Giant plasmonic circular dichroism in Ag staircase nanostructures

Chunrui Han; Ho Ming Leung; C. T. Chan; Wing Yim Tam

doi:10.1364/OE.23.033065

1. Introduction

Circular dichroism (CD), defined as the difference in absorption for left- and right-handed circularly polarized light, is a useful tool in spectroscopic techniques for the detection and characterization of biomolecules [1] and hence plays a crucial role in analytical chemistry and biomedicine [2, 3 ]. However, the spectral analysis of biomolecules has always been obstructed by the low sensitivity of CD measurements until recently when plasmonic nanostructures are employed to enhance the CD response in which surface plasmons of the nanostructures are in resonance with the electronic transitions of the biomolecules [4–6 ]. Moreover, the sensitivity can be further enhanced by using superchiral electromagnetic fields [7, 8 ] generated through resonances in chiral plasmonic nanostructures [9, 10 ]. Consequently, plasmonic chiral systems, consisting of either metallic elements arranged with a sense of twist/rotation [11–19 ] or metal-chiral molecule complexes [20–23 ], have attracted great scientific interest in biomolecule research.

Single metallic elements, such as wire, strip, sphere, etc., with sizes much smaller than the wavelength of incident light, typically have induced electric dipole moments along the incident polarization as the fundamental plasmon mode. Interestingly, in complex plasmonic nanostructures elemental plasmon modes can couple and exhibit novel properties, such as magnetic response [24–28 ], negative refractive index [29–31 ], Fano resonance [32–34 ], electromagnetically induced transparency [35, 36 ] and chiral optical response [37, 38 ]. In particular, the high geometrical dependence of plasmonic responses allows the tailoring of the plasmon interactions to enhance the above novel properties. Plasmon interactions [5, 12, 39, 40 ] in chiral nanostructures can be shown to be analogous to the dipole/multipole Coulomb interactions in chiral molecules [1, 41 ]. Correspondingly, plasmon hybridization [42, 43 ] of complex nanostructures follows similar rules for the molecular orbital hybridization theory [44]. On the other hand, contrary to the weak hybridization interactions in biomolecules, the strength of the interactions in plasmonic nanostructures can be orders of magnitude larger due to strongly enhanced local electric and magnetic fields through plasmon resonances. Thus chiral plasmonics, as model systems, are of fundamental importance in the elucidation of chiral interaction mechanisms for biomolecules.

In this letter, we investigate the electromagnetic interactions and the CD responses in 3D chiral Ag staircase nanostructure in the visible range. We show, using calculations based on retrieved effective parameters for the Ag staircase, that the CD originates from the spatial coupling between the Ag elements of the staircase in which the induced magnetic dipole moment has a component aligned parallel or antiparallel with the induced electric dipole moment. We also find that the CD correlates well with the coupling strength which can be tuned by varying the physical parameters, e.g. the widths of the Ag elements of the staircase. More importantly, we have also fabricated topologically similar chiral plasmonic nanostructure as the Ag staircase, using a simple and effective shadowing vapor deposition (SVD) method [45, 46 ], exhibiting large chiral optical responses in the visible range in good agreement with the numerical simulations. Our results could lead to new designs and applications in chiral plasmonic nanostructures for biomolecule sensing and characterization.

2. Model

The 3D schematic view of the Ag staircase nanostructure for the visible range is shown in Fig. 1(a) with geometrical parameters shown in Figs. 1(b) and 1(c). The Ag staircase consists of two horizontal Ag strips (steps), with one positioned above the other like the steps of a staircase, aligned in the y-direction and connected at one end by a slanted (titled at θ ~48° from horizontal plane) Ag strip as shown in Fig. 1(a). The tilted Ag strip breaks the reflection symmetry but preserves the handedness of the structure, similar to that of a helix. Hence the staircase is expected to exhibit 3D chiral responses, e.g. the transmissions are identical for forward and backward illuminations.

Fig. 1 (a) 3D schematic of Ag staircase. (b-c) Geometrical parameters of the staircase: a = 65 nm, b = 70 nm, d = 200 nm, l = 110 nm, w = 45 nm, h = 77 nm, t = 11 nm and θ = 48°. Bottom Ag strip (orange) in (b) has the same dimensions as the top Ag strip (yellow). Blue arrows indicate the directions of incident light.

