1. Introduction

In recent years much attention has been focused on optical properties of nanopatterned metallic films. One particularly intriguing characteristic of these plasmonic nanostructures is their ability to resonantly trap and tightly confine light in spatial domains comparable or smaller than the optical wavelength, leading thus to the formation of so-called localized surface plasmon (LSP) resonances [1–3]. These modes are spacially local collective oscillations of conduction electrons at the surface of metals. They can form at the surface of metallic nanoparticles, such as spheres, rods, disks, and rings, or in metallic nanocavities, e.g. apertures in metallic films or surface indentations. Because the frequencies of LSPs are strongly dependent on the shape and size of the plasmonic nanoparticles, as well as the properties of the dielectric environment, they can be tuned over the entire visible and infrared domains [4, 5]. Equally importantly, because of the large electric permittivity of metals, the resonant excitation of LSPs induces a significant field enhancement at metal-dielectric interfaces. These unique phenomena associated with the formation of LSPs have led to many exciting applications, including in chemical and biomedical sensing [6–9], surface-enhanced Raman excitation spectroscopy [10–12], metallic nanotips for near-field optical microscopy [13–15], and optical nanoantennae [16–18].

One fascinating property of LSP resonances is that in many aspects they are similar to the electromagnetic response of an atom or a molecule, as a result of which they are sometimes called meta-atoms or meta-molecules. Moreover, similar to the case of interacting atoms or molecules, electromagnetic coupling induces the hybridization of LSP resonances of closely-spaced interacting nanoparticles [19], thus leading to complex plasmonic resonance spectra. This analogy can be extended even further: plasmonic nanoparticles can be assembled into one-dimensional (1D) plasmonic chains [20, 21], 2D metasurfaces [22, 23], and 3D bulk metamaterials [24–31] with remarkable properties. Demonstrated phenomena include the induction of a macroscopic magnetic moment in metallic resonators [32] at frequencies as large as optical frequencies; strong optical chirality [22, 28, 29, 32, 33]; properly designed metallic resonators have remarkably large optical absorption [30, 31, 34, 35]; for increasing optical power, LSPs exhibit second- and third-order nonlinear polarizability [23, 36, 37].

Some of us have recently theoretically predicted [38] that one can tailor the properties of LSPs formed in a 2D array of asymmetric apertures in metallic films so that the mid-infrared optical transmittance of the corresponding plasmonic metasurface becomes strongly dependent on the polarization of the incoming field. Here we experimentally confirm this prediction and, furthermore, extend our theoretical and experimental analysis to the reflectance and absorptance. In particular, we use a simple design for an asymmetric aperture whose properties can be conveniently tuned, namely, a Swiss cross with asymmetric arms. The plasmonic response of arrays of symmetric cruciform apertures has been extensively studied both theoretically and experimentally [34, 39–42]. The LSP resonances of such symmetric apertures, however, consists of two degenerate modes orthogonally polarized with respect to each other and therefore the optical transmission of the corresponding plasmonic metasurfaces is polarization insensitive. Here we demonstrate that by introducing structural asymmetry in the design of the cruciform aperture, the optical transmission and reflectance of a uniform, periodic array of such apertures show enhanced optical anisotropy. In particular, the maximum of the transmission spectra, which corresponds to the resonant excitation of a LSP in the array of asymmetric cruciform apertures, can be tuned by almost 50% by simply rotating the plane of polarization of the incident wave. Moreover, using Babinet’s principle, the ideas presented in this work can be readily extended to the complementary geometry of metallic crosses placed on a dielectric substrate [43,44]. Similar phenomena could be found in arrays of rectangular or elliptical apertures. However, in both of these cases the maximum dimensions of such apertures are similar to the size of the wavelength at which resonances occur and so do not truly operate within the metamaterial regime. In the case of our cruciform apertures the lengths of the arms are around 6 times smaller than the resonant wavelengths, and therefore function within the metamaterial regime.

