1 Introduction

Surfaces containing two-dimensional periodic arrangement of sub-wavelength patterns interact with electromagnetic waves and either reflect or transmit or absorb a large fraction of the incident field at a specified frequency range (Anwar et al. 2018). Such frequency selective surfaces (FSS) are required for numerous applications in the frequency range of millimetre waves and terahertz frequency range, and the fabrication of these patterns is possible with lithographic tools. FSS is also proposed for many futuristic commercial applications such as in the development of 5G and 6G communications (Dang et al. 2020; Ruan et al. 2022), in defence for shielding purposes (Lin et al. 2021) and absorbers (Lan et al. 2021), in antennas for enhancing the gain, directivity and bandwidth (Li et al. 2020; Hu et al. 2022), and in filters (Li et al. 2021) and lenses (Gao and Yang 2022). In addition, these types of surfaces can locally tailor the optical properties on subwavelength scale and are widely in demand for functional optical and photonic devices (Liu et al. 2020, 2018; Yoon et al. 2020; Haldar and Ramarao 2020; Chen et al. 2017). To fulfil the demands of the next generation devices, components must meet the conditions of being economical, miniaturized, simple to manufacture and possess compact geometry. All these requirements can be addressed using FSS (Dickie et al. 2011). Thus, FSS is ideal for a variety of applications in a wide frequency range spanning the GHz and the THz range (Bashiri et al. 2017; Kesavan et al. 2016; Wang and Cheng 2018; Poojali et al. 2017; Das et al. 2012). While the FSS filters are in demand due to their tunability and selectivity of passbands and stopbands in the terahertz range, they are also limited by their fixed frequency band operation and non-flat frequency response (Gavdush et al. 2020). Therefore, to satisfy the demand of utility over a broad THz range, one method has been to attach a series of narrow band response filters in a rotating wheel (Gavdush et al. 2020; Zhai et al. 2018). This option is often bulky and complex in nature. Other design methods have obtained bandpass response by cascading multiple layers of FSS (Shen et al. 2018; Vegesna et al. 2012). While these structures have been demonstrated to provide flat passband or quad-band responses respectively, use of a large number of layers and large thickness values appears counter-productive to the requirement of smaller designs. Even though the desired frequency selective response can only be accomplished by including a sufficient number of constituting elements, FSS is always required in small and finite size for practical use. In millimeter and THz ranges, it is essential to use miniaturized and simple FSS structures. As it is common knowledge that a small array of finite FSS will restrict its performance, there is a constant need for FSS structures in millimeter and THz frequency ranges which bridge the over-arching demands of miniaturized geometry, simplicity of fabrication and superlative performance characteristics even with its small and finite size.

Our approach in this work is to design an FSS with a miniaturized and simple pattern of unit cell on its surface, and one which can be fabricated by inexpensive methods. This is targeted for tunable multifrequency transmission in the range of millimter wave band, useful for W-band (70–110 GHz), D- band (110–170 GHz), G-band (140–220 GHz) and H-band (220–325 GHz). As our FSS design shows dual-band resonance, further characteristics of multiple band selectivity and frequency tunability are obtained by cascading two surfaces with identical designs. In the sections below, we present the design of a single layer, perforated, all-dielectric, miniaturized FSS with overall size in mm. It uses a high frequency microwave substrate which is very economical in comparison with other terahertz-range substrates such as silicon, quartz, and graphene. In addition, we have opted for CNC drilling for the fabrication of the FSS structure, as it is an inexpensive, easy, fast, and a more commonly available tool. The single layer FSS structure has dual narrow pass bands at 166.40 GHz and 257.56 GHz with a stopband of nearly 36.69% ranging from 175 to 252 GHz. The FSS also showed invariance in its frequency response to the angle of incidence up to 45°.

Further, this single layer miniaturized FSS is cascaded with an identical FSS and studied towards multi-band transmission with high selectivity and frequency tunability. By varying the spacing between the two surfaces, an improvement in out-of-band rejection as well as multiple tunable passbands is achieved. Conventionally, cascading.

