6. Conclusions

Several examples for the rectangular and circular waveguides with the discontinuous dielectric profile in the cross section of the straight waveguide were demonstrated in this research, according to Figure 1(a)–(g).

Figure 4(a)–(c) demonstrates the output field as a response to a half-sine (TE10) input-wave profile in the case of the slab profile (Figure 1(a)), where a = b = 20 mm, c = 20 mm, and d = 2 mm for ε<sup>r</sup> = 3 and 5, respectively. By increasing only the value of the dielectric profile from ε<sup>r</sup> = 3 to ε<sup>r</sup> = 5, the width of the output field decreased, and also the output amplitude decreased.

Figure 5(a)–(e) demonstrates the output field as a response to a half-sine (TE10) input-wave profile in the case of the rectangular dielectric profile in the rectangular waveguide (Figure 1(b)), where a = b = 20 mm and c = d = 2 mm, for ε<sup>r</sup> = 3, 5, 7, and 10, respectively. By increasing only the dielectric profile from ε<sup>r</sup> = 3 to ε<sup>r</sup> = 5, the width of the output field increased, and also the output amplitude increased. The output fields are strongly affected by the input-wave profile (TE<sup>10</sup> mode), the location, and the dielectric profile, as shown in Figure 4(a)–(c) and Figure 5(a)–(e).

The behavior of the output fields (Figures 5(a)–(e) and 6(a)–(e)) is similar when the dimensions of the rectangular dielectric profile (Figure 1(b)) and the circular profile (Figure 1(c)) are very close. The output field (Figure 5(a)–(e)) is shown for c = d = 2 mm as regards to the dimensions a = b = 20 mm. The output field (Figure 6(a)–(e)) is shown where the radius of circular profile is equal to 1 mm (viz., the diameter 2 mm), as regards to the dimensions a = b = 20 mm.

Figures 6(a)–(e) and 7(a)–(e) show the output field as a response to a half-sine (TE10) input-wave profile in the case of the circular dielectric profile (Figure 1(c)), for ε<sup>r</sup> = 3, 5, 7, and 10, respectively, where a = b = 20 mm, and the radius of the circular dielectric profile is equal to 1 mm. By changing only the value of the radius of the circular dielectric profile (Figure 1(c)) from 1 mm to 2 mm, as regards to the dimensions of the cross section of the waveguide (a = b = 20 mm), the output field of the Gaussian shape increased, and the half-sine (TE10) input-wave profile decreased.

Figure 8(a)–(c) shows the output field as a response to a half-sine (TE10) inputwave profile in the case of the hollow rectangular waveguide with one dielectric material between the hollow rectangle and the metal (Figure 1(e)), where a = b = 20 mm, c = d = 14 mm, and d = 14 mm, namely, e = 3 mm and f = 3 mm.

Figures 9(a)–(c) and 10(a)–(c) show the output power density in the case of the hollow circular waveguide with one dielectric coating (Figure 1(f)), where a = 0.5 mm. By changing only the values of the spot size from w<sup>0</sup> = 0.15 mm, w<sup>0</sup> = 0.2 mm, and w<sup>0</sup> = 0.25 to w<sup>0</sup> = 0.26 mm, w<sup>0</sup> = 0.28 mm, and w<sup>0</sup> = 0.3 mm,

The Influence of the Dielectric Materials on the Fields in the Millimeter and Infrared Wave… DOI: http://dx.doi.org/10.5772/intechopen.80943

respectively, the results of the output power density for a = 0.5 mm are changed as shown in Figure 10(a)–(c).

The output modal profile is greatly affected by the parameters of the spot size and the dimensions of the cross section of the waveguide. Figure 10(a)–(c) demonstrates that in addition to the main propagation mode, several other secondary modes and symmetric output shape appear in the results of the output power density for the values of w<sup>0</sup> = 0.26 mm, w<sup>0</sup> = 0.28 mm, and w<sup>0</sup> = 0.3 mm, respectively.

The two important parameters that we studied were the spot size and the dimensions of the cross section of the straight hollow waveguide. The output results are affected by the parameters of the spot size and the dimensions of the cross section of the waveguide.
