Effective Surface Plasmon Polaritons Induced by Modal Dispersion in a Waveguide

We provide further theoretical insights and experimental verification of the modal-dispersion-induced effective surface-plasmon polaritons (ESPPs) by engineering the transverse-electric (TE) modes in conventional rectangular waveguides. The complete field distributions, dispersion relations, and asymptotic frequency of the ESPPs are derived analytically. Wave-port excitations and smooth bridges are designed for the mode conversion between propagating modes in rectangular waveguides and the ESPPs. Analytical calculations and numerical simulations are performed for ${\mathrm{TE}}_{10}$- and ${\mathrm{TE}}_{20}$-mode-induced ESPPs, showing excellent agreement. Moreover, we design a double-layered substrate-integrated waveguide showing that ESPPs are supported at the interface between the two layers with different dielectric constants. This work opens up an avenue for low-frequency designer surface plasmons and may find potential applications in the design of compact filters, resonators, and sensors of ESPPs in the microwave and terahertz frequencies.

Figure 1

A conventional rectangular waveguide with the cross-section dimensions $a\times b$ filled with double-layered isotropic and homogeneous dielectrics with relative permittivities ${ϵ}_{r1}$ and ${ϵ}_{r2}$ and relative permeabilities ${\mu }_{r1}=1$ and ${\mu }_{r2}=1$. The interface (denoted as the solid blue line) between them is supposed to support modal-dispersion-induced ESPPs transmitted along the $z$ direction.

Figure 2

Evolution of the dispersion curves of the TE modal-dispersion-induced ESPPs in a standard $X$-band rectangular waveguide (WR90, $a\times b=22.86\times 10.16{\mathrm{mm}}^2$) with the variations of the dielectric thickness $t=0.05b\sim b$ with a step of $0.05b$. (a) ${\mathrm{TE}}_{10}$ case. (b) ${\mathrm{TE}}_{20}$ case.

Figure 3

Comparison of the analytical dispersion relations of the ${\mathrm{TE}}_{10}$ modal-dispersion-induced ESPPs with four simulated dispersion relations of different periodicities $d=a/40$, $d=a/20$, $d=a/10$, and $d=a/5$.

Figure 4

Simulation of the ${\mathrm{TE}}_{10}$ modal-dispersion-induced ESPPs in a standard $X$-band rectangular waveguide (WR90) with cross-section dimensions $a\times b=22.86\times 10.16{\mathrm{mm}}^2$ and length $L=12a$. The brown region in the guide is filled with a dielectric of relative permittivity ${ϵ}_{r2}=4$, and the light blue region is filled with air of ${ϵ}_{r1}=1$, in which $l_2=2a$, $l_3=6a$, and $l_4=l_2$. (a) Structure of the interface. (b) Distributions of electric force of lines on the $y\text{−}z$ plane. (c) Distributions of $E_y$ on the $y\text{−}z$ plane. (d) Distributions of $E_y$ on the $x\text{−}z$ plane. (e) ESPPs spectrum.

Figure 5

Simulation of the ${\mathrm{TE}}_{20}^z$ modal-dispersion-induced ESPPs in the same waveguide as that in Fig. 4. (a) Structure of the interface. (b) Distributions of $E_y$ on the $y\text{−}z$ plane. (c) Distributions of $E_y$ on the $x\text{−}z$ plane. (d) ESPPs spectrum.

Figure 6

Schematic drawing of each layer in the double-layered SIW for the transmission of ESPPs. All the numbers are in units of millimeters. (a) Front view of layer I. (b) Back view of layer I. (c) Sticking layer. (d) Front view of layer II. (e) Back view of layer II.

Figure 7

ESPPs in a real fabricated sample of the double-layered SIW and the ESPPs spectrum. (a) Front view. (b) Back view. (c) Simulated $E_y$ distributions in layer I at 5.2 GHz. (d) Simulated $E_y$ distributions in layer II at 5.2 GHz. (e) ESPPs spectrum obtained in the simulations and experiments.