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为实现自旋依赖的光学响应,所设计超构表面在相互正交的圆偏振光垂直入射下,满足下列关系式[20]:
$$ {J_0}(x)\left| {LCP} \right\rangle = \exp \left[ {i{\varphi ^ + }(x)} \right]\left| {RCP} \right\rangle $$ (1) $$ {J_0}(x)\left| {RCP} \right\rangle = \exp \left[ {i{\varphi ^ - }(x)} \right]\left| {LCP} \right\rangle $$ (2) 式中:J0(x)为入射光的琼斯矩阵;
$\left| {LCP} \right\rangle {\text{ = }}\dfrac{1}{{\sqrt 2 }}{\left[ {1{\text{, i}}} \right]^{\rm{T}}}$ 为左旋圆偏振光矢量;$\left| {RCP} \right\rangle {\text{ = }}\dfrac{1}{{\sqrt 2 }}{\left[ {1, - i} \right]^{\rm{T}}}$ 为右旋圆偏振光矢量;φ+(x)和φ−(x)分别为LCP和RCP光对应的柱状透镜空间双曲相位分布。结合公式(1)、(2)和左/右旋圆偏振光矢量,琼斯矩阵J0(x)可以表示为:$$ {J_0}\left( x \right){\text{ = }}\frac{1}{2}\left[ {\begin{array}{*{20}{c}} {\exp \left[ {i{\varphi ^ + }(x)} \right]}&{\exp \left[ {i{\varphi ^ - }(x)} \right]} \\ { - \exp \left[ {i{\varphi ^ + }(x)} \right]}&{ - \exp \left[ {i{\varphi ^ - }(x)} \right]} \end{array}} \right]{\left[ {\begin{array}{*{20}{c}} 1&1 \\ i&{ - i} \end{array}} \right]^{ - 1}} $$ (3) 由公式(3)可得J0(x)的本征值和本征向量。将圆坐标转换为笛卡尔坐标,通过推导,得到如下关系:
$$ {P_{XX}}(x) = \left| {{\varphi ^ + }(x) + {\varphi ^ - }(x)} \right|/2 $$ (4) $$ {P_{YY}}(x) = \left| {{\varphi ^ + }(x) + {\varphi ^ - }(x)} \right|/2 - \pi $$ (5) $$ \theta (x){\text{ = |}}{\varphi ^ + }{\text{(}}x{\text{) + }}{\varphi ^ - }{\text{(}}x{\text{)|/4}} $$ (6) 式中:PXX,PYY与TXX,TYY分别代表x和y方向线偏振入射光透过各向异性矩形纳米柱后沿矩形纳米柱长轴和短轴方向的透射相移和透射率。PXX与PYY决定透射光的传输相位,旋转角θ决定透射光的PB相位。
为满足琼斯矩阵J0(x),需要建立一个覆盖0~2π相移库;同时,为提高偏振转化效率,实现高清晰、少混沌的聚焦效果,组成超构透镜的所有矩形纳米柱单元结构应满足半波片或准半波片要求,即:
$$ \left| {{P_{XX}}(x) - {P_{YY}}(x)} \right| \approx \pi $$ (7) $$ {T_{XX}} \approx {T_{YY}} \approx 1 $$ (8) 基于以上分析,从GSST各向异性单元结构的设计入手,采用具备高深宽比、高折射率GSST矩形纳米柱(ng≈3.19 + 0.001i)作为基本结构,并以低折射率无损介质CaF2(nc=1.47)作为衬底,如图1(a)所示。高折射率对比度使得单元结构在中红外波段内(λ0=4200 nm)获得了类似截断波导的响应,将大部分入射光限制在矩形纳米柱内。通过优化,最终确定单元结构周期p=3000 nm,GSST矩形纳米柱高度h=2800 nm。同时为获得0~2π相位覆盖,GSST矩形纳米柱长轴a和短轴b是变化的,变化范围均为300~2800 nm。
图 1 (a) GSST超表面及其单元结构示意图;(b) 两方案对应的最优单元结构在波长λ0 = 4200 nm圆偏振光入射下的交叉偏振透射光的振幅和相位;(c)~(f) 线偏振光下,透射率TXX ,TYY以及相移PXX ,PYY 对GSST矩形纳米柱面内尺寸a和b的扫描图
