Metamaterials are artificially engineered materials created using sub-wavelength elements, known as meta-atoms or unit cells [
64]. Metasurfaces are the planar alternative to metamaterials and are sometimes referred to as 2D electromagnetic surfaces [
65]. Metasurfaces are used for various applications, such as polarization conversion, filtering, designing phase-shifting surfaces and phase-gradient metasurfaces [
24,
26]. Passive phase-gradient metasurfaces are freestanding surfaces with a saw-tooth phase profile in a specific direction while maintaining a constant phase in the orthogonal direction. An array of distinct cells (periodically repeated in one of the directions, either
x or
y, while aperiodic in the orthogonal direction) determines this phase gradient, with each cell designed to provide a predetermined transmission phase shift to a normally incident electromagnetic wave. In some applications, the amplitude of the near-electric field can also be manipulated using these cells. We can refer to the antenna array theory to understand the working principle behind the PGMs. As per the antenna array theory [
66], if several discrete identical radiating elements are arranged in a straight line, the field radiated by such an array can be given by Equation (1). in its simplest form.
where
represents the total electric field. The array factor depends on the number of elements (N), the geometrical properties of the elements, their spacing (d), their relative magnitudes and their relative phase. When all the array elements are identical, with equal magnitude and a progressive phase delay among the adjacent elements, the array is called a uniform linear array. For a uniform linear array, the array factor (AF) is given by Equation (2).
where
d is the spacing between the elements,
k is the free space wave-number, and
N is the total number of elements. The maxima of the beam occurs at
, where
. Secondary maxima, known as the grating lobes, occur in array antennas when the inter-element spacing is large relative to the operating wavelength. These lobes occur at an angle away from the main beam, and their angular position can be calculated using Equation (3).
To direct the radiated beam away from the broadside direction, all the antenna elements are fed with a signal that has been phase-shifted. This is done so that the phase shift between adjacent antenna elements remains constant, denoted by . For example, if we want to tilt the radiated beam at an angle away from the broadside direction, between adjacent elements can be set as . One method to achieve a constant phase shift among adjacent elements is directly exciting the feed with phase-shifted signals, often utilizing active phase shifters. Alternatively, the feed length (microstrip or strip-line length) can be adjusted so that each element receives a phase-shifted input.
Similarly to antenna arrays, in the case of passive phase-gradient metasurfaces, if an array of cells on the surface is arranged such that the phase difference between adjacent cells remains constant, denoted by
, the incident beam on the surface can be tilted to an angle
away from the broadside direction, depending on this phase gradient. In
Figure 4, we observe how an array of cells with an element-to-element phase difference equal to
resembles a metasurface comprised of cells with a gradient phase profile. The fundamental phase-shifting element in the phase-gradient metasurface is a sub-wavelength cell. Based on structure and composition, the different types of cells available in the literature can be broadly classified, as shown in
Figure 5.
3.3. Composite Metal-Dielectric Unit Cells
Composite (metal-dielectric) unit cells are made up of both metal and dielectric material. A detailed analysis of the choice of resonating element for such unit cells was presented in [
76]. Multilayer printed unit cells can be used to design the metasurfaces. For implementing metasurface, only those cells that offer high transmission magnitude, ideally less than -1 dB, are selected. However, when the complete phase range is impossible using only -1 dB cells, a few cells with up to -3 dB transmission magnitude can also be selected. According to the detailed analysis of metasurfaces conducted in [
77], the transmission phase of any single layer (one conductor layer placed over a dielectric substrate) surface is a function of substrate electrical thickness
, where
is the phase constant (
) and
is the height of the substrate. With a single-layer unit cell, the maximum phase range that can be achieved regardless of the implemented metallic element shape is
with a transmission coefficient magnitude within -1 dB and
with a transmission coefficient magnitude greater than -3 dB. To increase the phase range, the number of layers must be increased.
Wide-band dual resonant double square ring unit cells were presented in [
78]. The unit cell structure had four metal-dielectric layers separated by an air gap. Adding the inner rings increased the achievable phase range and improved the 1 dB gain bandwidth by 7.5%. For any selected unit cell geometry, the phase range of a multi-layer unit cell structure depends on the substrate material, the number of layers, and the spacing between the layers. A minimum 3-layer structure with two dielectric layers and three metal layers is required to provide a phase range of
, which also comes at the cost of a reduced transmission coefficient magnitude of -3 dB. Increasing the number of layers increases the phase range with transmission coefficient magnitude closer to 0 and more significant than -1 dB. It was also deduced that the electrical thickness of a substrate
should be at least 90 degrees at the resonant frequency to achieve the maximum transmission phase range [
77]. The complete analysis of two-, three-, and four-layer FSSs was given for different relative permittivity values. It was concluded that the height of the dielectric layer should be selected according to the required phase range and the dielectric permittivity. If
is decreased below 90 degrees, the phase range is reduced to 120 degrees. If
increases above 90 degrees, the transmission phase range is reduced to 240 degrees. For a three-layer FSS, with the increase in relative permittivity, the phase range increases. For
and
, a transmission phase range of 360 degrees can be achieved with a four-layer unit cell with a reasonable transmission magnitude of
. The analysis included conducting experiments with different shapes of unit elements.
The main challenge in building a thin and lightweight metasurface is to achieve a complete 360-degree phase range while minimizing the number of layers. This optimization is essential to reduce the design expense. To design a dual-band beam steering system, the unit cell should be able to resonate in two different frequency bands. Many structures reported in the literature focus solely on dual-band metasurface design without addressing the beam steering aspect. Designing a dual-band unit cell for a dual-band phase-gradient metasurface is more challenging than designing a single-band PGM, primarily due to the need for independent phase range coverage required at the dual frequency bands, which is often achieved by varying the dimensions/rotation angle of resonant elements of the cell.
