太赫兹超表面的色散特性控制

Terahertz  (THz) metasurfaces have been explored recently due to their properties  such as low material loss and ease of fabrication compared to  three-dimensional (3D) metamaterials. Although the dispersion properties  of the reflection/transmission-type THz metasurface were observed in  some published literature, the method to control them at will has been  scarcely reported to the best of our knowledge. In this context,  flexible dispersion control of the THz metasurface will lead to great  opportunities toward unprecedented THz devices. As an example, a THz  metasurface with controllable dispersion characteristics has been  successfully demonstrated in this article and the incident waves at  different frequencies from a source in front of the metasurface can be  projected into different desired anomalous angular positions.  Furthermore, this work provides a potential approach to other kinds of  novel THz devices that need controllable metasurface dispersion  properties.

Introduction

Metamaterials have attracted much attention around the world since J. B. Pendry1 and D. Smith2 proposed  the concept of negative permittivity and permeability, due to their  many interesting phenomena which cannot be normally found in nature,  e.g., negative or near-zero refractive index. When small inclusions in  the three-dimensional (3D) metamaterial are placed into a  two-dimensional (2D) pattern on a surface, the newly formed structure  can also present some similar electromagnetic properties, called  metafilm or metasurface. The behaviour of metasurfaces can be  characterized by the electric and magnetic polarizabilities of their  constituent inclusions, also similar to that of 3D metamaterials.  Comparatively, metasurfaces have many inherent advantages of their own,  e.g., less space occupation, possibility of lower loss and cost and ease  of fabrication. Therefore, the researches on metasurfaces are  explosively expanded from microwave to optics in recent years3,4.

Terahertz (THz) technology has an increasing variety of applications5,  such as non-destructive detection, security, biology and medical  sciences. Benefited from recent technological innovation in photonics  and nanotechnology, great progress has also been made in  reflection/transmission-type THz metasurfaces. THz metasurfaces as  absorbers are reported in some literature, e.g., THz absorbers with a  broad and flat high absorption band by using I-shaped resonators6, polarization-insensitive broadband terahertz absorbers with multilayered cross7 or square patch elements8 and wide-angle absorber with Tungsten wire array9. As metasurface lens has an ultrathin profile, its aberration can be removed after a careful design10. Other metasurface based flat THz lenses, like an ultra-thin THz lens with an axial long focal depth11,  have also been explored by some research groups. Moreover, a  metasurface for anomalous reflection and refraction is obtained by using  the unit cells with V-shaped inclusions, after the generalized laws of  reflection and refraction are introduced firstly in Ref. 12.  Based on similar ideas, interesting out-of-plane reflection and  refraction of light by an anisotropic metasurface have also been  reported13.

In Ref. 14,  a metasurface is used to efficiently manipulate the wavefront of  incident waves, as well as to convert the incident polarization into an  orthogonal one. Recently, a metasurface with the capability of  polarization conversion at THz frequencies are also reported in Ref. 15and  based on the same idea a metasurface based lens with anomalous  refraction is presented. Meanwhile, the efficiency of a metasurface is  studied by Jansen et al.16 and  the quality factor can be significantly improved by introducing some  asymmetries into the metasurface unit cell. Moreover, since the resonant  property of the unit cell is quite sensitive to the surrounding  material, it can also be applied in sensing applications17,18. Other attention is shifted to the tunable metasurfaces based on thermal effect19,20, for purposes like sensing or cloaking21. The so-called programmable beams of a metasurface under plane-wave incidence are presented in Ref. 22.  However, poor agreements between simulated and experimental results can  be found when the metasurface is experimentally illuminated by a horn,  i.e., under the spherical wave incidence. Furthermore, the programmable  devices are also unsuitable for THz operations due to the reasons like  unavailability of THz switches. Active metasurfaces have also been  explored for THz modulator uses23,24,25 and  both spatial or phase modulation are demonstrated for prospective THz  system applications based on a semi-insulating GaAs or  silicon-on-sapphire wafer when they are biased by direct current (DC)  voltage or pumped by a near-infrared laser pulses at 800 nm.  Additionally, birefringent photonic device is generally bulky because it  operates based on light path accumulation, but metasurface can help to  solve this problem, e.g., the birefringent reflectarray metasurface in  Ref. 26.

However,  it is worth noting that the dispersion characteristics of the THz  metasurface are often overlooked in many papers. In most cases,  dispersion properties of metasurface are merely narrated, e.g., in  Refs. 15 and 27,  but without explanations on the reasons of beam/focus dispersion or any  attempts to handle it. More importantly, studies on controlling the  dispersion can scarcely be found although it is one of the most  important properties of THz metasurfaces. It is found that a scanning  beam within a small range of the metasurface is reported by Li, Y. B. et al.28,  however, which operates based on holographic concept. Moreover, the  scanning beams are caused by dispersive nature of the metasurface  element and no method to control the dispersion property of the  holographic metasurface are mentioned therein. In this article, by using  a specific kind of unit cells, a broadband dispersion controllable THz  metasurface (DCTM) is demonstrated which can accurately project the  incident THz waves of different wavelengths into different controllable  anomalous directions. The device can be easily scaled downwards or  upwards to microwave or optical frequencies after taking the material  properties into account.

