# Plasmonic Metasurfaces for Superposition of Profile-Tunable Tightly Focused Vector Beams and Generation of the Structured Light

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basic Principles

_{2}substrate; they are specified as the inner and outer sets of slit-pairs according to the radii of the rings, whereas the slits have the same size and the orientation angles of the slit-pairs rotate with the azimuths. For clarity and convenience, the slits in each set of slit-pairs are also signified as inner-ring slits and outer-ring slits, respectively. Under the illumination of linearly polarized light, a set of slit-pairs produces both the left-handed and right-handed circularly polarized vortices |L, −q> of order −q and |R, q> of order q, yielding the VB of order q; while for both the inner and outer sets of slit-pairs, the tightly focused VBs of orders q = n and q = g are produced at the same time, respectively, and the superposition of the two VBs are realized. Since the light field of each VB in the area near the center point O′ of the observation plane are simply the Fourier transform of the waves from the corresponding set of slit-pairs, the doughnut size of intensity profile is decreased with the increase of the corresponding slit-pair ring. Thus, by controlling the rotational orders of the two sets of slit-pairs and adjusting the radii of the two sets of slit-pair rings, the doughnuts of the VBs of the orders n and g can be tuned to be with the same size, and the superposition of the two VBs with equal doughnuts is realized.

**E**

_{x}|

^{2}and |

**E**

_{y}|

^{2}of x- and y-components and the total intensity |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}, respectively, for the VBs of orders 1 and 3 and the superimposed light fields.

_{0}+ mθ to form a helical profile of geometric phase, where θ and m are the azimuthal angle and the rotational order of the slit-pair, respectively, and φ

_{0}denotes the orientation angle of the initial slit at θ = 0. By setting φ

_{0}= 0°, it arrives at φ = mθ, which is the case we use for the metasurface designs. Additionally, ${\widehat{\mathit{e}}}_{x}$ and ${\widehat{\mathit{e}}}_{y}$ are unit vectors in the x and y direction, ${\widehat{\mathit{e}}}_{r}$ and ${\widehat{\mathit{e}}}_{t}$ in radial and azimuthal directions, and $\widehat{\mathit{u}}$ and $\widehat{\mathit{v}}$ are in the directions parallel and perpendicular to the long side of the slit.

**E**

_{v}generated by the inner slit at p (r, θ) can be written as [61]

**E**

_{pr}(r, θ) and

**E**

_{pt}(r, θ) of the wavefield produced by the slit-pair are obtained [73]:

^{2}+ r

^{2})

^{1/2}. Remembering the orientation angle φ = mθ and using the properties of the Bessel function, the calculations on Equation (10) give the following expression:

**E**

_{g}(R, α) produced by the set of slit-pairs on the outer ring is the superposition of the two circularly polarized vortices of topological charge ±g:

**E**

_{n}(R, α) can be expressed as follows:

**E**

_{n}(R, α) and

**E**

_{g}(R, α), the light field

**E**(R, α) produced by the entire metasurface is the following:

**E**

_{x}and

**E**

_{y}given in Jones vector, respectively, and the corresponding intensities |

**E**

_{x}|

^{2}and |

**E**

_{y}|

^{2}and the total light intensity |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}are readily obtained.

**E**

_{z}smaller than a resolution limit (0.61λ/N.A.), and the two VBs can be regarded as tightly focused. Consequently, the superposition of tightly focused VBs can be realized. Based on Equation (14), it can be also deduced that the radius R

_{n}and R

_{g}of the doughnut intensity profiles of the two VBs are related to the first maximum points X

_{n}and X

_{g}for the Bessel functions of the orders n and g, respectively, with ${X}_{n}=k{R}_{n}{r}_{n}^{(i)}/{s}_{n}^{(i)}$ and ${X}_{g}=k{R}_{g}{r}_{g}^{(i)}/{s}_{g}^{(i)}$. Yet, for the superposition of traditional Bessel VBs, it can be considered as the case in which the radius ${r}_{n}^{(i)}$ and ${r}_{g}^{(i)}$ of the two slit-pair rings are equal; whereas the higher the order of Bessel VB, the larger the maximum point X

_{n}or X

_{g}and the larger the radius R

_{n}or R

_{g}of the doughnut. Different from conventional VBs, here by adjusting radii ${r}_{n}^{(i)}$ and ${r}_{g}^{(i)}$ of the slit-pair rings in accordance with the given rotation orders, respectively, the radii R

_{n}and R

_{g}of the doughnuts are modulated to be equal for the two generated VBs, i.e., R

_{n}= R

_{g}; thus, the superposition of the tightly focused VBs of profile tunability is finally realized, and the related structured light is also generated.

