Microwave and optical devices such as prisms, reflectors, gratings, or lenses are indispensable in modern science and technology, and their high-quality developments represent significant technical achievements in the history of humankind. These traditional elements mostly rely on the phase change along the light trajectory inside three-dimensional structures, which leads to the whole devices usually being very bulky and heavy, which limits their further applications for some miniaturized and integrated systems.

Over the last decade, there has been much interest focusing on two-dimensional (2-D) ultra-thin periodical metallic or dielectric structures, namely metasurfaces or metastructures to design various functional devices and systems. In addition, the working principles can be controlled by the generalized laws of reflection and/or refraction [1]. Among these, metasurface lenses (or metalenses) are an important metadevice and have become an active research field in recent years owing to their superior performances and much lower profile design compared to traditional designs [2–8].

The dispersion property of most materials and devices is positive, which relies on the traditional refractive laws. This is intrinsically caused by their increased refractive index along with increased frequency range. For example, prisms deflect more blue light than red light with larger refractive angle. As a result, traditional microwave or optical refractive lenses focus incident waves of larger operation frequency on the focal plane with smaller focal length. This phenomenon is schematically illustrated in Fig. 1(a). For incident waves with larger operation frequency of f1, its larger refractive angle leads to smaller focal length of F1 because of the above-mentioned normal material dispersion. Another important type of negative dispersion control is typical diffractive devices such as conventional Fresnel lenses or blazed grating [9–11] which have long existed in the optical and/or microwave society. Diffractive-type devices and systems demonstrate a larger focal length of F1 with a larger operation frequency of incident wave f1 which is originally caused by an interference effect, as shown in Fig. 1(b).

Recent studies and advancements demonstrate that metasurfaces or metalenses dispersion is more like that of diffractive-type since their constitute elements are various sub-wavelength 2-D dielectric or metallic patterned geometric structures [4,5,12–16]. Controlling the fundamental chromatic dispersion in metasurfaces or metalenses is of great importance and also has attracted great interest in recent years [12–30]. It should be noted that these progress and achievements are mainly obtained for the all-dielectric metasurfaces or metalenses in the high-frequency band such as in the visible or infrared regimes. On the other hand, metalens designs by using plasmonic or metallic metasurfaces in a low spectrum such as terahertz (THz) or microwave are also presented but most designs suffer from low efficiency or low NA especially for a continuous broadband range [31–42]. In order to improve their transmission performances and extend their phase control range, multi-layer metallic metasurfaces of at least three or more are commonly used as a meta-atom which makes the whole device bulky and need multiple fabrication processes and strict alignments [43–56]. Some broadband metalens designs even adopt and combine different metasurface shapes which also pose a great challenge for practical applications [35–37]. Very recently, an ultra-thin double-layer broadband high focusing efficiency of above 40% for a plasmonic metalens from 8.0 to 10.5 GHz was demonstrated and reported in the microwave band but the dispersion characteristic is still traditional refractive-type [38]. To design plasmonic metalenses with broader bandwidth and higher efficiency by using a reduced device thickness is urgent especially for a diffractive-type dispersion property, which can enrich the studies on broadband high-performance plasmonic metalenses in the community [31–38].

In this paper, an ultra-thin broadband plasmonic metalens from 9 to 12 GHz based on a bi-layer phase gradient circular split-ring metasurface is designed, fabricated, and characterized both numerically and experimentally. Both high transmissive efficiency and high focusing efficiency in the entire operation bandwidth are realized in the simulations. In addition, a moderate high NA is also achieved. Experimental measurement results also verify its high focusing efficiency for the designed broadband metalens. These excellent focusing performances can outperform previous broadband plasmonic metalenses largely in low spectra [31–38]. Furthermore, both numerical and experimental results of wavelength-dependent focusing demonstrate its diffractive-type dispersion property which is also ready for numerous applications such as wideband and high-gain transmitarray antennas [43–56].

Chromatic dispersion control of sub-wavelength metalenses in the high-frequency band is usually based on the multiple parameters optimizations of the all-dielectric meta-atom on the substrate [19–22]. In addition, some broadband achromatic metalenses are also obtained by combining different types of meta-atoms by controlling the phase and phase slope of the meta-atom simultaneously. Although the chromatic dispersion can degrade imaging performances for some applications, its intrinsic dispersion property, especially diffractive-type along broadband frequency in low spectra, is of great importance for some novel applications such as wideband microwave transmitarray antennas [43–56], nanoparticle trapping [57,58], edge detection [59,60], and broadband retroreflectors [61–63]. Additionally, understanding its original dispersion of single plasmonic metalens simultaneously with high-performance focusing properties can pave the way for further studies on broadband achromatic metalenses [36,37]. The dispersion issues for plasmonic metalenses are not well addressed and talked about so far because of their complicated multi-layer metal–dielectric configurations [31–38]. Here, we first give the general dispersion control condition for broadband plasmonic metalens design and then demonstrate an ultra-thin broadband diffractive-type microwave metalens both numerically and experimentally. In order to realize broadband and highly-efficient focusing for normally incident waves, the frequency f and focal length F dependent quadratic phase profile should be satisfied as follows [17–38]: φ(f,F)=2πfc(r2+F2).(1)

