Plasmonics without negative dielectrics

Plasmonic phenomena are exhibited in light-matter interaction involving materials whose real parts of permittivity functions attain negative values at operating wavelengths. However, such materials usually suffer from dissipative losses, thus limiting the performance of plasmon-based optical devices. Here, we utilize an alternative methodology that mimics a variety of plasmonic phenomena by exploiting the well-known structural dispersion of electromagnetic modes in bounded guided-wave structures filled with only materials with positive permittivity. A key issue in the design of such structures is prevention of mode coupling, which can be achieved by implementing thin metallic wires at proper interfaces. This method, which is more suitable for lower frequencies, allows designers to employ conventional dielectrics and highly conductive metals for which the loss is low at these frequencies, while achieving plasmonic features. We demonstrate, numerically and analytically, that this platform can provide surface plasmon polaritons, local plasmonic resonance, plasmonic cloaking, and epsilon-near-zero-based tunneling using conventional positive-dielectric materials.

Figure 1

A parallel-plate waveguide (PPW) with the $\mathrm{T}{\mathrm{E}}_{10}$ mode, exhibiting specific effective permittivity tailored by the geometric dispersion. (a) The PPW height $a$ and the relative permittivity of the filling medium ${\varepsilon }_b$ determine the effective permittivity of the propagating $\mathrm{T}{\mathrm{E}}_{10}$ mode. The field distribution of the $\mathrm{T}{\mathrm{E}}_{10}$ mode inside the PPW shows that the electric field is always orthogonal to the direction of propagation (the $y$ axis in this case). We also note that the longitudinal component of the magnetic field vanishes on the middle mathematical plane of the PPW. (b) Field distribution of the $\mathrm{T}{\mathrm{M}}_{10}$ mode that may be generated at the interface between two media inside the PPW, due to the mode coupling from $\mathrm{T}{\mathrm{E}}_{10}$ to $\mathrm{T}{\mathrm{M}}_{10}$. (c) Thin metallic wires parallel to the $z$ axis may short-circuit the electric field $E_z$ of the $\mathrm{T}{\mathrm{M}}_{10}$ mode, thus preventing coupling from the dominant $\mathrm{T}{\mathrm{E}}_{10}$ mode to the undesirable $\mathrm{T}{\mathrm{M}}_{10}$ mode.

Figure 2

Surface plasmon polariton (SPP) at the interface between two conventional (i.e., positive permittivity) dielectric materials. (a) View of the interface inside the PPW. The top and bottom metallic plates of the waveguide are not shown here for easy observation. A series of thin metallic wires is located at the interface in order to short-circuit the $\mathrm{T}{\mathrm{M}}_{10}$ mode. (b) Snapshot value of the $y$ component of the electric field revealing an SPP-like mode propagating along the interface between the two media and exponentially decaying in the direction orthogonal to it. Furthermore, the sign of the $y$ component of the $E$ field flips from one side of the interface to the other, analogous to the SPP propagation characteristics. (c) SPP along an arbitrarily curved interface between positive-permittivity media with the same effective permittivity as for case (b). The thin metallic wires are located all along the curved interface between the two media. (d) Conventional SPP generated in the ideal case of two natural media with true relative permittivities of 1 and $–2$.

Figure 3

Resonant scattering with all-positive-dielectric materials inside a rectangular waveguide. (a) Cylinder of relative permittivity ${\varepsilon }_2=3.16$ embedded into a bulk medium of permittivity ${\varepsilon }_1=5.16$ and surrounded by thin metallic wires. According to the dispersion relation of the waveguide, the effective relative permittivities of the cylinder and the surrounding medium become ${\varepsilon }_{\mathrm{eff}2}=-1$ and ${\varepsilon }_{\mathrm{eff}1}=1$, respectively. (b) Normalized integral of the electric field amplitude (blue line) over a square surface $S$ crossing the cylinder at the middle plane of the waveguide and orthogonal to its axis, for different values of the cylinder relative permittivity. In the insets, the total electric field magnitude (normalized with respect to the incident field) and the position of the integration surface (on the right) are shown. We note that at the value of cylinder relative permittivity of 3.16 (when its effective relative permittivity becomes $–1$), we get resonant scattering.

