Simultaneous control of polarization and amplitude over broad bandwidth using multi-layered anisotropic metasurfaces

Jeong-Geun Yun; Jangwoon Sung; Sun-Je Kim; Byoungho Lee

doi:10.1364/OE.26.029826

1. Introduction

Polarization and amplitude of electromagnetic waves are fundamental properties that can be used to manipulate the manner of light-matter interactions. Thus, controlling the polarization state and amplitude of light is essential in complex and multifunctional optical applications such as optical communication, chemistry, biology, and diffractive optics [1–4]. Conventional methods for manipulating polarization states are implemented using multiple optical elements such as polarizers, waveplates, liquid crystals, and magneto-optical crystals. However, their weak light-matter interaction and highly dispersive optical activity result in a narrow bandwidth and bulky configurations. In addition, multiple optical components are required to control the polarization and amplitude simultaneously, which is a bottleneck in the miniaturization of optical information processing systems.

Metasurfaces are arrays of nanoantennae and serve as promising solutions for engineering optical properties within a subwavelength thickness. It is possible to use metasurfaces to manipulate the complex amplitude and polarization of transmitted light in a subwavelength thickness. Hence, many flat optical devices based on metasurfaces such as polarizers [5], waveplates [6,7], and meta-holograms [8] have been studied. Recently, optical rotators that can rotate the polarization plane of linearly polarized (LP) light have been demonstrated using metasurfaces for various wavelengths [9–13]. However, the transmission-type rotators suffer from problems of a narrow bandwidth and dispersive optical activity, and their application is limited due to their low transmission and modulation depth. Therefore, it has been an ongoing challenge to realize large and nondispersive optical activity with high transmittance over a broad wavelength range. Furthermore, to the best of our knowledge, nanophotonic devices that enable the simultaneous control of polarization and amplitude have not yet been reported.

Here, we propose a transmission-type polarization-amplitude modulator that can independently control the polarization and amplitude of the transmitted light simultaneously using multi-layered anisotropic metasurfaces (grating-nanorod-grating layers). This simultaneous control is accomplished by the phenomenon that the rotation of the polarization plane and amplitude of the transmitted light are determined by the distinct geometric parameters of the metasurface layers. First, the upper grating layer determines polarization rotation that can pass through it. Next, the nanorod layer controls the amount of polarization conversion and serves to align the polarization rotation to the upper grating layer. This scheme is different from the stacking three subwavelength wire grid polarizers that provides polarization rotation. Also, the staking three wire polarizer is not suitable approach to realize independent control of polarization and amplitude. That is because the wire grid polarizers, in contrast to the nanorod layer, do not serve to align the polarization rotation to the upper grating layer but serve to align the polarization rotation to their rotation angles. Here, broadband polarization rotation with an arbitrary angle and high transmission over a broad wavelength range is demonstrated numerically for multi-layered metasurfaces. High transmission and nondispersive optical rotation are obtained by Fabry-Pérot-like cavity that originates from the adjacent two anisotropic metasurface layers and improves the light-matter interactions over a broad bandwidth. The proposed structure allows extreme miniaturization of optical systems and can be applied to optical communication, polarization resolved image, and displays. In this paper, we theoretically analyze and numerically verify the proposed structure.

2. Results and discussion

Figure 1 shows schematic illustrations of the proposed multi-layered metasurface that can independently control the polarization and amplitude of the transmitted light simultaneously. The multi-layered structure consists of three aluminum (Al) metasurfaces. The nanorod and top nanograting layer are twisted by θ₁ and θ₂ with respect to the bottom nanograting layer, respectively. When unpolarized light impinges on the multi-layered structure from the substrate side, only x-polarized light can pass through the nanograting. Then, the twisted nanorods partially convert the x- to y-polarized light. Finally, the specific light with rotation angle perpendicular to the axis of the upper grating layer can pass through the last layer. Thus, the more light appropriately rotated from the lower two layers, the more light is transmitted through the upper grating layer. Based on this scenario, the proposed multi-layered structure can independently control rotation angle φ and transmitted amplitude by adjusting θ₂ and θ₁, respectively. Here, we assume that θ₁ and θ₂ satisfy the following conditions,

