**2. Design**

Basic polarization manipulation properties of metasurfaces are achieved due to cross-coupling between electric and magnetic fields' resonances in the presence of an incident wave. In order to achieve dual-band LP-to-CP operation, the unit-cell structure of the metasurface needs to be designed deliberately to tailor the cross-coupling e ffects in two separate bands of interest. The same structure will behave di fferently under di fferent frequencies. Each frequency band will correspond to a di fferent Eigenmode. In the past, many diagonal symmetry/semi-symmetric anisotropic structures have been proposed for single band LP-to-CP conversion [41–45]. Dual band LP-to-CP operation has been achieved using center-connected [38] and semi-diagonal symmetric [37] structures. Symmetric structures with horizontal and vertical axis symmetry cannot be a choice for LP-to-CP operation because the electric response for such components at normal incidence and horizontal polarization will not generate a vertical component [42]. A good choice is to have a diagonal symmetric structure so that incident wave can be divided into two equal orthogonal components. The first design consideration for the unit cell is to have two di fferently sized square patches, with each square corresponding to a single band LP-to-CP operation. They are arranged to have diagonal symmetry. The second consideration is a square ring to have closed form electric field distribution between the top and bottom surfaces. In a nutshell, the proposed structure is a diagonal symmetric structure which consists of multiple resonating structures to have wider bandwidths in two operational bands. Figure 1 shows the design of the proposed converter. It consists of two identical sheets of conductor patches having substrate layer sandwiched between. Gold was used as a conductor and flexible polyimide having εr of 3.5 was used as a substrate. The shaded region in Figure 1b shows the conductor layer, which consists of two parts: the outer part is a square ring consisting of a conductor with width *w* and an inner part consisting of three squares diagonally intersecting each other. Top right and bottom left squares have

dimensions *c* × *c*, while the middle square has dimension *c*1 × *c*1. The bottom layer is identical to the top layer. The design was optimized to have the best results and optimized parameters for the unit cell, as follows: *p* = 50.67 μm, *v* = 54.65 μm, *c* = 13.4 μm, *d* = 3.5 μm, *c*1 = 14 μm. The scheme for the operation of the dual-wide-band LP-to-CP converter is shown in Figure 2.

**Figure 1.** Schematic of the design: (**a**) Two-dimensional (2D) periodic array structure; (**b**) top view; (**c**) 3D perspective view.

**Figure 2.** Scheme for dual-wide-band LP-to-CP converter with outgoing Left Handed Circular Polarization (LHCP) and Right Handed Circular Polarization (RHCP) waves.

#### **3. Simulation and Analysis**

Design and optimization for the proposed dual-band LP-to-CP converter was carried out using standard electromagnetic software, High Frequency Structure Simulator (HFSS). HFSS is based on the finite element mesh (FEM) solver. The design was simulated using master–slave boundary conditions, and Floquet ports at the input and output of the unit cell were applied to realize the periodic array structure. In order to validate the performance of the proposed structure, an optimized unit cell was re-simulated in Computer Simulation Technology (CST) software (2015 Version, Dassault Systèmes SE, Vélizy-Villacoublay, France). The finite difference time domain (FDTD) solver was selected for CST. Scanning time was set to 200 ns to ge<sup>t</sup> accurate results. Close agreemen<sup>t</sup> between FEM results and FDTD results validate the performance of the proposed structure. Total transmission in the X direction can be computed by Tall = --tyx---2 + |txx|<sup>2</sup> [46], and for transmission in the Y direction by Tall = --tyy---2 + --txy---2 [46]. Figure 3a,b depict transmission characteristics for the incident X polarized and Y polarized wave travelling in the -Z direction in CST and HFSS. It is pertinent to mention here that transmission spectra with incident X and Y polarizations are not exactly equal due to the absence

of symmetry in X and Y planes. Figure 4 shows the phase difference in degrees with incident X polarization. Further discussion on Figures 3 and 4 is carried out in Section 4.

**Figure 3.** Transmission characteristics of proposed structure with incident: (**a**) X polarized wave, and (**b**) Y polarized wave.

