1. Introduction

Metamaterial has attracted increasing interests in the past decade due to its fantastic electromagnetic response and various applications, such as negative refraction, sub-diffraction imaging, and invisibility cloaks [1–3]. Metamaterial with strong symmetry breaking can exhibit the propagation direction-dependent polarization selectivity, known as asymmetric transmission, for both circular and linear polarizations [4–6]. Plenty of polarization devices with asymmetric structure have been investigated, such as polarization rotators [7, 8], polarization spectrum filters [9, 10] and circular polarizers [11–13]. Optical circular polarizers find their wide use in a variety of applications like displays, optical communication, photography, sensors and spectroscopy [14, 15]. A perfect circular polarizer should transmit one state of the circularly polarized light (CPL) and completely block the other CPL state. To date, most circular polarizers based on chiral metamaterial are composed of metallic components for the advantages of subwavelength thickness and scalability [16–20]. This will, however, inevitably suffer from strong Ohmic loss and the absence of magnetic response. The intrinsic absorptive loss leads to low transmission efficiency and poor polarization suppression ratio (PSR), which is defined as the ratio of the transmitted light intensity of one state of the CPL to the other state of the CPL. On the other hand, for metallic inclusions, in order to achieve strong magnetic response, one has to break the geometric symmetry or add a substrate layer, which takes price of more complex constructions [21].

All-dielectric materials capable of achieving electric and magnetic dipole resonances naturally become good candidates to construct circular polarizers, which also feature the advantages of high temperature resistance and damage threshold [22]. However, only a few all-dielectric circular polarizers are reported till now and most of them are constructed with complex three-dimensional structures, such as helical structure [23] and bulky grating structure [24]. These complex structures are difficult to fabricate and integrate with other optical devices, precluding further practical application.

In this paper, we demonstrate an all-dielectric circular polarizer with high-efficiency and broadband transmission in the near-infrared frequency range by leveraging the recently developed Huygens surface. In the rotationally twisted strips array, the chiral effect from the asymmetric construction and the spectral overlapping of tensorial electric and magnetic resonances in each layer lead to a high-efficiency circular polarization selectivity over two broad spectral bands. Specifically, the proposed circular polarizer shows high polarization transmission ($T_{-\max }=0.97$) and high polarization suppression ratio ($PS{R}_{\max }=911:1$), which shows a great advantage compared with previously reported circular polarizers. Furthermore, our all-dielectric metamaterial inherently with electric and magnetic resonances extremely simplifies the basic unit structure, and extends the concept of Huygens surface to shorter wavelength ranges.

2. Design and simulations

To get a high-efficiency all-dielectric circular polarizer, we design a periodic array by cascading two tensor Huygens surfaces. Recently, a rigorous formulation of Huygens’ principle is applied to design reflectionless surfaces. These reflectionless surfaces, referred to as metamaterial Huygens surface, are realized with two-dimensional arrays of polarizable particles that provide both electric and magnetic polarization currents to generate prescribed wave fronts [25–30]. These electric and magnetic polarization currents are described by parameters of electric and magnetic impedances (or electric and magnetic polarizabilities). Since electromagnetic fields are vectorial at the surface, the impedances (or polarizabilities) are tensorial capable of decomposing these fields into TE and TM waves at the surface [26, 30]. More intuitively, tensor Huygens surface consists of two groups of electric and magnetic dipoles, which are induced by TE and TM fields respectively and described by tensorial electric and magnetic impedances (or electric and magnetic polarizabilities).

A scalar Huygens surface, as a special case of tensor Huygens surface, has realized high transmission [31], so one can imagine that tensor Huygens surface has more freedom to control the transmission. The transmission coefficients of the x- and y-polarized incident light ($t_x$ and $t_y$) are related to the electric and magnetic surface polarizabilities [32],

Figure 1(a) illustrates the design methodology of the proposed circular polarizer. Incident CPL can be decomposed into two perpendicular components along x and y directions respectively. Each component will excite corresponding electric and magnetic dipole resonances in the same spectral position by adjusting geometric parameters and the resonances will superimpose together without cross coupling. The fields scattered by orthogonal electric and magnetic dipole resonances will be a sum of TE and TM fields and can be homogenized by effective tensorial electric and magnetic impedances. Figure 1(b) is the top view of a unit cell and the period of the structure is 1100 nm in both x and y directions. The thicknesses of the two strips are 1000 nm and 400 nm respectively and the space between two layers is 500 nm. Figure 1(c) shows the scheme of the metamaterial consisting of periodic array with two-layer rotationally twisted strips. The all-dielectric device is excited by CPL propagating in the direction of -z. The refractive index of silicon strips is 3.5 in the near-infrared range [33], while the surrounding media is assumed to be air (n = 1).

