Polarized evanescent waves reveal trochoidal dichroism

Abstract

Matter's sensitivity to light polarization is characterized by linear and circular polarization effects, corresponding to the system's anisotropy and handedness, respectively. Recent investigations into the near-field properties of evanescent waves have revealed polarization states with out-of-phase transverse and longitudinal oscillations, resulting in trochoidal, or cartwheeling, field motion. Here, we demonstrate matter's inherent sensitivity to the direction of the trochoidal field and name this property trochoidal dichroism. We observe trochoidal dichroism in the differential excitation of bonding and antibonding plasmon modes for a system composed of two coupled dipole scatterers. Trochoidal dichroism constitutes the observation of a geometric basis for polarization sensitivity that fundamentally differs from linear and circular dichroism. It could also be used to characterize molecular systems, such as certain light-harvesting antennas, with cartwheeling charge motion upon excitation.

Keywords: Born–Kuhn model for circular dichroism; evanescent field polarization; plasmonic nanorod dimers; single-particle spectroscopy.

Fig. 1.

SAM and geometry drive distinct polarization-dependent light-matter interactions. (A) Circularly polarized light has a longitudinal SAM vector (S_CPL) that couples to electrons with coaligned spins (S_el). (B) The Born-Kuhn model for CD of two charged masses (gray spheres) attached to two coupled, orthogonal springs displaced along a third orthogonal axis. (C) Trochoidal polarizations produce a transverse SAM vector (S_EW) that similarly couples to electrons with coaligned spins. (D) A modified Born-Kuhn model for trochoidal dichroism where one oscillator is aligned along the direction of light propagation.

Fig. 2.

Orthogonal and offset nanorods are a model system for observing trochoidal differential scattering. (A) Experimental TIR geometry. LP: linear polarizer, E_s, E_p: incident electric field components, $\theta$: angle of incidence. (B) Isolated in-sample-plane components of the evanescent wave for E_s = −E_p and E_s = E_p incident polarizations, tracing CW and ACW trochoids, respectively. (C) Plasmon hybridization for the ⅃-dimer. The light-induced electric dipoles are shown with black arrows and are excited opposite with respect to the electric field, with the curved arrow solely indicating the trochoidal polarization. Excitation from a CW (ACW) trochoidal field gives a high (low) energy antibonding (bonding) mode. In the corresponding spring system, attached masses are positively charged and are attracted toward the trochoidal electric field drawn with dashed lines and curved arrows. (D) Plasmon hybridization for the mirror-image ⅂-dimer. Normalized measured and simulated scattering spectra of the (E) ⅃-dimer and (F) ⅂-dimer under CW and ACW trochoidal excitation. (Insets) Correlated scanning electron microscopy (SEM) images with scale bars of 100 nm and charge distributions calculated at the scattering maxima for CW and ACW trochoidal excitation, matching the black arrows in C and D.

Fig. 3.

L-dimers have trochoidal and linear dichroism of opposite sign. (A) Plasmon hybridization for the L-dimer with trochoidal excitation resulting from TIR of E_s = E_p (45°) and E_s = −E_p (−45°). Excitation from a CW (ACW) trochoidal field gives a high- (low-) energy antibonding (bonding) mode. (B) Plasmon hybridization for the L-dimer with oblique E_s = ±E_p incident polarizations. E_s = E_p (E_s = −E_p) linearly polarized light excites the high- (low-) energy antibonding (bonding) mode. Note that while magenta and blue arrows indicate the ±45° linear polarization of the incident light, the polarization once projected onto the sample plane is ±70° (SI Appendix, Supplementary Text). (C) Normalized single-particle scattering spectra of an L-dimer under CW and ACW trochoidal excitation. (Inset) Correlated SEM image. (Scale bar, 100 nm.) (D) Normalized scattering spectra of the same L-dimer under oblique incident excitation. Consistent results are observed also with normal incidence excitation (SI Appendix, Fig. S11). The increase in noise is due to the reduced sensitivity of oblique incidence scattering spectra (35). (E) Summary of symmetry operations relating each geometric isomer to another and the effect on trochoidal and linear dichroism (TD and LD). Each mirror operation (σ_v) gives opposite linear dichroism, but mirroring over the (x, y) plane maintains trochoidal dichroism. Therefore, the two effects are consistently distinguishable across L-dimers and Γ-dimers (quadrants I and IV) (SI Appendix, Fig. S12). These isomers have reduced resonance shifts relative to those of ⅃- and ⅂-dimers (quadrants II and III) (SI Appendix, Fig. S12), likely resulting from competing contributions of both dichroisms. However, trochoidal dichroism dominates (SI Appendix, Fig. S6 and S12).

Fig. 4.

Observation of trochoidal differential scattering in self-assembled gold nanorod dimers (A) Schematic of self-assembled dimers utilizing DNA origami, forming an approximate L-dimer. (B) Sample rotation of 180° forms a ⅂-dimer, reversing the trochoidal dichroism and promoting opposite mode excitation. (C and E) Normalized scattering spectra of the L-dimers at 0° sample orientation with CW and ACW trochoidal excitation. SEM images depict dimer orientation relative to k. (Scale bar, 50 nm.) (D and F) Normalized scattering spectra of the same dimers after 180° rotation. Dashed and dotted lines identify bonding and antibonding modes, respectively. As for the ideal dimers in Figs. 2 and 3, the trochoidal polarization of the incident field allows for mode selective excitation of hybridized nanorod dimer plasmons.