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Non-radiative dielectric waveguide
The non-radiative dielectric (NRD) waveguide has been introduced by Yoneyama in 1981.〔T. Yoneyama, S. Nishida, "Non radiative dielectric waveguide for millimeter-wave integrated circuits," IEEE Trans. Microwave Theory Tech., vol. MTT-29, pp. 1188–1192, Nov. 1981.〕 In Fig. 1 the cross section of NRD guide is shown: it consists of a dielectric rectangular slab of height a and width b, which is placed between two metallic parallel plates of suitable width. The structure is practically the same as the H waveguide, proposed by Tischer in 1953.〔F. J. Tischer, "A waveguide structure with low losses," Arch. Elekt. Ubertragung, 1953, vol. 7, p. 592.〕〔F. J. Tischer, "Properties of the H-guide at microwave and millimetre-wave regions," Proc. IEE, 1959, 106 B, Suppl. 13, p. 47.〕 Due to the dielectric slab, the electromagnetic field is confined in the vicinity of the dielectric region, whereas in the outside region, for suitable frequencies, the electromagnetic field decays exponentially. Therefore, if the metallic plates are sufficiently extended, the field is practically negligible at the end of the plates and therefore the situation does not greatly differ from the ideal case in which the plates are infinitely extended. The polarization of the electric field in the required mode is mainly parallel to the conductive walls. As it is known, if the electric field is parallel to the walls, the conduction losses decrease in the metallic walls at the increasing frequency, whereas, if the field is perpendicular to the walls, losses increase at the increasing frequency. Since the NRD waveguide has been deviced for its implementation at millimeter waves, the selected polarization minimizes the ohmic losses in the metallic walls.
The essential difference between the H waveguide and the NRD guide is that in the latter the spacing between the metallic plates is less than half the wavelength in a vacuum, whereas in the H waveguide the spacing is greater. In fact the conduction losses in the metallic plates decrease at the increasing spacing. Therefore, this spacing is larger in the H waveguide, used as a transmission medium for long distances; instead, the NRD waveguide is used for millimeter wave integrated circuit applications in which very short distances are typical. Thus an increase in losses is not of great importance.
The choice of a little spacing between the metallic plates has as a fundamental consequence that the required mode results below cut-off in the outside air-regions. In this way, any discontinuity, as a bend or a junction, is purely reactive. This permits radiation and interference to be minimized (hence the name of 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 it is possible that the above-mentioned phenomena of losses are generated.〔A. A. Oliner, S. T. Peng, K. M. Sheng, "Leakage from a gap in NRD guide", Digest 1985 IEEE MTT-S, pp. 619–622.〕 This occurs when in general any asymmetry in the cross section transforms a confined mode into a "leaky" mode.
==The dispersion relation in the NRD waveguide==
As in any guiding structure, also in the NRD waveguide it is of basic importance to know the dispersion relation, that is the equation yielding the longitudinal propagation constant as a function of the frequency and the geometric parameters, for the various modes of the structure. In this case, however, this relation cannot be expressed explicitly, as it is verified in the most elementary case of the rectangular waveguide, but it is implicitly given by a transcendental equation.
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