 

Fig. 1 (a) The design methodology of the proposed circular polarizer. The circles represent the magnetic dipole resonances and the arrows represent the electric dipole resonances. These resonances are excited by the incident waves polarized along x- and y- direction. $\beta$ is the angle between the strips on the second layer and the positive direction of y axis, which means the angle between the two layers. (b) The top view of a unit cell and the geometric parameters are chosen as w1 = 200 nm, l1 = 400 nm, w2 = 200 nm, l2 = 800 nm and period = 1100 nm. (c) The 3-D scheme of the proposed circular polarizer with two twisted silicon strips arrays.

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The transmission spectra and the excitation of associated electric and magnetic resonance modes were simulated at the wavelength from 1.3 to 1.7 µm using commercial software, CST Microwave Studio. The simulation is based on a frequency-domain finite integration technology (FIT) using a unit cell boundary coupled with the Floquet port, and E-Field monitor and H-Field monitor are used at 1.42 µm to detect the distribution of electric and magnetic fields. Meanwhile, a Finite Difference Time Domain (FDTD) method was also adopted to simulate the polarization transmission spectra of the proposed structures, as shown in Fig. 2. The similar results verify the validity of CST simulation.

 

Fig. 2 Transmission coefficient spectra and transmission spectra of the proposed structure under the excitation of normally incident CPL. (a) $t_{--},t_{+-},t_{-+},t_{++}$ represent the transmission coefficients of left-to-left, left-to-right, right-to-left, right-to-right circularly polarized light. (b) Red and green solid lines represent transmission spectra of LCP and RCP light from CST, respectively. Pink and dark green dashed lines represent transmission spectra of LCP and RCP light from FDTD, respectively.

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3. Results and discussion

Figure 2(a) shows the transmission coefficient spectra of the all-dielectric cascaded tensor Huygens surface under the excitation of normally incident CPL. $t_{--},t_{+-},t_{-+},t_{++}$ represent the transmission coefficients of left-to-left, left-to-right, right-to-left, right-to-right circularly polarized light, respectively. Transmitted intensities of the incident right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) waves were calculated as $T_{-}={\left|t_{--}\right|}^2+{\left|t_{+-}\right|}^2$ and $T_{+}={\left|t_{-+}\right|}^2+{\left|t_{++}\right|}^2$. Figure 2(b) gives out the transmission spectra, where red and green solid lines represent the transmission of incident LCP light and RCP light, respectively. A significant transmission difference appears between LCP and RCP light. The transmission of LCP light ($T_{-}$) is above 0.8 in the two bands of 1.32-1.47 µm and 1.50-1.67 µm, especially, the maximum transmission of LCP ($T_{+}$) light reaches 0.97 at the wavelength of 1.42 µm. In contrast, the transmission of RCP light is almost near zero at the same spectral position. The maximum PSR (911:1) of the proposed structure is better than the circular polarizers made of silicon helix and metal helix [22]. Another key parameter for circular polarizer is dissymmetry factor, which is defined as $g=2(T_{-}-T_{+})/(T_{-}+T_{+})$ [34], and the dissymmetry factor of our structure is 1.88 at 1.42 µm. The high-efficiency and broad transmission of LCP light is from the spectral overlapping of strong tensorial electric and magnetic resonances. Because the electric field components of the orthogonal electric and magnetic dipole resonances are in the same direction, which lead to a wideband and nearly unit transmission. Furthermore, there are two groups of orthogonal and strong electric and magnetic resonances corresponding TE and TM modes respectively in strips when LCP light incidents. The nearly unit transmission efficiency for zero absorption also can be described in terms of resonant impedance matching in metamaterials with effective electric and magnetic polarizabilities. However, due to the symmetry break of the rotationally twisted strips, the weak electric and magnetic resonances result in nearly zero transmission when RCP light incidents.

In order to verify the resonance mode is the overlapping of tensorial electric and magnetic resonances, we plot the distributions of electric and magnetic field vectors as shown in Fig. 3. When the electric dipole resonance dominates, the electric fields point from one pole to another pole and the magnetic fields form closed circles, which mimicked the radiation pattern of electric dipole in the far-field. When the magnetic dipole resonance dominates, the electric fields form closed circles with strong circulating displacement currents and the magnetic fields point from one pole to another pole, which generate corresponding magnetic responses. The circular electric fields in the middle and parallel electric fields on the both sides of the strip showed in Figs. 3(a), (b) are the magnetic and electric dipole modes in x-z and y-z planes under the excitation of LCP light. In addition, the parallel electric fields on both sides and circular magnetic fields in the middle of the strip further demonstrate the resonance modes are magnetic and electric dipole resonances as shown in Figs. 3(e), (f). Similarly, the distributions of electric and magnetic fields in Figs. 3(c), (d), (g) and (h) also show electric and magnetic dipole resonances exist simultaneously in the x-z and y-z planes under the excitation of RCP light. Differently, the resonances under the excitation of LCP light are stronger than the resonances of RCP light. It is worth noting that the simultaneous excitations of electric and magnetic dipole resonances in x-z and y-z planes mean the electric and magnetic polarizabilities of the Huygens surface array are tensorial, which is in consistent with the design methodology as shown in Fig. 1(a).

