Waveguide Mode Converters

1. Introduction

Metallic waveguides have major advantages, such as low propagation loss and high power transmission in the microwave frequency range. However, one disadvantage is that the usable frequency range is restricted to f _c< f< 2f _c, because the TE₂₀ mode is possible in a frequency region higher than 2f _c for rectangular metallic waveguides. A ridge waveguide (Cohn, 1947) (or double-ridge waveguide) has an advantage in that it can spread the propagating frequency range as a result of reduction in the cutoff frequency for the TE₁₀ mode. However, one disadvantage is that the attenuation constant becomes large.

Power sources, such as watt class IMPATT diodes or Gunn diodes, are readily available, and for high frequency use, power sources are sometimes combined, due to their low power rating. However, power combiners consisting of cavity resonators usually have narrow bandwidths (For example, Matsumura et al., 1987). Power dividers and power combiners may be easily setup using mode converters. For example, a TE₁₀–TE₃₀ mode converter easily offers a three-port power divider, and a three-way power combiner can be composed by reversal. A power combiner is useful for application to Gunn diodes in a waveguide array (Bae et al., 2000), because it converts the TE₃₀ mode to the TE₁₀ mode.

2. Design method of the mode converters

We have reported that single-mode propagation is available for a metallic waveguide with dielectric rods arrayed at the center of the waveguide in the frequency under twice the cutoff frequency region using the TE₁₀ mode, and in the frequency over twice the cutoff frequency region using the TE₂₀ mode, because of restrictions of the TE₁₀ mode (Kokubo, 2007; Kokubo & Kawai, 2009 ). However, a TE₂₀-like mode, which is propagated in the second band, is an odd mode, and generation systems for odd modes have seldom been reported. In this investigation, a mode converter is proposed which passes through the TE₁₀ mode for the low frequency range and efficiently converts TE₁₀ to TE₂₀ mode for the high frequency range.

2.1. Design method of the TE₁₀-to-TE₂₀ mode converter

The frequency eigenvalues of a conventional metallic waveguide in a given k wavevector are shown in Fig. 1. In this figure, the wavevector k and frequency ω are normalized using the width of the waveguide w. The electromagnetic wave propagates the TE₁₀ mode only for 0.5<ωw/2πc<1, and can propagate TE₁₀ and TE₂₀ modes for 1<ωw/2πc<1.5. If these two modes are excited by only the TE₁₀ mode, the group velocity of TE₁₀ (A) must be changed to that of TE₂₀ (B) for 1<ωw/2πc<1.5. On the other hand, the group velocity (C) is not changed for 0.5<ωw/2πc<1, because this remains in the TE₁₀ mode. If the distribution of the transverse electromagnetic field is gradually changed from TE₁₀ to TE₂₀, and group velocity (A) is also gradually changed to (B), then the reflection may be reduced for 1<ωw/2πc<1.5. On the other hand, if the group velocity (C) is not significantly changed, the reflection may also be suppressed for 0.5<ωw/2πc<1. Since the mode profile gradually shifts from TE₁₀ to TE₂₀, the dielectric rods are replaced from near the sidewall to the center of the waveguide. In other words, the basic setup is shown in Fig. 2.

Figure 1.

The frequency eigenvalues of a conventional metallic waveguide in a given k wavevector.

Figure 2.

The proposed structure of the TE₁₀ to TE₂₀ mode converter.

Figure 3.

The group velocity in a metallic waveguide with a periodic array of dielectric rods for various distances from the sidewall, d, and various radii of the rods, r, at 15 and 9 GHz. (Kokubo, 2010)

The group velocity is given by $$v_g=\frac{1}{\left(\raisebox{1ex}{$dk$}\!\left/ \!\raisebox{-1ex}{$d\omega $}\right.\right)}$$ . However, it is not simple to determine the group velocity in the waveguide shown in Fig. 2. The propagation modes in a waveguide having in-line dielectric rods with period a are calculated using a supercell approach (Benisty, 1996) by application of appropriate periodic Bloch conditions at the boundary of the unit cell (Boroditsky et al.; Kokubo & Kawai, 2008). When the location of the dielectric rods is fixed at a distance d from the sidewall, the group velocity v _g at both of the first and the second bands is changed by varying the radius r. However, the group velocities are also changed at the same time and cannot be changed individually.

If the group velocity is normalized using light velocity in a vacuum, v _g/c is the same as the gradient of the characteristic curve. Therefore, when d and r are fixed to certain values, v _g/c is calculated for the periodic structure of the dielectric rods at a specific frequency. If group velocity (A) is gradually changed to (B) for 1<ωw/2πc<1.5 when d is varied, and group velocity (C) is not changed for 0.5<ωw/2πc<1, then one unit of each pair of d and r connects to its respective pair to form a structure shown in Fig. 2.