2. Fabrication

Our cruciform aperture arrays were fabricated on 0.5 mm thick single-crystal calcium fluoride substrates, due to the low absorption of this crystal at mid-infrared wavelengths. A 30 nm thick layer of Au was then thermally-evaporated onto the substrate, preceded in situ by a 5 nm thick Cr adhesion layer. Arrays of asymmetric cruciform apertures were then milled into the surface of the gold using a 30 keV gallium focused-ion-beam. The beam current was 50 pA and the dose 50 pC/μm². The device structure and a fabricated array are shown in Fig. 1. The devices were designed so as to operate in the mid-infrared band, but we also fabricated several samples for C-band operation (λ ∼ 1.55 μm). Each array has 15×15 unit cells and a periodicity in both the x and y directions of Λ = 2 μm; thus the array has dimensions 30×30 μm². The size of the arrays is large enough so that size-dependent array effects are negligible [2]. A similar array of symmetric cruciform apertures was fabricated as a control sample. This array had the same periodicity and same number of unit cells as the arrays of asymmetric apertures.

 

Fig. 1 (a) Schematic of the unit cell also showing the definition of the in-plane electric-field polarization angle, θ. (b) Scanning electron micrograph of an array with the inset showing magnified detail. (c) Schematic cross-section through the XY-segment, as shown in (b).

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3. Measurements

3.1. Experimental setup

The transmission spectra of the arrays were measured using Fourier-transform infrared (FTIR) microscopy. The corresponding experimental setup is shown in Fig. 2. The optical source is a mid-infrared globar and the signal was detected using a mercury cadmium telluride detector. The spot size of the incident beam on the sample was 0.33 mm and is thus substantially larger than the array. For reflection measurements the light is incident upon the top (gold) side of the sample. As expected, in the spectral range considered in our experiments (λ > Λ), measured transmission spectra are independent of which side of the sample was irradiated. The metal films are optically opaque for the thickness used in our experiments and therefore the measured transmission corresponds to the light transmitted through the aperture array. The transmission spectra were normalized to the bare CaF₂ substrate while the reflection spectra were normalized to the unpatterned gold surface. Data were obtained for incident in-plane polarization angles (as defined in Fig. 1a) between θ = 0 and θ = 90° in 15° increments. The minimum extinction ratio of the polarizer across the wavelength measurement range is 100.

 

Fig. 2 Optical arrangement of FTIR microscope showing optical paths for obtaining both reflection and transmission spectra.

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Due to increase in noise of the FTIR spectrum below 2 μm, a second separate approach was used to measure the transmission spectrum around the telecommunication C-band. An Optical Parametric Amplified (OPA) Ti:Sapphire source was used to generate 100 fs laser pulses at a series of wavelengths from 1440 nm to 1670 nm. At any given wavelength a Berek’s variable waveplate was used to vary the laser polarization. The polarized light was focused onto the plane of the patterned array at an angle normal to the surface. Focusing was accomplished using a 10× objective lens so as to produce a 12 μm spot size (1/e²). The transmitted signal was then reimaged onto a germanium photodetector. Care was taken to ensure that any spurious intensity modulation due to beam ”walk-off” as the waveplate was rotated was eliminated via position averaging. The array in this case, was separately designed for use in the 1.55 μm region using the same materials system as for the mid-infrared array described in the text.

