With the increasing requirements for communication transmission rate and capacity，the utilization of existing microwave and millimeter wave bands tends to be saturated to the extent that they cannot meet the requirements of military and civilian communications，so the use of terahertz bands in wireless communications is rapidly developing^［1-2］. The frequency range of terahertz waves includes the sub-millimeter wave band of 0.1-10 THz，and it is widely used in fields such as environmental monitoring，object imaging，and broadband communication due to its strong penetration，short wavelength，and rich spectral information^［3-5］. One of the important components of terahertz communication networks is the terahertz antenna. Currently，various types of antennas in the terahertz band are widely studied，including microstrip antennas^［6］，dipole antennas^［7］，butterfly antennas^［8］，Vivaldi antennas^［9］，etc. Graphene is a two-dimensional material composed of tightly arranged single-layer carbon atoms，with high thermal conductivity，high electron mobility，and other characteristics. Importantly，its surface conductivity can be controlled by changing the bias voltage applied to it^［10］，and based on this feature，the reconfigurable antenna loaded with graphene has been widely studied by scholars^［11-16］.

The reconfigurable antenna with a directional pattern can dynamically change the radiation pattern of the antenna according to the demand while ensuring the polarization mode and operating frequency band of the antenna remain unchanged，which can improve the communication capacity and security of the antenna. Ref. ［11］ studied a type of Yagi antenna that used a set of orthogonal dipole antennas as the feed source antenna. The beam direction can be dynamically controlled in four states through two sets of graphene-based directors and reflectors. Ref. ［12］ proposed an active frequency-selective surface （AFSS） by directly adding a graphene layer to the metal-dielectric structure to form a hexagonal radome，which could achieve beam steering within 360°. Ref. ［13］ introduced six parasitic graphene strips around the microstrip antenna，and the direction and reflection of the graphene strips could be controlled by applying electrical bias，resulting in a beam steering of 120°. Ref. ［14］ presented cylindrical graphene-based frequency-selective surface，which could achieve dual beam direction diagrams of front and rear radiation by placing traditional omnidirectional dipoles in the radome. Although all these antennas can achieve the radiation direction map reconstruction，they have the problem of limited beam scanning range or single operating frequency band.

In this paper，a dual-frequency multi-beam reconfigurable terahertz antenna based on GFSS is proposed. A broadband omnidirectional monopole antenna is utilized as the feed antenna and loaded with a positive hexagonal radome composed of GFSS，which divides the radiation direction equally into six 60° sections. The graphene chemical potential is controlled by the bias voltage，which can freely realize the dual-band independent directional beam steering or omnidirectional radiation within 360°. In addition，the directional radiation gain of the antenna can be further improved.

In this study，based on the theory of slot-type frequency selective surfaces （FSS），we designed a FSS with cross-shaped gaps distributed in the center of the unit cell and arrow-shaped gaps at the four corners. This FSS structure was engineered to generate resonance at two distinct frequencies，creating a dual-frequency band-pass filter response. To effectively harness the tunable surface conductivity of graphene，it was loaded at the locations where the electric field was concentrated on the FSS. Furthermore，to achieve independent control over the two frequency response points，we proposed a novel graphene loading method. In this method，cross shaped graphene patches were loaded beneath the cross shaped slot，while square shaped graphene patches were loaded beneath the arrow shaped slot，with both graphene patches separated from the metal layer by a dielectric material. By applying two different vertical bias voltages between the metal FSS layer and the graphene thin film layer，the chemical potential and surface conductivity of the graphene patches can be controlled. Through the individual adjustment of the direct current bias voltage on the two shapes of graphene patches，the transmission and reflection characteristics of the two pass-bands can be independently regulated，achieving independent control over the frequencies.

Figure 1 illustrates the cell structure of GFSS. The top layer consists of a cross and four arrow shaped slots with metal patches placed on the p-type silicon，and two sets of graphene structures and metal wires are added to the top and bottom of the silicon dioxide layer to connect the bias voltages. P-type silicon and silicon dioxide have dielectric constants of 11.7 and 4，respectively. This allows the surface conductivity of graphene to be controlled within a certain range and its conversion from dielectric to metallic properties. The dimensional parameters of the designed structure are listed in Table 1.