The metallic waveguide is assumed to be a WR-90 (22.9×10.2 mm, cutoff frequency f _c ≈ 6.55GHz) and period a is fixed at 9.54 mm. Fig. 3 shows a sample of calculated results of normalized velocity along the axis of the waveguide at 15 GHz and 9 GHz for dielectric rods (LaAlO₃: ε_r= 24, radius r [mm]) aligned at a distance from the sidewall d [mm] (Kokubo, 2010). It is desirable that the normalized velocity (A) (TE₁₀: v _g/c =0.900) monotonically decreases to (B) (TE₂₀: v _g/c =0.487) at 15 GHz and normalized velocity (C) (TE₁₀: v _g/c =0.686) is not changed at 9 GHz. However, at 15 GHz, such a condition is not found around d=10 mm, because the placement of the dielectric rod at the center of the waveguide is the same as that where the electric field becomes a minimum. On the other hand, placement of the dielectric rod near the sidewall of the waveguide is the same as that where the electric field becomes a maximum. At the transition region, around d=10 mm, the characteristics are complex. The design takes priority, in order to not vary the group velocity at 9 GHz. Since the group velocity must become slow with dielectric material at 9 GHz and becomes slowest at d=5 mm, the design takes priority at 15 GHz for mode conversion, because both 15 GHz and 9 GHz conditions cannot be satisfied at the same time. The final design of the mode converter is shown in Fig. 2. Three dielectric rods are located at the center of the waveguide. Two of these have r = 0.515 mm and the remainder have a half cross-section radius of 0.36 mm in order to decrease electromagnetic reflection. Nine dielectric rods are placed from the center of the waveguide to near the sidewall with increasing radius of the rods r and with constant a = 9.54 mm. Table 1 shows the relation between the distance d and radius r (Kokubo, 2010). The S parameters between the input port (Port 1) and output. port (Port 2) are calculated using the HFSS software by Ansys Inc. and the results are shown as solid lines in Figs. 4(a) and (b). The electromagnetic waves pass through as the TE₁₀ mode for 7-11.2 GHz and are converted to the TE₂₀ mode for 14.1-16.1 GHz under a condition of over 95% efficiency. However, as the TE₂₀ mode is not sufficiently small under -15 dB, optimization of the design is necessary for reduction of reflections. Though reflection as TE₂₀ is not small at high frequency, if a coaxial-waveguide converter is used for the introduction of electromagnetic waves to a waveguide, odd mode may not have a strong influence on even symmetry structure.

Rod Number i	Distance di from the Sidewall [mm]	Radius ri of the dielectric rod [mm]
1	11.45	0.36
2	11.45	0.515
3	11.45	0.515
4	10.45	0.52
5	9	0.57
6	7	0.64
7	5	0.69
8	3	0.76
9	1.3	1.0

Table 1.

Location and radii of the dielectric rods

2.2. Simple fabrication method

For the fabrication of a mode converter, such as the Type A illustrated in Fig. 5(a), it is necessary to locate the dielectric rods in the waveguide without a gap at top and bottom.

Such a structure may be difficult to fabricate. As a solution, holes with diameters 0.2 mm larger than the rods were fabricated at the top of the waveguide and the dielectric rods were inserted (Type B, Fig. 5(b)). The S parameters were calculated using the HFSS software and the results are shown as dotted lines in Figs. 4(a) and (b). The results for these different structural conditions (solid lines and dotted lines) are almost same.

Figure 4.

S parameter for the mode converter; (a) |S₂₁| and (b) |S₁₁|.(Kokubo, 2010)

Figure 5.

a) Dielectric rod located in a waveguide without gaps at top and bottom. (b) Dielectric rod inserted in a hole made at the top of the waveguide with a diameter 0.2 mm larger than the diameter of the rod. (Kokubo, 2010)

2.3. Reduction of reflection for TE₂₀ mode

As shown in Fig. 4(b), reflection as TE₂₀ mode is not small enough. This reason is dielectric rods are asymmetric arrangement for electromagnetic wave. Fig. 6 shows an improved structure of the TE₁₀ to TE₂₀ mode converter.

Figure 6.

An improved structure of the TE₁₀ to TE₂₀ mode converter.

Rod Number i	Distance di from the Sidewall [mm]	Radius ri of the dielectric rod [mm]
1	11.45	0.38
2	11.45	0.55
3	11.45	0.55
4	11.45	0.55
5	10.45	0.515
6	9	0.57
7	7	0.64
8	5	0.69
9	3	0.76
10	1.25	0.92
11	21.65	0.96

Table 2.

Location and radii of the dielectric rods

Figure 7.

S parameter for the mode converter; (a) |S₂₁| and (b) |S₁₁|.

2.4. Design method of the TE₁₀-to-TE₄₀ mode converter

A TE₁₀ to TE₄₀ mode converter can be considered by combination of TE₁₀ to TE₂₀ mode converters. Another structure of the TE₁₀-to-TE₂₀ mode converter is proposed and is shown in Fig. 8. The locations of the dielectric rods are indicated in Table 1. The structure of the proposed TE₁₀-to-TE₄₀ mode converter, which is composed of three TE₁₀-to-TE₂₀ mode converters, is shown in Fig. 9. The S parameters between the input port (port 1) and output port (port 2) calculated using HFSS are shown in Figs. 10(a), (b) and (c).

