CN113872021A - Dual-band terahertz wave generating device and method - Google Patents
Dual-band terahertz wave generating device and method Download PDFInfo
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Abstract
The invention relates to a double-frequency-band terahertz wave generating device and method. The device includes: an emission cathode, a collector and a metal grating; the emission cathode and the collector are arranged above the metal grating, the emission cathode can emit electron beams, and the collector can receive the electron beams; one side of the metal grating, which is close to the emission cathode and the collector, is provided with N first rectangular grooves and N second rectangular grooves, the depths of the first rectangular grooves and the second rectangular grooves are different, and the first rectangular grooves and the second rectangular grooves are periodically arranged on the metal grating; when the working voltage of the electron beam is larger than the maximum cut-off working voltage in the metal grating, a dual-band surface plasmon can be excited, so that terahertz waves are generated by the interaction of the electron beam and the surface plasmon. The scheme provided by the invention can realize high-efficiency excitation of the dual-band terahertz wave and has the advantage of broadband work.
Description
Technical Field
The invention relates to the technical field of terahertz waves, in particular to a dual-band terahertz wave generating device and method.
Background
Surface Plasmon Polaritons (SPP) are a special optical mode existing at the interface between metal and medium, but as the frequency shifts down to the terahertz and microwave bands, the local adhesion of Surface plasmons on the Surface of uniform metal becomes poor due to the quasi-ideal conductor properties of metal. The local attachment of the surface plasmon can be strengthened by periodically slotting or perforating on the metal surface, and the equivalent progressive frequency can be randomly adjusted through periodic structural parameters, so the surface plasmon is also called as artificial surface plasmon.
In recent years, the artificial surface plasmon of the periodic metal structure has a wide application prospect in the fields of terahertz integrated waveguides, couplers, power splitters, slow light systems, terahertz radiators and the like due to excellent electromagnetic properties such as strong near-field coupling, sub-wavelength locality and enhancement of substance-light interaction.
In particular, terahertz waves generated by the interaction of an external light source or an electron beam with surface plasmons of periodic metal gratings are of widespread interest, such as terahertz cerenkov lasers of sub-wavelength periodic metal gratings (s.kim, i.baek, r.bhattachara, et al, adv.opt.mater, 2018,1800041), periodic metal grating terahertz generation devices based on infrared lasers (m.fang, k.niu, z.huang, et al, opt.express,2018,26(11), 14241-one 14250), terahertz radiation sources based on electron beam excitation of periodic metal gratings (y.liu, l.kong, c.du, trae.s.plasma sci, 2016,44(6), 930-one 937) (j.zhu, c.du, l.bao, et al, New j.20121, 021, et al).
However, the above-mentioned terahertz generation device has low conversion efficiency by infrared laser injection, and the electron beam threshold required for generating terahertz radiation by free laser excited by an electron beam is large, and the adopted periodic metal structure has a single depth, and the surface plasmon can only work in a single frequency band, so that the generated terahertz radiation also works in a single frequency band, and the bandwidth is relatively narrow.
Disclosure of Invention
The invention provides a double-frequency-band terahertz wave generating device and method, which are used for realizing high-efficiency excitation of double-frequency-band terahertz waves and have the advantage of broadband work.
In a first aspect, an embodiment of the present invention provides a dual-band terahertz wave generating device, including:
an emission cathode, a collector and a metal grating;
the emission cathode and the collector are arranged above the metal grating, the emission cathode can emit electron beams, and the collector can receive the electron beams;
one side of the metal grating, which is close to the emission cathode and the collector, is provided with N first rectangular grooves and N second rectangular grooves, the depths of the first rectangular grooves and the second rectangular grooves are different, and the first rectangular grooves and the second rectangular grooves are periodically arranged on the metal grating;
when the working voltage of the electron beam is larger than the maximum cut-off working voltage in the metal grating, a dual-band surface plasmon can be excited, so that terahertz waves are generated by the interaction of the electron beam and the surface plasmon.
In one possible design, the height of the electron beam from the surface of the metal grating on the side close to the emission cathode and the collector is determined by the excitation power of the excited surface plasmons.
In one possible design, the metal grating is made of the desired metal copper or iron.
