The symmetry dependences of plasmon excitation modes are studied in 3D silver nanorod trimers. The degenerate plasmon modes split into chiral modes by breaking the inversion and mirror symmetry of the nanorod trimer through translation and/or rotation of the middle rod. With a translation operation, successive evolution of the circular dichroism (CD) spectrum can be achieved through gradual breaking of the inversion symmetry. An additional rotation operation produces even dramatic spectral changes due to breaking a quasi-mirror symmetry resulted from the same angular distance of the middle rod to the top and bottom rods. Especially, pairs of new chiral modes can be excited due to the contact of the middle rod with the top-bottom rod pair. The spectral changes in the simulations, which are also demonstrated experimentally, envision the 3D chiral nanorod trimer system as plasmon ruler for spatial configuration retrieval and dynamic bio-process analysis at the single molecule level.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Circular dichroism (CD) and circular birefringence, characterized by the differences of absorption and refractive indexes of circularly polarized light, left-handed (LCP) and right-handed (RCP), are two important optical properties of chiral materials. These properties enable diverse applications in chiral sensitive spectroscopic techniques and polarization dependent optoelectronic devices such as CD spectroscopy , polarization resolved Raman spectroscopy , chiral sensors [3,4], circularly polarized light detector/mirror/convertor [5–8], optical rotatory dispersion polarimeters , etc.. Recently, three dimensional (3D) chiral nanostructures through different fabrication methods, such as nanodot clusters by e-beam [10,11] and colloidal lithography , helices by direct laser writing , nanorod dimers  and particle clusters  by self-assembly, 3D L-shaped arrays by shadowing vapor deposition  and on-edge lithography , have been intensively studied based on multi-fold reasons. Firstly, natural chiral materials exhibit only small chiral signals due to the weak coupling of organic compositions with the external fields  and thus they have limited applications. Secondly, optical responses in 3D metallic nanostructures can be significantly enhanced due to the highly efficient dipole interactions with the external fields and strong resonant couplings across the whole metallic structures. Thirdly, versatile resonant modes from fundamental to higher orders can be observed in 3D chiral nanostructures which enable deeper understanding of light-matter interactions in complex chiral materials [19,20]. Fourthly, the configuration similarity between 3D chiral nanostructures and chiral molecules enables direct modeling the chiral molecular units, such as amino acids and proteins, and hence paves a way in probing the basic functions of life as optical spectra of structural configurations can be recorded as database for molecule conformation retrieval . Lastly but not the least, in three dimensions the plasmonic CD depends very much on the configuration symmetries and the spatial couplings of the metallic constituents of the nanostructures. Thus, an electric-magnetic coupled chiral mode could be tuned by structural transformations, resulting in well-modulated CD spectra with high resolution.
A simple and efficient design for 3D chiral nanostructure is nano-dimer consisting of two individual nanorods stacked and twisted with respect to each other. Gold nanorod dimer system made by self-assembly method has demonstrated highly tunable chiral optical responses in the visible wavelength range [22–24]. In addition, planer nanodot trimer has been chosen as a chiral model system for the studies of the near field coupling effect  and the chirality through material compositions . Currently, most lithography based 3D nanostructures are limited in the near infrared range because the scaling down towards shorter wavelength is hampered by the configuration complexity in three dimensions and the technical challenges in nanoscale accuracy. Planer nanorod trimer with either symmetric and asymmetric configurations have been systematically studied to show the plasmonic coupling behaviors in bonding/antibonding modes [27,28]. However, visible range 3D nanorod trimer which have a larger number of degree of freedom including both in plane displacement and out-of-plane rotation of one rod relative to the others has not been fully addressed.
Here we propose a 3D nanorod trimer (ruler) based on its spectral sensitivity to structural transformation. In contrast to the previous plasmon rulers which report on the change of optical spectrum in terms of one dimensional movement of single nanoparticles [29,30], we study the continuous change of the chiral optical responses as functions of both translation and rotation motions of nanorods in three-dimensions. In addition, our trimer nanostructures are sensitive to both orthogonal linear polarizations which enables developing polarization manipulation for nanometer scale sensing. Based on this 3D nanorod trimer model, we demonstrate the change of resonant coupling of the nanorods as a function of symmetry breaking. Chiral modes appear only when structural, inversion and/or mirror, symmetries for the nanorod trimer are broken. Symmetry breaking lifts the energy degeneracy, leading to the coupling of the electric and magnetic dipolar resonances in both parallel and antiparallel directions, and respectively, negative and positive CD bands at higher and lower energy levels. In particular, the CD spectra are shown to be highly sensitive to not only the nanoscale linear displacement but also to the angular orientation of the electric dipole relative to the magnetic dipole, hence enabling modulated CD spectra for dynamic signal processing.