Figure 1. (a) Schematic diagrams of GSST-based metasurface and its constituent; (b) Propagation phase and transmitted amplitude under CP incidence for selected 30 meta-atoms corresponding to the proposed two schemes; Scanning plots of transmission (c), (e) and propagation phase (d), (f) versus dimensions a and b of GSST rectangular nanopillars for LP incidences, respectively
文中所有的结果均通过仿真商业软件Comsol Multiphysics 5.5得到。对于超构透镜单元结构,仿真时在x轴和y轴方向设置周期性边界条件(Periodic boundary conditions,PBCs),沿z轴在单元结构的上下设置两周期性端口(Ports),且激励源设置在单元结构的下端口。对于超构透镜,完美匹配层(Perfectly matched layer,PML)包围在模型四周,并且通过背景场设置激励源。模型中CaF2折射率设置为常数1.47,所采用的波长依赖的Ge2Sb2Se4Te1光学常数[21]。此外,所提方案易于制备及性能表征。在制备方面,可首先通过控制Ge2Sb2Te5靶和Ge2Sb2Se5靶的蒸镀速率,用热蒸镀法在CaF2基底上沉积2800 nm厚的Ge2Sb2Se4Te1薄膜;之后在薄膜上方旋涂1000 nm 的ZEP520A光刻胶,经过电子束曝光(或光刻)、显影及反应离子刻蚀等工艺获得微结构图案;最后用N-甲基-2-吡咯烷酮去除残留的ZEP光刻胶,即完成制备。在表征方面,使超连续准直激光依次经过半波片、1/4玻片、样品、物镜、1/4玻片、偏振片、CCD等即可实现对光场分布的研究。
图1(b)~(f)表示对单元结构透射性能的仿真结果,其中图1(c)~(f)表示波长λ0=4200 nm的x和y方向线偏振入射光透过各向异性矩形纳米柱后,沿矩形纳米柱长轴和短轴的透射相移(PXX, PYY)和透射率(TXX, TYY),图1(b)表示根据公式(7)、(8)为所设计两种方案选取的所有优化单元结构在波长λ0=4200 nm的圆偏振光入射下对应的交叉偏振透射光的振幅和相移。可知,两种方案所选的30个矩形纳米柱结构均可以保证完整的 2π(−π~π)动态相位调制,并且透射振幅均保持在0.7以上(均值大于0.8),即满足半波片的设计。值得一提的是,利用超表面方案实现光自旋霍尔效应在参考文献[22-23]中早已提出并证实,然而由于采用等离子体超表面方案,不可避免地会引入欧姆损耗,因此两工作的聚焦效率并没有提及或者很小。而所提两种方案均采用了全介质超表面方案,即用GSST介质柱代替金属微纳结构,可有效避免因金属吸收导致的欧姆损耗,不仅显著提高了所选单元结构的透射振幅(效率),而且可有效地提高器件的聚焦效率和整体性能,因此具有一定的研究价值。
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图2(a)为TSSM聚焦效果示意图。由图可知,LCP或RCP光垂直透过TSSM后在相反横向偏移处实现单焦点聚焦;左旋椭圆偏振(Left-handed elliptically polarized, LEP)或右旋椭圆偏振(Right-handed elliptically polarized, REP)光垂直透过TSSM后形成两个强度不同的焦点,且分布在横向偏移相反的位置上;当线偏振(Linearly-polarized, LP)光垂直透过TSSM后形成两个同强度焦点,同时也分布在横向偏移相反的位置上。
图 2 (a) TSSM聚焦效果示意图;(b)两焦点光强与入射光椭偏度χ之间的关系曲线;(c)~(g) 波长λ0 = 4200 nm的LCP、椭圆偏振光(χ=−0.5)、LP光、椭圆偏振光(χ=0.5)及RCP光透过TSSM后,在x-z平面上的电场强度分布;(h)~(l) 对应(c)~(g)情形下,在焦距(f ≈90 µm)处沿x轴的电场强度分布
Figure 2. (a) Schematic diagram of TSSM focusing performance; (b) Electric field intensity of the two focal points of TSSM versus the incident polarization χ; (c)-(g) Electric field intensity distributions in the x-z plane of TSSM upon incident light with different polarization states at λ0 = 4200 nm; (h)-(l) Electric field intensity of focal points along x axis corresponds to (c)-(g), respectively