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We carried out numerical simulations using a commercial finite-integration time-domain algorithm (CST Microwave Studio) to model optical response of the 3D Ag staircase nanostructure using periodic boundary conditions in a square lattice as shown in Fig. 1(b). The simulated transmittance (T) and reflectance (R) spectra are shown in Figs. 2(a) and 2(b) , respectively, for left-, LCP, (red) and right-, RCP, (blue) handed circularly polarized incident light. It is clear that the results for forward (solid lines) and backward (open symbols) incidences coincide well with each other. The transmission difference of RCP and LCP, defined as

Δ_{T} = T_{RCP} - T_{LCP},

is shown as the blue line in Fig. 2(c) for forward incidence. More importantly, the absorption difference, defined as

Δ_{A} = A_{RCP} - A_{LCP},

exhibits nearly opposite responses to Δ_T, as shown by the red line in Fig. 2(c) because of the small and equal circular polarization conversions and also the small reflection difference. Thus, the CD (defined as

A_{LCP} - A_{RCP} = - Δ_{A}

) can be well approximated by the transmission difference Δ_T for the staircase structure. The result remains the same for backward incidence (open symbols in Fig. 2(c)). It is obvious that the CD (Δ_T) spectrum composes of positive and negative bands around 460 and 540 THz, respectively.

Fig. 2 (a, b) Simulated transmission and reflection of Ag staircase shown in Fig. 1 for forward/backward (solid line/symbol) LCP (red) and RCP (blue) incident light, respectively. (c) Transmission (blue) and absorption (red) difference of LCP and RCP incident light.

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In order to find the origin of the CD and to clarify the coupling effects in 3D chiral plasmonic nanostructure, we have retrieved the effective parameters, permittivity (ε _eff), permeability (μ _eff) and coupling constants (ζ _eff and ξ _eff), of the Ag staircase nanostructure from the simulated data for linearly polarization incidence using a retrieval method as described before [47]. We then calculated the CD of the Ag staircase using the retrieved effective parameters.

Our derivation starts with transmission matrices $(t_{i j}^{f})$ and $(t_{i j}^{b})$ defined by electric field $E_{i} (z = h) = t_{i j}^{f} E_{j} (z = 0)$ and $E_{i} (z = 0) = t_{i j}^{b} E_{j} (z = h)$ respectively, where superscript f (b) stands for forward (backward) incidence and h is the sample thickness. The subscript ij stands for incident mode (polarization) j and transmitted mode i. For a Lorentz-reciprocal structure, the scattering matrix must be symmetric [48], requiring $(t_{i j}^{f}) = (t_{j i}^{b}) .$ On the other hand, from the forward and backward symmetry of 3D chiral structure the forward and backward transmission matrices in circular basis must be the same (i.e. modes +/− are RCP/LCP, respectively):

(t^{f}) = (t^{b}) .

As a result,

(\begin{matrix} t_{+ +}^{f} & t_{+ -}^{f} \\ t_{- +}^{f} & t_{- -}^{f} \end{matrix}) = (\begin{matrix} t_{+ +}^{b} & t_{+ -}^{b} \\ t_{- +}^{b} & t_{- -}^{b} \end{matrix}) = (\begin{matrix} t_{+ +}^{f} & t_{- +}^{f} \\ t_{+ -}^{f} & t_{- -}^{f} \end{matrix}),

and hence,

t_{+ -}^{f} = t_{- +}^{f} .

A similar expression is obtained for the backward transmission matrix. (For simplicity, the superscript is dropped from now on.) Furthermore, from the relation between the circular and linear transmission matrices [29] we have

(\begin{matrix} t_{+ +} & t_{+ -} \\ t_{- +} & t_{- -} \end{matrix}) = \frac{1}{2} (\begin{matrix} (t_{x x} + t_{y y}) + i (t_{x y} - t_{y x}) & (t_{x x} - t_{y y}) - i (t_{x y} + t_{y x}) \\ (t_{x x} - t_{y y}) + i (t_{x y} + t_{y x}) & (t_{x x} + t_{y y}) - i (t_{x y} - t_{y x}) \end{matrix}),

