1. Introduction

In the strive to minituarize photonics to the scale comparable with electronics, controlling the flow of light at the micro- and nanoscale is at the heart of current nanophotonic research. One approach that has been extensively explored in recent years is man-made materials, the so-called metamaterials, in which almost arbitrary values of the permittivity and permeability can be obtained by structuring the artificial material on a subwavelength scale with, e.g., resonant plasmonic nanostructures. The expansion of the material parameter space has led to fascinating new discoveries, such as negative refraction [1, 2], super imaging [3, 4], invisibility cloaks [5, 6], and metamaterial nanocircuits [7, 8]. The widespread usage of plasmonic metamaterials at visible and near-infrared wavelengths, however, is currently limited by the high losses related to Ohmic heating in metals [9] and the difficulty in fabrication.

An alternative approach that has gained increasing attention in recent years deals with one- and two-dimensional (1D and 2D) plasmonic arrays with subwavelength periodicity, also known as metasurfaces. Due to their negligible thickness compared to the wavelength of operation, metasurfaces can (near resonances of unit cell constituents) be considered as an interface of discontinuity enforcing an abrupt change in both the amplitude and phase of the impinging light [10]. Accordingly, metasurfaces based on resonant scatterers may function as compact and planar optical elements, as has been demonstrated by the design of wave plates [11–13], wavelength-selective surfaces [14, 15], and lenses [16] – the latter functionality is achieved by gradient (i.e., inhomogeneous) metasurfaces. It is worth noting that the resonant elements constituting the metasurfaces possess a Lorentzian-like polarizability, thus limiting the possible change of transmission/reflection phase to π. In order to reach the full phase space of 2π, two different approaches are typically employed. In the first approach, the 2π-space is reached by only manipulating light that is cross-polarized relative to the incident field, which by a proper design of gradient metasurfaces has led to the laws of generalized refraction and reflection [17–19], a variety of flat optical components [20–23], and metasurfaces converting propagating waves to surface waves [24]. Nevertheless, the cross-polarization condition sets an upper limit to the efficiency of the devices that is theoretically estimated to ∼ 25% in the case of negligible material loss [25]. The second approach borrows the design of reflectarray antennas [26] in which the metasurface is placed in proximity of a metal substrate, only separated by an optically thin dielectric spacer. These kind of metal-backed metasurfaces only work in reflection mode, but the advantage is the high efficiency of light manipulation, reaching 100% in the lossless case. Accordingly, metal-backed metasurfaces may function as efficient wave plates [27–29], blazed gratings [30], focusing mirrors [31, 32], and devices interfacing propagating and surface waves [33, 34]. However, the most attractive feature lies in the ability to design gradient birefringent metasurfaces [35,36] with functionalities not otherwise accessible with conventional optical components. For example, we have recently demonstrated how the reflection phase of orthogonally polarized light at the wavelength around 800 nm can be controlled efficiently and independently, hereby allowing one to design polarization beam-splitters and polarization-independent beam steering devices [36].

In this paper, we continue the work on gradient birefringent metasurfaces, but first we take one step back and start off by discussing the very basic element of metal-backed metasurfaces, i.e., metal-insulator-metal (MIM) resonators. In the view of MIM structures as gap-surface plasmon (GSP) resonators [37, 38], we numerically study the optical properties of three different configurations of 2D GSP-resonators, followed by a GSP interpretation of the (almost) 2π-phase control in GSP-based (i.e., metal-backed) metasurfaces. Next, we show how one can extend the range of functionality of GSP-based birefringent metasurfaces by employing a combination of nanobrick and nanocross elements. The approach is exemplified by the design of a blazed grating-like metasurface in which two orthogonal polarization states are anomalously reflected into +2 and −3 diffraction order, respectively, with an efficiency up to ∼ 80% at the design wavelength 800 nm. Finally, we introduce the concept of metascatterers, which are wavelength-sized polarization-sensitive scatterers that can be viewed as a single super cell of a metasurface with a specific functionality. The concept is demonstrated by the design of a polarization beam-splitter metascatterer that scatters light of orthogonal polarizations into orthogonal directions in the near- and intermediate-field zones.

