Quasi-B-mode generated by high-frequency gravitational waves and corresponding perturbative photon fluxes

Interaction of very low-frequency primordial(relic) gravitational waves(GWs) to cosmic microwave background(CMB) can generate B-mode polarization. Here, for the first time we point out that the electromagnetic(EM) response to high-frequency GWs(HFGWs) would produce quasi-B-mode distribution of the perturbative photon fluxes, and study the duality and high complementarity between such two B-modes. Based on this quasi-B-mode in HFGWs, it is shown that the distinguishing and observing of HFGWs from the braneworld would be quite possible due to their large amplitude, higher frequency and very different physical behaviors between the perturbative photon fluxes and background photons, and the measurement of relic HFGWs may also be possible though face to enormous challenge.


I. INTRODUCTION
On 11th Feb 2016 and June 2016, LIGO reported two very important evidences [1,2] of GW detection. One of them is the GW having amplitude of h ∼ 10 −21 and frequency of ∼ 35 to 350Hz. Another one is the GW with amplitude of h ∼ 10 −22 and frequency of ∼ 35 to 450Hz, and they are all produced by black hole mergers, which come from distance of 1.3 and 1.4 billion light-years from the Earth, respectively. Obviously, such results are very big encouraging to GW project, and they should push forward research of GW projects, including observation and detection for GWs in different frequency bands, different kinds of GWs, and in different ways. Thus, they should be highly complementary each other.
Before this, in 2014, observation of the B-mode polarization caused by primordial(relic) gravitational waves(GWs) in the cosmic microwave background(CMB) has been reported [3].
If this B-mode polarization can be completely confirmed by experimental observation, it must also be a great encouragement for detection of GWs in the very-low frequency band, and will provide a key evidence for the inflationary model.
On the other hand, influence of cosmic dusts might swamp the signal of the B-mode polarization [4]. In addition, if strength of these primordial GWs can reach up to the value reported by the B-mode experiment, then the temperature perturbation induced by the primordial GWs should also be observed, but the Planck satellite did not observe such temperature perturbation. Therefore, further analysis to the B-mode polarization results by data of Planck satellite and other observation ways, will provide critical judgement for the B-mode polarization. However, no matter what the current result is, it should not impact the scheme of observation for B-mode effect caused by the relic GWs, but should strongly attract further attentions of scientific communities on this important phenomenon from the tensor perturbation, and in the future, it would be promising that the research works of B-mode polarization will bring us crucial constraints on the inflationary models.
It should be pointed out that almost all mainstream early universe models and inflation theories predicted primordial (relic) GWs, which have a very broad frequency band distribution. During the very early universe and the inflation epoch of the universe, since extreme small spacetime scale and huge high energy density (they are close to the Planck scale), the quantum effect would play important role and might provide important contribution to generation of the relic gravitons. Then Heisenberg principle would govern the creation and the annihilation of the particles. In this case severe quantum fluctuation would have pumped huge energy into the production of gravitons. In this period, the gravitons having huge energy correspond to extreme-high frequency.
However,the rapid expansion of the universe would have stretched the graviton wavelengths from microscopic to macroscopic length, and present values of these graviton wavelengths would be expected to be from ∼ 1cm to the cosmological scale. In other words, the frequency spectrum of the relic GWs would be from ∼ 10 −17 Hz to ∼ 10 10 Hz, roughly. Nevertheless, the spectrum densities and dimensionless amplitudes expected by different universe models and scenarios are different due to the different cosmological parameters. Moreover, string theory [5], loop quantum gravity [6] and some classical and semi-classical scenarios [7,8] also expected the HFGWs, and some of them have interesting and significant strength and properties. Frequency band of the relic GWs predicted by the ordinary inflationary models [9,10], the quintessential inflationary model [11][12][13] and the pre-big-bang model [5,14] have been extended to very high frequency range (∼ 10 8 to 10 10 Hz). Moreover, highfrequency GWs(HFGWs) expected by the braneworld senarios [15] and interaction of astrophysical plasma with intense electromagnetic(EM) radiation from high-energy astrophysical process [7] have been extended to ∼ 10 9 Hz to 10 12 Hz or higher frequency, and corresponding dimensionless amplitudes of these HFGWs might reach up to h ∼ 10 −22 to 10 −27 (see Table I) [7,15]. Besides, even high-energy physics experiments [16,17][e.g., see our previous work: Large Hadron Collider(LHC)] also predicted extremely-high frequency GWs(highenergy gravitons) [17], and their frequencies might reach up to 10 19 to 10 23 Hz, but the dimensionless amplitude may be only ∼ 10 −39 to 10 −41 . Obviously the frequencies of these HFGWs are far beyond the detection or observation range of the intermediate-frequency GWs(e.g., LIGO, GEO600, Virgo, TAMA [18][19][20][21][22], ν ∼ 1 to 10 4 Hz), the low-frequency GWs detection(e.g., LISA, BBO, DECIGO.... [23][24][25], ν ∼ 10 −7 to 1Hz),and very low-frequency GWs(ν ∼ 10 −16 to 10 −17 Hz, e.g., B-mode experiment in the CMB). Thus, detection and observation of these HFGWs need new principle and scheme. Once the HFGWs can be detectable and observable, then which will open a new information window into the cosmology and the high-energy astrophysical process, and would be highly complementary for the observation of the GWs in the intermediate-, the low-frequency and the very low-frequency bands.
