Non-corner Localized Surface Plasmons Resonance Based Ultrathin Metasurface Single-layer Quarter Wave Plate

We report on a non-corner quarter wave plate (NCQW) within the single Ag hollow elliptical ring array layer of only 8 nm thickness, where the strong localized surface plasmons (LSP) resonances are excited. By manipulating the parameters of the hollow elliptical ring, the transmitted amplitude and phase of the two orthogonal components are well controlled. The phase difference of π/2 and amplitude ratio of 1 is realized simultaneously at the wavelength of 834 nm with the transmission of 0.46. The proposed NCQW works perfectly at the wavelength of 834 nm and works well at a ultrawide wavelength range of 110 nm, which suggests an ecient way of a new way of exciting LSP resonances and designing wave plates, and provides a great potential for liquid crystal display, optical communication, sensor detection and imaging.


Introduction
Wave plates are important optical devices that are used to realize phase modulation and polarization conversion, which is realized by adding different phase delays to the two polarization components perpendicular to each other. Traditional wave plates are mostly manufactured by bulky birefringent crystals, which suffer from depth of phase modulation and di culties in integration. Recently, as the very fast development of metasurface structures, localized surface plasmons (LSP) resonance based wave plates have been widely researched and published [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . Zhao et al. proposed plasmonic metasurfaces formed by orthogonal elongated nanorods and complementary nanoslits 3 . The structure produces strong LSP resonance at the sharp corners of the rectangular holes, and the resonance intensity is adjusted by the size of the two rectangular holes to control the phase delays of the two polarization components within the 40 nm thick silver layer. Li et al. demonstrate a metal/insulator/metal tri-layer structure with Lshaped hole arrays inside to realize the polarization conversion in optical transmissions at near-infrared wavelength in totally 460 nm thicknesses 6 . Strong LSP resonances are excited inside the L-shaped holes around the corners, which contribute to the phase delay of the two polarized components. The x-proposed polarized incident light can be conversed to the y-polarized light by the e ciency of 93% at the wavelength of 1400 nm. Chen et al. proposed a strategy to realize plasmonic quarterwave plate with subwavelength rectangle annular aperture arrays in Ag lm of 200 nm thickness 7 . The incident light can excite strong LSP resonances around the corners of the rectangle and is located in the different region with the hole according to the polarization. The transmission of their proposed quarter wave plate is 46% at the wavelength of 1550 nm. A plasmonic quarter-wave plate based on 60 nm thick U-shaped silver nanopatches array in the near-infrared range is designed and presented by Chen et al 15 . Strong LSP resonances are excited around different corners of the U-shaped silver nanopatches according to the polarization of the incident light, which cause the different phase delays between x-and y-polarized components. The transmission of 46.3% and phase deference of 1.57 is realized at the wavelength of 1550 nm. Li et al. also proposed a re ective half-wave plate composed of single L-shaped antennas, and a re ective quarter-wave plate composed of double L-shaped antennas 17 . By exciting strong LSP resonances around the corners of the L-shaped antennas, the phases of different polarized light can be delayed differently within totally 600 nm thicknesses. In these LSP based wave plates, the strong LSP resonances are all excited around the sharp corners, leading to the different phase delays of the two mutually perpendicular polarization components. However, the designed structures with sharp corners cannot be manufactured perfectly, but will be prepared as rounded corners, which can extremely weaken the LSP resonances such that the e ciencies of these wave plates will drop signi cantly.
In fact, the LSP resonances can be excited at structures with no sharp corners, such that the performance is less sensitive to the structural errors. In this paper, we proposed a non-corner quarter wave plate (NCQW) within the single Ag layer of only 8 nm thickness, where the strong LSP resonances are excited in the hollow elliptical ring array. The phase difference between the x-and y-polarized components is from 1.5 to 1.59 and the amplitude ratio is from 0.78 to 1.18 at the wavelength band from 770 nm to 880 nm.
The phase difference of π/2 and amplitude ratio of 1 is realized simultaneously at the wavelength of 834 nm with the transmission of 0.46. This proposed NCQW suggests a new way of exciting LSP resonances and designing wave plates, which has huge application prospects in optical communication, data storage, information processing, and imaging.