为验证TSSM方案的可行性,设计了一个60×1(沿x和y轴的各向异性单元结构的数量,且沿x轴的60个各向异性单元结构关于原点对称分布)的超构透镜,LCP和RCP入射光对应的双曲相位分布分别为:
$$ {\varphi ^ + }(x) = \frac{{2\pi }}{{{\lambda _0}}}\left( {\sqrt {{{\left( {x - \Delta x} \right)}^2} + f_0^2} - {f_0}} \right) $$ (9) $$ {\varphi ^ - }(x) = \frac{{2\pi }}{{{\lambda _0}}}\left( {\sqrt {{{\left( {x{\text{ + }}\Delta x} \right)}^2} + f_0^2} - {f_0}} \right) $$ (10) 式中:入射波长λ0=4200 nm;横向偏移Δx=20 μm;焦距f0=90 µm。图2(c)~(g)给出了GSST为非晶态时,不同形式的偏振光透过TSSM,在x-z平面内的聚焦电场强度分布图。χ表示入射偏振光的椭偏度,χ=−1, −0.5, 0, 0.5和1分别对应LCP、LEP光(椭偏度为−0.5)、LP、REP(椭偏度为0.5)和RCP光。可以看到,对于LCP(图2(c))和RCP(图2(g))入射光(χ=−1或1),TSSM将透射光聚焦为一个亮斑,焦距均为90 µm,且分布在横向偏移相反的位置上;对于LP(χ=0)入射光(图2(e)),TSSM使透射光“一分为二”,产生横向偏移相反的两个独立焦点,且聚焦强度基本相同,这主要是由于任何LP光都可以看成是LCP和RCP分量的等量叠加。而χ=±0.5的椭圆偏振入射光透过TSSM后,同样产生横向偏移相反的两个独立焦点,但聚焦强度出现显著差异,这主要归因于任何椭圆偏振入射光均可以看成是LCP和RCP分量的非等量叠加。以上研究与理论预测完全吻合。图2(h)~(l)给出了对应上述情形下焦距处沿x轴的光强分布,可以发现,LCP(图2(h))或RCP(图2(l))光透过TSSM后,在焦距处沿x轴各自只产生一个显著的光强峰(两强度近似相等),并且分别位于−Δx和+Δx处;当换为LP光入射时(图2(j)),在焦距处沿x轴形成两个强度几乎完全相同的独立光强峰,并且分别位于−Δx和+Δx处;而对于椭圆偏振入射光(图2(i)和(k)),在焦距处沿x轴同样形成两个独立光强峰,分别位于−Δx和+Δx处,但是两光强峰值却显著不同;这进一步证实了预测的准确性。由于衍射透镜的菲涅耳常数相对较小,模拟和理论之间的焦距差异可忽略不计[24]。
图2(b)还给出了两焦点光强与椭偏度χ之间的关系曲线。当χ=−1时,x=−Δx处焦点光强最大(≈34),x=Δx处焦点光强最小;随着χ逐渐增大,x=−Δx处焦点光强近乎线性减小,而x=Δx处焦点光强却近乎线性增加;当χ=0时,两焦点光强度基本相等;随着χ进一步增大,x=Δx处焦点光强呈现出明显优势,并在χ=1时光强达到最大(≈34),而x=−Δx处焦点光强此时最小。表明通过调控入射光的椭偏度可实现焦斑光强连续可调谐性能。
综上,可知TSSM不仅能够有效地将入射光在横向空间上进行分离,实现显著的横向光自旋霍尔效应;并且通过调控入射光的椭偏度还可实现类似旋转偏振片功能,对焦斑光强连续实时调谐。
与Ge2Sb2Te5类似,Ge2Sb2Se4Te1的相变同样是一个渐变过程,产生了许多中间态,这为可重构超表面的设计提供了一种崭新的自由度。GSST中间态被认为是由不同比例的非晶态和晶体组分构成,其有效介电常数可表示为[25]:
$$ \frac{{{\varepsilon _{{\rm{eff}}}}(\lambda ) - 1}}{{{\varepsilon _{{\rm{eff}}}}(\lambda ) + 2}} = m \times \frac{{{\varepsilon _{\rm{c}}}(\lambda ) - 1}}{{{\varepsilon _{\rm{c}}}(\lambda ) + 2}} + (1 - m) \times \frac{{{\varepsilon _{\rm{a}}}(\lambda ) - 1}}{{{\varepsilon _{\rm{a}}}(\lambda ) + 2}} $$ (11) 式中:m代表GSST的结晶度,变化范围0~1;εc(λ)和εa(λ)分别为cGSST和aGSST的介电常数。为阐明GSST相变对TSSM聚焦性能的影响,图3(a)~(g)给出了在LCP光入射下,TSSM在不同GSST结晶水平时(为简单起见,m=0、0.2、0.4、0.5、0.6、0.8和1.0)在x-z平面上的电场强度分布。可知,从aGSST逐渐演变为cGSST的过程中,TSSM聚焦光斑是逐渐变暗的,直至完全消失。图3(h)给出了焦点强度随结晶度m的变化曲线,m=0时,聚焦光斑电场强度最大,随着结晶度m增大,聚焦光斑电场强度逐渐减小,并在m=1时达最小。上述结果有效地证明了TSSM通过调谐GSST相态,不仅可以实现对聚焦光斑亮度的连续调谐,还能实现对聚焦功能“ON”和“OFF”的动态切换。因此,该方案可显著提升超表面的多功能性。GSST相态可以通过加热、加偏压以及光学调制等手段进行调控。