It should be pointed out that the tensor perturbation of GWs is a very common prop-  [9,10] inflationary [11][12][13] [5,14] Oscillation [15] astrophysical plasma with intense EM radiation [7] Frequency bands ∼ 10 8 − 10 10 Hz ∼ 10 9 − 10 10 Hz ∼ 10 9 − 10 10 Hz ∼ 10 8 − 10 14 Hz ∼ 10 9 − 10 12 Hz erty, which can be not only expressed as B-mode polarization [3,26] in the CMB for very low-frequency relic GWs, but also quasi-B-mode distribution of perturbative photon fluxes in electromagnetic response for HFGWs. However, the duality and similarity between the B-mode of the CMB experiment for the very low frequency GWs and the quasi-B-mode of electromagnetic(EM) response for the HFGWs, almost have never been studied in the past.
In fact, these effects are all from the same physical origin: tensor perturbation of the GWs and not the density perturbation, and they would be highly complementary , not only in the observable frequency bands, but also in the displaying ways.
In this paper we shall study the similarity and duality between the B-mode polarization in the CMB for very low frequency primordial GWs and the quasi-B-mode distribution of the perturbative photon fluxes(i.e., signal photon fluxes) in the EM response for HFGWs.
It is shown that such two B-modes have a fascinating duality and strong complementarity, and distinguishing and observing of the HFGWs expected by the braneworld would be quite possible due to their large amplitude, higher frequency and very different physical behaviors between the perturbative photon fluxes and the background photon fluxes. The measurement of relic HFGWs may also be possible though it face to enormous challenge.
The plan of this paper is follows. In Sec.II we study the strength and angular distribution of the perturbative photon fluxes generated by the HFGWs expected by some typical cosmological models and high-energy astrophysical process, and discuss the duality and similarity between such two B-modes, especially their complementarity due to the same physical reason: the tensor perturbation. In Sec.III we consider displaying conditions for the HFGWs, including the quasi-B-mode experiment in the EM response for the HFGWs. In Sec.IV we discuss wave impedance and wave impedance matching to the perturbative photon fluxes and the background photon fluxes. Our brief conclusion is summarized in Sec.V.

FREQUENCY GWS
It is well known that, "monochromatic components" of the GWs propagating along the z-direction can often be written as [27] h µν = (1) For the relic GWs, A ⊕ = A(k g )/a(t), A ⊗ = A(k g )/a(t), [9,10] are the stochastic values of the amplitudes of the relic GWs in the laboratory frame of reference, ⊕ and ⊗ represent the ⊕-type and ⊗-type polarizations, and k g , ω g and a(t) are wave vector, angular frequency and the cosmology scale factor in the laboratory frame of reference, respectively. For the non-stochastic coherent GWs, A ⊕ and A ⊗ are constants.