In one possible design, the operating voltage of the electron beam is greater than the maximum cut-off operating voltage in the metal grating when the phase velocity of the electron beam satisfies the following relationship:
ve>fcmax/kz
ve＝βc
β＝(1-(1+γ)-2)0.5
γ＝U/U0
U0＝5.11×105V
in the formula, veIs the phase velocity of the electron beam, fcmaxIs the maximum cut-off frequency, k, in the metal gratingzAnd c is a normalized wave vector corresponding to the maximum cut-off frequency in the metal grating, c is the free space light velocity, and U is the working voltage of the electron beam.
In one possible design, the maximum cut-off frequency in the metal grating is determined by:
fcmax＝c/4hmin
in the formula, hminIs the minimum depth in the first and second rectangular grooves.
In a second aspect, an embodiment of the present invention provides a dual-band terahertz wave generating method, including:
the metal grating is provided with N first rectangular grooves and N second rectangular grooves; the first rectangular groove and the second rectangular groove are different in depth, and are arranged on the metal grating periodically;
arranging an emission cathode and a collector at one side of the metal grating provided with the rectangular groove so as to transmit electron beams between the emission cathode and the collector;
and setting the working voltage of the electron beam to be greater than the maximum cut-off working voltage in the metal grating so as to excite a dual-band surface plasmon on one side of the metal grating provided with the rectangular groove, and generating terahertz waves by utilizing the interaction of the electron beam and the surface plasmon.
In one possible design, the height of the electron beam from the surface of the metal grating on the side close to the emission cathode and the collector is determined by the excitation power of the excited surface plasmons.
In one possible design, the metal grating is made of the desired metal copper or iron.
In one possible design, the operating voltage of the electron beam is greater than the maximum cut-off operating voltage in the metal grating when the phase velocity of the electron beam satisfies the following relationship:
ve>fcmax/kz
ve＝βc
β＝(1-(1+γ)-2)0.5
γ＝U/U0
U0＝5.11×105V
in the formula, veIs the phase velocity of the electron beam, fcmaxIs the maximum cut-off frequency, k, in the metal gratingzAnd c is a normalized wave vector corresponding to the maximum cut-off frequency in the metal grating, c is the free space light velocity, and U is the working voltage of the electron beam.
In one possible design, the maximum cut-off frequency in the metal grating is determined by:
fcmax＝c/4hmin
in the formula, hminIs the minimum depth in the first and second rectangular grooves.
According to the scheme, the double-band terahertz wave generating device and the method can realize the transmission of the surface plasmons of the double bands through the slotted structures at different depths, and realize the excitation of the double-band terahertz waves through the high-efficiency interaction of the surface plasmons excited on the surface of the metal grating by reasonably setting the working voltage of the electron beam and the maximum cut-off working voltage in the metal grating and through the same electron beam, meanwhile, the required energy of the emitted electron beam is small, the near-field coupling is strong, the excitation efficiency is high, and compared with the excitation through the single-period metal grating, the double-band terahertz wave generating device and the method have the advantages of double-band and wide-bandwidth working.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained based on these drawings without creative efforts.
Fig. 1 is a schematic structural diagram of a metal grating according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a dual-band terahertz wave generating device according to an embodiment of the present invention;
FIG. 3 is a graph illustrating the transmission characteristics of a single periodic metal grating at different depths according to an embodiment of the present invention;
FIG. 4 is a dispersion relation diagram of dual-band surface plasmons of an electron beam excited metal grating;
FIG. 5 is a graph of the mode-output power spectrum of an electron beam excited metal grating;
FIG. 6 is a graph of the mode two output power spectrum of an electron beam excited metal grating.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer and more complete, the technical solutions in the embodiments of the present invention will be described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention, and based on the embodiments of the present invention, all other embodiments obtained by a person of ordinary skill in the art without creative efforts belong to the scope of the present invention.
In the prior art, in order to overcome the defects that an optical source or an electronic source is adopted to generate surface plasmons at the present, the energy of an excitation source required by a terahertz frequency band is large, the conversion efficiency is low, or the working bandwidth is narrow and the terahertz wave generating device works in a single mode, the invention provides a composite periodic metal grating with depth modulation and a dual-band terahertz wave generating device for efficiently exciting the surface plasmons by adopting an electron beam near field.
