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Abstract
Realizing versatile functionalities in a single photonic device is crucial for photonic integration. We here propose a polarization-switchable and wavelength-controllable multi-functional metasurface. By changing the polarization state of incident light, its functionality can be switched between the flat focusing lens and exciting surface-plasmon-polariton (SPP) wave. Interestingly, by tuning the wavelength of incident light, the generated SPP waves can also be controlled at desired interfaces, traveling along the upper or lower interface of the metasurface, or along both of them, depending on whether the incident light satisfies the first or second Kerker condition. This polarization-switchable and wavelength-controllable multifunctional metasurface may provide flexibility in designing tunable or multifunctional metasurfaces and may find potential applications in highly integrated photonic systems.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Miniaturization and integration are two continuous trends in the production of versatile photonic devices [1], and integrating multiple independent functionalities into one single sub-wavelength photonic device at the same time is one of the intensively investigated fields because it can offer miniaturized footprint, reliability and large-scale system integration [2,3]. Recently, metasurfaces have attracted much attention due to their remarkable light manipulation on the subwavelength scale, low loss, and ease of on-chip fabrication thanks to their planar profiles [4–9]. The specific implementation principle [4] of light manipulating is that local and space-variant abrupt phase changes are introduced at the interface between two media, consequently breaking the momentum continuity and providing an additional tangential momentum to scattered light [7]. Many applications based on metasurfaces have been demonstrated, such as light bending [7], surface plasmon polariton (SPP) excitation [10,11], plasmonic lenses [12], beam splitter [13], polarization manipulation [14], and so on. However, it is noted that most reported metasurfaces are just for a single function.
Very recently, some efforts were devoted to incorporating multi-functions into a single metasurface [15–22]. The realization method is to impose independent phase profiles on each of two orthogonal polarizations [17–20]. For instance, in [17], Chen et al reported a metasurface functioning either as a hologram or a convex lens, depending on the helicity of the incident light. And bi-functional metasurfaces possessing the functionalities of focusing and beam bending or even exciting surface-plasmon-polaritons (SPPs) under different polarizations are also reported in [18–20]. Quite different from these works, we in this paper design a polarization-switchable and wavelength-controllable transmissive multi-functional metasurface, which can realize flat focusing and the excitation of surface plasmon polaritons (SPPs) depending on the polarization state of incident light. More importantly, it can manipulate the excitation of SPP waves at the desired interfaces by tuning the wavelength of incident beams.
SPPs, electromagnetic (EM) waves coupled to the density waves of free electrons in metals, propagate along the metal/dielectric interface and decay exponentially away into both media [23–26]. Owing to the ability to confine EM waves in the subwavelength scale, SPP-based devices are promising for applications in highly integrated optical circuits such as optical interconnects and optical signal processing [1]. And SPP excitation from a free-space light in a controllable manner is an essential step toward more complex and integrated applications. A variety of approaches have been proposed for tunable launching of SPPs, where its propagation direction is manipulated by changing the incidence angle, wavelength, or polarization of the excitation light [23,27–30]. But, flexibly controlling the excitation of SPPs at desired interfaces by tuning the wavelength of incident beams based on metasurfaces have not yet been reported in open literatures.
In this paper, the proposed transmissive multifunctional metasurface cannot only realize polarization–resolved SPP excitation and focusing, but also flexibly control the excitation of SPPs at desired interfaces. By tuning the wavelength of incident beams, the generated SPPs can travel along the upper or lower interface, or along both of them, depending on whether the incident light satisfies the first or second Kerker condition. This multifunctional metasurface may have potential applications in highly integrated photonic systems, including imaging and optical signal processing.
The organization of this paper is as follows, section 2 presents the design principle of the multifunctional metasurfaces, and section 3 shows the results and discussion. Brief conclusions are given in the final section.
