1. Introduction

Terahertz electromagnetic wave is one of the most attractive topics to worldwide researchers for its great potential applications [1, 2]. Yet lack of desirable terahertz radiation source has still been one of the main bottlenecks for the development of related technologies [3, 4].

Compared with other kinds of terahertz sources, the free electron beam driving sources, such as backward-wave oscillator (BWO), gyrotron, and free electron laser (FEL), are very attractive for their remarkable advantages of high radiation power and working in room temperature. Yet unfortunately, their disadvantages are also noticeable. The traditional BWO can only generate radiation with frequency much lower than 1 THz due to the limitations of very tiny-size structure and extremely high starting current density [5, 6]. Gyrotron can generate kilowatt radiation with frequency close to 1 THz [7, 8]. However, it requires intense external magnetic field which is not easy to obtain. FEL can generate megawatt to gigawatt (peak power) radiation over the whole terahertz band, yet its practical application is limited by the large equipment, enormous cost, and complicate peripheral supporters [9]. Exploring a new free electron terahertz source which is compact, broad tunable, and easily achievable is of great significance, and it is the major goal of the present paper.

The schematic of the proposed terahertz radiation source is shown in Fig. 1. A train of electron bunches is applied to excite a periodic-loaded waveguide (PLW), in which the guided modes are coupled by the electron bunches and then generate coherent radiation through the apertures of the waveguide. The preliminary experimental and theoretical studies about this kind of radiation were carried out in [10] and [11], in which the fundamental guided mode of the PLW was excited to generate visible light radiation. Recently, [12] applied a train of electron bunches to excite the PLW to generate terahertz radiation. Yet in all previous literatures, only a single guided mode was coupled into radiation, and the radiation frequency was fixed once the structure parameters and bunch velocity are specified. In present paper, we introduce a photocathode based direct current (DC) electron gun to produce a train of bunches with tunable bunching frequency. Then we apply the electron bunches with different bunching frequencies to excite different order guided modes in the PLW. By this means, the tunable radiation with frequency extending from 0.1 THz to 1.2 THz can be generated from one single structure model. And we will also show that the proposed scheme is compact and easily achievable.

 

Fig. 1 Schematic cut-away section of the proposed radiation source. P-C denotes the photocathode, and T_b is the time period of the bunches train. The inset shows the zoomed figure of the PLW with its structure parameters. L is the spatial period, d and h are respectively the width and depth of the groove, W is the waveguide width in the y-direction, and s denotes the distance between the groove and the middle plane of the waveguide in the x-direction.

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2. Theoretical analyses and simulation results

Firstly, we would like to consider the generation of a train of tunable electron bunches, the schematic of which is presented in Fig. 1. A train of laser pulses illuminates the photocathode, from which a train of electron bunches is emitted. The bunching frequency is exactly the repetition frequency of the laser pulses. Thus a train of well controlled laser pulses is of importance. In experiment, it can be obtained by the polarization-beam-splitter (PBS) based pulse stacking method. By this method, a train of 2ⁿ (n is a integer) laser pulses can be generated after n-stage of stacking, and the time spacing between adjacent laser pulses, namely the repetition frequency, can be well tuned by adjusting the optical delay lines [13]. To reach the desirable property, the electron bunches emitted from the photocathode should be accelerated and focused by the electron gun. In consideration of the compactability, the DC-gun with acceleration voltage of hundreds of kilovolts is applied. And in order to get the bunches with relatively large charge density (which will lead to relatively high radiation power), the focusing electrode is used to transversally compress the bunches. Note that as the charge quantity of the bunch is large enough, the space charge effect will be significant, which will increase the transversal emittances and smear out the structure in the temporal bunch profile. This will reduce the working stability and efficiency of the device. Thus to get the optimum operation, the charge quantity of the bunches should be well chosen. Simulations of the DC-gun and of the electron bunches are respectively carried out by applying the Poisson Superfish and ASTRA codes [14]. A set of simulation results is presented in Fig. 2, in which, after optimization, a train of 32 laser pluses with Gaussian shapes is applied to excite the circular photocathode with radius of 2 mm, the repetition frequency of the laser pulses is 0.5 THz, the initial electron kinetic energy from the cathode is about 0.5 eV, and the acceleration voltage of the DC-gun is 200 kV. Figure 2(a) and Fig. 2(b) respectively illustrate the evolutions of the transversal and longitudinal profiles of electron bunches. It can be observed that the initial radius of the bunch is 2 mm. After compression, the electron bunches get the stable radius of 0.4 mm in the region (0.2–0.3 m away from the cathode) where the PLW is located at. The bunch length almost keeps steady after the bunches are fully accelerated. The inset of Fig. 2(a) shows the x-t distribution of the electron bunches in the PLW. One can observe that a train of 32 electron bunches with good bunching characters is obtained. The inset of Fig. 2(b) shows that each bunch has a Gaussian profile with RMS of 200 fs and the bunch current is about 0.6 A. Thus the total charge quantity of the bunches train is about 9.6 pC, namely 300 fC per bunch. In actual experiment, both the acceleration voltage of the gun and the repetition frequency of the laser pulses can be tuned as needed. For the DC-gun, the operation voltage can be changed from tens to hundreds of kilovolts [15, 16]. And the repetition frequency of the laser pulses can be tuned from 0.1 THz to over 1 THz.