Equation (5) implies that

t_{x y} = - t_{y x},

where t_xy and t_yx are the linear polarization transmission conversion coefficients. Then, the transmission difference Δ_T, hence the CD, can be calculated as

\begin{matrix} CD = Δ_{T} = {| t_{+ +} |}^{2} + {| t_{- +} |}^{2} - {| t_{- -} |}^{2} - {| t_{+ -} |}^{2} \\ = {| t_{+ +} |}^{2} - {| t_{- -} |}^{2} \\ = 2 Im [t_{x y}^{*} (t_{x x} + t_{y y})] . \end{matrix}

From Eq. (8), it is obvious that the prerequisite for CD is non-zero t_xy, i.e. the linear polarization conversion should be non-zero. To find the relation between the CD and the effective parameters (ε _eff, μ _eff, ζ _eff and ξ _eff) of the structure, we need the general constitutive relation given by

(\begin{matrix} D_{x} \\ D_{y} \\ B_{x} \\ B_{y} \end{matrix}) = (\begin{matrix} ε_{x x} & ε_{x y} & ξ_{x x} & ξ_{x y} \\ ε_{y x} & ε_{y y} & ξ_{y x} & ξ_{y y} \\ ζ_{x x} & ζ_{x y} & μ_{x x} & μ_{x y} \\ ζ_{y x} & ζ_{y y} & μ_{y x} & μ_{y y} \end{matrix}) (\begin{matrix} E_{x} \\ E_{y} \\ H_{x} \\ H_{y} \end{matrix}) = [C] (\begin{matrix} E_{x} \\ E_{y} \\ H_{x} \\ H_{y} \end{matrix}),

where E(D) and B(H) represent the electric and magnetic fields, respectively. The transmission and reflection coefficients for a thin slab metamaterial can be expressed using transfer matrix (TMM) as

(\begin{matrix} 1 \\ 0 \\ r_{x x} \\ r_{y x} \end{matrix}) = {[B]}^{- 1} {[e^{i k h [D] . [C]}]}^{- 1} [B] (\begin{matrix} t_{x x} \\ t_{y x} \\ 0 \\ 0 \end{matrix}),

And

(\begin{matrix} 0 \\ 1 \\ r_{x y} \\ r_{y y} \end{matrix}) = {[B]}^{- 1} {[e^{i k h [D] . [C]}]}^{- 1} [B] (\begin{matrix} t_{x y} \\ t_{y y} \\ 0 \\ 0 \end{matrix}),

where

[D] = (\begin{matrix} 0 & 0 & 0 & 1 \\ 0 & 0 & - 1 & 0 \\ 0 & - 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{matrix}),

and

[B] = (\begin{matrix} 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & - 1 & 0 & 1 \\ 1 & 0 & - 1 & 0 \end{matrix}) .

Since the Ag strips of the staircase are either aligned along the x- or y- direction (Fig. 1(a)), the interactions of the fields mainly contribute to the diagonal terms (

p a r a m e t e r_{i j}, i = j

) of the matrix but not to the off-diagonal terms (

p a r a m e t e r_{i j}, i \neq j

) which are very small (~10⁻³). Thus, we get

(\begin{matrix} D_{x} \\ D_{y} \\ B_{x} \\ B_{y} \end{matrix}) = (\begin{matrix} ε_{x x} & 0 & ξ_{x x} & 0 \\ 0 & ε_{y y} & 0 & ξ_{y y} \\ - ξ_{x x} & 0 & μ_{x x} & 0 \\ 0 & - ξ_{y y} & 0 & μ_{y y} \end{matrix}) (\begin{matrix} E_{x} \\ E_{y} \\ H_{x} \\ H_{y} \end{matrix}) .

Note that

[ζ] = - {[ξ]}^{†}

has been applied to Eq. (9) as required by the reciprocity for chiral structure. Therefore, the electromagnetic couplings in the Ag staircase come from the diagonal terms of effective parameters rather than the off-diagonal terms. Furthermore, from the matrix exponential of the constitutive relation, we obtain

t_{x y} = 2 i k h (\frac{ξ_{x x}}{- 4 + 2 i k h (ε_{x x} + μ_{x x}) + k^{2} h^{2} (ε_{x x} μ_{x x} + ξ_{x x}^{2})} + \frac{ξ_{y y}}{- 4 + 2 i k h (ε_{y y} + μ_{y y}) + k^{2} h^{2} (ε_{y y} μ_{y y} + ξ_{y y}^{2})}),

