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In this paper, we report on the design, fabrication and subsequent investigation of a broad band cross polarization converter based on a C2-symmetric ring/disk cavity. Different plasmon hybridization modes are excited in the ring/disk cavity and enable the polarization manipulations. The designed cross polarization converter can convert the x or y polarized incident wave to its cross polarized wave in the frequency range from 9.65 to 14.16 GHz with a bandwidth of ~38% of the central wavelength and an efficiency higher than 80%. At 9.25 GHz and 14.35 GHz, the x (y) polarized incident wave is converted to a left (right) handed and right (left) handed circularly polarized wave, respectively.
© 2014 Optical Society of America
1. Introduction
Polarization is an important property of electromagnetic waves and great efforts have been made to manipulate it [1–4]. For instance, metamaterials have been used to realize circular polarizers [5], polarization rotators [6] or metasurface with asymmetric transmission [7] to manipulate the polarization of electromagnetic waves. Circular polarizers or polarization rotators can be realized by applying anisotropic metamaterials which cause different phase delays for differently polarized waves [8, 9]. Chiral metamaterials have also been used to manipulate the polarization [10, 11] and obtain asymmetric transmission [12, 13] in both the microwave band and the optical band. Especially, in the microwave band the structures with diodes can be used to actively manipulate the polarization [14].
Recently, plasmon resonances and plasmon hybridizations were observed in metamaterials [15–18], and have been applied for the manipulation of polarization [19], as absorbers [20], to study negative refraction [21], for wave guiding and for biological sensing [22, 23]. Polarization dependent plasmonic resonances in the same structure can interfere with each other and contribute to the polarization conversion [24]. Using multi-order plasmon resonances, a broadband polarization rotator can be realized [25]. Plasmon hybridization can also occur within a single, complex structure if the structure supports multiple plasmon resonances. Plasmon hybridizations, including Fano resonances, have been observed in metamaterial structures at microwave wavelengths [26–33]. A Fano resonance can be excited in metamaterials by symmetry breaking or by oblique incidence which causes an interference between a broad bright plasmon mode and a narrow dark plasmon mode [18, 32]. A Fano resonance can be regarded as the classical analogue of electromagnetically induced transparency (EIT). The EIT-like effect has been used to realize a metasurface which can manipulate the polarization of electromagnetic waves, although only in a narrow band [34].
A ring is a highly tunable structure and can support multipolar plasmon modes. These modes can be excited by oblique incidence, retardation effects or coupling with a disk [35]. A ring/disk cavity is a structure with a disk inside or outside of a ring [36] and a concentric ring/disk cavity is a highly tunable metallic structure with significant potential to support plasmon hybridization [37]. Because of symmetry breaking, Fano resonances can be excited in nonconcentric ring/disk cavities due to the interaction of higher multipolar modes [38, 39]. Recently, resonant cavity modes in elliptical and circular plasmonic nanoantennas have been studied [40, 41]. The azimuthal symmetry breaking of the elliptical plasmonic nanoantenna leads to even and odd cavity resonant modes which can result in the polarization conversion and absorption [42, 43].
In this article, we propose a structure which consists of a layer of a C2-symmetric ring/disk cavity and a layer of a perfect electric conductor separated by a dielectric layer. The plasmon resonances of the ring can couple with the cavity modes of the elliptical disk, resulting in different plasmon hybridizations. The plasmon hybridizations in the C2-symmetric ring/disk cavity are polarization dependent and lead to a broad band cross polarization conversion. The cross polarization converter can work in two orthogonal polarization directions with a bandwidth of ~38% of the central wavelength and an efficiency of more than 80%. Furthermore, at 9.25 GHz and 14.35 GHz, a linearly incident wave is converted to a left handed or right handed circularly polarized wave. Thus, the designed structure can also be used as a linear-to-circular polarizer.
