Multi-channel terahertz focused beam generator based on shared-aperture metasurface

Jiu-Sheng Li(李九生) and Yi Chen(陈翊)

Centre for THz Research,China Jiliang University,Hangzhou 310018,China

Keywords: terahertz wave,multi-channel,shared-aperture,focused beam

1.Introduction

As a simple and effective method to control electromagnetic waves, coding metasurfaces have attracted extensive attention in recent years.[1-4]By pre-arranging coding elements with different amplitudes and phases based on periodic or aperiodic laws, coding metasurfaces achieve radar cross section(RCS) noise reduction,[5,6]focusing,[7,8]beam splitting,[9,10]vortex,[11,12]etc.For example, in 2020, Hanet al.designed a metasurface composed of an inner rectangular ring and an outer Jerusalem cross structure combining“C”shaped branch to realize the RCS reduction function.[13]Fuet al.proposed a metasurface based on C-shaped symmetric split ring with the central cross-shaped metal structure to generate the suppression of RCS.[14]Shenet al.arranged a silicon column structure with graphene electrode to realize an adjustable focusing imaging.[15]Zhouet al.also used silicon column structure with external graphene electrode to generate adjustable the position and number of focused beams.[16]In 2021, Guet al.demonstrated a multi-layer metasurface made of anisotropic rectangular patches and cross metal strips to produce splitting vortex beam.[17]Zhenget al.used a silicon dielectric square column metasurface based on propagation phase and Pancharatnam-Berry (PB) phase theorem to achieve annular radiation.[18]In 2022, Zhou and Song employed “I” shaped metal structure according to the octagonal spiral sequence to control the vortex beam topological charges by changing the Fermi energy level of graphene.[19]However, the abovementioned metasurfaces usually have only a single channel and limited functions.A few metasurfaces often require complex calculations to achieve multi-channel functionality, and most of these metasurfaces mainly operate in an infrared or microwave frequency band.[20-22]And composite multichannel and multifunctional focused beam generators based on reflective metasurface in a terahertz region are rarely reported.In this article, we propose a coding metasurface with sharedaperture nesting and parallel connection, which can generate any number of focused beams at any position.By changing the size of the shared aperture array, the designed structure can also control the energy intensity of the focused beam.

Here, the proposed multichannel terahertz focused beam generator consists of a square metal bar layer and a metallic bottom plane layer, between which a silica substrate is sandwiched.The simulation results shows that complete 2πphase coverage can be obtained in a frequency ranging from 0.8 THz to 1.2 THz by independently rotating the metallic strip structures for normally incident RCP (right circularly polarized)wave.And then,we design the vortex focus metasurface with a focus length ofF=1000µm for the topological charges ofl=±1 andl=±2.Furthermore,we also realize four-channel focused beam and vortex focused beam generation with different topological charges.Moreover,by replacing part of the array group with a shared-aperture array method,the designed metasurface generates five-, six-, and eight-channel focused beams with different energy intensities.The numerical simulation results are in good agreement with the theoretical predictions.Our structure provides a new method of designing terahertz multichannel mesurface-based devices, which can greatly extend the functions and the application scope of metasurface.This structure also provides a new method of manipulating the terahertz wave communication and detection.

2.Structure design

Figure 1 shows a schematic diagram of the multi-channel terahertz focused beam generator based on a shared-aperture principle.When RCP wave is incident along the-z-axis direction, the matasurface produces multiple channels reflected LCP focusing beams.The unit-cell is composed of a top square metal strip,an intermediate dielectric layer,and a bottom metal plate, as shown in Figs.1(b)and 1(c).The dielectric substrate layer is of silicon dioxide with a dielectric constant of 3.9 and loss angle of 0.0004.[23]The metallic parts in top layer and bottom layers are of gold with a conductivity of 4.6×107S/m and a thickness of 1µm.By using the commercial software CST Microwave Studio,we simulate and optimize the electromagnetic transmission amplitude and phase response of the unit cell.The optimized geometric parameters of our proposed unit-cell are as follows:a= 10 µm,b= 90 µm (Here, the parameter scanning results are displayed in Figs.2(a) and 2(b)), and the period of the unit cellP=100µm.In addition,the thickness of the silicon dioxide is 40µm.[24]In order to meet the gradient phase,eight kinds of coding elements are designed and illustrated in Table 1,whereϕis the gradient phase of the corresponding unit cell,andαis the rotation angle of the unit cell along theyaxis.The corresponding reflection coefficient (CRC) and phases under RCP wave incidence are shown in Figs.2(c) and 2(d).From the figure, one can see that the reflection coefficients of the eight kinds of unit cells are larger than 0.9 THz at 1 THz, and the phase spectra are parallel to each other with a phase difference of 45◦.

Fig.1.(a)Function sketch,(b)three-dimensional view of unit cell,and(c)top view of unit cell, for proposed multi-channel terahertz focused beam generator.

