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Abstract
We present a bifunctional polarization converter based on Dirac semimetals (DSMs) and vanadium dioxide (VO2), which consists of two layers of DSMs on both sides, a metal grating and a VO2 board. The polarization converter frequency is dynamically tuned by changing the Fermi energy level of the DSMs. The result suggests that when VO2 is in an insulated state, the device behaves as a transmissive polarization converter. The dual-band transmissive polarization conversion and asymmetric transmission (AT) function of circularly polarized (CP) waves are realized at 1.99 THz and 3.46 THz, with the polarization converter ratio (PCR) reached 97.6% and 95.8%, respectively. In addition, when VO2 is in the metal state, the designed polarization converter is a reflective device, which can maintain the chirality of the reflected CP wave to the incident wave in a wide band. The polarization-maintaining ratio (PMR) in the range of 2 THz to 3.55 THz is higher than 88%. When the angle of incidence is less than 60°, the frequency band of the PMR is narrowed and the amplitude reaches more than 90%.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarization is one of the important properties of electromagnetic (EM) waves, and it is desirable to effectively control the polarization states of EM waves. The polarization converter controls the polarization of EM waves by designing an anisotropic structure [1] or a chiral structure [2], which have many applications in imaging [3], detection [4] and optical communication [5]. However, conventional polarization converters are usually achieved based on magneto optic effect [6] and dichroic crystal [7], which requires a long propagation distance and a large volume device. Therefore, these methods are not conducive to miniaturization and integration of equipment. Metamaterials (MMs) are sub-wavelength artificial composite materials with some special properties, such as negative refraction [8], electromagnetic coding [9–11], absorbers [12,13], and polarization converters [14–19], which are often used to design ultrathin miniaturized polarization converters. In recent years, a lot of research has been done on the polarization conversion of MMs in terahertz band [20–22]. In 2013, Chen et al. [23] proposed an ultra-thin, broadband, and highly efficient terahertz polarization converter with reflection and transmission conversion efficiency of 50% and 80%. In 2017, Jiang et al. [24] designed an ultra-wideband CP converter using metal MMs, with a conversion efficiency of 80%. Cheng et al. [25] proposed a dual-band transmission CP converter in terahertz band. Usually, after the fabrication of traditional metal MMs completed, the working frequency and amplitude cannot be changed, thus dynamic tuning cannot be completed [26,27]. So research on tunable polarization converter based on active material has become a better development direction.
In recent years, some active materials have been used to design polarization conversion devices, such as liquid crystal [28], graphene [29–35], DSMs [36], and VO2 [37]. Among these active materials, DSMs and VO2 have attracted great interest because of their excellent electrical and optical properties, such as voltage tuning [38] and thermal tuning [37]. DSMs are brand-new three-dimensional topological quantum materials, which has the advantages of easy processing, low loss, and ultrahigh electron mobility [39,40]. Scientists have used DSMs to do a lot of research in electromagnetically induced transparency [41], absorbers [42] and polarization converters [43]. Dai et al. [44] designed a reflective polarization converter based on the Dirac semimetals, the polarization conversion efficiency can reach 80%. In 2019, Meng et al. [45] proposed a wideband polarization converter based on Dirac semimetals, the polarization conversion rate reaches 85% in the range from 2.072 THz to 2.428 THz. VO2 is a new type of phase change material with large modulation depth, fast response and many modulation methods [46–49]. The insulator-metal phase transition of VO2 occurs by changing the temperature, and the critical temperature is 340K [50–52]. Based on the insulator-metal phase transition characteristics of VO2 [53,54], the researchers designed a polarization converter. Zheng et al. [55] designed a reflective polarization converter based on VO2, with polarization conversion efficiency exceeds 90%. Liu et al. [56] proposed an active terahertz polarization converter based on VO2, and realized the switch between linear polarization (LP) state and CP state from 0.8 THz to 1.5THz. The transmission circular polarization converter converts the incident right-handed circular polarization (RCP) or left-handed circular polarization (LCP) wave to the LCP or RCP wave, which changes the chirality of the CP wave. The reflective CP converter needs to keep the chirality, right-handed or left-handed, of the CP wave, so the reflective CP converter is actually the chiral holder of the CP wave [57,58]. But these works achieve only a single reflection or transmission function, the research on bifunctional devices has not been found.
