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In this work, plasmonic metasurfaces with abrupt phase discontinuities operating in high order modes are investigated for manipulating the wavefront of light. We first design two types of meta-super-cells consisting of V-shaped antennas with the phase shift coverage larger than 2π. And then, we create two linear gradient phased metasurfaces using the designed cells, which exhibit exceptional abilities for light-steering functioned as meta-echelette gratings operating in high order diffraction modes, may be valuable for using in high resolution spectrographs and advantage to achieve high numerical aperture plasmonic lenses. Based on the new designed super cells we further build another two azimuthal gradient phased metasurfaces that are able to generate high order optical vortex beams. Our results could lead to wide applications in photonic research.
© 2016 Optical Society of America
1. Introduction
Metasurfaces typically consist of a two-dimensional array of photonic resonators with subwavelength separation, which exhibit unusual abilities of manipulating electromagnetic waves and promise many intriguing applications [1,2 ]. In particular, combining with the concept of phase discontinuities, a number of novel wave-manipulation scenarios have been proposed and demonstrated [3–21 ]. For instance, it was shown that plasmonic metasurfaces composed by V-shaped optical antennas with gradient phase profile along the interface would bend the reflected and refracted light beams into anomalous directions [3]. Metasurfaces consisting of orientated dipole antenna array support anomalous refraction/reflection for circularly polarized waves over a broadband wavelength range [4]. Metal-insulator-metal configuration metasurfaces can efficiently convert a propagating wave to a surface wave as long as the phase gradient is designed properly [5]. Such reflection-type metasurfaces has been designed to function as flat focusing mirrors [6] and holographic devices [7] as well. Moreover, other recent studies showed that metasurfaces can be used as broadband infrared chemical sensors [8], planar subwavelength spatial light modulators [8], vortex beam generators [9,10 ] and aberration-free wave plates [11], etc. However, it is noted that almost all of the functionalities of metasurfaces presented in previous works are just based on the fundamental mode, namely the metasurfaces is working in ± 1st order diffraction modes, few of them use high order modes to manipulate the wavefront of light [3–21 ].
Here we propose an alternative approach to control the wavefront of light using the concept of abrupt phase discontinuities operating in high order modes. Planar V-shaped resonant antennas, thanks to their greatly adjustable optical properties and the ease of fabrication in the micro/nano-scale, have been widely used to realize plasmonic metasurfaces with their desirable properties and have become a quintessential example in the family of metasurfaces [3,8,9,11–14 ]. In the present work, the similar structures are adopted to illustrate our idea. However, it should be noted that our methodology and conclusions drawn in the work are applicable to the other abrupt phase discontinuity metasurfaces (such as, dielectric metasurfaces [22,23 ]) as well. We first design two types of meta-super-cells comprised of V-shaped antennas with phase shifts covering larger than 2π. And then, we create two linear gradient phased metasurfaces (LGPMs) using the designed cells, which enable to drastically bend light in unusual ways compared to the one made of the unit with phase shift coverage only 2π. Our proposed metasurfaces can be viewed functionally as novel echelette gratings [24,25 ] operating in high diffraction orders but with their own peculiar features such as easier preparation and broadband wave manipulation performance. To display the versatility of such idea, based on the new designed super cells we further build another two azimuthal gradient phased metasurfaces (AGPMs) that are able to generate high order optical vortex beams.
2. Design and analysis
As schematically shown in the inset of Fig. 1 , the building block of the concerned structures is a plasmonic nanoantenna constructed by two rectangular gold arms forming a V-shape with a splitting angle α. The azimuthal angle between the symmetry center of the antenna and the x axis is denoted by β. The length, width and thickness of the arms are represented by l, w and t, respectively. It has been demonstrated that by properly choosing the geometric parameters of the antennas in an array, one can introduce an abrupt phase discontinuity along an interface constructed by the antennas, and then impart additionally phase shift to the cross-polarized scattered light in the optical path, which can provide an alternative way to tailor the scattered wavefront. The first row of the bottom panel of Fig. 1 shows a super cell (denoted by C1, as control sample) of a plasmonic metasurface, which consists of seven antennas reproduced with a periodicity of P = 7a in the x direction and a in the y direction, where a denotes the spacing between the antennas. The parameters of the antennas are engineered in the cell to have uniform scattering amplitudes and a constant interval of phase difference about 2π/7 between neighbours, thereby providing a total phase shift coverage of 2π for the cross-polarized scattered light (green dashed line with triangles shown in Fig. 1).
Fig. 1 Phase shift and amplitude in cross-polarization for three sets of V-shaped antennas. The inset shows a schematic of a constituent antenna. C1: a super cell of the control sample, which provides phase shifts covering [0, 2π] range for the cross-polarized light. S1 and S2: two new proposed super cells, where the coverage of their phase shifts have been extended to 2*2π and 3*2π.