{\begin{matrix} \frac{θ_{2}}{2} \leq θ_{1} \leq 90 ° & (0 \leq θ_{2}), \\ - 90 ° \leq θ_{1} \leq \frac{θ_{2}}{2} & (θ_{2} < 0) . \end{matrix}

As shown in Fig. 1(b), the proposed structure becomes the “on state” and shows maximum transmission when θ₁ = θ₂/2 which leads to the rotation angle matching the upper grating layer. The proposed structure becomes the “off state” when θ₁ is 90° which indicates minimum polarization conversion.

Fig. 1 (a) A schematic illustration of the polarization-amplitude modulators based on multi-layered metasurface simultaneously generating an arbitrary amplitude and rotation angle φ. (b) The magnification of the proposed structure. The Al nanograting layers have a period = 150 nm, width = 40 nm and thickness = 100 nm. The Al nanorods have a period = 300 nm, width = 85 nm, length = 290 nm and thickness = 70 nm. Each layer is sequentially stacked with separation = 50 nm. The nanorod and top nanograting layer are twisted by θ₁ and θ₂ with respect to the bottom nanograting layer, respectively. The amplitude and optical rotation angle are modulated by θ₁ and θ₂, respectively.

Download Full Size | PDF

To investigate the simultaneous control in the multi-layered structure, the electric field distributions at the wavelength of 1000 nm are numerically calculated. For the numerical simulations, a commercial finite-difference time-domain method tool (Lumerical Solutions, Inc.) is used. Dielectric constants for Al are taken from a textbook [14], and the refractive index of the surrounding environment including substrate and dielectric spacer between the stacked layers is assumed to be 1.5. Figure 2 shows the calculated electric distributions at 500 nm from the surface of the upper grating layer under various θ₁ and θ₂. It is clear that the transmitted light is polarized perpendicular to the axis of the upper grating layer regardless of the twisted angle of nanorod θ₁. Also, the amplitudes change from maximum to minimum as θ₁ changes from θ₂/2 to 90°. Since the light modulation is determined by the geometric parameters, it is possible to implement a spatial light modulator that can generate arbitrary transmitted amplitudes and rotation angles as shown in Fig. 1(a). This spatial light modulator can be realized by positioning the nanorods and the upper gratings with different θ₁ and θ₂ in each position.

Fig. 2 Electric field distributions of the multi-layered structures with various θ₁ and θ₂ are presented. The insets indicate the top view of the multi-layered structures with the bottom grating (blue), the nanorods (purple), and the upper grating (red). (a) θ₁ = 15°, θ₂ = 30°, (b) θ₁ = 65°, θ₂ = 30°, (c) θ₁ = 90°, θ₂ = 30°, (d) θ₁ = 30°, θ₂ = 60°, (e) θ₁ = 60°, θ₂ = 60°, (f) θ₁ = 90°, θ₂ = 60°, (g) θ₁ = 45°, θ₂ = 90°, (h) θ₁ = 65°, θ₂ = 90°, (i) θ₁ = 80°, θ₂ = 90°.

Download Full Size | PDF

In addition, Fig. 3 shows the total transmission spectra and rotation angle φ of the proposed structures with different θ₂ while changing θ₁. It is apparent that the transmission can be tuned continuously from the maximum to minimum value by adjusting θ₁ from θ₂/2 to 90° over broad wavelengths. Furthermore, it is noticeable that φ provides a nearly constant value and satisfies φ = θ₂ while varying θ₁. Therefore, the proposed structures can provide independent control of amplitude and polarization over broad wavelengths ranging from 700 nm to 1300 nm. The amplitude modulation depth (defined as (|E_max| - |E_min|)/(|E_max| + |E_min|)) reaches up to 0.95 over a broad bandwidth (600 nm), and an arbitrary rotation angle of polarization plane can be obtained. Thus, the proposed strategy can be an excellent solution for simultaneous control of the amplitude and optical rotation without requiring any other optical components.