2. Design principle of multifunctional metasurfaces
The proposed transmissive multifunction metasurface is designed to convert an X-polarized incident optical wave into SPPs and focus the Y-polarized incident wave into a spot. Let’s assume an X-polarized wave normally impinges on a metasurface, which lies in the x-y plane and has phase gradient ξx along the x direction. That is, the wave-vector components of the incident light are kx,i = 0, ky,i = 0 and kz,i = k0, respectively, with k0 being the propagation constant in free space. According to the momentum conservation law [4,7], the wave-vector components of the transmissive beam is written as:
It is clear that, if phase gradient ξx is bigger than k0, kz,t becomes imaginary, then the normally incident X-polarized light will be converted into SPPs propagating along the interface. That is to say, to generate SPPs, the metasurface should provide the normally incident X-polarized light with a transmission phase profile ΦX(x) expressed as:
If we hope this same metasurface to focus the transmitted beam at a spot with focal length f0 for a Y-polarized incident wave, the corresponding phase distribution ΦY(x) could be designed to have a parabolic profile along the x direction [12,15]:
It should be mentioned that ΦX(x) is the transmission phase profile that an X-polarized light sees at the metasurface; whereas ΦY(x) stands for the transmission phase profile that a Y-polarized wave experiences at the same metasurface, with the capital letters ‘X’ and ‘Y’ in the subscripts for X- and Y-polarized waves, respectively. Obviously, to realize the bi-functionality of exciting SPP wave for the X-polarized light and focusing effect for the Y-polarized light, we should independently design ΦX(x) and ΦY(x). Fortunately, metasurfaces composed of anisotropic antennas possess strong polarization dependence. Therefore, by selecting proper antennas and arrange them appropriately, an X-polarized or a Y-polarized wave can only “see” the phase distribution ΦX(x) or ΦY(x) expressed in Eq. (2) or (3), hence we can realize polarization-controlled multifunctional metasurface.
Moreover, in order to further enrich its functionalities, we design a unique geometric structure to realize wavelength-controlled SPP coupling, i.e., the metasurface can flexibly control the SPP excitation at the desired interface depending on the wavelengths of the incident X-polarized waves and how the incident beams satisfy Kerker condition. To more intuitively interpret the related mechanism, we adopt a simple one-dimensional (1D) model, as shown in Fig. 1.
Fig. 1 (a) Schematic and working principle for manipulating propagative SPPs. By properly adjusting working wavelength, the generated SPPs can propagate along the upper interface at wavelength λa, or lower interface at wavelength λb, or along both of them at wavelength λc. (b) Schematic of dipole p and image diploe p' in a structural unit of the metasurface.
The metasurface in Fig. 1 consists of a metallic film layer sandwiched between two identical layers of metallic nanorod antenna arrays, with each other separated by a dielectric spacer. And the thickness of the metallic film layer is thinner than the light penetration depth in the metal. When an X-polarized wave normally illuminates the metasurface along the negative z-axis, the light first hits the upper nanorod-array and excites an array of electric dipole p along the x-axis. Meanwhile, an array of image electric dipole array with p' = (1-ɛeff)/(1 + εeff)p is induced accordingly in the lower nanorod-array [31], as shown in Fig. 1(b). Here ɛeff represents the effective permittivity resulting from the sandwich structure. The upper and lower antennas can be designed to control the electric response of the entire structural unit along the x-direction by tuning their geometric size. And an anti-parallel current is generated in the two antenna array layers, thereby creating an equivalent magnetic current to form magnetic dipole responses along the y-direction [32–34]. Hence this metasurface is able to provide complete phase control covering [0, 2π] to achieve almost arbitrary wavefront shaping. Here we define my as the magnetic dipole moment and px = (p + p')/2 as the electric dipole moment for the structural unit of the metasurface. Then the normalized forward/backward (i.e., along the negative or positive z-axis) scattering cross section of the structure unit can be expressed as [35–37]:
where k is the wavenumber in a background material with the electric permittivity ɛ = ɛ0ɛr, c is the speed of light, and A is the geometric cross section. |Einc| is the amplitude of the incident electric field, and ± signs correspond to the forward and backward scattering cross sections, respectively.According to Eq. (4), zero backward scattering occurs when the first Kerker condition is met, which is expressed as [35]:
And zero forward scattering takes place when the second Kerker condition is fulfilled, which is written as [35]:
It should be noted that px and my are dependent on the wavelength and polarization of the incident light, and on the structure of the metasurface as well.