According to Eq.(1) and electrodynamic equation in curved spacetime, the perturbative EM fields produced by the direct interaction of the incoming GW, Eq.(1), with a static magnetic fieldB (0) , can be give by [28,29](we use MKS units) , , , where ∆l is the interaction dimension between the HFGW and the static magnetic fieldB (0) , which is perpendicular to the propagating direction of the HFGW, "∧" stands for the static background magnetic field, "∼" represents time-dependent perturbative EM fields, and the superscript(0) and (1) denote the background and the first-order perturbative EM fields, respectively. Here the perturbative EM fields propagating along the negative z direction(i.e., the opposite propagation direction of the HFGW) are neglected, because they are much weaker or absent [28][29][30]. We shall show that using EM synchro-resonance (ω e = ω g ) system of coupling between the static magnetic fieldB (0) and a Gaussian type-photon flux(the Gaussian beam), the "quasi-B-mode" of strength distribution of the perturbative photon flux and the B-mode polarization in the CMB have interesting duality and they would be highly complementary.
According to the quantum electronics, form of the Gaussian-type photon fluxes[the Gaussian beam] is actually expressed by wave beam solution from the Helmholtz equation, and the most basic and general form of the Gaussian beams is the elliptic mode of fundamental frequency [31], i.e, where ψ 0 is the amplitude of the Gaussian beam, R x = z+f 2 x /(z−z x ) and R y = z+f 2 y /(z−z y ) are the curvature radii of the wave fronts at the xz-plane and at the yz-plane of the Gaussian , W 0x and W 0y are the minimum spot radii of the Gaussian beam at the xz-plane and at the yz-plane, respectively. Here, we shall study case of R x = R y = R, z x = z y = z, W x = W y = W and f x = f y = f , i.e., then the elliptic Gaussian beam, Eq.(3), will be reduced to the circular Gaussian beam [31].
By using the condition of non-divergence ∇ ·Ẽ (0) = 0 in free space andB (0) = −i/ω e ▽ ×Ẽ (0) , we find a group of special wave beam solution of the Gaussian beam as follows: HereB (0) z = ψ bz is a crucial parameter since the strength and physical behaviour of transverse perturbative photon flux(the transverse signal photon fluxes) mainly depend oñ z [see below and Eqs. (11) to (13)]. Using Eqs. (3) and (5), we havẽ From Eqs. (3) to (6), we obtain the strength of the transverse background photon fluxes in cylindrical polar coordinates as follows: where (0) T 02 are 01-and 02-components of the energy-momentum tensor for the background EM wave(the Gaussian beam), and are the transverse background photon fluxes in the x-direction and in the y-direction, respectively, where * denotes complex conjugate, and the angular brackets represent the average over time, and(also see Ref. [31]) From Eqs. (3) to (10), we obtain the strength distribution of n transverse perturbative photon flux(the signal photon flux) can be given by: where (1) T 01 ωe=ωg and (1) T 02 ωe=ωg are average values of 01-and 02-components of energymomentum tensor for first-order perturbation EM fields with respect to time, and where n It is very interesting to compare the polarization patterns(see Fig.2a) in the CMB caused by primordial density perturbation [26] , the polarization patterns(see Fig.2b) [26,32] produced by the relic GWs(in the very low frequency band) and the strength distribution(see Fig.2c and 2d) of the perturbative photon fluxes(in the high-frequency band), Eqs. (12) to (13), caused by the HFGWs, respectively. The density perturbation had no right-and-left handed orientation, thus their polarization are expressed as the tangential-type and radiated type patterns. Unlike the density perturbation (Fig.2a), the polarization patterns (Fig.2b) in the CMB produced by the relic GWs are the left-handed and right-handed swirls, and the EM response( Fig.2c and 2d) generated by the HFGWs in our synchro-resonance system are the "left-handed circular wave" and "right-handed circular wave", the latter both (Fig.2b,2c and 2d) are all from the tensor perturbation of the GWs. Here the "left-handed circular" or the "right-handed circular" property in the EM response depends on the phase factors in Eqs. (12) and (13)(see Fig.3 and below).