## 3. Theoretical Calculation and Numerical Simulation

#### 3.1. Design of the Metasurfaces

_{q}is the first maximum point for the Bessel function of order q, which gives the relation between the radius R

_{q}of the doughnut and the radius ${r}_{q}^{(i)}$ of slit-pair ring. From this relation, the variation of the doughnut radius R

_{q}of the VBs of order 1 to 4 versus ${r}_{q}^{(i)}$ is obtained and is shown in Figure 2a. If the doughnut radius of the two VBs to be superimposed are both set as R

_{s}, by drawing the horizontal dashed line with vertical coordinate value of R

_{s}as shown in Figure 2a, the horizontal coordinate of its intersections with the curves gives the radius of the corresponding slit-pair ring. We choose two of these intersection points labeled in red and blue, and we can read the radius ${r}_{n}^{(i)}$ and ${r}_{g}^{(i)}$ of the inner and outer slit-pair rings for n = 1 and g = 3, respectively; accordingly, the corresponding radii ${r}_{n}^{(o)}$ and ${r}_{g}^{(o)}$ of the outer slit rings in each slit-pair rings are also obtained through simple calculations. Thus, by achieving the radius values of the two slit-pair rings with the setting rotational orders, the metasurface for the superposition of profile-tunable VBs of order n and g is designed. In addition, in Figure 2a, the intersections of the vertical dashed line with the blue and red curves represents the equal radius ${r}_{n}^{(i)}={r}_{g}^{(i)}$ of the two slit-pair rings with different rotation orders, and the corresponding doughnut radius values of R

_{s}and ${R}_{s}^{\prime}$ are for the usual VB of unmodulated intensity profiles and their superposition.

_{s}and the superimposed fields, respectively. Compared with the results in Figure 2b, the results in Figure 2c for the superimposed fields of the profile-tunable VBs with equal doughnuts have different characteristics from the those of unmodulated VBs, and the intensity profile exhibits a simple pattern and concentrating power.

#### 3.2. Calculation of the Superimposed Field of Tightly-Focused VBs

_{1}, S

_{2}, S

_{3}and S

_{4}, to realize the superposition of profile-tunable tightly focused VBs of the orders (n, g) = (1, 3), (2, 4), (1, 2) and (2, 3), respectively. We first performed theoretical calculation of the light fields generated by each of the four samples based on the Huygens-Fresnel principle, and then implemented numerical simulation by using the finite difference in time domain (FDTD) for the superimposed fields and intensities. In the simulation, the parameters for the optical system and the metasurfaces are the same as those given in Section 2. For the designed metasurface, the Au film is 200 nm thick. The incident light is linearly polarized in the horizontal direction; it illuminates the metasurface from the side of substrate, and the output fields are calculated on the focused plane. The radii ${r}_{n}^{(i)}$ and ${r}_{g}^{(i)}$ of the two slit-pair rings were originally set with the theoretical values and were finely adjusted according to the practical results of FDTD simulations. The practical radius values for the inner and outer slit-pair rings of the metasurface samples and the corresponding doughnut-radius values of R

_{s}are given in Table 1. In addition, we note that the complex refractive index of gold film is 0.12517 + 3.3326 i and the refractive index of SiO

_{2}is 1.4570 at wavelength 632.8 nm [76,77,78], as given in Table 2.

