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The interest in millimeter and terahertz (THz) waves is on the rise due to their unique properties and suitability for a wide range of applications[1-3]. Thanks to advancements in the microfabrication technology, high-powered vacuum electron devices (VEDs) are capable of generating microwaves in the millimeter and THz range[4-5].
In a typical VED, the amplitude of the synchronous slow-wave z-component in the electric field (EZ) decreases as its distance from the structure increases. Only a thin layer of electrons moving close to the structure can effectively interact with this high-frequency EZ field. At the millimeter- and terahertz-wave band, the beam interacting with the high-frequency EZ field decreases. A number of methods have been proposed to improve VEDs, through increasing efficiency and decreasing starting current density[6-8]. There have been attempts at using sheet electron beam devices[9-11] to improve VED performance by enlarging interaction space and providing sufficiently high currents. High-operating current density reduces the lifespan of cathodes in millimeter-wave and THz VEDs, therefore, currents should be kept as low as possible.
This article explores the photonic column array slow-wave structure (SWS), in order to improve the performance of THz VEDs[12-18]. The study designed and simulated a 0.28-THz backward-wave oscillator (BWO). The photonic column array SWS allows the flow of sheet beams. A planar SWS is a multi-column structure, which collects a large number of electrons on the surface of its columns. More electrons are lost in column array structures than in comb structures. This allows for the reduction of the starting current density in multi-column structures through increasing the length or width of the structure. Higher operating voltages (10～20 kV) can then be used to provide significant power and frequency increases. This article focuses on the design and analysis of a 0.28-THz BWO. We show that photonic column array structures are effective in improving the operation of microwave VEDs, such as BWOs.
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A schematic of the photonic column array SWS is shown in Fig. 1. The periodic slot-hole structure in this model can be extended along its length or breadth. Electron beams may flow through the structure, which increases the effective interaction of current with the slow-wave field. This makes the structure promising for applications in THz VEDs.
Figure 1. The photonic column array SWS
The parameters of the structure are shown in Fig. 2. To enable a VED operating at 0.28 THz, the dimensions of the structure were chosen as follows: d1 = 0.17 mm, a1 = 0.08 mm, d2 = 0.30 mm, a2 = 0.12 mm, and h = 0.20 mm. Fig. 2b shows the EZ field amplitude as a function of distance at a frequency of 0.28 THz. The EZ field peaked at height h=0.20 mm. The beam interacted with the EZ field inside the structure, so it can be seen from Fig. 2b that the beam thickness is δ = 0.30 mm. This increased the effective beam-wave interaction.
Figure 2. Dimensions of the photonic column array SWS and electric field amplitude at gap
The simulation software CST was used to analyze the cold cavity. After the simulation calculation, the dispersion curves of the photonic column array SWS, for BWOs are shown in Fig.3. The point of beam-wave interaction (at about f = 280 GHz) and the intersection of the dispersion curve with the beam lines for 10 kV, 12.5 kV and 15 kV electrons are shown in Fig. 3. The operating frequency is changed by adjusting the operating voltage. The electric field distribution of the TM11 mode is shown in Fig. 4.
Figure 3. Dispersion curves of the photonic column array SWS
Figure 4. Field distribution of the TM11 mode in the photonic column array SWS
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A 0.28-THz BWO was designed and simulated using CHIPIC, a three-dimensional (3D) electromagnetic particle-in-cell (PIC) finite-difference time-domain (FDTD) code. The system used the photonic column array SWS.
The SWS and baseplate cover consisted of copper. The simulation parameters of the BWO are shown in Table 1. Fig. 5 shows the electron beam passing through the photonic column array SWS on the Y-Z and X-Z planes. The THz signal output through a coupler, which consisted of a slot coupled to a WR10 waveguide.
Table 1. Operating parameters of the BWO
Parameters Value Beam voltage/kV U = 12.5 Beam current/mA I = 78 Beam thickness/mm δ = 0.3 Current density/A·cm−2 10 Number of periods N = 80 External magnetic field/T 0.5 Baseplate-cover height/mm H = 0.45 
Figure 5. Position distribution of the electron beam in the SWS
The results of the PIC simulation are shown in Fig. 6. The average beam energy was reduced through absorption by the SWS, as shown in Fig. 6a. The total current in the SWS was 78 mA, and the interaction current was about 51.5 mA. About 29.7% of electrons were lost in the multi-column structures, because the sheet beam was immersed in the SWS, as shown in Fig. 5a. However, this increased the surface of the beam-wave interaction.
Figure 6. The results of PIC simulation
The output power as a function of time, and the corresponding FFT power spectrum are shown in Figs. 6c and 6d, respectively. In accordance with the power law P∝E2, the amplitude on the FFT power spectrum corresponding to 0.56 THz was much higher than that corresponding to 0.28 THz. The operating frequency of 0.28 THz matches the intersection in Fig. 3.