t_{y x} = - 2 i k h (\frac{ξ_{x x}}{- 4 + 2 i k h (ε_{x x} + μ_{x x}) + k^{2} h^{2} (ε_{x x} μ_{x x} + ξ_{x x}^{2})} + \frac{ξ_{y y}}{- 4 + 2 i k h (ε_{y y} + μ_{y y}) + k^{2} h^{2} (ε_{y y} μ_{y y} + ξ_{y y}^{2})}),

t_{x x} = - \frac{k h (ε_{x x} (2 i + k t μ_{x x}) + k t ξ_{x x}^{2})}{- 4 + 2 i k h (ε_{x x} + μ_{x x}) + k^{2} h^{2} (ε_{x x} μ_{x x} + ξ_{x x}^{2})} + \frac{- 4 + 2 i k h ε_{y y}}{- 4 + 2 i k h (ε_{y y} + μ_{y y}) + k^{2} h^{2} (ε_{y y} μ_{y y} + ξ_{y y}^{2})},

t_{y y} = - \frac{k h (μ_{x x} (2 i + k h ε_{x x}) + k h ξ_{x x}^{2})}{- 4 + 2 i k h (ε_{x x} + μ_{x x}) + k^{2} h^{2} (ε_{x x} μ_{x x} + ξ_{x x}^{2})} + \frac{- 4 + 2 i k h μ_{y y}}{- 4 + 2 i k h (ε_{y y} + μ_{y y}) + k^{2} h^{2} (ε_{y y} μ_{y y} + ξ_{y y}^{2})} .

Finally, in thin sample approximation, the CD given by Eq. (8) can be written as:

\begin{matrix} CD = 2 Im [t_{x y}^{*} (t_{x x} + t_{y y})] \\ \approx 2 \frac{- k h Re [ξ_{x x} + ξ_{y y}]}{1 + k h Im [ε_{x x} + ε_{y y} + μ_{x x} + μ_{y y}]} . \end{matrix}

Note that a minus sign is added to Eq. (17) to account for the different convention used in CST simulation and the parameter retrieval method [47]. Equation (17) provides the physical insight for CD in chiral structures, namely that it comes from the real part of the coupling constants ξ_xx and ξ_yy, indicating that the induced magnetic field/dipole moment must consist of a component along the same direction as the electric field/dipole moment. This equation also provides the mechanism in obtaining large CD by maximizing the numerator (sum of the real part of the coupling constants ξ_xx and ξ_yy) and/or minimizing the denominator (sum of the imaginary parts of effective permittivity and permeability ε_xx, ε_yy, μ_xx, μ_yy, i.e. the losses of the material). Thus, to get large CD, one possible way is to increase the coupling constants. However, increasing ξ could also increase the imaginary parts of ε and μ. Thus optimal CD could be obtained by balancing the effective coupling constants with the effective permittivity and permeability.

3. Results

Figures 3(a)-3(c) shows the spectral behaviors of retrieved effective ε, μ and ξ for the Ag staircase nanostructure using the simulated data. In particular, three prominent chiral resonance modes (labeled I, II, and III as determined by the extrema for Re[ξ] in Fig. 3(c)) at 398, 456, and 530 THz are observed. The resonance frequencies coincide with the electric resonances (peaks of Im[ε]) and magnetic resonances (peaks of Im[μ]) as shown in Figs. 3(a) and 3(b), respectively, as well as the transmission coefficient dips for linear polarizations shown as solid dotted lines in Fig. 3(d). Furthermore, they also correlate well with the extrema of CD and the transmission coefficient dips from CST simulation at 410, 460 and 540 THz, respectively (See Fig. 2 and solid lines in Fig. 3(d)) The small difference in the resonance frequencies is due to the thin film approximation used in the parameter retrieval method.

Fig. 3 (a-c) Retrieved effective parameters ε, μ and ξ of the Ag staircase for x- (blue) and y- (red) polarization incident light, respectively for the Ag strip width w = 45 nm. (d) Forward transmission coefficient from CST (lines) and calculation using the retrieved effective parameters (symbols). (e) CD (Transmission difference, T _RCP –T _LCP) by CST (blue line), retrieved effective parameters using Eq. (8) (green dots) and Eq. (17) (red line). The resonances obtained from the extrema of Re[ξ] in (c) are labelled as I (398 THz), II (456THz), and III (530 THz), guided by vertical gray lines in (d) and (e). Bottom insets: Current distributions calculated by CST at resonances as labelled. Arrows are: black for current, blue for magnetic field, and red for electric field. The color scale on the right is for the current density.