 

Fig. 3 The field distributions of a unit cell under the excitation of CPL at the wavelength of 1.42 µm. The black dashed frames in crosscuts along -z direction marked the positions of strips. (a), (b) The electric field vectors driven by LCP light at y-z plane and x-z plane respectively, (c), (d) The electric field vectors driven by RCP light at y-z plane and x-z plane respectively, (e), (f) The magnetic field vectors driven by LCP light at y-z plane and x-z plane respectively, (g), (h) The magnetic field vectors driven by RCP light at y-z plane and x-z plane respectively.

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To understand how to gain circular polarization selectivity, we visualize the contributions of electric and magnetic resonances in combination with the incident plane wave to the polarization transmission in Fig. 4. Red ellipse represents the distribution diagram of phase difference, where $\phi =0$ or $\phi =\pi$ means the wave is linearly polarized light and $\phi =\pm \pi /2$ means the wave is circularly polarized light. The blue circle represents the polarization plane, where $\theta =0$ means the electric field vector of incident wave is polarized along x direction at this moment. Similarly, $\theta =\pi /2$ represents the electric field vector of the incident wave is polarized along y direction at that moment. Thus, black solid arrow in the position of $\phi =\pm \pi /2$ and $\theta =0$ represents that incident light is circularly polarized and the electric field vector is polarized along x direction at this moment in Fig. 4. Notice that the vector diagram is just an ideal case (supposing the maximum transmission is unit and the minimum transmission is zero) to understand the difference between two polarization transmissions. As shown in Fig. 4(a), when LCP light incidence, because of the strong electric and magnetic dipole resonances, the electric field components of electric and magnetic resonances are equal as green and watchet arrows denoted in Fig. 4(a). Thus the field vector of the incident plane wave and the electric field components of electric and magnetic resonances lie on an circle of $\left|E_{out}\right|=1$, which means $T_{-}\approx 1$. While under the excitation of RCP wave, the weak electric and magnetic resonances induce the small amplitude of electric field components as shown in Fig. 4(b). The superposition of the electric field components of electric and magnetic resonances (green arrow or watchet arrow) generates unit field amplitude $E_d$ (black dashed arrow). Obviously, the sum of the unit field amplitude (black dashed arrow) and the electric field vector of the incident plane wave (black solid arrow) in the opposite direction come to zero amplitude. Then, with the implementation of nearly unit LCP transmission and nearly zero RCP transmission, the circular polarizer based on cascaded tensor Huygens surface achieves polarization transmission selectivity.

 

Fig. 4 Vector diagram depicts the decomposition of the transmitted electric field vector into the contributions from the electric ($E_{ed}$, green) and magnetic ($E_{md}$, watchet) resonances and the incident waves ($E_{in}$, black solid) at the wavelength of 1.42 µm. (a) For LCP wave excitation, the sum of the electric components of the electric and magnetic dipoles and the incident electric field vector is unit, which means $T_{-}\approx 1$ . (b) For RCP wave excitation, the sum of the electric components of the electric and magnetic dipoles and the incident electric field vector is zero, which means$T_{+}\approx 0$ .

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In addition, we change the polarity of the polarization transmission selectivity to the other one by rotating anticlockwise the second-layer strips 90 degrees as shown in Fig. 5(a). On the contrary, the device with the changed structure can pass through RCP light and block LCP light in certain frequency bands as shown in Fig. 5(b). This is because the rotation of the second layer exchanges the resonances under the excitation of RCP light with the one of LCP light.

 

Fig. 5 (a) The top view of a unit cell in the changed structure. (b) Transmission spectra of the changed structure excited by CPL. Red and green lines represent transmission spectra of LCP and RCP light, respectively.

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4. Summary and Conclusion

In conclusion, a high-efficiency, wideband circular polarizer operating in the near-infrared wavelengths has been numerically demonstrated in this paper. The cascaded tensor Huygens surface array with asymmetric all-dielectric strips passes the LCP (RCP) light and blocks the RCP (LCP) light. The nearly unit LCP (RCP) transmission results from the spectral overlapping of the electric and magnetic resonances and the symmetry breaking of the rotationally twisted strips leads to the transmitted difference between LCP and RCP light. In addition, the new design methodology of circular polarizer is available for different frequency ranges by scaling the size of the unit cell. The all-dielectric metamaterial inherently with electric and magnetic resonances extremely also simplifies the basic unit structure and extend the concept of Huygens surface to shorter wavelength ranges. In general, the high-efficiency circular polarizer with simple inclusions makes great progress in performance compared to the structures previously reported and paves a way to construct polarization devices by cascading tensor Huygens surfaces with all-dielectric materials.