In this work, all modeling results have been obtained with the commercial finite element software COMSOL Multiphysics where the refractive indexes of gold and silicon dioxide (SiO₂) are described by an interpolation of experimental data [39] and the constant value n_SiO2 = 1.45, respectively. The gold-SiO₂ structures are in all simulations surrounded by air.

2. Gap-surface plasmon resonators

We begin the discussion of GSP-resonators by revisiting the 2D configuration shown in Fig. 1(a), which consists of two metal strips of width w and thickness t, separated by a dielectric spacer of height d. This type of configuration has been studied quite extensively in the past with respect to its scattering properties [38,40,41], and within the metamaterial community it is also known as a magnetic meta-atom [42, 43]. Nonetheless, there is (to the best of our knowledge) still no study on how both scattering and absorption is influenced by geometrical parameters, nor is it clear how the lowest order multipoles contribute to the scattering. These questions are discussed in the following.

 

Fig. 1 (a) Sketch of a two-dimensional gold-SiO₂-gold resonator surrounded by air. The incident field is TM-polarized and propagates along the y-axis. (b) Scattering and absorption cross sections (CS) normalized to the width w of the gold strips for three different combinations of w and d. The strip thickness is fixed at t = 30 nm.

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The configuration in Fig. 1(a) is often interpreted as a hybridized system with a high-energy symmetric mode (parallel polarization currents) and a low-energy anti-symmetric mode (anti-parallel polarization currents) [44]. Although this being true, the asymmetric mode is in the retardation-based regime related to the lowest order GSP mode originating from efficient reflection of the GSP at the structure terminations. The resonance position of these standing-wave GSP modes can be described by a simple Fabry-Perot resonator formula [40]:

In order to gain further insight into the control of scattering losses with GSP resonators, we have multipole expanded the induced polarization current [50] and subsequently calculated the power scattered by the lowest order multipoles [Figs. 2(a) and 2(b)]. Note that the small discrepancy between the numerically exact scattering CS and the multipole calculation owes to the approximations involved in the latter approach. It is clearly seen that the scattering at the GSP resonance is dominated by the magnetic dipole (MD) and a contribution from the electric dipole (ED) mode situated at lower wavelengths. The electric quadrupole (EQ) moment is also considered, but it is evident that the scattering is approximately one order of magnitude smaller than MD scattering making the contribution rather small. Looking at the field plots and polarization currents of the two modes [Figs. 2(c) and 2(d)], it is apparent that they represent different multipoles. The GSP mode at 800 nm shows a characteristic MD response with out-of-phase currents in the gold strips and a minimum of the E-field in the center of the gap (corresponding to a maximum of the H-field). One should, however, note that the field distribution in Fig. 2(d) also represents a standing GSP wave of first order (p = 1) and, hence, demonstrates how the intuitive GSP picture (discussed above) complements the magnetic resonator view. For this reason, we can equally well describe the strong dependence of scattering losses on the gap height d by the fact that power scattered by MD is proportional to A², where A is the area of the resonator. For example, if we consider the gold strips in Fig 1(a) to effectively behave as detuned EDs at the height y = ±(d + t)/2, respectively, the effective area is A = w(t + d) and an increase in d from 10 nm (w = 84 nm) to 50 nm (w = 145 nm) would change the normalized MD scattering CS by a factor of ∼ 7, which is in perfect agreement with the calculations in Figs. 2(a) and 2(b).

 

Fig. 2 (a,b) Contribution to the scattering cross section (SCS) from the lowest order multi-poles (ED=electric dipole, MD=magnetic dipole, EQ=electric quadrupole). SCS is normalized with the resonator width w, and t = 30 nm [see Fig. 1(a)]. Note that in order to compare the relative contributions to the scattering from MD and EQ, we choose the center of mass as the coordinate origin. (c,d) Electric field enhancement at the ED mode (λ = 585 nm) and GSP mode (λ = 800 nm). The color bars are chosen as to emphasize the mode profiles rather than the high electrostatic field enhancement at the corners. Arrows indicate the direction of polarization current at a representative moment of time.

