Polarization-independent longitudinal multi-focusing metalens

Wei Wang; Zhongyi Guo; Keya Zhou; Yongxuan Sun; Fei Shen; Yan Li; Shiliang Qu; Shutian Liu

doi:10.1364/OE.23.029855

1. Introduction

In the past few years, researches on metamaterials are one of the fastest growing fields due to their unconventional electromagnetic properties that are not available in natural or its constituent materials [1,2 ], in which more and more novel applications have been proposed, such as flat lenses [3,4 ] holography [5], invisibility cloaking [6,7 ], and so on. Recently, the concept of interfacial phase discontinuities has been proposed [8] and the metamaterial surfaces (or metasurfaces) based on this new concept have been demonstrated experimentally [8–10 ]. The metasurfaces consisted of inhomogeneous optical antenna arrays that partially converted the incident light into its cross-polarization light with a phase discontinuity. Furthermore, the phase variation across 2π can be readily realized while maintaining constant scattering amplitudes. The arbitrary phase profiles can be realized easily by varying the geometry of each sub-wavelength antennas. Based on the phase discontinuities principle, the metasurface could be utilized to create various integrated devices, such as vortex phase plates [11,12 ], polarization converters [13,14 ], metalenses [15–17 ], and holographic plates [18,19 ].

Lenses are the indispensable tool for various fundamental and practical applications. Most lenses, such as conventional lens, Fresnel lens, Luneburg lens, plasmonic lenses, are usually designed based on phase accumulation along the optical path, and the thickness of the lens is greater than or comparable to the incident wavelength. However, metalens based on metasurfaces, as an alternative lens to generate focusing, can be very thin even in the sub-wavelength size. Meanwhile, the metalens is also planar and without aberration [20]. The metalens based on metasurfaces provides a promising route to miniaturized, planar, and integrated components on a chip. In previous papers, the metalens with one focus have been paid lots of attentions and many kinds of single-focusing metalens have been realized successfully [21–27 ]. The double-focusing and multi-focusing lens is very important for coupling the incident plane wave to multiple channels in optical interconnections. Recently, plasmonic lenses with two focusing spots have been proposed by using simulated annealing algorithm [28] and Yang-Gu algorithm [29]. However, these two works are also very time-consuming in computation, and the focuses are on the same output plane. Later, the multi-focus plasmonic lens have also been designed based on holography [30], which doesn’t need complex computation and iteration. Furthermore, multi-focusing plasmonic lens can also be produced on the different output planes. However, these reported multi-focusing metalenses are off-axial focusing, and the focus located at the same horizontal plane or different horizontal planes. Longitudinal multifoci metalens based on metasurface is rarely reported. Only recently, Prof. Chen have designed a longitudinal multifoci metalens based on the controllable phase discontinuity, but it is only suitable for the circular-polarization incident lights [31]. To our knowledge, the longitudinal multi-focusing metalens with the polarization-independent characteristics has not been proposed and investigated before.

In this paper, we have proposed a novel polarization-independent multi-focusing metalens in the longitudinal direction based on the metasurface of the designed L–shaped gap nanoantennas array on a thin gold film. Three novel designing methods: partitioned mode, radial alternating mode and angular alternating mode, have been proposed to construct the longitudinal multi-focusing metalens based on the equal optical path theory by modulating the concrete L–shaped nanoholes on a thin gold film. The focusing lengths and focusing intensities of every focusing spots from the multi-focusing metalens can be controlled and modulated by the concrete designs effectively. The simulated results show that all of our three designing methods are effective for focusing the incident lights, which shows great potential applications in designing plasmonic devices. Due to the polarization-independent characteristic of the used L-shaped nanoantennas, our longitudinal multi-focusing metalenses are also suitable for both the linear polarizations (LP) and circular polarizations (CP) simultaneously.