Analytical expression of the signal photon flux n (1) φ−⊗ , Eq. (12), is a slow enough variational function in the propagating direction z of the HFGW. This means that "rotation direction" of n (1) φ−⊗ is as slow variational and it remains stable in the almost whole region of coherent resonance. For the HFGW of ν = 3 × 10 9 Hz(i.e., λ g = 10cm), r = 20cm(distance to the symmetrical axis of Gaussian beam), the "rotation direction" of n (1) φ−⊗ keeps invariant in the first region of coherent resonance[the coherent resonance region keeping the righthanded rotation, i.e., from z = 10cm to z = 40cm, see the curve in Fig.3(a)], and then, the "rotation direction" will keep invariant in the next region of the coherent resonance[the coherent resonance region always keeping the left-handed rotation, i.e., in the region z > 40cm[see the curve in Fig.3(a)]. For the case of r = 6cm[see Fig.3(b)], the rotational direction has a better and more stable physical behavior, i.e., it will always keep left-handed rotational direction in the almost whole coherent resonance region. In other words, the effective receiving area for the HFGW can be ∼ 300 cm 2 . This means that it has enough large receiving surface to display the perturbative photon flux having ν g = 3GHz. Especially, numerical calculation shows that this coherent effective resonance region will be enlarged as the frequency increases, so that the HFGWs having higher frequency will have a larger effective receiving surface(see Fig.4). Fig.4 shows relation between the frequencies of the HFGWs and the effective receiving surface.
Besides, because there are yet other different physical behaviours between the signal photon fluxes n  φ−⊗ in the EM synchro-resonance system would be more stable for the suitable region, and such distance can be effectively enhanced as the resonance frequency ν g increases. than the total noise photon flux fluctuation at the receiving surface ∆s. This displaying condition was discussed in Ref. [33], we shall not repeat it in detail here, and only give the main numerical calculation results. The displaying condition can be given by: where ∆t min is the requisite minimal accumulation time of the signal, and are the total signal photon flux and the total noise photon flux passing through the receiving surface ∆s, respectively. Actually, there is a narrow frequency distribution of the Gaussian beam, and then the aimed signals caused by HFGWs also should not be monochromatic but with a sensitive frequency range. However, due to this frequency range is very short comparing to the HFGWs frequency band predicted by inflationary models or other scenarios, so we here calculate by a typical representative frequency instead of a frequency window. Pre-big-bang [5,14], Quintessential inflationary [11,12] or upper limit of ordinary inflationarye [9,10] It should be pointed out that the background photon flux(in our synchro-resonance system, typical value of the Gaussian beam is 10W) will be major source to the noise photon flux, i.e., other noise photon fluxes[e.g., shot noise, Johnson noise, quantization noise, thermal noise(if operation temperature T < 1k), preamplifier noise, diffraction noise, etc.] are all much less than the background photon flux [34]. In other words, the Gaussian beam(the φ (total) ) and not the background photon flux itself n (0) φ (total) . In this case, the relevant requirements to signal-to-noise ratio can be further relaxed. Table 2 shows displaying condition of the HFGWs for some cosmological models and high-energy astrophysical process, where n (1) φ−⊗(total) are the total signal photon fluxes at the receiving surface ∆s (φ = π/2 or 3π/2 , ∆s ∼ 3 × 10 −2 m 2 ), which might be produced by the HFGWs in the Brane oscillation, quintessential inflationary, pre-big-bang models, and the interaction of high-energy plasma with EM radiation, and n (0) total is allowable upper limit of the total noise photon flux at the surface ∆s for various values of the HFGW amplitudes and ∆t min , Eq. (15), ν e = ν g = 3GHz, the background static magnetic field B (0) is 10T, the interaction dimension ∆l is 2m, the power of the Gaussian beam is ∼ 10W and operation temperature should be less than 1K. Fortunately, one of institutes of our research team (High Magnetic Field Laboratory, Chinese Academic of Science) has been fully equipped with the ability to construct the superconducting magnet [35] (this High Magnetic Field Laboratory is also the superconducting magnet builder for the EAST tokamak for controlled nuclear fusion). The magnets can generate a static magnetic field withB (0) = 12 T esla in an effective cross section of 80cm to 100cm at least, and operation temperature can be reduced to 1K even less. The superconducting static high field magnet will be used for our detection system. Then maximum of n (0) total is ∼ 10 22 s −1 at the receiving surface ∆s of φ = π/4, 3π/4, 5π/4 and 7π/4, but it vanishes at φ = π/2 and 3π/2(see Fig.1). This means that at such surfaces even if the noise photon flux reach up to the maximum ( n  Table 2) of noise photon flux. Thus, direct detection of the HFGWs [15] in the braneworld scenarios would be quite possible due to larger amplitudes, higher frequencies, discrete spectral nature and extra polarization states for the K-K gravitons [15,36,37]. Observation of the relic HFGWs predicted by the pre-big-bang [5,14], the quintessential inflationary model [11,12] or the upper limit of the relic HFGWs expected by the ordinary inflationary models [9,10], will face to enormous challenge, but it is not impossible.