Figure 4

Plasmonic cloaking with all-positive-dielectric materials inside a rectangular waveguide. (c) Dielectric cylinder surrounded by a dielectric layer, which acts as a plasmonic cloak when considering the effective values of the relative permittivity inside the waveguide. Both the cylinder and the cloak are surrounded by thin metallic wires that suppress the $\mathrm{T}{\mathrm{M}}_{10}$ mode. (d) Amplitude of the electric scattered field (normalized with respect to the incident field) for the uncloaked (left) and the cloaked (right) cylinder, showing a significant reduction of the scattering signature of the cylinder when the cloak is applied. We emphasize that all materials in our simulations possess positive permittivity.

Figure 5

Epsilon-near-zero (ENZ) supercoupling with all-positive-dielectric materials. (a) Two waveguides filled with a dielectric medium with relative permittivity ${\varepsilon }_b=5$, connected via a channel filled with a dielectric with relative permittivity ${\varepsilon }_c=4$. Owing to the waveguide structural dispersion, the effective relative permittivity for the bulk and the channel are 1 and 0, respectively, and thus the ENZ supercoupling occurs at our design frequency. The channel length is $l_c=0.6{\lambda }_0$. In the reflection and transmission plots ($s$ parameters, $s_{11}$ and $s_{21}$) underneath we notice two transmission peaks; the first peak is associated with the ENZ tunneling effect and it occurs at the design frequency, whereas the second peak is due to a Fabry-Perot effect. (b) Waveguide with ENZ channel similar to the configuration described in (a), but with a longer channel $l_c=0.9{\lambda }_0$, revealing the fact that while the transmission peak due to the Fabry-Perot effect exhibits a redshift as expected, the ENZ tunneling remains at the design frequency. (c) The waveguide has the same channel length as in (a), but the channel is now sharply bent at 90°. The reflection-transmission characteristics do not change, showing again one of the characteristics of ENZ supercoupling. (d) All-air-filled waveguides with narrow channel. The channel is achieved with a waveguide whose height is reduced with respect to the feeding arms of the waveguides, in order to achieve an effective relative permittivity close to zero in the channel. The $s$ parameters of the waveguide show a transmission peak at roughly the design frequency. (e) Configuration similar to (d), but with a longer channel in order to show that the ENZ tunneling stays at the design frequency.

Figure 6

Snapshot of the $y$ component of the electric field in V/m for a dielectric interface similar to the results of Fig. 2 in the main manuscript, but without using the thin metallic wires at the interface between the two slabs. The top plot has the same scale as the plot in Fig. 2. We clearly notice the absence of a surface wave along the interface. The bottom panel has an expanded scale in order to show the difference in the field distribution when compared with the field map of Fig. 2. We can also notice that the sign of the electric field $E_y$ does not change across the interface (since the actual permittivity of the two dielectric regions have the same signs), unlike the case where the metallic wires are used as shown in the main text.

Figure 7

Similar to Fig. 6, except here the plots shows the $z$ component of the electric field in V/m at the top plate of the waveguide. Owing to the absence of the thin metallic wires, there is a significant nonzero $z$ component of the electric field at the top plate, indicating the presence of the $\mathrm{T}{\mathrm{M}}_{10}$ mode due to mode coupling.

Figure 8

Amplitude of the normalized total electric field at the middle plane of the waveguide (left) and of the normalized $z$ component of the electric field $E_z$ at the top plate of the waveguide (right), in the absence of the thin metallic wires surrounding the cylinder. The left plot shows the absence of any resonant phenomenon, whereas the right plot reveals that near the waveguide plates there is a significant value for the $z$ component of the electric field orthogonal to the metallic plates, implying the presence of the $\mathrm{T}{\mathrm{M}}_{10}$ mode generated due to coupling from the $\mathrm{T}{\mathrm{E}}_{10}$ more to the $\mathrm{T}{\mathrm{M}}_{10}$ mode at the interface between the bulk medium and the cylinder.

Figure 9

Similar to Fig. 8, except here the material inside the cylinder and the material in the bulk are the same. The plot on the left shows the amplitude of the normalized total electric field on the middle plane of the waveguide being constant everywhere, indicating that there is no interaction between the bulk and the cylinder regions, as well as there is no effect produced by the metallic wires by themselves. The plot on the right reveals the absence of any $z$ component of the electric field orthogonal to the top metallic plate since there is no material interface between the inside and outside of the cylinder inside the waveguide and the metallic wires by themselves do not contribute to field perturbation.