited anomalous behavior (e.g., Fig. 5P: $\text{CSD}=+11\%$; $\text{CSR}=-0.2\mathrm{\pi }$), deviating from trends observed in Fig. 5 (N and O). These outliers likely arise from subtle nanoscale structural variations, which are entirely averaged out in bulk-phase CD measurements but can be sensitively resolved by our SCW-based platform.

Several particles exhibited pronounced CSR despite only moderate CSD values (e.g., Fig. 5, N to P). This observation suggests that amplitude (CSD) and phase (CSR) responses may reflect partially independent aspects of the chiral near-field interaction. Specifically, CSD primarily arises from polarization-dependent scattering and absorption asymmetries (dissipative response), whereas CSR reflects polarization-dependent phase retardation effects (dispersive response) (47). Subtle variations in particle geometry or local plasmonic resonances can modulate these responses differently, naturally leading to cases where CSD and CSR are not strictly correlated. Although further investigation is needed to elucidate the precise mechanisms, this decoupling underscores the importance of simultaneously measuring both amplitude and phase signatures. Together, these results underscore the unique strength of our SCW-based approach in capturing the complete electromagnetic fingerprint of nanoscale chirality at the single-particle level.

DISCUSSION

In summary, we have introduced and experimentally validated a dual-parameter platform for resolving optical chirality at the single-particle level by simultaneously accessing amplitude and phase information. By leveraging SCWs under a tailored excitation geometry ($\mathrm{\theta }=45°$), we generate a polarization-balanced, interferometric background composed of equal-amplitude LCP and RCP components with a built-in π-phase offset. Within this symmetric field, any structural chirality-induced imbalance manifests as measurable deviations in amplitude and phase—quantified as CSD and CSR, respectively. This approach departs fundamentally from conventional ensemble CD/ORD, single-particle intensity-only techniques, superchiral light strategies, and magnetic-free chiral eigenmode spectroscopy by providing simultaneous amplitude and phase information from individual nanoparticles (table S1). This study rigorously benchmarks the platform using both EBL-fabricated gammadions and chemically synthesized chiral nanoparticles and demonstrates rapid, robust, and sensitive performance with broad generalizability. Notably, the platform resolves particle-to-particle variations and reveals hidden structural asymmetries that remain inaccessible to ensemble measurements.

Leveraging the near-field confinement of surface plasmons and the interferometric sensitivity of SCWs, this platform provides a versatile and scalable foundation for high-resolution chiral sensing. Because SCWs arise from the interference of SPPs at a metal-dielectric interface, the underlying mechanism is not restricted to the specific wavelength or measurement conditions demonstrated here but can, in principle, be generalized across different spectral regimes and material platforms. Built on this foundation, a range of applications can be realized: SCWs may serve as spatially encoded chiral excitation fields for single-particle circularly polarized photoluminescence (CPL) (48, 49), enabling position-dependent mapping of LCP and RCP emission, and integration with plasmonic nanocavities offers a potential route toward single-molecule chiral detection via strong near-field enhancement (14, 28, 50). Together, these capabilities define a unified framework for SCW-based chiral sensing across multiple scales and readout modalities (see the roadmap in Supplementary Materials, text S9). This framework underscores the platform’s broad adaptability, providing a solid basis for future exploration of nanoscale chiral phenomena, including single-molecule enantiomer identification, real-time chiral imaging, nanoscale optomechanics studies, and the development of on-chip chiral photonic devices.

MATERIALS AND METHODS

Experimental setup for SCW-based single-nanoparticle chiral sensing

As schematized in Fig. 4A, a 633-nm laser beam first passes through a linear polarizer and a half-wave plate and then expands via a beam-expansion system to fully illuminate the active area of an SLM (PLUTOdd-2-VIS-016, Holoeye). A custom phase profile: $\mathrm{\varphi }=\text{angle}\left\{{\sum }_{m=1}^{2}A{e}^{i{k}_{\mathrm{t}}[x\text{cos}\left({\mathrm{\theta }}_m\right)+y\text{sin}\left({\mathrm{\theta }}_m\right)]}\right\}$ is encoded onto the SLM, where $k_{\mathrm{t}}$ is the transverse wave vector, adjusted to match the objective’s entrance pupil, and ${\mathrm{\theta }}_m$ denotes the azimuthal angles of the incident wave components (e.g., 45° and 135°). Upon reflection from the SLM, the modulated beam is converted into radially polarized light using a half-wave plate and a vortex retarder ($m=1$). Radial polarization is essential for generating high-contrast, symmetric SCWs as it produces uniform longitudinal fields across all azimuthal angles and ensures equal SPP excitation amplitudes for the two interfering beams. A long focal-length lens then performs a Fourier transform of the beam, and a 4f telescope relays the beam to the back focal plane of a high-NA oil-immersion objective ($\text{NA}=1.49$), thereby launching SCWs at the gold-air interface under total internal reflection conditions. Back-focal-plane images are recorded using a charge-coupled device (CCD) camera (Fig. 4B) to verify SCW excitation.