In this paper, a bifunctional CP wave converter is designed on the terahertz frequency. It consists of two layers of DSMs strips on both sides, and two layers in the middle which is a metal grating and a VO2 board. When VO2 is in an insulating state, the structure behaves as a transmission CP converter, which converts RCP or LCP into LCP or RCP at two frequencies. When VO2 is in metal state, it behaves as a reflective device, and achieves high efficiency CP wave chirality maintenance in a wide range. It has wide application prospects in the fields of wireless communication, imaging and detection, and opens a new way for designing new terahertz functional devices.
2. Structure design and method
The designed polarization converter based on DSMs is shown in Fig. 1. It consists of four parts: two lays of DSMs, a dielectric layer, a metal grating, and a VO2 board. The front and back strips are DSMs; with the direction tilted 45° relative to the x axis. There are two layers in the middle, which are metal grating and VO2 plate. The relative permittivity of copper can be described by the Drude model with the plasma frequency$\; \; {\omega _p} = 1.12 \times {10^{15}}\; rad/s$, the damping rate$\; \gamma = 1.38 \times {10^{13}}\; rad/s$. The dielectric layer filled in the middle is loss-free benzocyclobutene (BCB) with permittivity of 2.67. The optimized geometric parameters are$\; p = 30\mathrm{\mu}\textrm{m},\; \; {L_1} = 30\mathrm{\mu}\textrm{m},{\; \; }{L_2} = 3\mathrm{\mu}\textrm{m},{\; \; }{L_3} = 15\mathrm{\mu}\textrm{m},{\; }w = 2\mathrm{\mu}\textrm{m},{\; \; }g = 3\mathrm{\mu}\textrm{m},\; h = 0.2\mathrm{\mu}\textrm{m},{\; }t = 0.2\mathrm{\mu}\textrm{m},{\; }{t_m} = 2\mathrm{\mu}\textrm{m},{\; }{t_s} = 15\mathrm{\mu}\textrm{m}, {\; }d = 2\mathrm{\mu}\textrm{m}.{\; \; \; \; }$The frequency domain solver of the commercial simulation software CST Microwave Studio was used to simulate the polarization converter. The finite-difference-time-domain (FDTD) is adopted, the periodic boundary conditions are set in x- and y- directions, while the open boundary condition is set in z- direction. In the simulation, the dynamic conductivity of the DSMs can be written as [42]:
In the terahertz band, the Drude model is used to describe the frequency dependent complex permittivity of VO2 [46], it can be expressed as:
At the Cartesian coordinates of x-y-z, the incident EM wave propagates along the z-axis direction and the transmission coefficient is expressed as$\; {{\boldsymbol T}_{\boldsymbol{ij}}} = {\boldsymbol E}_i^t/{\boldsymbol E}_{\boldsymbol{j}}^{\boldsymbol i}$, where the subscripts$\; i\; $and$\; j\; $correspond to the polarization states of the transmitted and incident fields, respectively. And using the Jones matrix, the corresponding transmission coefficient matrix of LP wave is denoted as [31]:
AT is the novel phenomenon that occurs when EM waves pass through a medium in different directions [34]. In the polarization conversion MMs structure, the giant AT effect mainly comes from the combination of polarization conversion effect and Fabry-Perot-like cavity enhancement effect. In order to ensure the giant AT effect of the LP wave and the CP wave, the AT effect occurs only when$\; {t_{yx}} \ne {t_{xy}},{t_{xx}} = {t_{yy}},{t_{ -{+} }} \ne {t_{ +{-} }},{t_{ +{+} }} = {t_{ -{-} }}\; $are satisfied at the same time. The AT need to satisfy the equation [29]:
3. Results and discussions
3.1 Transmission circular polarization converter
Firstly, we verified the polarization conversion characteristics of the transmission CP converter when VO2 was used as the insulating dielectric layer. As shown in Fig. 2(a) and (b), we simulated the transmission coefficient when the CP wave is incident along the backward (-z) directions, and the Fermi level of DSMs is 90 meV. The co-polarization transmission coefficient t++=t--, and the minimum values are 0.13 and 0.15 at 1.92 THz and 3.46 THz, respectively. At 1.92 THz, the maximum amplitude of the cross-polarization transmission coefficient t-+ is 0.87, and the minimum value of t+- is 0.01. Figure 2(b) adds more information by showing the PCR, where$\; \textrm{PC}{\textrm{R}_ + } = {t_{ -{+} }}^2/({{t_{ +{+} }}^2 + {t_{ -{+} }}^2} )$,${\; PC}{\textrm{R}_ - } = {t_{ +{-} }}^2/({{t_{ -{-} }}^2 + {t_{ +{-} }}^2} )$. PCR+ reached 98%, which means that the incident RCP wave is almost completely converted to LCP wave. At 3.46 THz, the maximum value of the amplitude of t+- is 0.70, the amplitude of t-+ is only 0.06, and the PCR- is about 95%, which also indicates that the incident LCP is converted into an RCP wave. Therefore, this structure can realize efficient CP wave conversion.