Most cells reported in the literature are selected based on identifying phase pairs that simultaneously provide the required phase for both frequencies while maintaining a high transmission magnitude. However, this process is time-consuming, involving rigorous parameter sweep simulations where cell parameters are varied to analyze the phase response at both frequencies. This generates datasets with the maximum possible phase combinations for two frequencies with a high transmission coefficient magnitude. The highly transmitting cells are then selected from these generated datasets depending upon the required phase profile of the metasurface. Such dual-band PGMs have been reported in [
40,
43,
52] where the phase shift through the cell is tuned either by varying the length or width of the geometric shape within the cell or by rotating the shape itself at various angles within the cell. In [
40], phase tuning was achieved using phase delay (PD) unit cells, and a generic methodology to reduce the complexity of dual-band metasurface was presented. This work was an extension of the work presented earlier in [
79,
80]. The PD unit cell structure reported in [
81] was combined with the PD cell reported in [
82] to design the dual band unit cell. According to [
81], the cell corresponding to the frequencies
and
can be designed using square loops corresponding to the lower frequency and square patches corresponding to the higher frequency. Using square patch and loop as resonant elements in the dual frequency bands, [
40] further suggested that if the frequency in the two bands is selected to maximize the greatest common divider between them, it will result in fewer non-repeated cells to achieve
independent phase wrapping at the dual frequency bands. In the given analysis, the cell period was
for the lower frequency band and
at the higher frequency band. The square patch within the unit element controls the phase at a higher frequency, and a square ring controls the phase at a lower frequency band. The reported unit cell was a seven-layer structure, and cell sizes were optimized to obtain the specific dimensions, giving required phases with high transmission coefficient magnitudes for both bands. Along with the time-consuming cell selection process discussed previously, another design limitation was utilizing seven metal and six dielectric layers, leading to a thicker metasurface. These layers were also bonded together, increasing the overall cost and complexity of the design and fabrication process. A comparison of the response of PD and phase rotation (PR) unit cells in terms of the scattering parameters of the surface was also discussed in [
83]. The paper compared the working principles of PD and PR cells, their effect on the polarization of incident waves, and their design complexity.
In another study, a dual-band cell was introduced with circular polarization, operating at frequencies of 20 GHz and 30 GHz [
50]. The unit cells designed for each frequency allowed independent phase variation at the respective bands, achieved by adjusting distinct cell parameters separately. To achieve this, the resonating element for the higher frequency band was strategically positioned at the corners of each cell. This placement ensured that when the cells were arranged in a periodic lattice, they formed complete resonating elements. In contrast, the resonating element was placed in the center of each cell for the lower frequency band. This approach of interleaving the resonating elements specific to different frequency bands reduced the computational time required compared to previous techniques that aimed to identify common phase pairs. The overall structure of the proposed design consisted of three layers, comprising three metal and three dielectric layers, with dual-polarized slot elements. Beam steering was achieved by translational sliding of the transmit array relative to the feeder. The proposed unit cell design was also converted to an all-metallic structure, eliminating the requirement of expensive laminates and making the cell suitable for high-temperature applications. The same approach of strategically positioning the resonant elements within the unit cell to achieve independent frequency tuning at the dual frequency bands has also been utilized in [
42,
45,
51]. Interleaved cells, however, acquire more space. Arranging the elements in a gradient metasurface while avoiding corner discontinuities can also be challenging.
A linearly polarized unit cell with vertical and horizontal dipoles corresponding to the dual frequency bands was also utilized to design a dual-band transmitarray for wide beam scanning in [
51]. The proposed design can be used for the uplink and downlink Ka-bands. Beam scanning of
and
was achieved independently at the two frequency bands. The results suggested that the transmitted beam can be scanned over
for
GHz and
for 29 GHz in elevation with only 2 dB scan loss in the peak gain. Displacement of the feed horn antenna at the focal distance from the surface was proposed for tilting the beam. Another similar dual-band unit cell with double horizontal and vertical dipoles was reported in [
46].
Another dual-band design allowing independent phase tuning through the cell at dual frequency bands was reported in [
49]. The reported cell was a single-layered substrate meta-atom. The two metallic layers at the top and bottom of the substrate layer were composed of a modified Jerusalem cross-resonator seated in a circular hole, a modified complementary split-ring resonator, and a ring connector. The modified Jerusalem cross resonator was used to tailor the phase of the cell at the lower frequency band
. In contrast, the modified complementary split-ring resonator was utilized to tailor the phase at the higher frequency band
. In this case, the PR technique independently tunes the phase response at the dual frequency bands. In [
41], a dual-band lens was implemented, operating in orthogonal polarization for the X-band and Ku-band. A rectangular dual-band cell with two orthogonal rectangular patches printed on four metal layers separated by three dielectric layers was used. At
=8 GHz, a y-polarized feed was used, with the resonant elements’ dimensions parallel to the y-direction tuned for phase control. At
=14 GHz, an x-polarized feed was used, with the resonant elements’ dimensions parallel to the x-axis being tuned for phase adjustment.
Recently, another dual-band cell with independent frequency tuning was reported in [
84]. The unit cell consisted of four metal layers and four dielectric layers of a thin substrate. It was composed of interleaved square slot and cross slot resonant elements, following the orthogonal principle of resonance to allow independent phase tuning at the dual frequency bands.
The composite unit cells reported in this section provide more design flexibility and wider bandwidth at the dual frequency bands of operation. Moreover, such PGMs can be precisely fabricated at higher frequency bands using the standard printed circuit board fabrication techniques. However, high-performance laminates are costly. The dielectric electric field breakdown threshold is also lower than that of metals, making it less feasible for space applications or where environmental conditions are harsh [
57,
84].