Samples consist of 50-nm-thick gold films deposited on silica substrates, onto which either EBL-fabricated or drop-cast chiral nanoparticles are positioned. These nanoparticles act as near-field scatters that outcouple the SCW field into the far field. The SCW center is experimentally determined using a surface Bessel beam with topological charge $l=1$ as a spatial reference. Because this excitation shares the same illumination geometry as the SCW, both are generated at the same metal-dielectric interface. The phase singularity of the Bessel mode provides a well-defined alignment point for subsequent nanoparticle scans relative to the SCW center. The sample is mounted on a piezoelectric scanning stage (Physik Instrument, P-545) with a scanning resolution of 1 nm and a typical step size of 20 nm.

The scattered light is collected by a second objective lens (Olympus, $50\times$, $\text{NA}=0.5$) and directed through CP-L or CP-R, which operates in reverse mode to function as a polarization analyzer. These polarizers are mounted on a rotating wheel, allowing alternate measurements of the LCP and RCP components without optical realignment. Simultaneously, a reference arm continuously monitors the LCP signal to correct for mechanical or temporal drift. The polarization-resolved scattered signals are detected by a photomultiplier tube (PMT; Hamamatsu R12829), and the corresponding CSD and CSR values are computed to quantify the optical chirality of each individual nanoparticle.

The overall acquisition speed is primarily determined by the response of the scanning stage and the PMT. In our experiments, the PMT exhibits a 2.2-ns rise time, and the piezo stage operates on the millisecond timescale. For stable data acquisition, we use a 5-ms integration time per position. Scanning a typical 1.5-μm range along the x axis with 30-nm steps (51 points) yields a total acquisition time of ∼0.25 s per polarization-resolved scan, demonstrating rapid dual-parameter characterization of individual nanoparticles.

Sample preparation and characterization

EBL-fabricated gammadions

Gammadion structures were fabricated using standard EBL techniques. A 50-nm gold layer was first deposited onto a silica substrate using a multichamber vacuum sputtering system. A 100-nm-thick polymethyl methacrylate (PMMA) resist was spin coated and baked at 150${}^{°}\mathrm{C}$ on a hotplate for 1 min. The pattern was exposed using an EBL system (Raith BV, EBPG 5150). After exposure, the sample was developed sequentially in methyl isobutyl ketone (MIBK):isopropyl alcohol (IPA) (1:3) and IPA for 1 min each, followed by nitrogen blow-drying. A 60-nm gold layer was subsequently deposited by sputtering. Last, the residual PMMA was removed by immersing the sample in acetone for 2 hours, yielding clean gammadion structures on the gold substrate.

Helicoidal gold nanoparticles

Chiral Au nanoparticles were synthesized using a modified biomolecule-directed growth protocol, following previously reported methods (51–53). CD and extinction spectra in bulk solutions were acquired using a J-1700 spectropolarimeter (JASCO). The Kuhn’s dissymmetry factor (g-factor) is a dimensionless quantity that is useful for quantitative comparisons of chiro-optical properties among different systems and was calculated from the measured extinction and CD values as (52): $\mathit{\text{g}}\text{-factor}=2(A_{\mathrm{L}}-A_{\mathrm{R}})/(A_{\mathrm{L}}+A_{\mathrm{R}})\propto \text{CD}/\text{extinction}$, where $A_{\mathrm{L}}$ and $A_{\mathrm{R}}$ are the extinction values for LCP and RCP light, respectively. The morphology of the chiral nanoparticles was characterized by SEM (ZEISS SIGMA) at an accelerating voltage of 5 kV.

Numerical simulations

Numerical simulations were performed using a combination of custom MATLAB scripts and full-wave FDTD methods. Detailed modeling procedures, boundary conditions, material properties, and fitting strategies are described in Supplementary Materials, text S1 to S7.

Supplementary Materials

This PDF file includes:

Supplementary Text S1 to S9

Figs. S1 to S10

Table S1

References