Coherent Terahertz Radiation from Multiple Electron Beams Excitation within a Plasmonic Crystal-like structure
Coherent Terahertz Radiation from Multiple Electron Beams Excitation within a Plasmonic Crystal-like structure
Yaxin Zhang 0 1
Yucong Zhou 0
Yin Gang 0
Guili Jiang 0
0 Terahertz Science and Technology Research Center, School of Physical Electronics, University of Electronic Science and Technology of China , Chengdu 610054 , China
1 National Key Laboratory of Application Specific Integrated
OPEN Coherent terahertz radiation from multiple electron beams excitation within a plasmonic crystal-like structure (a three-dimensional holes array) which is composed of multiple stacked layers with 3 ? 3 subwavelength holes array has been proposed in this paper. It has been found that in the structure the electromagnetic fields in each hole can be coupled with one another to construct a composite mode with strong field intensity. Therefore, the multiple electron beams injection can excite and efficiently interact with such mode. Meanwhile, the coupling among the electron beams is taken place during the interaction so that a very strong coherent terahertz radiation with high electron conversion efficiency can be generated. Furthermore, due to the coupling, the starting current density of this mechanism is much lower than that of traditional electron beam-driven terahertz sources. This multi-beam radiation system may provide a favorable way to combine photonics structure with electronics excitation to generate middle, high power terahertz radiation.
Terahertz (THz) frequency band has been demonstrated of great interest for applications in biomedical imaging,
communication, and security checking as the electromagnetic (EM) waves have various physical properties
merging photonics and electronics1?3. The exploitation of these applications progresses slowly at present for the lack
of powerful and compact THz sources. THz waves are usually obtained by optical devices4?6, solid state electron
devices (SSEDs)7?9 and vacuum electron devices (VEDs)10?12. Although many progresses have been achieved, the
output power level so far is still hard to keep up with demand of the applications11,12. Compared to the optical
devices and SSEDs, the VEDs are more favorable to achieve high power since the electron transport medium
is vacuum, which is a ?perfect material? for high power devices12. Among the VEDs, the linear electron beam
(e-beam)-driven sources have been actively investigated in the THz region13?19. However, for these radiation
sources, with increased working frequency, higher starting current density is required and lower radiated power
obtained17. Therefore, many efforts in the linear e-beam-driven sources are concentrated on the design of
effective interaction structures as well as on the interaction mechanism so as to improve the radiation intensity and to
lower the starting current density.
Multi-beam sources are highly promising candidates to reduce the starting current density and to improve the
radiated power. Therefore, in the earlier days, multi-beams have been applied in the microwave sources such as
klystrons and free-electron lasers (FELs)20?23. Recently, there are some papers concentrating on multiple beam?
wave interaction in the THz region. Such as refs 24?27 suggested two sheet e-beams interaction with mimicking
surface plasmons (MSPs); ref. 28 proposed two sheet e-beams interaction within a composite sandwich structure;
ref. 29 reported three- and six-beam folded waveguide traveling-wave tube (TWT) operating at fundamental
mode; refs 30?34 presented two and three e-beams interaction with higher order mode; and ref. 35 theoretically
investigated wave coupling in multi-beam TWTs. Although strong efforts have been made and some progress has
been achieved in this aspect, an effective mechanism for the multi-beam interaction still seems to be a problem,
especially for the case of more than 5 e-beams. Nowadays, the successful exploration of the plasmonic crystal36?38
may lead to a bright perspective of multi-beam THz radiation sources.
In ref. 16, we have proposed the interaction between a square-shaped e-beam with guiding wave mode in
multiple stacked layers with single sub-wavelength holes (MSLS). The most important is that the MSLS can be can
be integrated to construct a plasmonic crystal-like structure that can support multi-beam interaction. Moreover,
the coupling of the electromagnetic fields may bring an enhancement of the interaction. Therefore, in this paper,
we have proposed an efficient way to generate THz wave from the multi-beam interaction in such plasmonic
The plasmonic crystal that made of three-dimensional hole-array layers (3DHA) can support MSP waves which
give the possibility of electron beam?MSP interaction and can also provide holes array to act as multi-beam
channels. Therefore, multi-beams (9-beams) excitation within such structure which could lead to middle and high output
power THz radiation has been studied in detail. The results show that such radiation source system leads to a
significant improvement with higher efficiency and lower starting current density than traditional e-beam-driven sources.