Fig. 1 is a schematic structural diagram of a metal grating according to an embodiment of the present invention; fig. 2 is a schematic structural diagram of a dual-band terahertz wave generating device according to an embodiment of the present invention. As shown in fig. 1 and 2, an embodiment of the present invention provides a dual-band terahertz wave generating device, including: an emission cathode 1, a collector 3 and a metal grating 4;
the emitting cathode 1 and the collector 3 are arranged above the metal grating 4, the emitting cathode 1 can emit an electron beam 2, and the collector 3 can receive the electron beam 2;
one side of the metal grating 4 close to the emission cathode 1 and the collector 3 is provided with N first rectangular grooves C1 and N second rectangular grooves C2, the depths of the first rectangular grooves C1 and the second rectangular grooves C2 are different, and the first rectangular grooves C1 and the second rectangular grooves C2 are arranged on the metal grating 4 periodically;
when the working voltage of the electron beam 2 is greater than the maximum cut-off working voltage in the metal grating 4, a dual-band surface plasmon can be excited to generate terahertz waves by using the interaction between the electron beam 2 and the surface plasmon.
In the embodiment of the invention, the transmission of the dual-band surface plasmons can be realized through the slotted structures (namely the first rectangular groove C1 and the second rectangular groove C2) with different depths, and the excitation of the dual-band terahertz waves can be realized through the high-efficiency interaction of the surface plasmons excited on the surface of the metal grating by reasonably setting the working voltage of the electron beam and the maximum cut-off working voltage in the metal grating and through the same electron beam, meanwhile, the required emitted electron beam energy is small, the near-field coupling is strong, the excitation efficiency is high, and compared with the excitation through a single-period metal grating, the dual-band terahertz wave surface plasmon polaritons have the advantages of dual-band and wide-band width work.
Referring to fig. 1 and 2, in the metal structure with the depth H, the composite periodic metal grating structure is etched with two different depths H1 (H1)<H) And h2(h 2)<H) The widths of the two rectangular grooves are respectively a1 and a2, and the repetition period is respectively d1(d 1)>a1) And d2(d 2)>a2) In that respect The composite period metal grating structure transmits two different artificial surface plasmon modes on an x-z surface along the z direction, and independent control can be realized through the sizes of the parameters of respective slotting structures. When the two types of slotting depths are equal, namely h 1-h 2-h, the two types of slotting depths return to a single-period metal grating, and only one type of artificial surface plasmon mode with the plasma cutoff frequency fc-c/4 h (c is the free space light velocity) is transmitted; when the two types of slotting depths are not equal, namely h1 is not equal to h2, the composite periodic metal grating transmits two types of artificial plasmons in different modes, and the cutoff frequencies of the plasmon modes are respectively fc1C/4h1 and fc2C/4h2, determined by different slot depths h1 and h2, respectively, and when h1<h2, the cut-off frequencies of the artificial surface plasmon modes I and II supported by the composite periodic metal grating are respectively fc2C/4h2 and fc1＝c/4h1(fc2<fc1) When h1>h2, the cut-off frequencies of the artificial surface plasmon modes I and II supported by the composite periodic metal grating are respectively fc1C/4h1 and fc2＝c/4h2(fc2>fc1). Herein, the cutoff frequency of mode two is defined as the maximum cutoff frequency.
As shown in fig. 3, the first mode and the second mode of the artificial surface plasmon transmitted by the composite periodic metal grating of the present invention can be determined by the depth, width and period size of the respective slots C1 and C2, respectively, and the transmission amplitude shows the superposition of two single uniform periodic metal grating stop bands along with the distribution of frequency. When the composite period metal grating only has one etched notch C1, the transmission amplitude changes with the frequency to be f at the center frequencyc1A nearby stop band; when the composite period metal grating only has one etched notch C2, the transmission amplitude changes with the frequency to be f at the center frequencyc2A nearby stop band. When the composite period metal grating has two slots with different depths, the transmission amplitude changes with the frequency to be f at the same timec1And fc2The size of the stop band interval of the adjacent double stop bands is determined by the difference between the etching notch depth sizes h1 and h2, when the difference between h1 and h2 is not large, the frequency interval between the double stop bands is smaller, and when the difference between h1 and h2 is large, the frequency interval between the double stop bands is also larger.