Nanorods are selected as the elementary building blocks of our 3D nanostructure due to its flexibility in spatial configuration transformation compared with nanoparticle clusters, especially in the aspects of controlling the inversion and mirror symmetries within a chiral architecture. We choose silver as the rod material due to its supreme optical properties in the visible and near infrared wavelength range. Silver nanoparticles are extraordinarily efficient in absorbing and scattering light as compared to gold  due to the stronger collective oscillations of the conduction electrons on the surface of metal excited by the external fields as well as the less resonant loss in the visible range.
Figure 1 shows the schematics of the nanorod trimer unit consisting of three stacked Ag nanorods in air. Two parallel rods, laterally displaced in the x-direction, with the same dimensions (green in Fig. 1(a)) are stacked on the top and bottom layers with another rod (pink in Fig. 1(a)) perpendicularly stacked in between the parallel rods in the middle layer. The key point of such arrangement lies in the fact that both electric and magnetic dipole resonances can be excited simultaneously by either x- or y-polarization due to the mutual inductive coupling between the horizontally and vertically oriented nanorods [32,33]. The trimer system has two high symmetry configurations. One is the inversion symmetry for the middle rod at s = 0 nm as shown in Fig. 1(b); the other is the quasi-mirror symmetry with a mirror plane locating at θ ≈132° as shown in Fig. 1(c). Hence, the structural symmetry can be tuned by either translating or rotating the middle rod with respect to the other rods to produce various chiral optical responses. To make a comprehensive study on the symmetry dependence of chiral plasmon modes, the middle rod (pink) is first laterally displaced along the y- direction from the symmetry axis (s = 0), as shown in Fig. 1(b). It is then rotated clockwise or counterclockwise relative to the quasi-mirror plane (θ = 132°) for fixed s (−40 nm) as shown in Fig. 1(c). We then calculate the spectral responses for different configurations by using commercial finite-integration time-domain algorithm software (CST microwave studio) for x-, y- and also circular polarization excitations propagating along the z-direction using effective dielectric parameter of Ag obtained from a recent work .
3. Results and discussions
3.1 Discontinuous nanorod trimer
We start from a nanorod trimer configuration with inversion symmetry where the middle rod is placed horizontally (θ = 0°) at the center of the top-bottom rod pair (s = 0 in Fig. 1(b)). In this case, only a single broad resonance A0x is excited by the x-polarization incidence, shown as the blue dash curve in Fig. 2(a). The current distribution of mode A0x (Fig. 2(d)), characterized by collective charge oscillations mainly in the middle rod, produces an electric dipole (purple arrow in Fig. 2(d)) in the x-direction. When excited by the y-polarization incidence, a resonance (mode A0y) is excited with a relatively narrow bandwidth as shown by the red dash curve in Fig. 2(b). This mode is characterized by strong displacement currents oscillating out of phase in the top and bottom nanorods (black arrows in Fig. 2(e)), leading to a magnetic dipole in the x-direction (green arrow in Fig. 2(e)). The narrower bandwidth results from the smaller radiative damping of the magnetic dipolar resonance. (Note that there is another mode, the shoulder of the dashed line in Fig. 2(b), being excited. This mode corresponds to in-phase current flows in the top and bottom nanorods, leading only to electric dipole moments along the y-direction.) Even though the electric and magnetic dipole moments in A0x and A0y are pointing to the same direction, they are excited at different frequencies, 415 and 406 THz for the x- and y- polarizations, respectively. As a result, circular dichroism is exactly zero when the structure is excited by the circularly polarized light as shown by the green dash line in Fig. 2(c) because firstly there is no coupling between the electric and magnetic dipole moments; secondly the structure still has inversion symmetry even though the mirror symmetry is broken, i.e. . It is noteworthy that the absorption difference, defined as ΔA = ARCP-ALCP, exhibits nearly opposite response to the transmittance difference ΔT = TRCP-TLCP. Hence, the CD (defined as ALCP-ARCP = -ΔA) can be well approximated by the transmittance difference ΔT. This is valid for all 3D chiral media whose CD is determined by the transmission difference of co-polarizations while the cross polarizations are either equal or zero [35,36].