图 3 (a)~(g) 在LCP光入射下,不同GSST结晶度α的TSSM在x-z平面的聚焦电场强度分布;(h) TSSM焦点处电场强度随GSST结晶度α的变化曲线
Figure 3. (a)-(g) Distributions of electric field intensity in the x-z plane of TSSM with different crystallinity α of GSST under RCP incidence; (h) Electric field intensity of focal point of TSSM versus crystallinity α of GSST
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文中还设计了一种自旋相关纵向分裂的超构透镜LSSM。对于LSSM,LCP和RCP入射光对应的双曲相位φ+(x)和φ−(x)遵循以下形式:
$$ {\varphi ^ + }(x) = \frac{{2\pi }}{{{\lambda _0}}}\left( {\sqrt {{x^2} + f_ + ^2} - {f_ + }} \right) $$ (12) $$ {\varphi ^ - }(x) = \frac{{2\pi }}{{{\lambda _0}}}\left( {\sqrt {{x^2} + f_ - ^2} - {f_ - }} \right) $$ (13) 式中:入射波长λ0=4 200 nm,对应的焦距f+和f−分别设置为70 µm和110 µm。图4(a)为LSSM的原理示意图。可以看出,LCP或RCP光透过LSSM后以不同焦距实现聚焦。由于任何椭圆偏振光和线偏振光都可以看作是LCP和 RCP光的有机叠加,LSSM可以同时将其聚焦在不同焦距位置上。需要注意的是,椭圆偏振光中LCP和RCP光的“含量”不同,透过LSSM后,形成的分裂焦点光强度不同;而线偏振光中LCP和RCP光的“含量”相同,透过LSSM后,形成的分裂焦点光强几乎一致。
图 4 (a) LSSM工作原理示意图;(b) 不同偏振光透过LSSM后两焦点电场强度随椭偏度χ的变化曲线;(c)~(g) 波长λ0 = 4200 nm的LCP、椭圆偏振光(χ=−0.5)、LP光、椭圆偏振光(χ=0.5)及RCP光透过LSSM后,在x-z平面上的电场强度分布;(h)~(l) 对应(c)~(g)沿白虚线的电场强度分布
Figure 4. (a) Schematic diagram of LSSM working principle; (b) Electric field intensity of the two focal points of LSSM versus the incident polarization χ; (c)-(g) Electric field intensity distributions in the x-z plane of LSSM upon incident light with different polarization states at λ0 = 4200 nm;(h)-(l) Electric field intensity of focal points along z axis (x=0) corresponds to (c)-(g), respectively
为验证该方案可行性,图4(c)~(g)给出了不同偏振光透过LSSM后在x-z平面形成的电场强度分布。由图可知,对于LCP入射光(χ=−1),在z≈70 µm,x=0处可以观察到一个明亮的焦点;对于RCP入射光(χ=1),明亮焦点移动到z≈110 µm,x=0处;而对于LP(χ=0)光,沿纵向(z轴)产生两个不同焦距的独立焦点,且两焦点光强度几乎一致。而对于椭圆偏振入射光,同样产生沿纵向(z轴)分布的两独立焦点,但两焦点光强差异明显。为进一步量化入射光椭偏度对光束劈裂的影响,图4(h)~(l)对应给出了图4(c)~(g)沿白虚线的光强分布,充分证明了LSSM可实现显著的纵向光自旋霍尔效应。
为了更进一步说明入射光椭偏度χ对焦点光强分布的影响,图4(b)还给出了两焦点光强与椭偏度χ之间的关系曲线。当χ=−1时,z= f+处焦点光强最大,x= f−处焦点光强最小;随着χ逐渐增大,x= f+处焦点光强减小,x= f− 处焦点光强增加;当χ=0时,两焦点光强度相等;随着χ进一步增大,x= f−处焦点光强呈现出明显优势,并在χ=1时光强达到最大,而x= f+处焦点光强此时最小。表明通过调控入射光的椭偏度可实现焦斑光强连续可调谐。
Spin-dependent intensity-adjustable phase-change metalenses
