1. Introduction

Polarization is the most fundamental and important characteristic of electromagnetic (EM) waves or lights. It is highly desirable to have full control of polarization states due to its practical applications in imaging, communication, sensing, etc [1]. Traditionally, the method to manipulate and control the polarization state is based on gratings, birefringent materials, and liquid crystals [2–5]. They usually had intrinsic defects: such as bulkiness, less efficiency, and narrow bandwidth, thus seriously restricting their practical applications, especially in terahertz (THz) region. These traditional methods are different to meet the requirements of integration and miniaturization of current optoelectronic system. Therefore, developing the new devices for THz polarization controlling is in an urgent need for many practical applications.

Recently, the metamaterial (MM) as artificial sub-wavelength periodic composite material/structure has provided new approaches for flexible polarization manipulation of the THz waves [6–9]. MMs have some advantages for controlling THz polarization compared with traditional methods in size, efficiency, and bandwidth. Therefore, much efforts have been devoted to using the MMs concept for designs of the polarization manipulation devices [10–18]. For a variety of THz applications, a tremendous amount of novel polarization manipulation devices, such polarization rotators and convertors based on anisotropic or chiral MMs (AMMs and CMMs) has been proposed both in transmission and reflection modes [6–9,16–21]. CMMs have been attracted great interest since they can realize not only polarization conversion but also asymmetric transmission (AT) effect due to its enhanced chirality and time-reverse symmetry breaking [14–17]. It is important that CMMs with polarization conversion and AT effect could be utilized as circulators or isolators for integrated photonic circuits or all-optical processing photonic devices [22–24]. Although these devices exhibit high polarization manipulation efficiency and large bandwidth, they lack efficient tunability once designs are finished, which limits their suitability for practical applications. One effective way to overcome this limitation is to use tunable MMs by hybridizing special materials, such as graphene, vanadium dioxide (VO₂) and photoconductive silicon [24–36]. These tunable composite MMs are capable of dynamically manipulating polarization states of THz waves with great flexibility by external stimulus, such as electric voltage [24–28], thermal [29–31], and photo-excitation [32–34], which open a bright perspective to design tunable polarization manipulation devices. However, to the authors’ best knowledge; there is still a lack of an efficient design of CMMs for the tunable polarization conversion and AT effect simultaneously in THz region. Hence, there is still a need to design high performance CMMs for tunable polarization conversion and AT effect simultaneously. Among the various tunable methods, photo-excitation control based on photoconductive silicon is one of the relative simple ways in practical operations. The conductivity of photoconductive silicon can be tunable dynamically by changing the pump optical power [33–37].

In this work, we propose a photo-excited complementary chiral metamaterial (CCMM), which can realize a broadband switchable linear polarization conversion and asymmetric transmission (AT) effect simultaneously in THz region. The CCMM is based on complementary cut-wire (CCW) structure integrated with photoconductive silicon (Si). The polarization conversion ratio (PCR) and AT parameter of the CCMM can be tunable continuously through photo-excited carrier injection by changing the pump optical power. In addition, electric field and surface current distributions are plotted to explain the physics mechanism of switchable polarization conversion and (AT) effect.

2. Unit -cell design and simulation

 Figure 1 shows the design schematics of the photo-excited switchable CCMM, which consists of a bi-layer twisted CCW structure integrated with semiconductor photoconductive silicon (Si). As shown in Fig. 1(a), the top resonator is composed of a CCW structure with photoconductive Si inserted in the slit of the metallic film. It is well known that the arbitrary metallic structures on the front and back layers are equivalent, and the back layer is rotated by 90° so that the symmetry of the chiral structure in the wave propagation direction is broken [14,15]. As shown in Fig. 1(c), the slit orientation back CCW is rotated by 90° respect to the front one along the wave propagation direction, which can exhibit giant AT effect due to the strong EM cross coupling generated in the composite structure. The incident wave enables strong coupling to the structure when the electric field is perpendicular to the slit orientation of the CCW structure, whereas it does not couple much when the one is parallel to the slit. Hence, the careful selection of CCW structure with 90° to each other which enhances the AT for linear polarization waves. In addition, since the unit-cell structure CCMM has no line of mirror symmetry, thus enabling the high efficiency polarization conversion. The optimized parameters of unit-cell structure are as follows: p_x= p_x= 120 µm, l = 100 µm, w = 22 µm, α = 80°, t_m= 0.2 µm, t_s= 10 µm.

 

Fig. 1. Design schemes of the proposed compound CCMM: (a-c) the front, back and perspective views of the unit-cell structure, (d) three-dimensional (3D) array structure.