However, it turns out that the uncoupled A0x and A0y modes can couple with each other by breaking the inversion symmetry to form 3D chiral modes. To achieve this, the middle rod is displaced laterally to s = −40 nm; the spectral modes change accordingly as shown by the solid curves in Figs. 2(a)-2(b). For the x-polarization excitation, the mode A0x (415 THz) splits into A1x and A2x at 385 and 437 THz, respectively, as shown by the blue solid curve in Fig. 2(a). The distributions of the displacement currents (black arrows) as well as the induced electric (purple arrow) and magnetic (green arrow) dipole moments for the split modes are shown in Figs. 2(f) and 2(h), respectively. Obviously, the electric dipolar resonance of the middle rod and the magnetic dipolar resonance of top-bottom rod pair are excited simultaneously, leading to the coupling between them in either antiparallel or parallel at the low and high energy levels, respectively. Hence, symmetry breaking lifts the energy degeneracy, resulting in antiparallel and parallel electric and magnetic couplings accounting for positive and negative CD bands respectively, as shown by the solid green curve in Fig. 2(c). The different couplings between A1 and A2 are actually determined by different orientations of displacement currents in the 3D trimer, i.e. head-to-tail in mode A1 and head-to-head in mode A2, which resemble the acoustic and optical vibration modes in a linear atomic chain . This enables opposite absorptions for LCP and RCP (Fig. 2(c)) and consequently distinct interactions to a chiral molecule, which can be used as enantiomer differentiation.
For y-polarization incidence, the split modes A1y and A2y are located at the same resonant frequencies as those of A1x and A2x, respectively, as shown by the red solid curve in Fig. 2(b). They exhibit also the same coupling behaviors between electric and magnetic dipole moments as shown in Figs. 2(g) and 2(i), even though the strengths are smaller. It indicates that the inductive coupling between the horizontally and the vertically oriented nanorods is essential in exciting 3D chiral modes.
3.2 Symmetry breaking by translation and rotation transformations
It has been reported that quadrupole resonance possesses high sensitivities to spatial and structural changes due to its sharp spectral features [21,38–40]. The magnetic resonance of the stacked top-bottom rod pair resembles the quadrupole resonance of a planer rod-pair , and thus can serve as a sensitive plasmon ruler. Furthermore, the electric-magnetic coupled resonance of the nanorod trimer greatly increases the flexibility in controlling nanoscale sensing because it can be engineered to generate well-defined CD spectra with high resolution through tailoring the position and orientation of the electric dipole relative to the magnetic dipole.
To test the sensitivity of CD spectrum to translation, the middle rod in the trimer is displaced from s = 0 to ± 120 nm. The CD spectra for opposite displacements exhibit anti-symmetric responses as shown by the solid and dash curves in Fig. 3(a). The amplitude and frequency at resonance as a function of the lateral displacement s are shown in Figs. 3(b) and 3(c). The most significant change of the amplitude occurs in the range from −30 to 30 nm at the initial stage of symmetry breaking, where the decrease/increase of CD behaves almost linearly from ~0.6/-0.2 to −0.6/0.2 for mode A1/A2, respectively, shown as the green/red curves in Fig. 3(b). From ± 30 to ± 90 nm, despite increasing structural asymmetry, the amplitude of the CD does not change much. This is because the actual coupling strength decreases concomitantly as a result of the increased distance between the excited electric and magnetic dipole moments. From ± 90 to ± 120 nm the CD drops quickly (Fig. 3(b)) due to firstly the dramatically enlarged distance of electric dipolar rod to the magnetic dipolar rod pair in a unit cell, and secondly the periodic trimer in one unit cell becomes more symmetric with neighboring unit cells by increasing s. As a result, the CD becomes zero for s = 125 nm, where the middle rod has the same distance from the top-bottom rod pair of neighboring unit cells. Comparing with the amplitude change, the frequency exhibits a much shaper shift as a function of s within the whole range from −120 to 120 nm, as shown by the green/red curves in Fig. 3(c), thereby allowing nanoscale distance sensing to be extended to a wider range. Moreover, the frequency difference, as denoted by the blue dotted curve in Fig. 3(c), between mode A1 and A2 as a function of s exhibits a much larger change than the frequency shift of the individual mode, which enhances the sensitivity for the nanoscale displacement sensing. To conclude, the symmetry breaking through the translation of the middle rod enables successive spectral changes in both the amplitude and frequency and hence resulting in high resolution CD spectra for ultrasensitive nanoscale distance sensing.