2. Structure design
The anisotropic structures support polarization dependent effects. The manipulation of the polarization states occurs due to the interference between the polarization dependent reflections or transmissions. The ring/disk cavities are demonstrated to support different plasmon hybridizations [39]. The structure of the proposed cross polarization converter is shown in Fig. 1(a). The proposed ring/disk cavity is a C2-symmetric structure with an elliptical disk in a circular ring. Thus, the proposed structure supports multiple polarization dependent plasmon hybridizations and these plasmon hybridizations lead to a broad band cross polarization conversion.
Fig. 1 (a) The proposed structure of the ring/disk cavity. (b) A photograph of the fabricated sample. (c) The polarization of the incident wave.
The geometrical parameters of the designed ring/disk cavity are given by p = 12.5 mm, r1 = 4 mm, r2 = 3.8 mm, a = 1.3 mm and b = 3.46 mm. The broad band cross polarization converter is fabricated by the printed circuit board fabrication process. The relative dielectric constant and the loss tangent of the substrate are 3.5 and 0.003, respectively. The thickness of the substrate is 4mm. The designed ring/disk cavities were etched from 0.035mm flat copper on one side of a substrate. On the other side of the substrate a metallic sheet was placed which ensures that most of the incident power is reflected. The fabricated sample consists of 32 × 32 unit cells with a total square area of 400 mm × 400 mm as shown in Fig. 1(b).
As shown in Fig. 1(c), the incident and reflected electric fields can be projected onto two directions parallel to the major axis (135deg) and the minor axis (45deg) of the elliptical disk, respectively. Thus, the amplitude and the phase of the waves in these two directions can be controlled independently, and the polarization state of the reflected wave can then be manipulated by the interference of these waves. Under illumination of an x polarized or y polarized wave, the two orthogonal components (polarized along 45deg and 135deg) of the reflected wave have almost the same amplitude. Then, if the structure generates a phase difference of π between the two components of the reflected wave, the reflected wave is linearly polarized and rotated 90deg to the incident wave, i.e. the x (y) polarized incident wave is converted to its cross polarization wave. In another case, if the phase difference of the two components of the reflected wave is designed to be π/2 or -π/2, the reflected wave is a left handed or right handed circularly polarized wave, i.e. the linearly x (y) polarized wave is converted to a circularly polarized wave.
3. Results and discussion
3.1. Simulation and measurement results
To numerically investigate the performance of our design, the frequency domain solver of the commercially available software CST MICROWAVE STUDIO was employed. The underlying simulation method is the Finite Integration Technique (FIT). For the simulations, the unit cell boundary condition was used for the x and y directions, and the absorbing boundary condition was used for the z direction. The model is excited by using a Floquet port with a normal incidence of linearly polarized waves in the frequency range from 8 to 16 GHz. When the incident wave is x polarized or y polarized, due to the symmetry of the structure, the amplitude and the phase of the co-polarized and cross-polarized reflected wave do not change. Thus, for sake of simplicity, only the simulation results for an incident y polarized wave are shown in Fig. 2. Because a homogeneous copper layer was introduced beneath the ring/disk structure, the transmission of the proposed cross polarization converter is zero.
Fig. 2 The simulated (a) and the measured (b) reflectance of the broad band cross polarization converter.
Rij refers to the complex amplitude of the i-polarized component of the reflected wave when a j-polarized wave incides with unit power, where the subscripts i and j could be x or y. Figure 2(a) shows the simulated amplitude of the reflectance for a y polarized incident wave propagating along the z-axis. The simulation results show that, in the frequency range from 9.65 to 14.16 GHz, the power of the reflected cross-polarized wave is larger than 0.8, indicating an efficiency higher than 80%. With a value of below 0.1, the power of the reflected co-polarized wave is strongly suppressed. Thus, the incident wave is converted to its cross polarized wave with a bandwidth of ~38% of the central wavelength. Figure 2(b) shows the measured amplitude of the reflectance, which confirms the results of the simulation.