According to Eqs. (5) and (6), at certain operation wavelengths, an incident X-polarized wave satisfying the first Kerker condition will undergo zero backward scattering. And then in the subsequent forward propagating process, it will be efficiently coupled into SPP wave propagating along the lower interface of the metasurface (see wavelength λc in Fig. 1(a)), under the condition that it obtain a large enough phase gradient ξx from the metasurface to excite SPPs, i.e, Eq. (2) is satisfied on the lower-layer metallic antenna/dielectric interface. In a similar way, at another wavelength, the incident X-polarized light meeting the second Kerker condition will undergo zero forward scattering, and then in the following backward propagating process, it will be efficiently coupled into SPP wave propagating along the upper interface (see wavelength λa in Fig. 1(a)) if Eq. (2) is satisfied there. And at some other wavelengths, the incident X-polarized wave, who neither satisfies the first Kerker condition nor the second Kerker condition, will be converted into SPP wave propagating along both the upper and lower interfaces (see wavelength λb in Fig. 1(a)) if Eq. (2) is satisfied there.
Based on above analyses, we can anticipate a polarization-dependent and wavelength-controlled metasurface, which can focus an incoming Y-polarized light while couples the X-polarized one into SPP wave. Besides, depending on the wavelength of the incoming light, the SPP excitation can be controlled at the upper or the lower interface, or both interfaces. In the following section, to illustrate the basic ideas and thereby better understand the working mechanism, we design and characterize such a transmissive multi-functional metasurfaces working around 1.3 µm optical communication waveband.
3. Results and discussion
As discussed in Section 2, for efficient wavelength-controlled SPP excitation at both interfaces, the geometrical structure of the transmissive metasurface is required to be symmetric about the z-axis. Figure 2 schematically depicts the structure of the metasurface with the inset showing its symmetric structural unit, which consists of an Au film (thickness t3 = 20 nm) sandwiched by two identical orthogonal I-shaped Au antenna array layers (thickness t1 = 30 nm), with each other separated by SiO2 dielectric spacers (thickness t2 = 50 nm). And the period of the structural unit d is 300 nm, the width of the Au antennas w is 90 nm. As discussed earlier, some incident light at specific wavelength will meet the first or second Kerker condition, or neither of them, then, when the SPP excitation condition in Eq. (2) is also met at the metasurface, it will be subsequently coupled into SPP wave propagating along the upper or lower interface or both of them.
Fig. 2 Schematic of the designed transmissive metasurface, the inset shows a symmetric structural unit.
To obtain the required polarization-dependent transmission phase distributions expressed in Eqs. (2) and (3), the first step is to find their dependence on the arm lengths of the orthogonally I-shaped antennas, Lx and Ly. And we carried out full three-dimensional finite-difference time-domain (FDTD) simulations, in which periodic boundary conditions are applied to the x-and y-directions, and perfectly matched layer condition is used along the z-direction. The gold is modeled with a lossy Drude dispersion, ɛ(ω) = ɛ∞-ωp2∕ω(ω + iγ), where ɛ∞ = 7, ωp = 1.37 × 1016 rad/s, γ = 4.08 × 1013 rad/s and the refractive index of the SiO2 dielectric is set as nd = 1.5.