The controlled conductivity of graphene is a key property for designing reconfigurable terahertz devices，which can be expressed by the Kubo formula ^［10］：

where σintra is the intra-band conductivity，σinter is the inter-band conductivity，ω is the electromagnetic wave angular frequency，μc is the graphene chemical potential，Γ=2/τrepresents the graphene scattering rate，where τ is the relaxation time，T is the temperature，e is the electron power，ℏ=h/2πis the approximate Planck constant，where h is the Planck constant. In fact，in the terahertz band，the surface conductivity of graphene is dominated by the intra-band conductivity，while the inter-band conductivity is negligible. In the present work，τand T are 100 fs and 300 K，respectively. In practice，the adjustable function is usually achieved by introducing a bias voltage，and the relationship between the graphene chemical potential μc and the applied bias voltage Vg can be expressed as：

where Vf is the Fermi velocity of graphene，εris the relative dielectric constant of the dielectric plate，and tis the thickness of the dielectric plate. In this study，the graphene layer has two distinct chemical potential states，namely 0 eV and 0.5 eV. Based on the relationship between the chemical potential and bias voltage，we can calculate that it requires a voltage of 50 V to raise the chemical potential of graphene from 0 eV to 0.5 eV. Previous research has shown that achieving lower chemical potential states in graphene can be easily accomplished through bias voltages^{［10，17］}.It should be noted that in practice it is more difficult to apply a DC bias voltage directly to the graphene patch，we can use a self-biased voltage source connected to the opposite pole of the voltage source to achieve reconfigurable performance for the proposed antenna^［18］.

The cell structure is simulated using CST-MW to control the four rectangular graphene chemical potentials （denoted by u1） and the cross shaped graphene chemical potential （denoted by u2） switching between two states of 0 ev and 0.5 ev. Figure 2 shows the transmission and reflection curves of the proposed cell in four different graphene states when u1 and u2 are combined. When Case1，u1 and u2 are set to 0 eV，both rectangular and cross-shaped graphene exhibit dielectric properties，so the resonance occurs at each of the two points of the arrow structure and cross-structure gaps. The two resonance points occur at 1.08 THz and 1.58 THz in which bandpass effects are achieved in both frequency bands； Case2 and Case3 change u2 and u1 to 0.5 eV respectively，when controlling the chemical potential of the graphene structure to 0.5 eV，when the graphene structure in a specific frequency band behaves as a metal characteristic. By controlling u1 or u2 individually，it can effectively control whether the resonance occurs at the arrow slit and the cross-shaped slit，then low-pass high-resistance and high-pass low-resistance can be realized respectively； at Case4，both u1 and u2 are controlled to be 0.5 eV to realize the dual-band band-resistance effect. In addition，a high degree of independence can be observed at the two operating frequency points of 1.08 THz and 1.58 THz.

The surface current and electric field distribution of GFSS cell in Case2 and Case3 states are shown in Fig. 3. At 1.08 THz，the surface currents are mainly distributed at the edge of each set of arrows and the dielectric voltage is distributed in the middle of the arrows； at 1.58 THz，the surface currents are distributed at the edge of the cross and the dielectric voltage is distributed in the middle of the cross； according to the equivalent circuit，1.08 THz and 1.58 THz correspond to an LC parallel circuit exhibiting bandpass characteristics. It is consistent with the transmission characteristics of the GFSS cell discussed earlier. Also，considering the need to construct the radome using the GFSS cell （as analyzed in Section 3），the electromagnetic wave on the GFSS cell after loading the source antenna does not always remain incident vertically. As shown in Fig. 4，when the incident wave is incident at different angles within the 40° range，the reflection and transmission characteristics still work effectively within a specific frequency band.

Firstly，a broadband omnidirectional monopole antenna （fed by 50 Ω） with a simple structure is proposed as a feed antenna as shown in Fig. 5. The trapezoidal patch and rectangular metal ground are placed on both sides of the dielectric substrate with the dielectric constant of 3.66 and the thickness h. The operating band contains the GFSS cell operating band，in addition，the feed antenna keeps omnidirectional radiation in the XOZ plane within the GFSS cell operating band，and the peak gain reaches 3.24 dBi and 3.53 dBi at 1.08 THz and 1.58 THz，respectively.