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To realize the switchable polarization conversion and AT effect, the rectangular photoconductive Si (grey part) strip with dimension of 22×100×0.2 µm³ is inserted in the slit of the CCW structure. The filled photoconductive Si is simulated as a dielectric with permittivity of ɛ_Si=11.7, while the conductivity σ_Si is dependent on external pump optical power [37–40]. As shown in Fig. 1(d), when pump beam is incident on the surface of the CCMM slab, the conductivity of the Si will be changed with the generation of the excess photo-carrier density [37,38]. As long as pump optical power exceeds the band gap energy of the Si, an excess photo-carrier density will be generated, and the corresponding conductivity will be changed. The photo-excited carrier density is proportional to the optical pump power [38]. It should be noticed that the entire area of the CCMM array is all covered by the pump optical illumination. The conductivity of the Si will be tunable dynamically with the change of pump optical power [37–40]. To optically excite charge carriers of the Si, the near-infrared laser pulse with different power is used as an optical pump source in practices [33,38]. Under the upper power limit of infrared laser illumination, the (σ_Si) conductivity of the Si is about 1×10⁵ S/m, while the one is about 1 S/m without illumination [37,38]. With application of external pump infrared laser illumination, the designed CCMM can form a tunable resonating structure, and the resonance strength could be changed actively. In simulation, the benzocyclobutene (BCB) with relative dielectric constant of 2.67 and thickness of 10 µm was selected as middle dielectric layer, and the copper film with an electric conductivity σ = 5.8×10⁷ S/m and thickness of 0.2 µm was selected as metallic structure layers [17].

To study its efficiency of the proposed CCMM, we performed a full wave simulation based on the standard finite integration technology (FIT) by using the frequency domain solver of CST Microwave Studio. The periodic boundary conditions were applied in x-axis and y-axis direction of the unit-cell structure while the open boundary condition was set in z-axis direction. Simulation can generate complex transmission coefficients from which the PCR and AT parameter are calculated. The dimensions of the CCMM unit-cell structure are optimized to give the broadband maximum polarization conversion efficiency and AT parameter without infrared laser illumination. The transmission coefficients of the designed CCMM can be defined in terms of the complex amplitude of the electric field of the transmitted and incident waves:$\ {t_{xx}} = \ |E_x^t|/|E_x^i|$,$\ {t_{yx}} = \ |E_y^t|/|E_x^i|$, ${t_{xy}} = \ |E_x^t|/|E_y^i|$, and $\ {t_{yy}} = \ |E_y^t|/|E_y^i|$. The superscripts i and t denote the incident and transmitted THz waves, and the subscripts x and y indicate the polarization directions of plane waves, respectively. To measure the polarization conversion performance of the proposed CCMM, we define the polarization conversion ratio (PCR) as [41]: PCR_x= |t_yx|²/ (|t_yx|²+|t_xx|²+|r_yx|²+|r_xx|²) and PCR_y= |t_xy|²/ (|t_xy|²+|t_yy|²+|r_xy|²+|r_yy|²) for normal incident THz wave with x-pol. and y-pol., respectively. To guarantee linear polarization conversion and giant AT effect, the one transmission (t_xy or t_yx) of the two off-diagonal (cross-polarization) components should be enhanced and all the others (t_yx or t_xy, t_xx, t_yy) should be suppressed significantly. In addition, the cross-polarization transmission coefficients ($t_{yx}^{f(b)}$ and $t_{xy}^{f(b)}$) are different when propagation direction is opposite, which should be satisfied as [17]: $\Delta _x^{f(b)} = \textrm{|}t_{yx}^{f(b)}{|^2} - |t_{xy}^{f(b)}{|^2} = - \Delta _y^{f(b)} \ne 0$.

3. Results and discussions

Firstly, we study the polarization conversion properties and AT effect of the proposed CCMM without infrared laser illumination. As shown in Fig. 2, we present the transmission coefficients ($t_{xx}^{f(b)}$, $t_{yx}^{f(b)}$, $t_{xy}^{f(b)}$ and $t_{yy}^{f(b)}$) of the CCMM without and with Si (σ_si= 1 S/m without optical pump) for normal incident waves propagation along backward (–z) direction forward (+z) direction, respectively. It can be seen that the transmission coefficients curves of the proposed structure with Si without optical pump are near the same ones without Si. As shown in Figs. 2(a,c), it can be seen that the two co-polarization transmission coefficients ($t_{yy}^b$ and $t_{xx}^b$) are equivalent and both of them less than 0.12 across the whole frequency range of 0.5-1.1 THz for both incident y- and x-polarization wave propagation along the –z axis direction. Nevertheless, the two cross-polarization transmission coefficients ($t_{xy}^b$ and $t_{yx}^b$) are significant different.

