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超透镜技术通常涉及两种相位:传输相位和几何相位。传输相位是通过改变单元结构的几何参数,利用等效折射率来实现对相位的调控。因此,通过控制单元结构的几何尺寸,可以得到覆盖0~2π范围的传输相位。几何相位也称为Pancharatnam-Berry (PB)相位,通过改变单元结构的方位角来实现对圆偏振散射光相位的调控。因此,通过控制单元结构的方位角,可以得到覆盖0~2π范围的几何相位。可以实现聚焦功能的超透镜须拥有传统球面透镜的功能,从超透镜发出的电磁波在焦平面处要发生相长干涉。根据等光程原理,单焦点超透镜中任意一点的相位可表示为:
$$ \varphi (x,y) = {{2\pi } \mathord{\left/ {\vphantom {{2\pi } \lambda }} \right. } \lambda }\left( {\sqrt {{x^2} + {y^2} + {f^2}} - f} \right) $$ (1) 式中:
$\lambda $ 为入射波长;x和y为超透镜平面坐标;$f$ 为超透镜的焦距。只要选定了$\lambda $ 和$f$ ,任意位置的结构单元所满足的相位也随之确定。为了设计一个对于圆偏振(CP)光有两个横向分开焦点的二维聚焦超透镜。左旋圆偏振(LCP)光入射时,透镜各点的相位可表示为:$$ {\varphi _{RL}} = {{2\pi } \mathord{\left/ {\vphantom {{2\pi } \lambda }} \right. } \lambda }\left[ {\sqrt {{{\left( {x - {x_0}} \right)}^2} + {f^2}} - f} \right] $$ (2) 右旋圆偏振(RCP)光入射时,透镜各点的相位可表示为:
$$ {\varphi _{LR}} = {{2\pi } \mathord{\left/ {\vphantom {{2\pi } \lambda }} \right. } \lambda }\left[ {\sqrt {{{\left( {x + {x_0}} \right)}^2} + {f^2}} - f} \right] $$ (3) 式中:
$x{}_0$ 为焦点偏离中心位置的距离。对于半波片来说,透射光只含有交叉偏振光,基于几何相位和传输相位可以得到
${\varphi _{RL/LR}} = {\phi _{xx}} \pm 2\theta $ ,其中${\phi _{xx}}$ 为x线偏振(XLP)光入射时x线偏振透射光所对应的相位。也就是说,通过为单元结构选择合适的几何尺寸和旋转角度,可以分别得到其在LCP和RCP光入射时所对应的相位。进一步来说,如果单元结构同时工作于LCP和RCP入射光,那么XLP光所对应的传输相位和旋转角度满足的方程可分别写为:$$ {\phi _{xx}} = \frac{1}{2}\left[ {\left( {{\varphi _{RL}} - 2{n_1}\pi } \right) + \left( {{\varphi _{LR}} - 2{n_2}\pi } \right)} \right] $$ (4) $$ \theta = \frac{1}{4}\left[ {\left( {{\varphi _{RL}} - 2{n_1}\pi } \right) - \left( {{\varphi _{LR}} - 2{n_2}\pi } \right)} \right] $$ (5) 式中:
${n_1}$ 和${n_2}$ 为整数。因此,通过选择具有合适的几何尺寸和旋转角的单元结构,可以实现任意的相位分布,从而可以设计具有任意横向距离为$2{x_0}$ 的双焦点超透镜。
High numerical aperture bifocal metalens with regulatory focusing intensity
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摘要: 基于超表面对光波的振幅、相位和偏振进行调控来实现聚焦与成像的超透镜受到广泛关注。设计了一种聚焦强度可调的高数值孔径的双焦点超透镜,并进行了理论分析和仿真验证。仿真结果表明,该超透镜能有效地将圆偏振入射光聚焦到半高宽为0.44λ的光斑上,对应的数值孔径高达0.95。此外,通过改变入射光的偏振态,可以灵活地调制两个焦点的相对强度,而不同于以往的双焦点超透镜需要对光强进行重新组合。更重要的是,当圆偏振光入射时,它的聚焦效率可达65%,可适用在0.8~1.2 THz的较宽频率范围和0°~20°的入射角内,同时该工作为多焦点超透镜的设计提供了重要思路,也将在多成像系统、光学层析成像技术等许多领域具有较高的应用价值。Abstract: The metalenses with focusing and imaging based on metasurfaces, which can manipulate the amplitude, phase, and polarization of light waves, have attracted enormous attentions. A high numerical aperture bifocal metalens with regulatory focusing intensity was designed, and both theoretical analysis and simulation verification were demonstrated. The simulation results reveal that the designed metalens can focus circularly polarized incident light efficiently to a spot of full width at half-maximum as small as ~0.44λ, and the corresponding numerical aperture reaches up to 0.95. Besides, the relative intensity of two focal points can be adjusted flexibly through changing the polarization states of the incident light, which is unlike previous bifocal metalenses with repatterned intensity. More importantly, when the circularly polarized light is incident, the focusing efficiency is both up to 65%, and it is available for a relatively broad frequency range from 0.8 to 1.2 THz and a wide incident angles of 0°-20°. This work provides an important idea for designing the multi-focal metalenses, and it will also have high application value in many fields such as multi-imaging system, optical tomography.
