1. Introduction

Polarization is an important parameter in areas of science dealing with transverse wave propagation, such as optics, seismology, radio, and microwaves. Especially impacted are technologies such as lasers, wireless and optical fiber telecommunications, and radar [1–5]. A polarized wave can be commonly classified by its polarization state: linear, circular, or elliptical. Therein, a circularly polarized (CP) wave has the advantages of low atmospheric absorption and susceptibility to the multi-path. A linear-to-circular polarization converter can be used to convert the polarization from the linearly polarized (LP) state to the CP state, which has attracted much attention and extensive studies over the past decade [6–17].

Conventional linear-to-circular polarization converters are designed using dielectric gratings with different velocities for two perpendicular components of the incident LP wave [7,8]. These configurations usually feature an extremely thick thickness and cannot be easily integrated in a compact system. For this reason, ultrathin split-ring resonator of various shapes [9–11] and metasurface [12–14] were explored and proposed to realize polarization converters with compact and planar structures, which can achieve the CP wave within a subwavelength thickness. Unfortunately, such converters often suffer from their intolerable insertion loss, and are difficult to be used in practical systems. Another classic method is to use birefringence [16] to obtain 90° phase difference between two perpendicular components. However, the polarization conversion efficiency (PCE) of this converter is relatively low. Thereupon, 3D chiral [5] and helical [17] metamaterials were exploited to realize the polarization conversion from linear to circular. Although such converters feature high PCE, large angular tolerance, and scalability, the fabrications become challenging and expensive due to their overly complex structures. Recently, cavity-based structures of low-profile have been proposed to rotate the polarization direction of an incident LP wave [18,19], which feature excellent performance with a very low insertion loss.

In this paper, we demonstrate that a linear-to-circular polarization converter can be realized using an array of cavities with each cavity etched with three slots. The operating modes in the cavity are carefully investigated to understand the polarization conversion mechanism. Later, a prototype of the proposed converter is fabricated and measured to verify the numerical simulations. Results show that a perfect CP wave can be obtained at the other side of the converter. The proposed polarization converter exhibits extremely low insertion loss of 0.1 dB, high polarization conversion coefficient and efficiency of over 0.97, as well as small thickness of 0.1λ₀ (λ₀ is the wavelength at the center frequency).

2. Description of the structure

The proposed linear-to-circular polarization converter is schematically depicted in Fig. 1(a). It is constructed by a 2D periodic array of square substrate integrated waveguide cavities, with a y-directed and two orthogonal (x- and y- directed) slots etched on the front and back surfaces of each cavity, respectively. An x-polarized wave propagating along the z-direction strikes normally onto the converter, and a CP wave is subsequently transmitted out on the other side of the converter without attenuation.

 

Fig. 1 (a) Schematic diagram of the proposed linear-to-circular polarization converter and its function, where the electric field arrows indicate the polarization state of the wave. (b) Expended view the detail of a unit cell of the structure.

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Figure 1(b) shows the structural detail of a unit cell of the proposed converter. It consists of a square cavity formed by two metallized surfaces with a thin substrate. The width and thickness of the square cavity are marked as W and t, respectively. Specifically, the vertical walls of the cavity are implemented through the use of four rows of metallized cylindrical vias. The vias have the diameter of D and arrange along x- and y- directions with the period of P. In addition, the y-directed slot etched on the front surface is used to couple the x-polarized wave into the cavity, while two orthogonal slots etched on the backside surface are utilized to couple the field out of the cavity with same amplitude and 90° out-of-phase, so that the transmitted wave is CP. Here, three slots have the same widths of w_s, their lengths and shifts from the edge of surfaces are denoted by l₁, l₂, l₃, s₁, s₂, and s₃, respectively, as manifested in Fig. 1(b). It should be mentioned that the behavior of this structure is predicted by the finite element method using full-wave electromagnetic simulation ANSYS HFSS. Moreover, periodic boundary conditions Master and Slave are applied along the x- and y- directions to characterize the infinitely large structure. Furthermore, excitations of Floquet with two orthogonal modes, representing the x- and y- polarized components, are imposed on the two ports of a unit cell to capture the co- and cross- transmissions performance.

