Dynamically Reconfigurable Broadband Polarization Converter

Abstract

A polarization converter with broadband polarization characteristics and capable of dynamic reconfiguration is proposed. By introducing outofplane degrees of freedom, dynamically tunable broadband and highefficiency linear polarization conversion within the wavelength range of 20002800 nm is achieved. Research results indicate that when a twodimensional (2D) splitring resonator (SRR) is irradiated by a lowdose focused ion beam, it will deform upward and transform into a threedimensional (3D) SRR, achieving a linear polarization conversion efficiency of over 90%. The 3D SRR can be driven by electrostatic force to return to the 2D SRR state, thereby realizing the dynamic reconfiguration of this polarization converter. By changing the applied voltage and adjusting the structural parameters, a tailored polarization converter that exhibits broadband performance and high polarization conversion efficiency is also achieved. The results may provide novel ideas and technical methodologies for various applications such as polarized optical imaging, emerging display technologies, polarized optical communication, and optical sensing.

Keywords

broadband polarization conversion / reconfigurable / split-ring resonator / deformation

1 Introduction

Polarization is an important characteristic parameter of electromagnetic waves, reflecting the vibration state of the electric field vector during the transmission of the electromagnetic wave. Compared with three-dimensional (3D) metama-terials [ 1 - 3 ], which face the limitations such as complex manufacturing and high optical loss, metasurfaces have the advantages of small size, easy integration, low loss, and simple fabrication process. More importantly, they have shown extraordinary potential in the fields of optical chirality \(\left\lbrack {4,5}\right\rbrack\) , optical vortices \(\left\lbrack 6\right\rbrack\) , Fano resonance [ 7 ], reconfigurable optical holography [ 8 ], and optical orbital angular momentum regulation [ 9 ].

Most traditional polarization converters are based on optically active crystals, liquid crystals or the Faraday effect [ 10 - 17 ]. Compared with traditional polarization devices, metasurface-based polarization converters have the advantages of large operational bandwidth, high polarization conversion ratio and miniaturization. In recent years, researchers have conducted in-depth studies on metasurface-based polarization converters. Yong et al.[ 18 ] proposed a reflective ultra-broadband polarization converter, which can convert linearly polarized electromagnetic waves into cross-polarized linearly polarized waves in the range of \({0.53}- {1.36}\mathrm{{THz}}\) . However, the polarization conversion ratio is relatively low \(\left({ \leq {50}\%}\right)\) . Li et al.[ 19 ] proposed a Z-shaped reflective polarization converter, achieving cross-polarization conversion of linearly polarized waves in the range of \({0.116}- {0.26}\mathrm{{THz}}\) . Although the polarization conversion ratio reached \({80}\%\) , the operation bandwidth is relatively narrow. Therefore, it is still challenging for the polarization converter to simultaneously satisfy the characteristics of broadband, high polarization conversion efficiency and dynamic regulation, which greatly limits its practical application.

Recently, we have studied a series of polarization conversions based on Nano-kirigami structures and developed a dynamic reconfiguration method based on electrostatic forces \(\left\lbrack {8,{20},{21}}\right\rbrack\) . In fact, besides electrostatic methods, there are some other driving methods, such as mechanical stress [ 20 , 22 ] , pneumatic pressure \(\left\lbrack {23}\right\rbrack\) , thermal expansion [ 10 ]and magnetic drive [ 24 ]. Based on the previous research, this work proposes a novel architecture for a dynamically reconfigurable broadband polarization converter. The polarization conversion device we studied has a three-layer structure of \(\mathrm{{Au}}/{\mathrm{{SiO}}}_{2}/\mathrm{{Si}}\) . The top-layer Au patterns, consisting of split-ring resonator (SRR) like nanostructures, are supported by beneath \({\mathrm{{SiO}}}_{2}\) pillars. The deformation of the SRRs is regulated by applying external stress or electrostatic forces, thereby realizing the dynamic reconfiguration of the polarization direction. Simulation results show that the value of the polarization conversion ratio (PCR) within the wavelength range of \({2200}- {2800}\mathrm{\;{nm}}\) can reach more than \({90}\%\) . The maximum linear polarization rotation angle reaches \({119}^{\circ }\) . Our results may provide novel research ideas for polarized optical imaging, emerging display, optical sensing, and other fields.