The model and electromagnetic coupling mode. The 3DHA structure is made of multiple stacked
layers with 3 ? 3 subwavelength holes array. Figure?1(a) illustrates two periodic units, and each periodic unit is
composed of two different hole-layers. One of them is with a large hole and the other is with uniformly
distributed 3 ? 3 smaller holes array. Each layer can be fabricated separately with metal such as copper. Then, several
periodic units are assembled to form the 3DHA structure (Fig.?1(b)). Figure?1(c) demonstrates a 3-D view of
the whole design of this 3DHA THz source. A direct-current (DC) e-beam is extracted from the cathode to the
anode on which centered 3 ? 3 holes array is constructed. Some electrons are intercepted by the anode while the
others pass through the 3 ? 3 holes array on it to form 3 ? 3 multi-beam array and then pass through the 3DHA as
shown in Fig.?1(c,e). The cross-sectional and longitudinal views of this structure with multi-beam trajectories and
dimensional parameters are shown in Fig.?1(d,e), respectively. It can be found that each hole of the 3DHA acts as
an e-beam channel where the injected e-beam passes through and interacts with the MSP wave in the structure.
As we know, for the coherent radiation from the beam?wave interaction, the field intensity and distribution in
the structure are key factors. Firstly, the EM field distribution in the 3DHA has been investigated by applying the
finite-integral-technique (FIT) eigenmode solver in CST Microwave Studio39.
Figure?2 demonstrates that the field distributions in different hole-array structures, where the boundary
condition is perfect electric conductor (PEC). For the 1-hole structure in Fig.?2(a), the field distribution is regular
around the structure. With the number of holes increasing, the field distribution has been changed as shown in
Fig.?2(b?d). Due to the wave coupling among the holes, the distortion of the field takes place. On the other hand,
in the longitudinal section, the contour map of the field distribution demonstrates that the mode in the 3DHA
has the same EM characteristics of surface plasmons. However, due to the coupling in the center, the mode is not
an evanescent wave so that this mode is just a mimicking surface plasmon wave.
The dispersion relation further shows the EM characteristics of this mode. It can be found from Fig.?3 that
with the number of holes decreasing, the upper and cutoff frequencies increase and the dispersion passband
becomes narrower. It should also be noted that, since the wave can be coupled through the holes array, 1st spatial
harmonics of the dispersion curves in 3 ? 3 hole-array structures are backward waves while it is forward wave for
the 1-hole structure.
Moreover, by comparing the contour map of the field in Fig.?2, it is shown that the coupling has enhanced
the field intensity. Next, we have undertaken a comparison of amplitude of the longitudinal electric field (Ez)
among the modes in the 3DHA, 5-hole, 3-hole, and 1-hole structures under PEC boundary condition by a 3D
finite-difference time-domain (FDTD) simulation40. From the comparison result shown in Fig.?4, it can be found
that the field intensities of the mode in the 3DHA are much stronger than those in the rest structures. As we know,
in the beam?wave interaction, the intensity of Ez at the e-beam location determines the interaction efficiency and
radiation intensity. Thus, it can be expected that the multiple beam?MSP wave interaction in the 3DHA structure
may be quite favorable.
Multi-beam interaction in 3DHA. We now analyze the multi-beam excitation and interaction with such
mode in 3DHA system. First of all, when the longitudinal direct-current (DC) e-beam is injected in the
modulation area, the fundamental mode of the structure will be excited. The synchronization and interaction occurs
when the phase velocity of the mode matches the velocity of the e-beam. During the interaction, the DC e-beams
exchange energy with the mode so the velocity and density of the DC e-beams will be modulated and the DC
e-beams be bunched. Figure?3 illustrates the mechanism of the interaction. The synchronization condition is
fulfilled kz = ?/vz, where vz is the beam velocity. The intersection between the e-beam line and the dispersion
noted that one period of this structure is composed of two layers, the one is with a large hole and the other is
with 3 ? 3 holes array. Therefore, in the 2-beam interaction shown in Fig.?6(b), when the beams pass the larger
hole-layer, they meet with each other face to face. Then the space charge waves of both e-beams couple with each
other through the hole so that the field intensity has been improved. It can be observed that at the border between
the two beams, the field has enhanced significantly. With the number of e-beam increased, the coupling intensity
is enhanced. For the 3-beam and 5-beam interaction, the Fig.?6(c,d) demonstrated that hence the center beam
couple with beside beams the field intensity at the edge becomes larger and the size of the strong field location
also has been enlarged. As a result, as shown in Fig.?6(e), due to the strong coupling among the 9-beam, the field
intensity become much higher and such field covers larger region.
