Abstract
This study introduces a novel phase compensation-based, asymmetric frequency selective surface (FSS). Aimed at enhancing angular stability, the phase compensation method utilizes the reflected phase gradient changes generated by two FSSs at large grazing angles. The ultimate improvement in angular stability comes from unit amalgamation to achieve phase complementarity, effectively dealing with the phase shift of incident waves caused by large grazing angles. Based on this principle, the asymmetric FSS structure is built with 3 components: a Minkowski fractal cell, a bent-line square-loop cell, and a thin square-loop parasitic cell. Simulation results show the structure demonstrates a 0 relative shift of resonant frequency within an incidence range of 0-80° under transverse electric (TE) polarization. However, it exhibits a maximum relative shift of 5.12% in resonant frequency at an 80° incidence under transverse magnetic (TM) polarization. Compared with and units, this structure significantly reduces frequency deviation—by 100% at 80° incidence under TE polarization and by 80.12% and 83.26% compared with and units under TM polarization. Finally, the proposed FSS model was fabricated and processed, with measured data basically aligning with the simulated results.
1. Introduction
Frequency selective surface (FSS) is a periodic array structure with the capacity to manipulate the transmission or reflection of electromagnetic waves. These arrays usually consist of single or multiple resonant cells composed of metal patches arranged in a specific pattern. Given its practical applications, FSS often encounters a broad range of incident wave angles, demanding a consistently performing structure across these varying angles. Consequently, exploration of FSS angular stability becomes critical.
Prevailing strategies to tackle angular stability include the adoption of compact cell arrangement with miniaturization attributes to postpone the appearance of the gate flap. Designs such as folded cross-finger [1–3], multilayer [4–9], and fractal [10] help to achieve the angular insensitivity of FSS. Certain methods like 2.5-dimensional FSS [11, 12] and 3-dimensional FSS [13, 14] have also been employed for improved angular stability. These approaches have proven effective for ensuring good angular stability within a 0-60° range. This work introduces a phase compensation method for FSS design, thereby augmenting angular stability up to 0-80°. This allows for a more flexible deflection of the refracted beam wave vector, expanding the possibilities for enhancing angle stability.
To validate this method, a mm FSS comprising a Minkowski fractal cell, a bent-line square-loop cell, and a thin square-loop parasitic cell is presented. This novel FSS demonstrates resonant angular stability of up to 80° for both transverse electric (TE) and transverse magnetic (TM) modes. The paper is further organized as follows: Section 2 presents the FSS unit cell’s design and characterization. Section 3 delves into an investigation of angular stability. The FSS prototype’s fabrication and measured results are reported in Section 4.
2. Structure and Operating Principles
2.1. Generalized Snell Theorem
When the electromagnetic wave emitted from the feed source interacts with the array surface at an oblique incidence, as shown in Figure 1, each resulting return signal will form a distinct phase difference through each propagation path.
Assuming the electromagnetic wave originates from point A, the electromagnetic wave ranges of ABD and ACD are infinitely close to each other. Therefore, when a wave traverses these two optical ranges, an identical phase gradient can be produced, yielding a phase difference of 0 in both cases. In Figure 2, the phase accumulation for these two wave ranges is as follows: where is the phase of the incident wave.
(a)
(b)
(c)
Assuming , is obtained as follows:
Let , then . Assuming °, , thus , substituting these into
Similarly, Equation (4) can be obtained as follows:
Upon sorting the above equation and removing similar terms, the generalized Snell reflection and refraction theorem is obtained as follows:
2.2. Principle of Anomalous Refraction
The generalized Snell theorem introduces a phase gradient to achieve relative quiescence of the overall phase shift, culminating in anomalous refraction phenomena.
From Equation (6), a relationship can be derived between the refraction angle, the incident angle, and the phase compensation angle on the dividing surface: where the wave vector and the refractive index in free space. Since the domain of definition for is [−1, 1], the equation must satisfy for the refraction angle to have a solution. Specifically, this circumstance signifies the onset of anomalous refraction.