2 Structural Design

The SRR like structure we proposed is an open-loop structure and exhibits a higher susceptibility to deformation compared with other geometric structures. This structure consists of the \({60}- \mathrm{{nm}}\) -thick top gold film, the intermediate \({\mathrm{{SiO}}}_{2}\) cuboid supporters with thickness of \({200}\mathrm{\;{nm}}\) and the bottom Si dielectric layer. We define that compared to initial two-dimensional (2D) SRR structure, the upward-deformed SRR is described by \(3{\mathrm{D}}_{\mathrm{{up}}}\mathrm{{SRR}}\) , and the downward-deformed SRRs is described by \(3{\mathrm{D}}_{\text{down }}\mathrm{{SRR}}\) . Fig. 1 shows a schematic diagram of the broadband linear polarization conversion. According to the bilayer stress distribution model [ 25 , 26 ], the 2D SRR can undergo deformation into \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR through irradiation with a low-dose focused ion beam (FIB). Also, an external voltage can be applied to the 2D SRR or \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR to generate an electrostatic attraction between the top-layer gold film and the bottom-layer Si. By modulating the applied voltage, the \(2\mathrm{D}\mathrm{{SRR}}\) or \(3{\mathrm{D}}_{\mathrm{{up}}}\mathrm{{SRR}}\) can be deformed downward into \(3{\mathrm{D}}_{\text{down }}\) state. Ideally, when a linearly polarized light with an \(x\) -polarized direction is incident in the 2D SRR state, the reflected light contains a linearly polarized light with an \(x\) -polarized direction and a linearly polarized light with a \(y\) -polarized direction. When a linearly polarized light with an \(x\) -polarized direction is incident in the \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR state, the reflected light is almost entirely a linearly polarized light in the \(y\) -polarized direction. When a linearly polarized light with an \(x\) -polarized direction is incident in the \(3{\mathrm{D}}_{\text{down }}\) state, the reflected light is almost a linearly polarized light with an \(x\) -polarized direction. In Fig. 1 , the enlarged view is the structural diagram of the 2D SRR unit. The square hole in the middle \({W}_{1}\) is \({0.15\mu }\mathrm{m}\) , the slit width \({W}_{2}\) is \({0.07\mu }\mathrm{m}\) , the radius of the circular arc \(r\) is \({0.52\mu }\mathrm{m}\) , the angle \(\theta\) is \({30}^{\circ }\) , the arc length \(C\) corresponding to the angle \(\theta\) is \({0.27\mu }\mathrm{m}\) , and the period \(P\) is \({1.45\mu }\mathrm{m}\) .

For a better understanding of the principle of polarization conversion, we decompose the electric field vector of the linearly polarized light with the \(x\) -polarized direction under normal incidence into two components, \({E}_{iu}\) and \({E}_{iv}\) along the \(u\) - and \(v\) - directions respectively, as shown in the left diagram in Fig. 2 (b).

(1) \[{\mathbf{E}}_{i}= \left({\mathbf{u}{E}_{iu}+ \mathbf{v}{E}_{iv}}\right)\]

The electric field components of the reflected wave are expressed as

(2) \[{\mathbf{E}}_{r}= \left({\mathbf{u}{E}_{ru}+ \mathbf{v}{E}_{rv}}\right)= \left({\mathbf{u}{\mathbf{r}}_{u}{E}_{iu}+ \mathbf{v}{\mathbf{r}}_{v}{E}_{iv}}\right)\]

where \({\mathbf{r}}_{u}= {r}_{u}{\mathrm{e}}^{i\varphi u},{\mathbf{r}}_{v}= {r}_{v}{\mathrm{e}}^{i\varphi v}\) are the reflection coefficients in the \(u\) -direction and \(v\) -direction, respectively. Owing to the anisotropic characteristics of SRR metasurfaces, there is a difference in the propagation phase of the components in the \(u\) -direction and \(v\) -direction of the polarized light, as \({\Delta \varphi }= \left|{{\varphi }_{u}- {\varphi }_{\mathrm{v}}}\right|\) . The preconditions should be satisfied: \({r}_{u}= {r}_{v},{\Delta \varphi }= \pi\) . The resultant electric field polarization direction of \({E}_{ru}\) and \({E}_{rv}\) will be rotated from a horizontal to a vertical orientation. A linear polarization converter achieving \(x\) - to- \(y\) polarization conversion can be realized.

PCR is used to evaluate the performance of the proposed SRR, and it is defined as [ 27 , 28 ]

(3) \[\mathrm{{PCR}}= \frac{{R}_{yx}}{{R}_{xx}+ {R}_{yx}}\]

where \({R}_{xx}\) is co-polarized reflection, and \({R}_{yx}\) is cross-polarized reflection.