 

Fig. 2 (a) Evolution of the transversal profile of the train of bunches. The inset shows the charge distribution in the x-t plane, which is detected by a screen 25 cm from the photocathode. (b) Evolution of the total length of the train of bunches. The inset shows the beam current in the bunches.

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In the following, we apply the electron bunches obtained above to excite the PLW to generate tunable terahertz radiation. Taking into consideration of the power capacity and manufacture, the PLW is chosen as a rectangular waveguide with the periodical rectangular grooves symmetrically loaded as shown in Fig. 1. When the electron bunches are injected into the waveguide, the guided mode with phase velocity close to bunch velocity will be coupled into radiation. The radiation frequency and direction are determined by the coupling point on the dispersion curve. To get the enhanced coherent radiation over a broad spectra, we let the operation frequencies of different order guided modes be close to each other. When we continuously tune the bunching frequency, different order guided modes with coupling frequencies close to the bunching frequencies will consecutively be excited to generate radiation. Namely, by tuning the bunching frequency, the radiation frequencies are tuned accordingly. Note that here a series of guided modes, including the fundamental and high order modes, can act as the operation modes for radiation, namely, the PLW is an overmoded waveguide. It is essentially different from the ordinary vacuum electronic devices, where only the fundamental mode can be used to generate radiation. By the proposed method, the broad tunable radiation can be generated from one single PLW with relatively big-size structure, which is attractive especially in the terahertz region.

Without loss of generality, we set the waveguide parameters (shown in the inset of Fig. 1) as: s=0.5 mm, h=1 mm, d=0.07 mm, L=0.1 mm, w=1 mm. The structure size here is an order of magnitude larger than that of the traditional BWO in the 1-THz region, which means it is much easier for manufacture. The dispersion curves of different guided modes can be theoretically obtained by applying the mode matching method [17], the results of which are given in Fig. 3(a). Here only the low order modes are shown as they dominate the radiation. One can observe that all the nine lowest guided modes in the PLW can be coupled with the 200 kV electron beam. The coupling frequencies extend from 0.15 THz to 1.2 THz (respectively are 0.16 THz, 0.25 THz, 0.38 THz, 0.52 THz, 0.66 THz, 0.81 THz, 0.95 THz, 1.1 THz, and 1.2 THz). The seven lower modes are in the forward wave region, indicating the forward radiations will be excited in the PLW, and the two higher modes are in the backward wave regions which lead to the backward radiations.

 

Fig. 3 (a) Dispersion curves of the guided modes in the PLW. (b) Radiation field spectra from different bunching frequencies.

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The simulations of the radiation from over-mode waveguide are carried out by applying the fully electromagnetic particle-in-cell (PIC) code [18, 19]. The structure and bunch parameters follow that presented above, and the simulation model follows that given in [12]. We first adjust the bunching frequency to respectively match the coupling frequency of each guided mode, namely, the bunching frequency is respectively set as 0.16 THz, 0.25 THz, 0.38 THz, 0.52 THz, 0.66 THz, 0.81 THz, 0.95 THz, 1.1 THz, and 1.2 THz. The simulation observed radiation spectra are given in Fig. 3(b). One can see that the radiations with frequencies equal to bunching frequencies are exactly achieved. For the four lowest bunching frequencies (from 0.16 THz to 0.52 THz shown in the figure), high order harmonics of the bunches can also excite radiation. This can be understood that the frequencies of high order harmonics match that of the high order guided modes of the PLW. The radiation intensity decreases as the bunching frequency increases because the coupling efficiency decreases as the mode order increases. Figure 4 shows the power density distributions around the PLW for the nine bunching frequencies which signify nine guided modes. For the seven lower frequencies (from 0.16 THz to 0.95 THz shown in the figure), the radiations are mainly in the forward direction. While for the two higher frequencies (1.1 THz and 1.2 THz), the radiations are largely in the backward direction. These agree with the theoretical expectations. The radiation power density ranges from 10¹¹ W/m ² to 10⁹ W/m ², and it roughly decreases with the increase of frequency.

