CST – Computer Simulation Technology

Design and Simulation of a Novel Slow-Wave Structure for THz Applications

The development of slow-wave structures for generation in the terahertz regime is a popular ongoing area of research. Minghao Zhang et al. [1] have presented the design of a novel 'quasi-parallel-plate' slow-wave structure to be used in Backward-Wave Oscillators (BWOs) operating at that regime. The continuous wave (CW) BWO is a frequency-tunable, high frequency, and compact dimension source of THz radiation. As its core component, the slow-wave structure determines its performance.



Figure 1: Structure of the 'quasi parallel plate' slow-wave structure modeled as vacuum. Three periods are shown here (a) Three-dimensional view (b) Cut-section view.

The structure shown in Figure 1 is a modification of a folded waveguide (FWG) slow wave structure, in an effort to build on its advantages such as high frequency and power operation and suitability for circular beams by further improving its operational characteristics. The resulting structure is termed a "quasi parallel plate" (QPP). Its middle part is similar to that of a conventional FWG with E-plane bending at a right angle. The side metal walls are removed and replaced with vacuum, giving it a parallel-plate-like charater. This results in expansion of the frequency bandwidth. Compared to a conventional BWO, the QPP BWO has higher interaction impedance and efficiency, lower operating voltage and focusing magnetic field, and a shorter circuit length. As an added advantage, the structure can fabricated by microfabrication techniques....



Figure 2: (a) Normalized phase velocity and interaction impedance (b) S-parameters of the slow-wave structure

The Eigenmode Solver in CST STUDIO SUITE® is used to calculate the frequency characteristics of the structure such as dispersion curves and beam-wave interaction impedance. The 10 kV beam line and the dispersion curve intercept at operating frequency of 1 THz. The operating frequency range can be tuned roughly from 0.8 to 1 THz by changing the beam line between 5 and 10 kV. The on-axis interaction impedance is greater than 5 ohm.

Next, the transmission characteristics are analyzed by considering copper as the fabrication material. The S-parameters are calculated by the Transient solver. As can be seen from Figure 2b, the S11 and S21 are less than 20 dB and more than 2 dB within the designed bandwidth, respectively, showing that the structure is suitable for transmission at THz range.



Figure 3: Electric field distribution of the fundamental mode at the cross section of (a) E-plane (b) H-plane

Figure 3 shows the electric field distribution of the fundamental mode which propagates along the slow-wave structure. As can be seen, the fundamental mode is similar to the TE10 mode. The field distribution characteristics indicate that the electric field is concentrated in the middle part of the structure.

A simulation of the fully operational device, including the non-linear interaction between the electron beam and the electromagnetic waves, is carried out using the fully transient 3D Particle-In-Cell (PIC) solver in CST PARTICLE STUDIO® (a module of CST STUDIO SUITE). A BWO employs a magnetically-focused electron beam, and the velocity of the electron beam is adjusted to be approximately equal to the phase velocity of the backward wave at a specified frequency, determined by the dispersion characteristics. This results in an interaction between the electron beam and the electromagnetic waves, causing the electrons in the beam to get bunched. The energy extracted from the beam during this process is transferred to the electromagnetic field. As the beam travels along the slow-wave structure, the electrons lose their energy which is converted to the output electromagnetic wave power, making the device an amplifier. Figure 4 shows the bunched electron beam and the corresponding generated electric field.



Figure 4: Visualization of particles and fields at stable operation (a) Bunched electrons (b) Electric field pattern near the output port

The generated electromagnetic wave is extracted at the output port. A peak power of 0.97 W is obtained. The reflected signal is about 23 dB lower than the generated signal, which is consistent with the S-parameters obtained during the initial stages of the design process. The results for the case where the beam voltage is set to 10 kV are shown in figure 5.



Figure 5: Particle-in-cell simulation results (a) Signal power at output port, the blue curve is reflected signal power (b) Electron energy along axial distance (c) Power growth in slow-wave circuit along the axial distance

Summary

CST STUDIO SUITE provides suitable tools to carry out a complete device design. Initial design and verification of the novel slow-wave structure for frequencies at THz range is done using the Eigenmode and Transient solvers to chracterize parameters such as interaction impedance and S-parameters, respectively. Once the initial design is created, it is verified using the fully transient and self-consistent Particle-in-cell solver is used to simulate the complete BWO, simulating the injection of a DC electron beam. A peak output power of 0.82 W is obtained in the frequency range from 0.82 to 1 THz.

References:

[1] Minghao Zhang; Yanyu Wei; XianbaoShi; Lingna Yue; Wanghe Wei; Jin Xu; Guoqing Zhao; Minzhi Huang; ZhanliangWang; Yubin Gong; Wenxiang Wang; Dazhi Li, "A Modified Slow-Wave Structurefor Backward-Wave Oscillator Design in THz Band," Terahertz Scienceand Technology, IEEE Transactions on , vol.4, no.6, pp.741,748, Nov. 2014

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