Fig. 2. The co-polarization transmission coefficients t++, t-- and the cross-polarization transmission coefficients t+-, t-+ when CP waves illuminate in the backward (-z) directions.
In Fig. 3, we verify the AT function of the transmission device. It can be seen in Fig. 3(a) that the total transmission coefficient t+ of RCP waves propagating in the + z and -z directions is significantly different, where$\; {t_ + } = {|{{t_{ +{+} }}} |^2} + {|{{t_{ -{+} }}} |^2}$. At 1.92 THz, the amplitude of t+ along the -z direction reaches 0.79, and decreases to 0.01 in the + z direction. At 3.46 THz, the value of t+ in the -z direction decreases to 0.03, while the value of t+ in the + z direction increases to 0.54 which indicates that a great diode-like effect is realized when RCP wave illuminates. As shown in Fig. 3(b), the$\; \Delta _{cir}^ + \; $is 0.75,$\; \Delta _{cir}^ - \; $is -0.75 at 1.92 THz, and at 3.46 THz,$\; \Delta _{cir}^ + \; $and$\; \Delta _{cir}^ - \; $are -0.49 and 0.49, respectively. This is due to the symmetry of the structure, so that the two transmitted CP waves have the same characteristics. In addition, the AT of the LP wave is always 0, which suggests that this structure suppresses the asymmetric power transmission of the LP wave.
Fig. 3. (a) Total transmittance t+ of RCP waves propagating in the forward (+z) and backward (-z) directions, (b) AT of linear polarization waves and CP waves.
In addition, we studied the influence of other parameters of the polarization converter on CP wave conversion. As shown in Figs. 4(a) and 4(b), as the width w of the DSMs strips increase from 1µm to 4µm, PCR+ and AT$\; \Delta _{cir}^ + \; $and$\; \Delta _{cir}^ - \; $decreased slightly in the low-frequency region. In the high-frequency region, with increasing w, the resonance frequencies are blue-shifted, the amplitude of PCR- and AT reaches maximum value at w=2 µm. In Figs. 4(c) and 4(d), PCR+,$\; \Delta _{cir\; }^ + $and$\; \Delta _{cir}^ - \; $do not change at 1.92 THz when tm gradually increases, while in the high-frequency region, the PCR- and AT shift to the blue side, and the amplitude of PCR- reaches the maximum value 0.99 at tm = 4µm. It can be seen from Figs. 4(e) and 4(f) that when the thickness of the dielectric is increased from 5µm to 20µm, PCR+,$\; \Delta _{cir}^ + \; $and$\; \Delta _{cir}^ - \; $ in the low frequency region are significantly red shift and the amplitude increases, which reaches maximum when ts = 10µm. The amplitude increases when the thickness increases in the high frequency region. Therefore, changing these physical parameters can effectively adjust the PCR and AT.
Fig. 4. Polarization conversion ratio PCR+, PCR- and AT $\Delta _{cir}^ + $ and $\Delta _{cir}^ - $ under different physical parameters.
Then, we considered the case of oblique incidence. From Figs. 5(a) and 5(b), we can clearly see that when the incident angle θ increases from 0° to 50°, PCR+ and PCR- have the similar changes for both TE and TM waves, there was a slight blue shift and the amplitude of PCR+ increases slightly in the low-frequency region. As shown in Fig. 5(a), the bandwidth of the low-frequency region increases and the amplitude of the high-frequency region decreases with the increasing incident angle θ. As shown in Fig. 5(b), the amplitude of PCR- at high frequency decreases gradually. Therefore, the proposed structure maintains good polarization conversion characteristics for incident angle θ from 0° to 50°.