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Gap-surface plasmon resonators are not limited to the highly symmetric configuration in Fig. 1(a), but can just as well consist of different-sized metal strips or even one metal part being of infinite extend [51, 52]. Here, we focus on the latter case where the lower gold strip is replaced by an optically thick gold substrate [see inset of Fig. 3(a)]. This kind of resonators has the property that part of the scattered light will couple to surface plasmon polaritons (SPPs) propagating along the metal-air interface, eventually being converted into heat. Figure 3(a) shows normalized scattering, absorption and SPP cross sections for the parameters defined in the inset, where the SPP CS is obtained by subtracting the amount of power scattered through a hypothetical semicircle of radius 1 μm (centered at the resonator) with the amount of power reaching the far field. One should note that the scattered power does not include light specularly reflected by the gold substrate, and that the evaluation distance of 1 μm is taken from Ref. [52]. Absorption CS includes the Ohmic losses in the gold strip and the energy absorbed in the nearby substrate due to the presence of the gold strip. Comparing the lower sub-figure of Fig. 1(b) with Fig. 3(a), we see that the resonance position is red-shifted ∼ 25 nm, which is a consequence of the less sharp terminations of the resonator, allowing GSPs to experience a resonator of slightly larger effective width. The second noticeable difference between the two configurations is concerned with the two-fold increase in scattering CS. The stronger scattering arises due to the less effective reflection of the GSP at resonator boundaries, hereby permitting more efficient coupling between GSP and far-field propagating waves. That said, comparing Figs. 2(d) and 3(c), it is evident that the resonance at λ = 825 nm is the first order GSP mode or, equivalently, the magnetic dipole resonance.

 

Fig. 3 (a,b) Scattering, absorption, and SPP cross sections normalized to the width w of the gold strip for normal incident TM-polarized light. The Insets show the configurations and dimensions of the GSP resonators. (c,d) Electric field enhancement at the GSP mode for the configurations in a) and b), respectively. The color bars are chosen as to visualize the mode profiles rather than the high electrostatic field enhancement at the corners. Arrows indicate the direction of polarization current at a representative moment of time.

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As a third kind of GSP resonator, one may also allow the dielectric spacer to be continuous [see Inset of Fig. 3(b)]. This kind of configuration is known as a continuous-layer GSP resonator and has the attractive properties of usual GSP resonators with the added advantage that it, using electron-beam lithography, can be fabricated by only depositing gold in the resist profile [53]. Using the same parameters as for the other two configurations, we see that scattering is again the dominating loss mechanism with a peak maximum at λ = 915 nm [Fig. 3(b)], corresponding to the excitation of the GSP mode [Fig. 3(d)]. This strong red-shift of the GSP mode compared to the second configuration [Fig. 3(a)] is caused by the removal of the horizontal refractive index contrast between air and SiO₂, resulting in a larger amount of the mode energy being stored in the dielectric spacer.

Having discussed characteristic optical properties of different GSP resonator designs, we now turn our attention to GSP-based metasurfaces. Moreover, we concentrate on the third kind of GSP resonators in which the upper metal layer now consists of a periodic arrangement of gold nanostrips separated by the interparticle distance Λ [Fig. 4(a)]. As GSP-based metasurfaces, by definition, consists of subwavelength unit cells (Λ ≪ λ), their optical properties can conveniently be described by the complex reflection coefficient r. This is exemplified in Fig. 4(b), where the reflection coefficient is calculated as a function of the strip width w when all other parameters are fixed (λ = 800 nm, Λ = 260 nm, d = 50 nm, and t = 30 nm). Characteristic of GSP-based metasurfaces, we see a strong variation of the reflection phase (∼ 275°) and a dip in the reflection amplitude (|r| = 0.88) around the GSP resonance at w = 115 nm. One should note that the rather shallow dip in Fig. 4(b) is a result of the strongly scattering GSP resonators [Fig. 3(b)]. In general, their is a trade-off between the attainable phase-space and the strength of the dip in reflection amplitude. For example, by decreasing the spacer thickness d, it is possible to approach the full 2π-phase space but at the cost of strong absorption near the GSP resonance. We would like to emphasize that the optical response of metal-backed metasurfaces can be described by a combination of homogenization and transmission line theory [28], or, as often used at radio frequencies, by an electric circuit model approach [54]. Here, however, we describe the functionality of GSP-based metasurfaces using the GSP picture and focusing on the transport of energy at the nanoscale. Figure 4(c) displays the electric field enhancement (color map) and the Poynting’s vector of the reflected light (arrows) for three strip widths corresponding to below, at, and above the GSP resonance [see Fig. 4(b)]. For small strip widths (w = 50 nm), it is seen that light is mainly reflected from the gold substrate, which owes to the small fraction of the unit cell being occupied by the strip. The situation is different above the GSP resonance (w = 200 nm), where the large strips ensure that light is primarily reflected from their upper surface. As the gap height d is deeply subwavelength, the strong variation in reflection phase relates to the excitation of the GSP that is being efficiently reflected at resonator boundaries near resonance, hereby accumulating phase as it propagates back and forth in the resonator until the mode is damped by mainly radiation into free space. This interpretation is supported by Fig. 4(c) (w = 115 nm), where it is evident that reflected light leaving the metasurface is coming from beneath the gold strip.