FSS creates Fabry–Perot resonances, which are undesirable and need to be removed (Zhai et al. 2018; Vegesna et al. 2012). But our design utilizes the Fabry–Perot resonances to achieve multiple passband resonances and to improve the out-of-band rejections. Utilizing the Fabry–Perot mechanism, we have achieved continuous passband frequency tunability and high selectivity. Traditional FSS structures are not tunable in their response. Tunable FSS structures have been demonstrated by incorporating electronic components such as varactor diodes (Zhai et al. 2018; Shen et al. 2018; Vegesna et al. 2012; Guo et al. 2019; Phon et al. 2019), and micro-electro-mechanical system switches (Schoenlinner et al. 2004) or by changing the electrical properties or geometric configuration (Hu et al. 2007; Sazegar et al. 2012; Haghzadeh et al. 2017; Wang et al. 2017; Azemi et al. 2013; Lei et al. 2011; Li and Behdad 2012; Ferreira et al. 2017) of the substrate. These techniques are expensive, labor-intensive, complex and bulky as the size of the FSS is increased. To overcome these problems, we propose a cascaded structure in which only two layers of FSS are used, and continuous tunability is achieved by varying the distance between the two layers from zero to 2.5 mm. This keeps the size small even in the cascaded design. Within this range of varying the spacing, we demonstrate that it is possible to obtain multiband transmission as well as tune the passband frequency over the entire range of 100–300 GHz without any forbidden range.

As our design is that of a miniaturized finite structure, we have not limited our computational analysis to infinite structures, and a finite structure analysis is also carried out. Spectral characteristics of infinite and finite structures showed a good correspondence. The practicality of cascading has to be robust, and this is studied through in-plane angular rotation of one surface with respect to the other, and in-plane shift by displacing the second layer with respect to the first layer along one direction. The cascaded structures are found to be insensitive to in-plane rotation and in-plane uniaxial shift. This design therefore provides enormous freedom from the ill-effects of misalignment in assembling the two surfaces. The novelty of our proposed single-layer and two-layer FSS structure lies in its extremely simple geometry, use of cost-effective substrate and a fabrication technique that is economical and mass producible, along with the utilization of a well-established mechanism for frequency tunability and selectivity.

2 Structure design and analysis

The FSS in this work consists of a dielectric substrate with periodically perforated holes on it, and the frequency range opted for the design and analysis is from 100 to 300 GHz. In this range, the metal losses are high. Therefore, the absence of metal and presence of perforations on a dielectric substrate offers complete freedom from metal losses, while at the same time providing selective stopband and passband response. The schematic of the perforated FSS structure and its unit cell view are shown in Fig. 1a. Commercially available dielectric material RT Duroid 5880 series from Rogers, with relative permittivity (εr) of 2.2 at 100 GHz, and thickness (t1) of 0.79 mm is used as the substrate for designing the FSS structure. The structure has through-holes arranged in a periodic square lattice arrangement. The radius (r) of each hole is 0.2 mm and the hole-to-hole spacing (a) is 0.6 mm.

Fig. 1
figure 1

a Schematic of the FSS shown along with unit cell dimensions, b perspective 3D view of the full FSS structure showing the incidence angle and field orientations and c photograph of the FSS sample made by CNC drilling

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Figures 1b, c illustrate the perspective three-dimensional view of the full FSS structure and a photograph of a finite FSS structure made by CNC drilling, respectively. As the unit cell is made of circular through-holes requiring no other special pattern shapes, use of CNC drilling technique is sufficient, making this simple and highly accessible for mass production. In our chosen structure, the perforated holes play a crucial role in changing the electromagnetic propagation dynamics. The through-holes contain air with a dielectric constant of 1. Thus, the presence of periodic holes affects the effective dielectric constant (εeff) of the host substrate, which is lowered to 1.78 for the chosen size of unit cell, lattice symmetry and hole diameter.

3 Single- layer FSS: parametric study and analysis of results

In our design of FSS, there is no metal present in the structure. Only periodic holes are present on a dielectric layer and therefore contains only dielectric-air interfaces. All the dynamics of electromagnetic resonances of this FSS structure are thus governed by the size of the holes, their periodicity, dielectric constant of the substrate and the thickness of the substrate. Since we have fixed the dielectric constant and thickness of the substrate, only the hole diameter and periodicity can be modified. The size and periodicity of the perforated holes is chosen such that it provides a stopband between 180 GHz (0.5λ180 GHz = 0.83 mm) to 200 GHz (0.5λ200 GHz = 0.75 mm), along with dual passbands, one below the cut-off frequency and another as higher order mode because of the effect of energy distribution of periodic array. The chosen value of d = 0.40 mm satisfies the λ or λ/2 or λ/4 condition simultaneously for some frequencies in the selected frequency range of 100–300 GHz.

