1. Introduction

The field of infrared and optical plasmonic metamaterials has witnessed a fast development over the last decade, thanks to major advances in modern nanofabrication techniques and a deeper understanding of the underlying physics [1–4]. Along the way, a number of photonic devices with improved functionalities and/or unprecedented optical behavior have been introduced and demonstrated including enhanced optical transmission (EOT) [5], negative refractive index [6], zero refractive index [7], electromagnetic-induced transparency [8], frequency selective near-perfect absorption [9], broadband polarization control [10], optical wavefront manipulation [11], and so on. Among them, the EOT effect and the exotic indices of refraction observed in plasmonic metamaterials are of particular interest to both scientists and engineers due to the novel physical phenomena they have exhibited as well as the rich potential they hold for practical applications in the field of optical imaging, high-resolution lithography, sensing and detection, optical signal processing, and many others.

Owing to previous research efforts, it has been well understood that the EOT effect provided by a single thin metallic film perforated with periodic air holes of various shapes and dimensions are primarily due to the excitation of surface plasmon polariton (SPP) modes [12, 13], whereas for a thick perforated metal film, the excitation of localized waveguide modes also plays an important role [14]. On the other hand, nanostructures perforated with either rounded or rectangular air holes, in the form of multilayer metallodielectric stacks, have also been explored to construct plasmonic metamaterials. Such structures have been shown to exhibit negative or near-zero indices of refraction, due to their ability to provide both magnetic and electric resonances that can be independently controlled [6, 7, 15–17]. It has been revealed by in-depth examination of the mode dispersion and field distribution that the electric response of a perforated multilayer metallodielectric stack is determined by the cutoff wavelength of the air hole waveguide, while its magnetic response is controlled by the gap SPP modes propagating along the dielectric spacers in between the metal layers [18, 19]. Recently, upon observing this structural and physical similarity, a link between the EOT effect and the novel indices manifested in metamaterials has been established by investigating the effective medium properties of the multilayer metallodielectric metamaterials at the wavelengths where the EOT effect occurs [20, 21]. It was found that the external SPP mode, denoting the surface mode on the interfaces between the outermost metal layers of the metamaterial nanostructures and the surrounding medium, gives the strongest enhanced transmission. This wavelength, corresponding to the cutoff wavelength of the air hole waveguide, coincides well with the effective plasma wavelength of the metamaterial nanostructure, i.e. an effective permittivity equal to zero. In addition to the external SPP mode, the internal SPP modes [22], which do not exist in a single-layer perforated metal film, also give rise to EOT peaks. These internal SPP modes propagate within the subwavelength dielectric spacers in between the metal layers of the nanostructures and show a curl-like current distribution which results in a magnetic resonance [18]. Based on these discoveries, researchers have adopted the higher order internal SPP mode, which is less lossy than the fundamental mode, to demonstrate negative index of refraction at visible wavelengths [23]. However, further exploitations of this EOT-metamaterial joint property have not yet been carried out for broadband operations, which could lead plasmonic metamaterials to a more widespread application in practical nanophotonic systems and components.

In this paper, we propose a synthesis methodology for designing broadband plasmonic metamaterials. Specifically, by strategically introducing nanofabrication accessible subwavelength perturbations to a base metamaterial structure, both the external and internal SPP modes can be finely controlled, thus enabling the shaping of the metamaterial dispersive properties over a broad wavelength range to meet the targeted spectral behavior. Here, a multilayer modified fishnet is designed to achieve a filtering functionality with both a broad, flat passband from 3.0 to 3.7 µm and a smooth and gapless negative-zero-positive index transition behavior within the passband. This further allows for the construction of a bifunctional metaprism – simultaneous broadband bandpass filtering and in-band polarization-independent passive optical beam-steering – which is verified by full-wave numerical experiments. Importantly, throughout the 20% bandwidth of the transmission window, the transmittance normalized to area is around 3 dB. This broadband EOT effect is realized by hybridizing the external SPP mode and the two internal SPP modes. The influence of the subwavelength nano-notches on the device performance and the wavelengths of the external and internal SPP modes are also investigated. Moreover, the SPP mode dispersion as a function of the transverse wave number magnitude is studied, which sheds light on the optical properties of the metamaterial under illumination at oblique incidence. With the demonstrated perspective of using subwavelength perturbation elements for dispersion tailoring, this work will benefit and inspire nanophotonics researchers toward designing other novel nanostructured plasmonic devices, particularly those with a broad operational bandwidth.