2. L-shaped gap nanoantennas

To realize the multi-focusing metalens, as shown in Fig. 1(a) , in the 30 nm thick gold film, the L-shaped nanohole with the same lengths and widths of the two arms is selected as the basic unit structure. The unit cell period Λ is set as 450 nm to avoid coupling between the adjacent L-shaped nanoholes. The symmetry axis of the L-shaped nanohole is oriented 45° with respect to the x-axis. As the special V-shaped nanoantennas, the incident light will excite two eigenmodes of “symmetric” and “antisymmetric” modes along the $\vec{e_{s}}$ and $\vec{e_{a}}$ respectively. Due to the special symmetry of the designed structure, under the incidences of XLP, YLP, LCP and RCP lights, the corresponding induced scattering field can be expressed as [32,33 ]:

E_{o u t} = {\begin{cases} \frac{1}{2} (S + A) \vec{e_{c o}} + \frac{1}{2} (S - A) \vec{e_{c r o s s}} X L P, Y L P \\ \frac{1}{2} (S + A) \vec{e_{c o}} + \frac{i}{2} (S - A) \vec{e_{c r o s s}} L C P \\ \frac{1}{2} (S + A) \vec{e_{c o}} - \frac{i}{2} (S - A) \vec{e_{c r o s s}} R C P \end{cases}

where

\vec{e_{c o}}

is the co-polarization with the incident light,

\vec{e_{c r o s s}}

is the cross-polarization with the incident light,

S

and

A

are the complex scattering amplitudes of the symmetric and antisymmetric modes.

Fig. 1 Basic functional units. (a) Schematic of a L-shaped nanohole. (b) Phase shifts and transmitted amplitudes of the cross-polarized electric field of the proposed eight L-shaped nanoholes units on a thin gold filmat 808 nm under LP and CP normal incident wave.

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The phase and amplitude can be manipulated through changing the length and width of the L-shaped nanoholes. To realize the metalens with well focusing functionality, the eight L-shaped nanoholes covering a 2π range (in equal steps of 45°) and possessing a nearly constant transmission amplitude are selected at 808 nm [17], as shown in Fig. 1 (b). The blue solid line and green dotted line correspond to the transmitted amplitude of linear polarization (ALP) and amplitude of circular polarization (ACP), respectively; the red solid line and black dotted line correspond to the phase shift of linear polarization (PLP) and the phase shift of circular polarization (PCP), respectively. Consistent with above theoretical analysis, the selected eight L-shaped nanoholes posses equal phase shifts and transmission amplitudes for the incident LP and CP lights.

3. Design and numerical simulations

The metalens can be designed based on equal optical path principle [15–17 ]. And in our earlier work, we have also designed the polarization-independent cylindric metalens (with 2-D simulations) with only one focus by L-shaped nanoantennas array [17]. Here, we try to design the longitudinal multi-focusing metalens (with 3-D simulations) with multiple focus. And the designing processes are as follows: firstly, extract the concrete phase distributions for the designed metalens according to equal optical path principle; secondly, arrange the L-shaped nanoholes according to the concrete phase distributions by different designing principles of partitioned mode, radial alternating mode and angular alternating mode, respectively; Lastly, verify and appraise the focusing properties of the designed metalens by numerical simulations using the FDTD (Finite Difference Time Domain) method.

3.1 Metalens with one focus

Firstly, the metalens with only one focus has been designed by the L-shaped nanoholes array in concentric rings as illustrated in Fig. 2(a) . The distribution of the designed metasurface possess a hyperboloidal phase profile, which can be seen as the rotating surface of the hyperbolic phase profiles. According to the equal optical path principle, the hyperboloidal phase profile can be expressed as

φ (r) = \frac{2 π}{λ} \cdot (\sqrt{r^{2} + f^{2}} - f)

where φ(r) represents the abrupt phase shifts between an arbitrary point R and the original point O; λ = 808 nm is the incident wavelength;

r = \sqrt{x^{2} + y^{2}}

is the distance from point (x, y) to the original point, and f is the focal length.

Fig. 2 (a) An illustration of one-focus metalens consisted of the L-shaped nanoholes array. (b) The solid curve shows the theoretical phase shift along radial direction, and the dots show the phase shifts that can be precisely provided by the designed different L-shaped nanoholes.

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Generally speaking, the phase of the designed metalens can be quantized into several values in the range of 0~2π (8 values here), and if we arrange the nanoantennas in an equally spaced way as usual, the errors will be brought about in the phase distributions inevitably. Therefore, for reducing the errors in the phase distributions, we can obtain the concrete phase in every point of the metalens, and the phase can be expressed as $φ = 2 m_{n} π$ , where $m_{n} = [(n - 5) / 8] + m$ , n represents the number of the concrete L-shaped nanoholes (1~8: shown in Fig. 1(b)), m is an integer. So Eq. (2) can be written as

r = \sqrt{2 m_{n} λ f + m_{n}^{2} λ^{2}}

Therefore, we can obtain the concrete values of r for the corresponding nanoantennas. That is to say we can determine the concrete positions for the relative nanoantennas 1~8 in this way. Meanwhile, for achieving the maximum density in the radial direction and avoiding coupling between adjacent nanoantennas, simultaneously, the optimized principle of choosing the nanoantennas should satisfy $r_{j + 1} - r_{j} \geq Λ$ , where $r_{j}$ is the radius of the jth nanoantennas' ring.