 

Fig. 4 (a) Sketch of 1D-periodic GSP-based metasurface. The incident field is TM-polarized and propagates normal to the surface. (b) Amplitude and phase of reflected light from metasurface in a) as a function of strip width w when λ = 800 nm, Λ = 260 nm, d = 50 nm, and t = 30 nm. The time convention is exp(−iωt). (c) Color maps show electric field enhancement within one unit cell of the metasurface for three different widths of the strips. Arrows represent the strength and direction of Poynting’s vector of the reflected light in the air and spacer region.

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3. Birefringent metasurfaces

In this section, we discuss the practical realization of 2D-periodic GSP-based metasurfaces with polarization-sensitive responses. Such birefringent metasurfaces were already discussed and experimentally verified in [36], however, it was at the same time noted that the exclusive usage of nanobrick unit cells [see Fig. 5(a)] constrained the possible metasurface functionality. Here, we overcome those constrains by combining unit cells consisting of nanobricks and nanocrosses [see Fig. 5(c)].

 

Fig. 5 (a) Sketch of unit cell of nanobrick metasurface. (b) Calculated reflection coefficient r as a function of nanobrick widths for Λ = 240 nm, d = t = 50 nm, and λ = 800 nm. Color map shows the reflection coefficient amplitude for TM polarization, while lines are contours of the reflection phase for both TM and TE polarization. Note that the reflection amplitude map for TE polarization can be obtained by mirroring the map for TM polarization along the line L_x = L_y. (c) Sketch of unit cell of nanocross metasurface. (d) Reflection coefficient as a function of nanocross arm lengths (L_x and L_y) for two values of w. The other parameters are as in b).

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Concerning nanobrick metasurfaces, the basic unit cell is of the continuous-layer GSP-type in which the gold nanobrick is characterized by the widths L_x and L_y and height t [Fig. 5(a)]. The nanobrick widths can be considered the two degrees of freedom (DOF), as we in the following fix the unit cell period Λ = 240 nm, the spacer thickness d = 50 nm, and the nanobrick height t = 50 nm. The design wavelength is 800 nm and the incident field propagates normal to the surface with polarization along either the x-axis (TM) or y-axis (transverse electric: TE). Studying the reflection of light as a function of L_x and L_y [Fig. 5(b)], one notices how the excitation of the GSP mode results in a decrease of the reflection amplitude and in a fast variation of the reflection phase. That said, the nanobrick metasurface has the favorable property that it is strongly reflective in a large part of the (L_x, L_y)-space. The drawback is the diverging equidistant contour lines of the reflection phase for increasing nanobrick size, hereby refraining all TM and TE contour lines to intersect each other. Consequently, it is not possible to design an element with arbitrary phase for both TM and TE polarization. In order to solve this issue, we study nanocross metasurfaces [Fig. 5(c)] where the arm width w is an additional DOF that can be used to control the reflected light. Clearly, the nanocross arm width allows one to control the range of reflection phase at the expense of a more pronounced absorption band throughout the (L_x, L_y)-space [Fig. 5(d)]. Moreover, the reflection phase contour lines are almost parallel, causing all the TM and TE contour lines to intersect each other. For this reason, nanocross metasurfaces give us the opportunity to design elements with arbitrary reflection phases (within the attainable phase range) for TM and TE polarization, though the presence of the absorption bands may degrade the performance of birefringent metasurfaces. Accordingly, we aim at using nanobrick elements when ever possible and resort to a nanocross design when needed. One should note that the difference in reflection maps for nanobrick and nanocross metasurfaces [Figs. 5(b) and 5(d)] is directly related to the geometrical influence on the resonance properties of the corresponding GSP modes. Particularly, the general narrow arm width w of nanocrosses compared to the arm lengths L_x and L_y ensures that the GSP resonance, corresponding to a standing-wave resonance in either x- or y-direction, is mainly determined by L_x, w and L_y, w for TM- and TE-polarized light, respectively. The outcome is the (almost) parallel reflection-phase contour lines and the pronounced absorption band being, for TM-polarized light, practically independent of L_y [Fig. 5(d)]. Nanobrick metasurfaces with only two DOF, on the other hand, do show resonance properties that are influenced by the brick dimension perpendicular to the standing-wave direction since this dimension serves as the width similar to w in nanocrosses. Accordingly, we see a reflection map that strongly depends on both L_x and L_y [Fig. 5(b)].