2. Multilayer broadband metamaterial filter analysis

The unit cell configuration of the multilayer metallodielectric metamaterial considered here is shown in Fig. 1(a). This structure is also compatible with large-area nanofabrication techniques, and thus can be readily fabricated [24, 25]. Gold (Au) is used for the metal layers and Kapton is employed for the dielectric spacers. As our design target, we selected a filter with a passband in the mid-infrared range between 3.0 µm and 3.7 µm, i.e. a 20% bandwidth, and stopbands on either side of the passband extending down to 2.5 µm and up to 4.5 µm. Within the passband, the effective index of refraction (or the transmission phase delay) should transition from negative through zero to positive seamlessly without a zero-index evanescent mode gap as observed in many previously demonstrated metamaterials [26]. It is worth mentioning that the salient optical properties of a multilayer metallodielectric nanostructure are driven by its fundamental Bloch mode, which was verified in [6], where the measured refractive index was found to correspond well with the calculated index of the fundamental Bloch mode. This observation was later confirmed by numerical studies that the energy transport inside a multilayer fishnet structure is indeed mediated by its fundamental Bloch mode [19], provided that a sufficient number of functional layers is employed. In this case, a five-functional-layer fishnet structure perforated with a doubly periodic array of air holes is adopted as the base configuration because it is able to provide a degree of flexibility to adjust the values of its effective permittivity and permeability. In order to provide a more delicate manipulation over the SPP modes related to the air hole waveguide and the subwavelength gap between the metal layers, two square subwavelength nano-notch cuts are made in each side of the square air holes, enabling a precise control over the metallic strip permittivity dilution percentage as well as the wavelengths and strengths of both the fundamental and second order magnetic resonances. Thus, extremely fine control of both the effective permittivity and permeability dispersion is achieved, as will be discussed in the following Sections.

 

Fig. 1 (a) Unit cell geometry of the multilayer metallodielectric metamaterial with eight square subwavelength nano-notches. The structure has six gold layers and five dielectric spacer layers. The dimensions are p = 1985 nm, w = 807 nm, g = 341 nm, t = 46 nm and d = 76 nm. (b) The simulated transmittance/reflectivity. The inset shows a magnified view of the transmittance in the passband. (c) The retrieved effective index of refraction and impedance. (d) The retrieved effective permittivity and permeability.

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The high frequency structure simulator (HFSS) finite element full-wave solver was employed to predict the scattering properties of the structure with the same simulation setup as was used in [17]. Importantly, the dispersive optical properties for the constituent metal and dielectric materials measured by variable angle spectroscopic ellipsometry were used in the full-wave solver to emulate the performance of an experimentally fabricated metamaterial. The dimensions of the geometrical parameters were tuned by utilizing a genetic algorithm (GA) optimizer [27] to meet the previously mentioned desired properties within the 2.5 ~4.5 µm band. The optimized geometrical dimenions of the nanostructured metamaterial were found to be p = 1985 nm, w = 807 nm, g = 341 nm, t = 46 nm and d = 76 nm. An advantage of the proposed structure is that it provides a polarization-insensitive response for normally incident waves due to its four-fold symmetry and square lattice. Figure 1(b) reports the simulated transmittance and reflectivity at normal incidence. A broad and flat passband can be observed ranging from 3.0 to 3.7 µm with an averaged transmitted power of 76.9%, i.e. −1.14 dB. Outside this passband, the transmittance is less than 4.7%, i.e. −13.28 dB in the 3.8 ~4.5 µm and 2.5 ~2.9 µm stopbands. The transitions between the passband and stopbands have steep roll-offs of 142 dBµm⁻¹ in the 3.7 ~3.8 µm band and 113 dBµm⁻¹ in the 2.9 ~3.0 µm band. In contrast to conventional filters which rely on bulky multilayer stacks of different materials, the proposed nanostructured metamaterial is more suitable for integration into micro- and nano-scale photonic systems. It also outperforms in terms of both transmittance level and bandwidth when compared to thin frequency selective surface based infrared filters reported in the literature [28, 29].