Fig. 3 Transmission spectra obtained for the polarization–amplitude modulators with (a) θ₂ = 30°, (b) θ₂ = 60°, and (c) θ₂ = 90° while varying θ₁. The white dashed lines indicate the condition, θ₁ = θ₂/2.Rotation angle φ of the polarization–amplitude modulators with (d) θ₂ = 30°, (e) θ₂ = 60°, and (f) θ₂ = 90° while varying θ₁.

Download Full Size | PDF

To understand the underlying mechanism of the multi-layered metasurfaces, a bi-layered anisotropic metasurface is considered firstly. Figures 4(a) and 4(b) show schematic illustrations for the bi-layered metasurface, which consists of Al nanograting and twisted Al nanorods with a twisted angle of θ and separation of d. The nanograting acts as a linear polarizer: it is nearly transparent to x-polarized incident light but reflects most of the y-polarized incident light. For the simplicity, the nanograting is assumed to be an ideal linear polarizer, and the transmission and reflection Jones matrices of the nanograting can be expressed as $T_{g} = (\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix})$ and $R_{g} = (\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix})$ . Additionally, the Al nanorod interacts dominantly with the light polarized along the direction parallel to the rod axis and generates a plasmonic resonance, which is determined by geometric parameters of the nanorods [15]. The transmission and reflection Jones matrices of the anisotropic nanorod with θ = 0 can be expressed as $T_{r} = (\begin{matrix} t_{x x} & 0 \\ 0 & t_{y y} \end{matrix})$ and $R_{r} = (\begin{matrix} r_{x x} & 0 \\ 0 & r_{y y} \end{matrix})$ , respectively [16]. Those for the nanorod twisted by θ can be described by the following equations,

T_{r} (θ) = R^{- 1} T_{r} R = (\begin{matrix} t_{x x} \cos^{2} θ + t_{y y} \sin^{2} θ & \cos θ \sin θ (t_{x x} - t_{y y}) \\ \sin θ \cos θ (t_{x x} - t_{y y}) & t_{x x} \sin^{2} θ + t_{y y} \cos^{2} θ \end{matrix}),

R_{r} (θ) = R^{- 1} R_{r} R = (\begin{matrix} r_{x x} \cos^{2} θ + r_{y y} \sin^{2} θ & \cos θ \sin θ (r_{x x} - r_{y y}) \\ \sin θ \cos θ (r_{x x} - r_{y y}) & r_{x x} \sin^{2} θ + r_{y y} \cos^{2} θ \end{matrix}),

where

R = (\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix})

is the rotation matrix.

Fig. 4 (a) An artistic illustration of the bi-layered anisotropic metasurface and (b) its unit cell structure. The Al nanograting, the first layer, is aligned along the y-axis and has a period = 150 nm, width = 40 nm and thickness = 100 nm. The Al nanorods, which have a period = 300 nm, width = 85 nm, length = 290 nm and thickness = 70 nm, are stacked on the nanograting with separation d and twisted angle θ. (c) Cross-sectional schematic illustration of the proposed structure for x-polarized incident light.

Download Full Size | PDF

For the case of bi-layered structure which is composed of the nanograting and twisted nanorods, Fabry-Pérot-like cavity effect that originates from the multiple reflections between the grating and the nanorod is induced only for y-polarized light as shown in Fig. 4(c). The total transmission of bi-layered structure is resulted from the superposition of the non-cavity and cavity modes. Thus, it can be expressed via Jones calculus as following equation:

\begin{array}{l} T_{t o t a l}^{b i} = e^{i k n d} T_{g} T_{r} (θ) + e^{i 3 k n d} T_{g} R_{r} (θ) R_{g} T_{r} (θ) + e^{i 5 k n d} T_{g} R_{r} (θ) R_{g} R_{r} (θ) R_{g} T_{r} (θ) + \dots \\ = = e^{i k n d} (\begin{matrix} t_{x x} \cos^{2} θ + t_{y y} \sin^{2} θ + e^{i 2 k n d} \sin^{2} θ \cos^{2} θ (t_{x x} - t_{y y}) (r_{x x} - r_{y y}) + \dots & 0 \\ \sin θ \cos θ [t_{x x} - t_{y y} + e^{i 2 k n d} (r_{x x} - r_{y y}) (t_{x x} \sin^{2} θ + t_{y y} \cos^{2} θ) + \dots] & 0 \end{matrix}) . \end{array}