As a way of demonstrating the improved control of reflected light with a combination of nanobrick and nanocross elements, we now design a gradient birefringent metasurface that anomalously reflect TM and TE waves at different angles. According to the equivalence between the generalized laws of refraction and reflection and diffraction theory, our design may also be viewed as flat blazed gratings for each polarization, where the angle of anomalous reflection is equal to the first order diffraction angle [55]. For this reason, we can construct a polarization beam splitter by realizing a metasurface with a linear phase gradient that is different for the two polarizations. To be specific, we will implement the reflection coefficient $r(x)=A\text{exp}(\pm i2\pi x/{\mathrm{\Lambda }}_{sc}^{(\pm )})$, where A ≤ 1 is the amplitude constant, x is the spatial coordinate, and $\pm {\mathrm{\Lambda }}_{sc}^{(\pm )}$ is the sign-factor multiplied with the super cell periodicity that depends on the polarization. Such a design can be derived from Figs. 5(b) and 5(d), where the reflection phase for TM (TE) polarization is discretized into six (four) contour lines with a 60° (90°) step, which results in a super cell period of ${\mathrm{\Lambda }}_{sc}^{(+)}=6\mathrm{\Lambda }\hspace{0.17em}\hspace{0.17em}({\mathrm{\Lambda }}_{sc}^{(-)}=4\mathrm{\Lambda })$, causing normal incident light to be reflected into first diffraction order at the angle of 33.7° (−56.4°). The different periodicity for TM and TE polarization results in an overall super cell of size Λ_sc = 12Λ in the x-direction, meaning that TM and TE polarized waves are effectively diffracted into +2 and −3 diffraction order, respectively. Retuning to Figs. 5(b) and 5(d), we realize that the super cell size of 12Λ, with linear (but different) phase gradients for both polarizations, requires twelve differently-sized nanobricks and nanocrosses whose dimensions are determined by the intersections of the phase contour lines marked with circles. Note how each phase contour line for TM- and TE-polarization is utilized two and three times, respectively, to take into account the different periodicity for orthogonal polarizations. The super cell of the birefringent metasurface is then obtained by placing the twelve elements with an interparticle separation of Λ = 240 nm and in an order that makes the reflection phase change linearly as a function of the x-coordinate for both orthogonal polarizations [Fig. 6(a)]. One should note that the success of this approach relies on the assumption that the coupling between neighboring elements is weak. Furthermore, it is worth noting that despite the seemingly complexity of the designed super cell [Fig. 6(a)], the birefringent metasurface can still be fabricated in one step of lithography.

 

Fig. 6 (a) Super cell of gradient birefringent metasurface functioning as a polarization beam splitter: TM (TE) waves are reflected into +2 (−3) diffraction order. (b,c) Theoretical performance of the metasurface for TM polarization, displaying b) the x-component of the reflected E-field ( $E_x^r$) just above the metasurface at the design wavelength (the amplitude of the incident E-field is 1 V/m), and c) amount of incident light reflected into the |m| ≤ 3 diffraction orders as a function of wavelength. (d,e) Performance of the metasurface for TE polarization.