**Figure 4.** Phase difference between X polarized and Y polarized transmitted waves with incident X polarized wave.

#### **4. Principle of Operation**

In the topology diagram shown in Figure 2, it is assumed that both X polarized and Y polarized waves can be made incident on the metasurface. The proposed device has different responses to incident X and Y polarized waves. For incident X polarized waves, transmitted waves behave as LHCP at f1 and RHCP at f2, whereas for incident Y polarized waves, transmitted waves behave as RHCP at f1 and LHCP at f2. In order to understand the operation of a dual-band LP-to-CP converter, a plane horizontal (X polarized) wave travelling in the -Z direction is made incident on the surface of the unit cell. The incident wave can be expressed by Equation (1). Magnitudes of this incident wave can be expressed by Equation (2).

$$\mathbf{E\_{xl}} = \mathbf{E\_{xi}} \mathbf{e\_{x}} \tag{1}$$

$$\text{where, } \mathbf{E}\_{\text{xi}} = \mathbf{E}\_0 \mathbf{e}^{\text{jkx}} \tag{2}$$

where **ex** is the unit cell in X direction. The transmitted wave can be expressed as the sum of two components, i.e., X polarized and Y polarized, as shown in Equation (3):

$$\mathbf{E\_{t}} = \mathbf{E\_{xt}}\mathbf{e\_{x}} + \mathbf{E\_{yt}}\mathbf{e\_{y}} = \mathbf{t\_{xx}}\mathbf{e^{j\varphi\_{xx}}}\mathbf{E\_{0}e^{jkx}}\mathbf{e\_{x}} + \mathbf{t\_{xy}}\mathbf{e^{j\varphi\_{xy}}}\mathbf{E\_{0}e^{jkx}}\mathbf{e\_{y}}\tag{3}$$

$$\mathbf{t}\_{\infty} = \frac{\mathbf{E}\_{\infty}}{\mathbf{E}\_{\text{xi}}} \tag{4}$$

$$\mathbf{t}\_{\rm{xy}} = \frac{\mathbf{E}\_{\rm{yt}}}{\mathbf{E}\_{\rm{xi}}} \tag{5}$$

where txx and txy represent transmission coefficients for X to X and X to Y polarization conversion as shown in Equations (4) and (5), respectively. ϕxx and ϕxy are phase angles corresponding to txx and txy, respectively. Since the proposed structure has an anisotropic structure, the magnitudes and phasers for X polarized and Y polarized transmitted wave components may be different. However, if for a certain frequency range these transmission coefficients become comparable and their phase angles are 90◦ apart, i.e., txx = txy and ϕxy = 2nπ ± π/2, with n being an integer, then the conditions for linear-to-circular polarization conversion will be met. In order to describe the transmission conversion performance of the proposed structure, the axial ratio for the transmitted wave is calculated as given in Equation (6) [38]:

$$\text{AR} = \left( \frac{\left| \mathbf{t\_{xx}} \right|\_2 + \left| \mathbf{t\_{xy}} \right|^2 + \sqrt{\mathbf{a}}}{\left| \mathbf{t\_{xx}} \right|\_2 + \left| \mathbf{t\_{xy}} \right|^2 - \sqrt{\mathbf{a}}} \right)^{1/2} \tag{6}$$

where a can be calculated from Equation (7) [38]:

$$\mathbf{a} = |\mathbf{t}\_{\mathbf{x}\mathbf{x}}|^4 + \left|\mathbf{t}\_{\mathbf{y}\mathbf{y}}\right|^4 + 2|\mathbf{t}\_{\mathbf{x}\mathbf{x}}|^2 \left|\mathbf{t}\_{\mathbf{x}\mathbf{y}}\right|^2 \cos(2\varphi\_{\mathbf{x}\mathbf{y}})\tag{7}$$

For an ideal LP-to-CP operation, AR should be 1 (0 dB). However, for most systems, a 3-dB value of the axial ratio is acceptable.

Figures 3a and 4 show that in frequency bands from 1.16 THz to 1.634 THz and 3.935 THz to 5.29 THz, the transmission coefficient magnitudes are comparable, and the phase difference between them is −90◦ or +270◦ with ±15◦ variation. Thus, the conditions for linear to circular polarization conversion is fully met at some frequencies, while for a range of frequencies, it partially fulfils the requirements (in this case the transmitted wave will be slightly elliptically polarized). Nonetheless, the performance criterion for linear to circular transmission type conversion (axial ratio within 3 dB) is maintained. Furthermore, in the frequency range from 1.16 THz to 1.634 THz, the Y component of the transmitted wave is ahead of the X component hence the transmitted wave is LHCP, whereas in the frequency range of 3.935 THz to 5.29 THz, the Y component of the transmitted wave lags the X component, hence the transmitted wave is RHCP. In addition, the proposed unit cell behaves equally well for the incident Y polarized wave resulting in RHCP and LHCP for the two frequency bands.

Total transmission in the X direction can be computed as Tall = --tyx---2 + |txx|<sup>2</sup> [46]. Figure 5 shows the axial ratio for the incident X polarized and Y polarized waves along with total transmission. For the sake of simplicity, total transmission in the X direction is only shown in Figure 5. A similar tendency is observed for transmission in the Y direction. It is clear from Figure 5 that the proposed structure has an axial ratio of 3 dB from 1.16 THz to 1.634 THz and 3.935 THz to 5.29 THz for both X polarized and Y polarized incident waves. Moreover, reasonable energy transfer (−1 to −5 dB) is observed in the dual-band except in the frequency range 5 THz to 5.29 THz. In fact, there is good energy transfer from 1 THz to 5 THz but the transmitted wave from frequency range 1.634 THz to 3.935 THz is not circularly polarized wave because the axial ratio is much larger than 3 dB.