3.2. Transmission, absorption, and reflection spectra

The resulting experimentally measured transmission spectra for the asymmetric cruciform array, presented in Fig. 3a, show two distinct peaks, A and B, the positions of which, to within the accuracy of the measurement, are invariant with respect to the polarization angle. As the polarization angle is changed from θ = 0 to θ = 90°, the amplitude of peak A decreases from its maximum value reached at θ = 0 and eventually decays to below the noise level, while the peak B begins to emerge and increases in amplitude to reach its maximum at θ = 90°. The spectra in Fig. 3a show another intriguing spectral point, I (at λ =4.46μm), at which transmission is independent of polarization. Drawing from an analogy from molecular spectroscopy, this point is termed an isosbestic point [38]. By comparison, the spectra for the control array of symmetric cruciform apertures show a single peak (see Fig. 3g) and, within the inherent variations introduced by the fabrication process, the transmission is insensitive to the polarization of the electric field. In addition, a transmission minimum, W, is seen at λ = 3.3 μm, for arrays of both asymmetric and symmetric apertures. This minimum corresponds to the Wood’s anomaly of the periodic array and is predicted to occur at ${\lambda }_W=n_d\Lambda /\sqrt{i^2+j^2}$ [1–3], where n_d is the index of refraction of the dielectric medium and i and j are mode indices. In the case of square arrays the largest wavelength at which the Wood’s anomaly occurs corresponds to i = 1 and j = 0. As such, for an array with Λ = 2 μm the wavelength of the Wood’s anomaly corresponding to Au-air (n_d = 1) and Au-CaF₂ (n_d = 1.4) is λ_W = 2 μm and λ_W = 2.8 μm, respectively. The measured reflection spectra (Fig. 3c) are qualitatively anti-correlated with the transmission spectra, with clear reflection minima at the wavelengths of the transmission peaks A and B. Absorption spectra were obtained using the formula A = 1 – (T + R). (This expression is valid at wavelengths exceeding the aperture period (here 2 μm) in the case where diffuse scattering is negligible.) Remarkably, for both the reflection and absorption spectra (Fig. 3e) there is an isosbestic point, its wavelength being blue-shifted with respect to that of the isosbestic point in the transmission spectra (the isosbestic point of the reflection and absorption spectra is at the wavelength λ_r = 4.36 μm and λ_a = 4.32 μm, respectively). The wavelength of the isosbestic point is dependent on the amplitude and width of the two resonances and, since these may differ in reflection, transmission and absorption, it is not surprising that the wavelength of the isosbestic point shifts.

 

Fig. 3 (a), (c), and (e) Measured FTIR transmission, reflection and absorption spectra (respectively) for an array of asymmetric cruciform apertures with L_x = 1675 nm, L_y = 1003 nm, g_x = 418 nm and g_y = 165 nm. These spectra show polarization angles varying from θ = 0 (blue) to θ = 90° (brown) in increments of 15°. (b), (d), and (f) Simulation of FTIR transmission, reflection and absorption spectra for asymmetric cruciform apertures with the above dimensions. (g) and (h) Measured transmission and simulation spectra for the control array of symmetric cruciform apertures with dimensions L_x = L_y = 1264 nm and g_x = g_y = 368 nm.

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3.3. Measured aperture dimensions

In order to investigate theoretically the optical properties of the fabricated arrays, it was necessary to know the fabricated dimensions of the arrays, as defined in Fig. 1a. Owing to fabrication process variability, the dimensions of each aperture vary. Therefore measurements were taken of 10 fabricated apertures in each array using scanning electron microscopy and the dimensions averaged. For the array of asymmetric cruciform apertures the lengths of the arms of the cruciform were found to be L_x = 1675 nm and L_y = 1003 nm, whereas their width was g_x = 418 nm and g_y = 165 nm. Note also that for the array of symmetric cruciform apertures fabrication tolerances led to a small degree of asymmetry, the corresponding mean values being L_x = 1270 nm, L_y = 1258 nm, g_x = 362 nm, and g_y = 373 nm. Therefore, in this case the values of L_x and L_y were averaged to arrive at a single mean value: L_x = L_y = 1264 nm. Similarly, the values of the width of the arms, g_x and g_y, were averaged to the mean value g_x = g_y = 368 nm.

4. Simulations

Device simulations were carried out using commercially available software, RSoft’s Diffract-MOD, [45] which implements the rigorous coupled-wave analysis method. Simulated spectra for the arrays of asymmetric and symmetric cruciform apertures are shown in Fig. 3. In our simulations numerical convergence was reached when we included N = 17 diffraction orders for each transverse dimension, which amounts to a total of N² = 289 diffraction orders. Furthermore, we assume that the frequency-dependent dielectric constant of Au is described by the Drude model, ${\varepsilon }_{\text{Au}}\left(\omega \right)={\varepsilon }_0\left[1-\frac{{\omega }_p^2}{\omega \left(\omega +i\gamma \right)}\right]$, where ω_p and γ are the plasma and the damping frequencies, respectively. In the case of Au, ω_p = 13.72 × 10¹⁵ rad/s and γ = 4.05×10¹³ s⁻¹ [46]. Note that since our devices operate in the mid-infrared frequency domain the contribution to the dielectric constant of inter-band effects can be neglected. We have observed, however, that in order to achieve a good agreement between the experimental data and the numerical results we had to use an increased damping frequency of γ → 1.5γ = 6.08 × 10¹³ s⁻¹. This fact is not surprising since it is well known that due to electron scattering into surface states the dielectric constant of metallic nanostructures depends on their size when the corresponding characteristic size is comparable to the skin depth. For metallic films, the bulk damping frequency is replaced by γ_film = γ_bulk + αv_F/d, where α is a theory-dependent quantity on the order of 1, v_F is the Fermi velocity, and d is the thickness of the film [5]. Interestingly enough, at optical frequencies the corresponding scaling factor was found to be equal to 3 [26].