Here, k and n are free space wavenumber and refractive index of dielectric spacer between the two layers, respectively. The first term of the equation indicates the transmitted light without the cavity effect, and the other terms represent the light enhanced by Fabry-Pérot-like cavity effect. It is noticeable that the total transmitted light is decided by the interference between the non-cavity and the cavity modes. Also, the cross polarized component (from x- to y-polarized light) implies that the bi-layered structures act as a polarization converter when the nanorod provides anisotropic response that is critically achieved around the plasmonic resonance wavelength of the nanorod. If the separation length d is small enough to make the phase retardation (eⁱ²^knd) negligible, the transmitted y-polarized lights can be enhanced over broad wavelengths. Additionally, since the polarization conversion is proportional to sinθcosθ, it can be controlled by θ.

Figure 5(a) shows the transmission spectra of the co- and cross-polarizations and optical rotation angle (φ) of the bi-layered structure when θ = 45° and d = 50 nm for x-polarized incidence. The rotation angle φ accounts for the rotation of the polarization plane for the LP light. Here, the nanograting and nanorod are designed to work as a linear polarizer and exhibit anisotropic transmission at approximately 1000 nm, respectively. Owing to the Fabry-Pérot-like cavity, the polarization conversion to y-polarized light is enhanced compared to the single nanorod; thus, a rotation angle of 40 - 47° is achieved over a wide wavelength range (600 - 1850 nm). Since the cross-polarized light experiencing the Fabry-Pérot-like cavity is vulnerable to Ohmic losses of Al, its transmission and optical rotation angle are deteriorated at approximately 800 nm where the interband transition in Al occurs. In spite of this loss, our structure can be a good candidate for highly efficient transmission type polarization generator owing to its large modulation angle with high transmission over 0.8 for a wide bandwidth.

Fig. 5 (a) For x-polarized incidence, the transmission spectra of co- (black solid line) and cross-polarization components (black dotted line) and rotation angle φ (red solid line) of the proposed structure, with θ = 45° and d = 50 nm. (b) The phase difference between the transmitted x- and y-polarized light (black solid line) and DoLP (red solid line). The shaded region refers to the operating bandwidth that ensures high quality linearly polarized light. (c) The electric field distributions for x-polarized (left) and y-polarized light (right) in the x-z plane at a wavelength of 1000 nm. The grating and the nanorod are indicated by black solid lines.

Download Full Size | PDF

Next, to investigate the quality of the transmitted LP light, the phase difference between the transmitted x- and y- polarized light and the degree of linear polarization (DoLP = $\frac{\sqrt{S_{1}^{2} + S_{2}^{2}}}{S_{0}}$ and S₀, S₁, and S₂ are Stokes parameters [10]) are calculated. As shown in Fig. 5(b), the proposed structure shows a wavelength-dependent phase difference. When the DoLP is above 0.9, the transmitted light can be considered as a high-quality LP light. Thus, the transmitted light is nearly LP light from 750 nm to 1260 nm, but it is considered elliptically polarized (EP) light at the other wavelengths. Figure 5(c) shows the electric field distributions in the x-z plane. The incident x-polarized light sequentially passes through the nanograting and the nanorod. However, it is apparent that the y-polarized light excited from the nanorod cannot penetrate the nanograting layer and propagate in the + z direction. Based on this field distribution, it can be deduced that our Fabry-Pérot-like cavity works in different manner than does a conventional Fabry-Pérot cavity. The conventional Fabry-Pérot resonator exhibits high electric field confinement between adjacent layers, and thus it provides a highly dispersive transmission spectrum. In contrast, our anisotropic bi-layered metasurface, Fabry-Pérot-like cavity, does not concentrate the electric field inside it. This enables the structure to maintain the enhanced transmission and nondispersive optical rotation angle over a wide bandwidth, as shown in Fig. 5(a).