**Figure 5.** Axial ratio for the transmitted wave with incident X and Y polarized wave and total transmission with incident X polarization.

#### **5. Physical Explanation and Equivalent Circuit**

Since the unit cell is based on an anisotropic structure having dual diagonal symmetry, the incident X polarized wave will generate transmitted X and Y polarized wave components and the incident Y polarized wave will generate transmitted X and Y components. To explain the physical phenomenon behind the proposed LP-to-CP, we considered the surface current vectors within two frequency bands; let these be f1 and f2: f1 = 1.398 THz and f2 = 4.82 THz. Figure 6 shows the surface current distribution with the incident X polarized wave at the output surface of the proposed converter for t = 0, T/4, T/2, 3T/4 at f1. The orientation of the electric field vectors shows that with every T/4 cycle, it rotates by 90◦. Further, it can be seen that the surface current at f1 is concentrated in the inner tri-square conducting patches with an anti-clockwise rotation. Thus, the transmitted wave is LHCP at f1.

**Figure 6.** Surface current distribution of the proposed LP-to-CP converter at 1.398 THz at (**a**) t = 0, (**b**) t = T/4 (**c**) t = T/2 (**d**) t = 3T/4.

Figure 7 shows the surface current vectors at the output surface at f2. It can be clearly seen that with every quarter cycle, surface currents are rotated 90◦ in a clockwise rotation. Unlike in Figure 6, this time surface current vectors are concentrated in the outer square ring. The opposite direction of rotation for surface current vectors in time cycle T validates our proposed opposite handedness of circular polarization for the same structure at two different frequencies.

**Figure 7.** Surface current distribution of the proposed LP-to-CP converter at 4.82 THz at (**a**) t = 0 (**b**) t = T/4 (**c**) t = T/2 (**d**) t = 3T/4.

Figures 8 and 9 indicate the response of the proposed structure to the incident X polarized electromagnetic field. Figure 8a,b show electric field distribution at 1.398 THz and 4.82 THz, respectively. It is clear from Figure 8a that the electric field concentrates on the outer two conducting patches of the tri-square patch with a minor contribution from corners of an outer square ring, whereas for 4.82 THz, the electric field is concentrated on the whole tri-squares patch and outer square ring. This multi-resonance structure validates the dual-wide-band performance of polarization conversion.

 (**a**) (**b**) **Figure 8.** Electric field strength at (**a**) f1 = 1.398 THz, (**b**) f2 = 4.82 THz.

**Figure 9.** Magnetic field strength at (**a**) f1 = 1.398 THz, (**b**) f2 = 4.82 THz.

Figure 9a shows the magnetic field strength at f1 = 1.398 THz. It shows that the magnetic field is concentrated in the intersected corners of the tri-squares conductor patch. Figure 9b shows that for the second frequency band, at f2, the magnetic field is predominantly attributed to the outer square ring and vertical sides of the squares in the tri-square patch.

Figure 10a,b show the equivalent circuit for the unit cell of the proposed dual-wide-band LP-to-CP converter with incident X and Y polarizations, respectively. With incident X polarizations, upper and lower arms interact with the incident waves, whereas the left and right arms of the outer square ring will have no interaction. Thus, inductors L1 representing the outer square ring will appear as shown in Figure 10a. C1 represents the value of capacitance induced between the corner of the square ring and the diagonal conducting patch with incident X polarization. L2 shows the combined inductive effect of the two outer squares (area: C × C) and inner square (area: C1 × C1). It is interesting to note that due to the discontinuity between the three square inductors in a diagonal position, there will also be a capacitive effect, but the overall effect for three inductors will be inductive. Thus, it is represented as L2. Zo and Zd represent transmission line models for free space layers and the substrate. In the lower frequency band of operation, the impedance corresponding to L1, Z\_L1 will be lower compared to its value in a higher frequency band of operation. Similarly, impedance corresponding to C1, Z\_C1 will be large in the first frequency band while it will become much smaller in the second frequency band.

**Figure 10.** Equivalent circuit for the proposed converter under incident (**a**) X polarization, (**b**) Y polarization.