 

Fig. 2. Simulated transmission coefficients ($t_{xx}^{f(b)}$, $t_{yx}^{f(b)}$, $t_{xy}^{f(b)}$ and $t_{yy}^{f(b)}$) of the CCMM (a,b) without Si and (c,d) with Si (σ_si= 1 S/m without pump infrared laser illumination) for (a,c) backward (–z) direction (b,d) forward (+z) direction propagation.

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The magnitude of $t_{xy}^b$ is near zero across the whole frequency range while the one of $t_{yx}^b$ is over 0.9 in the frequency range of 0.68-0.8 THz for the normal incident wave propagating along the backward (-z) direction. In addition, at 0.7 THz and 0.78 THz, the magnitude of $t_{yx}^b$ are up to maximal values of 0.93 and 0.94, respectively. Figs. 2(b,d) present the transmission spectra for the forward (+z) propagating waves. When the propagation direction is reversed, the $t_{xy}^f$ and $t_{yx}^b$ interchange with each other, while the $t_{xx}^b$ $t_{yy}^b$, $t_{xx}^f$ and $t_{yy}^f$ are the same. It indicates that the proposed CCMM can realize a high-efficient cross-polarization conversion for the incident x(y)-polarization waves propagation along –z (+z) axis direction as well as AT effect. Thus, it can be expected that the proposed CCMM can be functioned as a transparent broadband selective cross-polarization convertor. This distinct cross-polarization conversion for the reversed propagation directions via AT effect are mainly attributed to the special structure of the CCMM.

To study the cross-polarization conversion efficiency and AT effect of the proposed CCMM without infrared laser illumination, as shown in Figs. 3(a,b), we calculated PCR_x(y) of the normal incident x(y)-polarization wave propagation along the backward (-z) direction and AT parameters of both circular and linear polarization wave. From Fig. 3(a), it can be seen that the PCR_x for the incident x-polarization wave is more than 90% in the frequency range of 0.69-0.82 THz, while the PCR_y is near zero across the whole frequency range for the incident y-polarization wave. As shown in Fig. 3(b), for the normal incident linear polarization wave, the absolute values of $\Delta _{lin}^x$ and $\Delta _{lin}^y$ are exactly equal and both of them are greater than 0.8 in a broadband frequency range of 0.69-0.82 THz. In addition, it can be observed that the AT parameters ($\Delta _{cir}^{-}$ and $\Delta _{cir}^ +$) for circular polarization are close to zero across the whole frequency range. Thus, the proposed CCMM can only realize the giant AT effect for the linear polarization waves, but not for the circular polarizations.

 

Fig. 3. PCR_x(y) of the normal incident x(y)-polarization wave propagation along the backward (-z) direction, (b) AT parameters for both circular and linear polarization waves.

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The physical mechanism of polarization conversion and AT effect of the proposed CCMM without infrared laser illumination can be visualized with the electric field distributions within the structure for the normal incident x- and y-polarization incidences. Figure 4 presents the visualized evolution process of electric fields in the x-z plane of the middle of unit-cell structure including incoming and outgoing waves regimes at f₁= 0.69 THz and f₂= 0.77 THz, respectively.

 

Fig. 4. Simulated electric field distributions of the CCMM unit-cell structure in the x-z plane in case of the incident (a,e) x-polarized and (b,f) y-polarized wave propagation along backward (-z) direction, and (c,g) y-polarized and (d,h) x-polarized wave propagation along forward (+z) direction at different resonance frequencies: (a-d) f₁= 0.69 THz, (e-h) f₂= 0.77 THz.

