Guiding Waves Along an Infinitesimal Line between Impedance Surfaces

We present a new electromagnetic mode that forms at the interface between two planar surfaces laid side by side in free space, effectively guiding energy along an infinitesimal, one-dimensional line. It is shown that this mode occurs when the boundaries have complementary surface impedances, and it is possible to control the mode confinement by altering their values correspondingly. The mode exhibits singular field enhancement, broad bandwidth, direction-dependent polarization, and robustness to certain defects. As a proof of concept, experimental results in the microwave regime are provided using patterned conducting sheets. Our proposed effective-medium-based approach is general, however, thus allowing for potential implementation up to optical frequencies. Our system is promising for applications including integrated photonics, sensing, switching, chiral quantum coupling, and reconfigurable waveguides.

Figure 1

Simulated field characteristics of the line wave: (a) Magnitude distribution and vector plot of the $E$ field above the interfaced TE and TM surfaces (linear scale), (b) decay profile of the $E$ field at different directions about the interface line, (c) dispersion of the line mode at different values of complementary impedances, and (d) pseudospin states excited by electric and magnetic Hertzian dipoles along the $y$ axis in phase (above) or out of phase (below).

Figure 2

Measurement setup and characteristics of the fabricated FSS sheets: (a) A probe antenna (right) oriented along the interface line is used as the excitation source while another probe (left) oriented vertically at a $1\sim 2\mathrm{mm}$ distance above the surface is used to scan the relative intensity of the normal $E$-field component; (b) enhanced complementary FSS sheets fabricated on a printed circuit board on Rogers 5880 ($ϵr=2.2$, $\delta t=0.001$) substrate with a 0.8 mm thickness; (c) dispersion characteristics of TM and TE FSS cells of different sizes; and (d) $\zeta$ values versus frequency for different sizes of FSS cells. Prototypes 1 and 2 both have a unit cell period of 4 mm. Prototype 1 (2) has a grid-line width of 0.2 mm (1.2 mm) and gap width of 0.8 mm (2.2 mm) between patches.

Figure 3

Measured results of the line wave: (a) $E$-field magnitude distribution at different frequencies on top of prototype 1 (left) and prototype 2 (right), and (b) normalized decay curves of the normal $E$-field component along the transverse direction to the interface line (linear scale) at $1\sim 2\mathrm{mm}$ above the two prototypes (left) and comparison with simulated results at 2 and 0 mm above the surface as well as through the origin along the normal (vertical) direction to the surface (right).

Figure 4

Influence of a finite discontinuity in surface impedance on the line wave: (a) Transmission and reflection coefficients of the mode due to a defect ($\zeta \ne 10$) at one or both sides of the interface over a distance of $0.6{\lambda }_0$, and (b) snapshot of a field magnitude depicting an increased enhancement and a shorter wavelength over a finite distance due to change in surface impedances across the interface.

Figure 5

Full-wave simulations for potential applications of the line wave: (a) Wave transmission in four-port network (magic-$T$) of a junction due to surface-impedance reversal; (b) wave transport along a curved interface line with a proper change in TM and TE surface impedances; (c) coupler structure showing excitation of a reversed pseudospin mode; and (d) an implementation of a ring resonator showing frequency selection.