Electromagnetic metasurface lenses with the characteristic of being conformal to a cylindrical geometry are presented in this study. Based on the formulated principle of the cylindrical metasurface lens operating with transmission or reflection mode, the transmission or reflection phase gradient varying along the circumferential direction of a cylinder is implemented. A focused beam is observed at the objective focal point for each lens illuminated by a plane electromagnetic wave with transverse magnetic or transverse electric polarization. A coaxial-fed microstrip patch antenna element is used as a feeding of cylindrical metasurface lenses and positioned at their focal points, so as to evaluate their application in the enhancement of antenna gain along the boresight direction. By virtue of the focusing ability of presented lenses, effectively enhanced boresight gain from the cylindrical metasurface lens antennas are obtained, in comparison with the freestanding feeding antenna. The agreement between simulation and measurement validates the designs. Conformal integration or embedment of the electromagnetic lens into a certain platform skin with cylindrical characteristics is therefore potentially demonstrated, which implies an enhancement of boresight gain without obviously disturbing the local shape of the skin by apparent weight or drag.
Electromagnetic lens has found wide applications in the gain enhancement of various antennas, due to its ability to transform a nonplanar wavefront into a planar one. The traditional electromagnetic lens mainly relies on its transition of medium parameter and shape to alter the electric path length and thus to achieve the phase compensation necessary for the wavefront transformation [
Depending on the manipulation of refraction or reflection, the reported electromagnetic metasurface lens can be classified as transmission type (T-type) or reflection type (R-type). For both types of operation, a feeding antenna is typically fixed at the focal point of the metasurface lens so that the whole structure can function as a lens antenna. Compared with the freestanding feeding antenna, the lens antenna results in radiation enhancement through the redistributed aperture. For the T-type operation, a flat metasurface lens with a circular shape of 16.2
With an aim of demonstrating the conformal integration or embedment of the lens into the cylindrical structure, passive metasurfaces conformal to a cylindrical geometry are employed to implement curved lens antennas in this study. Since the cylindrical structure is typically involved in many moving platform bodies, the conformal integration or embedment of the lightweight lens into the curved platform skin can potentially lend the lens itself to be a part of the platform body. In such a case, the local shape of the platform skin can remain unchanged, and thus, enhanced radiation can be probably obtained without obviously increasing the air drag, while directly integrating the traditional lens or planar metasurface lens onto the cylindrical skin tends to incur increased drag and disturbed aerodynamics. Initially, a cylindrical metasurface lens operating with T-type or R-type for both transverse magnetic (TM) and transverse electric (TE) polarizations is designed. The phase gradient of the metasurface lens and its angular sampling for calculating the phase distribution are formulated along the circumferential direction of the cylinder. An etched slot is used to constitute the four-layer unit cell, and slot dimensions are varied to achieve the transmission phase gradient for the T-type cylindrical metasurface lens, while a printed copper loop is used as the unit cell, and its outer or inner edge length is changed to attain the reflection phase gradient for the R-type cylindrical metasurface lens. Then, a dual-polarized microstrip patch antenna element is deployed as the feeding antenna of designed lenses to mainly investigate the boresight gain enhancement. By virtue of the focusing ability of cylindrical metasurface lenses, effective enhancement of boresight gain is observed from the T-type or R-type cylindrical metasurface lens antenna, in comparison with the freestanding feeding antenna.
The T-type cylindrical metasurface lens that can focus an incident plane electromagnetic wave is formulated in this section. Figure
Cross-sectional view of the cylindrical geometry considered for the lens operating in (a) T-type or (b) R-type. Arbitrary position
Calculated (a) phase gradient and (b) phase distribution for the T-type or R-type cylindrical metasurface lens.
Figure
By substituting the determined angles of incidence and reflection into the generalized laws of reflection, the reflection phase gradient of this cylindrical metasurface lens is expressed as follows:
Calculated with
In order to map the calculated phase gradient onto the cylindrical surface, the unit cell involving a certain periodicity is utilized to constitute the lens. As a result of the discrete unit cell, the continuously varying angle of incidence as well as phase gradient of the metasurface lens has to be sampled along the circumferential direction of the cylinder with an angular interval
Based on the transmission phase gradient of the T-type lens, the dimensions of the
Using
For the R-type cylindrical metasurface lens, the dimensions of the
With the circumferential periodicity of the unit cell
According to the transmission phase limit of multilayered frequency-selective surfaces [
The utilized unit cell geometry for the T-type cylindrical metasurface lens.
Simulated (a) transmission phase and magnitude of the unit cell and (b) edge lengths of the inner patch at every sampled position.