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摘要: 超表面是一种基于亚波长各向异性单元结构的超薄平面光学器件,能够在微观尺度下调制电磁波相位、偏振和振幅等,从而实现波前的任意调控。超构透镜作为超表面走向实用化的重要代表,凭借其超强的光波操控能力、超紧凑结构、多功能性及与半导体工艺兼容等突出优点,引起了研究学者的极大兴趣。然而,已报道的超构透镜受限于相位分布设计,难以同时实现偏振复用及强度可调谐聚焦功能;且结构一旦确定,其电磁性能就被锁定,在灵活调制电磁波方面受到很大限制。为此,文中从各向异性单元结构的设计和优化入手,协同PB相位和传输相位,设计了两种能够在不同空间取向(横向和纵向)上实现自旋分裂的Ge2Sb2Se4Te1 (GSST) 相变超构透镜。通过改变入射圆偏振光的椭偏度,两超构透镜均可实现强度可调谐聚焦性能;通过调控相变材料Ge2Sb2Se4Te1从非晶态逐渐转变为结晶态,两超构透镜均可实现聚焦性能的连续调谐并最终达到“ON”和“OFF”的动态切换。所设计的自旋依赖强度可调谐相变超构透镜有望在多成像系统、机器视觉和显微成像等领域发挥重要作用。
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关键词:
- 光学超表面 /
- 超构透镜 /
- 相变材料Ge2Sb2Se4Te1 /
- 自旋依赖 /
- 强度可调谐
Abstract: Metasurfaces, artificial subwavelength planar structures based on anisotropic units, manifest an unparalleled ability in manipulating the amplitude, phase and polarization of the incident electromagnetic (EM) waves, thus enabling arbitrary modulation of wavefront. As of the most metasurface embodiments, metalenses have aroused great interest of researchers by virtue of their extraordinary wavefront manipulation, ultracompact size, versatility and high compatibility with semiconductor processes. However, current approaches are mostly restricted by predefined phase profiles, disabling polarization multiplexing and intensity-adjustable focusing performance simultaneously. Moreover, the functionalities of metalens are immediately locked once the structure is determined, seriously hindering their broader potential applications. To this end, two Ge2Sb2Se4Te1-assisted spin-decoupled metalenses are proposed, which enable completely transverse or longitudinal spin-dependent split focusing upon the illumination of left-/right-handed circularly polarized (LCP or RCP) light by synergizing PB and propagation phase. Since the spin-dependent focusing are susceptible to the polarization states of incidence, the relative intensity of split focal spots can be controlled by manipulating the weights of LCP and RCP component, leading to the intensity-adjustable virtue. Furthermore, the focusing performance of our scheme can be continuously tuned and ultimately realize dynamically switching of "ON" and "OFF" states by actuating GSST from amorphous transiting into crystalline state, showing huge potential applications in the fields of spin-controlled nanophotonics, optical imaging and optical sensors. -