In one embodiment of the present invention, the height of the electron beam 2 from the surface of the metal grating 4 on the side close to the emission cathode 1 and the collector 3 is determined by the excitation power of the excited surface plasmon.
In one embodiment of the present invention, the metal grating 4 is made of copper or iron, which is an ideal metal.
In one embodiment of the present invention, when the phase velocity of the electron beam 2 satisfies the following relationship, the operating voltage of the electron beam 2 is greater than the maximum cut-off operating voltage in the metal grating 4:
ve>fcmax/kz
ve＝βc
β＝(1-(1+γ)-2)0.5
γ＝U/U0
U0＝5.11×105V
in the formula, veIs the phase velocity, f, of the electron beam 2cmaxIs the maximum cut-off frequency, k, in the metal grating 4zIs the normalized wave vector corresponding to the maximum cut-off frequency in the metal grating 4, c is the free space light velocity, and U is the working voltage of the electron beam 2.
In the embodiment of the invention, the same electron beam is emitted from the emitting cathode at a distance g from the surface of the grating structure (namely the height of the electron beam 2 from the surface of the metal grating 4 close to one side of the emitting cathode 1 and the collecting electrode 3), surface plasmons are excited on the grooved surface through the electron beam, and when the working voltage U of the electron beam is greater than the cut-off working voltage (namely f) of the composite period metal grating mode twocmax) And when the surface plasmon polaritons are excited, the surface plasmon polaritons of the double frequency bands can be effectively excited and amplified at the same time. In order to determine that the operating voltage of the electron beam 2 is greater than the maximum cut-off operating voltage in the metal grating 4, an indirect determination of the phase velocity of the electron beam 2 may be used, i.e., the phase velocity of the electron beam 2 needs to satisfy the above formula.
In addition, the distance g of the electron beam from the surface of the composite periodic metal grating can be properly selected according to the intensity of the generated surface plasmon, and generally, the power of the generated surface plasmon is increased and then decreased along with the gradual increase of g. When the dispersions of the electron beam and the composite period metal grating are matched, the energy of the electron beam is transferred to the surface wave, so that the energy of the electron beam is gradually reduced, the rest energy of the electron beam is recovered by a collector at the tail end of the interaction structure, the generated dual-band surface plasmon is transmitted along the surface of the structure, and the generated surface wave is radiated to the free space through the specific coupling structure for transmission. In order to effectively generate the dual-band surface plasmons, the length L of the composite periodic metal grating should be properly selected, which can be optimized simultaneously with the height g of the electron beam to maximize the output, generally, when the height g of the electron beam reaches the optimum, the electric field energy distribution of the surface wave is in the optimum interaction state with the electron beam, under such a condition, the interaction length of the composite periodic metal grating can be properly selected to ensure that the electron beam is transmitted within the shortest distance as possible without divergence, and the energy exchanged with the surface plasmons also reaches the maximum.
The output power frequency spectrum of the dual-band terahertz wave generating device can be obtained through an analog simulation test, the output peak power of the mode I is slightly larger than the peak power of a surface plasmon excited by the same electron beam for a single period of metal grating, and the frequency at the peak power is shifted upwards; the output peak power of the mode II is slightly smaller than the peak power of the surface plasmon excited by the same electron beam of the single-period metal grating, and the frequency at the peak power is shifted downwards.
In one embodiment of the present invention, the maximum cut-off frequency in the metal grating 4 is determined by:
fcmax＝c/4hmin
in the formula, hminIs the minimum depth in the first rectangular groove C1 and the second rectangular groove C2.
The above solution is exemplified below.
The structure diagram of the composite periodic metal grating is shown in figure 1, two rectangular grooves C1 and C2 with different depths H1 and H2 are etched in metal with the depth H, the widths of the grooves are a1 and a2, the arrangement periods along the z axis are d1 and d2, transmitted dual-waveband surface plasmon polaritons are attached to the x-z surface, and the metal structure is represented by ideal metal copper or iron. Giving a terahertz frequency band dual-band surface plasmon polariton transmission waveguide parameter: h1 ═ 66 μm, h2 ═ 86 μm, a1 ═ a2 ═ 15 μm, and d1 ═ d2 ═ 60 μm. The variation of the transmission coefficient with frequency in one period is shown by the solid line in FIG. 3, which has two cut-off frequencies fc1C/4h 1-0.95 THz and fc2The variation of the transmission coefficient of a single period metal grating with different depths h1 and h2, respectively, is also given as c/4h 2-0.76 THz stop band superposition.