Now it will be explained how dual polarizations exist within two bands. For this, assume Z\_L1 (f1) and Z\_L1 (f2) represent impedances corresponding to L1 at f1 and f2, respectively. Similarly, Z\_C1 (f1) and Z\_C1 (f2) represent impedances corresponding to C1 at f1 and f2, respectively, and Z\_L2 (f1) and Z\_L2 (f2) represent impedances corresponding to L2 at f1 and f2, respectively. f1 corresponds to any frequency within the first frequency band while f2 corresponds to any frequency within the second frequency band. Thus, |Z\_L1 (f1)|<|Z\_L1 (f2)|, |Z\_C1 (f1)| >> |Z\_C1 (f2)|, |Z\_L2 (f1)|<|Z\_L2 (f2)|. Overall impedance for the top layer can be calculated as |Z\_L1| |Z\_L1| (2 × |Z\_C1|+|Z\_L2|). At f1, |Z\_C1(f1)| will be larger than that at f2, |Z\_C1(f2)|. Thus, the 2 × |Z\_C1|+|Z\_L2| component will be larger. Hence, the overall effect for a parallel combination of large capacitive impedance and small inductive impedance will be small inductive impedance. For a frequency f2 in higher frequency band, 2 × |Z\_C1|+|Z\_L2| will become small and the overall effect will be capacitive. At f2, the resultant impedance will be a parallel combination of large inductance and small capacitance, which will result in small capacitive effect. Thus, the overall change in impedance behavior at f2 explains the idea of dual polarization.

#### **6. Performance Analysis**

For design considerations, the effect of different dimensions of the unit cell on the performance of the dual-band polarization converter was analyzed. Figure 11a shows the plot of the axial ratio for the proposed converter for different values of *p* keeping all the other parameters constant. It is observed that with the increase in *p* from 49.9 μm to 51.9 μm, the lower end of the first frequency band remains almost constant while higher-end shifts towards the right cause the bandwidth of the first band to increase. In the second band, increasing *p* has greater impact: it shifts the lower frequency towards the left while the higher-end remains almost stable with some exceptions. Thus, periodicity *p* has an impact on both conversion bands. This can be explained as follows: increasing *p* increases the length of the outer square ring on the metasurface, since this square ring contributes to the electric field strength at f1 less than that at f2 (as seen in Figure 8). Thus, variation in the second conversion band is found to be larger than for the first conversion band. Figure 11b shows the plot of the axial ratio for different values of *c* from 13.2 μm to 14.2 μm. It is clear that with the increase in *c*, the first frequency band shifts towards the left, which decreases operational bandwidth. A similar tendency is observed for the second frequency band due to the larger variation per wavelength as compared to the first frequency band. This change is supported by Figure 8, in which both conversion bands' operation depends upon corner square-conducting patches.

**Figure 11.** Effect of (**a**) *p* and (**b**) *c* on the performance of dual-band LP-to-CP converter.

The effect of substrate thickness *d* and inner square dimension *c*1 is analyzed as shown in Figure 12a,b, respectively. Figure 12a shows that as *d* is increased from 3.2 μm to 4.2 μm, the performance of dual-band LP-to-CP deteriorates in terms of axial ratio. A slight decrease in bandwidth is observed

as the higher frequency end of the first band moves towards the left. This variation in second frequency band seems to be abrupt due to higher sensitivity at high frequency, although performance remains more or less stable (within 3 dB), except at *d* = 4.2 μm. This phenomenon can be explained quantitatively as follows: the incident electric field on the top metasurface can be divided into two parts: the reflected wave to the air and the transmitted wave inside the substrate. Assuming the conductor thickness to be negligible, the transmitted wave travels inside the substrate and upon striking the substrate to the ground interface, is partially reflected back to the substrate, whereas the remainder of the portion is transmitted into the air. The portion of electromagnetic wave which was reflected back to the substrate travels back to the top surface to the substrate interface and, upon striking that interface, is again divided into two portions. One portion is reflected back to the substrate, while the other portion is transmitted into the air. The reflected wave traveling inside the substrate experiences the phase delays and, upon striking the substrate to ground interface, some portion of this wave reflects back to the substrate, while some part is transmitted into the air. These multiple transmitted waves interfere with each other constructively and destructively producing two polarized waves: one X polarized and the other Y polarized. These waves generate circularly polarized waves when they have comparable magnitudes and di fferences in phase angles around 90◦. Varying the substrate thickness changes the phase angles and hence a ffects the axial ratio for the proposed converter. Figure 12b shows the e ffect of *c*1 on the performance of dual-band LP-to-CP converter. It shows that the first frequency band remains almost stable with a change in *c*1, whereas the second frequency band is sensitive towards *c*1. Although its performance remains within 3 dB for 13.76 to 14.06 um, the value of *c*1 a ffects the second frequency band. The same is obvious from the physical mechanisms discussed earlier and as shown in Figure 8, where it is clear that the central conducting patch contributes to the higher frequency band and does not significantly impact the lower frequency band.

**Figure 12.** Effect of (**a**) *d* and (**b**) *c*1 on the performance of dual-band LP-to-CP converter.