_{1}, S

_{2}, S

_{3}and S

_{4}, respectively. Figure 3(a1–d1,a2–d2,a3–d3) are the theoretical results for the x- and y- component and total intensities |

**E**

_{x}|

^{2}, |

**E**

_{y}|

^{2}and |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}of the four samples, respectively; the overlaid blue arrows denote the polarization states of light fields. Figure 3(a4–d4,a5–d5,a6–d6) are the corresponding results of FDTD simulations, respectively. It can be seen that these intensity images have unique and interesting characteristics; particularly, for the superimposed fields of VBs of the orders 1 and 3 by samples S

_{1}and the orders 2 and 4 by S

_{2}, respectively, the total light intensities |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}both show a unique double petal pattern, while patterns of the component intensities |

**E**

_{x}|

^{2}and |

**E**

_{y}|

^{2}have petals of variable numbers. These petal-shaped intensity distributions are not only different from those of the conventional single VBs [79], but also different from the superimposed fields of the VBs with unmodulated doughnuts [80] while for the superimposed fields of VBs of the orders 1 and 2 by samples S

_{3}and the orders 2 and 3 by S

_{4}, respectively, the total intensity |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}still exhibits the well doughnut-shaped distribution. The component intensities |

**E**

_{x}|

^{2}and |

**E**

_{y}|

^{2}of the superimposed fields are apparently similar to those of the single VB of the order 2 and 3, respectively, which indicates that the VB of the higher order plays the dominant role in the superposition in the case when the order difference of two VBs is 1. Furthermore, we find it very interesting that for samples S

_{1}and S

_{3}, the intensity distributions are entirely different from the VB of the order 1, but their spatial distributions of polarization are the same and are identical to the radially polarized VB of the order 1. Similarly, for samples S

_{2}and S

_{4}, the intensity profiles are completely different from those of the VB of the order 2, but the distributions of polarizations are coincidentally the same as radially polarized VB of the order 2. This might be an example of inconsistent topologies in polarization singularity and helicity of the wavefronts in the superimposed VB fields.

#### 3.3. Analysis of Results

**E**

_{x}|

^{2}and |

**E**

_{y}|

^{2}and total intensity |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}, respectively. We take sample S

_{1}as an example to analyze the intensity curves, in which the two VBs involved in generating the superimposed fields are of orders 1 and 3, respectively. From the x- and y- components

**E**

_{x}and

**E**

_{y}of the superimposed fields given in Equation (14), the corresponding component and total intensities are $|{\mathit{E}}_{x}{|}^{2}={J}_{1M}^{2}{\mathrm{cos}}^{2}\alpha +{J}_{3M}^{2}{\mathrm{cos}}^{2}3\alpha -2{J}_{1M}{J}_{3M}\mathrm{cos}\alpha \mathrm{cos}3\alpha $, $|{\mathit{E}}_{y}{|}^{2}={J}_{1M}^{2}{\mathrm{sin}}^{2}\alpha +{J}_{3M}^{2}{\mathrm{sin}}^{2}3\alpha $ $-2{J}_{1M}{J}_{3M}\mathrm{sin}\alpha \mathrm{sin}3\alpha $ and $|\mathit{E}{|}^{2}={J}_{1M}^{2}+{J}_{3M}^{2}-2{J}_{1M}{J}_{3M}\mathrm{cos}2\alpha $, respectively. Here J

_{1M}and J

_{3M}are the first maxima of Bessel functions of orders 1 and 3, respectively.

**E**|

^{2}takes the maxima at α = 90° and 270°, which is in consistency with the two bright petals in the theoretical and simulation intensity patterns in Figure 3(a3,a6), respectively. For the expression of |

**E**

_{x}|

^{2}, the maxima of intensity are at α = 53.0°, 127.0°, 233.0° and 307.0°, which conforms with the four bright petals of the intensities in Figure 3(a1,a4), while for the expression of |

**E**

_{y}|

^{2}, two major maxima appear at α = 90° and 270°, which are verified by the curves in Figure 4a; interestingly, four minor maxima also appear at α ≈ 21.7°, 158.2°, 201.8°and 338.3°, which are demonstrated in the inset of Figure 4a as the magnified view of the central part of the curve I = |

**E**

_{y}|

^{2}and are also observed in both the theoretical and simulation patterns in Figure 3(a2,a5). Coincidentally, the superimposed field of the VBs of orders 2 and 4 by sample S

_{2}has the similar characteristics, and the curves of the intensity versus α in Figure 4b are consistent with the theoretical and simulation results in Figure 3(b1–b6).