图 1 (a) GSST超表面及其单元结构示意图;(b) 两方案对应的最优单元结构在波长λ0 = 4200 nm圆偏振光入射下的交叉偏振透射光的振幅和相位;(c)~(f) 线偏振光下,透射率TXX ,TYY以及相移PXX ,PYY 对GSST矩形纳米柱面内尺寸a和b的扫描图
Figure 1. (a) Schematic diagrams of GSST-based metasurface and its constituent; (b) Propagation phase and transmitted amplitude under CP incidence for selected 30 meta-atoms corresponding to the proposed two schemes; Scanning plots of transmission (c), (e) and propagation phase (d), (f) versus dimensions a and b of GSST rectangular nanopillars for LP incidences, respectively
图 2 (a) TSSM聚焦效果示意图;(b)两焦点光强与入射光椭偏度χ之间的关系曲线;(c)~(g) 波长λ0 = 4200 nm的LCP、椭圆偏振光(χ=−0.5)、LP光、椭圆偏振光(χ=0.5)及RCP光透过TSSM后,在x-z平面上的电场强度分布;(h)~(l) 对应(c)~(g)情形下,在焦距(f ≈90 µm)处沿x轴的电场强度分布
Figure 2. (a) Schematic diagram of TSSM focusing performance; (b) Electric field intensity of the two focal points of TSSM versus the incident polarization χ; (c)-(g) Electric field intensity distributions in the x-z plane of TSSM upon incident light with different polarization states at λ0 = 4200 nm; (h)-(l) Electric field intensity of focal points along x axis corresponds to (c)-(g), respectively
图 3 (a)~(g) 在LCP光入射下,不同GSST结晶度α的TSSM在x-z平面的聚焦电场强度分布;(h) TSSM焦点处电场强度随GSST结晶度α的变化曲线
Figure 3. (a)-(g) Distributions of electric field intensity in the x-z plane of TSSM with different crystallinity α of GSST under RCP incidence; (h) Electric field intensity of focal point of TSSM versus crystallinity α of GSST
图 4 (a) LSSM工作原理示意图;(b) 不同偏振光透过LSSM后两焦点电场强度随椭偏度χ的变化曲线;(c)~(g) 波长λ0 = 4200 nm的LCP、椭圆偏振光(χ=−0.5)、LP光、椭圆偏振光(χ=0.5)及RCP光透过LSSM后,在x-z平面上的电场强度分布;(h)~(l) 对应(c)~(g)沿白虚线的电场强度分布
Figure 4. (a) Schematic diagram of LSSM working principle; (b) Electric field intensity of the two focal points of LSSM versus the incident polarization χ; (c)-(g) Electric field intensity distributions in the x-z plane of LSSM upon incident light with different polarization states at λ0 = 4200 nm;(h)-(l) Electric field intensity of focal points along z axis (x=0) corresponds to (c)-(g), respectively
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