For most cases, this radial position r-dependent phase profile varies for a broadband frequency range; thus, its focal length F is also different with different operation frequency f, i.e., the well-known chromatic dispersion. c is light speed in free space. This chromatic dispersion commonly exists in low spectra with plasmonic metasurfaces [31–38]. To give a close look at its dispersion characteristic along a broadband frequency range, we should calculate its phase-shift differential equation which includes two variables, i.e., f and F. Hence, the following expression can de deduced and obtained: dφ=2πc(r2+F2)+2πfcFr2+F2.(2)

It can be noted that the key to control its dispersion property is the simultaneous control of the phase φ and its phase-shift slope dφ of plasmonic meta-atom carefully [17–21]. Some broadband plasmonic metalenses in the THz or microwave spectrum are demonstrated by using triple-layer metasurfaces [31–35], but the working efficiency and NA are relatively low. More importantly, the dispersion characteristic of these broadband plasmonic metalenses is inconclusive [31–35,38], which hinders its further studies on arbitrary dispersion control based on plasmonic metasurfaces. There is only one double-layer refractive-type high-efficiency broadband plasmonic metalens in the microwave regime [38]. There are two basic conditions for a broadband plasmonic metalens realization according to the above expressions. The first is that the phase change range of the proposed meta-atom along a broadband frequency range should be linear as much as possible. Second, the phase slope in Eq. (2) should change faster than the designed focal length for the considered broadband frequency range for the refractive-type dispersion while the inverse condition for diffractive-type dispersion [31–35,38]. An achromatic doublet lens with opposite dispersion such as the combination of refractive-type and diffractive-type can pave the way for further broadband microwave studies but reducing its whole device thickness is still very challenging according to some recent studies [35–37].

Different from previous broadband metallic metalenses based on multi-layer patch metasurfaces patterned on the dielectric media [31–35], we here propose an ultra-thin double-layer symmetric complementary circular split-ring resonator (SRR) metasurface to design frequency-dependent broadband metalenses, which only need a single-step fabrication process. In addition, the complementary SRR metastructure can realize higher transmission magnitude compared to previous square or circular patched ones [32–35], which can be very promising to design high-performance plasmonic metalenses in low spectra. The single-layer simple configuration can largely reduce the design complexity and ease the device burden and fabrication cost. Figure 2(a) plots the perspective views of the identical double-layer SRR metasurface which is sandwiched by the filled dielectric medium (dielectric permittivity ε=2.2) in between with a device thickness of t=2.6mm. The whole device thickness is only 0.09λ0 (λ0 is at the central wavelength), which is much thinner than previous broadband all-dielectric metalenses [12–30] and plasmonic metalenses [31–38]. The patterned metallic film is copper and is assumed as a perfect electric conductor in the simulations. Its detailed structural parameters and cross-sectional views of the SRR metasurface are given in Fig. 2(b). The symmetric complementary SRR is designed to have an open angle of α with respect to the y axis and the same circular groove width of w. The radius and period of the meta-atom are shown by r and p, respectively.

In order to design an ultra-thin broadband high-efficiency plasmonic metalens based on the above bi-layer SRR phase gradient metasurfaces, its unit cell transmission performances are first simulated and obtained by using commercial CST Microwave Studio based on the finite integrated algorithm. Here, the considered broadband range is within X band, and thus the main structural parameters of the SRR meta-atom are optimized and carefully set as w=1mm, p=11.5mm, and α=150°. The phase gradient elements of the metalens are created by varying the radius of r for simplicity. The transmission magnitude and phase changes with different r along the frequency range as indicated by different color lines, are plotted in Figs. 3(a) and 3(b), respectively. It can be noted that an average high transmission magnitude above 80% within the target band from 9 to 12 GHz, as shown by the gray bar, is realized. In addition, the phase slope nearly obeys linear relation both with sufficient change within the considered frequency range for the radius range from 3.5 to 4.7 mm. In the simulations, the unit cell boundary condition along x and y and the open space boundary condition along z are used. The polarization of incident waves is along the x axis in Fig. 2. Compared to the previous double-layer double-SRR broadband metalens [38], the transmission magnitude of the unit cell is much higher, and the meta-atom is also simpler with extended operation bandwidth. Furthermore, the phase change slope of the meta-atom is different; thus, its dispersion of plasmonic metalens is also different. The demonstrated SRR metasurface with proper structural parameters and polarization behaves as a weakly coupled high-contrast resonator, which contributes to its frequency-dependent high transmission. To further verify the high transmission performance of the proposed single SRR meta-atom, the normalized surface current distributions at the central frequency of 11 GHz with different radii of r=4.7mm, 4.1 mm, and 3.5 mm are plotted in Figs. 4(a), 4(b), and 4(c), respectively. The strong and symmetric corner surface modes around the circular split ring are excited, which contributes to the high transmission performance under the single x-polarized incident wave. Figures 4(d)–4(f) plot the corresponding near-field distributions of the unit cell with different SRR radii. The strong and gradient intensity patterns of near-field distributions further illustrate the linear transmission phase profile of the SRR metasurface with different radii.