The above equation derives the quantitative correlation between the refraction and the transmission phase difference between adjacent cells of FSS exhibiting anomalous refraction. By rationalizing the cell size and the phase difference between adjacent cells, scattered waves can be steered more towards the normal direction. This is close to the transmission performance at normal incidence and it ultimately improves the angular stability of the structure.
2.3. Description of the Proposed FSS Structure
Based on this theory, the one-dimensionally distributed FSS structure comprises two units having specific transmission phases and transmission amplitudes. This is used to compensate for the phase difference, which is formed when waves propagate through different paths to the array surface. The transmitted wave undergoes anomalous refraction so that the beam refraction direction is biased towards the normal direction, thereby improving angular stability. Therefore, as shown in Figure 3, the design of FSS is meticulously structured as follows: is the Minkowski fractal FSS and is the bending line square ring FSS. Both FSS structures are mounted on an FR-4 sheet measuring mm. To bolster stability and optimize performance, a parasitic patch is strategically employed, surrounding the main radiating patch. This parasitic patch, designed in the form of a box cell with an inner diameter of 0.05 mm, contributes significantly to enhancing the overall electromagnetic coupling effect within the FSS configuration. A crucial objective of arranging the box cell is to avoid the appearance of additional resonance points within the low-frequency band, which could affect the original filtering characteristics. Its detailed structure and dimension parameters are presented in Table 1.
The resonant performance of and units are similar, along with different resonant frequency points. Specifically, for frequency GHz and period size mm, is determined in the range of (-180°, 2.3°) at an incident angle of 80° by substituting into Equation (8).
The phase difference between and is depicted in Figure 4, revealing that phase compensation is not observed within the nonresonant band. However, a significant transmission phase difference between and manifests within the interval of the resonant frequency. The designed phase difference shown in Figure 4(e) satisfying condition for achieving anomalous refraction allows for the emergence of anomalous scattering behavior in FSS configuration.
(a)
(b)
(c)
(d)
(e)
3. Simulation Results and Discussions
3.1. Angular Stability Analysis
As evidenced in Figures 5(a)–5(c), the reflection coefficients of , , and the hybrid FSS are presented by the microwave simulation software CST.
(a)
(b)
(c)
(d)
(e)
In TE mode, the resonant frequencies of were observed at 10.05 and 10.16 GHz at 0° and 80° incident angles, respectively. This accounts for a relative frequency shift of 1.09% from the center frequency at 80° compared to the frequency at normal incidence. The resonant frequencies of at 0° and 80° incident angles were 9.06 and 9.04 GHz, respectively, yielding a relative frequency shift of 0.33%. Additionally, the hybrid cell’s resonant frequency points remain consistent at 7.108 GHz at both 0° and 80° incident angles, exhibiting no shift.
In TM mode, the resonant frequency points of at 0° and 80° incident angles stood at 10.08 and 12.67 GHz, respectively, indicating a relative frequency shift of 25.69%. The resonant frequency points of at 0° and 80° incident angles were 9.11 and 11.79 GHz, respectively, yielding a relative frequency shift of 29.42%. Conversely, the resonant frequency points of the hybrid unit at 0° and 80° incident angles were 9.46 and 9.94 GHz, respectively, yielding a relative frequency shift of 5.07%.
The resonant frequency shifts to each cell at each angle of incidence compared to the normal incidence in both TE and TM modes are depicted in Figures 5(d) and 5(e), respectively. The figure demonstrates a significant decrease in the resonant frequency shift for each polarization and incident angle when the cells were combined.
Figures 6(a)–6(c) display the transmission coefficient of , , and the hybrid FSS. Based on this, the insertion loss of and the hybrid FSS is given in Table 2. In TE mode, the insertion loss of the hybrid FSS at 0° and 80° incident angles was reduced by 0.1 dB and 0.53 dB, respectively, compared with . However, the insertion loss had no improvement in TM mode. These results indicated that the insertion loss of the FSS can be improved by using phase combination units.