Moreover, the space charge wave in the e-beam directly corresponds to the modulation and efficiency. Thus,
in order to further illustrate the role of coupling in the multi-beams?3DHA interaction, different number of
holes and e-beams interaction have been applied in the simulation as shown in Fig.?7. It is clear that with the
beam-number decreasing the modulation depth is becoming smaller. Such results show that the coupling among
e-beams can enhance the interaction efficiency to improve the modulation depth.
It is known that the coherent radiation requires high current density (generally > 30 A/cm2) for
the VEDs in THz frequency band11, which is a key factor limiting developments of the e-beam-driven
THz oscillator-sources. In this radiation system, the starting current density is considerably low.
In a 50-period 3DHA structure, fixing the beam energy at 50 keV, we sweep the beam current
density. The optimized simulation results are shown as black squares in Fig.? 7. The region between the
threshold and saturation points is the linear growing region where the radiation intensity from the
interaction linearly increases with the current density. The starting current density is only 5 A/cm2,
which is a fairly low value for THz radiation sources, and the saturation point is about 65 A/cm2.
Besides, we also obtained the optimized radiation intensities as a function of the beam current density in the
5-hole (5-beam) and 3-hole (3-beam) cases, which are respectively illustrated as red circle and blue triangle in
Fig.?8. It can be found that the threshold and saturation current density decrease with the number of e-beams
increases, which could be considered as the coupling among the multi-beams could enhance the interaction
coupling impedance so that the starting current can be reduced.
Next, the output structure has been studied. As shown in Fig.?9(a,b) and Fig.?9(c), for this radiation system the
T-coupler waveguide has been applied to output the radiation. The output window is just a standard waveguide
port which can connect with an antenna to emit the THz beam. The contour map of the output field is illustrated
in Fig.?9(d) and (e). It is clearly that the fundamental mode TE01 could be observed.
Moreover, for this structure, the simpler fabrication procedure could be easier than traditional gratings. In
general, grating, bi-grating and so on are used the entirely machined technique and the parameters of such
structures are always very small at THz, so the microfabrication techniques such as lithographie, galvanoformung und
abformung process (LIGA) and deep reactive ion etching (DRIE) have been used. For this structure, it can be
made of stacked multiple planar sub-wavelength holes layers. Thus, we can fabricate the holes layers separately
and assemble them together to construct the whole structure.
In summary, generation of coherent terahertz radiation from an interaction between multi-electron beam
with the coupling mode in a plasmonic crystal-like structure (three-dimensional hole-array structure) which
is made of multiple stacked layers with 3 ? 3 subwavelength holes array is proposed in this paper. The results
show that such multi-beam interaction mechanism can enhance the modulation depth and reduce the current
density. Due to multi-beam working, this mechanism can generate high power THz radiation. Moreover, this
plasmonic crystal-like structure could provide larger size with more number of holes so that more than 3 ? 3
multi-beam array can be applied in this radiation source. At last, this concept of multi-beam excitation within
three-dimensional hole-array structure could provide a promising way to develop the compact THz radiation
sources with middle or high power.
Y.Z. presented the idea, guided the research work and wrote the manuscript, Y.Z., G.Y. and G.J. carried out the
computer simulations, Y.Z. and Z.Y. discussed the research and revised the manuscript.
Competing financial interests: The authors declare no competing financial interests.
How to cite this article: Zhang, Y. et al. Coherent Terahertz Radiation from Multiple Electron Beams Excitation
within a Plasmonic Crystal-like structure. Sci. Rep. 7, 41116; doi: 10.1038/srep41116 (2017).
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This work is supported by National Natural Science Foundation of China under Contract Nos 61270011 , 91438118 , and 61501094, National Key Basic Research Program of China under Contract No. 2014CB339806, Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No.
NECT_13_0100) and Sichuan Youth Science and Technology Foundation No. 2014JQ0013.
? The Author(s) 2017