Selective Enhancement of the Optical Chirality and Spin Angular Momentum in Plasmonic Near-Fields

Abstract

The interaction between circularly polarized (CP) light and matter is governed by two fundamental quantities: spin angular momentum (SAM) and optical chirality (OC). While these quantities are inseparable in free space, they can be selectively enhanced in plasmonic near-field regions through appropriately designed structures. We demonstrate that the excitation of circular plasmonic nanostructures with CP light enables the selective or simultaneous enhancement of the SAM and OC through the excitation of rotating plasmon modes. Electromagnetic field analysis reveals that SAM enhancement originates from transverse SAM induced by unidirectional evanescent waves, whereas OC enhancement is governed by the interference between the plasmonic electric field and the incident magnetic field. The finite-element method simulations confirm that circular differential absorption signals arising from these enhanced near-fields clearly depend on the SAM and OC of the local fields, underscoring the importance of structural design in the detection and enhancement of CP light–matter interactions at the nanoscale.

Circularly polarized (CP) light, characterized by its helical electromagnetic fields, induces unique optical phenomena on the interaction with matter. A prominent example is the differential response of a material to left- and right-handed CP light. This includes effects such as circular dichroism (CD) in chiral molecules and Faraday rotation in magneto-optical (MO) materials, where the response varies with the handedness of the incident CP light. These phenomena are ubiquitous in natural substances and have been extensively studied, particularly in biomolecular analysis, , crystallography, , and MO effects. ,

To describe CP light–matter interactions, two key quantities that characterize CP light are commonly employed: spin angular momentum (SAM) and optical chirality (OC). In vacuum, SAM is described by a three-dimensional vector. ,

$$\mathbf{S}=\frac{1}{2\omega }\mathrm{Im}({ϵ}_0{\mathbf{E}}^{*}\times \mathbf{E}+{\mu }_0{\mathbf{H}}^{*}\times \mathbf{H})$$ 1

The optical chiral density is described by a scalar quantity. −

$$\begin{array}{c}C=\frac{{ϵ}_0}{2}\mathbf{E}·(\nabla \times \mathbf{E})+\frac{{\mu }_0}{2}\mathbf{H}·(\nabla \times \mathit{H})\\ =\frac{\omega }{2c^2}\mathrm{Im}({\mathbf{E}}^{*}·\mathbf{H})\end{array}$$ 2

Here, E and H denote the electric and magnetic fields, respectively, ϵ₀ and μ₀ denote the vacuum permittivity and permeability, respectively, and ω and c denote the angular frequency and speed of light, respectively.

Although both are associated with CP light and change sign upon handedness reversal, they describe fundamentally different aspects of the electromagnetic field. − The vector S represents the temporal rotation of the electromagnetic fields, as illustrated in the yellow panels of Figure . By contrast, C quantifies the phase relationship between the codirectional components of the electric and magnetic fields. As shown in the green panels of Figure , the sign of C depends on whether the electric field leads to or lags the magnetic field in phase.

1.

CP light propagating in the z direction, exhibiting the electric field E (red) and magnetic field H (blue) for right- and left-handed polarization. The yellow and green panels represent the characteristic features of the SAM and OC, respectively.

As quantities that characterize CP light, the SAM and OC have been used to explain various handedness-dependent phenomena in light–matter interactions. However, the physical quantity that mediates the CP light–matter interactions depends on the material properties (section S1). For example, the responses of MO substances and chiral molecules to CP light are governed by the SAM and OC, respectively. ,, Furthermore, in complex systems, such as oriented chiral molecules, , or magnetochiral materials, the signal induced by CP light involves combined contributions of the SAM and OC, rather than being governed by a single quantity. In such cases, the individual contributions of the SAM and OC to the observed signals need to be evaluated. However, this task remains challenging because the two quantities are inherently inseparable in free space. ,

Nevertheless, it has been shown that in structured optical near-fields, such as those arising from evanescent waves or resonant nanostructures, the otherwise inseparable quantities SAM and OC can become partially decoupled under certain conditions. , While partial decoupling of the SAM and OC has been reported, the mechanisms responsible for their respective enhancements remain not fully understood, and systematic strategies for their individual or combined control have yet to be established.

