1. Introduction

As an important property of light, the polarization provides great degree of freedom for manipulating light and developing new photonic devices. Conventionally, the linearly polarized light can be generated by the transmission of an absorption-type polarizer, the reflection at a medium interface, the birefringence of a crystal, and the scattering of micro-particles. With the use of wave plates composed of birefringence materials, one can realize the transformation from linear to elliptical or circular polarization. Besides the half-wave plate, the Faraday effect of optical active materials also owns the ability to rotate the linear polarization, with the rotation angle determined by the propagation length and applied magnetic field. Nonetheless, the devices based on these effects are usually bulky in size, thus not beneficial for the photonic integration.

Metamaterials and metasurfaces provide new potential for the polarization control and miniaturization of devices. Metamaterials usually refer to artificially structured three-dimensional materials, which consist of subwavelength components and are macroscopically homogeneous [1]. With the metamaterials, circular polarizers and 90-degree rotation of linear polarization have been demonstrated [2, 3 ]. Nonetheless, metamaterials usually suffer from both fabrication difficulty and high material loss, thus not appropriate for operation in the high-frequency band. On the other hand, metasurface, a quasi-two-dimensional counterpart of metamaterial, may overcome these shortcomings and show remarkable abilities for controlling light [4, 5 ]. With the metasurface composed of subwavelength particle arrays on a metal substrate, reflective half-wave plates operating in a broadband have been constructed [6, 7 ]. The metasurface concept can be extended to include the thin metal film milled with subwavelength slit/hole arrays [8]. With the single perforated metal film, various transmittive quarter- or half-wave plates have been reported [9–12 ], albeit with the low conversion efficiency and/or narrow bandwidth.

A composite plasmonic structure consisting of multilayered but usually different meta-surfaces may play an important role in the control of polarization [13, 14 ]. This material differs in structure from the metasurface (an ultrathin and planar single layer) and metamaterial (a multilayer usually formed by the periodic stacking of single layers). Moreover, its optical properties are neither that of a single layer nor that of a periodic layer stacking, but determined by the individual different layers as well as their coupling (in many cases, it is difficult to find an effective medium description, as used for the metamaterials). Such a structure may be termed the “multilayer metasurfaces” or “coupled metasurfaces”. Actually, this type of structure has received much interest recently [13–21 ]. One example is that, by using three layers of metal gratings (or cut wires) with different orientations, broadband 90-degree polarization conversion can be achieved in the THz regime [14–16 ].

A pair of orthogonal plasmonic polarizers, each with subwavelength rectangle holes in a metal film, represents another form of the coupled metasurfaces [18]. Compared with the three layers of metal gratings [14–16 ], two layers of plasmonic structure is relatively easier to fabricate and can work in the optical frequencies. Previously, by coating a free-standing SiN film with the gold films and fabricating, respectively, the rectangle holes on both sides, we have successfully fabricated such an asymmetrical structure [18]. The experiments and simulations suggested that the resulting orthogonal polarizers, which will conventionally forbid the transmission of light, can induce a transmission and 90-degree polarization rotation [18]. Nonetheless, around the working wavelength 1000 nm, the obtained conversion efficiency is relatively low (~40%) and the working bandwidth is very narrow (~75 nm). This may hamper the possible practical applications. In this paper, we go a step further to show that this structure can be highly efficient and broadband in the near-infrared region. By utilizing the low-loss metal, the telecom working wavelength, and the propagating waveguide mode, conversion efficiency more than 80% has been suggested theoretically. With a systematical investigation of the effect, we further found that an overlapping of the internal surface-plasmon (ISP) modes can give rise to a wideband polarization conversion. At the wavelength 1340 nm, for example, the conversion efficiency attains 83% with a full width at half maximum (FWHM) of 300 nm. The effect has also been extended to the THz band.

2. Results and discussions

Figure 1(a) shows the schematic view of the plasmonic system under study. Two metal films perforated with rectangular hole arrays are separated by an insulated spacer layer (the physical effect does not depend on the refractive index of spacer). Due to the polarization-dependent cutoff effect of the rectangle holes, the metal films will behave as two linear plasmonic polarizers in certain wavelength region, where the polarization axis is perpendicular to the long hole edges [22]. By setting the angle between the two polarizer holes as 90 degrees, a pair of orthogonal linear polarizers can be constructed. Moreover, to enhance the polarization coupling effect, the rectangular holes in the two polarizers are designed to present the ∟-shaped “crossing” in the projection plane, as shown in Fig. 1(b). Here, the thickness of metal film and spacer layer is denoted as t and h, respectively; the rectangular holes with the length l and width w are arranged in a square array with the lattice constant of d; and the refractive index of the spacer layer is set as n_s. The pasmonic system was simulated with the finite-difference time-domain (FDTD) method, employing the commercial software package FDTD Solutions 6.5 (Lumerical Solutions, Inc., Canada). In the numerical simulations, the metal film (silver) was modeled by the Drude model ${\epsilon }_m={\epsilon }_{\infty }-{\omega }_p^2/\omega (\omega +i\gamma )$ [23], where ε_∞ = 3.8, ω_p = 1.37*10¹⁶ rad/s is the plasma frequency, and γ = 5*10¹³ Hz is the electron collision frequency.