To further understand the underlying mechanisms of the bi-layered structure, the spectra for the total transmission and rotation angle φ are numerically investigated while changing the twist angle of the nanorod θ and separation d. As shown in Figs. 6(a) and 6(b), it is noticeable that the rotation angle φ increases almost linearly over a wide wavelength range when θ increases to 70°. Additionally, the total transmission, for θ < 45°, remains over 0.8 in a broad wavelength range, but it drops rapidly after 45°. These facts can be understood from the fact that the transmitted co- and cross-polarized light are adjusted by the twist angle θ (cf. Eq. (4)); the cross-polarized light has a maximum value when θ is 45°, and the co-polarized light is steeply decreased at large θ. In addition, the separation d plays a significant role in the performance of the structure because the distance condition, 2d << 2π/k, should be satisfied to make the phase retardation from the Fabry-Pérot-like cavity negligible. Additionally, when d is too small, the interaction between the adjacent layers becomes strong, and the effect of the higher order Floquet modes must be taken into account, which makes the structure vulnerable to interlayer alignment errors. As shown in Figs. 6(c) and 6(d), the transmission and rotation dips, due to destructive interference between the non-cavity and cavity modes, are periodically explored for varying d from 100 nm to 600 nm. Additionally, when d is less than 50 nm, transmission fluctuations caused by the interlayer interaction occur. Therefore, we chose a distance d of 50 nm, which is short enough to render the phase retardation negligible.

Fig. 6 For x-polarized incident light, rotation angle φ and (b) total transmission of the bi-layered anisotropic metasurface while varying the twisted angle of the nanorod θ. (c) Rotation angle φ and (d) total transmission of the bi-layered anisotropic metasurface for varying d.

Download Full Size | PDF

In the aforementioned bi-layered structures, the optical rotation angle and operation bandwidth guaranteeing high quality LP light are limited. To eliminate this bandwidth limitation and increase the rotation angle, a tri-layered anisotropic metasurface is considered, which stacks an additional Al nanograting layer, identical to the nanograting in the first layer, on the top of the bi-layered metasurface, as shown in Fig. 7. The nanorod layer and upper grating layer are twisted by θ₁ and θ₂ with respect to the lower grating layer, respectively. The tri-layered structure can be considered as a series of two bi-layered metasurfaces. Thus, the transmission Jones matrix of the lower configuration that is composed of the bottom grating and the nanorod layer can be derived by assigning θ₁ to Eq. (4), and it is indicated by $T_{t o t a l}^{b i - l o w} = (\begin{matrix} e_{x} (θ_{1}) & 0 \\ e_{y} (θ_{1}) & 0 \end{matrix}) = (\begin{matrix} e_{1 x} & 0 \\ e_{1 y} & 0 \end{matrix})$ . Similarly, the transmission Jones matrix of the upper configuration composed of the nanorod and the top grating layer can be derived by assigning θ₂-θ₁ and transforming Eq. (4), and it can be expressed as following equation:

Fig. 7 (a) Schematic illustrations for the tri-layered anisotropic metasurface. The nanorod layer and upper grating layer are twisted θ₁ and θ₂ with respect to the lower grating layer, respectively. (b) The transmission spectra and DoLP of the tri-layered metasurface with θ₁ = 45°, θ₂ = 90° and d = 50 nm for x-polarized incident light. (c) Rotation angle φ and (d) total transmission of the tri-layered structures for varying θ₂. (e) Transmission spectra of the tri-layered structure having various grating periods of 300 nm (black) and 150 nm (red) with same filling factor (width of the gratings are 80 nm and 40 nm, respectively). The inset shows the electric field distribution (at 550 nm) of the tri-layered structure having P_g = 300 nm. (f) The transmission spectra of the tri-layered structure having various nanorod periods of 450 nm (black) and 300 nm (red) with same filling factor (width/length of the nanorods are 120nm/435nm and 80nm/290nm, respectively).