The relationship between $φ$ and r may be illustrated by using the metalens with f = 1μm, as shown in the Fig. 2(b). The solid line is the calculated phase shift according to Eq. (2), and the colored dots describe the phase shifts provided by the different L-shaped nanoholes. All the L-shaped nanoholes can realize constructive interference and produce focusing phenomenon. Figure 3(a) shows the intensity distribution |E_y|² at x-z plane and x-y plane at z = 1.15 µm (inset) of the metalens with f = 1μm, under the incidence of XLP light. The exit plane of the metalens is laid in the place of z = 150 nm and the real focal plane is at z = 1.15 µm. Figures 3(b)-3(d) show the cross-polarized intensity distributions at x-z plane under the incidence of YLP, LCP, RCP lights, respectively. There are good focusing effects for the incidences of the LCP and RCP lights simultaneously, which implies the polarization-independence of the designed metalens.

Fig. 3 (a) The intensity profile of the cross-polarized transmitted light at the x-z plane with XLP incidence, and the inset shows the intensity distribution in x-y plane at z = 1.15µm. (b-d) show the similar cases for the YLP, LCP, RCP incidences respectively.

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As shown in Fig. 3, the full width at half maximum (FWHM) of the focal spot is 400 nm. To differentiate the transmittance through the metalens and the focusing efficiency by the metalens (power ratio toward the focus by the focusing metalens), we define the focusing efficiency as the ratio of the power integration of the focus (with the radius of just three times the FWHM spot size) to the incident power, and define the transmission efficiency as the ratio of the transmitted power to that of the incident light. The simulation indicates that for our designed single-focusing metalens, the transmission efficiency and the focusing efficiency can reach to 12% and 1.4% respectively.

3.2 Double-focusing metalens based on the partitioned mode

The designing plane of the multi-focusing metalens has been divided into different regions (the inner four rings and the outer four rings), which is called partitioned mode. As illustrated in Figs. 4(a) and 4(b) , we have designed the double-focusing metalens based on the L-shaped nanoholes array successfully. For the inner four rings and the outer four rings, the relations between the phase shifts and radius of the jth ring can be expressed by $φ (r_{j}) = \frac{2 π}{λ} \cdot (\sqrt{r_{j}^{2} + f_{1}^{2}} - f_{1})$ and $φ (r_{j}) = \frac{2 π}{λ} \cdot (\sqrt{r_{j}^{2} + f_{2}^{2}} - f_{2})$ respectively. That is to say, for focusing the incident light into two focus with different focal lengths, the nanoholes arrays of the metalens are partitioned into the inner and the outer regions along the radial direction. The inner four rings are used to form the first focus with f₁ = 1μm, and the outer four rings are used to form the second focus with f₁ = 5μm. Figure 4(c) shows the phase shifts along the radial direction for the double-focusing metalens with f₁ = 1μm and f₂ = 5μm, under the incident wavelength of 808 nm. The solid line are the calculated phase shifts, and the dots imply the phase shifts of the used corresponding L-shaped nanoholes. Because the coupling effects between adjacent nanoholes can be neglected ( $r_{j + 1} - r_{j} \geq Λ$ ), the inner and the outer nanoholes array, which respectively satisfy equal optical path principles with different focal lengths, will produce two focuses along the optical axis (longitudinal direction).

Fig. 4 (a) Top-view of the designed double-focusing metalens consisted of L-shaped nanoholes based on the partitioned mode. (b) Schematic illustration of the designed double-focusing metalens. (c) The red and blue solid curve show the theoretical phase shift along radial direction for f = 1μm and f = 5μm respectively, and the dots show the phase shifts that can be precisely provided by the different L-shaped nanoholes.