 

Fig. 1 (a, b) Schematic view of the coupled metasurfaces: two orthogonal plasmonic polarizers separated by a spacer layer; (c) transmission of a single metal film with rectangle holes; (d) polarization conversion of the coupled metasurfaces (the incident light is x-polarized). Here, d = 1000 nm, l*w = 750 nm*280 nm, t = 150 nm, h = 120 nm, and n_s = 2.

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2.1. Highly efficient polarization rotation near the telecom wavelength

Because of the near-field coupling, the two orthogonal plasmonic polarizers can induce a transmission and 90-degree polarization conversion. That is, in a narrow frequency band (965~1040 nm), the x-polarized incident light can be transformed partly (less than 40%) into the y-polarized transmitting light [18]. Can we enhance the 90-degree polarization conversion efficiency significantly? The answer to this question is critical for the practical applications. The question has been considered carefully and several methods can be proposed here. A possible way is to use the low-loss plasmonic materials such as the silver and shift the working point to the longer wavelength such as the telecom wavelength around 1500 nm. Another way is to increase the hole size and the cutoff wavelength, thus the hole waveguides may work in the propagating mode regime. For the purpose, here the lattice constant is set as d = 1000 nm, the hole size is l*w = 750 nm*280 nm (a larger aspect ratio is needed for a linear plasmonic polarizer), the thickness of silver film is t = 150 nm, and the spacer layer is a SiN film with a thickness h = 120 nm and refractive index n_s = 2. The longer wavelength band studied here ranges from 1200 nm to 2200 nm.

Firstly, to test the linear polarization property of the plasmonic polarizer, Fig. 1(c) presents the calculated transmission spectra of a single metal film milled with rectangle holes (the structural sizes mentioned above were used). For the polarization component along the long hole edges (E // l), the transmission of light is almost completely forbidden in the whole considered wavelength band. In contrast, for the polarization component along the short hole edges (E + l), a wide transmission peak (with the peak efficiency of ~86%) appears at the wavelength around 1736 nm. This demonstrates that the perforated metal film has a good linear polarization property. The transmission maximum is the well-known EOT phenomenon [8]; compared with the normalized area of holes (21%), the enhancement factor of transmission attains 4.1 at the maximum. The peak position, 1736 nm, is found to be very close to the cutoff wavelength of the rectangle holes, ${\lambda }_c=2\left(l+2\delta \right)\sqrt{1+2\delta /w}$ = 1708 nm (δ = 22 nm is the skin depth) [24], indicating a waveguide cutoff resonance. In many cases, the planar SPP wave and hole waveguide mode will be coupled to form an effective surface mode. Only when the resonance wavelengths of the two types of modes are well separated, can a pure waveguide resonance be resulted. Here, the presence of pure waveguide resonance originates from the rectangle holes with the larger hole sizes.

Figure 1(d) presents the transmission spectra of the crossed plasmonic polarizers. Here, the incident light is x-polarized with an amplitude E₀, $T_{xx}\equiv E_{tx}^2/E_0^2$ and $T_{xy}\equiv E_{ty}^2/E_0^2$ represents the efficiency of transmitted wave with x- and y- polarizations, respectively. One can see that, from 1200 nm to 2200 nm, T_xx is almost zero. This agrees with the linear polarization property of the output plasmonic polarizer [Fig. 1(c)]. Nonetheless, T_xy exhibits two transmission peaks around the wavelength 1500 nm and 1870 nm. That means the x-polarized incident light can pass through two orthogonal plasmonic polarizers and rotate its polarization by 90 degrees. Especially, around the wavelength 1500 nm, the polarization conversion efficiency T_xy attains 80%. This efficiency is much larger than that achieved in our previous work, suggesting that our system may be highly efficient and thus useful for the practical applications. The working bandwidth or FWHM is 170 nm for the peak around 1500 nm (the relative bandwidth is 11%). Instead, the transmission peak at 1870 nm owns much smaller conversion efficiency (35%) and narrower bandwidth (~60 nm). Note that the hole cutoff wavelength is around 1700 nm. Thus the effect at 1500 nm operates in the propagating waveguide-mode regime while that at 1870 nm in the evanescent mode regime. In the latter case, the waveguide modes will decay obviously in the rectangle holes, leading to the low transmission. Hence, all these factors including the low-loss metals, the longer working wavelength, and the propagating waveguide modes contribute to the much higher conversion efficiency.

