Non-radiative dielectric waveguide
The polarization of the electric field in the required mode is mainly parallel to the conductive walls.
Since the NRD waveguide has been devised for its implementation at millimeter waves, the selected polarization minimizes the ohmic losses in the metallic walls.
The choice of a little spacing between the metallic plates has a fundamental consequence that the required mode results below the cut-off in the outside air regions.
This permits radiation and interference to be minimized (hence the name of the non-radiative guide); this fact is of vital importance in integrated circuit applications.
Instead, in the case of the H waveguide, the above-mentioned discontinuities cause radiation and interference phenomena, as the desired mode, being above cutoff, can propagate towards the outside.
In any case, it is important to notice that, if these discontinuities modify the symmetry of the structure with reference to the median horizontal plane, there is anyway radiation in the form of TEM mode in the parallel metallic plate guide and this mode results above cutoff, the distance between the plates may be no matter short.
This aspect must always be considered in the design of the various components and junctions, and at the same time much attention has to be paid to the adherence of the dielectric slab to the metallic walls because the above-mentioned phenomena of losses are generated.
This condition brings to a transcendental equation that, numerically solved, gives possible values for the transverse wavenumbers.
Exploiting the well-known relation of separability which links the wavenumbers in the various directions and the frequency, it is possible to obtain the values of the longitudinal propagation constant kz for the various modes.
In fact, supposing that the field evanescent in the outside air-regions is negligible at the aperture, one can assume that the situation substantially coincides with the ideal case of the metallic plates having infinite width.
In it kxε and kx0 are the wavenumbers in the x transverse direction, in the dielectric and in the air, respectively; Yε and Y0 are the associated characteristic admittances of the equivalent transmission line.
The presence of the metallic plates, considered perfectly conductive, imposes the possible values for the wavenumber in the y vertical direction:
It is assumed that kz = β, because the structure is non-radiating and lossless, and moreover kxo= – j | kxo | , because the field has to be evanescent in the air regions.
Unlikely kxo, kxε is real, corresponding to a configuration of standing waves inside the dielectric region.
This fact is due to the continuity conditions of the tangential components of the electric and magnetic fields, at the interface.
This mode always results above cutoff, no matter small a is, but it is not excited if the symmetry of the structure with reference to the middle plane y = a/2 is preserved.
In this case, it is possible to bisect the structure with a vertical metallic plane without changing the boundary conditions and thus the internal configuration of the electromagnetic field.
This corresponds to a short circuit bisection in the equivalent transmission line, as the simplified network shows in Fig.
The cutoff frequency fc is obtained by solving the dispersion equation for β =0.
Then, as previously shown, the transverse resonance method allows us to easily obtain the dispersion equation for the NRD waveguide.
1, TM and TE fields can be considered with respect to the z longitudinal direction, along which the guide is uniform.
As already said, in NRD waveguide TM or (m≠0) TE modes with reference to the z direction cannot exist, because they cannot satisfy the conditions imposed by the presence of the dielectric slab.
Moreover, the TM field can be derived from a purely longitudinal Lorentz vector potential
In dual manner, the TE field can be derived from a purely longitudinal vector potential
As it is known, in a sourceless region, the potential must satisfy the homogeneous Helmholtz electromagnetic wave equation:
The wavenumbers ky and kz must be the same in the dielectric as in the air regions in order to satisfy the continuity condition of the tangential field components.
Introducing equations (19), (20), and (22)-(25) in the four continuity conditions at x = w, the E and F constants can be expressed in terms of A, B, C, D, which are linked by two relations.
Finally, from the remaining continuity conditions a homogeneous system of four equations in the four unknowns A, B, C, D, is obtained.
A similar simplification does not occur when using the transverse resonance method since kz only implicitly appears; then the equations to be solved in order to obtain the cutoff frequencies are formally the same.
A simpler analysis, expanding again the field as a superposition of modes, can be obtained taking into account the electric field orientation for the required mode and bisecting the structure with a perfectly conducting wall, as it has been done in Fig.