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To further analyze the spectral behaviors of the effective parameters and to provide physically intuitive pictures of the three chiral modes, snapshots of the maximum current distributions at resonance for the three chiral modes are shown in the bottom insets of Fig. 3. For mode I, excited by y-polarization (E _{y_in}) incidence at 398 THz, a strong electric resonance (peak of Im[ε_yy] in Fig. 3(a)) manifests as symmetric currents (indicated by the arrows) flowing along the top and bottom horizontal Ag strips, corresponding to electric dipole moments along the y-direction. A weaker magnetic resonance (peak of Im[μ_yy] in Fig. 3(b)) shows up as currents flowing along the slanted Ag strip starting roughly from the middle of the slanted Ag strip towards both the top and bottom Ag strips, leading to two parallel magnetic dipole moments with components along the y-direction (B _{y_induced}). Thus, the electric resonance is coupled to the magnetic resonance, giving rise to a chiral mode corresponding to the dip in the real part of ξ_yy at 398 THz (see Fig. 3(c)). Since the electric resonance is much stronger than the magnetic resonance, mode I is dominated by electric resonance.

For mode II, excited by x-polarization (E _{x_in}) incidence at 456 THz, a strong magnetic resonance (peak of Im[μ_xx] in Fig. 3(b)) now appears as opposite currents along the two horizontal Ag strips, producing a magnetic dipole moment with a component along the x-direction (B _{x_induced}) (indicated by the blue arrow in the inset), while a weaker electric resonance (peak of Im[ε_xx] in Fig. 3(a)), characterized by current flows along the slanted Ag strip, leads to an electric dipole moment with a component along the x-direction. Thus the electric dipole moment can couple the magnetic dipole moment to generate another chiral mode corresponding to the dip in the real part of ξ_xx at 456 THz (see Fig. 3(c)). In contrast to mode I, the magnetic resonance is now the dominating effect in mode II.

Excited by y-polarization (E _{y_in}) at 530 THz, mode III exhibits a strong electric resonance (peak of Im[ε_yy] in Fig. 3(a)) as symmetric currents (indicated by the arrows) flowing along the top and bottom horizontal Ag strips, similar to the electric resonance in mode I. However, current flows on the slanted Ag strip, denoting the weak magnetic resonance (peak of Im[μ_yy] in Fig. 3(b)), are opposite to that of mode I (indicated by the arrows). Consequently, the induced magnetic dipole moments are antiparallel to the electric dipole moments. The coupling of the electric and magnetic resonances now shows up as a peak, instead of a dip as in modes I and II, in the real part of ξ_yy at 530 THz (see Fig. 3(c)). This also correlates well with the sign of the resulting CD as shown in Fig. 3(e). Note that mode III is electric resonance dominating, similar to mode I.

In Fig. 3(e), we compare the CDs calculated by Eqs. (8) (green dots) and 17 (red line) using retrieved effective parameters with that of the CST simulation (blue line). They all agree well with each other. The broad positive CD band around 400-460 THz is attributed to the sum of the resonances of modes I and II while the resonance of mode III dominates the negative CD band around 540 THz. Thus positive CD corresponds to parallel coupling between the electric and induced magnetic dipole moments (modes I and II), and negative CD to antiparallel coupling (mode III). Furthermore, the significant lower loss of magnetic resonance in mode II leads to the largest CD (red line) among the three chiral modes.

To further support the above analysis, we also calculated, using another software COMSOL, the induced electric dipole moment

p_{i} = \frac{1}{i ω} \int J_{i} d V^{'}

and magnetic dipole moment

m_{i} = \frac{1}{2} \int {({\vec{r}}^{'} \times \vec{J})}_{i} d V^{'},

from the current density on the Ag strips of the staircase obtained from the simulations. The integration was carried over a unit cell with the origin at the center of the staircase nanostructure. Figures 4(a)-4(d) show the magnitude of the induced electric and magnetic dipole moments for linearly polarization incidence. Note that the transverse components of the electric and magnetic dipole moments around the chiral resonances are excited simultaneously by both x- and y-polarization incidences. Following the criteria for optical chirality [7, 49 ] and the insensitiveness of CD to longitudinal component for normal incidence, we calculated the dot-product of the electric and magnetic dipole moments on the xy-plane (i.e.

