Mode hopping in arrays of resonant thin wires over a dielectric interface

This work studies the guided localized electromagnetic waves propagating along finite and infinite chains of parallel thin resonant wires periodically arranged over an interface of a dielectric half-space. Both issues of guided wave propagation in an infinite chain and resonant excitation of hybridized eigenmodes of a finite chain are solved analytically and numerically. The effect of changing the modes' resonant frequency order is observed as the chain approaches the interface closer than its periodicity staying inside the dielectric. This effect, called mode hopping, has been directly demonstrated by solving the problem of a finite chain excited by a plane wave using Pocklington's system of integral equations. Moreover, the effect was further related to the dispersion properties of the corresponding infinite array. The analytically described mode-hopping effect was verified numerically and experimentally.

Figure 1

Schematic view of the problem to study. (a) Infinite chain of parallel thin perfectly conducting wires with total length $2L=0.255$ m with period $d$ located at height $h$ above the interface between two dielectric media supporting a guided wave; (b) finite chain of $N=6$ wires with the same parameters as in (a) excited by a normally incident plane wave. The inset shows the perspective view of the enlarged chain of wires.

Figure 2

Analytically and numerically calculated dispersion diagrams of the infinite chain of wires with period $d=10$ mm for $h=5$ mm and $h=50$ mm.

Figure 3

Analytically and numerically calculated resonance frequencies of the second (black) and fourth (red) eigenmodes of a chain with $N=6$ wires excited by a normally incident plane wave as functions of height above the interface. Insets demonstrate the magnitude patterns of the normal magnetic field component $H_z$ at the resonance frequencies (10 mm above the wires).

Figure 4

Numerically calculated magnetic field distribution $|\vec{H}|$ in the plane orthogonal to the wire axis for different $h$ at the resonance of mode 2 (left column) and mode 4 (right column). In this case the incident plane wave propagates upwards.

Figure 5

Measured and numerically calculated resonance frequencies of the finite chain with $N=6$ wires for the second (black) and fourth (red) modes for different $h$. The inset schematically illustrates the experimental setup with wires in a distilled-water box and small loop antenna.