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Enhanced coherent terahertz Smith-Purcell superradiation excited by two electron-beams

Yaxin Zhang and Liang Dong

Open Access Open Access

Abstract

This paper presents the studies on the enhanced coherent THz Smith-Purcell superradiation excited by two pre-bunched electron beams that pass through the 1-D sub-wavelength holes array. The Smith-Purcell superradiation has been clearly observed. The radiation emitting out from the system has the radiation angle matching the 2nd harmonic frequency component of the pre-bunched electron beams. The results show that the two electron beams can be coupled with each other through the holes array so that the intensity of the radiated field has been enhanced about twice higher than that excited by one electron beam. Consequently superradiation at the frequency of 0.62 THz can be generated with 20A/cm2 current density of electron beam based on above mechanism. The advantages of low injection current density and 2nd harmonic radiation promise the potential applications in the development of electron-beam driven THz sources.

©2012 Optical Society of America

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Figures (8)
Fig. 1
Fig. 1 (a) The 3-D geometry. (b) the 2-D sketch map.(c) the Smith-Purcell radiation when two electron bunches pass close over the holes array.(d) the comparison of theoretical SP law and simulation results.

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Fig. 2
Fig. 2 (a) the structure of bi-grating (b) dispersion Brillouin diagram: the blue line is the calculated dispersion curve of the bi-grating, the red cross line is the beam line with beam energy 50kV and the point P is the interaction point of the dispersion curve. The area between P1 and P2 is the radiation area of the SHA.

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Fig. 3
Fig. 3 Simulation of interaction in bi-grating structure.(a)The e-beams phasespace in bi-grating. (b)The time evolution of the electric field Ez(t). (c)The associated FFT of the Ez(t). (d)The contour map of Ez.

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Fig. 4
Fig. 4 The simulation model of superradiation excited by ideal periodical electron bunches

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Fig. 5
Fig. 5 The simulation results of ideal electron beam bunches superradiation.(a)Distribution of superradiation frequency and it’s Bx(t) field amplitude.(b)Contour map when the periodic electron bunches passing over the 1-D holes array.(c)Time evolution of the Ez(t) field at the radiation angle and associated FFT.

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Fig. 6
Fig. 6 The simulation model of superradiation in the whole system

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Fig. 7
Fig. 7 The simulation results of two pre-bunched electron beams superradiation. (a).The process of two well bunched electron beam passing over the 1-D holes array. (b)The contour map at 4.245ns when bunched electron beam passing over the holes array.(c)Time evolution of the Ey(t) field at the radiation angle and associated FFT.

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Fig. 8
Fig. 8 (a) the comparison of the intensites of Ez(t) field excited by one pre-bunched beam and two beams (b) contour map of the field in the holes array (c) the frequency spectrum of radiation excited by one beam (d) the frequency spectrum of radiation excited by two beams

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Tables (1)

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Table 1 Main parameters of the simulation

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Equations (5)

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λ=L/| n |(1/β−cosθ)
E z Ι =Q Ι sin k cx ( A 2 + D 1 −x) sin k cx ( A 2 + D 1 ) sin( k y y); H y Ι = jωε k cx Q Ι cos k cx ( A 2 + D 1 −x) sin k cx ( A 2 + D 1 ) sin( k y y)
{ E z ΙΙ = ∑ n=−∞ ∞ [ Q ΙΙ n cosh( k xn x)+ P ΙΙ n sinh( k xn x) ]sin( k y y) e −j k zn z H y ΙΙ = ∑ n=−∞ ∞ jωε k xn k 2 zn − k 2 [ Q ΙΙ n sinh( k xn x)+ P ΙΙ n cosh( k xn x) ]sin( k y y) e −j k zn z
E z ΙΙΙ =Q ΙΙΙ sin k cx ( A 2 + D 1 +x) sin k cx ( A 2 + D 1 ) sin( k y y); H y ΙΙΙ =- jωε k cx Q ΙΙΙ cos k cx ( A 2 + D 1 +x) sin k cx ( A 2 + D 1 ) sin( k y y)
cot( k 0 D 1 ) k 0 = W L 1 ∑ n=−∞ ∞ sin c 2 ( k zn W 2 ) k yn k 2 zn − k 2 0 tanh( k yn A 2 )
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