{\vec{p}}_{∥} \cdot {\vec{m}}_{∥}

) to investigate the relationship with the three chiral modes. The results are shown in Figs. 4(e) and 4(f) for x- and y-polarization incidence with the maxima of the dot-product corresponding well to the chiral resonances (and also the extrema of CD’s) of mode II, and modes I and III, respectively, indicating clearly that the observed CD’s come from the coupling of electric and magnetic dipole moments.

Fig. 4 Induced electric (a-b) and magnetic (c-d) dipole moments of the Ag staircase for x- (left column) and y- (right column) polarization incidence. The vertical thin black lines mark the mode I, II, and III as labeled. (e-f) The dot-product of electric and magnetic dipole moments.

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To further study the interplays between the resonances observed in Figs. 3 and 4 , and also to optimize the CD, we show in Fig. 5 contour plot of the CD as a function of incident frequency and width of the slanted Ag strip (w). On the contour plot, we overlay the resonance frequencies, determined by the extrema of Re[ξ], for the three chiral modes. Overall, there is a good correspondence between the extrema of CD (dashed lines) and the extrema of Re[ξ], despite of a small shift in frequency due to approximations used in the parameter retrieval method. To compare the strength of coupling with the maximum CD, we also display the amplitudes of Re[ξ_xx] and Re[ξ_yy] as scaled by the sizes of the symbols in Fig. 5. Take mode II as an example, the coupling strength increases from zero at w = 0, reaches maximum at w ~55 nm, then decreases to zero at w = 110 nm in good agreement with the amplitudes of extrema of CD (guided by the blue dashed line) obtained from the simulation with maximum value ~0.66 at w ~60 nm. The good match indicates clearly the correlation between CD and the coupling of electric and magnetic resonances. Note that CD vanishes for w = 0 (no slanted strip) and 110 nm (full-step staircase) as expected because the structures are achiral in which only single electric or magnetic resonance can be excited at resonant frequency (see Fig. 6 ). Thus there is no coupling between the electric and magnetic resonances and hence does not produce CD. As a result, controlling the coupling is essential in the optimization for practical applications. Here we only study the CD dependence on the width of the slanted Ag strip. In principle changing the lengths of the Ag strips or the pitch angle θ of the staircase could also be used to optimize the CD. We believe higher CD could be obtained by fine tuning all the parameters.

Fig. 5 CST simulated Δ_T contour map as a function of the slanted Ag strip width w. The solid symbols are resonance frequencies determined by the extrema of Re[ξ_yy] (inverted triangles mode I and red triangles mode III) and Re[ξ_xx] (blue dots mode II) as shown in Fig. 3(c). The sizes of the symbols are scaled to the amplitudes of the extrema of ξ. The dashed lines correspond to maximum CD for different chiral modes.

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Fig. 6 Retrieved parameters: Im[ε] (top), Im[μ] (middle), and Re[ξ] (bottom) for different width (top labels) of the slanted Ag strip. Vertical glide solid lines are for mode I (red), mode II (blue solid), mode III (green solid), and grey dashed lines are electric or magnetic resonance alone.

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5. Experiment

To demonstrate the chiral characteristics of the staircase, we fabricated Ag nanostructures topologically similar to the proposed staircase using a shadowing vapor deposition method (SVD) [45]. A 120 nm thick PMMA film was first coated on ITO glass by spin coating. The PMMA array (size 60 μm × 60 μm each) consisting of “mirror-L” shaped columns (200 nm square lattice) were then fabricated by standard e-beam lithography (Raith E-line system). Note that the “mirror-L” shaped PMMA column has a small thin extension (dark green in Fig. 7(a) ) attached to the horizontal ‘leg’ of PMMA column such that the bottom Ag strip is now discontinuous as compared to the continuous Ag strip obtained previously without the extension [46]. After that, the PMMA array sample was placed inside a Peva 600 EI electron-beam evaporator and was coated at θ = 45° deposition angle at a rate of 0.1 nm/s, resulting in ~100 nm thick sample as shown by the AFM profile in Fig. 7(b). The transmission spectra of circularly polarized light, from 350 THz to 660 THz generated from a polarizer and a quarter waveplate (APSAW-5, Astropribor), were then measured using a microscope-spectrometer (20X objective, NA = 0.25). We define forward direction as the light incident from the substrate side. The measured spectra were normalized with respect to bare ITO glass.