In spite of all the above factors that contribute to the high efficiency, the qualitative effect of the orthogonal plasmonic polarizers can be attributed to the ISP resonance in the spacer and the near-field coupling between the rectangle holes of the two polarizers [18]. Our previous work has suggested that, at the transmission maximum, the fields are highly confined and enhanced in the spacer, corresponding to the ISP resonances phase matched by the reciprocal lattice vectors. Roughly, the ISP resonance wavelength may be expressed as [18, 25 ]

 

Fig. 2 Electric field (a) Ex and (b) Ey distributions in the xz plane (y = 235 nm, λ = 1500 nm); magnetic-field (H_z) distributions, in the middle planes of output and input polarizers, for the split peaks at 1430 nm (c, d) and 1504 nm (e, f).

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2.2. Structural dependence & wide bandwidth by overlapping the ISP modes

Other questions may be that, how does the polarization conversion effect depend on the material and structural parameters? And, can we increase the bandwidth of the effect? To answer these questions, we have systematically investigated the proposed plasmonic structure and the results are shown in Figs. 3-5 (here, only the polarization conversion efficiency T_xy is shown; T_xx is very small and thus omitted). In the study, we changed the parameter one at a time and other parameters, as used in Fig. 1(d), were fixed. The optical properties of the structure can be influenced by several aspects: the metal film, the hole array, and the spacer layer. In Fig. 3(a), we changed the electron collision frequency of the Drude model from γ = 5*10¹³ Hz to γ = 9*10¹³ Hz. With the increase of metal loss, the peak positions remain unchanged but the peak efficiencies drop obviously (the maximal efficiency around 1500 nm is reduced to be 67%). This confirms that the low-loss metal indeed plays an active role. In Fig. 3(b), the thickness of metal film is decreased from t = 150 nm to 100 nm. The spectrum only shows very slight modifications. The transmission peak at 1870 nm, associated with the evanescent waveguide mode, grows and redshifts slightly. This redshift can be predicted with Eq. (1), relating to the weak dependence of ISP mode on the metal thickness [25]. The peak around 1500 nm decreases instead, where the reduction of metal thickness (i.e., the hole waveguide length) may suppress the propagating waveguide mode. In practice, an appropriate metal thickness such as 150 nm can be chosen. A much larger metal thickness may increase the loss and fabrication difficulty, while a much smaller thickness will be insufficient to prevent the T_xx component.

 

Fig. 3 Dependence of polarization conversion efficiency Txy on the parameters: (a) electron collision frequency; (b) metal film thickness; (c) hole lattice constant; and (d) hole size. Here, the thin solid lines (green) in the four figures correspond to the same structure parameters: d = 1000 nm, l*w = 750 nm*280 nm, t = 150 nm, h = 120 nm, n_s = 2, and γ = 5*10¹³ Hz.

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Fig. 4 Polarization conversion efficiency T_xy as a function of wavelength for different spacer thickness (h = 100, 140, 180, and 220 nm). Here, d = 1000 nm, l*w = 750 nm*280 nm, t = 150 nm, n_s = 2.

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Fig. 5 Polarization conversion efficiency T_xy as a function of wavelength for different spacer refractive index (n_s = 2.0, 1.73, 1.5, and 1.3). Here, d = 1000 nm, l*w = 750 nm*280 nm, t = 150 nm, and h = 120 nm.

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The hole arrays are characterized by the lattice period and the hole sizes. In Fig. 3(c), the lattice period is increased from d = 1000 nm to 1100 nm. In this case, the transmission peaks shift to the longer wavelength significantly. The period-dependence of the peaks is a signature of the ISP mode resonance. The wavelength shift around the peaks of 1500 nm and 1870 nm is 96 nm and 178 nm, respectively, which is close to 117 nm and 165 nm as predicted by Eq. (1). In addition, with the increase of lattice period and peak positions, the maximal efficiencies decrease. This is associated with the reduction of normalized hole area as well as the departure of longer wavelength peak from the hole cutoff wavelength. In Fig. 3(d), we also changed the hole sizes from 750*280 nm² to 600*224 nm² (the aspect ratio is fixed as 2.68). The smaller hole sizes correspond to a shorter hole cutoff wavelength 1409 nm. This gives rise to a decrease of peak efficiencies and a slight blueshift of the peaks. The blueshift due to the hole size cannot be revealed by Eq. (1), as the approximated ISP dispersion does not take account of the waveguide mode. The results demonstrate that the larger hole sizes and cutoff wavelength are beneficial to the high polarization conversion. Nonetheless, when the hole length approaches the lattice period (l~d), the situation will become degenerate instead (not shown here). In this case, besides the hole interaction in a unit cell, a “vertical” hole can also couple increasingly to the “horizontal” holes in the adjacent unit cells [for convenience, here the “vertical” and “horizontal” holes refer to the rectangle holes in Fig. 1(b)]. This will cancel the charges accumulated near the opening of “vertical” holes, thus suppressing the waveguide mode in the output polarizer as well as the transmission.