Download Full Size | PDF

T_{t o t a l}^{b i - u p} = (\begin{matrix} e_{2 x} \cos^{2} θ_{2} + e_{2 y} \cos θ_{2} \sin θ_{2} & e_{2 x} \cos θ_{2} \sin θ_{2} - e_{2 y} \cos^{2} θ_{2} \\ e_{2 x} \cos θ_{2} \sin θ_{2} + e_{2 y} \sin^{2} θ_{2} & e_{2 x} \sin^{2} θ_{2} - e_{2 y} \cos θ_{2} \sin θ_{2} \end{matrix}),

where e₂_x = e_x(θ₂-θ₁) and e₂_y = e_y(θ₂-θ₁). When the interaction among the metasurface layers can be negligible, the total transmission of the tri-layered structure can be obtained by the product of the transmission matrices of the two bi-layered structures as following equation:

T_{t o t a l}^{t r i} = T_{t o t a l}^{b i - u p} T_{t o t a l}^{b i - l o w} = (\begin{matrix} \cos θ_{2} [(e_{1 x} e_{2 x} - e_{1 y} e_{2 y}) \cos θ_{2} + (e_{1 x} e_{2 y} + e_{2 x} e_{1 y}) \sin θ_{2}] & 0 \\ \sin θ_{2} [(e_{1 x} e_{2 x} - e_{1 y} e_{2 y}) \cos θ_{2} + (e_{1 x} e_{2 y} + e_{2 x} e_{1 y}) \sin θ_{2}] & 0 \end{matrix}) .

This equation indicates that the transmitted light is, regardless of θ₁, LP light with rotation angle of θ₂ which is perpendicular to the axis of the upper grating layer. In other words, the incident light is converted from LP to EP light while passing through the first and second layers, then the second and third layers convert the EP light to LP light. Also, it is noticeable that θ₁ = θ₂/2 leads to e_2x = e₁_x and e₂_y = e₁_y, and the amplitude of the transmitted light in Eq. (6) becomes maximum value. This is a good agreement with the results of Figs. 3(a)-3(c). Figure 7(b) shows the simulation result of the transmitted light waves and DoLP for the tri-layered structure with θ₁ = 45°, θ₂ = 90°, and d = 50 nm. The data show an almost unity DoLP and nondispersive optical rotation of 90° over a broad wavelength range (600 nm - 2050 nm) except for short wavelengths where the 150 nm periodic nanograting does not act as a perfect linear polarizer. Moreover, it is easy to understand that the maximum total transmission appears near the resonance wavelength of the nanorod. Based on this scenario, it can be deduced that the operation bandwidth of the multi-layered metasurfaces can be tuned by scaling up and down of the twisted nanorods. Figures 7(c) and 7(d) show the transmission spectra and rotation angle φ for varying θ. It can be seen that φ in the tri-layered structure is determined in the direction perpendicular to the axis of the top nanograting layer and satisfies φ = θ₂ which shows a good agreement with the result from Eq. (6). Any rotation angle for the polarization plane can be provided by the tri-layered structure as twisting θ₂ from −90° to 90°. This structure also exhibits an additional transmission dip near 1800 nm due to the interlayer interactions, but it shows a high transmission over a broad bandwidth of 600 nm or more. Also, to understand the physical effects of the geometrical parameters of each layer, it is important to understand the design method of the proposed structures. Firstly, as described above, the operation wavelength can be controlled by the dimensions (period, width, length and thickness) of the nanorod. Secondly, the nanograting layers are designed to act like a linear polarizer for the operation wavelength range to form the cavity-like effect. Based on these design rules, if the period of the nanograting increases, the transmitted light at short wavelengths cannot be controlled by the multi-layered structures. As shown in Fig. 7(e), the non-rotating light leaks in the short wavelength range where the nanograting having P_g = 200 nm does not act like a linear polarizer. Also, when the period of nanorod increases, a red shift of the operation wavelength range occurs as shown in Fig. 7(f). Intuitively, theses design rules indicate that the proposed multi-layered structures have flexibility in the dimensions of the metasurfaces. In this paper, we chose P_g = 150 nm to ensure that the nanograting works as a linear polarizer at the short wavelengths (~600 nm), but it is not the unique solution. It is possible that the nanograting layer having P_g = 200 nm is a solution if the width and thickness are carefully designed [17].