Herein, we demonstrate that this decoupling can be exploited for geometry-driven control over SAM and OC enhancement in plasmonic nanostructures. By exciting unidirectionally rotating plasmon modes via CP light incident on disk- or hole-shaped metal structures, we show that the resonator geometry dictates whether the SAM or OC is selectively or simultaneously controlled in the plasmonic near-field. Analysis of the three-dimensional orientations and phase relationships of the electric and magnetic fields reveals the distinct physical mechanisms underlying these behaviors. Finite-element method (FEM) simulations incorporating MO and chiral materials further confirm the experimental feasibility of selectively enhancing the SAM and OC. The demonstrated geometry-dependent control over optical responses significantly broadens the functional scope of plasmon-enhanced near-fields, offering a pathway to engineer electromagnetic environments for light–matter interactions beyond the reach of conventional free-space optics.

Figure a shows the finite-difference time-domain (FDTD) simulation model. The left and right panels depict the disk and hole structures, respectively. A 50-nm-thick Ag structure with radius r is placed on the xy plane, and CP light is normally incident from a total-field scattered-field source. The observation planes (P ₁ and P ₂) and point (P ₃) are defined as shown in the figure. All simulations are performed using ANSYS Lumerical (2023 R1). Details of the simulation conditions are provided in section S2.

2.

(a) FDTD simulation model showing the CP light source, plasmonic structures, and observation planes (P ₁ and P ₂) and point (P ₃). P ₁ and P ₂ are placed in the xy plane at z = 5 nm and in the xz plane at y = 0, respectively. P ₃ (white circle) is positioned 5 nm from the wall surface in the same plane as P ₁. The bottom surfaces of the structures are located at z = 0, with the radii of the disk and hole structures given by r _d = 80 nm and r _h = 90 nm, respectively. (b) Enhancement spectra of the z component of the SAM [S _z (ω)/S _z (ω), green] and OC [C(ω)/C ^ref(ω), purple] at observation point P ₃. The background represents the normalized electric-field enhancement spectrum [|E|(ω)/|E ^ref|(ω)]. (c) Spatial distributions of S _z (ω)/S _z (ω) and C(ω)/C ^ref(ω) at representative wavelengths, indicated by the color markers in part b.

The SAM and OC are calculated based on eqs and and normalized to the corresponding values obtained from a reference model without the structure. Here, we focus on the z component of the SAM, aligned with that of the incident CP light, while the OC is evaluated as a scalar quantity. Figure b shows the enhancement spectra of the z component of SAM [S _z (ω)/S _z (ω), green] and OC [C(ω)/C ^ref(ω), purple] at P ₃. The light-red region indicates the normalized electric-field enhancement spectrum [|E|(ω)/|E ^ref|(ω)] at the same point, showing a broad plasmon resonance centered at around 600 nm. The wavelength dependence of S _z and C around the disk structure exhibits markedly different behavior: S _z displays a sign-inverted profile relative to the electric-field enhancement, while C shows a dispersive profile centered near the resonance wavelength. By contrast, both S _z and C for the hole structure exhibit peak shapes similar to those of the electric-field enhancement. These wavelength-dependent behaviors of S _z and C are consistent with previous studies on related nanostructures. −

The spatial distributions in the P ₁ plane at typical wavelengths (color markers) are shown in Figure c. In the disk structure, at λ = 540 nm, S _z is enhanced along the circular boundary, whereas C is nearly absent despite CP light excitation. At λ = 800 nm, the situation is reversed, with C being enhanced and S _z nearly vanishing. The hole structure exhibits the simultaneous enhancement of both quantities within the hole region at its resonance wavelength (λ = 600 nm). The xz-plane cross section at the P ₂ plane (bottom panel) shows that the OC retains the same sign throughout the region, unlike typical plasmon-induced OC enhancement, which often exhibits opposite signs across spatial coordinates. Interestingly, this coordinate-dependent sign variation instead appears in S _z : at 540 nm, S _z with opposite signs is clearly visible on the sidewalls and the top and bottom surfaces.

First, we discuss the behavior of SAM. To better understand its complexity, it is useful to separately examine the contributions from the electric and magnetic fields. Parts a and b of Figure present the spatial distributions of the electric and magnetic contributions to S _z , namely, $S_z^E=\frac{1}{2\omega }\mathrm{Im}[{ϵ}_0(E_x^{*}{E}_y-E_y^{*}{E}_x)]$ and $S_z^H=\frac{1}{2\omega }\mathrm{Im}[{\mu }_0(H_x^{*}{H}_y-H_y^{*}{H}_x)]$ at their resonance wavelength, λ = 600 nm. These distributions reveal that S _z with a reversed sign on the walls of the disk and hole structures is primarily governed by the electric field, whereas the strong S _z observed on the planar surface of the disk is predominantly determined by the magnetic field.

3.