As shown in fig. 2, the dual-band terahertz wave generating device includes an emitting cathode 1, a collector 3 and a composite periodic metal grating 4, wherein the distance g between an electron beam and the surface of the grating is, and the length of the metal grating is L. Table supported by given above composite period metal grating parameterThe first and second surface plasmon modes are, as shown by the circular and rectangular curves in fig. 4, set such that the excited surface wave is below the respective cutoff frequencies by setting the electron beam voltage, and the frequencies of the excited surface plasmon modes are the intersections of the electron beam dispersion and the respective modes, and are f2And f1. After the parameters of the composite period metal grating and the electron beam are given, the power spectrum of the dual-band terahertz surface plasmon excited by the composite period metal grating and the electron beam can be obtained. Through the interaction of an electron beam with a voltage of U35 kV and a current of 0.5A with the above composite period metal grating, the distance g between the electron beam and the grating surface is 3.75 μm, and the length L of the metal grating is 3.8mm, the power spectrums of the mode one and the mode two of the dual-band terahertz surface plasmon polariton emitter are obtained as shown in fig. 5 and 6, and it can be seen that the center frequencies of the output power spectrums of the mode one and the mode two are respectively f2And f1Peak power mode one is greater than mode two.
In summary, by designing two periodic metal grating composite structures with different depths h1 and h2, the same electron beam simultaneously excites the first mode and the second mode of the composite periodic metal grating1And f2The surface plasmons near the two frequency points are excited in the near field, so that the near field enhancement effect of the two frequency band plasmon modes can be simultaneously utilized, the high-efficiency excitation of the double frequency bands can be simultaneously realized, and the broadband dual-mode surface plasmon polariton device also has the advantage of broadband work. The principle is verified in the terahertz frequency band, a dual-band terahertz generating device with a composite period metal grating structure and electron beam injection parameters working near the frequency of 0.76THz and 0.95THz is reasonably designed, and a dual-band surface plasmon output power spectrum is obtained through a particle simulation test.
An embodiment of the present invention further provides a dual-band terahertz wave generating method, including:
the metal grating is provided with N first rectangular grooves and N second rectangular grooves; the first rectangular groove and the second rectangular groove are different in depth and are periodically arranged on the metal grating;
an emission cathode and a collector are arranged on one side of the metal grating, which is provided with the rectangular groove, so that electron beams are transmitted between the emission cathode and the collector;
the working voltage of the electron beam is set to be larger than the maximum cut-off working voltage in the metal grating, so that double-frequency-band surface plasmons are excited at one side of the metal grating, which is provided with the rectangular groove, and terahertz waves are generated by utilizing the interaction of the electron beam and the surface plasmons.
In one embodiment of the present invention, the height of the electron beam from the surface of the metal grating on the side close to the emission cathode and the collector is determined by the excitation power of the excited surface plasmon.
In one embodiment of the invention, the metal grating is made of the desired metal copper or iron.
In one embodiment of the present invention, when the phase velocity of the electron beam satisfies the following relationship, the operating voltage of the electron beam is greater than the maximum cut-off operating voltage in the metal grating:
ve>fcmax/kz
ve＝βc
β＝(1-(1+γ)-2)0.5
γ＝U/U0
U0＝5.11×105V
in the formula, veIs the phase velocity of the electron beam, fcmaxIs the maximum cut-off frequency, k, in the metal gratingzIs the normalized wave vector corresponding to the maximum cut-off frequency in the metal grating, c is the free space light velocity, and U is the working voltage of the electron beam.
In one embodiment of the present invention, the maximum cut-off frequency in the metal grating is determined by:
fcmax＝c/4hmin
in the formula, hminIs the minimum depth in the first rectangular groove and the second rectangular groove.