Fig. 7a shows the high-frequency field power as a function of SWS length. Most of the field power was retained in the BWO, unlike the output power in Fig. 6c. This shows that the output coupling efficiency of this device was very low. Fig. 7b shows the surface power loss in the BWO. Surface power loss was much higher than the output power loss shown in Fig. 6c. Power loss to structures cannot be ignored in simulations, especially for high-frequency devices.
Figure 7. High-Frequency field power and loss
Fig. 8 shows power as a function of various parameters. Fig. 8a shows that the power increased as the number of periods increased, and Fig. 8b shows that power increased as the number of rows increased. After a series of calculations and comparisons, the numbers of periods and rows were chosen to be 80 and 7, respectively.
Sweeping simulation of the beam voltage, as shown in Fig. 8c, shows that the power peaked at operating voltage U = 12.5 kV, and the frequency increased with increasing voltage. This suggests that the operating frequency of the oscillator can be changed by adjusting the operating voltage. Power increases with increasing current density, as shown in Fig. 8d. The BWO functioned at a current density of 6 A/cm2 and must maintain a relatively low operating current density to increase the lifespan of the cathode. Referring to Fig. 8e, the output power increased as the guiding magnetic field increased. Stronger magnetic fields increased the size and cost of the device. A 0.5-T guiding magnetic field was adopted for the device in this study.
Figure 8. Output power as a function of different parameters
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The structure was fabricated using the lithography-galvanoformung-abformung (LIGA) fabrication technology, as shown in Fig. 9. Some issues were identified using a scanning electron microscope (SEM), manufactured by ZEISS. First, thin irregular burrs were found on the top of the structure, as highlighted by the blue squares in Fig. 9. These burrs were formed during the polishing process, and they may obstruct beam-wave interaction. The burrs can be removed with applied acid or thermal shocking by an electron beam. Second, thin wires were found to have accumulated inside the structure, as highlighted by the red square in Fig. 9a. These wires can also affect beam-wave interaction. They can be removed using ultrasonic methods or a micromanipulator. Finally, the actual size deviates from the design size by 5 μm (about 3%) because of the lack of optical precision during the fabrication process. The aforementioned issues can be resolved through advanced processing techniques and equipment. However, the obtained outcome was satisfactory because of its superior collimation of the metal column, its periodicity, and its bottom smoothness. The LIGA fabrication technology is suitable for such small structures and high frequencies.
Figure 9. High-frequency structure diagram
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A 0.28-THz BWO, driven by sheet beams, was designed and simulated. The device was based on photonic column array SWS. The SWS allowed beams move through its structure, which effectively reduced the operating current density of the BWO. The simulation results showed that the starting current density was below 6 A/cm2. The SWS was fabricated using the LIGA fabrication technology. The fabricated structure was satisfactory, and more experimental results will be published in future. This study shows that multi-column SWS represents a viable means for improving the performance of millimeter wave and THz VEDs.
Research on Terahertz Backward-Wave Oscillator Based on Photonic Column Array Slow-Wave Structure
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摘要: 研究了一种光子晶体的慢波结构，通过对该结构的色散、场分布和粒子模拟计算，设计和仿真了一个0.28-THz的带状注返波管。在阴极电流密度仅10 A/cm2(最小可低于6 A/cm2)，电压12.5 kV，磁场0.5 T的情况下，该结构通过与带状电子注浸没式互作用，输出功率为435 mW。在此基础上，采用了LIGA加工技术制备了该慢波结构。研究表明，光子晶体结构能有效提高互作用效率和降低起振电流密度，有效提高太赫兹真空电子器件阴极的使用寿命，是提高太赫兹真空辐射源性能的一种有效途径。Abstract: This article explores a photonic column array slow-wave structure (SWS). A 0.28-THz sheet beam backward-wave oscillator (BWO) was designed and simulated by calculating the dispersion, field distribution and particle simulation. When the cathode current density is only 10 A/cm2 (the minimum is less than 6 A/cm2), the voltage is 12.5 kV and the magnetic field is 0.5 T, the structure interacts with the sheet beam by immersion and the output power is 435 mW. On the basis of previous work, the SWS was fabricated using Lithography-Galvanoformung-Abformung (LIGA) fabrication technology. The results show that the column array structure can effectively improve the interaction efficiency and reduce the starting current density; and effectively improve the lifespan of terahertz (THz) vacuum electron device (VED) cathodes, which is a viable means of increasing the performance of THz vacuum radiation sources.
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Key words:
- column array slow-wave structure /
- THz BWO /
- starting current /
- vacuum electron device
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Figure 2. Dimensions of the photonic column array SWS and electric field amplitude at gap
Table 1. Operating parameters of the BWO
Parameters Value Beam voltage/kV U = 12.5 Beam current/mA I = 78 Beam thickness/mm δ = 0.3 Current density/A·cm−2 10 Number of periods N = 80 External magnetic field/T 0.5 Baseplate-cover height/mm H = 0.45 
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