Finally, a potential fabrication method for the proposed multi-layered metasurfaces is briefly discussed. The multi-layer structures can be manufactured by performing multiple fabrication methods using focused ion beam (FIB) [12] and electron-beam (E-beam) lithography [5,18]. Here, we suggest a potential fabrication method for the proposed multi-layered structure using E-beam lithography because it has advantages to fabricate large area metasurfaces. First, Al film is deposited on a glass substrate using an evaporator machine. Next, the nanopatterns are transferred to positive E-beam resist using E-beam lithography, and then the metal layer is patterned by plasma etcher using Cl₂ BCl₃, and Ar gases [19,20]. After fabricating the single layer, the planarization of the metasurface is conducted by spin-on glass coating. These processes can be repeated several times to produce the proposed multilayer structures. Since the proposed structures allowing only the fundamental Floquet mode are robust to interlayer alignment errors [21], the above fabrication process can be a promising method for fabricating the structures.

3. Outlook and conclusions

The proposed structures are demonstrated as a powerful solution for ultrathin polarization-amplitude modulators in transmissive optical systems. Such structures can adjust both the polarization plane of LP light and the transmitted amplitude over a wide wavelength range. Additionally, the proposed structures exhibit nondispersive optical activity originating from phase compensation among the layers and the non-resonant characteristic of the Fabry-Pérot-like cavity. Based on our structure, the simultaneous control of the polarization and amplitude is realized within a subwavelength thickness. The proposed structures provide high modulation depths for rotation by any rotation angle and amplitude of 0.95. In addition, since the operating wavelength region is determined by plasmonic resonance of the nanorod, our design can be exploited for various wavelength regions by scaling the structures up or down. The layered metasurfaces could be fabricated by multiple lithography techniques, but with their thicknesses remaining below the operating wavelengths. Therefore, our structure is an excellent candidate for realizing extreme miniaturization of various multifunctional nanophotonic systems. Moreover, the proposed devices can be exploited to realize functionalities such as asymmetric transmission, linear polarization conversion and amplitude modulation. For the tri-layered structure with θ = 45°, the x-polarized incident light in the forward direction ( + z direction) is converted into y-polarized light with high conversion efficiency of up to 80% (cf. Figure 7(b)). In contrast, the x-polarized incident light in the backward direction (-z direction) cannot penetrate the third layer with the grating axis parallel to the x-axis. Thus, the tri-layered structure can provide tremendous asymmetric transmission (T_forward/T_backward = 10 - 170) over an ultrabroad wavelength range (550 nm - 3000 nm). Our structures offer a promising alternative to previous studies of polarization conversion and asymmetric transmission [22–24]. Therefore, it is expected that the extreme miniaturization of various optical systems can be realized based on the proposed structures.

Funding

Basic Science Research Program through the National Research Foundation of Korea (NRF) (2017R1A2B2006676).

References

1. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, 2004).