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The performance of the designed metasurface is studied numerically, and Figs. 6(b) and 6(d) display the reflected E-field just above the metasurface for TM and TE incident waves, respectively. It is readily seen how the two orthogonal polarizations are reflected at different angles and opposite sides of the surface normal, corresponding to the +2 and −3 diffraction order. The less perfect plane wave construction for TE polarization [Fig. 6(d)] compared to TM polarization [Fig. 6(b)] is a result of the more apparent stair-casing of the linear phase profile for TE polarization (phase is discretized in steps of 90°). The performance of the birefringent metasurface is quantified by calculating the amount of light reflected into diffraction orders |m| ≤ 3 as a function of wavelength [Figs. 6(c) and 6(e)]. As expected, practically all light is reflected into +2 diffraction order for TM polarization at the design wavelength of 800 nm, with the total reflectivity being limited to ∼ 80% because of Ohmic losses [Fig. 6(c)]. Furthermore, it is evident that the metasurface shows a broadband response with reasonable performance in the wavelength range ∼ 700–950 nm. The performance is slight decreased for TE polarization, where ∼ 70% of the incident light reflects into the −3 diffraction order out of a total reflectivity of ∼ 75% at the design wavelength [Fig. 6(e)]. Likewise, we see a slight narrowing of the operation bandwidth (∼ 700–900 nm), which is caused by the fast decrease in performance on the long-wavelength side of λ = 800 nm and related to the fact that the third diffraction order disappears at λ = 4Λ = 960 nm.

As a final remark, it should be noted that metasurfaces based on gold nanostructures have an intrinsic lowest operating wavelength of λ ∼ 550 nm, corresponding to the onset of strong absorption in gold. Away from this lower wavelength-limit, however, metasurface designs should still satisfy the criterion of subwavelength-sized unit cells, which, following metamaterial homogenization theory [56], can be stated as λ > 2Λ. In practical designs (see, e.g., Fig. 6), though, it seems that the lower wavelength limit is dictated by the degradation of metasurface performance when moving away from the design wavelength rather than by the unit cell size criterion.

4. Metascatterers

In the remaining part of this paper, we would like to introduce the concept of metascatterers, which are polarization-sensitive wavelength-sized scatterers. We would like to emphasize that such metascatterers can, in principle, be constructed by controlling the scattered field of the individual subwavelength elements making up the metascatterer. Here, however, the parameters of the scatterer are designed in the same way as for birefringent metasurfaces, but at the implementation stage only a single super cell, functioning as the metascatterer, is retained. The proposed procedure is valid due to the weak coupling between neighboring elements in meta-surfaces [36], and it allows us to make a clear link between meta-surfaces and -scatterers.

As a way of example, we design a GSP-based metascatterer with a linear phase profile that scatters light of orthogonal polarization into orthogonal directions, which corresponds to the polarization-dependent reflection coefficient r(q) = Aexp(i2πq/Λ_sc), where q is the x- and y-coordinate for TM and TE polarizations, respectively. Using the same geometrical parameters as in the birefringent metasurface example and a design wavelength of 800 nm, Figs. 7(a) and 7(b) replicate the reflection maps for nanobrick and nanocross (w = 50 nm) metasurfaces. This time, however, the constant-phase contour lines are discretized in steps of 90° for both polarization states, meaning that the super cell periodicity is Λ_sc = 4Λ in both the x- and y-direction. Accordingly, the super cell, i.e., metascatterer, must contain sixteen different elements, which corresponds to all possible intersections of the reflection phase contour lines, marked with circles in Figs. 7(a) and 7(b). A top-view of the metascatterer is shown in Fig. 7(c), while Fig. 7(d) depicts, in spherical coordinates, the direction of reflected/scattered light on a hemispherical surface two wavelengths away from the metascatterer when the normal incident wave is a Gaussian beam with beam radius w₀ = 800 nm. It is clearly seen that the scattering properties of the metascatterer are the same for TM and TE polarizations, with the only difference that light is scattered into orthogonal directions. Furthermore, one notices that the scattered light seems to occupy three regions of space. The first region, corresponding to the polar angle θ = 0°, is the specularly reflected (i.e., backward scattered) light, occurring as not all incident light interacts with the metascatterer. The second region, which is centered around (θ, ϕ)=(50°, 0°) for TM polarization, is the part of light scattered by the metascatterer, and the θ-angle is closely related to the first order diffraction angle of the associated metasurface ( ${\theta }_r^{(1)}=56.4°$). Finally, the third region [(θ, ϕ)=(90°, 0°) for TM polarization] is associated with directional excitation of SPPs along the gold-air interface. One should note that the angular distribution of scattered light in Fig. 7(d) changes with the distance to the hypothetical hemisphere on which the Poynting vector is evaluated. The reason is that light scattered by a wavelength-sized scatterer is strongly divergent, resulting in a progressively less confined spot as one moves into the far-field. Consequently, the scattered far-field will be dominated by the specularly reflected light (at θ ∼ 0°), unless one resorts to a metascatterer consisting of several super cells or even a regular metasurface.