The two transmission maxima and their polarization-dependence, as well as the spectral location of the isosbestic point and the Wood’s anomaly in the experimentally-measured spectra are well reproduced in the simulated spectra for the asymmetric apertures. An additional peak, labeled C (λ = 2.6 μm), is however observed in the simulation, which in the experimental data appears to be only slightly above the noise level. Likewise for the array of symmetric apertures, the simulation reproduces the single peak of the experimental data at λ = 4.6 μm, but also predicts the existence of an additional peak C at shorter wavelength. This additional peak is at the same wavelength as for the asymmetric apertures. The insensitivity of the position of peak C to the detailed geometry of the unit cell suggests that it is due to extended surface plasmon polariton (SPP) resonances. This is confirmed by simulations of the electric field at peak C (not shown) which show significant amplitudes in the region away from the apertures covered by the gold. Indeed, the wavelength of SPPs is given by the relation ${\lambda }_{\text{SPP}}=\left(\Lambda /\sqrt{i^2+j^2}\right)\Re 𝔢\sqrt{{\varepsilon }_d{\varepsilon }_{\text{Au}}/\left({\varepsilon }_d+{\varepsilon }_{\text{Au}}\right)}$ [1–3], which implies that for Au-air and Au-CaF₂ interfaces the SPP wavelength is λ_SPP = 2.005 μm and λ_SPP = 2.807 μm, respectively (here the symbol ℜ𝔢 means the real part of a complex number). Since |ɛ_Au| ≫ ɛ_d, λ_SPP is only slightly larger than λ_W. Note that in this analysis the coupling between the plasmons excited at the air-metal and metal-substrate interfaces is neglected. This is a valid approximation because, as our experiments demonstrate, the transmission through a bare metallic film is essentially equal to zero and therefore there is no coupling between the two plasmons. The extended SPP resonances are significantly weaker in our experimental measurements, as compared to those in simulations, presumably due to losses resulting from the surface roughness of the evaporated metal film [47] and low signal-to-noise ratio of the detector in the lower-wavelength spectral domain.

In contrast, peaks A and B result from local surface plasmon resonances in the shorter and longer arms of the asymmetric aperture, respectively. More specifically, they correspond to the cut-off wavelength of the waveguide modes supported by the cruciform apertures. This interpretation is further supported by the fact that the simulated spectra for the symmetric apertures are polarization-independent as in this case the two modes are degenerate. Importantly, since the properties of these modes are defined entirely by the shape of the apertures, the corresponding transmission depends only on the optical coupling between these modes and the incoming plane wave and as such it is not affected by the roughness of the top surface of the metallic film. The linewidths of the two peaks in both our simulations and our experiments are in excellent agreement. Since the simulated spectra are derived from an infinite array of identical apertures, this confirms that inhomogeneous broadening plays no significant role in our measurements. The amplitudes of the measured LSP transmission peaks A and B are however suppressed by comparison with the simulated peaks due to similar loss processes which suppress the extended SPP modes as described above.

In order to confirm our interpretation that peaks A and B correspond to LSP resonances, we show in Fig. 4 and Fig. 5 the simulated field distributions within the apertures. The field profiles correspond to a depth of half of the thickness of the Au film. Figure 4 shows the field distributions at polarization angles of θ = 0 and θ = 90° at the two transmission peaks in Fig. 3b. The field profiles in panels (a)–(d) in Fig. 4 illustrate the in-plane electric-field components at λ = 3.9 μm (corresponding to peak A), while panels (e)–(h) in this same figure show the field profiles at λ = 5.75 μm (corresponding to peak B). From these simulations it is clear that peak A occurs due to the resonant excitation of a waveguide mode that is primarily polarized transverse to the shorter, y-oriented arm of the aperture (as shown in Fig. 4a). Similarly, peak B corresponds to the cut-off wavelength of a waveguide mode with polarization primarily transverse to the longer, x-oriented arm (as shown in Fig. 4h). Switching between these two modes is accomplished by changing the polarization of the incident plane wave. It should be noted that these LSP resonances do not correspond to the cut-off modes of the separate arms of the cruciform apertures, as in this case the cut-off wavelength would obey the relation λ_c < 2max(L_x, L_y). Importantly, this result suggests that the wavelength of the transmission peaks can be readily tuned over a wide spectral range by simply changing the shape of the apertures.