The second row of the bottom panel of Fig. 1 depicts a new designed super cell (denoted by S1). In comparison to the control super cell, it seems that we just simply rearrange the order of the antennas in the new one (selecting every other element from a periodic array consisting of the control super cell), whereas the particularity of the strategy is that the phase coverage of our super cell has been extended far beyond 2π, covering from 0-to-2*2π (with increments of 4π/7) for the cross-polarized light (navy-blue dashed line with spheres shown in Fig. 1). More importantly, this strategy would endow the plasmonic metasurfaces with some specific physical properties applicable for many interesting applications. For instance, a LGPM made of the new designed super cell, it is applicable to mold the wavefront of light, and the resulted bending angles of the anomalous refraction and reflection should be larger than the ones exhibited by an interface constructed by the control super cell, which would be helpful for creating focusing flat lenses with high numerical aperture [11]. An AGPM with phase shift coverage of 2*2π, which can facilitate to yield more complex formation of wavefront such as generating second charged optical vortex beams.
Another newly developed super cell (denoted by S2) is schematically shown in the third row of the bottom panel of Fig. 1, which is also comprised of the same set of seven antennas. In contrast to the above two cells, the sequence of antennas has been rearranged again (selecting every three elements from a periodic array consisting of the control super cell) in order to cover a larger phase range [0, 3*2π], as presented by red dashed line with stars in Fig. 1. As a result, a device made of this kind of super cell is capable of steering the wave with much larger anomalous bending angles or can be used to create higher order mode optical vortex beam. Moreover, we note that in principle much larger phase shift coverage (multiples of 2π) can be obtained based on rearrangement scenario with an appropriate basic super cell.
In order to determine the shaping effects of the optical wavefronts by the new designed plasmonic metasurfaces, we perform numerical simulations using commercial software Lumerical FDTD solutions based on finite-difference-time-domain method. In our simulations, the optical constants of gold are extracted from the experimental data [26]. Plasmonic metasurface is assumed to be designed on a silicon substrate (ε = 12.1) and illuminated by a normally incident plane wave with polarization along x axis. After some numerically computational efforts, the optimized dimensions of the seven constituent antennas with central operating wavelength of 1.5 μm are as follows. The antennas numbered from 1 to 4 have β = 45°, α = 60°, 90°, 120°, 180° and l = 173, 159, 128, 101 nm, while the parameters of antennas from 5 to 7 are β = −45°, α = 60°, 90°, 120° and l = 153, 143, 110 nm. The rest ones are fixed as w = 40 nm, t = 50 nm, and a = 230 nm.
3. Results and discussions
Figure 2(a) displays the simulated results of Ey component of the scattered electric fields for a linear gradient phased metasurface composed by the control super cell (LGPM-C1) at the wavelength of 1.5 μm. As comparison, the corresponding results of the other two linear gradient phased metasurfaces made of our new designed super cells (LGPM-S1 and LGPM-S2) are plotted in Figs. 2(b) and 2(c), respectively. It notes that well-defined planar wave features are retained for all the results, and the bending effects are clearly observed for the cross-polarized scattered electric fields (Ey) in all cases. Moreover, one can readily see that the angles of refraction θt and reflection θr of the latter two new designed plasmonic metasurfaces are as expected much larger than the control sample. θt and θr of the control metasurface are estimated to be −16° and −69°, while for the new designed cases, the angles of refraction θt are about −32° and −53°, and the reflected beams of both cases become evanescent, namely, total internal reflection occurs even for the impinging light with the angle of normal incidence. Here the reason is exactly that the new designed metasurfaces have wide ranges of phase shift coverage and lager gradients of phase discontinuity compared to the one of the control sample. We note that although the angles of refraction and reflection are negative, the physics is quite distinct from negative refraction occurring in materials with negative refractive index [27]. Such kind of metasurfaces cannot be used to make perfect lenses [28], since they are limited to restore the evanescent waves.
Fig. 2 Electric field distribution of Ey component simulated by FDTD method under the illumination of a normally incident x-polarized light at the wavelength of 1.5 μm. (a) is the control sample. (b) and (c) are the new designed linear gradient metasurfaces consisting of super cell S1 and S2, respectively. The black arrows indicate the directions of the incident, reflected and refracted light. The black dashed lines show the locations of the structures.
