Supplementary information for all-metal metamaterial slow-wave structure
for high-power sources with high efficiency
Yanshuai Wang1, Zhaoyun Duan1,*, Xianfeng Tang1, Zhanliang Wang1, Yabin Zhang1, Jinjun Feng2, and
Yubin Gong1
*E-mail: zhyduan@uestc.edu.cn
1
National Key Laboratory of Science and Technology on Vacuum Electronics in Chengdu, School of Physical
Electronics, University of Electronic Science and Technology of China, No. 4, Section 2, North Jianshe Road,
Chengdu 610054, China
2
National Key Laboratory of Science and Technology on Vacuum Electronics in Beijing, Beijing Vacuum
Electronics Research Institute, Beijing 100015, China
This file includes:
Supplementary Text
Figs. S1 to S17
-----------------------------------------------------------------Supplementary Text
1. Descriptions of the transmission experiment
Two types of the new metamaterial (MTM) unit cells have been manufactured as shown in
Fig. S1. The unit cell sketched in Fig. S1(a) is only fixed on the two ends of the MTM slow wave
structure (SWS), and another type of the unit cell is located in the middle of the SWS. As shown
in Fig. S2, a new SWS which consists of 11 MTM unit cells is fabricated and used in the
transmission experiment. The MTM unit cells are arranged with the period p=30 mm, and a
brass component is located between the adjacent unit cells to support the MTMs. Therefore, the
gaps between the components would inevitably have effects on both the alignment accuracy and
the attenuation in the experiment. This’s why the measured results have higher transmission loss
compared to the simulated results, as stated in main text.
Fig. S3 and Fig. S4 show that a brass sleeve is utilized to fix the MTM SWS. The brass
sleeve can isolate the MTM SWS from the air and keep a vacuum environment for the future hot
test.
The setup of the transmission experiment is shown in Fig. S5: the vector network analyzer
Agilent N5230A PNA-L is used in the experiment, and it should be noticed that the signaling
system is symmetric about the center of the MTM SWS as mentioned in the manuscript. The
input coaxial line connected to a port of the vector network analyzer is used to excite a
TM-dominant mode in the input circular waveguide junction, and then the signal is coupled into
the MTM SWS by the first MTM unit cell near to the junction. In the meantime, another same
output coaxial line connected to another port of the vector network analyzer is utilized in the
output circular waveguide junction to receive the signal that has transmitted through the MTM
SWS.
(a)
(b)
Fig. S1. Photographs of the fabricated unit cell samples.
Fig. S2. The assembled MTM SWS.
Fig. S3. The brass sleeve used in the experiment.
Fig. S4. The side view of the assembled MTM SWS packed in the brass sleeve.
(a)
(b)
(c)
Fig. S5. Sketches of the experimental setup.
2. Supporting information of the simulation results of electric and magnetic
fields
We use the Time Domain Solver of CST Microwave Studio 2012 to simulate the electric
and magnetic fields corresponding to the transmission experiment, as shown in Figs. S6 and S7.
Fig. S6 shows the axial electric field component is strong and Fig. S7 shows the calculated
results of the magnetic field. From Figs. S6 and S7, we can see that the axial component of the
electric field and the transverse component of the magnetic field are major components of the
electromagnetic wave. It states a quasi-transverse magnetic (TM) wave which can be utilized in
the vacuum electron devices. For comparison, the simulation has also been done by using the
Eigenmode Solver of CST Microwave Studio 2012. The simulation results are illustrated in Figs.
S8 and S9. Through comparing Figs. S6 to S9, we can conclude that the fundamental mode of
this new MTM SWS is a TM-dominant mode.
(a)
(b)
Fig. S6. Simulation results of the electric field corresponding to the transmission experiment, (a) cutaway view
along the X-axis, and (b) along the Y-axis.
Fig. S7. Simulation results of the magnetic field corresponding to the transmission experiment.
Fig. S8. Simulation results of the electric field for the new SWS which consists of infinite MTM unit cells.
Fig. S9. Simulation results of the magnetic field for the new SWS which consists of infinite MTM unit cells.
3. Supporting information of the Particle-in-cell (PIC) simulation results
Fig. S10 shows the output signal of the S-band MTM backward wave oscillator (BWO), it’s
seen that the peak power of the signal is about 4 MW, which is promising to be improved in the
next work. Figs. S11 and S12 show the distributions of the electric and magnetic fields of the
output signal in the proposed structure. Here, it should be pointed out that the coordinate system
is in accord with that in Part 2 above. Figs. S11 (a) and (b) show that the maximum of the
electric field mainly locates in the slots of the MTM and in the area of the beam tunnel. Figs. S12
(a) and (b) show that the magnetic field mainly locates near the surface of the MTM. From Figs.
S11 and S12, it can be seen that the output signal is a TM-dominant wave, not pure TM mode. In
the end, it is summarized that the microwave electric field or magnetic field is mainly coupled
from the cell to cell through the slots.
Fig. S10. Output signal of the S-band MTM BWO.
(a)
(b)
Fig. S11. Simulation results of the electric field of the output signal (a) in the yoz plane and (b) in the xoy
plane.