Components contributing to S _z around plasmonic nanostructures. Spatial distributions of the electric- and magnetic-field contributions to S _z for both disk (left) and hole (right) structures: (a) $S_z^E=\frac{1}{2\omega }\mathrm{Im}[{ϵ}_0(E_x^{*}{E}_y-E_y^{*}{E}_x)]$ and (b) $S_z^H=\frac{1}{2\omega }\mathrm{Im}[{\mu }_0(H_x^{*}{H}_y-H_y^{*}{H}_x)]$ . (c) Rotational behavior of the electric field associated with the rotating plasmon mode at the wall surface. (d) Schematic diagram of the magnetic field induced by charge motion.

The S _z sign reversal from the electric-field term can be explained by the rotation of the electric field in a unidirectional evanescent wave, known as transverse SAM (t-SAM). , Originally introduced in the context of uniform surface waves, t-SAM has since been generalized and is now understood as a general quantity applicable to a broad class of structured optical fields, including tightly focused beams and rotating localized modes. ,,, The direction of t-SAM in a unidirectional evanescent wave is given by S = ∇ × P, where P is the time-averaged Poynting vector. , This relationship indicates that, for a given energy flow direction, the SAM direction is determined by the decay direction of the evanescent field.

In typical localized surface plasmon modes, the fields are composed of counterpropagating components, and the t-SAM tends to cancel out. However, when a circular structure is excited by CP light, a rotating plasmon mode is generated, which sustains unidirectional circulation (section S3). In such a case, this cancellation is avoided, sustaining a finite and uniform t-SAM localized in the near-field, transverse to the rotational plane of the plasmon mode, that is, along the axial direction of the incident light. In the case of the disk and hole structures excited by the same CP light, their evanescent fields decay inward and outward, respectively, while their rotation directions remain identical. − As a result, the SAM direction is reversed between the two structures, as illustrated in Figure c.

Conversely, the strong SAM observed on the planar surface of the disk structure can be attributed to the magnetic field induced by the collective oscillatory motion of charges within the metal. As illustrated in Figure d, the induced magnetic field resulting from charge motion is distributed in the xy plane on the surfaces of both the disk and hole structures. In the hole structure, the orthogonal components of the in-plane magnetic field are spatially separated and exhibit linear oscillation, whereas in the disk structure, the magnetic field exhibits rotational behavior on the planar surface, directly contributing to the SAM.

To analyze the wavelength dependence of the OC, it is important to note that a planar plasmon wave does not exhibit OC even if the plasmonic field possesses SAM because the electric and magnetic fields consistently oscillate in orthogonal planes. ,, However, this constraint does not apply when incident and scattered fields are taken into account. , In this configuration, where a circular structure is excited by normally incident CP light (Figure a), both the plasmonic electric field (E _SP) and the incident magnetic field (H _Light) have coaxial components in the xy plane, resulting in finite values of the OC. In this case, the incident magnetic field cannot serve as a variable in the enhancement of OC as described by eq ; rather, the degree of enhancement is determined by two factors related to the plasmonic electric field: its amplitude and phase delay.

Figure a shows the wavelength dependence of the phase-delay characteristics obtained by replacing the CP excitation light with linearly polarized light in the same model as in Figure . The phase delay is calculated relative to a reference model without a plasmonic structure. Both the disk and hole structures exhibit similar dispersive wavelength dependencies centered at the resonance wavelength with a noticeable difference only in their baseline offsets. At resonance, the phase difference ϕ₀ is approximately π/2 for the disk structure and close to 0 for the hole structure.

4.

(a) Phase-delay characteristics of the enhanced electric field for the disk (left) and hole (right) structures. The red lines represent the wavelength dependence of the phase delay, and the light-red regions indicate electric-field enhancement spectra. The insets show the electric-field intensity distributions, |E|, at λ = 600 nm. (b) Simplified model calculation results. (Top panels) Phase difference between the plasmonic electric field E _SP and the incident magnetic field H _Light, relative to the incident electric field E _Light. The red and blue backgrounds indicate the amplitude spectra of the electric and magnetic fields, respectively. (Bottom panels) Calculated OC based on the phase-delay characteristics.