Figures 3(a) and 3(b) respectively show the simulated transmittance and transmission phase at wavelength λ0 = 1265 nm for X- and Y-polarized incident waves, when varying Lx from 90 nm to 300 nm while fixing Ly = 200 nm. As can be seen, the X-polarized light can excite localized plasmonic resonance for Lx = 195 nm, and the transmission phase varies rapidly from 5° to 345° in the vicinity of the resonance peak. In contrast, for the Y-polarized light, its transmittance is always close to 0°, and both transmittance and transmission phase are nearly insensitive to the variation of Lx. Similarly, if we change Ly while fixing Lx, the Y-polarized wave experiences a significant change in transmittance and transmission phase, while the X-polarized wave is hardly affected (not shown here). Hence, by individually tailoring Lx and Ly of the orthogonally I-shaped antennas, we can independently manipulate the transmission phases of the X- and Y-polarized waves to realize polarization-controllable multiple functionalities.
Fig. 3 The transmittance and transmission phase of (a) X-polarized and (b) Y-polarized EM waves as a function of Lx at wavelength λ0 = 1265 nm.
Now, by fixing other parameters while choosing appropriate Lx and Ly for the constituent antenna units, we design a transmissive multifunctional metasurface, which provides a linear phase distribution along the x-axis for the X-polarized light, and offers a parabolic phase distribution to the Y-polarized light. The phase gradient ξx(x) is set as 1.05k0 (see Eq. (2)) for the X-polarized wave at wavelength λ0 = 1265 nm, and the parabolic phase profile with focal length f0 = 5 µm (see Eq. (3)) is chosen for the Y-polarized wave at the same wavelength.
We first examine the conversion of propagating waves into SPPs. As mentioned above, a metasurface with phase gradient ξx(x)>k0 can convert a normally incident wave into a SPP wave. Figure 4 gives the simulated spectra of reflection (R), transmission (T) and absorption (A) as a function of incident wavelength under the illumination of a normally incident X-polarized wave. Here, the absorption is calculated using A = 1-T-R. Obviously, the absorption spectrum of the metasurface exhibits a typical electromagnetically induced absorption (EIA) feature [38], namely, a narrow absorptive band at wavelength λb = 1265 nm between the two absorption dips at λa = 1247 nm and λc = 1278 nm.
Fig. 4 Simulated reflectance (R), transmittance (T) and absorbance (A) of the transmissive metasurface under the illumination of a normally incident X-polarized light. Points ‘a’, ‘b’ and ‘c’ correspond to the three wavelengths discussed.
In order to elucidate the mechanism of the EIA, we observe the z-component of the electronic filed patterns at wavelengths λa = 1247 nm, λb = 1265 nm and λc = 1278 nm. And Figs. 5(a)-5(c) map their Ez field distributions in the x-z plane, which clearly indicate that, at wavelength λa = 1247 nm or λc = 1278 nm, the excited SPP wave only propagates along the upper or lower interface between the metasurface and the air. While at λb = 1265 nm, two identical SPP waves associated with the upper and lower interfaces become coupled to form a hybrid mode, since the corresponding Ez filed distribution is symmetric about the z axis, this symmetric surface plasmon wave mode is long-range surface plasmon polariton (LRSPP). And LRSPP has drawn much attention owing to that its attenuation coefficient is at least 2 to 3 orders of magnitude lower than that of single-interface SPP [24].
Fig. 5 (a)-(c) Ez field amplitude distributions on the x-z plane under the illumination of the X-polarization light at λa = 1247 nm, λb = 1265 nm and λc = 1278 nm, respectively. The white dashed rectangles denote the location of metasurfaces. (d)-(f) Corresponding normalized Ez field distributions along the z-direction at x = 2.1 µm, where metasurfaces with thickness 180 nm are represented by light blue areas.