Figure 2 depicts the simulated S-parameter results of the unit cell and the full structure. S11 and S21 correspond to the reflection and transmission coefficients. The simulation is performed using commercially available EM simulator CST Microwave studio™. The unit cell boundary condition is used for the simulation of the infinite structure. For the finite structure, the PML (open) boundary conditions at ± x and ± y- directions along with waveguide ports in ± z- directions are used for performing the simulation under time domain analysis. The structure is simulated for its reflection and transmission spectra in the broad frequency range of 100–300 GHz.

Fig. 2
figure 2

Simulated S-parameters of a unit cell (infinite geometry) of FSS structure and b finite FSS structure of 10 × 10 array. Black solid line represents the reflection coefficient (S11), and pink dotted line represents the transmission coefficient (S21). The passband frequencies are indicated as fa in the unit cell and fb in the full structure. c Simulated reflection and transmission phase (black solid and pink dash dot line, respectively) for the unit cell of FSS

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Figure 2a shows the reflection and transmission coefficients using black solid line and pink dotted line respectively, for the unit cell of the structure. The dual pass bands (with low reflection and high transmission) are centered at 164.20 GHz (fa1) and at 255.40 GHz (fa2) in the frequency range of 100–300 GHz. In addition, there is a wide stop band (with high reflection and low transmission) (nearly 41.42% of stopband) with a width ranging from 166.26–253.25 GHz. The unit cell of the structure also provides the upper rejection band from 183.60 GHz to 235.80 GHz (for S21 ≤ − 10 dB). Moreover, it also possesses fairly low transmission in the rejection band. Figure 2b depicts the simulated reflection and transmission coefficients, shown with black solid line and pink dotted line respectively, for the finite structure containing a 10 × 10 array of unit cells. Its dual narrow passbands are at 166.40 GHz (fb1) and 257.56 GHz (fb2). The purple shaded region shows the wide stopband of the structure where the transmission coefficient is less than − 3 dB. The frequency range of the stopband is from 174.70 GHz to 251.75 GHz. The finite structure has a stopband width of 36.69% of its centre frequency. Apart from a few minor differences such as the observation of a small shift in passband frequencies, slight reduction in stop bandwidth, and a few additional features at non-resonant frequencies, the S-parameters of the finite array and of the unit cell are largely similar in their frequency response. The smallest possible array size, which can simultaneously attain comparable characteristics to that of the unit cell (infinite size) structure and satisfy the demand for miniaturized size of filters in THz devices, is chosen for this study.

The phase change on reflection and transmission through the FSS is important for constructing a tunable frequency filter. Figure 2c shows the frequency dependence of the simulated phase change of reflection and transmission coefficients for the unit cell at normal incidence. The black solid line corresponds to reflection phase whereas the pink dash dotted line corresponds to transmission phase of the structure. Firstly, the reflection phase is decreasing from zero as it approaches towards fa1 at the resonant frequency, it undergoes a sharp phase change. Afterwards, it starts decreasing gradually and repeats the same nature at the resonance at fa2. At the two passbands of 164.20 GHz (fa1) and at 255.40 GHz (fa2), the reflection phase change is 0.91π and 0.86π respectively. On the other hand, the transmission phase at passbands fa1 and fa2 indicates constructive interference. At 164.20 GHz (fa1) the transmission phase is 0°, while at 255.40 GHz (fa2), it indicates a phase change of 1.99 π. These values indicate that there is near-ideal constructive interference in transmission, while the destructive interference in reflection is non-ideal. In the range of the stopband from 166.26 GHz to 253.25 GHz, the transmission phase lies in the range of 0 to – π, with a value of – π/2 at the centre of the stopband.

As the FSS is made of periodically arranged holes with a diameter of 0.4 mm accessible to CNC drilling, it is important to analyze whether a small error in periodicity will impact the resonance features to a large extent. For very small error values, there was no observable change in resonance features. But on increasing the periodicity from 0.5 mm to 0.7 mm, covering an error range of hundreds of microns, both the passband resonance frequencies (fa1 and fa2) shifted towards lower frequency values by –10 GHz. The magnitudes of the reflection coefficient also decreased slightly when the period of the structure deviated from the design value of 0.6 mm. This is shown in Supplementary information Fig. S1(a). It is equally important to analyze the role of the incidence angle in the performance characteristics of the FSS because in many applications, especially in radomes and in shielding applications, FSS with high stability to oblique incidence angles is required. In Supplementary information Fig. S1 (b), the simulated results of reflection coefficient as a function of frequency for the range of 100–300 GHz are shown for different angles of incidence (θ) ranging over 0°–45°. No significant shift in the resonance frequency has been observed for this angular range. A small variation is observed in the magnitudes of the reflection coefficient. To a large extent, the FSS has shown invariance to the angle of incidence, possessing angular stability as it contains an array of circular holes in a symmetric configuration.