3 Results and Discussion

The finite-element software COMSOL Multi-physics 6.0 is used to simulate the optical response of the nanostructure. Periodic boundary conditions are adopted in the \({xy}\) -plane, and perfectly matched layer (PML) conditions are used on the \(z\) -axis. When linearly polarized light in the \(x\) -polarized direction is normally incident upon the \(2\mathrm{D}\mathrm{{SRR}}\) , both \({R}_{xx}\) and \({R}_{yx}\) can be observed within the operational wavelength range of \({2000}- {2800}\mathrm{\;{nm}}\) . Notably, \({R}_{xx}\) is significantly higher than \({R}_{yx}\) , as shown in the left of Fig. 2 (a). In this state, the electric field is concentrated and distributed within the slit, as shown in Fig. 2 (b). By exposing the 2D SRR with a low-dose FIB irradiation, the 2D SRR is deformed upward to form a \(3{\mathrm{D}}_{\mathrm{{up}}}\mathrm{{SRR}}\) , and the out-of-plane structural degree of freedom of the structure increases, which can be used to adjust the optical response of the structure. In the operating wavelength range of \({2000}- {2800}\mathrm{\;{nm}},{R}_{xx}\) of the \(3{\mathrm{D}}_{\mathrm{{up}}}\mathrm{{SRR}}\) structure almost completely disappears and the incident light in the x-polarized direction is fully converted into \({R}_{yx}\) , as shown in the middle of Fig. 2 (a). This occurs because the mirror symmetry of the deformed structure is broken, resulting in the change of light-matter interaction, and the slit mode of the concentrated distribution of the electric field is also disrupted, as shown in Fig. 2 (c). By applying an external voltage to generate an electrostatic attraction, the 2D SRR deforms downward into a \(3{\mathrm{D}}_{\text{down }}\mathrm{{SRR}}\) . In the operating wavelength range of \({2000}- {2800}\mathrm{\;{nm}},{R}_{yx}\) almost completely disappears, and the reflected light is completely converted into \({R}_{xx}\) , as shown in the right of Fig. 2 (a). Meanwhile, the electric field is concentrated and distributed in the slit, as presented in Fig. 2 (d).

To further illustrate the characteristics of this linear polarization converter, the effects of external stress, voltage, arc length and incident angle on this linear polarization converter are studied in Fig. 3 . Apparently, with a constant arc length, the deformation height \(H\) increases with the increase of the applied stress and voltage. With the fixed external stress and voltage, the deformation height \(H\) decreases with the increase of the arc length. It can be seen from Fig. 3 (a)-(b) that when the constant arc length is \({267}\mathrm{\;{nm}}\) and the external stress is \(2\mathrm{{GPa}}\) , the upward deformation height reaches a maximum value of \({524}\mathrm{\;{nm}}\) . In comparison, when the applied voltage is \({21}\mathrm{\;V}\) , the downward deformation height reaches a maximum value of \({145}\mathrm{\;{nm}}\) . Withintheoperationalwavelengthrangeof2000-2800 \(\mathrm{{nm}}\) , when the structure gradually transforms from \(3{\mathrm{D}}_{\mathrm{{up}}}\) to \(2\mathrm{D}\) and then to \(3{\mathrm{D}}_{\text{down }},{R}_{xx}\) gradually increases while \({R}_{yx}\) gradually decreases. When the structure height is fixed, with the gradual increase of the arc length, the response bands of \({R}_{xx}\) and \({R}_{yx}\) are blue-shifted, as plotted in Fig. 3 (c). Within the operational wavelength range of \({2000}- {2800}\mathrm{\;{nm}}\) , as the incident angle gradually increases, \({R}_{xx}\) gradually increases while \({R}_{yx}\) gradually decreases, as shown in Fig. 3 (d)-(e).

Our extended investigation into the frequency-dependent PCR reveals that within the \({100}- {200}\mathrm{{THz}}\) range, the polarization conversion efficiency varies significantly with deformation height. The structure demonstrates exceptionally high PCR in the \(3{\mathrm{D}}_{\mathrm{{up}}}\) state, reaching a peak value of 0.99 at \({134}\mathrm{{THz}}\) . However, both 2D and \(3{\mathrm{D}}_{\text{down }}\) states exhibit considerably lower PCR, with values of 0.05 and 0.02 respectively at \({134}\mathrm{{THz}}\) , as shown in Fig. 4 (a). Furthermore, we have examined the impact of incident angle on PCR, demonstrating excellent robustness within the \({0}^{\circ }- {20}^{\circ }\) range, as shown in Fig. 4 (b).