The behavior of the CD spectra can be altered dramatically due to the rotation of the middle rod. Figure 4(a) shows the schematic for the rotation of the middle rod whose displacement is fixed at s = −40 nm, implying the inversion symmetry has already been broken. The rotation axis is along the y direction passing through the center of the middle rod and the rotation angle θ is defined in counterclockwise direction with respective to the x-axis. The chiral modes A1 and A2 as shown in Figs. 2 and 3 are calculated at different angles with the CD spectra shown in Figs. 4(b)-4(d). We start from the highest mirror symmetry configuration at θ = 132° (Fig. 4(a)) where the CD is almost zero (gray curve in Fig. 4(b)) due to the quasi-mirror symmetry of the trimer. This mirror symmetry is broken when the middle rod rotates counterclockwise or clockwise, resulting in CD spectra of reversed handedness as depicted by the violet curve of θ = 140° and pink curve of θ = 120° in Fig. 4(b). Following the counterclockwise rotation from 132° to 180° (Fig. 4(c)), red/blue shift of mode A1/A2 (Fig. 4(f)) is observed, in addition to the increasing amplitudes (Fig. 4(e)), as the mirror symmetry is broken gradually, indicating that the splitting of the two chiral modes is determined by the degree of structural asymmetry. From 180° to 200°, the red/blue shift of mode A1/A2 become much more dramatic as the middle rod is getting closer to touching the top-bottom rod pair resulting in significant increase of the spectral separation between A1 and A2 (blue dot curve in Fig. 4(f)). From 205° (25°) to 245° (65°), the middle rod touches the top-bottom rod pair with one particular case at θ = 230° (50°) elucidated in Fig. 5 in the section of continuous nanorod trimer.
Upon clockwise rotation of middle rod from 132° to 90° (Fig. 4(d)), the CD amplitudes first increase then decrease for both A1 and A2 (Fig. 4(e)) due, respectively, to the increased symmetry breaking and the vanishing of the horizontal electric dipole at 90°. At 90°, the CD is expected to be zero since the x-component of the electric dipole resonance in the middle rod vanishes leaving only the magnetic dipole resonance. However, it turns out that the CD is nonzero as shown by the light blue curve in Fig. 4(d). This is due to the finite thickness of the middle rod used in the model, and thus electric charges induced by the nearby top and bottom rods accumulate at the diagonal ends of the middle rod with opposite signs, resulting in nonzero electric dipole moment in x direction. This x-component almost vanishes at ~96° leading to zero CD as shown in Fig. 4(e). From 100° to 90°, the handedness of the CD changes sign as shown by the light green and light blue curves in Fig. 4(d), due to the reversing of electric dipole relative to the magnetic dipole. From 90° to 65°, the spectral shifts of mode A1 and A2 (Fig. 4(f)) behave similarly to those for the range from 170° to 200°, because the middle rod is approaching the rod pair in both cases.
To summarize, the rotation of a middle rod provides a more sophisticated way to achieve symmetry breaking and spectral evolutions. The frequency difference during counterclockwise/clockwise rotation of the middle rod (blue curve in Fig. 4(f)) can be two times larger than that from the translation (blue curve in Fig. 3(c)). The amplitude change of mode A2 (red curve in Fig. 4(e)) is more than two times due to the mirror symmetry breaking than the case by inversion symmetry breaking (red curve in Fig. 3(b)). The CD bands change signs around two particular angles, 96° and 132° respectively, by flipping the direction of the electric dipole with respect to the magnetic dipole. Such flipping behavior inspires a new path way for dynamic interconversions between the chiral enantiomers .
3.3 Continuous nanorod trimer
A special configuration described as a continuous nanorod trimer is formed when the middle rod electrically bridges the top and bottom rod pair at θ = 50°. (Note that this configuration is equivalent to the u-shaped patterns at oblique incidence .) In this case, mode A1 experiences a dramatic red shift from 350 THz (θ = 200°) to 200 THz (θ = 50°) as shown in Fig. 5, since the head-to-tail aligned current loop is now extended to the maximum length by joining the rods (Fig. 5(d)). Mode A2 exhibits significant CD amplitude increase (Fig. 5(c)) as compared with the discontinuous case (Fig. 4(c)) because this is a hybrid mode in which the chiral resonance is strengthened by suppressing the achiral mode in the top-bottom rod pair shown as the shoulder mode in Fig. 2(b). Furthermore, a pair of new chiral modes marked as B1 and B2 appear at 391 and 530 THz are excited. The new modes arise from the charge transfer effect between the individual nanorods when the ohmic contact is formed . This can be manifested as the displacement current flows from the middle rod to the top and bottom rods, respectively (Figs. 5(e) and 5(g)). The new modes in combination with the original ones to form a four-level chiral system.