_{3}and the orders 3 and 4 by S

_{4}, the intensity distributions have the common characteristics. Similarly, taking sample S

_{3}as the example, we obtain that

**E**

_{x}∝ J

_{1M}cosα − iJ

_{2M}cos2α and

**E**

_{y}∝ J

_{1M}sinα − iJ

_{2M}sin2α; the corresponding intensities are $|{\mathit{E}}_{x}{|}^{2}={J}_{1M}^{2}{\mathrm{cos}}^{2}\alpha +{J}_{2M}^{2}{\mathrm{cos}}^{2}2\alpha $, $|{\mathit{E}}_{y}{|}^{2}={J}_{1M}^{2}{\mathrm{sin}}^{2}\alpha +{J}_{2M}^{2}{\mathrm{sin}}^{2}2\alpha $ and $|\mathit{E}{|}^{2}={J}_{1M}^{2}+{J}_{2M}^{2}$. These expressions correspond to the intensity curves versus α for sample S

_{3}in Figure 4c; it is interesting that the curve of the total intensity |

**E**|

^{2}is of constant value, as indicated by circle of constant radius ${J}_{1M}^{2}+{J}_{2M}^{2}$, which is supported by the homogeneous doughnut distributions in Figure 3(c3,c6). In addition, |

**E**

_{x}|

^{2}takes the major maxima at α = 0° and 180°, and the minor maxima at α = 90° and 270°, and |

**E**

_{y}|

^{2}takes the maxima at α ≈ 55.2°, 124.7°, 235.2° and 304.7°, as demonstrated in the corresponding curve in Figure 4c. Apparently, these features are consistent with the theoretical and simulation patterns for sample S

_{3}in Figure 3(c1–c6).

_{1}and for that of the orders 2 and 4 by S

_{2}, respectively, the double petals in the total intensity are originated from the cross term −2J

_{n}J

_{g}cos(g − n)α, which causes the maxima at α = 90° and 270°. Similarly, the cross terms also provide diverse petal distributions for the intensities of the component fields. However, for the superposition of VBs of orders n = 1 and g = 2 and VBs of orders 2 and 3 by samples S

_{3}and S

_{4}, respectively, the cross terms are vanished owing to the orthogonality of the real and imaginary parts in the VB fields, and total intensities are reduced to the incoherent additions of the VB intensities. Thus, the doughnuts of the total intensities appear to be homogeneous. Additionally, as the cosine or sine function squared of α, the intensities of the VBs of higher orders vary more rapidly versus α; thereby the component intensities of sample S

_{3}and S

_{4}exhibit the distributions with more petals, very much similar to the involved higher-order VB in the superposition. Here we note that these phenomena are unique in the superimposed fields of tightly focused VBs with equal doughnuts in this work, and they would enrich the structured light fields with novel constituents.

## 4. Experiment

_{2}substrate, which is placed on the three-dimensional translation stage. The microscopic objective lens (MO, N.A. = 0.9/100×) is used to magnify and image the superimposed field, which is obtained at 5 μm from the sample surface. Then the image intensity pattern is captured by the sCMOS (Zyla-5.5, 16) placed on the image plane. An analyzing polarizer (P) is used to extract the light intensities |

**E**

_{x}|

^{2}and |

**E**

_{y}|

^{2}of the x and y components of the superimposed fields. The quarter-wave plate (QWP) is typically removed from the optical path; when it is placed in, the setup will be used to measure the superimposed fields of the profile-tunable higher-order Poincaré VBs, which will be discussed in the following section.

_{2}substrate by magnetron sputtering, and then two sets of orthogonal slit-pairs were etched in the gold film with the focused ion beam (FIB) system (FEI Helios G4 UX) with the resolution 4.0 nm at 30 kV using the preferred statistical method. The radius parameters of the slit-pair rings for the fabricated samples S

_{1}, S

_{2}, S

_{3}and S

_{4}are the same as those in Table 1, and the nanoslit parameters are the same as those in the FDTD simulations. Again, the four fabricated samples are used to generate the superimposed fields of the VBs of the orders (n, g) = (1, 3), (2, 4), (1, 2) and (2, 3), respectively. Figure 6a–d are the SEM images of samples S

_{1}–S

_{4}, respectively, and the insets show the local magnified views. From the variation of the orientation angles of the nanoslits in the images, the rotational orders of the two sets of slit-pairs (n/2, g/2) = (0.5, 1.5), (1, 2), (0.5, 1) and (1, 1.5) could be qualitatively judged for the four samples, respectively. Figure 6(a1–d1,a2–d2,a3–d3) are the images of the component and total intensities |