 

Fig. 4 Simulated spatial profiles of the electric field for θ = 0 and θ = 90°. Panels a, b, c, and d show the field profiles at a wavelength of 3.9 μm (corresponding to peak A in Fig. 3b), while panels e, f, g, and h show the field profiles at a wavelength of 5.75 μm (corresponding to peak B in Fig. 3b). The electric field is normalized to the amplitude of the incident plane wave.

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Fig. 5 Simulated spatial profiles of the electric field at the isosbestic point (λ = 4.75 μm, corresponding to point I in Fig. 3b) for θ = 0, θ = 45°, and θ = 90°. The electric field is normalized to the amplitude of the incident plane wave.

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Figure 5 shows the in-plane electric field distributions at the transmissive isosbestic point in our simulations (Fig. 3b), λ = 4.75 μm, at polarization angles of θ = 0, θ = 45°, and θ = 90°. Unlike the fields corresponding to transmission maxima, the fields calculated at the isosbestic point do not have a predominant polarization state. This phenomenon also explains why such an isosbestic point exists. Thus, let us denote by T_x(λ) and T_y(λ) the transmission spectra corresponding to an incident plane wave polarized along the x- and y-axis, respectively, and assume that there is a wavelength, λ₀, for which T_x(λ₀) = T_y(λ₀). Then, at λ = λ₀, the total transmission corresponding to the polarization angle θ is T(λ₀) = T_x(λ₀) cos² θ + T_y(λ₀) sin² θ, i.e., it is independent of the polarization angle θ. In other words, despite the fact that the plasmonic metasurface is anisotropic, at λ = λ₀ it is optically isotropic (as far as transmission is concerned). A similar argument holds for the isosbestic points in the reflection and absorption spectra, although the wavelength at which the reflectivity coefficients, R_x(λ) and R_y(λ), and the absorption components, A_x(λ) and A_y(λ), are mutually equal would differ in the three cases. This is an expected result as the total transmission and reflection coefficients and, implicitly, the total absorption, depend in an intricate way on the reflection and transmission coefficients at the top and bottom facets of the metal film as well as the coupling coefficients between the LSPs excited in the cruciform apertures and the incoming/outgoing plane waves [2]. Going back to the analogy with physical chemistry, we can view the plasmonic metasurface as a 2D distribution of meta-molecules whose polarizability, at the isosbestic point, is independent on polarization.

5. Further investigations

In order to further validate our interpretation of the physical origin of the resonant peaks, experimentally measured transmission spectra are now presented for an ensemble of asymmetric cruciform aperture arrays, in which one geometrical parameter (in this case the length of the shorter arm, L_y, is systematically varied. Each array has 15 × 15 unit cells and a periodicity of Λ = 2 μm. The mean and standard deviation of L_y for each array were determined using SEM, with the standard deviation of L_y ranging from 22 nm to 43 nm. Typical values for the standard deviation in L_x were around 35 nm for each array. The transmission spectra for θ = 0, θ = 45°, and θ = 90° are displayed in Fig. 6. The extracted spectral location of the resonant peaks A and B, as well as that of the isosbestic point I, are plotted in Fig. 7. As expected, peak A (the shorter wavelength peak) shifts to longer wavelengths as the length, L_y, of the shorter arm increases, whereas peak B (the longer wavelength peak) is invariant with L_y. Also, as the length of L_y increases, the cruciform apertures tend toward symmetry in L_x and L_y. Thus peaks A and B, and the isosbestic point I, tend to converge toward a single peak with the amplitude of peak A increasing (due to an increasing area of the optical mode) and the amplitude of peak B decreasing. Also plotted in Fig. 7 are the results of our simulations for varying L_y. The values of L_x, g_x, and g_y used in the simulations are given by the mean of all these values across all the arrays, as measured by SEM. The results of our numerical simulations agree well with the experimental data, using a single value of the damping frequency γ = 6.08 × 10¹³ s⁻¹. This confirms our physical interpretation of the features observed in the experimental spectra.