 

Fig. 7 (a,b) Calculated reflection coefficient r as a function of L_x and L_y for nanobrick and nanocross (w = 50 nm) metasurfaces, respectively. The parameters are Λ = 240 nm, d = t = 50 nm, and λ = 800 nm [see, e.g., Figs. 5(a) and 5(c)]. Color map shows the reflection coefficient amplitude for TM polarization, while lines are contours of the reflection phase for both TM and TE polarization. Note that the reflection amplitude map for TE polarization can be obtained by mirroring the map for TM polarization along the line L_x = L_y. (c) Top-view of metascatterer functioning as wavelength-sized polarization beam splitter: TM and TE waves are scattered into orthogonal directions. (d) Normalized Poynting’s vector of reflected/scattered light evaluated on a hemispherical surface with radius 1.6 μm centered at the metascatterer. The incident wave is a TM or TE polarized Gaussian beam with beam radius w₀ = 800 nm propagating normal to the surface. The power flow is displayed in spherical coordinates, where the polar angle θ (measured from the z-axis) is represented by the radial distance, whereas the azimuthal angle ϕ (counted in the xy-plane from the x-axis) is displayed in the figure plane with the x-axis being horizontal.

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From the above discussion, it is clear that the functionality of metascatterers is mostly pronounced in the near- and intermediate-field zones and, hence, can be of interest in ultracompact nanophotonic systems. Moreover, we envision that the polarization-sensitive response of metas-catterers (and birefringent metasurfaces as well) represents a new way to design optical devices with unforeseen functionality, among these polarization and spectral beam splitters with wave propagation in orthogonal directions, polarization-dependent functionality such as combined beam-splitting and beam-focusing, or polarization converters. In addition, metascatterers or their periodic arrays may solve the tantalizing problem of efficient unidirectional polarization-controlled excitation of surface plasmon polaritons [24, 57]. As a final comment, it should be noted that anisotropic scattering can be realized with photonic crystals [58], but, in order for this feature to appear in the scattering by a small volume (like in metascatterers), the latter should still contain a few crystal units, i.e., to be substantially larger than the wavelength.

5. Conclusion

In summary, we have numerically studied the optical properties of three different configurations of 2D MIM-resonators, emphasizing the equivalence between first order GSP modes and magnetic dipole resonances, and how resonators can be designed to mainly absorb or scatter light. The GSP interpretation is further applied to 1D-periodic metal-backed metasurfaces, allowing one to intuitively explain the almost 2π-phase control of reflected light.

In relation to the design of complex birefringent metasurfaces, we have studied the reflection from GSP-based nanobrick and nanocross metasurfaces, underlining the advantages and disadvantages of the two types of metal-backed surfaces. From this discussion, it is clear that the simultaneous phase control of orthogonally polarized light in reflection can be significantly improved by combining nanobrick and nanocross elements within one birefringent metasurface. As a way of example, we construct a blazed grating-like polarization-sensitive metasurface in which orthogonal polarization states are reflected into +2 and −3 diffraction order, respectively. Numerical modeling confirms the designed functionality, demonstrating reflectivity up to ∼ 80% in the specific diffraction orders and a broadband response covering ∼ 20% of the design wavelength (800 nm).

Finally, we have introduced the concept of metascatterers, which is wavelength-sized polarization-sensitive scatterers. Metascatterers can be constructed following the design approach of birefringent metasurfaces, with the only difference that it is the super cell that defines the metascatterer. The concept is exemplified by the design of a GSP-based polarization beam splitter in which orthogonal polarized light is scattered into orthogonal directions. Due to the nature of light, the functionality of metascatterers is mostly pronounced in the near- and intermediate-field zones. For this reason, we envision that devices based on metascatterers can be of interest in ultracompact nanophotonic systems.