3. Cavity modes and operating principle

As a cavity, it is very important to understand the operating modes inside the cavity. Generally, a cavity of very low profile only supports TM_mn0 modes [19]. The fields are uniform in the z-direction since the cavity is very thin along this direction. In addition, TE modes cannot exist in the cavity because the electric current density on the lateral side walls can flow only in the z-direction along the metallized vias. In our case, both x- and y- polarized components of the outgoing CP wave come from an x-polarized incident wave, which require the proposed structure has the ability of co- (T_xx) and cross- (T_yx) transmissions simultaneously. Therefore, we choose two orthogonal modes of TM₁₂₀ and TM₂₁₀ as the operating modes inside the cavity. They are the lowest degenerate modes and thus have the same resonant frequency of f, which can be accordingly estimated from the physical dimension as follows [19]

To gain insight into the polarization conversion mechanism, the electric field distributions inside the cavity are carefully investigated, as shown in Fig. 2. Obviously, the fields are well constrained in the vias-surrounded cavity, which suggests that a good cavity is obtained by using four rows of metallized vias with proper values of D and P. Additionally, the numbers of extremes in the cavity in Fig. 2(a) are 2 and 1 along the x- and y- directions, respectively, which sufficiently indicates that the mode of TM₂₁₀ indeed exists inside the cavity. Similarly, Fig. 2(b) reveals that another mode of TM₁₂₀, which is the orthogonal degenerate mode of the TM₂₁₀ mode, also exists in the cavity. From the mode distribution, it is easily observed that the TM₁₂₀ and TM₂₁₀ modes can be excited through the x- and y- directed slots, respectively.

 

Fig. 2 Perspective view the electric field distributions of (a) TM₂₁₀ and (b) TM₁₂₀ modes.

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To excite the cavity, slot-coupling technique is employed on its both front and back surfaces, and this technique has the advantage of stable performance under oblique incidence. The initial lengths of three slots are accordingly equal to half a guided wavelength $c_0/(2f\sqrt{({\epsilon }_r+1)/2})$. Moreover, the initial positions of three slots are located at a distance of W/4 away from the edge of the cavity, where the field is the strongest according to Fig. 2.

When an x-polarized wave (E_ix) irradiates to the polarization converter, the cavity will be excited with TM₂₁₀ mode through the y-directed slot on the front of the cavity. Subsequently, TM₂₁₀ mode will be automatically converted into TM₁₂₀ mode due to they are degenerate modes and they can coexist in the cavity. Then, the field inside the cavity can be coupled out through the x- and y- directed slots on the back side, corresponding to the TM₁₂₀ and TM₂₁₀ modes, which produce the y- and x- components (E_ox and E_oy) of the outgoing wave, respectively. The wave transmission process can be described as

4. Experimental results

To verify the functionality of the proposed linear-to-circular polarization converter, a sample is fabricated using the standard printed circuit board and plated through-hole technology. This design concept can be implemented in optical frequency using dielectric cavity based on silicon lithography. The photograph of the fabricated sample is shown in Fig. 3. The substrate used is Rogers 5880 with dielectric constant ε_r = 2.2, and the metal surface has the thickness of 0.017 mm. The physical dimensions of the polarization converter are designed as D = 0.8 mm, P = 1.34 mm, W = 21.5 mm, t = 3.175 mm, l₁ = 12.5 mm, l₂ = 12 mm, l₃ = 12.5 mm, s₁ = 5.75 mm, s₂ = 4.25 mm, s₃ = 4.15 mm, and w_s = 0.8 mm.

 

Fig. 3 Photograph of the fabricated polarization converter. (a) Front view. (b) Back view.