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As shown in Figs. 4(a,e) and (c,g), at 0.69 THz and 0.77 THz, when normal incident waves are propagating along -z and + z axis directions, electric fields of the incoming waves are along the + x and + y axis directions, the ones of outgoing waves are along the -y(+y) axis and -x(+x) axis directions, respectively. These results indicate that the normal incident x(y)-polarization wave propagation along -z and + z axis directions from the front and back CCMM structure can excite the guided resonant modes and are finally perfectly converted to the y(x)-polarizations at 0.69 THz and 0.77 THz, respectively. In other words, the polarization on the input port surface is fully converted into its orthogonally polarization on the output port (see Figs. 4(a,e) and (c,g), the electrical field in the xoz-plane). In addition, it also can be observed that the transmitted waves of cross-polarization have almost the same magnitude as the incident waves, thus the proposed structure can achieve an almost perfect cross-polarization conversion. While as shown in Figs. 4(b,f) and (d,h), the incident y(x)-polarization waves propagation along backward (-z) and forward (+z) directions are suppressed extremely at the entrances of outgoing waves regimes at above resonance frequencies, resulting in a very low transmission. These results further reveal that only the x(y)-polarization waves can be selected to pass through the CCMM and finally converted to the transmitted y(x)-polarization waves when the waves are propagating along the –z (+z) axis directions direction, while y(x)-polarization waves are inhibited by the structure. Essentially, all the field patterns will be twisted inside the unit-cell structure as a consequence of cross coupling effect of electric and magnetic fields at resonance frequencies [15]. The field distributions further indicate that the excitations of local resonant modes and cross coupling among the bi-layer asymmetric structure are crucial to the broadband cross-polarization conversion and giant AT effect [41]. These electric field distributions pictures are excellent consistent with the transmission coefficients as shown in Figs. 2. These features of electric field distributions of CCMM are also further confirmed that the CCMM can be functioned as a selective cross-polarization convertor.

In the next section, we study the switchable polarization conversion and AT effect of the CCMM will different pump power of infrared laser illumination. Obviously, the conductivity of the integrated photoconductive Si of the CCMM will be changed dynamically with the different pump power of infrared laser illumination. The conductivity of photoconductive Si is 1 S/m without infrared laser illumination. In this case, photoconductive Si is in the insulating state, and the corresponding energy flux of the pump infrared laser is 0 µJ/cm². The photoconductive Si will become metallic state with conductivity of 10⁵ S/m when the energy flux of the pump infrared laser is increased to 294.6 µJ/cm² [37,39]. Figs. 5(a,b) show the simulated cross-polarization transmission coefficients ($t_{yx}^f$ and $t_{xy}^b$) of the designed CCMM with different conductivity of the Si for the wave propagation along the –z and + z axis direction, respectively. It is clearly that the magnitudes of both $t_{yx}^f$ and $t_{xy}^b$ are decreased gradually with the increase of the conductivity of the Si as shown in Figs. 5(a,b). When using the lower pump power with the Si conductivity of σ_si = 1×10² S/m, the Si is in the insulator state, almost all of the incident THz waves can go through the slit of the CCW structure of the CCMM. It means that the cross-polarization conversion is nearly unaffected when conductivity of the Si is relative lower (<1×10² S/m). When the Si is in the metal state with σ_si = 1×10⁵ S/m for the upper power limit, the magnitudes of both $t_{yx}^f$ and $t_{xy}^b$ are decreased to near zero (<0.1), revealing that almost all of the incident THz waves are reflected directly by the CCMM.

 

Fig. 5. The (a) simulation and (b) calculation cross-polarization transmission coefficients (r_yx) of the proposed polarization convertor for different Si conductivity (σ_si) under normal incident x-pol. wave.

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It can be more intuitively that both the PCR_x and AT parameter will change greatly with the various pump power of infrared laser illumination. As shown in Figs. 6(a,b), similarly to the changes of the cross-polarization transmission, the magnitudes of both the PCR and AT parameter are decreased continuously with the increase of the Si conductivity. When using the lower power of pump infrared laser with σ_si = 1×10² S/m, the normal incident wave can be converted to its orthogonal polarization in a broadband frequency range after transmission by the CCMM. In other words, for the lower pump power (in this case, σ_si < 1×10² S/m), the CCMM makes the x(y)-pol. to y(x)-pol. conversion and AT effect for wave propagation along –z (+z) axis direction into the “on” state. When increasing the pump power of infrared laser illumination (>>1×10² S/m), the integrated Si will experience a change in electrical conductivity. When the Si is in the metal state with σ_si = 1×10⁵ S/m for the upper limit power, the magnitudes of both the PCR and AT parameter are decreased to near zero across the whole frequency range, revealing that the cross-polarization conversion and AT effect disappear. It is because that the photo-excited charge-carriers in the slit of the CCW structure will increase when increasing the pump power of infrared laser illumination, which will make the sandwiched structure resonance weaker [35,37,39]. In this case (σ_si = 1×10⁵ S/m), the surface of the CCMM will become continuous copper film approximately, which will inhibit the normal incident THz wave to pass. In other words, for the upper limit power of pump infrared laser (σ_si = 1×10⁵ S/m), the CCMM makes the x(y)-pol. to y(x)-pol. conversion and AT effect into the “off” state. Thus, the state-transition process of the Si is accompanied by remarkable changes in various conductivities with the different pump power of infrared laser illumination [35]. The different state resonators are resulted from the various states of the Si. The obvious changes of the PCR_x and AT parameter of the CCMM are mainly from the different state resonators. Therefore, the CCMM embedded with Si can alternatively realize an optical switching effect of the polarization conversion and AT effect. It should be noticed that the geometric parameter of the unit-cell structure will also affect the polarization conversion and AT effect of the proposed CCMM (not shown). However, the polarization conversion and AT effect is not easily to adjust once the fabrication of the proposed CCMM is finished.