Figure 8.

Structure of the proposed TE₁₀-to-TE₂₀ mode converter.

Figure 9.

Structure of the proposed TE₁₀-to-TE₄₀ mode converter. (Kokubo, 2011a)

Figure 10.

S parameters for the TE₁₀-to-TE₄₀ mode converter. (a) |S₂₁|, (b) |S₁₁|, and (c) |S₂₂|. (Kokubo, 2011a)

2.5. Design method of the TE₃₀-to-TE₁₀ mode converter

A structure that contains two arrays of dielectric rods can convert the TE₃₀ mode into the TE₁₀ mode ( Kokubo, 2009 ). The TE₃₀ mode electromagnetic waves in this type of waveguide are converted to the TE₁₀ mode for 7.1–8.9 GHz with over 95% efficiency. However, this structure cannot pass through electromagnetic waves around 2.5–3 GHz without high reflection even if the waveguide is straight. Therefore, a mode converter is proposed that passes the TE₁₀ mode at low frequencies and efficiently converts the TE₃₀ mode into the TE₁₀ mode at high frequencies.

A metallic waveguide that contains two in-line dielectric rods can propagate single modes in two frequency regions (Shibano et al., 2006). The propagation modes in a waveguide with two in-line dielectric rods with period a are calculated using a supercell approach (Benisty, 1996) by applying appropriate periodic Bloch conditions at the boundary of the unit cell (Boroditsky et al., 1998; Kokubo & Kawai, 2008).

The metallic waveguide width is assumed to be w ₁ = 21.4 mm, which is 3 times wider than the WR-28 waveguide (7.11× 3.56 mm; f _c ≈ 21.1 GHz), and period a is fixed at 5 mm. Fig. 11 shows a sample of the calculated normalized velocity along the waveguide axis at 9 and 27 GHz for dielectric rods (LaAlO₃: ε_r = 24; radius r [mm]) aligned at a distance w ₂ [mm] between two arrays. The waveguide must be designed so as not to vary the group velocity (C) (TE₁₀: v _g/c = 0.627) at 9 GHz. After calculating v _g for pairs of w _2i and r _i, if group velocity (A) (TE₃₀: v _g/c = 0.627) is gradually changed to (B) (TE₁₀: v _g/c = 0.966) at 27GHz, then each pair of w _2i and r _i are combined (see Fig. 12).

Figure 11.

Group velocity (dotted lines) in a metallic waveguide containing a periodic array of dielectric rods with various distances w _2i between the rods and corresponding radii r _i (solid line) of the rods, at 9 and 27 GHz. (Kokubo, 2011b)

Figure 12.

Proposed structure of the TE₃₀-to-TE₁₀ mode converter. (Kokubo, 2011b)

Rod Number i	Distance w2i between a pair of the rods [mm]	Radius ri of the dielectric rod [mm]
1	7.13	0.22
2	7.13	0.32
3	7.13	0.32
4	7.13	0.32
5	8.3	0.32
6	10.2	0.36
7	12.7	0.43
8	15.2	0.51
9	17.7	0.62
10	19.5	0.78

Table 3.

Location and radius of the dielectric rods

The first pair of rods has r ₁ = 0.22 mm to reduce electromagnetic reflection at low frequencies. If the first pair of rods is absent, then reflections will be above −10 dB at low frequencies. Twenty dielectric rods are placed from one third of the width of the waveguide to near the sidewall with increasing rod radius r _i and constant a (= 5 mm). Table 3 shows the relation between the distance w _2i and radius r _i. The S parameters between the input port (port 1) and output port (port 2) are calculated using HFSS software by Ansys Inc., and the results are shown in Figs. 13(a-c). Electromagnetic waves propagate as the TE₁₀ mode for 8.2–14.8 GHz and the TE₃₀ mode is converted into the TE₁₀ mode for 22.2–28.4 GHz at an efficiency of over 95%.

Figure 13.

S parameters for the mode converter; (a) |S₂₁|, (b) |S₁₁|, and (c) |S₂₂|. (Kokubo, 2011b)

3. Conclusion

We have previously reported that single-mode propagation is available for a metallic waveguide with dielectric rods arrayed at the center of a waveguide using the TE₁₀ mode, and the TE₂₀ mode. However, a TE₂₀-like mode, which is propagated in the second band, is an odd mode, and generation is not easy. In this investigation, a mode converter is proposed which passes through the TE₁₀ mode for the low frequency range and converts TE₁₀ to the TE₂₀ mode for the high frequency range by small variation of the group velocity. It was shown that the electromagnetic waves pass through as the TE₁₀ mode for 7-11.2 GHz and are converted to the TE₂₀ mode for 14.1-16.1 GHz under a condition of over 95% efficiency.

It was shown that electromagnetic waves propagate as the TE₁₀ mode around 8 GHz and that the TE₄₀ mode is converted into the TE₁₀ mode around 16 GHz.

Acknowledgments

This work was supported by JSPS KAKENHI 22560336.