Results

THz Metasurface Configuration

Figure 1 shows  a DCTM on the top layer of a dielectric. There is a solid metallic  layer on the bottom to reflect the transmitted waves and therefore, the  incident waves can interact with the metasurface twice, which means that  more obvious interactions can be observed. Assume that a metasurface is  located in the xy plane, a point source is placed in the xz plane by a  distance F above the metasurface and the incident angle from the source to the origin of the coordinate system is denoted by θo. Meanwhile, at an arbitrary position  on the metasurface with a distance R to the source, the incident waves will impinge on the DCTM by an angle related to .

THz DCTM in the xy plane with a point source in the xz plane.

For  clarity, the metallic layer on the bottom is not shown. The origin of  the coordinate system is located at the center of the first column of  unit cells and two referenced lines, i.e., Lines 1 and 2, have a common  starting point but are oriented to the x and the y axes, respectively.

The waves incident on the metasurface are expected to be reflected to an identical angle θr with respect to the z axis at a given frequency f.  As we know, the phase shift Φ of the metasurface unit cell is frequency  dependent due to its dispersive nature. Meanwhile, the unit cells at  different positions on the DCTM should be assigned by different phase  shifts to compensate different spatial phase delay, meaning that the  required phase shift Φ is also position dependent Φ(f, ). Additionally, θris a function of frequency because of the dispersive nature of the metasurface, i.e., θr = θr(f).  Therefore, it can be derived that if the dispersion properties of the  metasurface are expected to be controllable, e.g., an arbitrarily  designed regular or anomalous θr at any given f, the required phase distributions should satisfy the condition in Eq. (1):

in which k0 is the free-space wave number at f, Φo(f) is the frequency-dependent phase shift of the unit cell at the origin of the coordinate system and  denotes  the unit vector of the propagation direction of the reflected waves.  Here, the physical dimensions of the DCTM are designed to be Dx = 14.58λ0 and Dy = 11.67λ0 at the center frequency f0 = 250 GHz, composed of 50 × 40 unit cells. The source is placed at the location (−22.5λ0, 0, 25λ0)  or (−27 mm, 0 mm, 30 mm), for considerations of measurements. The  reflected beams are desired to be oriented to anomalous angles for the  same reason, i.e., θr = −35°, −25°, −15°, −10° and −5° at 200, 225, 250, 275 and 300 GHz, respectively.

To  show the required phase by different unit cells on the metasurface, two  representative lines along the x and y axes are chosen, i.e., Lines 1  and 2, both starting from the origin of the coordinate system. Figures 2a and 2b show  the designed reflection phases at different positions of the two  referenced lines, respectively, versus normalized frequency. A  practically available Φo(f) is chosen, as shown by the solid black curves and Φ(f) at other positions of Lines 1 and 2 can be calculated according to Eq. (1). It can be seen from Figure 2a that  the phase curve versus frequency becomes steeper and steeper as the  unit cell on Line 1 is farther away from the starting point.  Comparatively, the phase curve in Figure 2b becomes  flatter for the unit cells farther away from the starting point of Line  2. These phenomena put severe limitations on the feasible sizes of the  DCTM along the y-axis direction, which will be discussed later.

Designed reflection phases of the unit cells versus normalized frequency.

Labels  in the two figures are the numerical order of the unit cells from the  starting point of the two referenced lines, i.e., the origin of the  coordinate system. The horizontal axes represent the frequency  normalized by the centre f0 =  250 GHz. (a) A phase delay in degree, instead of a phase advance, for  the unit cell on Lines 1 is always required and the curve with large  numerical order becomes steeper. (b) The required reflection phase curve  gradually becomes flatter and flatter when the numerical order of the  unit cell on Line 2 goes larger.

Configuration and Characteristics of Unit Cell

If  the reflected beam dispersion of the metasurface is expected to be  flexibly controlled, the property of the unit cell is one of the key  factors. It must have the ability to present a variety of reflection  phase curves with different ranges and different slopes when its  physical size varies. Figure 3 shows  the geometry of the employed unit cell which can meet the phase  requirements of the 50 × 40 element DCTM. It is a three-layer structure,  an aluminum film with a thickness of 1 μm as the bottom layer as well  as a benzocyclobutene (BCB) layer with a thickness h and a refractive index 1.565 at the center, as shown in Figure 3a.  Two loops and an I-shaped dipole on the top layer are made of 1 μm  thick aluminum, each of which provides one resonance. Generally, one  resonance can provide a phase range of over 300° and therefore the  proposed unit cell can present a phase range as large as over 900°.  Parameters of the structures on the top layer are given in Figure 3b and another two are implicitly defined, i.e., v equal to lv over the total length of I-shaped dipole and b equal to wb over  the total width of I-shaped dipole, for a proportional size variation  of the I-shaped dipole to control the reflection phase。

Unit cell geometry and its simulated properties.

