# A TE/TM modal solution for rectangular hard waveguides

Abstract: A TE/TM modal solution for a longitudinally corrugated rectangular waveguide is developed. These longitudinal corrugations can be used to excite a quasi-TEM wave and form a hard waveguide by correctly choosing the impedance at the guide wall. The correctly chosen impedance is referred to as the hard boundary condition. The modal solution developed here solves the problem of longitudinal corrugations filled with a dielectric material by first finding and solving the characteristic equation for a complete TE/TM modal set. It is shown that this TE/TM mode solution can be used to achieve the hard boundary condition resulting in the quasi-TEM wave in a hard waveguide for discrete values of corrugation depth. Beyond each of these depths, a mode becomes a surface wave. The theoretical mode set is amenable to the solution of problems using the mode-matching method. A combination of the mode-matching method and the TE/TM modal solution will allow the solution of larger problems.

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##### Citations

69 citations

14 citations

### Cites background or methods from "A TE/TM modal solution for rectangu..."

...PDET is FEM-based toolbox, which is capable of solving the eigenvalue problems (1) and (4) for arbitraryshaped waveguide with constant parameters ai and bi on its contour C ....

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...Among them are the field expansion method [15], [16], the finite-element method (FEM) [4], [5], [7], [8] [10], [11], [17], and the finite-difference timedomain method [9], [12], [17], which now find use in various commercial software packages....

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...For example, kx is invariant with ω in the following cases: a1 = a3 = 0 [2]–[4], [6]–[8] (kx = πn/w, n = 0, 1, 2 ....

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...Among them, the best-studied case is that when two opposite walls of the rectangular waveguide possess zero surface impedance [2]–[4], [7], [8]....

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...The numerical results have been validated against those followed from the perturbation theory and the FEM....

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9 citations

### Cites background from "A TE/TM modal solution for rectangu..."

...Note, that the non-uniform quasi-TEM waves described above represent a new type of the eigenmodes different from the well known uniform quasi-TEM modes existing in the waveguides and horns of rectangular (or square) cross section considered in [9–11]....

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...The concept of artificial electromagnetic hard and soft surfaces or walls [1, 2], that can be realized by corrugations with grooves filled with dielectric or by strips on a grounded dielectric layer, find important applications in design of conical horn antennas [3–8] and pyramidal horn antennas [9–11]....

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6 citations

### Cites background from "A TE/TM modal solution for rectangu..."

...Note, that this is a new type of the quasi-TEM modes different from the well-known TEM mode existing in a rectangular waveguide with corrugated hard walls [13], [14]....

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5 citations

### Cites background from "A TE/TM modal solution for rectangu..."

...…may be grouped into the following categories: 1) circular waveguides that are either a) transversely [10]–[18] or b) longitudinally [9] corrugated and 2) rectangular waveguides having either a) just two opposite walls that are i) transversely [19] or ii) longitudinally [20] corrugated or b) only…...

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...…so, the and components of the and fields of the TE and TM modal fields within the various grooves are stated as follow; these upcoming expressions are also more directly derived in [20]–[24]. a) Left Groove: and Right Groove: (TE and TM to ): (1a) (1b) (1c) (1d) (1e) (1f) or (1gi) or…...

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##### References

5,482 citations

### "A TE/TM modal solution for rectangu..." refers methods in this paper

...The process begins by looking for and modes, and applies the techniques described in Harrington [15]....

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4,300 citations

### "A TE/TM modal solution for rectangu..." refers background in this paper

...If the two guides are identical, the coupling integral becomes a test for the orthogonality of the modes within a given hard waveguide [17]....

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636 citations

### "A TE/TM modal solution for rectangu..." refers background in this paper

...I N RECENT years, there has been increasing interest in forms of spatial combining where a large number of antennas are placed in either a longitudinally corrugated dielectric-filled waveguide or a dielectric-filled waveguide meant to simulate a hard waveguide [1]....

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187 citations

93 citations

### "A TE/TM modal solution for rectangu..." refers result in this paper

...Contrary to [12] and postulated previously [13], [14], TE modes can also exist, albeit in a modified form....

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