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The intensity distribution of |E_y|² in the x-z plane is shown in the Fig. 5(a) for the XLP incidence. The intensities of the two focuses are almost equal, and they are strongly and exactly focused at the preset positions along the optical axis. The upper and lower insets show the intensity distributions at two focal plane of f₂ = 5μm and f₁ = 1μm, respectively. For a quantitative analysis of the focusing effect, the according intensities of |E_y|² in the corresponding focal planes are presented in Fig. 5(b). It clearly shows there are good focusing qualities and roughly equal intensities for two focal spots. From Fig. 5(b), we can obtain that the FWHMs are 423 nm and 581 nm respectively at two focal planes of f₁ = 1μm and f₂ = 5μm, respectively, and the concrete focusing efficiencies of two focusing planes are 1.48% and 0.87% respectively. In fact, the ratio of the two focusing intensity can also be tuned based on the practical applications. The radial nanoholes array can form two parabolic phase profiles with two different focal lengths, and two hyperboloidal phase profile can be seen as the coherent superposition of many radial arrayed hyperbolic phase profiles. Therefore, through increasing or decreasing the number density of the nanoantennas in the inner and the outer nanoholes array, we can tuned the intensity ratio of two focal spots effectively. As shown in Figs. 5(c) and 5(d), the intensity distributions of |E_y|² in the x-z plane demonstrate that the designed metalenses with the intensity ratios of 3:2 and 3:4 have been realized by changing the density of the outer nanoholes array (f = 5μm).

Fig. 5 (a) Intensity distributions of the YLP light at the x-z plane, under the XLP normal incidence, and the insets show the intensity distribution in x-y plane at the corresponding focusing positions respectively. (b) The electric field intensity along the x-axis at the focusing plane. Intensity distributions of the YLP light at the x-z plane, for the metalens with the intensity ratios of 3:2 (c) and 3:4 (d), under the XLP normal incidence.

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Figure 6 shows the focusing intensity distributions of the designed double-focusing metalenses at 808nm for YLP, LCP and RCP incidences respectively, which shows the designed double-focusing metalenses have a superior polarization-independent focusing characteristics. That is to say that, unlike previous reported longitudinal double-focus metalenses [31], our designed longitudinal double-focusing metalens based on the L–shaped nanoatennas is insensitive to the incident polarization states and can work very well for both linear polarization (LP) and circular polarization (CP) incidences simultaneously.

Fig. 6 The intensity profiles of the cross-polarized transmitted light at the x-z plane with YLP, LCP, RCP incidences.

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3.3 Double-focusing metalens based on radial alternating mode

The concentric rings of the multi-focusing metalens have been labeled by the natural numbers from the center to the outer in the radial direction, and the odd rings and the even rings will focus the incident light into two different spots respectively in the longitudinal direction, which is called the radial alternating mode. The double-focusing metalens can also be realized by arranging the L-shaped nanoholes array in the radial alternating mode as shown in Figs. 7(a) and 7(b) . Here, for the odd rings, the relation between the phase shift and radius of the (2j + 1)th ring can be given by $φ (r_{2 j + 1}) = \frac{2 π}{λ} \cdot (\sqrt{r_{2 j + 1}^{2} + f_{1}^{2}} - f_{1})$ , but for the even rings, the relation between the phase shift and radius of the (2j)th ring can be expressed by $φ (r_{2 j}) = \frac{2 π}{λ} \cdot (\sqrt{r_{2 j}^{2} + f_{2}^{2}} - f_{2})$ . That is to say, different from the foregoing partitioned mode, the nanoholes array for producing different focal lengths are alternated arranged along radial direction. For the double-focusing metalens with f₁ = 1μm and f₂ = 5μm, the phase shifts and designed antennas distributions along the radial direction are shown in Fig. 7(c).

Fig. 7 (a) Top-view of the designed double-focusing metalens based on the radial alternating mode. (b) Schematic illustration of the designed double-focusing metalens. (c) The red and blue solid curves show the theoretical phase shifts along radial direction for f = 1μm and f = 5μm, respectively. The different dots indicate the phase shifts provided by different designs.