Figure 1(c) displays the extracted effective index of refraction and impedance [30]. The retrieved effective index shows a smooth transition from −1.18 to 1.14 in the 3.0 ~3.7 µm passband with a small imaginary part, whose magnitude is less than 0.12, due to the fact that the passband is located in between the two plasmonic resonant modes at 3.85 and 2.85 µm. The peak figure of merit (FOM) for the negative and positive index bands, which are calculated by Re(n_eff)/Im(n_eff), are 4.2 at 3.69 µm and 7.1 at 3.07 µm, respectively. At the zero-index band (where |n_eff | < 0.2), the FOM, as defined by 1/|n_eff| [7], is 6.1 at 3.35 µm. It should be noted that the absorption loss, even though at a low level, can be further mitigated by incorporating gain materials into the structure such as distributing quantum dots in the air holes or dielectric spacers [31, 32]. The effective impedance of this structure is matched to free-space throughout the passband except for small differences, giving rise to its low reflectance across this band. Outside the passband the impedance is purely imaginary, which appears to be capacitive in the short wavelength regime and inductive in the long wavelength range. Figure 1(d) presents the retrieved effective permittivity and permeability. The plasma wavelength of the effective permittivity is located at 3.31 µm, where the transmittance reaches its peak. An eigen mode simulation for the gold air hole waveguide was performed in Ansoft HFSS showing a cutoff wavelength at 3.28 µm, corresponding with the effective plasma wavelength of the structure, which signifies the excitation of the external SPP mode. The effective permeability has two Lorentz-shaped resonances – a fundamental mode in the 3.75 ~3.85 µm band and a second mode at 2.85 ~2.95 µm, corresponding to the two internal magnetic gap SPP modes. Outside the passband, the permeability and permittivity have either opposite signs or the same sign but with significantly different values, thus causing an impedance mismatch which produces the stopbands. Within the passband, the permittivity and permeability follow a similar profile thereby enabling a good impedance match such that the majority of the incident light passes through the structure. For the fundamental magnetic resonance mode, the maxima in the permeability corresponds to a transmission null, while for the second mode, the minima in the permeability indicates a transmission null, due to the opposite sign of the effective permittivity in these two wavelength ranges. The quality factors of these two modes determine the rolloff values of the transition between the passband and stopbands. As previous studies have shown, a multilayer metamaterial can be treated as an effective homogeneous medium for a normally incident wave due to the fact that the zeroth-order Bloch mode dominates light propagation inside the structure [23]. The validity of this statement can be confirmed by examining the convergence of the effective refractive index as the number of functional layers increases. The modified fishnet geometry has previously been demonstrated experimentally for a single functional layer, which confirms the broadband filtering properties of the proposed metamaterial [24]. However, bulk effective properties can only be observed by combining multiple functional layers of the metamaterial. The convergence of the effective index of refraction to a bulk property for this geometry is considered in Fig. 2. The real part of the effective index (n_eff) as a function of the number of functional layers (N) is presented, showing that the effective index in the passband begins to converge with N = 5, i.e. a total of eleven material layers, which corroborates previous findings in the literature [33, 34].

 

Fig. 2 Evolution of the real part of the effective index (n_eff) as a function of the number of functional layers (N) for the multilayer modified fishnet structure.