4 Stacked structure: design and analysis of fabry–perot cavity

Cascading of similar FSS structures improves the selectivity of filtering frequency. In addition, large out-of-band rejection and improvement of roll-off rate can be achieved. Varying the spacing in the stack gives the liberty to generate multiple resonances. The air gap between the parallel surfaces of the two partially reflecting dielectric layers creates a Fabry–Perot cavity and generates Fabry–Perot resonances governed by the spacing and the refractive index of the medium, along with the reflection/transmission/phase characteristics of the surfaces. Conventionally, Fabry–Perot resonances are considered undesirable and need to be removed (Zhai et al. 2018; Vegesna et al. 2012). But we have designed our structure in such a way that Fabry–Perot resonances can be utilized for providing multiple pass band resonances and improve the out-of-band rejections. For obtaining multi-spectral features of cascaded FSS, commutative effects of electromagnetic effect of the hole, redistribution of energy caused by periodic array and Fabry–Perot effect of field confinement have been utilized.

Figure 3 shows the different views of cascaded unit cell (infinite structure) of structure 1 with structure 2. The structures 1 and 2 are of the same dimensions as discussed in the above section. The air spacing between the structures 1 and 2 is d. We have carried out our analysis for four cases of cascaded design. Case I is for d = 0 as shown in Fig. 3a. Figures 3b–d show the cases II, III and IV when d is increased to λ/4, λ/2 and λ, respectively. The value of λ is 1.66 mm corresponding to the centre frequency of the stopband of the individual surface. The effect of cascading leads to multi-frequency transmission.

Fig. 3
figure 3

Schematic of cascading the unit cell of FSS structure; a–d the spacing is 0, λ/4, λ/2 and λ

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4.1 Analysis of reflection and transmission coefficients in cascaded design (unit cell calculations)

The reflection and transmission coefficients for all the cascaded structures shown in Fig. 3 are calculated using the simulation. While the earlier work reports scattering matrix responses for designing and analysing theoretically cascaded structures (Wang et al. 2017; Azemi et al. 2013), we have presented our analysis through simulation approach which is faster and reliable. Figure 4 shows the S-parameters in terms of magnitude and phase calculated for the unit cell of cascaded structures on varying d from 0 to λ. Figure 4a, b represents the case I for d = 0. On cascading identical structures with d = 0 between them, the overall thickness (2t1) of the structure gets doubled from that of the single structure. Two additional resonances appear for d = 0 in Fig. 4a with the presence of four narrow pass bands at 101.60 GHz (fA1), 156.40 GHz (fA2), 211.39 GHz (fA3), and 265.79 GHz (fA4). Three upper rejection bands are also observed with low transmission, spanning 105.88–152.16 GHz, 160.66–208.25 GHz, and 215.05–262.02 GHz. In addition, an improvement in upper rejection band has been observed with wider upper rejection (S21 ≤  − 10 dB) in all three bands in the frequency range of 100–300 GHz.

Fig. 4
figure 4

S- parameters analysis in terms of magnitude (in dB) and phase of the unit cell of cascaded structures on varying d from 0 mm to λ

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The phase spectrum of the cascaded structure is useful to analyze the quality of reflection/transmission. In Fig. 4b, the blue solid line corresponds to reflection phase and the red dash dotted line corresponds to transmission phase of the cascaded structure (case I). Among the four pass bands, the reflection phase change is π for fA2, fA3 and fA4, while it is 2π at fA1. The transmission phase curve, on the other hand, is similar at passbands fA1 and fA3 and at fA2 and fA4. In the first set, it is zero at the resonant frequencies, while in the second set, it is 2π at the resonant frequencies. With the cascaded structure, the transmission and reflection phase changes are close to ideal values according to these phase plots.