IV. WAVE IMPEDANCE AND WAVE IMPEDANCE MATCHING TO THE PER-TURBATIVE PHOTON FLUXES
The wave impedance to an EM wave(photon flux) depends upon the ratio of the electric component to the magnetic component of the EM wave, and the wave impedance of free space to a planar EM wave is 377Ω [38], and the wave impedance of copper to EM wave(photon flux) of ν = 3 × 10 9 Hz is 0.02Ω [38](see, Table 3). In fact, the wave impedance to the background photon flux(the Gaussian beam) and the planar EM waves in free space have the same order of magnitude(∼ 377Ω). Unlike case of the wave impedance to the background photon flux, the ratio of the electric component of the perturbative photon  (1) φ(total) and the background photon fluxes (BPFs) n (0) φ(total) at the receiving ∆S where φ = 89 • is azimuth angle in the cylindrical polar coordinates, and r is the distance to the symmetrical axis of the GB. We emphasize again that the important difference among the four main physical behaviors of n (1) φ(total) and n (0) φ(total) : different angular distribution (see Fig.I and Fig.2(c),(d), the latter are just from the quasi-B-mode), different decay rate (see Eq. (7) and Eq.(12)), very different wave impedance (see Tables IV and V) and different propagation directions in special regions. Importantly, in specific area of the detection system, the propagation direction of n (1) φ(total) and n (0) φ(total) are totally inverse each other, so in this case we can observe the signals using highly-oriented photon detector. Thus, only the signals will enter the photon detector and the background noise (of Gaussian Beam) can be effectively depressed. However, some other sources of noise should also be considered. In this table, by acceptable accumulation time of observation, we give the upper limit of these noise such as thermal noise, scattering and diffraction noise, Johnson noise, preamplifier noise and quantization noise [34]. It was shown [34] that such noise photon fluxes are less or much less than the upper limit of noise photon fluxes listed in this table.

Amplitude(A)
Position of Wave impedance to Wave impedance to dimensionless receiving surface(cm) perturbative photon flux n φ−⊗ has very small wave impedance(see Table  4), and it would be easier to pass through the transmission way of the synchro-resonance system, i.e., the selected wave zone in the synchro-resonance system would be equivalent to a good "superconductor" to the perturbative photon flux. Contrarily, the wave impedances to the background photon flux and other noise photons, are much greater than the wave impedance to the signal photon flux. I.e., Ohm losses produced by the background photon flux and the other noise photons would be much larger than Ohm losses generated by the signal photon flux in the photon flux receptors and transmission process. Therefore, the signal photon flux could be distinguished from the background photon flux and other noise photons by the wave impedance matching(see Fig.5).
According to definition for the wave impedance [38] and Eqs.(2),(6), (11) and (12), we obtain the wave impedance Z of the typical receiving surface ∆s to the perturbative photon flux n (1) φ−⊗ as follows: By using the typical parameters in the synchro-resonance system and in the typical cosmological models, i.e., A ⊗ ∼ 10 −23 , ν g = 3T Hz(e.g., the HFGWs in the braneworld mode [15]),  Table 4 and Fig.6. In the same way it can be shown that there are smaller wave impedance to the signal photon fluxes produced by the HFGWs expected by the pre-big-bang, and quintessential inflationary models(see Fig.6).

V. CONCLUDING REMARKS
(i)The B-mode in the CMB is from the interaction of the relic GWs with CMB, and this interaction produces the B-mode polarization in the CMB; the quasi-B-mode in the synchro-resonance system is from EM resonance response to the HFGWs; (ii)The GW frequencies of the former are located in very low frequency band(∼ 10 −16 to 10 −17 Hz), and the GW frequencies of the latter are occurred in typical microwave range(∼ 10 9 to 10 12 Hz).
(iii)The B-mode of the former is distributed in astrophysical scale, and the quasi-B-mode of the latter is localized in typical laboratory dimension.