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As has been revealed previously, both external and internal SPP modes can give rise to narrow EOT peaks due to their efficient coupling with the incident light [21, 35]. The structure proposed here, however, supports a broadband EOT effect covering a broad wavelength range in between the various SPP modes, rather than being limited to the few narrow wavelength bands where the SPP modes are excited. This is primarily achieved by the hybridization of the external and internal SPP modes, as will be discussed below. Figure 3(a) plots the transmittance normalized to area (T_norm), which can be calculated by

 

Fig. 3 (a) Transmittance normalized to area. (b) Magnitude of the E-field distribution in the y-z plane at 3.31 µm. Arrows represent the directions of the E-fields. (c) Transmittance normalized to area for a single 276 nm thick gold layer perforated with the proposed air hole array. (d) The corresponding effective permittivity with a zero crossing at 3.3 µm. (e) Magnitude of the E-field (only E_y component) in the air hole waveguide at the wavelengths of 4.5, 3.7, 3.3, and 2.9 µm.

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Figures 4(a)-4(d) show the magnetic field distributions at the wavelengths where the fundamental and the second order internal SPP modes are excited. The internal SPP modes can be excited by a plane wave when the parallel momentum provided by the periodic nanostructure satisfy the condition, $\left|{\stackrel{\rightharpoonup }{k}}_{spp}\right|=\left|{\stackrel{\rightharpoonup }{k}}_{\parallel }+i{\stackrel{\rightharpoonup }{G}}_x+j{\stackrel{\rightharpoonup }{G}}_y\right|$where${\stackrel{\rightharpoonup }{k}}_{\parallel }$is the transverse wave number of the incident plane wave and $\left|{\stackrel{\rightharpoonup }{G}}_x\right|=\left|{\stackrel{\rightharpoonup }{G}}_y\right|=2\pi /p$ [12]. At both 3.85 and 2.85 µm, in the y-z plane, the magnetic field displays similar characteristics with strong fields located within the internal dielectric spacers in between the metal layers and weak fields in the air hole region. It should be noted that on the outer metal-air interfaces at the top and bottom of the structure, strong fields can still be observed that are primarily attributed to the previously discussed broadband external SPP mode. The external and internal SPP modes hybridize with each other at the vertical sides of the air hole, i.e. the interfaces between air and the multilayer metallodielectric structure inside the air hole. In contrast, as Ortuño et al. have shown, when the external and internal SPP modes do not couple, no fields can be observed on the outer metal-air interfaces at the internal SPP wavelengths [21]. Further simulations of the structure without the subwavelength notch cuts also confirmed this behavior (not shown here). Such hybridization of external and internal SPP modes allows electromagnetic energy to transmit through the structure by way of simultaneous electric and magnetic coupling, which, instead of separated narrow EOT bands, results in a broad and continuous EOT band with a near-constant in-band transmittance. From another perspective, the properly controlled external and internal SPP mode wavelengths and bandwidth, as well as their hybridization make possible the tailoring of the effective permittivity and permeability profiles. Consequently, an impedance match can be achieved indirectly by balancing the SPP modes in order to form a passband. The spectral width and location of the passband can be tuned by fine manipulation of the wavelengths and coupling of the external and internal SPP modes. By examining the magnetic field distributions in the x-y plane, which are in the middle of the central dielectric spacer, it is found that the mode patterns of the two internal SPP modes exhibit distinct features as shown in Figs. 4(c) and 4(d), respectively. For the fundamental mode at 3.85 µm, the wavelike pattern indicates that the internal SPP mode is propagating along the y-direction, corresponding to a (i, j) = (0,1) mode, i.e. a SPP Bloch mode along the Γ-X direction of the Brillouin zone of the square unit cell [23]. By contrast, for the second mode at 2.85 µm, the mode pattern exhibits field nodes in both the x- and y-directions, signifying that it is a (i, j) = (1,1) mode propagating along the diagonal direction in the x-y plane, i.e. a SPP mode along the Γ-M direction of the Brillouin zone.