The number of resonances is decided by the spacing of the Fabry–Perot cavity and the chosen frequency range for the analysis. Therefore, on increasing d from λ/4 to λ/2 to λ in cases II, III and IV, more pass bands are observed, and they increase on increasing the d as shown in Fig. 4c–h. In the frequency range of 100–300 GHz, we observe four pass bands at 139.39 GHz (fB1), 179.60 GHz (fB2), 235.80 GHz (fB3), and 276.00 GHz (fB4) in Fig. 4c for d = λ/4. These are shifted with reference to those obtained for d = 0 seen in Fig. 4a. From the reflection and transmission phases shown in Fig. 4d, it is observed that the reflection phase change is 0.88π, which is comparable at all the four frequencies while the transmission phase change is nearly 2π at fB1 and fB3 and zero at fB2 and fB4. Once again, the transmission phase change is close to the ideal value.

Similarly, for cases III and IV, on further increasing d to λ/2 and λ, the number of resonances in the chosen frequency range increase to 5 and 6 respectively (Fig. 4e, g). The reflection and transmission phase values are seen in Fig. 4f, h and are very similar to those in Fig. 4d. The multiple resonances are due to the commutative effects of electromagnetic effect of hole, redistribution of energy caused by periodic array and Fabry- Perot effect due to air in between the two dielectric layers. Thus, cascading two layers of FSS improves the filtering selectivity and provides the flexibility to be used for obtaining multiple pass and stop bands.

4.2 Finite structure study of cascaded FSS structures

The above analysis of cascaded structures was performed for infinite perforated FSS. As mentioned earlier, these FSS surfaces are small in size, and a finite structure calculation is warranted even for the cascaded design. The schematic of the finite structure of 10 × 10 array of holes is shown in the inset of Fig. 5a–d for the four cases of cascading studied here. As before, the spacings of d = 0, λ/4, λ/2 and λ are analysed. The simulated reflection coefficients for all the four cascaded finite structures are shown in Fig. 5a–d. The structures are designed under full structure module, and PML (open) boundary conditions at ± x and ± y- directions along with waveguide ports in ± z- directions are used. The simulations are carried out under time domain analysis.

Fig. 5
figure 5

a–d Simulated reflection coefficient of all the four cases of cascaded finite FSS structures. The value of spacing in each case is mentioned in the figures. e–f Photographs of the cascaded design to emphasize its small size

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The spacings of d = 0, λ/4, λ/2 and λ result in four, four, five and six resonances, respectively in the chosen frequency range in Fig. 5a–d, as in the previous case with stacked infinite structures. It is also observed that the passband resonance frequencies of infinite structures shown in Fig. 4 match well with the finite structure passband frequencies for all the four cascaded cases. Small additional features are noticed in the stacked finite structure case, due to the edge effect from the smaller size. These can be avoided by impinging smaller-sized beams. Figure 5e is the photograph of our double layer FSS structure and Fig. 5f shows the size comparison of the fabricated double layer FSS structure with the lead of a pencil. This picture clearly emphasizes the miniature size, simplicity and the ease of fabrication, and the possibility of mass production at very low cost.

The effect of any misalignment arising from in-plane rotation of one structure with the other may influence the performance. This aspect of angular stability is also analyzed in our simulation. With the results shown in Supplementary information Fig. S2 (a-b), we conclude that the cascaded structures possess angular insensitivity of the resonance frequency for in-plane rotation from 0° to 60° with respect to each other. However, the amplitude of the passband resonance gets changed to a different extent at different angles of in-plane rotation. Thus, a suitably chosen in-plane rotation angle can be helpful to enhance the performance as required in applications, without changing the resonance frequency. The cascaded structure shows in-plane rotation insensitivity for all angles, and we have presented our results up to 60° for pictorial clarity. This advantage is primarily due to the circular shape of the unit cells in our design. We have also investigated in-plane displacement of one FSS layer (FSS-1) with respect to the other (FSS-2) along the x-direction. The variation of displacement is taken from the center of FSS-1 and varied from X1 = 0.0 mm when x- and y-axes of both FSS-1 and FSS-2 are coinciding with each other, to X1 = 0.3 mm. This effect is presented in Supplementary information Fig. S3(a-b). No shift in the passband resonance frequency is observed. This confirms the robustness of the structure for spatial misalignment of the double layer design.