To further identify the characteristics of the anomalous refraction, far field pattern of the transmitted waves are simulated by FDTD method. Figures 3(a)-3(c) show polar-plots of the normalized transmitted field intensities for the above three metasurfaces at the wavelength of 1.5 μm. We note that the transmitted waves are increasingly deflected from the normal direction as the sample from LGPM-C1 to LGPM-S2. The corresponding results of the three cases versus θt are plotted in Figs. 3(d)-3(f). Based on these results, it is clearly obtained that the angles of refraction of the three cases are in turn −15.5°, −32.3° and −53.4°, which agree with the above results estimated from the wavefronts of the scattered electric fields. The point of our designed metasurfaces is of benefit to realization of ultrathin flat lenses with high numerical aperture. However, we also note that the perfomrmances of the metasurfaces operating in high order modes become worse compared with the control one, owing to some of energy is scattered to the other modes and spectral broadening effect. In practice, if the rearranged metasurfaces cannot be satisfied for applications in anomalous light manipulating, one can properly add the number of antenna elements of the basic super cell to improve their performances.
Fig. 3 Normalized transmitted field intensities are plotted in polar coordinate system (a)-(c) and as function of the angle of refraction (d)-(f) for the wavelength of 1.5 μm. (a) & (d) control sample; (b) & (e) linear gradient metasurface consisting of super cell S1; (c) & (f) linear gradient metasurface consisting of super cell S2.
We now show that the functionalities of the new designed metasurfaces can be regarded as optical devices operating in high order modes. As reported in previous works, for an interface characterized by a phase shift that varies as a function of position linearly, the angles of the anomalous refraction are dictated by the generalized vesion of Snell’s law [3]
where θi is the incident angle, ni and nt are the refractive indices of incident and tranmitting media. is the gradient of phase discontinuity along the interface. Furthermore, in the light of diffraction theory, the optical behavior of such a interface with periodic phase shift profile is governed by the following diffraction equation [29]where m is an integer and denotes the order of the diffraction spectrum. According to Eqs. (1) and (2) , we immediately note that for the interface with the phase shift coverage 2*2π (3*2π) over a periodicity P, i.e., (), the resulting anomalous refraction corresponds to the second (third) order diffraction, and the angle of refraction can be predicted by Eq. (2) with m = 2 (m = 3). This is verified by our FDTD numerical simulations.Figure 4 plots the angle of refraction as a function of the angle of incidence for the metasurfaces with operating wavelength of 1.5 μm. The curves are the calculated results using Eq. (2), and the symbols denote the simulated angles of refraction versus the angles of incidence. It is noted that the numerical simulated results for the new designed metasurfaces LGPM-S1 and LGPM-S2 are exactly consistent with the second and third order theoretical calculated results, respectively. From this perspective, our design can be viewed functionally as novel echelette gratings [24,25 ], while which do not only have the characteristic of echelette gratings such as high dispersion, high resolution and operating in higher diffraction order, but also process their own peculiar features, e.g. easier preparation and broadband wave manipulation performance.
Fig. 4 Angle of refraction versus angle of incidence, obtained by theoretical calculations using Eq. (2) (the curves), FDTD simulations on the control interface (solid triangles) and the new designed linear gradient plasmonic metasurfaces (metasurfaces consisting of S1 and S2 are respectively denoted by solid spheres and stars) at the wavelength of 1.5 μm.
Figures 5(a)-5(c) show the normalized transmitted field intensities as functions of wave-length and angle of refraction corresponding to the LGPM-C1, LGPM-S1 and LGPM-S2, respectively. It is observed that our devices indeed work in rather wide range of wavelengths, for LGPM-C1 and LGPM-S1 wavelength ranging from 1.1 μm to 2 μm, for LGPM-S2 from 1.1 μm to 1.8 μm (in the wavelength ranging from 1.8 to 2 μm, LGPM-2 does not work, as the angles of refraction is beyond 90°, the upper limit value of the angle of refraction. For this wavelength range, some of energy is scattered to the other order modes and the other possibly converted to surface waves). Shown in the insets of Figs. 5(a)-5(c) are the enlarged views of normalized transmitted field intensities spectra of each case around the centre wavelength of 1.5 μm. According to the definition of angular dispersion, we obtain that the angular dispersion for the three metasurfaces at the normal incidence are respectively 0.6'/nm, 1.5′/nm and 3.3′/nm. Our new designed metasurfaces have really higher dispersion than the control one (around three and five times). These features make our design valuable for using in high resolution precise measurements.
Fig. 5 Normalized transmitted field intensities as functions of the wavelength and angle of refraction. (a) Control sample; (b) linear gradient metasurface consisting of super cell S1; (c) linear gradient metasurface consisting of super cell S2. Insets: enlarged views of normalized transmitted field intensities spectra of each case.