Based on the above high-performance transmission of the proposed SRR meta-atoms and the broadband metalens phase profile of Eqs. (1) and (2), a broadband high-efficiency plasmonic metalens is designed by arranging a 15×15 square array on the x–y plane with F=100mm at a central frequency of 11 GHz. The transmission efficiency of the plasmonic metalens is fundamental which is defined by the ratio between the total transmissive plane power to the incident wave power across the whole metalens aperture [39]. Most of the previous plasmonic metalens designs suffer from low transmission efficiency [39–46] especially in the high-frequency band. Here, a very high transmissive efficiency above 80% within the frequency band from 9 to 12 GHz is achieved, as shown by the red dotted line in Fig. 5(a). The relative operation bandwidth is as large as 28.6%. Additionally, an extremely high peak efficiency even above 90% is observed at the central frequency of 11 GHz with an x-polarized incident wave. This is in accord with previous simulated maximum transmission magnitude distributions with different radii of the meta-atom around 11 GHz in Fig. 3(a). Figures 5(b)–5(e) present the normalized power distributions on the transmissive plane just across the metalens aperture for the operation frequency range from 9 to 12 GHz with a 1 GHz step, respectively. The normalized value in each element represents its transmission magnitude of the proposed meta-atom with corresponding varying radii.

The dispersion property of the broadband plasmonic metalens is also highlighted and the focal pattern on the x–z plane for the operation frequency range from 9 to 12 GHz with a 1 GHz step is plotted in Fig. 6(a)–6(d), respectively. The white line indicates its corresponding focal length. Figures 6(e)–6(h) present their corresponding focal spot on the x–y plane. Its detailed simulated focal length distribution along frequency is plotted in Fig. 6(i) as red points with the frequency range from 9 to 12 GHz with a 0.5 GHz step. It is shown that the focal length increases along with operation frequency and thus obeys diffraction-type in Fig. 1(b). This distinct dispersion characteristic is crucial for various applications such as wideband microwave transmitarray antenna where antenna location is closely dependent on the varying focal length with different operation frequency [43–56].

Its high-efficiency broadband focusing performances and the diffraction-type dispersion characteristic are also verified by experimental measurements. In the low-frequency microwave regime, plasmonic metalenses are usually fabricated by using the conventional printed circuit board technique. Compared to previous multi-layer broadband metalenses [31–38], a double-layer microwave metalens here only needs a single-step fabrication process and thus is promising for large-scale production. The metallic sheet of the identical double-layer is copper. The filled dielectric is Rogers F4B220 with ε=2.2 and loss tangent of 0.008. Other parameters are the same as the previous simulations. The detailed experimental setup in the microwave chamber laboratory is illustrated in Fig. 7(a). The source antenna (version is HD-100HA20SZ) emits a broadband linearly-polarized incident wave onto the metalens and a probe on the other side can detect its spatial power distributions at a cross section. The probe is connected to a vector network analyzer (VNA, Agilent N5242A), which can record its focused pattern at a desirable vertical distance across the metalens. The detailed fabricated sample is also given in Fig. 7(b), which is arranged by 15×15 square phase gradient transmitarrays.

In order to verify its broadband focusing performance experimentally, the dispersion property of the plasmonic metalens should be set first with the considered broadband frequency range. After some tedious measurements and critical proof, the focal length with frequency range from 9 to 12 GHz with a 0.5 GHz step is obtained and is also plotted in Fig. 6(i) as green points. The fitted blue line of F=13×(f−9)+74 agrees well with both simulations and measurements; F is the focal length and f is the frequency. Both simulation and measurement results indicate that the focal length increases along with operation frequency and thus obeys diffraction-type dispersion as shown in Fig. 1(b). The measured focal length is slightly larger than simulated results and the maximum error is observed at around 10.5 GHz. This discrepancy may come from the imperfect open-space boundary condition of the measurement environment; the fabrication error of the sample; and the unavoidable misalignment among the source, sample, and probe in the measurement. This negative dispersion is fundamentally different from most of previous broadband metalenses based on plasmonic metasurfaces [34–39] and so provides a new regime to control its dispersion characteristic based on plasmonic metasurfaces. In addition, high-performance focusing along the broadband frequency range of the proposed bi-layer plasmonic metalens can extend its potential applications in the microwave regime [43–56].