Fig. 7 (a) Schematic for shadowing vapor deposition. Orange arrow indicates the deposition direction, θ = 45°. (b) AFM profile of the sample nanostructure array.

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Figure 8(a) shows a top-view SEM image of our sample consisting of one bottom Ag strip/step (orange) connected to a top Ag strip/step (yellow) by a bridging Ag strip/step (dark red) while the corresponding schematic view is shown in Fig. 8(e). In our sample, the bottom Ag strip was coated directly on ITO glass substrate while the top and the bridging Ag strips on “mirror-L” shaped PMMA columns. The slanting effect of the bridging Ag strip originates from the rounded edges and corners of the PMMA columns resulted from the double exposures in electron beam lithography and the heating of directional Ag vapor during shadowing deposition. Our sample nanostructure exhibits the salient features of the staircase, i.e. three Ag strips in a chiral arrangement. As expected, the transmittance of the sample nanostructure presents the dominant features of the staircase for circularly polarized incident light as shown in Figs. 8(b) and 8(c). More importantly, the sample nanostructure is 3D chiral as inferred by the identical transmittance for forward and backward incidence for circularly polarized light of the same handedness as shown in Fig. 8(d). Moreover, the transmission difference, hence CD, exhibits a positive (350-460 THz) and also a negative (460-600 THz) band, which are similar to the prediction of the simulation model of Ag staircase as shown in Figs. 2(c) and 3(e) and also to the spectra obtained by using the same parameters as the sample nanostructure shown in Figs. 8(f)-8(h). The dielectric constant of Ag for simulations in this paper was extracted following the same procedures in [50], Leung et al. The agreement between the experiment and simulation is very good. Overall, our sample nanostructure exhibits chiral characteristics resulted from effective coupling between the electric and magnetic dipoles as proposed in the theoretical model of Ag staircase nanostructure. This demonstrates the conciseness and effectiveness of the SVD method in the fabrication of 3D chiral nanostructure in the visible range.

Fig. 8 Left column is for experimental results: (a) SEM image of Ag sample staircase by shadowing vapor deposition: bottom Ag strip (orange), connecting Ag strip (dark red), and top Ag strip (yellow). (b-c) Normal transmittance of circularly polarized light for forward and backward incidence, respectively. (d) Transmission difference (T _RCP -T _LCP). Right column: corresponding simulation results. Black scale bars in (a) and (e) are 100 nm. Parameters for the experiment and model are: a (65), h (95), w (70), l (130), t (11 nm). (e) Corresponding model and (f-h) simulation results.

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6. Conclusions

We discussed the mechanism of circular dichroism in a class of metallic staircase structures and demonstrate experimentally substantial CD in the visible range in topologically similar nanostructures. Using an effective parameter approach, we show that large CD, as high as ~0.66, can be obtained from the plasmonic chiral resonances arising from the coupling (parallel/antiparallel) between induced electric and magnetic dipole moments of the Ag staircase. Our sample chiral nanostructure fabricated by a simple shadowing method exhibits good agreement with the simulation results. Our work provides a fundamental understanding of chiral plasmon modes as well as a simple technique for achieving large circular dichroism which could lead to possible biosensing and/or optoelectronic applications.

Acknowledgments

Support from Hong Kong RGC grants AoE P-02/12 and CUHK1/CRF/12G is gratefully acknowledged. The technical support of the Raith-HKUST Nanotechnology Laboratory for the electron-beam lithography facility at MCPF (SEG_HKUST08) is hereby acknowledged. The simulations were carried out using the server in the Key Laboratory of Advanced Micro-structure Materials, Ministry of Education, China; and also the School of Physics Science and Engineering, Tongji University in collaboration with Prof. Y. Li in Tongji University.

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Giant plasmonic circular dichroism in Ag staircase nanostructures

Abstract

1. Introduction

2. Model

3. Results

5. Experiment

6. Conclusions

Acknowledgments

References and links

Cited By

Figures (8)

Equations (21)

Optics Express