It can be understood that the dual-band terahertz wave generation method and the dual-band terahertz wave generation device are based on the same inventive concept, and therefore the two methods have the same beneficial effects, and the effects of the dual-band terahertz wave generation method are not repeated herein.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other similar elements in a process, method, article, or apparatus that comprises the element.
Finally, it is to be noted that: the above description is only a preferred embodiment of the present invention, and is only used to illustrate the technical solutions of the present invention, and not to limit the protection scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (10)
1. A dual-band terahertz wave generating device, comprising: an emission cathode, a collector and a metal grating;
the emission cathode and the collector are arranged above the metal grating, the emission cathode can emit electron beams, and the collector can receive the electron beams;
one side of the metal grating, which is close to the emission cathode and the collector, is provided with N first rectangular grooves and N second rectangular grooves, the depths of the first rectangular grooves and the second rectangular grooves are different, and the first rectangular grooves and the second rectangular grooves are periodically arranged on the metal grating;
when the working voltage of the electron beam is larger than the maximum cut-off working voltage in the metal grating, a dual-band surface plasmon can be excited, so that terahertz waves are generated by the interaction of the electron beam and the surface plasmon.
2. The dual-band terahertz wave generating device according to claim 1, wherein a height of the electron beam from a surface of the metal grating on a side close to the emission cathode and the collector is determined by excitation power of the excited surface plasmon.
3. The dual-band terahertz wave generating device according to claim 1, wherein the metal grating is made of an ideal metal of copper or iron.
4. The dual-band terahertz wave generating device according to any one of claims 1 to 3, wherein an operating voltage of the electron beam is larger than a maximum cutoff operating voltage in the metal grating when a phase velocity of the electron beam satisfies the following relationship:
ve>fcmax/kz
ve＝βc
β＝(1-(1+γ)-2)0.5
γ＝U/U0
U0＝5.11×105V
in the formula, veIs the phase velocity of the electron beam, fcmaxIs the maximum cut-off frequency, k, in the metal gratingzAnd c is a normalized wave vector corresponding to the maximum cut-off frequency in the metal grating, c is the free space light velocity, and U is the working voltage of the electron beam.
5. The dual-band terahertz wave generating device according to claim 4, wherein a maximum cutoff frequency in the metal grating is determined by:
fcmax＝c/4hmin
in the formula, hminIn the first rectangular groove and the second rectangular grooveA minimum depth.
6. A method for generating a dual-band terahertz wave, comprising:
the metal grating is provided with N first rectangular grooves and N second rectangular grooves; the first rectangular groove and the second rectangular groove are different in depth, and are arranged on the metal grating periodically;
arranging an emission cathode and a collector at one side of the metal grating provided with the rectangular groove so as to transmit electron beams between the emission cathode and the collector;
and setting the working voltage of the electron beam to be greater than the maximum cut-off working voltage in the metal grating so as to excite a dual-band surface plasmon on one side of the metal grating provided with the rectangular groove, and generating terahertz waves by utilizing the interaction of the electron beam and the surface plasmon.
7. The dual-band terahertz wave generating method according to claim 6, wherein a height of the electron beam from a surface of the metal grating on a side close to the emission cathode and the collector is determined by excitation power of the excited surface plasmon.
8. The dual-band terahertz wave generating method according to claim 6, wherein the metal grating is made of an ideal metal of copper or iron.
9. The dual-band terahertz wave generating method according to any one of claims 6 to 8, wherein an operating voltage of the electron beam is larger than a maximum cutoff operating voltage in the metal grating when a phase velocity of the electron beam satisfies a relationship:
ve>fcmax/kz
ve＝βc
β＝(1-(1+γ)-2)0.5
γ＝U/U0
U0＝5.11×105V
in the formula, veIs the phase velocity of the electron beam, fcmaxIs the maximum cut-off frequency, k, in the metal gratingzAnd c is a normalized wave vector corresponding to the maximum cut-off frequency in the metal grating, c is the free space light velocity, and U is the working voltage of the electron beam.
10. The dual-band terahertz wave generating method according to claim 9, wherein a maximum cutoff frequency in the metal grating is determined by:
fcmax＝c/4hmin
in the formula, hminIs the minimum depth in the first and second rectangular grooves.
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