 

Fig. 4 Simulation power density distributions in and around the PLW (in the x–z cutplane) for different frequencies. The negative value of the power indicates the backward radiation.

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Then we adjust the bunching frequency to gradually deviate from the perfect coupling frequency of the guided mode, i.e., we aim to look at the radiation property over the whole 0.1–1.2 THz region. Figure 5(a) shows the simulation results of the radiation spectra as the bunching frequencies deviate from the perfect coupling frequencies. Here for each guided mode, the deviation value is from −10 GHz to +10 GHz. One can observe that the radiations with the bunching frequencies (together with the harmonics) can still be obtained as the bunching frequencies deviate from the perfect coupling frequencies. The radiation intensity largely decreases with the increase of deviation, which is because the deviation reduces the coupling efficiency. Now we look at the radiation power. For each bunching frequency, the radiation power of the model can be evaluated by integrating the power density at the apertures of the PLW. Thus, by continuously tuning the bunching frequency, the radiation power over the whole 0.1–1.2 THz region can be obtained, and the results are shown in Fig. 5(b), in which the electron bunches and structure parameters are the same as that in Fig. 3. It can be observed that the radiation covers the whole 0.1–1.2 THz spectrum band. The radiation power reaches the relative peak at the perfect matching frequency of each guided mode. It ranges from hundreds of milliwatts (at the 0.16 THz) to several milliwatts (higher than 0.6 THz). Readily to know that, by increasing the bunch number or total charge quantity of the bunches train, higher radiation power can even be obtained. Based on the simulations, the power capacity of the model, which is determined by the breakdown threshold of the PLW structure, is further evaluated as shown in Fig. 5(b), in which the breakdown electric field is set as 10⁷ V/m. One can see that the highest reachable power from the structure model can be hundreds of watts over the whole 0.1–1.2 THz region.

 

Fig. 5 (a) Radiation spectra from different bunching frequencies. Here the bunching frequencies deviate from the perfect matching points. For each guided mode, four deviation values, respectively with −10 GHz, −5 GHz, +5 GHz, +10 GHz, are shown. (b) Simulation evaluated radiation power and power capacity of the model over the 0.1–1.2 THz band. Here the electron bunches and structure parameters are the same as that in Fig. 3.

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3. Discussion

In this section we would like to make a discussion about some additional features of the proposed radiation source. The first is about the tunability. In above analyses, the beam voltage and structure parameters are fixed. Actually, the tuning of the radiation can also be achieved by changing the beam voltage, which is similar to that of the traditional BWO. From the dispersion curve shown in Fig. 3(a) one can see that, by changing the beam voltage to 500 kV, the radiation from the 10-th order guided mode with frequency close to 1.5 THz will be excited. And naturally, the radiation can also be tuned by changing the structure parameters. The second is about the radiation power. In previous literature, the train of nonrelativistic bunches was applied to excite an open grating to generate the superradiant Smith-Purcell radiation (SPR) [20]. Simulations indicate that the radiation power from our proposed scheme can be several times higher than that from the superradiant SPR. Another important feature is about the experimental feasibility and practicality. The generation of electron bunches form a photocathode based DC-gun excited by train of laser pulses is a mature technique. And the tuning of the laser pulses by the pulse stacking method has also been achieved in experiments [21, 22, 23]. Compared with the microwave RF-guns which produces the relativistic bunches, the DC-gun together with the nonrelativistic bunches applied in the present paper is much more compact and has much lower cost.

4. Conclusion

In summary, a new free electron terahertz radiation source was proposed and investigated. It can generate tunable radiation with frequency extending from 0.1 THz to over 1 THz. Compared with other kinds of terahertz sources, it is compact and easily achievable. It may offer a new promising way for developing the broad-tunable terahertz source.