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Figure 8(a) show that the intensity distribution of |E_y|² in the x-z plane, under the XLP incidence, in which two focal spots of the designed metalens with roughly equal intensity are formed at z = 1μm and 5μm, respectively. The upper and lower insets show the intensity distributions at two focal planes (x-y plane) of f₂ = 5μm and f₁ = 1μm, respectively, which show the designed double-focusing metalens also has good focusing characteristics. The intensities of |E_y|² at two focal planes along the x axis are given in Fig. 8(b), which show nearly the same intensities of the two formed focuses. These results prove that the focusing performance of the double-focusing metalens arrayed based on radial alternation mode agrees well with the preset expectations. From Fig. 8(b), we can obtain that the FWHMs are 458 nm and 687 nm respectively at two focal planes of f₁ = 1μm and f₂ = 5μm, respectively, and the concrete focusing efficiencies of two focusing planes are 0.96% and 0.77% respectively. The double-focusing metalens with different intensity ratios can also be realized by tuning the densities of the nanoatennas in the special rings. And we have also designed and realized the double-focusing metalens with the intensity ratios of 3:2 and 5:6 very well as demonstrated in Figs. 8(c) and 8(d) respectively. These results demonstrate that the double-focusing metalens based on radial alternating mode can also work very well.

Fig. 8 (a) Intensity distributions of the YLP light at the x-z plane, under the XLP incidence, and the insets show the intensity distributions in x-y plane at the corresponding focusing positions respectively. (b) The intensity along the x-axis at the focusing plane. Intensity distributions of the YLP light at the x-z plane, for the metalens with the intensity ratios of 3:2 (c) and 5:6 (d), under the XLP normal incidence.

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3.4 Double-focus metalens based on angular alternating mode

The designing plane of the multi-focusing metalens have been divided into different lines in different angular directions, and the different angular lines will focus the incident light into two different spots in longitudinal direction, which is called the angular alternating mode. The structural diagram of longitudinal double-focusing metalens based on the angular alternating arrangement is illustrated in Figs. 9(a) and 9(b) . Of course, for avoiding the coupling effect between adjacent nanoholes, the nanoholes interval should be greater than the period ( $Λ$ ) of the nanohole. Here, for the angular alternating mode, the nanoatennas array of the metasurface have been arranged in lines with different angles, and nanoatennas array in the same direction (angle) are used to produce parabolic phase profile with a concrete focal length. Obviously, the corresponding values for the concrete nanoatennas should be satisfied with the formula of $φ (r) = \frac{2 π}{λ} \cdot (\sqrt{r^{2} + f^{2}} - f)$ . If we select some certain lines (in different angles) to form the metalens with focal length of f₁, and the others to form the metalens with focal length of f₂, the longitudinal double-focusing metalens can be formed easily. Figure 9(c) shows the corresponding phase distributions and selected nanoatennas along radial directions for forming the double-focusing metalens with f₁ = 1μm and f₂ = 5μm, respectively.

Fig. 9 (a) Top-view of the designed double-focusing metalens based on the angular alternating mode. (b) Schematic illustration of the designed double-focusing metalens. (c) The red and blue solid curves show the theoretical phase shift along radial direction for f = 1μm and f = 5μm, respectively. The dots show the phase shift that can be precisely provided by the designed L-shaped nanoholes.

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Figure 10(a) shows the intensity distribution of |E_y|² in the x-z plane of the designed double-focusing metalens by the angular alternating mode for the XLP incidence, and the upper and lower insets show the intensity distribution at two focal plane of f₂ = 5μm and f₁ = 1μm, respectively. Intensities of |E_y|² along the x-direction at two focal planes are presented in Fig. 10(b), which show good focusing characteristics too. From Fig. 10(b), we can obtain that the FWHMs are 538 nm and 688 nm respectively at two focal planes of f₁ = 1μm and f₂ = 5μm, respectively, and the concrete focusing efficiencies of two focusing planes are 1.78% and 0.96% respectively. Through manipulating component proportions of the angular alternating nanoholes array forming different focusing lengths, the intensity distribution of double-focusing metalens with intensity ratio of 4:3 and 3:4 have also been realized as shown in Figs. 10(c) and 10(d). These results confirm that the double-focusing metalens arranged based on angular alternating mode can also be a good potential candidate to realize two longitudinal focal spots.

Fig. 10 (a) Intensity distributions of the YLP light at the x-z plane, under the XLP normal incidence, and the insets show the intensity distributions in x-y plane at the corresponding focusing positions respectively. (b) The electric field intensity along the x-axis at the focusing plane. Intensity distributions of the YLP light at the x-z plane, for the metalens with the intensity ratios of 4:3 (c) and 3:4 (d), under the XLP normal incidence.