The simulated phase of Rij is shown in Fig. 3(a). Because |Ryy|2 is insignificant compared to |Rxy|2, in the frequency range from 9.65 to 14.16 GHz, the phase difference has little effect on the performance of the proposed design. Interestingly, however, at 9.25 GHz and 14.35 GHz, the amplitudes of the y and x components of the reflected wave have the same value, and the phase differences are ~-π/2 and ~π/2, respectively. Thus, for an incident y-polarized wave, the reflected waves at 9.25 GHz and 14.35 GHz are right handed and left handed circular polarized waves. Due to the symmetry of the designed structure, for an incident x-polarized wave, the reflected waves at 9.25 GHz and 14.35 GHz are left handed and right handed circularly polarized waves [44]. The measured phases of Rij are shown in Fig. 3(b) and also confirm the results of the simulations.
Fig. 3 The phase of the cross-polarized (black solid line) and co-polarized (red dashed line) reflectance.
To evaluate the performance of the proposed broad band cross polarization converter, the polarization rotation azimuth angle ψ and the ellipticity η were calculated from the simulation results using the following equations which are derived from the Stokes parameters [45]:
where R = |Rxy|/|Ryy| and φ = arg(Rxy) - arg(Ryy). The numerical value of tan η represents the ratio of the axes of an ellipse and the sign of η distinguishes the handedness. If η is ± 45 deg and tan η = 1, the wave is circularly polarized. The results for the calculation of ψ and η are shown in Figs. 4(a) and 4(b). In the interval from 9.65 to 14.16 GHz, the polarization rotation angle is ~90 deg and the ellipticity indicates that the reflected wave is almost linearly polarized. The results further indicate that the incident wave is reflected to its cross polarization wave with a bandwidth of ~38% of the central wavelength. Notably, at 9.25 GHz and 14.35 GHz, the ellipticity is ~45 deg and ~-45 deg, which suggests that, at these two frequencies, the linearly polarized incident wave is converted to a right handed and a left handed circularly polarized wave, respectively.Fig. 4 Comparison of the simulated rotation angle (a), ellipticity (b) and the PCR (c) with the measured rotation angle (d), ellipticity (e) and the PCR (f).
To further investigate the efficiency of the polarization conversion, the polarization conversion ratio (PCR) is introduced. It is defined as
The calculated PCR is shown in Fig. 4(c). In the range from 9.65 to 14.16 GHz the PCR is higher than 90%.To verify the simulation results, the performance of the fabricated sample was measured by employing the free-space test method in a microwave anechoic chamber. A vector network analyzer (Agilent E8363B) and two linearly polarized standard-gain horn antennas were used to transmit and receive the electromagnetic waves. Figure 5 shows a schematic illustration of the measurement setup. The reflection measurement was calibrated by replacing the sample with a metallic sheet of the same size. The co-polarization wave and the cross-polarization wave were measured with the receiving horn antenna rotated by 0 deg and 90 deg, respectively.
The measured amplitude of the reflectance is shown in Fig. 2(b) and is compared with the simulation results in Fig. 2(a). The polarization rotation azimuth angle ψ, the ellipticity η and the PCR calculated from the measurement results are shown in Figs. 4(d)-4(f). By comparing the measurement results with the simulation results, the validity of the simulation results and the performances of the designed structure were demonstrated. The divergence between the simulation and the measurement results were caused by machining errors and measurement errors.
3.2. Broad band cross polarization conversion mechanism
In order to understand the broad band polarization conversion mechanism, the plasmon hybridizations were investigated by observing the simulated distributions of the electric field Ez, i.e. the component of the electric field perpendicular to the metasurface. For a better understanding of the behavior of the proposed ring/disk cavity, the structure was simulated for frequencies in the range from 8 to 16 GHz under normal incidence of waves polarized along the major axis and the minor axis of the elliptical disk, respectively.