(a)  3D view. It is composed of a thin aluminum film, a BCB dielectric layer  and an aluminum pattern on the top. The total sizes of the unit cell  are Lx = Lyand h (fixed  to be 120 μm in all cases). The 1 μm thickness of both aluminum layers  are fixed in all cases of this paper. (b) Top view of the unit cell.  There are two loops and an I-shaped dipole along the x axis. (c) The  reflection phase in degree and reflectivity versus physical parameter L at  250 GHz. A linear phase curve and a large reflectivity are  simultaneously obtained by properly choosing the physical parameters: g1 = 35, g2 = 20, g3 = 9, w1 = w2 = 18.2, Lx = Ly = 500 in μm, b = 0.6 and v = 0.3. Note that the larger the reflectivity, the higher the efficiency of the DCTM is

According  to our studies, if a linear reflection phase curve is desired, mutual  coupling among the three components should be carefully tuned. Reducing  the two gaps with a size g3 in Figure 3b can  significantly enhance the electric coupling strength between three  components, which will push the three resonances closer and lead to a  linear reflection phase curve. However, if g3 is  too small, the reflection phase range would be reduced because the  three resonances go too close to each other. Comparatively, the two gaps  with dimensions g1and g2 determine  the magnetic coupling between three components, which can also enhance  the reflection phase range but at the cost of reduced reflectivity.

Figure 3c gives  the reflection phase curve and reflectivity of the metasurface unit  cell with the parameters shown in the caption of the figure under normal  incidence. It can be seen that the unit cell is able to present a phase  range of over 900° with good linearity as parameter Lis changed from 200 to 400 μm at 250 GHz. Meanwhile, the reflectivity of such a structure is over 0.75 as L varies  within the same range. Three dips on the reflectivity curve denote the  three resonances. The electric current distributions on three components  of the unit cell can be found in Section S.1 in the Supplementary Information,  which can provide more information about the three resonances. In the  whole interested frequency band of 200 ~ 300 GHz, the unit cell with the  given parameters can cover a reflection phase range of over 400° (See  Section S.2 in the Supplementary Information).  Meanwhile, the reflectivity across the whole frequency band is over  0.75 which is benefited from optimization of electric and magnetic  couplings between three components on the top layer of the unit cell.  Furthermore, the slope and range of its reflection phase can be flexibly  tuned as shown in Section S.3 in the Supplementary Information.  Three figures therein give us clear information that the phase required  by the metasurface to control the dispersion properties can be  satisfied by the employed unit cells.

Numerical and Experimental Results

Beam  positions of the fabricated DCTM at 200, 225, 250, 275 and 300 GHz are  originally designed at −35°, −25°, −15°, −10° and −5°, respectively. The  full-wave simulations show that the DCTM presents a slight beam shift  by around 1° from the designed values, as given in Figure 4, because of the numerical errors in the simulated phase of the unit cell.

Measured and simulated results of the DCTM prototype.

In  the figure, the power distribution within an angular range from −45° to  10° is shown. All measured and simulated results are normalized to  their maximum values. The measured results are shown by different types  of markers at different frequencies and the simulated ones are by the  smooth curves. The simulated results at five frequencies are given,  i.e., 200, 225, 250, 275 and 300 GHz, while the measurements are  performed with an angular step 1° by two pairs of the OML extenders from  140 to 220 GHz (for 200 GHz measurements) and from 220 to 325 GHz (for  measurements at 225, 250, 275 and 300 GHz), respectively.

From  the figure, we can see that measurements agree reasonably well with the  simulations near both sides of the position with maximum electric field  intensity. There are slight differences at the positions far away from  the peak, which is attributed by the errors in fabrications and  measurements, as explained in Section S.7 in the Supplementary Information.  The proposed idea of controlling the dispersion properties of the  metasurface has been proved both numerically and experimentally in this  article.