2. V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013). [CrossRef] [PubMed]

3. W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014). [CrossRef] [PubMed]

4. Y. Lee, S.-J. Kim, H. Park, and B. Lee, “Metamaterials and metasurfaces for sensor applications,” Sensors (Basel) 17(8), 1726 (2017). [CrossRef] [PubMed]

5. J.-G. Yun, S.-J. Kim, H. Yun, K. Lee, J. Sung, J. Kim, Y. Lee, and B. Lee, “Broadband ultrathin circular polarizer at visible and near-infrared wavelengths using a non-resonant characteristic in helically stacked nano-gratings,” Opt. Express 25(13), 14260–14269 (2017). [CrossRef] [PubMed]

6. F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9(4), 4111–4119 (2015). [CrossRef] [PubMed]

7. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012). [CrossRef] [PubMed]

8. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef] [PubMed]

9. D. Wen, F. Yue, C. Zhang, X. Zang, H. Liu, W. Wang, and X. Chen, “Plasmonic metasurface for optical rotation,” Appl. Phys. Lett. 111(2), 023102 (2017). [CrossRef]

10. P. Yu, J. Li, C. Tang, H. Cheng, Z. Liu, Z. Li, Z. Liu, C. Gu, J. Li, S. Chen, and J. Tian, “Controllable optical activity with non-chiral plasmonic metasurfaces,” Light Sci. Appl. 5(7), e16096 (2016). [CrossRef] [PubMed]

11. L. Cong, N. Xu, J. Han, W. Zhang, and R. Singh, “A Tunable Dispersion-Free Terahertz Metadevice with Pancharatnam-Berry-Phase-Enabled Modulation and Polarization Control,” Adv. Mater. 27(42), 6630–6636 (2015). [CrossRef] [PubMed]

12. C. Pfeiffer, C. Zhang, V. Ray, L. Jay Guo, and A. Grbic, “Polarization rotation with ultra-thin bianisotropic metasurfaces,” Optica 3(4), 427–432 (2016). [CrossRef]

13. E. Hasman, G. Biener, V. Kleiner, and A. Niv, “Polarization: spatial fourier-transform polarimetry by use of space-variant subwavelength gratings,” Opt. Photonics News 14(12), 34 (2003). [CrossRef]

14. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

15. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1998).

16. Y. Zhao and A. Alù, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013). [CrossRef] [PubMed]

17. S.-W. Ahn, K.-D. Lee, J.-S. Kim, S. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, “Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography,” Nanotechnology 16(9), 1874–1877 (2005). [CrossRef]

18. C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010). [CrossRef] [PubMed]

19. V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Aluminum plasmonics based highly transmissive polarization-independent subtractive color filters exploiting a nanopatch array,” Nano Lett. 14(11), 6672–6678 (2014). [CrossRef] [PubMed]

20. T. Weber, T. Kasebier, A. Szeghalmi, M. Knez, E.-B. Kley, and A. Tunnermann, “High aspect ratio deep UV wire grid polarizer fabricated by double patterning,” Microelectron. Eng. 98, 433–435 (2012). [CrossRef]

21. Y. Zhao, J. Shi, L. Sun, X. Li, and A. Alù, “Alignment-free three-dimensional optical metamaterials,” Adv. Mater. 26(9), 1439–1445 (2014). [CrossRef] [PubMed]

22. T. Li, X. Hu, H. Chen, C. Zhao, Y. Xu, X. Wei, and G. Song, “Metallic metasurfaces for high efficient polarization conversion control in transmission mode,” Opt. Express 25(20), 23597–23604 (2017). [CrossRef] [PubMed]

23. M. Kim, K. Yao, G. Yoon, I. Kim, Y. Liu, and J. Rho, “A broadband optical diode for linearly polarized light using symmetry-breaking metamaterials,” Adv. Opt. Mater. 5(19), 1700600 (2017). [CrossRef]

24. S. Hu, S. Yang, Z. Liu, J. Li, and C. Gu, “Broadband cross-polarization conversion by symmetry-breaking ultrathin metasurfaces,” Appl. Phys. Lett. 111(24), 241108 (2017). [CrossRef]

Simultaneous control of polarization and amplitude over broad bandwidth using multi-layered anisotropic metasurfaces

Abstract

1. Introduction

2. Results and discussion

3. Outlook and conclusions

Funding

References

Cited By

Figures (7)

Equations (6)

Optics Express