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The sample is measured by the free-space method using two horn antennas and a vector network analyzer. Figure 4 shows the performance of the proposed linear-to-circular polarization converter under normal incidence with the excitation of an x-polarized wave. All measured results are in close agreement to the theoretical predictions, while some small differences are attributed to the manufacturing and experimental errors. It is clear in Fig. 4(a) that the reflectance is below 0.3 from 9.85 to 10.15 GHz, representing to a fractional bandwidth of 3% at the center frequency of 10 GHz. It is worth mentioning that the field inside the cavity is perturbed due to the existence of the slot, which leads to the development of two different distinct poles within a certain frequency band, as shown in Fig. 4(a).

 

Fig. 4 Performance of the proposed linear-to-circular polarization converter. (a) Reflection characteristic of the x-polarized wave strikes on the converter. (b) Amplitudes of T_xx and T_yx. (c) Phase difference between T_xx and T_yx. (d) Electric field representation of an LP wave propagating through the converter.

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The co- and cross- polarization transmission characteristics of the proposed converter are shown in Fig. 4(b). It can be seen that the T_xx and T_yx have the same amplitude of around 0.7 at the desire frequency of 10 GHz. It should be noted that both x- and y- components come from a LP incident wave, which means that the maximum amplitudes of T_xx and T_yx theoretically equal to 0.707 when |T_xx| = |T_yx|. Therefore, our proposed converter features an extremely low transmission loss of 0.1 dB. In addition, Fig. 4(c) correspondingly plots the phase difference between T_xx and T_yx. It is clear that the 90° phase difference can be obtained at the center frequency. So far, the conditions of the same amplitude and phase difference of 90° between output x- and y- polarized components are satisfied simultaneously, thus the outgoing synthetic wave at the other side of the cavity is naturally CP.

Figure 4(d) depicts the electric field representation when a LP wave is normally incident upon the converter. It can be seen that the field intensity is of sinusoidal distribution for the incident LP wave, while the electric field vector of the propagating wave is rotating along the direction of propagation after the wave emits from the converter, which clearly verifies the linear to circular polarization conversion can be obtained by our proposed converter. It is worth mentioning that if the polarization direction of the incident wave is tilted from x-axis, only the x-component can be coupled into the cavity and exit from the other side with CP.

To assess the performance of the proposed polarization converter, the circular polarization conversion coefficients of left- and right- hand CP (LCP and RCP) waves are plotted in Fig. 5(a). Obviously, the conversion coefficient for the RCP wave is very close to 1 at the desire frequency. On the contrary, the cross-polarization component (LCP wave) is extremely small, with conversion coefficient less than 5% of the RCP wave, which illustrates the output CP wave is purely left-handed. It is worth pointing out that the LCP wave can be obtained by rearranging the x-directed slot on the backside to the opposite side. To evaluate the purity of the outgoing circular polarization wave, PCE is utilized and can be described as follows [8]

 

Fig. 5 Polarization conversion (a) coefficients and (b) efficiency of the proposed linear-to-circular polarization converter.

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5. Summary

In conclusion, we have experimentally demonstrated a linear-to-circular polarization converter using a 2D array of square cavities, with a y-directed and two orthogonal slots etched on the front and back surfaces of each cavity, respectively. The modes of TM₁₂₀ and TM₂₁₀ in the cavity have been thoroughly analyzed to reveal the polarization conversion mechanism. After that, a sample of the proposed converter has been fabricated and measured. Results show that a perfect RCP wave can be obtained around 10 GHz. Moreover, the proposed converter features an extremely low insertion loss of 0.1 dB with a very small thickness of 0.1λ₀, which makes the converter potentially useful in lasers, optical communications, spectroscopy, and navigation systems. Although the proposed cavity-based converter is verified in the microwave regimes, the design concept and our designed structure may inspire researchers working in the optical regime to come up with similar and even better designs for the mentioned optical converters.