Discussion

Although  controllable anomalous reflection beam angles of the THz metasurface  versus different frequencies are successfully demonstrated, there are  actually significant limitations on the maximum achievable sizes in the  x- and y-axis directions due to the following reasons. For an assumed  phase curve Φo(f), the required phase curves of the unit cells on Lines 1 and 2 in Figure 1 are given in Section S.4 in the Supplementary Information to show the conditions required by controlling dispersion properties of the metasurface. From Fig. S5a,  it can be seen that the required phase curve versus frequency becomes  steeper and steeper when the position of the unit cell is farther away  from the starting point of Line 1. Fortunately, a phase delay instead of  a phase advance is always required. However, the achievable slope of  the reflection phase for a given unit cell geometry is generally limited  within a reasonable range. Otherwise, if the unit cells are placed in  the -x-axis direction, the required phase curve would exhibit a positive  slope, which is actually unachievable in physics without significant  reflectivity degradation. Fig. S6a shows  the required reflection phase of the unit cells on Line 2. It can be  seen that the slope of the required phase curve is changed from a  negative to a nonphysical positive value as the unit cell is farther and  farther away from the starting point of Line 2. Moreover, nonlinearity  of the required phase curves along Lines 1 and 2 in Figs. S5b and S6b brings more restrictions on the achievable DCTM sizes.

Note that, if we find the first order derivative of Φ(f, ) in Eq. (1) with respect to independent variable r, Eq. (2) can be obtained:

Actually, when the source is placed by an infinite distance from the metasurface, indicating the plane-wave incidence, R will be independent on  and Eq. (2) can be simplified to the generalized law of reflection proposed in Ref. 12. Therefore, what we are studying is more general than the case in Ref. 12.  For the plane-wave incident case, the phase required by each unit cell  is actually independent on the y-axis position and then no limitation is  put on the dimension of the DCTM along y-direction. Therefore, only the  desired properties of unit cells along Line 1 are studied, as shown in Fig. S7 in the Supplementary Information.  It can be concluded that the design of such a DCTM in the plane-wave  incident case is much easier than the general case studied in this  article. In other word, the difficulties are gradually decreased as the  source is put farther and farther away from the DCTM.

Although the metasurface in Ref. 28 can  also present frequency scanning beams, only the phenomenon of  dispersive beams are mentioned, which is just a natural characteristic  of broadband devices and the dispersion properties cannot be controlled  therein. Secondly, the operating principles of both devices are totally  different. The holographic concept is employed in Ref. 28,  but the multiple frequency phase matching method is used in this work,  which means that the dispersive nature of the proposed THz metasurface  is purposely controlled.

Methods

THz metasurface design

To  successfully implement the proposed concept of the DCTM, a database of  the unit cell with different physical parameters is firstly built. Since  not all parameters are critical to tune the reflection phase, only five  are chosen to map the physical sizes of the unit cell to the achieved  reflection phase, as given in Section S.5 in the Supplementary Information.  In the multi-dimensional database, the index of each element indicates  the physical size of the unit cell and the value corresponds to the  reflection phase. Then, the DCTM can be designed based on the database  after the source position is provided.

To  design the DCTM, the unit cells with proper physical dimensions are  carefully selected from the well-prepared database by multi-frequency  phase matching method, i.e., simultaneously matching the achievable to  the desired reflection phases of each element at 200, 225, 250, 275 and  300 GHz29,30.  In this process quite strict demands are set on the element  performances which, however, can simplify the metasurface design in  return. The method to control the dispersion of a metasurface can be  also extended to other kinds of applications, e.g., a meta-lens with a  controllable focal position versus frequency.

Fabrication

The  DCTM was fabricated by standard micro-fabrication method in the City  University of Hong Kong. First, polymer BCB from Dow Chemical Company,  was spin-coated and cured (at 270°C for 2 hours) onto a flat aluminum  plate. As previously stated, the thickness of the BCB layer was set at  ~120 μm and determined by the spinning speed and time (1000 rpm, 2 min,  spin coating for 3 times). Then, a ~1 μm thick aluminum film was  deposited onto the BCB layer by thermal evaporation. Finally, the  aluminum pattern was fabricated by photolithography process followed by  aluminum wet etching. Photographs of the fabricated DCTM prototype can  be found in the inset of Figure 5a and Fig. S8 in the Supplementary Information.

(a)  Full view of the setup. A vector network analyzer (Agilent N5245A) with  a maximum operating frequency up to 50 GHz is located at the center of  the photograph. For THz measurement, two pairs of OML extenders (Model  V05VNA2-T/R and V03VNA2-T/R) are used to extend the operating frequency  up to 140 ~ 220 GHz and 225 ~ 325 GHz. The two DC power sources are used  for the two OML extenders. The monitor is used to display the measured  data more clearly. The left OML extender with a receiving horn antenna  is placed on a manual rotator to measure the electric fields within an  angular range, while the right one and the horn antenna are used for  transmitting purpose. The two OML extenders, rotator and DCTM prototype  are placed on an automatically horizontal optical table. The inset in  the upper-right corner shows photograph of the full DCTM prototype. (b)  Local view of the prototype. The DCTM prototype installed on a plastic  holder is clearly shown along with the transmitting horn antenna and the  planar reflector.

Figure 5