 

Fig. 6. (a) The PCR_x and (b) AT parameter of the proposed CCMM for different conductivity (σ_si) of the Si.

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To better understand the physical mechanism of the CCMM for switchable polarization conversion and AT effect, we study the surface current distributions of the front and back layer of the unit-cell structure at 0.72 THz with the different Si conductivity, as shown in Fig. 7. Under the lower pump power with σ_si = 1×10² S/m, as shown in Figs. 7(a1,a2), when the x-polarization wave is incident on CCMM, both parallel and anti-parallel induced surface currents are distributed on the unit-cell structure. These induced surface currents can contribute to the weaker magnetic and electric resonances, which resemble the cross-coupling of a pair of magnetic as well as electric dipoles [32–46]. The strong cross-coupling between electric and magnetic fields will lead to the enhanced chirality of the proposed CCMM, which are crucial for cross-polarization in transmission. Figs. 7(b1,b2) and 7(c1,c2) show the surface current distributions of the front and back layer when the σ_si = 1×10³ S/m and 5×10³ S/m. It can be observed that the induced surface current distributions are simirlar to the case of the σ_si = 1×10² S/m, but the current strength of the back layer is relative weak, revealing that the strong magnetic response intensity will decrease gradually with the increase of the pump power. Thus, the corresponding cross-polarization conversion efficiency and AT effect will decrease gradually.

 

Fig. 7. The surface current distributions of the (a1-d1) front and (a2-d2) back layer of the proposed CCMM for different Si conductivity (σ_si) under normal incident x-pol. wave at 0.72 THz: (a1,a2) σ_si= 1×10² S/m, (b1,b2) σ_si= 1×10³ S/m, (c1,c2) σ_si= 5×10³ S/m, and (d1,d2) σ_si= 1×10⁵ S/m. The solid arrows indicate flow direction of the surface currents

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As shown in Figs. 7(d1,d2), when the conductivity of the Si is up to 1×10⁵ S/m with the upper limited pump power, the surface current flow of the front layer is parallel to the ones of back layer and is along the y-asix direction. Obviously, in this case (σ_si= 1×10⁵ S/m), these induced surface currents only contributes to electric dipole resonances, and the chirality of the CCMM disappears accordingly. Essentially, the Si is in the metal state with the upper limit power (σ_si= 1×10⁵ S/m), and the incident THz waves nearly can’t be passed through the CCMM. Thus, the cross-polarization conversion and the AT effect can’t be realized when the Si is in the infrared laser illumination with upper limited pump power. This CCMM provides an alternative platform to promote the development of the THz polarization controlers and modulators.

4. Conclusions

In conclusion, we have demonstrated numerically a photo-excited switchable broadband cross-polarization conversion and AT effect based on the CCW structure embedded with photoconductive Si at THz region. The conductivity of the Si filled in the slit of the CCW structure can be adjusted dynamically by external optical excitation, resulting in changes of cross-polarization conversion efficiency and AT effect. When the Si is at insulating state (σ_si < 1×10² S/m) with the relative lower pump power of infrared laser illumination, the normal incident x(y)-polarization wave propagation along the -z (+z) axis direction pass through the CCMM can be converted into the y(x)-polarization wave, and the PCR is over 90% and AT parameter is over 0.8 in the frequency range of 0.69-0.82 THz. The broadband PCR and AT parameter can be adjusted dynamically with the change of Si conductivity by changing the pump power. When the Si is at metallic state (σ_si= 1×10⁵ S/m) with the upper limited pump power, the normal incident linear polarization wave (x-pol. and y-pol.) propagation along the -z (+z) axis direction is reflected directly by the CCMM, and the PCR and AT parameter is near zero across the whole frequency range. Our designs may provide a large degree of dynamical polarization manipulation of THz waves over a broadband range, and also find potential application in THz imaging or communication systems.