 

Fig. 4 (a) and (b) Magnitude of the H-field (only H_x component) distribution in the y-z plane at 3.85 µm and 2.85 µm, respectively. (c) and (d) Magnitude of the H-field distribution in the x-y plane at 3.85 µm and 2.85 µm, respectively. An area encompassing two by two unit cells is included.

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3. Impact of the subwavelength nano-notches on the external and internal SPP modes

In order to understand the role that the square subwavelength nano-notches play in the designed structure, their effect on its optical properties was investigated by varying the size of the nano-notches. Figure 5(a) shows the transmittance normalized to area and the retrieved index of refraction for the multilayered structure with different nano-notch sizes including g = 217, 279, 310, 341, 372, 434 nm. During the effective parameter retrieval process, different branches were selected to give the correct effective index values [36]. Figure 5(b) shows the evolution of the external and internal SPP modes as a function of the nano-notch size. It can be seen that by varying the value of g, the wavelengths of both the external and internal SPP modes can be gradually tuned. For g smaller than 372 nm, as g increases the external SPP mode undergoes a red shift due to the increased cross section of the air hole waveguide. The two internal SPP modes, however, move toward the shorter wavelengths, i.e. a blue shift, which is attributed to the decreased area of the dielectric spacer in the horizontal plane. For the central four cases, i.e. g = 279, 310, 341, 372 nm, a basic bandpass filter line-shape can be identified in the normalized transmittance because the external SPP mode resides in between the two internal SPP modes. In these cases, as explained in the previous section, the hybridization of the external SPP mode with the (0,1) internal SPP mode on the longer wavelength side and the (1,1) internal SPP mode on the shorter wavelength side gives rise to the broad EOT passband bracketed by stopbands. Among these cases, the structure with the optimized nano-notch dimension, g = 341 nm, has the best filter functionality. When reducing or increasing the value of g, the bandwidth of the EOT passband shrinks, the transmittance in the stopband rises, and ripples start to appear in the passband so that it no longer maintains a flat spectral domain response. When the nano-notch size is much smaller (e.g. g = 217 nm), the external SPP mode occurs at a wavelength shorter than both of the two internal SPP modes and is thus unable to support a passband in between two stopbands. When the size of the nano-notch becomes too large, the nano-notches merge, causing a significant shift in the (1,1) internal SPP mode to a much shorter wavelength, outside of the observed wavelength range of interest. Its strength is also weakened substantially, preventing the formation of a magnetic resonance strong enough to generate a negative effective permeability. Hence, the metamaterial becomes a highpass filter. The merging of the notches when g ≥ 403 nm also causes a jump in the wavelength of the external SPP mode due to the topology change of the air hole waveguide. Further eigen mode simulation performed in Ansoft HFSS confirmed this jump by showing a cutoff wavelength of 2.73 µm for the air hole waveguide when g = 403 nm. This study illustrates the importance these nano-notches hold in controlling the optical properties of the structure. Even tiny variations on the order of Δg = 31 nm, i.e. ~λ/100, cause critical changes in the SPP modes and, therefore, significantly affect the filtering performance of the metamaterial.

 

Fig. 5 (a) Transmittance normalized to area and the retrieved index of refraction for nanostructured metamaterial with different nano-notch sizes (g = 217, 279, 310, 341, 372, 434 nm). The insets show the 3D view of the unit cell for each case. (b) The evolution of the wavelength of the external and internal ((0,1) and (1,1)) SPP modes as a function of the nano-notch size. Note that the jump in E-SPP at 403 nm is due to the merging of neighboring nano-notches.