The reflectance for an incident wave polarized along the major axis of the elliptical disk is shown in Fig. 6(a). Because of the metallic sheet, the transmission is zero and the reflectance dips are caused by absorption. The reflectance is higher than 0.9 in the range from 9.65 to 14.16 GHz, and the reflectance dips are located at 9.74 GHz and 14.32 GHz. The simulated distributions of the electric field Ez at 9.74 GHz, 11.5 GHz, 14.32 GHz and 15.75 GHz are shown in Fig. 7(a). The dipolar ring mode and the e11 disk mode [40] are out of phase with each other at 9.74 GHz and cause a dark mode in the ring/disk cavity. At 11.5 GHz, an hexapole ring mode is excited in the ring and it is out of phase with the e11 disk mode. Mimicking gap surface plasmons are generated [40] at 14.32 GHz and suppress the hexapole ring mode. In addition, the elliptical disk oscillates in phase with the mimicking gap surface plasmons. At 15.75 GHz, the e11 disk mode is in phase with the hexapole ring mode. At 15.75 GHz, the intensity of mimicking gap surface plasmons has decreased and they are out of phase with the e11 disk mode.
Fig. 6 The reflected amplitude for an incident wave polarized along the major axis (a) and the minor axis (b) of the elliptical disk. The inset of the panels (a) and (b) shows the corresponding polarization of the incident wave.
Fig. 7 Simulated distributions of the electric field Ez for an incident wave polarized along the major axis (a) and minor axis (b) of the elliptical disk, respectively.
The reflectance for an incident wave polarized along the minor axis of the elliptical disk is shown in Fig. 6(b). Dips in reflectance occur at 12.9 GHz and 15.42 GHz. At 15.42 GHz, the reflectance is below 0.2. The simulated distributions of the electric field Ez are shown in Fig. 7(b). At 9.6 GHz, 12.9 GHz, and 14.85 GHz, the o11 disk mode [40] is out of phase with the dipolar ring mode and creates a dark plasmon mode in the ring/disk cavity. The o11 disk mode is out of phase with the hexapole ring mode at 15.42 GHz. At 15.42 GHz, mimicking gap surface plasmons are generated and are in phase with the o11 disk mode.
To understand how the plasmon hybridizations contribute to the broad band cross polarization conversion, the phase of the reflectance is shown in Fig. 8. The plasmon hybridizations excited by the incident waves polarized along the major axis and the minor axis cause a ~180 deg phase difference in the frequency range from 9.65 to 14.16 GHz. Thus, if waves polarize along the major axis and the minor axis simultaneously incide with the same phase, due to the ~180 deg difference in the reflected phase, the total reflected field is rotated 90 deg to the total incident wave, i.e. the total incident wave is converted to its cross polarized wave. Similarly, at 9.25 GHz and 14.35 GHz, the phase differences of the reflected waves are ~-90 deg and ~90 deg, respectively. Thus the total reflected waves at 9.25 GHz and 14.35 GHz are circularly polarized, i.e. the linearly polarized incident wave is converted to a circularly polarized reflected wave.
Fig. 8 The phase of the reflectance for an incident wave polarized along the major axis (red) and the minor axis (blue) of the elliptical disk, respectively.
4. Conclusion
In conclusion, we have numerically and experimentally demonstrated a broad band cross polarization converter based on plasmon hybridizations in a C2-symmetric ring/disk cavity. From 9.65 GHz to 14.16 GHz, the x or y polarized incident wave is converted to its cross polarized wave with a bandwidth of ~38% of the central wavelength and an efficiency higher than 80%. At 9.25 GHz and 14.35 GHz, the x (y) polarized incident wave is converted to a left (right) handed and a right (left) handed circularly polarized wave, respectively. The polarization rotation azimuth angle, the ellipticity and the polarization conversion ratio were calculated in order to evaluate the performance of the broad band cross polarization converter. The plasmon hybridizations were investigated by observing the distribution of the electric field Ez. Due to the plasmon hybridization, the phases of the reflected wave polarized along the major axis and the minor axis of the elliptical disk have a difference of ~180 deg in the frequency range from 9.65 to 14.16 GHz, and a phase difference of ~ ± 90 deg at 9.25 GHz and 14.35 GHz. These phase differences result from the plasmon hybridizations and are causing the manipulation of the polarization.
Acknowledgments
This work was supported by the National Natural Science Foundation (NSF) of China under Grant Nos. 61331005, 61001039 and 41390454.
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