This difference in the phase-delay characteristics is consistent with previous studies reporting that the resonances of disk-type and hole-type structures correspond to electric and magnetic resonances, respectively. − While the electric resonance is directly driven by the electric field, the magnetic resonance is induced by the time variation of the magnetic field, resulting in a π/2 phase difference in the charge dynamics. This contrast in phase behavior is also reproduced by an equivalent LCR circuit model, where positive-type and negative-type structures correspond to series and parallel configurations, respectively (section S4). −

On the basis of the observed phase relationship between the incident light and the plasmonic near-field, we conducted a simplified model calculation comprising the plasmonic electric field (E _SP), modeled as a Lorentz-type resonator, − and the magnetic field of the incident light (H _Light). Figure b shows the phase delays (lines) and amplitude spectra (shaded areas) of E _SP (red) and H _Light (blue), with both phases defined relative to E _Light under right-handed CP illumination. The phase difference ϕ₀ between E _Light and E _SP at the resonance wavelength was set to π/2 for the disk model and 0 for the hole model. Full details of the model are provided in section S5.

The OC calculated from these phase relationships, shown in the bottom panels, and the resulting spectral trends are consistent with those reproduced in the spectral trends observed in the FDTD simulations in Figure b. In the disk model, the π/2 phase delay compensates for the intrinsic phase difference between the electric and magnetic fields of CP light, causing them to oscillate in phase at the resonance wavelength. As the wavelength deviates from resonance, the lead–lag relationship between E _SP and H _Light reverses, resulting in a dispersive spectral profile centered at the resonance. By contrast, E _SP in the hole model is enhanced without a phase shift at the resonance frequency, resulting in a peak-shaped profile that reflects the electric-field enhancement spectrum (Figure b). This simplified model considers only E _SP and H _Light in the xy plane, while in reality, radiative and scattered fields also affect the OC. ,, Nevertheless, the phase delay between external and plasmonic fields remains the key to the observed differences between the hole and disk structures.

While the present analysis focuses on plasmonic systems, the same phase-based interference mechanism is also applicable to other resonant systems, such as high-index dielectric resonators exhibiting both electric and magnetic responses. In such systems, however, multiple combinations of electric- and magnetic-field components from both the resonator and incident wave can contribute to the OC, potentially yielding stronger effects but making the analysis more complex.

The distinct enhancement mechanisms of SAM and OC discussed above suggest the potential for their independent control using plasmonic structures. However, the enhanced electromagnetic fields deviate in several respects from those of free-space CP light, particularly in the amplitude ratio and relative rotation of the electric and magnetic fields. These deviations raise the question of whether the SAM and OC enhanced in this manner can be detected through conventional measurements. To evaluate this feasibility and investigate how the enhanced fields manifest in experimentally observable quantities, we conducted FEM simulations.

Figure a shows the schematic of the FEM simulation setup conducted using COMSOL Multiphysics. To simulate realistic experimental conditions, the structures were modeled as periodic arrays placed on a substrate in solution. The array periods were chosen to maximize near-field enhancement at the resonance wavelength for each structure. Two types of functional layers were considered, each supporting either a MO material responsive to SAM or a chiral material for OC. To limit the evaluation to plasmonic near-fields and to maintain consistent conditions between the disk and hole structures, the functional layers were added only along the sidewalls of the nanostructures. The MO material is modeled by modifying the dielectric constant tensor to include off-diagonal components, using an anisotropy coefficient g introduced by magnetization (ϵ _xy = −ϵ _yx = ig). , For the chiral material, the Pasteur parameter κ, which governs the coupling between the electric and magnetic responses of the medium, is introduced to incorporate chirality into the system − (section S6). In bulk materials, the real and imaginary parts of κ typically correspond to optical rotation and CD, respectively. For g, the real part manifests as a Faraday rotation, while the imaginary part corresponds to magnetic CD. In both cases, the background dielectric constant was set to ϵ = 1.43, and all other simulation conditions were kept identical.

5.

(a) Schematic and simulation results for the FEM simulation. The simulation setup consists of nanodisk and nanohole structures with optically active layers added around their wall surfaces. The disk structure used a radius of r _d = 105 nm and a period of P _d = 380, while the hole structure used r _h = 90 nm and P _h = 350. The thickness of all nanostructures was fixed at 50 nm. (b) CDA spectra for the disk (blue) and hole (red) structures. The top and bottom panels correspond to the MO and chiral models, respectively. The left and right columns show the absorptive and birefringent cases. (c) Conceptual illustration of how different CDA spectral shapes arise from variations in the absorption spectra.

To clarify the fundamental differences in how SAM and OC contribute to observable signals, substantially large constant values were assigned separately to the real and imaginary parts of g and κ. In each simulation, only one of these parameters was set to a nonzero value, while the others were kept at zero. We refer to the models with g = 0.003i and g = 0.003 as the absorptive and birefringent MO models, respectively; similarly, the models with κ = 0.01i and κ = 0.01 are referred to as the absorptive and birefringent chiral models, respectively. Details of the material parameters and simulation settings are provided in section S6.