Theory and structure design
The structure of the proposed NCQW is shown in Fig. 1. The Ag layer with the thickness of h is coated on a SiO 2 substrate and is shaped to the hollow ellipse ring array. As shown in Fig. 1(b) the short and long radius of the inner and outer ellipses are r 1 , r 2 , R 1 , and R 2 , respectively, and the period is p. A linearly polarized plane wave with prescribed polarization orientation θ (as seen in Fig. (b)) with respect to X axis is normally incident from the substrate side as seen the arrow in Fig. 1(a). The transmission performance and the electric eld inside the structures of the proposed NCQW is calculated and optimized using the nite difference time domain (FDTD, Lumerical FDTD Solutions, Canada) method. In the simulation, the periodic boundary conditions were set at the x and y boundaries such that the periodic structure can be simulated, and at z boundaries it was set as perfectly matched layers condition.
Different from the previous LSP resonances based wave-plate; there are no corners in the proposed structures. In fact, however, the LSP resonances can also be excited inside the non-corner structures. Fig.   2(a) shows the transmission spectrum ranging from 400 nm to 2000 nm and with the orientation θ = 45( i.e., xy-polarized incidence). In this simulation, we set R 1 = r 1 = 60 nm, 80nm and 100 nm, respectively, and the other parameters are R 2 = r 2 = 120 nm, h = 8 nm, and p = 330 nm. It is shown that there is a serious of dips in each transmission spectrum as a result of Wood's anomaly, and the peaks in each transmission spectrum correspond to excitation of SPP resonances 7 . The LSP resonant peaks aroused by the non-propagating modes supported by the hollow ring can also be seen in the spectrums. The LSP resonant wavelength red-shifts signi cantly with R 1 (or r 1 ) increasing (i.e. the width of the hollow ring decreasing), which is a distinctive feature of the LSP resonances. Fig. 2(b) shows the transmission and the phase shift relative to the structures without the Ag layer (i.e., only the substrate) when R 1 and r 1 are xed at 80 nm. It can be seen that the phase shift reaches approximately π/2 at the wavelength range around 755 nm and 858 nm near the peak of the transmission spectrum, which means that the phase shift of the transmission eld can be well controlled by appropriately designing the nanostructures and manipulating the LSP resonances. Fig. 3 shows the electric elds within the nanopatterns under normal incidence with the orientation θ = 45˚ when R 1 = r 1 = 80 nm (i.e., the red line in Fig. 2(a)). The wavelength of the incident light is 1075 nm in Fig. 3(a) corresponding to the peak of transmission in Fig. 2(a), and is 800 nm in Fig. 3(b) corresponding to the deviated wavelength. It is clearly seen that there is resonant eld at both the inner and the outer edges inside the hollow ring along the direction of incident orientation, which is much stronger Fig. 3(a) in than in Fig. 3(b). The electric elds better displays the physical mechanism of the LSP resonances induced extraordinary transmission, which occurs only if a matching condition between the metasurface structures and the incident light is satis ed. In other words, the resonant wavelength can be manipulated by carefully regulating the parameters of the nanostructures.
An ideal quarter wave plate requires an amplitude ratio of 1 and a phase difference of π/2, between the transmitted electric elds along X and Y axes, which require the difference along the two directions in the structures. In the nano-structures with sharp corners, the structures can be divided into horizontal and vertical parts, which can be separately adjusted to precisely control the features of the xand ycomponents of incident light, respectively. However, to simplifying the design and reducing the processing di culty, the non-corner nano-structure is seen as a whole such that its physical mechanism is very different from that of the sharp-corner nano-structures. Fig. 4 shows the amplitude ratio (E x /E y ) of the two orthogonal components of electric eld along X and Y axes and their phase difference under different parameters at the wavelength range from 770 nm to 880 nm with orientations θ = 45˚, where dr 1 = R 1 -r 1 , and dr 2 = R 2 -r 2 . The height h of the Ag structures is 8 nm and the period p is 330 nm. Fig. 4(a) shows the phase difference when dr 2 is xed at 31 nm and dr 1 varies from 37 nm to 77 nm. For comparison, the amplitude ratio when dr 1 is xed at 57 nm and dr 2 varies from 11 nm to 51 nm is shown in Fig. 4(b). It is obviously seen that the phase difference at the wavelength of 834 nm rise from 1.30 to 1.87 within dr 1 decreasing, but varies just between 1.59 and 1.61 when dr 2 decreasing. It means that the phase difference is much more