(a)
(b)
Fig. S12. Simulation results of the magnetic field of the output signal (a) in the yoz plane and (b) in the xoy
plane.
4. Supporting information of the pivotal differences between the traditional
coupled cavity SWSs and the proposed all-metal MTM SWS in the
manuscript
The proposed all-metal MTM SWS seems similar to some types of the coupled cavity (CC) SWS,
but it is actually different from the CCSWSs. There would be a drift tube for the typical
CCSWSs, such as the Chodorow-Nalos structure,1 the “Hughes” structure,2 and other CCSWS
with double slots and doubly tapered ferrules.3 In contrast, there is no drift tube in the proposed
all-metal MTM SWS. In fact, the biggest difference in the proposed structure is that we
creatively add four grooves in the new design based on the MTM theory and these grooves
mainly determine the high frequency characteristics of the structure.
The pivotal differences between the traditional CCSWSs and the proposed all-metal MTM SWS
in the manuscript exist not only in structure shape, but also in high frequency characteristics.
Among the family of the CCSWSs, the CCSWS with double slots is the most similar to the
proposed structure. In order to validate the differences, an S-band CCSWS with double slots has
been designed and then calculated by using Ansoft HFSS 13.0, as shown in Fig. S13.
Fig. S13. One unit cell of the S-band CCSWS with double slots for simulation.
Fig. S14(a) exhibits the dispersion characteristics of the CCSWS with double slots. From this
dispersion characteristics, we can find that for the n=0 space harmonic (the region of the phase
shift is from 0 to π) of the fundamental mode (Mode 1), its phase velocity is larger than the light
speed in vacuum c, while the phase velocity of its n=-1 space harmonic (the region of the phase
shift is from π to 2π) is smaller than c, thus the CCSWS working at the n=-1 space harmonic of
the fundamental mode (a ‘forward’ wave) is often used in the coupled-cavity traveling-wave
tubes (CCTWTs). The interaction impedances of the fundamental mode and the first higher-order
mode (Mode 2) are calculated by using the Ansoft HFSS post processing technique, as shown in
Fig. S14(b). The simulation results show that the interaction impedance of Mode 2 is nearly as
large as that of Mode 1, which means the unwanted self-oscillation can be easily caused by Mode
2, while the same risk can be ignored for the proposed structure, because the interaction
impedance of the first higher-order mode is lower than 1 Ω. This is a big advantage for the
proposed all-metal MTM SWS!
In addition, the n=-1 space harmonic of the fundamental mode for the CCSWS with double slots
can also be a ‘backward’ wave by only changing its geometric parameters, as shown in Fig. S15.
Similar risk to the ‘forward’ case still exists.
(a)
(b)
Fig. S14. High frequency characteristics of the CCSWS with double slots. (a) Dispersion curves and (b)
Interaction impedance curves for Mode 1 and Mode 2.
Fig. S15. Dispersion curve of Mode 1 for the CC-SWS with double slots.
According to the MTM theory, the waveguide loaded with the MTMs below the TM mode
frequency can be equivalent to a double-negative medium,4 so it can support a negative index
mode. As a result, for the proposed structure, the n=0 space harmonic of the fundamental mode
would only be a ‘backward’ wave.
In fact, the working bandwidth for our new structure is lower than the traditional CCSWS.
Relatively speaking, our structure is smaller than the traditional CCSWS for the same band.
According to the parameters in the literature,3 the radius of the corresponding CCSWS is 26.9
mm at the same operating frequency of 2.45 GHz, while the radius of our design in the
manuscript is only 20 mm. This is another advantage! More details are shown below. Fig. S16
exhibits four Models for our new design, including Model b, the parameters of which are
identical with those in the manuscript. We have mentioned that the grooves mainly determine the
high frequency characteristics. As a parameter, the depth of the groove strongly affects the
operating frequency band of the design, in other words, also affects the miniaturization.
Furthermore, the corresponding results presented in Fig. S17 clearly show that there is an
advantage of miniaturization, when compared to the conventional CCTWT. This is because the
radius of the SWS of the conventional S-band CCTWT (the center frequency is above 3 GHz) is
between 25 x 25 mm2 and 30 x 30 mm2.5
(a)
(c)
(b)
(d)
Fig. S16. Slight variants of our new design with the change of the groove depth.
Fig. S17. Simulated results corresponding to the models shown in Fig. S16.
References
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Chodorow and E. J. Nalos, Proc. IRE, 649 (1956).
2 J.
F. Gittins, Power Travelling-Wave Tubes, The English University Press Ltd, London (1965).
3 V.
L. Christie, L. Kumar and N. Balakrihnan, Microw. Opt. Technol. Lett. 35, 322 (2002).
4
J. Esteban, C. Camacho-Peñalosa, J. E. Page, T. M. Martín-Guerrero, and E. Márquez-Segura, IEEE Trans.
Microwave Theory Tech. 53, 1506 (2005).
5 Z.
Y. Duan, Y. S. Wang, X. Huang, X. W. Ma, T. Tang, M. Z. Huang, Z. L. Wang and Y. B. Gong, U. S. Patent
Application No. 14/572, 035, Dec. 16 (2014).