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Key words:
- physical optics /
- metalens /
- phase manipulation /
- dielectric metasurface /
- polarized light
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图 1 (a) 双焦点超透镜聚焦示意图;(b)~(c) 具有高度H、长度L、宽度W的硅微砖的侧视图和俯视图,其中单位晶胞尺寸为P;(d)具有旋转角度为θ的硅微砖的俯视图;(e) 构建的双焦点超透镜的俯视图
Figure 1. (a) Schematic of focusing of the bifocal metalens; (b)-(c) Side and top views of silicon microbricks with height H, length L and width W, and the unit cell size is P; (d) Top view of the silicon microbrick with rotation angle θ; (e) Top view of the constructed bifocal metalens
图 2 双焦点超透镜在RCP (a)、LCP (b)和XLP (c)光入射下的聚焦场的强度分布;(d) RCP(蓝线)和LCP(红线)光分别入射产生通过焦点的沿着x轴的强度分布曲线
Figure 2. Intensity distribution of the bifocal metalens under the RCP (a), LCP (b) and XLP (c) incidence light, respectively; (d) Intensity distribution curve along the x-axis through the focal point under the RCP (blue line) and LCP (red line) incidence light, respectively
图 3 当入射光分别为
$ {[ {\begin{array}{*{20}{c}} 1\;\;{6i} \end{array}} ]^{\text{T}}} $ (a),$ {[ {\begin{array}{*{20}{c}} 1\;\;{ - 6i} \end{array}} ]^{\text{T}}} $ (b),$ {[ {\begin{array}{*{20}{c}} 1\;\;{2i} \end{array}} ]^{\text{T}}} $ (c) 和$ {[ {\begin{array}{*{20}{c}} 1\;\;{ - 2i} \end{array}} ]^{\text{T}}} $ (d) 时,聚焦场的强度分布Figure 3. Intensity distribution of the focusing field when the incident light is
$ {[ {\begin{array}{*{20}{c}} 1\;\;{6i} \end{array}} ]^{\text{T}}} $ (a),$ {[ {\begin{array}{*{20}{c}} 1\;\;{ - 6i} \end{array}} ]^{\text{T}}} $ (b),$ {[ {\begin{array}{*{20}{c}} 1\;\;{2i} \end{array}} ]^{\text{T}}} $ (c) and$ {[ {\begin{array}{*{20}{c}} 1\;\;{ - 2i} \end{array}} ]^{\text{T}}} $ (d), respectively图 4 当RCP光以10°(a)和20°(c)分别入射时聚焦场的强度分布;当LCP光以10°(b)和20°(d)分别入射时聚焦场的强度分布
Figure 4. Intensity distribution of the focusing field when the RCP light incidence with the angle of 10° (a) and 20° (c), respectively; Intensity distribution of the focusing field when the LCP light incidence with the angle of 10° (b) and 20° (d), respectively
图 5 频率为0.8 THz的 RCP(a)和LCP(b)光垂直入射时聚焦场的强度分布;频率为1.2 THz的RCP(c)和LCP(d)光垂直入射时聚焦场的强度分布
Figure 5. Intensity distribution of the focusing field when the RCP (a) and LCP (b) light incidence with the frequency of 0.8 THz; Intensity distribution of the focusing field when the RCP (c) and LCP (d) light incidence with the frequency of 1.2 THz
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