Fig. 5. The polarization conversion ratio PCR+ and PCR- at different incident angles. (a) TE waves and (b) TM waves.
We investigated the transmission coefficients at different Fermi levels of DSMs, as shown in Fig. 6(a). It can be seen that the co-polarization coefficients t++ and t-- are almost equivalent, the cross-polarization coefficients t+- and t-+ have obvious difference with the increase of Fermi level. This suggests that the polarization conversion of RCP to LCP and LCP to RCP is achieved at 1.92 THz and 3.46 THz, respectively. As shown in Figs. 6(b) and 6(c), we have given the cross-polarization coefficients t+- and t-+ as functions of the Fermi level in order to clearly observe the tunability. When the Fermi level increases from 50 meV to 110 meV, t+- and t-+ both show blue shifts around 1.92 THz and 3.46 THz.
Fig. 6. (a) Transmission coefficient with difference Fermi level of DSMs. Cross-polarization transmission coefficient for (b) t+- and (c) t-+ as functions of Fermi level.
In order to better understand the physical mechanism of CP wave polarization conversion, we simulated the electric field distribution at 1.92 THz and 3.46 THz. As shown in Fig. 7, the DSMs strips of the first layer can be regarded as A, the metal grating as B, and the DSMs strips of the bottom layer as C. For the double-layer structure AB, A is responsible for the polarization conversion including transmission and reflection, and B has the perfect ability to select LP, that is, the electric field with polarization direction perpendicular to the grating is completely transmitted, while the electric field with polarization direction parallel to the grating is completely reflected. Therefore, A and B can be used as mirrors and constitute a Fabry-Perot cavity. From Fig. 7(a), CP wave is converted to y- polarized wave after passing through AB, and all others are reflected, since AB and BC are mirror-symmetrical, the y-polarized wave is eventually converted to LCP. As shown in Figs. 7(b) and 7(d), the resonant cavity formed by AB and BC is symmetrical, which shows that the electric field distribution of the two resonant cavities have the same characteristics. The CP wave undergoes a conversion, and the principal axis is the elliptical polarization (EP) transformation in the x and y directions. Then, the EP wave passes through B, the y component in EP wave will be transmitted, and the x component in EP wave will be reflected. Similarly, B and C form a reverse cavity, responsible for the conversion of LP wave to CP wave. After multiple reflections and conversions, an efficient CP waves cross-polarization conversion occurs.
Fig. 7. The electric field distribution at (a) 1.92 THz and (b) 3.46 THz, (b) and (d) Physical mechanism of CP conversion.
3.2 Circular polarization maintaining reflector
When the conductivity of VO2 is$\; \sigma = 3 \times {10^5}\; S/m$, VO2 behaves like a conductive metal, completely reflects EM waves, and constitutes a CP maintaining reflector. Figure 8(a) suggests the co-polarization and cross-polarization reflection coefficients of CP waves at 1-4 THz. It can be seen that the co-polarized reflection coefficients r++ and r-- exceed 0.78 and the maximum value can reach 0.93 in the range from 2 to 3.55 THz, and the cross-polarization reflection coefficients r-+ and r+- are suppressed below 0.3, with a minimum value of 0.15. That is to say, the reflection wave and the incident wave have the same chirality, and the chirality of the CP waves in the broadband range can be maintained.
Next, to study the efficiency and characteristics of polarization maintenance, we simulated and calculated the PMR [57] of the structure, according to${\; PM}{\textrm{R}_ + } = {r_{ +{+} }}^2/({{r_{ +{+} }}^2 + {r_{ -{+} }}^2} )$,$\; \textrm{PM}{\textrm{R}_ - } = {r_{ -{-} }}^2/({{r_{ -{-} }}^2 + {r_{ +{-} }}^2} )$, respectively. As shown in Fig. 8(b), both PMR+ and PMR- simulation results are greater than 88% in the range of 2 THz to 3.55 THz. These results verify that the designed structure can maintain the chirality of LCP or RCP waves well.
We also verified the effect of dielectric layer thickness ts on PMR. As can be seen from Figs. 9(a) and 9(b), the amplitude fluctuates around 0.95 as the ts increases from 11 µm to 15 µm and reaches the minimum value 0.6 when ts = 17 µm. The operating frequency has a blue shift of about 0.3 THz, which means that it has the ability to be tuned by thickness.