**E**

_{x}|

^{2}, |

**E**

_{y}|

^{2}and |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}generated by samples S

_{1}–S

_{4}, respectively. On the whole, they are in agreement with the corresponding theoretical and simulation results in Figure 3, validating feasibility of the method for metasurface designs. It should also be noted that there are still some discrepancies between the experimental and theoretical results. These discrepancies mainly stem from the unavoidable factors, such as the errors of nanoslit sizes in the fabrications, the imperfectness of optical elements, and misalignment in the optical setup for the measurements, which may deteriorate the quality of the intensity images in the experiments. In addition, there is a small amount of residual gallium ions on the samples fabricated with FIB; however, the surface plasmon polaritons (SPPs) excited by gallium ions are usually much weaker than those excited by noble metals or gold. So, the errors of the optical fields caused by the residual gallium ions might be much smaller than those due to the several factors as mentioned above, and then the influence of the residual gallium ions might be very insignificant. We believe that such interesting experimental phenomena are of potential applications in the fields such as optical communications, particle manipulations and quantum information.

## 5. Discussions

**E**

_{in}can be represented by the point (2Θ, 2Φ) on the conventional Poincaré sphere, and it is written as

_{σ}is expressed as a

_{σ =}

_{1}= sinΘ and a

_{σ = −}

_{1}= cosΘ for σ = 1 and σ = −1, respectively. Using the above Equation and following the derivations of

**E**

_{g}(R, α) in Equations (11) and (12), we derive the light field ${\mathit{E}}_{g}^{(e)}(R,\alpha )$ produced by the slit-pairs on the outer ring under the illumination of elliptical polarization, in which the circular polarization ${\mathit{E}}_{in}^{\sigma}=[\begin{array}{cc}1& \sigma i\end{array}]/\sqrt{2}$ were replaced by a

_{σ}exp (−iσΦ)

**E**

^{σ}for both σ = 1 and σ = −1; then we obtain

**E**

^{(e)}(R, α) of the HOP VBs of the orders n and g are written as

_{1}and S

_{3}, where the arrowed circle, ellipses and line in the upper title row indicate the polarization states corresponding to points i to ix on the conventional Poincaré sphere. The gray-scale images in rows A, C and E are the experimental intensity profiles for |

**E**

_{x}|

^{2}and |

**E**

_{y}|

^{2}and |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}of the superimposed fields produced by sample S

_{1}, respectively; the images in rows F, H and J are the corresponding experimental results of intensities by sample S

_{3}, respectively; and the colored images in rows B, D, G and I are the corresponding simulation counterparts to the experimental images, respectively, as labeled by the color bars; the double-arrowed lines in the left title column labels the transmitting direction of the analyzing polarizer. It can be seen that when the polarization state changes from that in column i to column ix, the boundary of the petals in intensity profiles changes from being blurred to being clear and then to being blurred again. Moreover, in the results for sample S

_{3}, the light intensity profiles undergo a rotation. The phenomena are related to the varying amplitudes of the left-handed and right-handed circularly polarized vortices in HOP VBs of orders n and g during the change of the incident polarization ellipticity. Apparently, for the polarization states at two symmetrical points with respect to the equator, the amplitude and phase of the left-handed and right-handed circularly polarized vortices are flipped, and this leads to the conversion of y components in the superposed fields; as a result, the intensity profiles appear to be rotating with evolution of the polarization states on the prime meridian. We believe that the superposition of profile-tunable tightly focused HOP VBs would be of significance for applications in fields such as quantum communications and cryptography, optical trapping and vector mode multiplexing.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic for superposing the profile-tunable tightly focused VBs by metasurface. (

**b**) The principle illustration for the metasurface superposes the VBs of the orders n = 1 and g = 3 with equal light intensity profiles. Panel I: metasurface of inner set slit-pairs; Panel II: metasurface of outer set slit-pairs; Panel III: metasurface consists of inner and outer sets slit-pairs. The white double arrows show the transmitting direction of the analyzing polarizer. (

**c**) Geometry and coordinate relations for points on the object and observations planes. The two sets of the orthogonal slit-pairs and the rings the slits lie on are illustrated. (