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4. Angular dispersion of the external and internal SPP modes

The angular dependence of the optical properties and the spectral locations of the external and internal SPP modes of the multilayer modified fishnet metamaterial structure have also been studied. The simulated dispersion of the normalized transmittance over a range of 0~30° is shown in Fig. 6. The E-field of the incident plane wave is polarized in the y-direction, corresponding to a transverse electric (TE) polarization, while the plane of incidence is in the x-z plane. Several interesting physical phenomena can be observed from this study. The most prominent one is that the filtering functionality is well maintained, which has a broad passband along with stopbands exhibiting less than 10% transmitted power elsewhere. Simultaneously, the EOT effect in the broad passband is also achieved. The bandwidth of the 3 dB EOT band is slightly narrowed from 700 nm down to 550 nm as the angle of incidence increases from 0° to 30°. This bandwidth reduction is due to the dispersion of the SPP modes excited by the incident wave with different transverse momentum. The wavelength of the external SPP mode (traced in blue dots), manifested by the transmittance maxima, shows an extremely weak dispersion – shifting only from 3.31 to 3.35 µm as the angle of incidence increases from 0° to 30°. This is because the incident E-field is always parallel to the interface of the structure, which ensures an efficient interaction with the air hole waveguide, thus enabling an angle insensitive cutoff wavelength and dispersion of the waveguide. The internal SPP modes, however, show different dependences on the angle of incidence. First, both of the internal SPP modes exhibit stronger dispersion than that of the external SPP mode. Secondly, the wavelengths of the two modes are shifting in different directions as the incident angle increases – a blue shift in the fundamental mode and a red shift in the second mode. The excitation wavelength of the fundamental internal SPP mode (traced in black dots) drifts from 3.85 to 3.78 µm, which is slightly more dispersive than the external SPP mode. The second internal SPP mode, however, shifts from 2.85 to 3.04 µm as the incident angle increases from 0° to 30°, which is a much more pronounced change than that exhibited by the fundamental internal SPP mode or the external SPP mode. This stronger dispersion exhibited by the (i, j) = (1,1) internal SPP mode is attributed to the fact that this second plasmonic mode is sensitive to the x-component of the transverse wave number of the incident wave. In addition, as a result of the hybridization between the external and internal SPP modes, a wide-angle and broadband EOT effect is ensured, within which the index transits smoothly from negative through zero to positive.

 

Fig. 6 Transmittance normalized to area (purple curves) as a function of both wavelength and angle of incidence under TE polarized wave illumination. Dispersion of the external SPP mode is plotted in blue dots (E-SPP). Dispersion of the first and second internal SPP modes are plotted in black ((0,1) I-SPP) and red ((1,1) I-SPP) dots, respectively.

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5. Construction and full-wave verification of a bifunctional metaprism

Utilizing the broadband filtering and smooth index transition properties offered by the designed multilayer modified fishnet structure with subwavelength nano-notches, a broadband, bifunctional plasmonic metamaterial device can be constructed by tilting the top interface to form of a prism. Similar metamaterial prisms have been demonstrated previously for the RF [37] and optical [6] regimes as qualitative and quantitative evidences of negative refraction. However, these previous demonstrations were limited to only a single polarization, suffered from high reflectivity due to impedance mismatch and significant losses due to the evanescent mode gap around the index zero-crossing wavelength region. In contrast, the device presented here is able to simultaneously provide two functionalities: a broadband bandpass filter and in-band wavelength-dependent passive beam-steering, both of which are polarization-independent. As Fig. 7(a) illustrates, the metaprism is composed of a stair-type multilayer metamaterial structure with eight steps. The steps range in number of functional layers from four to eighteen, forming a slope angle of approximately 13°, and each step has a width of a half unit cell.

 

Fig. 7 Full-wave verification of impedance matched, polarization-independent metaprism (Media 1). (a) 3D tilted view of the configuration of the metaprism and orientation of the incident beam. The inset shows the side view of the metaprism. (b) Simulated reflectivity of the actual metamaterial prism for both TE and TM polarizations. (c) Snapshots of electric field distribution for TE polarization at different wavelengths. (d) Snapshots of electric field distribution for TM polarization at different wavelengths. Outside the passband, no light is transmitted through the metaprism. Within the passband, the light is refracted with the exiting beam at angles of 24°, 13° and 0° relative to the incident beam, corresponding to the negative unity, near-zero, and positive unity index bands, respectively. (e) Angle of refraction with respect to top surface normal as a function of wavelength in the passband of the metaprism for both TE and TM polarizations.