5 Continuous tunability over 100–300 GHz range

The highlight of this work is the possibility of continuously tunable frequency filter using the two-layer design. In Fig. 6a, we observe that there is a variation in the passband resonance frequencies in the range from 100 to 300 GHz, on changing the cascading distance from zero to 2.5 mm. There is no frequency range which lacks multiple passband frequencies. It is important to note that, along with this absence of forbidden frequency range during the tuning, there are multiple passband frequencies for every cascading distance between the two layers. Therefore, multiple transmission frequencies can be achieved along with continuous tunability. Here, the extent of tunability is governed mainly by the Fabry- Perot cavity mechanism and dual pass band property of each FSS structure. Figure 6b illustrates the transmission in a linear scale, as a function of frequency, on varying the cascading distance (d) by small values. On varying the value of d from zero to 0.1 mm, slight shift in the transmission peak and a consequent change of passband frequency is observed. Similar is the effect for varying d further from 0.1 mm to 0.2 mm. With a change of the cascading distance (d) with a step size of 100 μm, the variation in transmission frequency is clearly observable. This is a realistic step size for spatial variation in a device.

Fig. 6
figure 6

a Tunability shown as a variation of passband frequency with a change of cascading distance from zero to 2.5 mm. b Transmission spectrum (in linear scale) shown for the three cascading distances of zero, 0.1 mm and 0.2 mm

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The cascaded FSS structure also provides a good frequency selectivity, defined through its Quality (Q) factor. The Q-factor is calculated as the ratio of the resonance frequency to its 3 dB bandwidth. In our design, the Q-factor value of the different resonances in 100–300 GHz lie in the range of 11.18–36.27. Thus, our design for the dual-metasurface Fabry–Perot cavity provides continuous tunability of passband frequencies and offers a high selectivity. This makes it a suitable candidate to be utilized in different applications in the broad range from W to H bands of millimeter waves of electromagnetic spectrum.

6 Comparative analysis

Table 1 shows the comparison between our design of single-layer and double-layer FSS structures with the recently reported high performance FSS in THz frequency range. The comparison is presented in terms of FSS design, geometry, complexity, fabrication cost and performance. It is clear that our design is the simplest in geometry, and highly cost-effective because of the substrate and fabrication technique. Its size is slightly more than the others. But it is small enough to be integrated very easily with miniaturized millimeter range and THz range devices. Our proposed double-layer cascaded FSS possesses wide band frequency tunability and high selectivity for passbands. While frequency tunability was also proposed in Zainud-Deen et al. (2012); Mittra et al. 1988; Wang et al. 2019; Li et al. 2018; Lv et al. 2022), it was either by using active elements or through structuring in multiple layers. Our design has just two layers and shows significant frequency tuning when the spacing is varied in steps of 100 µm. This makes the idea very realistic, inexpensive, light-weight and economical.

Table 1 Comparative study of our design (both single layer and double-layer FSS structure) with some recently reported high performance FSS structures in THz range
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7 Conclusion

We have designed and analyzed a THz range single layer, all-dielectric, miniaturized FSS which is also light in weight. Our design for metasurface-FSS possesses dual passband characteristic at 164.20–257.56 GHz and nearly 36.69% wide stop band ranging from 175 to 252 GHz. The performance is invariant to the angle of incidence over 0°–45°. This makes it highly apt for use as filter for different THz applications in defence or in communications field. In addition, our design for the FSS is highly cost-effective and mass- producible. To demonstrate the ease of fabrication, we have made the FSS by drilling holes in a 10 × 10 array on a high frequency RF material, with the minimum of cost. To extend its capability, we have cascaded two similar FSS and obtained multi-frequency response over the chosen range from 100 to 300 GHz, with a selectivity for the passband and stopband frequencies. For achieving multiple resonances, we have taken advantage of the Fabry- Perot cavity mechanism, requiring a mere change in the spacing of the two surfaces. In addition, our design for the cascaded FSS provides more in-band flatness with fast roll-off and improved out-of-band rejection. Furthermore, the design of the cascaded FSS is robust in nature as it provides freedom from misalignment of the multi-layer assembly, through invariant response to in-plane rotation of the first FSS with respect to the second FSS in the cascaded design. In addition, the cascaded FSS structure is also immune to in-plane shift, due to displacement of the second layer of cascaded FSS structure along the X direction. Our designs of both single-layer and double-layer cascaded structure can be good candidates for multiple applications as band-pass and band-stop filters, as well as in 5G and upcoming 6G communication system as they offer the freedom of broad frequency selectivity and tunability in the wide range of 100–300 GHz.