Further dynamic regulation research is carried out and the results are plotted in Fig. 5 . In this study, a voltage is applied to the \(3{\mathrm{D}}_{\mathrm{{up}}}\mathrm{{SRR}}\) featuring an upward warping height of \({292}\mathrm{\;{nm}}\) , resulting in the gradual reversion of the \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR back to its 2D configuration. When the applied voltage is stopped, the structure returns to the \(3{\mathrm{D}}_{\mathrm{{up}}}\mathrm{{SRR}}\) form. Under the maximum external applied voltage of \({65}\mathrm{\;V}\) , the structural deformation height is reduced to \({12}\mathrm{\;{nm}}\) , as shown in Fig. 5 (a). Interestingly, within the operational wavelength range of \({2200}- {2800}\mathrm{\;{nm}}\) , the PCR value of the \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR structure is higher than \({90}\%\) , and gradually decreases with the increase of applied voltage. The magnitude of PCR can be customized through the regulation of the applied voltage value, as demonstrated in Fig. 5 (b). In the \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR state, the magnitudes of \({R}_{xx}\) and \({R}_{yx}\) can be altered by adjusting the magnitude of the applied voltage. As the applied voltage increaes, \({R}_{xx}\) gradually increases while \({R}_{yx}\) gradually decreases, as shown in Fig. 5 (c)-(d). When the linearly polarized light in the \(x\) -polarized direction is vertically incident on the \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR structure, the polarization direction of \({R}_{yx}\) will be significantly deflected. The polarization rotation angles reach \({80}^{\circ },{93}^{\circ },{119}^{\circ }\) , \({88}^{\circ }\) and \({71}^{\circ }\) at2000,2100,2300,2500and \({2600}\mathrm{\;{nm}}\) , respectively, without making the polarization state elliptical, as shown in Fig. 5 (e).

We conducted a comparative analysis of key aspects, including device size, thickness, dynamic regulation, polarization conversion efficiency, and relative bandwidth. As shown in Tab. 1 , our device demonstrates superior polarization conversion ability and a larger relative bandwidth compared to existing designs. Furthermore, its compact size, thin profile, and dynamic regulation capability highlight its potential for a wide range of applications.

4 Conclusion

In this paper, a broadband and dynamically reconfigurable polarization converter is designed. The reflection, electric field distribution, polarization conversion efficiency and polarization rotation angle of the polarization converter are simulated and calculated. The effects of external stress, voltage, arc length and incident angle on the reflection and polarization conversion efficiency of the linear polarization converter are discussed. The research reveals that variations in arc length result in shifts in the response bands of co-polarized reflection, cross-polarized reflection and polarization conversion efficiency. Within the operational wavelength range of 2000 \(-{2800}\mathrm{\;{nm}}\) , as the incident angle gradually increases, the co-polarized reflection gradually increases while the cross-polarized reflection gradually decreases. When the external stress is applied, the 2D SRR will deform upwards into \(3{\mathrm{D}}_{\mathrm{{up}}}\mathrm{{SRR}}\) , causing the co-polarized reflection to decrease and the cross-polarized reflection to increase within the operational wavelength range of \({2000}- {2800}\mathrm{\;{nm}}\) . At \({2300}\mathrm{\;{nm}}\) , the polarization conversion efficiency increases from 7% to 92%. Further research shows that a voltage can be applied to the \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR structure and the deformation height of the SRR can be dynamically adjusted by controlling the applied voltage. When an external voltage of \({65}\mathrm{\;V}\) is applied, the \(3{\mathrm{D}}_{\mathrm{{up}}}\) SRR returns to the \(2\mathrm{D}\mathrm{{SRR}}\) , at which point the reflection returns to the value observed for the 2D SRR, and the polarization conversion efficiency also returns to 7%. Thus, we have demonstrated that the proposed polarization converter has high polarization conversion efficiency, a large broadband response, and can be dynamically regulated by an external voltage. The structural design and its appealing properties can provide novel ideas and technical methodologies for polarized optical imaging, emerging display technologies, polarized light communication, optical sensing, etc.

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Funding

National Natural Science Foundation of China(T2325005)

National Natural Science Foundation of China(62375016)

National Natural Science Foundation of China(62475250)

Science and Technology Project of Guangdong(2020B010190001)