The measured focused power patterns at the focal length with a frequency range from 9 to 12 GHz with a 1 GHz step are presented in the upper panels in Fig. 8. The focal length at each frequency is based on the measurement results as indicated by green points in Fig. 6(i) correspondingly. Based on the simulated results in Figs. 6(e)–6(h) and the above measured results in Fig. 8, the spot size (full width at half-maximum, FWHM) and its numerical aperture (NA=0.5λ/FWHM, λ is the working wavelength) can be calculated and compared with each other. The detailed spot size distributions along the x axis are plotted in the lower panels of Fig. 8 for frequencies of 9 GHz, 10 GHz, 11 GHz, and 12 GHz, respectively. The red lines are from simulated results and discrete blue points are from measurement results along its central line. It can be seen that good agreement between simulations and measurements is realized. To further evaluate its broadband focusing performance, the focusing efficiency is also calculated based on its focal plane with different operation frequencies as shown in Figs. 6(e)–6(h) from 9 to 12 GHz with a 1 GHz step, respectively. The focusing efficiency is defined by the focused power on the focal plane with 3 times FWHM width divided by the incident wave power onto the metalens [36,37,40–42]. The simulated focusing efficiency of the red line in Fig. 9(a) indicates that the high value range 30%–56% with the entire frequency band is obtained with a peak value around 56% at the central frequency of 11.5 GHz. The measured focusing efficiency distribution as a function of operation frequency ranging from 9 to 12 GHz with a 0.5 GHz step is also calculated and plotted as the green line in Fig. 9(a). It is calculated based on the ratio between the focal spot power integration with 3 times FWHM width area in Fig. 8 to the total incident power onto the metalens. It is shown that a much higher focusing efficiency range of 50%–66% is achieved compared to the simulated results in Fig. 5 for a broadband frequency range 9–12 GHz. The maximum value is above 65% at 11.5 GHz, which agrees well with that optimized operation frequency in Fig. 5(a). The presented high working efficiency of the broadband plasmonic metalens can outperform the previous designs in Refs. [31–38]. In addition, the measured large average NA=0.6 within the entire broadband range is also achieved, as shown by the green points in Fig. 9(b). The measured NA is slightly smaller than the simulated NA=0.7, as shown by the red lines in the diagram. This can be explained by the larger angular dispersion of the SRR meta-atom at the edge of the metalens. Thus, the refraction angle of θ is decreased in the measurement compared to simulations with ideal boundary conditions [35]. The decreased refraction angle leads to larger focal length and smaller NA according to NA=sin(arctanθ). Based on the focal length F variation trend in Fig. 6 along the broadband range, the NA also demonstrates a decreased value along with increased frequency which can be explained by NA=sin(arctan(d/2F)), where d is the aperture size of the metalens and F increases for diffraction-type dispersion, thus leading to NA decrease along the frequency range. The focusing efficiency is inverse to the NA; thus, the measured results are larger than the simulated ones in Fig. 9(a) [8,9]. This error can be decreased by increasing the focal length of the initial metalens design in simulations. The detailed discussion and analysis are given in Dataset 1, Ref. [64]. The demonstrated broadband high-performance focusing, such as high focusing efficiency, reduced device thickness, and moderate high NA, is very intriguing for various microwave applications such as imaging, sensing, and antennas [43–61]. In addition, the broadband diffraction-type dispersion control can open new regimes in diffractive optics based on plasmonic metasurfaces.

In summary, a broadband plasmonic metalens with only double-layer phase gradient complementary SRR metasurfaces from 9 to 12 GHz (relative bandwidth is 28.6%) is designed and demonstrated both numerically and experimentally. The device thickness is only 0.09λ0 (λ0 is the central wavelength). Both numerical simulations and experimental measurements show its increased focal length with increased operation frequency and this negative dispersion characteristic is distinct to traditional refractive-type broadband metalenses. Furthermore, its broadband high-performance focusing such as high working efficiency (both high transmissive efficiency and focusing efficiency) and large NA along the entire broadband frequency range is also achieved in simulations and measurements. These good merits are promising for some high-performance metalens-based applications such as microwave imaging and high-gain antennas, in the low-frequency regime. Also, the demonstrated negative dispersion property can open new avenues to control its dispersion relation based on plasmonic metasurfaces and can facilitate the development of high-quality achromatic plasmonic metalenses in the future.

Acknowledgment. The authors acknowledge helpful discussions with Dr. Liangsheng Li and Dr. Kainan Qi for this work.