(iv)The major noise source in the former would be from the cosmic dusts, key noise in the latter is from the microwave photons inside the synchro-resonance system, which are almost independent of the cosmic dusts; (v)Intuitive image of the former are the left-handed swirl and the right-handed swirl in  φ−⊗ and to the background photon fluxes having different frequencies and amplitudes in the selected wave zone of the synchro-resonance system. Here x and y are distances to the longitudinal symmetrical surface(the yz-plane and xz-plane) of the Gaussian beam, respectively, and z is distance to the minimum spot radius of the Gaussian beam(see Fig.3), and y = 5cm, z = 30cm, x ∈ [5, 30cm]. It is clear shown that the wave impedances(∼ 10 −4 Ω or less) to the transverse perturbative photon flux n (1) φ−⊗ produced by the HFGW of h = 10 −23 , ν = 3 × 10 12 Hz(e.g., the HFGWs in the braneworld mode [15]), are much less than that of the background photon flux n (0) φ in such region, and the wave impedances(∼ 10 −17 Ω or less) to the perturbative photon flux n (1) φ−⊗ generated by the HFGWs of h = 10 −30 , ν = 3 × 10 9 Hz(e.g., the HFGWs in the pre-big-bang [5,14] or in the quintessential inflationary model [11,12], are lot of orders of magnitude lower than that of the background photon flux in the wave zone. the CMB (Fig.2b), and the physical picture of the latter are expressed as the "left-hand circular wave" and the "right-hand circular wave" distribution of the perturbative photon flux( Fig.2c and 2d); (vi)The CMB displaying the B-mode are the EM waves(photon fluxes) in the free space, and in fact, it is also a thermal distribution of photons, and typical value of their wave impedance to the B-mode is ∼ 377Ω [38]. Unlike the CMB, the wave impedance(∼ 10 −4 Ω or less) to the signal photon flux in the typical wave zone of the synchro-resonance system is much less than that of the background photon flux and other noise photons. This means that the perturbative photon flux would be distinguished from the noise photons by the wave impedance matching. The similarity, complementarity and their difference between the two B-modes are listed in Table VI. Notice, although the above two B-modes correspond to the different situations, their similarity and duality show that they are from the same physical origin: the tensor perturbation of the GWs and not the density perturbation, and only the GWs can generate such similarity and duality, and this is a very important difference to other perturbations and GWs in ordinary inflation model and the pre-big-bang model [5,14,39] involve issues of very early universe and the beginning of time; GWs in the braneworld model [15,19] involves issues of the dimension of space, the multiverse, and direction of time arrow; GWs in the quintessential inflationary model [11,12] involve issues of the essence of dark energy, and GWs in high-energy astrophysical process [7] involve issues on the interaction mechanism of the interstellar plasma with intense EM radiation. These issues relate to important basic questions: Does the universe have a beginning? If so, how did the universe originate? Was the big-bang the origin of the universe? Was our big-bang the only one? Does the multiverse exist? If so, can it be verified through scientific testing? Would quintessence be a serious candidate for dark energy? Could the interaction between astrophysical plasma and intense EM radiation provide stronger GW sources?
If the GWs are observed in multiple frequency bands in the near future, and not only in the very low-frequency band(ν ∼ 10 −17 to 10 −16 Hz), but also in low-frequency band(ν ∼ 10 −7 to 1Hz), the intermediate-frequency band(ν ∼ 1 to 10 4 Hz) and in the high-frequency band(ν ∼ 10 8 to 10 12 Hz), and the observation results have highly self-consistence to the concrete cosmology parameters expected by certain cosmological model or a high-energy astrophysical scenario, then it will provide a stronger evidence for the model or the scenario.
If not, the detection sensitivities or observation ways will need further improvement, or these models and scenarios will need to be corrected or will be ruled out.
Finally, it should be pointed out that, the HFGWs can also interact with galacticextragalactic background magnetic fields, and then lead to EM signals with the same frequency as the HFGWs. Although the galactic-extragalactic background magnetic fields are very weak ∼ 10 −9 to ∼ 10 −11 T, the huge propagation distance could result in a useful spatial accumulation effect in the propagational direction [37], due to the same propagation velocities of HFGWs and EM signals. This may lead to a possibly observable effect on the Earth. Fortunately, such EM signals (10 8 to 10 9 Hz) sit in the detection frequency band of FAST (Five-hundred-meter Aperture Spherical Telescope) which is expected to be completely constructed in 2016 in Guizhou province, China. Therefore, the observation by FAST, detection of the HFGWs by our resonance detection system, and our cooperation with FAST can be strongly complementary. Those consequent works will be carried out in the near future.