**d**) The overlapping view of the object plane Oxy and the observation plane O′x′y′. (

**e**) Schematic for unit vectors of the coordinates and orientations of slits in a representative orthogonal slit-pair.

**Figure 2.**(

**a**) The variation of the doughnut radius R

_{q}for the VBs of orders 1 to 4 versus the radius ${r}_{q}^{(i)}$ of the slit-pair ring. Superposition of VBs of the orders 1 and 3 (

**b**) by two slit-pair rings of equal radius but with unequal radii of the formed doughnuts and (

**c**) by two slit-pair rings of modulated radius with equal radii of doughnuts.

**Figure 3.**The theoretical and simulation results for the intensities of the x- and y- components and total intensities |

**E**

_{x}|

^{2}, |

**E**

_{y}|

^{2}and |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}of the superimposed VBs with equal doughnuts for the samples S

_{1}, S

_{2}, S

_{3}and S

_{4}, respectively.

**Figure 4.**The curves of the intensity of superimposed VBs versus azimuthal angle α, (

**a**–

**d**) show the theoretical curves of the intensities |

**E**

_{x}|

^{2}, |

**E**

_{y}|

^{2}and |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}with α for samples S

_{1}–S

_{4}, respectively.

**Figure 5.**The diagram of experimental optical setup. From left to right, the optical devices including the laser, half-wave plate (HWP), quarter-wave plate (QWP), sample and three-dimensional translation stage, microscopic objective lens (MO), analytical polarizer (P), and sCMOS camera are shown.

**Figure 6.**SEM images of the four samples and the experimental intensity images of the superimposed VBs. The insets show the magnified local images of the orthogonal slit-pairs.

**Figure 7.**(

**a**) The left panel: the HOP spheres of order n; the right panel: HOP spheres of order g; middle panel: the illustration of the superposition of the two HOP VBs. (

**b**) Experimental and simulation intensities |

**E**

_{x}|

^{2}, |

**E**

_{y}|

^{2}and |

**E**

_{x}|

^{2}+ |

**E**

_{y}|

^{2}of the superimposed light fields for the HOP VBs of the order n and g with equal doughnut size produced by samples S

_{1}and S

_{3}, respectively.

**Table 1.**Parameters of designed four samples (the two VBs of orders n and g to be superimposed have the equal doughnut radius R

_{s}).

Sample | S_{1} | S_{2} | S_{3} | S_{4} |
---|---|---|---|---|

(n, g) | (1, 3) | (2, 4) | (1, 2) | (2, 3) |

R_{s} | 0.5458 | 0.63 | 0.432 | 0.4844 |

${r}_{n}^{(i)}$ | 1.807 | 2.7983 | 2.3775 | 4.1119 |

${r}_{n}^{(o)}$ | 2.587 | 3.3993 | 3.041 | 4.5939 |

${r}_{g}^{(i)}$ | 6.048 | 8.0784 | 5.0731 | 8.978 |

${r}_{g}^{(o)}$ | 6.448 | 8.4482 | 5.5085 | 9.3415 |

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**MDPI and ACS Style**

Li, L.; Zeng, X.; Gu, M.; Zhang, Y.; Sun, R.; Zhang, Z.; Cui, G.; Zhou, Y.; Cheng, C.; Liu, C.
Plasmonic Metasurfaces for Superposition of Profile-Tunable Tightly Focused Vector Beams and Generation of the Structured Light. *Photonics* **2023**, *10*, 317.
https://doi.org/10.3390/photonics10030317

**AMA Style**

Li L, Zeng X, Gu M, Zhang Y, Sun R, Zhang Z, Cui G, Zhou Y, Cheng C, Liu C.
Plasmonic Metasurfaces for Superposition of Profile-Tunable Tightly Focused Vector Beams and Generation of the Structured Light. *Photonics*. 2023; 10(3):317.
https://doi.org/10.3390/photonics10030317

**Chicago/Turabian Style**

Li, Lianmeng, Xiangyu Zeng, Manna Gu, Yuqin Zhang, Rui Sun, Ziheng Zhang, Guosen Cui, Yuxiang Zhou, Chuanfu Cheng, and Chunxiang Liu.
2023. "Plasmonic Metasurfaces for Superposition of Profile-Tunable Tightly Focused Vector Beams and Generation of the Structured Light" *Photonics* 10, no. 3: 317.
https://doi.org/10.3390/photonics10030317