 

Fig. 6 Experimentally measured transmission spectra for all fabricated arrays of asymmetric cruciform apertures at polarization angles of θ = 0 (black), θ = 45° (blue), and θ = 90° (red). The mean values of the other dimensions are L_x = 1645 nm, g_x = 418 nm and g_y = 165 nm.

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Fig. 7 L_y-dependence of the wavelength of the LSP transmission resonances A (blue) and B (red), and the isosbestic point I (green). Filled points are experimental data; unfilled points are data from simulations. Error bars in L_y correspond to the standard deviation of the fabricated device dimensions.

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One important property of the plasmonic arrays investigated here is that the operating wavelength can be varied by simply scaling the size of the asymmetric cruciform apertures. Of course, since the dielectric constant of metals depends on frequency the operating frequency does not scale linearly with the size of the structure. These ideas are illustrated by the experimental data presented in Fig. 8, which displays measurements of asymmetric cruciform arrays with dimensions L_x = 600 nm, L_y = 500 nm, g_x = 200 nm and g_y = 100 nm and a lattice constant of Λ = 700 nm. Thus, it can be seen that the main properties of the symmetric plasmonic arrays, namely, the existence of polarization dependent transmission maxima and of an isosbestic spectral point, are preserved when the size of the structure is scaled down so as the operating wavelength is shifted to the telecom C-band.

 

Fig. 8 Transmission through a cross array, designed for the 1.55 μm region, at several polarizations and for different wavelengths was measured using a 100 fs tunable optical parametric source. Each wavelength point was measured separately and averaged over many pulses. The dimensions of the array were L_x = 600 nm, L_y = 500 nm, g_x = 200 nm and g_y = 100 nm with a lattice constant of Λ = 700 nm.

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6. Conclusions

Our findings suggest that the functionality of our proposed plasmonic nanostructures can be greatly enhanced by interspersing arrays whose unit cell consist of cruciform apertures with different sizes or, more generally, apertures with different other shapes. Since the transmission maxima of the arrays and their optical reflectivity are determined solely by the frequency of the corresponding LSP resonances, the spectral optical response of these plasmonic nanostructures can be tailored for specific applications, allowing one to explore new designs of frequency-agile metasurfaces with enhanced functionality. One such potential application is to broadband negative index metamaterials. Specifically, it has been demonstrated that by layering 2D plasmonic arrays of symmetric crosses and dielectric thin-film spacers one obtains metamaterials with a negative index of refraction [40]. In this connection, our study suggests that employing plasmonic arrays made of asymmetric crosses opens up the possibility of achieving negative index of refraction over a broad frequency domain. Moreover, the frequency of LSP resonances changes significantly with the index of refraction of a chemical substance filling the apertures, an effect that can be used to develop new plasmonic-based nanodevices for parallel, on-chip sensing for chemical and biomedical applications. In particular, it has been recently demonstrated [48] that molecules deposited on an optically thick metallic film perforated by a periodic array of holes can dramatically affect the transmission spectra, at wavelengths at which they are strongly absorbent, an effect called absorption induced transparency. In this connection, it can be readily understood that our plasmonic structures can be used as tunable surface filters for chemical or biological analysis. Equally important, the conclusions of our work can be readily extended to the technically relevant 1.55 μm wavelength region by simply scaling the size of the apertures.

In summary, we have presented a comprehensive experimental and theoretical study of optical properties of plasmonic metasurfaces characterized by strong form-anisotropy of the unit cell. In particular, we have demonstrated that the excitation of LSP resonances strongly affects the transmission spectra of the plasmonic nanostructure by providing polarization-dependent transmission channels. This feature allows the transmission properties of the plasmonic arrays to be readily tuned by properly engineering the shape and size of the unit cell of the array. In short, our findings can have important relevance to new applications in nanophotonics and plasmonics, including frequency-agile surfaces, polarization-selective absorbers, strongly anisotropic metamaterials, plasmonic-based sensors for chemical and biomedical applications, and broadband negative index metamaterials.