(a)
(b)
(c)
Under an incident angle of 80°, the passband bandwidth (transmission dB) for was 1.3 GHz, for was 1.1 GHz, and for the hybrid FSS was 2.2 GHz in TE mode. Alternatively, the passband bandwidths of and were both 11 GHz, while the hybrid cell exhibited an overall bandwidth of 10.8 GHz in TM mode. For an 80° incident angle under TE polarization, the passband bandwidth of the hybrid cell increased by 69.2% and 100% compared to and , respectively. Conversely, for an 80° incident angle in TM mode, the bandwidth of the hybrid cell decreased by 0.2 GHz compared to and . This can be attributed to the coupling effect generated by the cell combination, which shifts the resonant frequency point of the reflection from a higher to a lower frequency.
3.2. Abnormal Refraction Effect Analysis
Figure 7 presents the far-field 3D scattering direction diagram. , , and the hybrid unit all produced a potent scattered beam in the direction when °. At an incident angle of 80°, the original scattered beam of shifted to °, that of shifted to °, and that of the hybrid FSS shifted to °.
(a)
(b)
(c)
(d)
(e)
(f)
The simulation outcomes indicate that, with increasing incident angle, the beam energy in the perpendicular direction of and weakened, while the primary beam energy shifted towards the traditional refraction direction. On the other hand, the hybrid FSS gradually shifted its primary beam energy, but the offset angle remained smaller than that of the conventional refraction direction. These results additionally supported the observation that the hybrid FSS achieved anomalous refraction.
4. Fabrication and Measurement
A physical sample of the hybrid FSS, employing the phase compensation principle, was tested in a microwave anechoic chamber. The sample consists of a unit arrangement, and the testing setup uses an Agilent N5230C vector network analyzer alongside two diagonal horn antennas. The antennas are arranged on opposite sides of the sample, serving as transmitting and receiving devices, as depicted in Figure 8. The testing aims to evaluate the reflection coefficient at incident angles of 0° and 80° in both TE and TM modes.
(a)
(b)
Figure 9 shows the measured curve and the simulated curve of the hybrid FSS’s reflection coefficient, with the electromagnetic wave incident at 0° and 80° under both TE and TM polarizations. The slight shift in the measured results’ central resonance frequency point of less than 0.43 GHz may be attributed to fabrication discrepancies and variability in the dielectric plate material. This discrepancy may also be due to the measurement being carried out on a finite array, while the simulation considered an infinite array through unit cell boundary conditions. The potential impact of fabrication tolerances, due to the unit cell’s minute dimensions, and the environmental conditions in the anechoic chamber also cannot be overlooked as contributing factors to this deviation.
(a)
(b)
The collected results, spanning a range from 2 to 13 GHz, reveal some objective observations. Objectively, the wave impedance change of FSS with the angle in both TE and TM polarizations yields contrasting results. In TE mode, the resonant frequency point shifted towards a higher frequency by 0.41 GHz. Conversely, in TM mode at 80° incidence, the resonant frequency point shifted to the lower frequency by 0.43 GHz. The relative drift of the resonant frequency point at an 80° incidence, compared to normal incidence, is 10.6% in TE mode and 2.1% in TM mode.
5. Conclusion
This study presents the design of a hybrid FSS that amalgamates miniaturized FSS cells. This configuration mitigates the emergence of the grating lobes through phase compensation. The relative offset of the hybrid unit’s reflected resonant frequency point in TE mode is 0 across an incident angle range of 0-80°. In TM mode, this offset sees a reduction of 80.12% and 83.26% compared to and units, respectively. These results suggest that the hybrid unit significantly affected the resonant frequency shift of FSS at large incident angles. The measured data aligned well with the simulation results.
Data Availability
The simulation and testing data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.