Similarities can be found for the spectral responses of the four level chiral modes under orthogonal linear excitations. All of them are characterized as dips in |txx| and |tyy| and peaks in |tyx| and |txy| as shown by the solid and dash curves in Figs. 5(a) and 5(b). Especially, |tyx| and |txy| are equal for x- and y- polarization excitations, indicating that the inductive coupling is reciprocal in our nanorod trimer system. The dips in |txx| and |tyy| represent the resonant losses of the electric and magnetic dipole moments and their sum determines the total losses of a chiral mode. Since the amplitude of CD is proportional to the intensities of the cross linear polarizations and inversely proportional to the total losses , they are thus determined by the peak values of |tyx| and |txy| when the total losses are almost equal which follow the sequence A2-B2-A1-B1 going from high to low as shown in Fig. 5(c).
The formation of the four-level chiral system is due to the hybridization of the electric dipoles excited in the nanorod trimer which is determined by the number, continuity and spatial orientation of the consisting rods. The energy level depends on the strength of the linear restoring force induced by the in-phase and out-of-phase dipole interactions, with repulsive force leading to a higher energy level than the attractive force . In our case, mode A1, consisting of three electric dipoles aligned in series (Fig. 5(d)), is dominated by the attractive force between neighboring rods with opposite charges, leading to the lowest energy level. One repulsive force is induced in mode B1 owing to the head-to-head alignment of the charge oscillations in the middle rod (Fig. 5(e)), contributing to a higher energy level of mode B1 than A1. Modes A2 and B2 are dominated by the repulsive forces between neighboring displacement currents with the same charges, thus are found at even higher energy levels. Moreover, mode B2 resides at the highest energy level due to the largest number of opposite aligned electric dipoles (Fig. 5(g)). As a result, the energy levels of the four modes increase along the sequence A1-B1-A2-B2.
As a proof of concept, we fabricated the discontinuous Ag nanorod trimer using the state-of-the-art electron beam lithography, followed by lift off processes, and then layer-by-layer stacking techniques . The nanorods were spaced by a dielectric medium (Ma2403) and resided on an ITO-glass substrate. The middle rod was displaced from the symmetry axis of the top-bottom rod pair by s. The ΔT spectra were measured using a microscope-spectrometer (20X objective, NA = 0.25) with circularly polarized light incident from the substrate side . Figure 6(a) shows the experimental ΔT spectra of the left (positive s) and right handed (negative s) enantiomers with scanning electron microscope (SEM) images on the right columns. The chiral characteristic of the trimer is demonstrated clearly by the excellent mirror symmetry of the CD spectra with middle rod displaced at 28 and −28 nm, respectively. The CD for mode A1 exhibits good agreement with the numerical simulations in Fig. 3(a), while the mode A2 is not visible due to the higher losses of the metal at higher frequencies. Figure 6(b) demonstrates the ΔT increases, step by step, from 0 to 50 nm during the translation of the middle rod. In particular, for s = 50 nm, ΔT reaches up to ~0.21, remarkably large for the visible range. As s increases, the maximum |ΔT| increases gradually (red open circles in Fig. 6(c)), and the spectral position shifts to the lower frequency (blue open circles in Fig. 6(c)). These spectral changes agree well with the numerical simulations in Figs. 3(b) and 3(c). The nanometer shifts of the middle rod are determined by the SEM images on the right hand side of Fig. 6, indicating good alignment during the complex sequences of nanolithography steps. To demonstrate further, we include the surrounding dielectric (without losses) and supporting ITO glass substrate in the simulations for our trimmers as shown in Figs. 6(d)-6(f). The agreement with the experiment is now much better.
To conclude, the dependence of electric and magnetic coupling on structure symmetry and incident polarizations are investigated for 3D Ag nanorod trimers. Chiral modes can be excited due to energy splitting when structural symmetries, inversion and/or mirror, are broken, resulting in parallel/antiparallel coupling of electric and magnetic dipolar resonances and hence negative and positive CD signals. The coupled electric-magnetic modes are tunable by tailoring the structural asymmetry, i.e. translation and rotation transformations of middle rod relative to the top-bottom rod pair, enabling modulated CD spectra with high resolution. The successive spectral changes in both amplitude and frequency facilitate a ruler function of the trimer for determing spatial nanoscale movement. Furthermore, several unique spectral characteristics induced by symmetry variations, such as the mode splitting, CD flipping, dramatic CD signals, the appearance of new chiral modes and the formation of four-level chiral system envision great potentials for developing advanced nano-optical devices for high precision spatial configuration retrieval and bioprocess sensing.
Hong Kong RGC grant AoE/P-02/12; Hong Kong Innovation and Technology Scheme (ITS/291/14).
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