Then，as shown in Fig. 6，the GFSS unit is formed into a 2×3 surface around the source antenna to form a hexagonal radome. In order to analyze conveniently，we use 0 to indicate the chemical potential of 0 eV，1 to indicate the chemical potential of 0.5 eV，then，the different chemical potential states on the hexagonal radome can be expressed using twelve binary digits，where Mode 1-6 are affected by the chemical potential of u1，which controls the low-frequency performance of the antenna； Mode 7-12 are affected by the chemical potential of u2，which controls the high-frequency performance of the antenna. The twelve working modes of the antenna after loading the hexagonal radome are shown in the table below. The antenna still maintains a good resonance at 1.08 THz and 1.58 THz for different operating modes，and the radiation direction diagrams of each mode are given，which means that the antenna loaded with GFSS radome can achieve dual-band independent 360° omnidirectional beam scanning.

Then，the antenna directionality and gain parameters in different modes after loading the radome are discussed specifically. As shown in Fig. 6（c），when the chemical potential of the graphene patches with control serial numbers 1，2 and 3 is 0.5 eV，and the chemical potentials of the other serial numbers are 0 eV （ Mode 1）. Due to the increase in the chemical potential of the graphene patches，the graphene changes from a dielectric to a metallic property. At this time，the GFSS exhibits the reflective property at 1.08 THz，and therefore the radiation beam changes from omnidirectional radiation at 1. If the chemical potential of the graphene patches with serial numbers 2，3 and 4 is 0.5 eV and the other chemical potentials are 0 eV （Mode 2），at this time the beam at 1.08 THz points at 60° and the omnidirectional radiation at 1.58 THz is maintained. Similarly，by controlling the chemical potential of the graphene patch to generate Mode 3-6，the radiation beam at 1.08 THz can be made to point to 0°，300°，240° and 180°，respectively，while the omnidirectional radiation characteristic at 1.58 THz is always maintained without any effect，as shown in Figs. 7（a） and 7（b） in the text. In Mode 1-6，the proposed antenna achieves a peak gain of 7.44 dBi at 1.08 THz，and the radiation gain remains within ±0.27 dBi compared to the source antenna at 1.58 THz. Similarly，Mode 7-12 are generated by varying the chemical potential of the graphene patches with control numbers 7-12，corresponding to which the radiation direction can be made to remain omnidirectional at 1.08 THz，with a minimum gain of 3.44 dBi，while the main beam is directed in each of the six directions within 360° at 1.58 THz，with a peak gain of 6.67 dBi，as shown in Figs. 7（c） and 7（d）.

Furthermore，when controlling the separation of the cross-shaped and square-shaped graphene structures at 0.5 eV intervals，the hexagonal antenna enclosure exhibits reflective characteristics at corresponding frequencies. The radiation patterns at 1.08 THz and 1.58 THz，as shown in Fig. 8，demonstrate directed three-beam radiation characteristics. This observation indicates that the proposed antenna structure possesses the capability to achieve directional beam radiation under more complex dual-frequency reflections and transmissions.

The comparison between the previously reported literature and the present work in terms of source antenna type，operating frequency，beam range and peak gain is presented below as shown in Table 3. The proposed multi-beam reconfigurable terahertz antenna based on the GFSS exhibits the capability of independently controlling six beams within a 360°coverage at dual frequencies. Additionally，it achieves high peak gains at the two resonant points.

In this paper，a GFSS radome-based multi-beam reconfigurable terahertz antenna is investigated. A graphene-based dual-band independently controllable frequency-selective surface is proposed，which is built into a hexagonal radome loaded on a monopole antenna，and the bias voltage is adjusted to control the graphene chemical potential size in the antenna to achieve the purpose of controlling the main beam direction and peak gain of the antenna. Finally，by switching two sets of graphene chemical potentials between 0 eV and 0.5 eV，the antenna can realize a dual-band independent six-beam reconfigurable antenna at 1.08 THz and 1.58 THz with peak gains of 7.44 dBi and 6.67 dBi，respectively. This work will have great prospects for applications in beam scanning of terahertz devices and systems，and gain enhancement of conventional antennas.