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3.5 Three-focusing metalens based on partitioned mode

To further verify our method, we have also designed the metalens with three focusing spots along optical axis based on the partitioned mode. And the focal lengths of the three-focusing metalens are set as f = 1μm, 2μm, 4μm, respectively. The objective intensity distribution of |E_y|² on the x-z plane under XLP incidence is shown in Fig. 11(a) , and the insets show the intensity distributions at three focusing planes with the preset focal lengths of f₁ = 1μm, f₂ = 2μm and f₃ = 4μm, respectively. We must note that compared to the single-focusing and double-focusing metalenses, the focusing precision of the designed three-focusing metalens has some deviations from the preset focal lengths, which is related to the interference between the closely spaced focusing spots. The intensities of |E_y|² at three focal plane along the x axis are shown in Fig. 11(b). The FWHM of three focuses are 411nm, 404 nm and 418 nm respectively, which reach to a scale in half wavelength (808 nm) nearly. And the focusing efficiencies of three focusing plane are 1.84%, 0.91% and 0.77% respectively. Although there are some deviations from the preset focal lengths, we still can announce that our designed three-focusing metalens works very well and there are three focusing spots that have been created in the corresponding focal planes successfully. Through changing the component proportions of the nanoholes array for different focal points, different intensity ratios of the focusing spots can also be achieved. The intensity distributions of two three-focusing metalenses with the intensity ratios of 4:4:3 and 5:6:7 are demonstrated in Figs. 11(c) and 11(d) respectively, which imply that the multi-focusing metalens based on our arrangements can also achieve the good focusing characteristics.

Fig. 11 (a) Intensity distributions of the YLP light at the x-z plane, under the XLP normal incidence, and the insets show the intensity distributions in x-y plane at the corresponding focusing positions respectively. (b) The electric field intensity along the x-axis at the focusing plane. Intensity distributions of the YLP light at the x-z plane, for the metalens with the intensity ratios of 4:4:3 (c) and 5:6:7 (d).

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4. Conclusions

In conclusion, we have proposed three novel designing principles: partitioned mode, radial alternating mode and angular alternating mode, for the longitudinal multi-focusing metalens based on equal optical path principle. The constructed planar longitudinal multi-focusing metalens is independent from the incident polarized states, and it can produce focusing phenomena for the LP and CP incidences simultaneously. The simulated results show that all of the designed metalenses by three design methods agree well with the designing expectations and have good focusing characteristics. And the focusing intensity of every focusing spot can be tuned easily by changing the density of the corresponding L-shaped nanoholes. These results show that our methods are effective and has potential application in the fields of designing plasmonic devices in sub-wavelength scale, micro-manipulating optics and the multi-imaging technology in the integrated optics.

Acknowledgments

The authors gratefully acknowledge the financial supports for this work from the National Natural Science Foundation of China (NSFC) under Grant No. 11374077 and No. 61575060, and the Fundamental Research Funds for the Central Universities (2015HGCH0010).

References and links

1. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

2. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]

3. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010). [CrossRef] [PubMed]

4. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010). [CrossRef] [PubMed]

5. S. Larouche, Y. J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11(5), 450–454 (2012). [CrossRef] [PubMed]

6. B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103(15), 153901 (2009). [CrossRef] [PubMed]

7. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]

8. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef] [PubMed]

9. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012). [CrossRef] [PubMed]

10. M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012). [CrossRef]

11. P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012). [CrossRef]

12. W. Wang, Y. Li, Z. Y. Guo, R. Z. Li, J. R. Zhang, A. J. Zhang, and S. L. Qu, “Ultra-thin optical vortex phase plate based on the metasurface and the angular momentum transformation,” J. Opt. 17(4), 045102 (2015). [CrossRef]

13. R. Li, Z. Guo, W. Wang, J. Zhang, A. Zhang, J. Liu, S. Qu, and J. Gao, “Ultra-thin circular polarization analyzer based on the metal rectangular split-ring resonators,” Opt. Express 22(23), 27968–27975 (2014). [CrossRef] [PubMed]

14. Z. Wei, Y. Cao, X. Su, Z. Gong, Y. Long, and H. Li, “Highly efficient beam steering with a transparent metasurface,” Opt. Express 21(9), 10739–10745 (2013). [CrossRef] [PubMed]

15. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012). [CrossRef] [PubMed]

16. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012). [CrossRef] [PubMed]

17. W. Wang, Z. Guo, R. Li, J. Zhang, Y. Li, Y. Liu, X. Wang, and S. Qu, “Plasmonics metalens independent from the incident polarizations,” Opt. Express 23(13), 16782–16791 (2015). [CrossRef] [PubMed]

18. F. Zhou, Y. Liu, and W. Cai, “Plasmonic holographic imaging with V-shaped nanoantenna array,” Opt. Express 21(4), 4348–4354 (2013). [CrossRef] [PubMed]

19. R. Z. Li, Z. Y. Guo, W. Wang, J. R. Zhang, K. Y. Zhou, J. L. Liu, S. L. Qu, J. Gao, and S. T. Liu, “Arbitrary focusing lens by holographic metasurface,” Photonics Res.in press.

20. Q. Yang, J. Gu, D. Wang, X. Zhang, Z. Tian, C. Ouyang, R. Singh, J. Han, and W. Zhang, “Efficient flat metasurface lens for terahertz imaging,” Opt. Express 22(21), 25931–25939 (2014). [CrossRef] [PubMed]

21. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012). [CrossRef] [PubMed]

22. D. Hu, X. K. Wang, S. F. Feng, J. S. Ye, W. F. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1(2), 186–191 (2013). [CrossRef]

23. X. Y. Jiang, J. S. Ye, J. W. He, X. K. Wang, D. Hu, S. F. Feng, Q. Kan, and Y. Zhang, “An ultrathin terahertz lens with axial long focal depth based on metasurfaces,” Opt. Express 21(24), 30030–30038 (2013). [CrossRef] [PubMed]

24. X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), 72–77 (2013). [CrossRef]

25. A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013). [CrossRef] [PubMed]

26. W. Wang, Z. Y. Guo, R. Z. Li, J. R. Zhang, Y. Liu, X. S. Wang, and S. L. Qu, “Ultra-thin, planar, broadband, dual-polarity plasmonic metalens,” Photonics Res. 3(3), 68–71 (2015). [CrossRef]

27. M. Kang, T. Feng, H. T. Wang, and J. Li, “Wave front engineering from an array of thin aperture antennas,” Opt. Express 20(14), 15882–15890 (2012). [CrossRef] [PubMed]

28. Q. Zhu, D. Wang, X. Zheng, and Y. Zhang, “Optical lens design based on metallic nanoslits with variant widths,” Appl. Opt. 50(13), 1879–1883 (2011). [CrossRef] [PubMed]

29. Q. Zhu, J. Ye, D. Wang, B. Gu, and Y. Zhang, “Optimal design of SPP-based metallic nanoaperture optical elements by using Yang-Gu algorithm,” Opt. Express 19(10), 9512–9522 (2011). [CrossRef] [PubMed]

30. H. Pang, H. Gao, Q. Deng, S. Yin, Q. Qiu, and C. Du, “Multi-focus plasmonic lens design based on holography,” Opt. Express 21(16), 18689–18696 (2013). [CrossRef] [PubMed]

31. X. Z. Chen, M. Chen, M. Q. Mehmood, D. D. Wen, F. Y. Yue, C. W. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015). [CrossRef]

32. W. Wang, Z. Y. Guo, R. Z. Li, J. R. Zhang, A. J. Zhang, Y. Li, Y. Liu, X. S. Wang, and S. L. Qu, “L-shaped metasurface for both the linear and circular polarization conversions,” J. Opt. 17(6), 065103 (2015). [CrossRef]

33. L. J. Black, Y. Wang, C. H. de Groot, A. Arbouet, and O. L. Muskens, “Optimal polarization conversion in coupled dimer plasmonic nanoantennas for metasurfaces,” ACS Nano 8(6), 6390–6399 (2014). [CrossRef] [PubMed]

Polarization-independent longitudinal multi-focusing metalens

Abstract

1. Introduction

2. L-shaped gap nanoantennas

3. Design and numerical simulations

3.1 Metalens with one focus

3.2 Double-focusing metalens based on the partitioned mode

3.3 Double-focusing metalens based on radial alternating mode

3.4 Double-focus metalens based on angular alternating mode

3.5 Three-focusing metalens based on partitioned mode

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (11)

Equations (3)

Optics Express