sensitive to the change of the structures in X direction than that in Y direction. It can be also seen that the phase difference does not change much at the wavelength band of 110 nm (For example, the phase difference varies between 1.5 and 1.59 at dr 1 = 57 nm as the blue line in Fig. 4(a)). The amplitude ratio of the structures in Fig. 4(a) and (b) are also investigated as seen in Fig.   4(c) and (d). In contrast to the phase difference, the amplitude ratio is more sensitive to the change of dr 2 than that of dr 1 . It is shown in Fig. 4(c) that the rises from 0.97 to 1.03 at the wavelength of 834 nm within dr 1 decreasing. When dr 1 is xed and dr 2 decreases as seen in Fig. 4(d), the amplitude ratio rises from 0.91 to 1.10 at the wavelength of 834. These characteristics can be advantages in designing the wave plate that the phase difference can be precisely controlled by adjusting the parameters in X direction without affecting the amplitude ratio, and as is the parameters in Y direction for adjusting the amplitude ratio. In this way, the parameters are optimized at dr 1 = 57 nm and dr 2 = 31 nm to realize the phase difference of π/2 and the amplitude ratio of 1 at the wavelength of 834 nm. Fig. 5 shows the distribution of the electric eld inside the structure under the incidence of x-, yand xypolarization, where the parameters are optimized at r 1 = 40 nm, r 2 = 125 nm, R 1 = 97 nm, R 2 = 156 nm, h = 8 nm, and p = 330 nm, respectively. It is clear that the electric eld is strongly bounded inside the hollow elliptical ring under both x- (Fig. 5(a)) and y- (Fig. 5(b)) incidence. It can be also seen that the electric eld is stronger in the top and down side in Fig. 5(a) and (b) (i.e., along Y direction), which is the reason of that the amplitude ratio is more sensitive to the change of parameters along Y direction (such as dr 2 ). It is shown in Fig. 3 that the strength of the electric eld characterizes the strength of LSP resonance, which determines the peak in the transmission spectrum. In contrast, when the parameters along X direction (such as dr 1 ) changes, the LSP resonance is not affected much, such that the amplitude ratio changes very little. On the other hand, the phase difference is more relevant to the effective refractive index, which is in uenced by the proportion of Ag and air. The proportion varies much more with the change dr 1 of than that of dr 2 , such that the phase difference is much more sensitive to the change of the structures in X direction than that in Y direction. Fig. 6 shows the performance under xy-polarized incidence of our proposed NCQW with the optimized parameters same as in Fig. 5. Fig. 6(a) shows the transmission and phase difference between the transmitted electric elds along X and Y axes at the wavelength band range from 770 nm to 870 nm. It is seen that the transmission is from 0.372 to 0.521 and the phase difference is from 1.5 to 1.59. At the wavelength of 834 nm the transmission reaches 0.46 and the phase difference is π/2. Fig. 6(b) shows the amplitude ratio of the two orthogonal components of electric eld along X and Y axes and their phase difference, where the amplitude ratio is from 0.78 to 1.18. An ideal quarter wave plate requires an amplitude ratio of 1 and a phase difference of π/2, which can be simultaneously realized at the wavelength of 834 nm as the dashed line seen in Fig. 6(b). These results mean that our proposed NCQW works perfectly at the wavelength of 834 nm and works well at the wavelength band range from 770 nm to 880 nm.

Discussion
In conclusion, a non-corner quarter wave plate within the single Ag layer of only 8 nm thickness is theoretically demonstrated, in which the strong LSP resonances are excited in the hollow elliptical ring array. The transmitted amplitude and phase of the two orthogonal components can be precisely controlled by manipulating the parameters of the hollow elliptical ring. The phase difference of π/2 and amplitude ratio of 1 is realized simultaneously at the wavelength of 834 nm with the transmission of 0.46. The phase difference between the xand y-polarized components is from 1.5 to 1.59, the amplitude ratio is from 0.78 to 1.18 at the wavelength band from 770 nm to 880 nm, and the transmission is from 0.372 to 0.521. The proposed NCQW is easy integration with simple structure, which suggests a novel way in exciting LSP resonances and designing wave plates, and has great potentials in liquid crystal display, optical communication, sensor detection and imaging.      Performance of the proposed NCQW. (a) The transmission and phase difference between the transmitted electric elds along X and Y axes of the proposed NCQW. (b) The amplitude ratio of the two orthogonal components of electric eld along X and Y axes and their phase difference of the proposed NCQW.