Since the transmission responses for TM and TE polarizations diverge for oblique angle of incidence, the slight difference between
To obtain the same reflection phase for both polarizations at sampled positions under oblique incidence, the copper loop geometry slightly modified with rectangular outer or inner contour is used as the unit cell to build the R-type cylindrical metasurface lens [
The utilized unit cell geometry for the R-type cylindrical metasurface lens.
Dimensions of the loop unit cell at every sampled position.
With the determined dimensions in Figure
Foam semicylinder coated with the T-type cylindrical metasurface lens.
Simulated magnitude of electric field
Analogically, the loop unit cells with determined dimensions in Figure
Copper semicylinder coated with the R-type cylindrical metasurface lens.
Simulated magnitude of electric field
Based on the beam-focusing effect produced by the T-type or R-type cylindrical metasurface lens, a feeding antenna can be placed at the focal point of the lens, with the aim of enhancing its boresight gain. Due to the narrow-band operation of the lenses, a probe-fed microstrip patch antenna element is simply designed to have the fundamental resonance at 10 GHz and used as the feeding antenna of both lenses to evaluate the enhancement performance. Other types of antennas may also be used as a feeding antenna of the lenses.
Figure
T-type cylindrical metasurface lens fed with a microstrip square patch antenna element.
Frequency-dependent magnitudes of input reflection coefficients, main lobe gain, and radiation efficiency of the freestanding microstrip patch antenna element and the T-type cylindrical metasurface lens antenna. (a, c) TE-polarized radiation. (b, d) TM-polarized radiation.
Moreover, the realized gain of the cylindrical metasurface lens antenna is compared with that of the freestanding feeding antenna at 10 GHz in Figure
Two-dimensional radiation patterns of the freestanding microstrip patch antenna element and the T-type cylindrical metasurface lens antenna. (a)
The cylindrical metasurface lens antenna operating in R-type is shown in Figure
R-type cylindrical metasurface lens fed with a microstrip square patch antenna element.
Frequency-dependent magnitudes of input reflection coefficients, main lobe gain, and radiation efficiency of the freestanding microstrip patch antenna element and the R-type cylindrical metasurface lens antenna. (a, c) TE-polarized radiation. (b, d) TM-polarized radiation.
Simulated two-dimensional radiation patterns of the freestanding microstrip patch antenna element and the R-type cylindrical metasurface lens antenna. (a)
Although the transmission-focusing and reflection-focusing differentiate the operating manners of the T-type and R-type cylindrical metasurface lenses, both lenses share a similar design and simulation procedures mentioned above. Therefore, only the cylindrical metasurface lens antenna operating in T-type is fabricated and measured in this section so as to verify the simulation-based observations. The aforementioned commercial laminates and foam are used for the prototype. The metasurface lens fabricated through printed circuit board (PCB) technology is attached to the cylindrical surface by plastic screws with M2 thread size. A photograph of the prototype under measurement is provided in Figure
Photo of the measurement setup of the T-type cylindrical metasurface lens antenna.
Cylindrical metasurface lenses with a thin radial profile have been presented to serve as an example of demonstrating the conformal integration or embedment of the electromagnetic lens towards the cylindrical shell of certain platform bodies. The conformal integration or embedment potentially ensures the undisturbed local shape as well as aerodynamics of the platform, which can hardly be achieved during direct integration of the traditional lens or planar metasurface lens onto a cylindrical skin. Based on the calculation and sampling of the phase gradient, transmission or reflection phase distribution of the cylindrical metasurface lens was determined for implementation. In order to relatively independently tune the TM and TE responses for oblique incidence, the basic and simple slot or loop geometry has been, respectively, employed as the unit cell of the T-type or R-type cylindrical metasurface lens. Other compact geometries that meet the consideration of tuning can be also used to construct the unit cell of the lens with dual-polarization capability. Due to the control of refraction or reflection, focused beam of each cylindrical lens has been observed. In comparison with the freestanding feeding antenna, enhanced boresight gain has been obtained from each cylindrical lens antenna for both TE- and TM-polarized radiation at the operating frequency. Meanwhile, certain limitations including the side lobe of the T-type cylindrical lens antenna, back lobe of the R-type cylindrical lens antenna, and narrow-band operation of the lenses are also observed. Introducing a certain gradient for focusing effect along the axial direction of the cylinder to reduce the side lobe level and using other unit cell design schemes with a smaller period to widen the operating bandwidth of the lenses may be exploited in a future study [
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported in part by the National Natural Science Foundation of China under Grant 61601379 and Grant 61771407 and in part by the Fundamental Research Funds for the Central Universities under Grant 2682018CX41.