Parallel-Plate Waveguide

The following animation sequences illustrate the guided TE modes in a parallel-plate waveguide shown in the figure below.

The width of the waveguide in the y-direction (perpendicular to the screen), , is much larger than the separation between the two plates (i.e., ). In each animation, the direction of the electric field vector is indicated by blue (in the positive y-direction) or red (in the negative y-direction). The intensity of the blue or red color represents the instantaneous magnitude of the electric field vector. The boundary conditions require the electric field to vanish on the surface of the perfectly conducting walls.

TE1 Mode Example No. 1 File Size: 324 KB

The electric field vector of the TE₁ mode can be described by

(1)

where

(2)

is a direct implication of the dispersion relation. It can be seen that the electric field vanishes on the surface of the upper and the lower conducting walls.

TE1 Mode Example No. 2 File Size: 221 KB

This second example of the electric fields of TE₁ mode is for a lower frequency than that for the previous example. When the frequency is lower, the propagation constant k_z is larger as implied by (2). Consequently, the wavelength of the guided mode is longer.

TE1 Mode At Cutoff Frequency File Size: 46 KB

When the frequency equals the cutoff frequency, the propagation constant k_z goes to zero as implied by (2). Consequently, the wavelength of the guided mode approaches infinity. However, the intensity of the electric field still oscillates in time.

TE1 Mode Below Cutoff Frequency File Size: 65 KB

When the frequency is lower than the cutoff frequency, the propagation constant k_z becomes imaginary as implied by (2). Consequently, the amplitude of the wave is decaying in the positive z-direction. The lower the frequency is, the more imaginary k_z becomes, and the faster the wave decays in the z-direction.

TE1 Mode Varying Frequency File Size: 632 KB

Each frame in this sequence shows the electric field pattern of the TE₁ mode for a particular frequency and at a fixed time. The frequency is varying among different frames from below the cutoff frequency to above the cutoff frequency to illustrate the change in the corresponding electric field structures.

TE2 Mode Example No. 1 File Size: 494 KB

The electric field vector of the TE₂ mode can be described by

(3)

where

(4)

is a direct implication of the dispersion relation. It can be seen that the electric field vanishes on the surface of the upper and the lower conducting walls.

TE2 Mode Example No. 2 File Size: 383 KB

This second example of the electric fields of TE₂ mode is for a lower frequency than that for the previous example. When the frequency is lower, the propagation constant k_z is larger as implied by (4). Consequently, the wavelength of the guided mode is longer.

TE2 Mode At Cutoff Frequency File Size: 45 KB

When the frequency equals the cutoff frequency, the propagation constant k_z goes to zero as implied by (4). Consequently, the wavelength of the guided mode approaches infinity. However, the intensity of the electric field still oscillates in time.

TE2 Mode Below Cutoff Frequency File Size: 68 KB

When the frequency is lower than the cutoff frequency, the propagation constant k_z becomes imaginary as implied by (4). Consequently, the amplitude of the wave is decaying in the positive z-direction. The lower the frequency is, the more imaginary k_z becomes, and the faster the wave decays in the z-direction.