Spectral Shifting in Extraordinary Optical Transmission by Polarization-Dependent Surface Plasmon Coupling
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Nanoapertures in a metallic film exhibit extraordinary optical transmission (EOT) owing to the surface plasmon resonance. Their transmission properties are known to be dependent on the structural parameters of the nanoapertures. In addition, the polarization of light has also a crucial influence on the transmission spectrum. In this study, we numerically found that the polarization state is a sensitive parameter in plasmonic EOT only when the gap size between triangular nanoapertures is less than ~ 20 nm. For a polarization of the light perpendicular to the axis between the nanoapertures, the optical transmission spectrum is nonlinearly redshifted with decreasing gap size. This spectral shifting of the transmission has potential applications for active optical filters, which can be manipulated by the polarization of light or by adjusting the gap size.
KeywordsExtraordinary optical transmission Surface plasmon Nanoplasmonics
In 1998, T.W. Ebbesen et al. firstly reported that nanoscale hole apertures in a metallic film induce extraordinary optical transmission (EOT), in which high transmission occurs at the resonance wavelength . The origin of EOT is mainly known to be the surface plasmons (SP), which are collective charge oscillations due to the resonant interaction between light and free electrons at a metal-dielectric interface [2, 3, 4]. A typical EOT structure consists of a periodic nanoaperture array and its optical properties such as transmission spectrum, efficiency, and linewidth depend on the complex permittivity of the materials and design parameters (hole size, pitch, and aperture shape) [5, 6, 7]. Since a SP can only be efficiently induced in designated nanoapertures or shaped nanostructures , the SP enables sensitive bio-sensing , sub-wavelength scale beam focusing or lithography [10, 11], novel optical filtering , plasmonic metrology , terahertz imaging , and next-generation photonic devices [15, 16, 17, 18]. Recently, electronically tunable EOT experiments in graphene plasmonic ribbons were introduced, showing that a graphene-coupled sub-wavelength Au slit array exhibits an active EOT structure at mid-infrared frequencies .
Since EOT provides selective transmission and efficient focusing of light at the sub-wavelength scale , it enables new applications for precise optical filters at the nanoscale. The optical transmission spectrum is tunable by adjusting the pitch of the nanohole array because efficient excitation of SPs primarily depends on the distance between the nanoholes. However, controlling the pitch size of a nanohole array for a significant spectral shift of the optical transmission is difficult in noble metal-based plasmonic structures because conventionally used metal film on a dielectric substrate is not highly stretchable to provide the enough pitch variation.
In this study, we demonstrate that the transmitted EOT spectrum through an asymmetric bow-tie nanoarray can be efficiently tuned by more than 90 nm in wavelength at the near-infrared regime by changing the gap size between the triangles. This shift of the transmitted optical spectrum only occurs for transverse electric (TE) polarization with respect to the bow-tie axis, whereas light with transverse magnetic (TM) polarization is insensitive to the variation of the bow-tie gap. In particular, the EOT resonance peak shifts nonlinearly by an average of 3.12 nm per one-nanometer increment of the bow-tie gap for the TE polarization when the gap size is less than 20 nm. Therefore, this EOT-based asymmetric nanoarray can facilitate wavelength-tunable optical filters without mechanical deformation in the field of novel flat optics.
Numerical Simulations and Results
The polarization state of light can significantly affect the SP resonance condition, especially in asymmetric metallic nanoapertures. In order to analyze this phenomenon, we performed finite difference time domain (FDTD) simulations with a unit cell of the bow-tie nanostructure shown in Fig. 1b. For simplicity, we chose fixed geometrical parameters except the gap size. The fixed geometrical parameters in this calculation are a pitch of 600 nm × 300 nm, a thickness of 50 nm, as well as a 90 nm height, and 60° internal angles of the triangles. A commercial FDTD software (FDTD Solution, Lumerical, Inc.) was used for all simulations. These parameters were chosen for efficient SP excitation considering typical nanofabrication constraints.
The bow-tie structure in the simulations consists of a free-standing gold film, and its optical properties such as the frequency-dependent complex permittivity were taken from Yakubovsky et al. . Fine adaptive meshes with a step size of 0.5–3.5 nm were additionally applied at the gap of the bow-tie aperture, while meshes with a step size of 1–8 nm were applied to the entire simulation volume. In addition, an adaptive mesh and a perfectly matched layer (PML) boundary condition were used for the z-axis (out-of-plane) direction, while symmetric and anti-symmetry boundary conditions were chosen in-plane for computational simplicity. The bow-tie structure was illuminated by a plane wave with a spectral bandwidth of 450–1000 nm in wavelength and a field strength of 1 V/m, and the transmitted spectrum was monitored for a duration of 100 fs with a step size of 0.93 as.
The origin of EOT can be either plasmonic transmission or Rayleigh anomaly that is associated with light diffracted parallel to the grating surface. In the case of the Rayleigh anomaly, the optical transmission peak should satisfy the formula denoted in ref. . The minor peak at ~ 605 nm for TM polarization is not explained by the Rayleigh anomaly, based on our simulation parameters. Therefore, we expect that the peak at ~ 605 nm is assumed to be one of the localized surface plasmon resonance modes whose resonance frequency is not affected by the gap of two triangular apertures.
Figure 3c shows the calculated transmission as a function of gap size for a reversed bow-tie geometry using the same structural parameters as shown in Fig. 1b and TE polarization. Two resonance peaks are present as in the case of ideal and rounded bow-tie geometries; however, no radical redshift of the optical transmission spectrum is observed in the reversed bow-tie geometry. Figure 3f shows the calculated E-field distribution at a wavelength of 634 nm, which is the resonance wavelength for a gap size of 20 nm for the reversed bow-tie geometry. Although the SPs are excited at the vertex of each triangle, they do not overlap due to the spatial separation and hence cannot couple efficiently with each other, even for zero gap size. This result further supports our explanation that the drastic redshift of the transmission spectrum is due to the interaction between SPs from adjacent triangular apertures.
In summary, we showed that the optical transmission spectrum by plasmonic EOT could be redshifted by a variation of the bow-tie nanogap rather than by changing the pitch of the array. Intriguingly, the drastic shift of the optical transmission peak for gap sizes below 20 nm is only observed for TE polarized light. This is due to the strong plasmonic coupling between SPs excited at the vertices of adjacent triangular structures by the TE polarized light. In practice, the redshift can be controlled by the polarization state of the input light beam or by changing the aperture gap size on a nanometer scale. Therefore, this induced spectral shift of the extraordinary optical transmission can be utilized for various applications such as active optical filters or displays.
Author Contributions Statement
The project was planned and overseen by S.K., K.K., and J. P. The simulations are performed by J.P and H. L. Data were analyzed by S.K. J.P and A.G. All authors contributed to the discussion and preparation of the manuscript.
This work was supported by the National Research Foundation of the Republic of Korea (NRF-2017R1C1B2006137), ICT, Future Planning (NRF-2017M3D1A1039287), and Basic Research Lab Program (NRF-2018R1A4A1025623).
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