The light–matter interaction in chiral and MO media is governed by the OC and electric components of the SAM, respectively (section S1). Accordingly, the coupling parameters κ and g are expected to manifest in the absorption difference between right- and left-handed CP light at each frequency, referred to as the circular differential absorption (CDA) spectrum.

The CDA spectra for each model are shown in Figure b. Reversing the sign of g or κ inverts the CDA signal, and no CDA response is observed when all parameters are set to zero (not shown). In the absorptive models (left panels of Figure b), the CDA spectra resemble the wavelength dependence of the near-field C and S _z shown in Figure b: the MO models exhibit inverted peak-shaped spectra for the disk and hole structures, whereas the chiral models display a peak-shaped spectrum for the hole structure and a dispersive spectrum for the disk structure. These spectral shapes indicate that the absorption changes at each wavelength directly reflect enhanced C and S _z .

The signal for the birefringent chiral model exhibits slight dips for the disk and hole structures. This behavior is consistent with the previously reported signals observed in metal nanoparticle–chiral molecule complexes under off-resonant conditions, where the molecular and plasmonic resonances are spectrally separated and the Pasteur parameter is dominated by its real part. − A possible explanation is chirality transfer arising from coupling between the resonator and the surrounding chiral material, causing the system to behave as an effective chiral medium. In this interpretation, the absorption spectrum would not directly reflect enhanced OC, leading to no notable difference in the spectral shape between the disk and hole structures.

By contrast, the CDA spectra for the birefringent MO model are inverted between the disk and hole structures, reflecting the modulated effective refractive index due to the oppositely enhanced S _z . Notably, both the absorptive chiral and birefringent MO models exhibit similar dispersive profiles for the disk structure despite arising from different mechanisms. As illustrated in Figure c, the dispersive CDA spectra observed in the MO birefringent models can be attributed to red or blue shifts of the resonance wavelengths due to modulation of the effective refractive index (top panels), while that in the chiral absorptive model results from a deformation of the absorption spectrum reflecting the enhanced OC (bottom panels).

These results indicate that enhanced OC and SAM generate detectable observables, whose spectral characteristics differ between the real and imaginary parts of g and κ. Simulations with a more practical model, in which both real and imaginary parts coexist, exhibit behavior that appears to be a linear combination of the individual contributions (section S7), suggesting that the parameter-dependent responses identified in this study provide valuable insights into CDA signals in realistic systems.

In summary, we have demonstrated that the CP excitation of circular plasmonic structures enables the selective control of SAM and OC. Through an analysis of their spatial distributions and wavelength dependencies, we clarified that SAM enhancement arises from transverse SAM induced by a unidirectional evanescent field, whereas OC enhancement is governed by the phase relationship between the plasmonic electric field and the incident magnetic field. FEM simulations incorporating chiral and MO materials confirm that these enhanced near-fields can generate CDA signals with spectral characteristics determined by both the plasmonic structure and the nature of the material.

Our findings suggest that plasmonic near-fields would serve as effective platforms for disentangling signals arising from CP light–matter interactions in complex systems, enabling the identification of SAM- and OC-derived contributions and the separate estimation of the real and imaginary parts of g and κ. Furthermore, such platforms could allow for detailed analysis of the underlying mechanisms, such as the respective roles of electric- and magnetic-field SAM, and the influence of the electric-to-magnetic field ratio on the OC in CDA signals. These capabilities provide a solid foundation for interpreting complex light–matter interactions.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.5c02776.

• Theoretical background for MO and chiral materials, simulation setup for FDTD simulations, identifying rotational plasmon modes via electromagnetic analysis, LCR circuit models for phase-delay spectra of the disk and hole structures, simplified interference model for OC, simulation setup and parameter details for FEM simulations, and FEM simulations with complex parameters (PDF)

All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

This work was supported by a Grant-in-Aid for JSPS Fellows (No. JP23KJ0355), a Grant-in-Aid for Scientific Research (A) (No. JP20H00325), a Grant-in-Aid for Scientific Research (C) (No. JP24K08359), a Grant-in-Aid for Challenging Exploratory Research (No. JP20K20560), Fujikura Co., Ltd., and JST, PRESTO (No. JPMJPR24L3). D.O. was supported by a JSPS Overseas Research Fellowship, the Institution of Engineering and Technology, and Fundação para a Ciência e a Tecnologia and Instituto de Telecomunicacõ̧es under Project UIDB/50008/2020. Moreover, D.O. was supported by the RIKEN special postdoctoral researcher program.

The authors declare no competing financial interest.