Fig. 9. The polarization maintaining ratio of (a) RCP wave and (b) LCP wave at different dielectric thickness ts.
Later, we investigated the effect of the incident angle θ on PMR, as shown in Figs. 10(a) and 10(b). When θ is gradually increased from 0° to 60°, the bandwidth of PMR is gradually narrowed, but the magnitude is still greater than 88% in the range from 2 THz to 3.55 THz. Therefore, both PMR- and PMR+ have good polarization maintaining performance at 0° to 60°.
As shown in Fig. 11, we simulated the reflection coefficients and PMR at different Fermi levels of DSMs to verify the tunability for the polarization maintaining reflector. It can be seen that the transmission coefficients show a blue shift and increase in amplitude as the Fermi level increases from 50 meV to 110 meV in Figs. 11(a) and 11(b). When the Fermi level is greater than 70 meV, the amplitudes of r++ and r-- are stable above 0.8. As shown in Figs. 11(c) and 11(d), PMR+ and PMR- gradually decrease, and the resonance bandwidth increases as the Fermi level increases. From the above results, it can be concluded that changing the Fermi level can achieve dynamic tuning of the operating frequency.
Fig. 11. Transmission coefficients for incident (a) RCP wave, (b) LCP wave, and (c) PMR+, (d) PMR- at different Fermi level
Later, we verify the CP wave maintenance mechanism by decomposing the incident and reflected CP waves into x and y polarization waves. The electric fields of the incident waves of x polarization wave and y polarization wave are${\;\boldsymbol{ E}}_{\boldsymbol{x}}^{\boldsymbol i}\; $and$\; {\boldsymbol E}_{\boldsymbol{y}}^{\boldsymbol i}$, respectively, and the electric field of the reflected waves are expressed by${\;\boldsymbol{E}}_x^r\; $and$\; {\boldsymbol E}_y^r$. Expressed as the following matrix [57]:
As can be seen from Fig. 12(a), in the range of 2 THz to 3.55 THz, the cross-polarization reflection coefficients$\; {r_{xy}}\; $and$\; {r_{yx}}\; $are greater than 0.8, and the co-polarization reflection coefficients$\; {r_{xx}}\; $and$\; {r_{yy}}\; $are below 0.3, which indicates that the LP waves occur a cross polarization conversion. Figure 12(b) suggests the amplitude ratio and phase difference of$\; {r_{yx}}\; $and$\; {r_{xy}}$, from which we can see that$\; {r_{yx}}/{r_{xy}} = 1$,${\; }{\varphi _{xy}} - {\varphi _{yx}} = 0$. Therefore, it is proved that the corresponding CP reflection can be obtained with the incident CP waves in the range from 2 THz to 3.55 THz.
Fig. 12. (a) Co-polarization and cross-polarization reflection coefficients when x-polarization and y-polarization waves are incident, (b) reflectance ratio and phase difference of cross-polarization coefficients.
4. Conclusions
In this paper, we have successfully proposed a structure that utilizes the phase transition characteristics of VO2 to achieve both transmission and reflection functions in a device. As a transmission CP converter, using a cascaded Fabry-Perot resonator, high-efficiency dual-band CP wave conversion and AT effect can be achieved in the terahertz band. At 1.92 THz and 3.46 THz, the cross-polarization transmission coefficients are 0.86 and 0.69,$\; \Delta _{cir}^ + \; $and$\; \Delta _{cir}^ - \; $are 0.74 and 0.47, respectively. We also studied the effects of other physical parameters and oblique incidence on polarization conversion. The results show that the polarization conversion effect is better when the incidence angle is in the range of 0°-50°. In the case of reflective devices, the chirality of the incident CP wave can be well maintained in the broadband range from 2 THz to 3.55 THz, with PMR more than 88%. For both transmission CP converter and CP maintaining reflector, the Fermi level of DSM can be changed to achieve dynamic tuning of the polarization conversion frequency band. Therefore, the designed MMs structure has a good inspiration for the study of multifunctional polarization converter in the terahertz band.
Funding
National Natural Science Foundation of China (61775123, 61875106); Key Research and Development Program of Shandong Province (2019GGX104039, 2019GGX104053); National Key Research and Development Program of China (2017YFA0701000).
Disclosures
The authors declare no conflicts of interest.
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