It should be pointed that not all initial super cells are suitable for rearrangement to build new super cells with phase shift coverage over 2π. The rule is that to create a new super cell with phase coverage a multiple of (e.g., two or three times, etc.) the basic one based on the method of rearranging the sequence of antennas, the number of antennas should not be divisible by the multiplying factor (two or three, etc.), otherwise the new obtained super cell would be composed of multiple repeating sub-super cells, which only include part of the constituent antennas and have a reduced smaller periodicity. For example, if the above control (7-element antennas) super cell change to the super cell with 8-element antennas that commonly used in previous works [3,8,9,11–14 ], the functionality of a newly designed metasurface obtained by selecting every other element from the basic periodic array cannot be regarded as a new device operating in high order mode, since it is in effect composed by a sub-super cell (antennas numbered 1, 3, 5, 7 or the other group 2, 4, 6, 8) with half period of the original one.
To advance the proposed idea further and enable its prospect in practical applications, we also design another two ultrathin plasmonic metasurfaces with azimuthal phase gradient property to generate high order optical vortices. Optical vortex beams, as a peculiar type of light beam, have spatially variant phase wavefronts that are related to the azimuthal angle (), where φ is the azimuthal coordinate and the integer number n is the topological charge denoting the order of the mode [3,30 ]. An orbital angular momentum is imparted to the beam owing to the presence of the spiral phase front. High order vortex beams are important for various applications, such as optical trapping [31], light focusing [32], and particle acceleration [33], in particular, in optical communication systems, where such beams can carry more quantum information [34,35 ]. It has been recently shown that optical beams with such spiral phase profile can be generated by flat plasmonic interfaces using the concept of phase discontinuities [3,9 ]. Nevertheless, to construct a phase plate that generates a high order vortex beam, if the phase shifts coverage of a super cell is limited to 2π, numerous antennas are required to pack the interface to introduce enough phase shifts. (for example, to construct a plate that generates a double (third) charged vortex beam n = 2 (n = 3) based on the control super cell, the interface is required to be segmented in 14 (21) equiangular sections for packing antennas), as a result, the spacing between the antennas would become very small. This will not only make the device difficult to fabricate and increase the production cost owing to their dense packing density, but also will affect its performance because the near-field coupling between adjacent antennas becomes strong and would interfere with the designed scattering properties [3,9 ]. These disadvantages can be overcome in some manner if the phase shifts coverage can cover several 2π. Here we design two AGPMs to generate high order charged vortex beams based on our proposed super cells. Depicted in Fig. 6(a) is a schematic picture of part of an AGPM composed by the control super cell, which is divided into seven equiangular sections, and each section is patterned by one constituent antenna of the control super cell. As the antennas are arranged with azimuthal phase shift merely varied from 0 to 2π in the whole interface, such a metasurface can only produce the first-order vortex beam. The simulated phase distribution of a vortex beam created by the control AGPM upon illumination by normally incident linearly polarized Gaussian beam is shown in Fig. 6(d), which exactly displays the phase profile characteristic of an optical vortex with topological charge n = 1. Our new designed two AGPMs are schematically shown in Figs. 6(b) and 6(c). They are also comprised of seven equiangular sections, whereas each section is occupied by the respective element of the above two new proposed super cells. Figures 6(e) and 6(f) depict the corresponding simulated phase distribution of vortex beams produced by the two new designed AGPMs. We observe that, in contrast to the vortex beam generated by the control AGPM, the vortex beams generated by the new designed AGPMs possess the high order phase profile properties with the topological charges n = 2, 3, respectively. The underlying physics is thus due to our azimuthal phase variant metasurfaces covering larger phase ranges (i.e. [0, 2*2π] and [0, 3*2π]).
Fig. 6 (a)-(c) Schematic view of three azimuthal gradient plasmonic metasurfaces. (d)-(f) the simulated phase distribution of the vortex beam patterns. (a) & (d) azimuthal gradient metasurface created based on the control super cell; (b) & (e) azimuthal gradient metasurface created based on super cell S1; (c) & (f) azimuthal gradient metasurface created based by super cell S2.
4. Conclusions
In summary, we have addressed a novel approach to shape the wavefront of light using the concept of abrupt phase discontinuity with phase shift coverage larger than 2π. To demonstrate this idea, we designed two different types of meta-super cells using the V-shaped antennas as the building blocks. Our super cells have the phase shift coverage of 2*2π and 3*2π, respectively. We showed that linear gradient phased metasurfaces created based on the designed super cells can be used to mold optical wavefronts in unusual ways with rather larger bending angles functioned as meta-echelette gratings operating in high diffraction orders. To advance our idea further, another two azimuthal phase gradient plasmonic metasurfaces have also been constructed based on our super cells to generate high order optical vortex beams. The design schemes presented in this work provide an alternative way for manipulating light propagation and would be useful in the compact nanophotonic systems.
Acknowledgments
This work was supported by National Natural Science Foundation of China (NSFC) (Grant No. 61471345), the National Young 1000 Talent Plan, Shanghai Science and Technology Committee (Grant No. 14PJ1409500) and the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (No. 20120142110064).
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