Furthermore, we also investigate the corresponding Ez field patterns near the metasurface at x = 2.1 µm, as shown in Figs. 5(d)-5(f). It can be clearly seen that, at wavelength λa = 1247 nm, the excited SPPs are mainly confined to the upper interface between the metasurface and the air, and decay exponentially away from this interface in the air, and the Ez field has positive value in the air. Similarly, at wavelength λc = 1278 nm, the generated SPPs are mainly distributed near the lower interface with a negative-value Ez field. Namely, the Ez fields at λa = 1247 nm and λc = 1278 nm have opposite signs, indicating these two Ez fields are out-of-phase, which results in the EIA phenomenon [38,39]. And this phenomenon can also be observed from Figs. 5(a) and 5(c), the peak locations of the SPPs at λa = 1247 nm correspond to the valley positions of the SPPs at λc = 1278 nm. While at wavelength λb = 1265 nm, the excited SPPs exhibit a symmetrical profile across the metasurface along the z-direction. These results suggest that we can indeed control the excited SPPs to propagate along the upper or lower interface of the metasurface, or along both of them, depending on the incident wavelengths of the X-polarized incident waves. It should be noted that, for all the three cases, there are also significant Ez fields in the dielectric layer of the metasurface. Due to the continuity of the electric displacement vector at the boundaries, the normal component of electric field (i.e., Ez) in the dielectric gap between the Au film and Au antennas is increased by a factor of (nm/nd)2, where nm is the index of the Au, and nd is the index of the SiO2 dielectric [40].
We now examine the focusing performance of the transmissive multifunctional metasurface. And the required phase distribution can be obtained from Eq. (3). When a Y-polarized wave normally illuminates the designed metasurface, the electric intensity patterns at the above three wavelengths are shown in Figs. 6(a)-6(c). Two focal points are clearly visible away from the metasurface, with one for transmissive beam and the other for the reflected beam. Namely, we realize a plasmonic flat focus lens with dual focal points [12]. This is because that neither the first nor the second Kerker condition is satisfied at this three wavelengths for Y-polarized wave, thereby the focused reflected and transmitted beams are simultaneously obtained by the metasurface of symmetric structure. The reason is that the structural units composing of the metasurface are anisotropic and possess strong polarization dependence, i.e., the electromagnetic responses are different for X- and Y-polarized incident waves. It should be mentioned that the strong oscillating pattern within 2.5 µm above the metasurface is due to the interference effect of the incident and reflected optical beams.
Fig. 6 Intensity distributions of electric field in the x-z plane under the illumination of the Y-polarization light at wavelengths (a) λa = 1247 nm, (b) λb = 1265 nm and (c) λc = 1278 nm, where the white dashed rectangles denote the location of the metasurface.
For a quantitative analysis of the focusing characteristics, some specific parameters as depicted in Figs. 7(a)-7(c) are investigated, and the focal length, depth of focus (DOF) for reflective and transmissive beams are also given in Table 1. Generally speaking, the focal points are around f0 = 5 µm, which are in relatively good agreement with the desired values. And DOF is about 1.6 µm, slightly larger than the incident wavelength, which shows this metasurface-based flat lens has good focusing property. It is noted that the transmissive and the reflective focusing characteristics, such as focal length and DOF, are slightly asymmetric, this is because the transmissive and the reflective optical beams experience different optical phase shift in the metasurface.
Fig. 7 Cross-section of intensity profile at x = 0 µm under the illumination of the Y-polarization light at wavelengths (a) λa = 1247 nm, (b) λb = 1265 nm and (c) λc = 1278 nm
Table 1. Focal length, DOF for reflective and transmissive beams.
4. Conclusion
To summarize, we demonstrate a transmissive multifunctional metasurface by introducing independent phase profiles to each of the two orthogonal polarizations. This multifunctional metasurface works as a flat focusing lens for Y-polarized incident light or as an SPP coupler for X-polarized incident light. More importantly, by tuning the wavelength of X-polarized incident beams, it can also control the confinement region of the excited SPP waves, making them travel along the upper or lower interface or along both of them according to whether the incident waves meet the first or second Kerker condition. Though the proposed device works around the 1.3 µm optical communication band, by properly scaling the unit size, operation wavelength could be extended to other spectral ranges, such as millimeter wave, terahertz, or even visible range. We believe that this polarization-switchable and wavelength-controllable multifunctional metasurface may open a new avenue to design tunable plasmonic metasurfaces and also find potential applications in highly integrated photonic systems.
Funding
National Natural Science Foundation of China (NSFC) (No. 61675074).
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