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For the full-wave verification of the metaprism, the HFSS finite element solver was employed. In the simulation domain, a portion of the metamaterial prism with a width of one unit cell in the x direction and a length of four unit cells in the y direction was considered. The metaprism has a step every half unit cell with a slope angle of around 13°. To mimic a one dimensionally infinite structure, perfect electric conducting boundary conditions were assigned to the front and back walls in the x direction for the TE polarization and perfect magnetic conducting boundary conditions were assigned for the transverse magnetic (TM) polarization. A waveguide and a wave port were employed to produce the incident waves impinging normally on the prism from the -z direction.

The full-wave simulated electric field distributions at different wavelengths and for both TE and TM polarizations are shown in Figs. 7(c) and 7(d). In keeping with the multilayer metafilter presented in Section 2, at normal incidence this prism has a passband from 3.0 to 3.7 μm outside of which the incident light is strongly reflected. Figure 7(b) shows the reflection properties of the metaprism for both polarizations, which demonstrate that the reflection amplitude is smaller than −12 dB only within the desired beam-steering passband, with a good out-of-band rejection by the prism. By virtue of the tilted interface of the metaprism and the smoothly changing index in the passband, the transmitted beam is directed at different angles upon passing through the structure, depending on the wavelength of the incident light. As can be observed from the snapshots of the electric field distribution at different wavelengths for both polarizations, outside the passband, there is almost no light passing through the metaprism due to the as-designed strong impedance mismatch between the metamaterial structure and free space. Within the passband, at 3.66 μm where the effective index is close to negative unity, the beam is directed at an angle of refraction of −11°. At 3.41 μm, where the effective index is approaching zero, the beam is directed at an angle of refraction of 0° (normal to the tilted interface of the metaprism), and at 3.06 μm, where the effective index is around positive unity, the beam is in the same direction as that of the incident wave. The angle of refraction as a function of wavelength is presented in Fig. 7(e), showing a smooth transition from negative through zero to positive values, thus validating the proposed design as well as the convergence of the effective index. The curves obtained for both TE and TM polarizations agree well with each other, confirming the polarization-independent properties of this metaprism. The field animations are available in the Media 1. It should be noted that this represents the first example of an impedance-matched metaprism with smooth negative-zero-positive index transition that works for both TE and TM polarizations. Truly, the observed transmitted wave steering is a direct consequence of the dispersive properties of the metamaterial without actively tuning the phase of each unit cell in the metaprism. Thus the passive angular deviation of the transmitted wave is wavelength dependent, similar to the behaviour of leaky-wave radiators [38], although operating under a different physical mechanism.

6. Conclusion

In summary, we have presented the methodology of exploiting the plasmonic modes to achieve bifunctional multilayer metallodielectric metamaterials for broadband applications. It has been shown that by strategically introducing subwavelength scale nano-notch cuts in the fishnet structure, both the external and internal SPP modes can be finely tuned, which further enabled the tailoring of the dispersive properties of the metamaterial over a broad wavelength range. Particularly, a multilayer modified fishnet metamaterial with optimized nano-notches was designed to achieve a filtering functionality with a broad and flat passband from 3.0 to 3.7µm, as well as a smooth and gapless negative-zero-positive index transition behavior within the passband. Furthermore, a bifunctional metaprism with simultaneous broadband bandpass filtering and in-band polarization-independent optical beam-steering was verified by full-wave numerical simulations. Notably, throughout the 20% bandwidth transmission window, the transmittance normalized to area is around 3 dB within a wide field-of-view. Analysis of the electromagnetic fields in the metamaterial structure has shown that this broadband EOT effect is realized by the hybridization of the external and internal SPP modes, which were achieved by a proper selection of the square nano-notch size. This work provides new perspectives and approaches for designing plasmonic metamaterials with broad operating bandwidth and multiple optical functionalities.