Fig.2.Reflection coefficients versus frequency for different values of(a)reflection coefficient a,(b)phase b,(c)reflection coefficient α,and(d)phase versus frequency.

Table 1.Top-view,gradient phase,rotation angle,corresponding reflection coefficients,and phase of 8 kinds of coding elements at frequency of 1 THz.

3.Simulation results and analysis

To generate a focused beam, the phaseϕA(x,y) of the coding metasurface need to satisfy the following relation:

Fig.3.(a)Phase distribution,(b)top view,(c)3D view of four-channel focused beam electric field.

Fig.4.Electric field strength, phase and mode purity of the vortex focused beams with different topological charges at 1 THz,(a)-(c)l=1,(d)-(f)l=-1,(g)-(i)l=2,(j)-(l)l=-2.

wherexandyrepresent the horizontal coordinate and vertical coordinate of the unit cell,λis the working wavelength,Fdenotes the focal length.Herein, the focal length of the focused beam is set toF=1000 µm, and the structure consists of 48×48 coding elements.Figure 3(a) gives the phase distribution of the designed metasurface structure.The electric field distribution in thexoyplane at the focal point and three-dimensional (3D) electric field distribution are displayed in Figs.3(b) and 3(c), respectively.The scales of the simulated multi-channel focused beam field patterns are all 4800µm×4800µm.Under the RCP wave normal incidence,the designed structure generates a four-channel focused beam,as illustrated in Fig.3.One can see that the reflected fourfocused beams have the same electric field intensity.The electric field efficiency of the focused beamηcan be given by

whereEORis the incident RCP electric field andERLis the reflected LCP wave electric field.According to Eq.(2),we can obtain that the electric field efficiency of four-channel focused beam is 33.0%.

Furthermore, we design a four-channel vortex focusing metasurface based on parallel array by combining the convolution theorem.In order to realize the vortex focusing function,the distribution law of the phaseϕB(x,y)can be expressed as

wherelis the topological charges of the vortex beam.Figure 4 illustrates the electric field, phase and mode purity of vortex focusing beam for the topological charges ofl=±1 and±2 with a focal length ofF=800 µm at frequency of 1 THz.From the figure,one can see that the phase of the vortex focusing beam rotates counterclockwise as the topological charges are positive.Likewise, when the topological charges are negative value, the phase of the vortex focusing beam rotates clockwise.Furthermore, the mode purities of the vortex focusing beam with topological chargesl=±1 and±2 are 87.46%,87.01%, 86.47%,and 78.31%, respectively.It is worth noting that the electric field diagram of the vortex focused beam is a ring with a dark spot in the center.The more the topological charges, the bigger the dark spot is.It is because the OAM vortex beam has a phase singularity, which causes the center field of the vortex beam to approach to 0.Figure 5(a) shows four vortex focusing metasurface arrays.The electric field and phase at the focal length are displayed in Fig.5(b).Obviously, the topological charges of vortex focusing beam in the upper-left channel, upper-right channel,lower-left channel and lower-right channel arel=1,-1, 2,and-2, respectively.And then, the corresponding electric field intensities are 3.1 V/m,3.0 V/m,2.7 V/m,and 2.6 V/m,respectively.The electric field efficiency of four-channel focused vortex beam is 55.5%.Their corresponding phases are shown in Figs.5(c)-5(f).In addition,from Fig.5(b),one can see that the vortex focusing beam has an annular profile.The diameter of the vortex focusing beam with topological charges ofl=±1 is significantly smaller than that of the vortex focusing beam with topological charges ofl=±2.It also verifies that the size of the vortex focusing beam depends on the topological charges.

To expand the channel number of the focused beam, a multi-channel terahertz focusing beam metasurface is proposed by combining the shared-aperture interlace cascade and array parallel arrangement.The shared-aperture metasurface consists of multiple interlaced sub-arrays, which share the same aperture of the metasurface.Each sub-array carries a geometric phase profile, which can stimulate different spatial channels for different functions.In order to obtain favorable performance,it is desirable to arrange sub-arrays regularly or randomly in an interlaced manner, rather than aggregate the unit cells of sub-arrays in local areas.Typically, in order to maintain relatively equal energy in each channel,different subarrays need to contain approximately the same number of unit cells.Figure 6 provides a schematic diagram of the principle of multi-channel functional multiplexing metasurface combining array parallel and shared-aperture.Figure 6(b)displays the middlepart phase distribution of the four-channel focused parallel array (see Fig.6(a)), and Fig.6(c) shows the phase distribution of the focusing beam with focal lengthF=1000µm.The two sub-arrays are staggered according to the following relation:

whereNrepresents the number of sub-arrays which are used to constructe the main array,ϕ1-ϕNdenote the phase distribution of the 1st toNth sub-arrays,iandjare the position of the corresponding unit cell alongxaxis andyaxis in the array,respectively.Figure 6(d)gives the phase distribution between the main array and the sub-array forN=2.Here,the sub-array 0 denotes the array in Fig.6(b),and the sub-array 1 is the array in Fig.6(c).The two-dimensional(2D)electric field intensity of the five-channel focused beam generated by the sharedaperture parallel array is shown in Fig.6(g).Figure 6(h)displays 3D electric field distribution of the five-channel focusing beam.As can be seen from the figure,the electric field intensity of the focused beam in upper left, upper right, lower left and lower right channel are 4.4 V/m, 4.2 V/m, 4.3 V/m, and 4.4 V/m respectively.In addition,the electric field intensity of the focused beam in the middle channel equals 3.4 V/m.The electric field efficiency of five-channel focused beam is 43.4%.

Figure 7(f) illustrates the phase configuration diagram of the six-channel focusing beam metasurface, in which the phase configurations of the middle-up part and middle-low part are shown in Fig.7(e).In fact, the middle-part phase configuration can be obtained by staggered cascade arrangement of the metasurface arrays(i.e.Figs.7(b)and 7(c))based on shared-aperture.The electric field distribution of the sixchannel focusing beam with a focal length of 820µm is given in Fig.7(g).Figure 7(h)shows 3D electric field distribution of the focused beam.One can see that the electric field intensity of the focused beam in upper left,upper-right channel,lowerleft channel, and lower-right channel are 3.7 V/m, 3.7 V/m,3.6 V/m and 3.7 V/m, respectively.In addition, the electric field intensity of the middle and upper channels are 2.84 V/m and 2.83 V/m,respectively.The electric field efficiency of sixchannel focused beam is 24.2%.

Furthermore,by replacing the intermediate array in Fig.6 with a four-channel focusing parallel array,we obtain an eightchannel focusing beam.Figure 8(f)shows the phase diagram of the eight-channel focusing beam metasurface.The phase distribution of the middle array part is displayed in Fig.8(e).We can find that the array based on 24×24 unit cells is generated by the middle part of the four-channel focusing array(see Fig.8(b)) and the four-channel focusing parallel array(see Fig.8(c)) by using shared-aperture principle.The electric field distribution of the eight-channel focusing beam with a focal length of 760 µm is displayed in Figs.8(g) and 8(h),which is in good agreement with the theoretical result.As can be seen from the figure,the focusing beam electric field intensity of the upper-left channel, upper-right channel, lower-left channel,and lower-right channel of the outer ring are 6.1 V/m,5.8 V/m,5.8 V/m,and 5.9 V/m,respectively.Furthermore,the focused beam electric field intensity of the upper-left channel,upper-right channel,lower-left channel,and lower-right channel of the inner circle are 1.9 V/m, 1.8 V/m, 1.9 V/m, and 1.9 V/m, respectively.The electric field efficiency of eightchannel focused beam is 62.9%.The proposed metasurface arrangement method based on shared-aperture can not only generate any number of focused beams at any position, but also control the energy intensity of focused beams.

Fig.7.(a)Phase distribution of four-channel focusing metasurface,(b)middle-up-part phase distribution of the four-channel focusing metasurface(black dash-line),(c)single-channel focusing metasurface,(d)dual-channel shared-aperture array pattern,(e)middle-part phase distribution of six-channel focusing metasurface,(f)phase distribution of six-channel focusing metasurface,(g)2D and(h)3D electric field intensities of six-channel focused beam.

Fig.8.(a)Phase distribution of four-channel focusing metasurface,(b)middle-part phase distribution of the four-channel focusing metasurface(black dash-line),(c)four-channel focusing metasurface(2400µm×2400µm),(d)dual-channel shared-aperture array pattern,(e)middle-part phase distribution of eight-channel focusing metasurface, (f) phase distribution of eight-channel focusing metasurface, (g) 2D and (h) 3D electric field intensity planes of eight-channel focused beam.

4.Conclusions

In this work, a metasurface based on shared-aperture is proposed to generate multi-channel terahertz vortex focused beam and multi-channel terahertz non-vortex focused beam.The patterned unit cell structure consists of a top square metal strip layer,a middle silicon dioxide layer,and a bottom metallic plate.Full-wave simulation results and theoretical calculation results show that the metasurface generates multi-channel focused LCP wave at 1 THz for a normally incident RCP wave.Through parallel array arrangement,the proposed metasurface achieves four-channel vortex focused beam generation and four-channel vortex focused beam generation with different topological chargesl=±1, andl=±2.Further, by replacing part of the area in the parallel array group with a shared-aperture array,the proposed metasurface realizes five-,six- and eight-channel focused beam generator with different energy intensities.The shared-aperture metasurface paves the way for designing the multi-channel terahertz devices.

Acknowledgements

Project supported by the National Natural Science Foundation of China (Grant No.62271460) and the Zhejiang Key Research and Development Project, China (Grant Nos.2021C03153 and 2022C03166).