The above results do not provide any significant clues for enlarging the bandwidth. We turn to the spacer layer and study the effect of spacer thickness or refractive index on the optical properties. Figure 4 presents the conversion efficiency T_xy as a function of wavelength for different spacer thickness: h = 100, 140, 180, and 220 nm. With the increase of h, the spectra display complicated evolution characteristics, some of which can be summarized as follows. Firstly, the longer-wavelength transmission peak related to the ISP (1, 1) mode blueshifts, splits, and grows in amplitude. The magnitude of blueshift, ~135 nm, is comparable to the value, 148 nm, calculated with Eq. (1). Note that the blueshift will be saturated when the spacer thickness is much larger than the metal skin depth (h>>δ). Because of the blueshift of the ISP mode, the peak becomes closer to the hole cutoff wavelength, which leads to the increase of peak efficiency and split of the peak. Secondly, the shorter-wavelength peak related to the ISP (2, 0) mode redshifts, further splits, and drops in amplitude. Although Eq. (1) predicts a smaller blueshift (~104 nm) for the ISP (2, 0) mode, the increment of spacer thickness can reduce the coupling and interaction energy between the orthogonal holes. In addition to a drop of peak, the competition between them gives rise to a slight redshift overall. If the spacer thickness is further increased (not shown here), all the peaks will be suppressed obviously due to the weak hole coupling. And lastly, when the spacer thickness is properly selected, the ISP (2, 0) and (1, 1) modes will approach each other, thus producing a continuous and wide operating bandwidth. For h = 180 nm, the 90-degree polarization conversion covers a wave band from 1450 nm to 1850 nm, with the efficiency ranging from 28% to 77%. This provides the possibility for realizing efficient and wideband polarization conversion.

The separation between the ISP (2, 0) and (1, 1) modes, Δλ = λ₁₁-λ₂₀, is linked to the material and structure parameters of the coupled metasurfaces. With the use of Eq. (1), one can obtain approximately that

2.3. Polarization rotation in the THz band

We extend the above effect from the near-infrared to THz wave band by presenting only one example. To realize an efficient and wideband 90-degree polarization conversion at the THz frequencies, the material and structure parameters are chosen as follows: the lattice period of hole array is d = 100 μm; the sizes of rectangle holes are l*w = 75 μm*30 μm; the thickness of metal film and spacer layer is t = 15 μm and h = 9 μm, respectively; the refractive index of spacer layer is set as n_s = 1.5, and the metal is still modeled by the Drude dispersion. Figure 6 presents the transmission as a function of frequency (f = 1.35~3.0 THz). Similar to the results in optical frequencies, here T_xx is negligible in the considered THz region, and T_xy shows enhanced transmission peaks indicating the 90-degree polarization rotation. The split peak around 1.6 THz is associated with the ISP (1, 0) mode, where the maximal conversion efficiency is 89% and the FWHM is 0.1 THz with a relative bandwidth of 6.3%. Remarkably, the overlapping of (1, 1) and (2, 0) ISP modes causes a wide transmission band around 2.6 THz, where the maximal efficiency attains 100%, the FWHM is 0.36 THz (2.40~2.76 THz), and the relative bandwidth reaches 14%. The above two transmission bands are separated by a hole cutoff wavelength locating around 2.0 THz. Additionally, a high and narrow peak at 2.82 THz (with the wavelength closer to the lattice period) is correlated with the external surface-plasmon (1, 0) modes, which are excited on the outer metal surfaces.

 

Fig. 6 Polarization conversion effect in the THz band: d = 100 μm, l*w = 75 μm*30 μm, t = 15 μm, h = 9 μm, and n_s = 1.5. The arrow indicates the hole cutoff wavelength.

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3. Conclusions

In summary, the 90-degree polarization rotation with the coupled metasurfaces, i.e., two perforated metal films working as a pair of orthogonal plasmonic polarizers, has been investigated. The effect is associated with the ISP resonance in the spacer and near-field coupling between the orthogonal rectangle holes. We found that, by integrating the low-loss metal (silver), the longer working wavelength, and a work style using propagating waveguide mode, highly efficient polarization rotation with the efficiency more than 80% can be achieved near the telecom wavelength. The dependence of conversion effect on the material and structure parameters has also been explored systematically. We further found that, by overlapping the ISP (2, 0) and (1, 1) modes, an efficient and wideband polarization conversion can be realized. The maximal efficiency is 83% around the wavelength 1340 nm, and the FWHM reaches 300 nm. Similar effect has also been suggested in the THz band. These results may find practical applications, such as in designing and constructing compact, efficient, and wideband polarization rotators.