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液晶q波片内的液晶分子取向排布[36]如下式所示:
$ \alpha (r, \varphi ) = q\varphi + {\alpha _0} $
(1) 式中,α(r, φ)是指向矢n(x, y)与x轴的夹角,α0为指向矢与x轴的初始夹角,q为整数或半整数,被称为液晶q波片的拓扑荷数。液晶q波片上的每一点都可以看作是一个相位延迟为δ的波片,每点波片光轴方向与x轴的夹角跟此点方位角φ的q倍相差一个固定的角度α0。
在x-y面内任意一点的液晶分子指向矢用n(x, y)=n(r, φ)=(cosα, sinα)描述。其中r, φ为极坐标下的极径和极角,α为局部任一点液晶分子指向矢与x轴的夹角。如图 4所示,当取不同的q和α0的值时,会得到不同的液晶分子指向矢排布。
Figure 4. Director distributions of liquid crystals with different topological charges q and different initial angl
利用琼斯矩阵把入射光和q波片表示出来,则可以计算出出射光的琼斯矩阵[37]。当入射光为左旋圆偏光时,出射光的琼斯矩阵可以由下式表示:
$ \begin{array}{l} {\mathit{\boldsymbol{E}}_{{\rm{out}}}} = \cos \left( {\frac{\delta }{2}} \right) \times \frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} 1\\ { - {\rm{i}}} \end{array}} \right] + \\ \;\;\;{\rm{isin}}\left( {\frac{\delta }{2}} \right){{\rm{e}}^{ - {\rm{i}}2\alpha }} \times \frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} 1\\ {\rm{i}} \end{array}} \right] \end{array} $
(2) 式中,δ表示液晶q波片引起的相位延迟。等号右侧第1项是保留项,偏振态与入射光保持一致,仍为左旋圆偏光;另一项是转换项,将左旋圆偏光变为右旋圆偏光,并携带有螺旋相位因子e-i2α。此外,可以通过外加电场对液晶q波片的相位延迟进行调控,实现对两项占比的调制。因此,可以分别通过改变液晶分子指向矢排布和液晶q波片的相位延迟来实现对入射光偏振和相位的调控。
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搭建了如图 5所示的光路进行特殊光场的产生和检测。使用He-Ne激光器产生的633nm激光,经过偏振片(polarizer, P)和λ/4波片(quarter wave-plate, QWP)形成左旋圆偏光,再利用空间滤波器(spatial filter, SF)滤掉激光光束中的高频部分。通过空间滤波器针孔的发散激光经透镜准直为大孔径平行光束,照射在液晶q波片上。在液晶q波片上施加频率为1kHz的方波电压,通过调节所施加的电压大小,实现对液晶q波片相位的调节,从而产生涡旋光和矢量涡旋光。为了检测所产生特殊光的种类,在液晶q波片后放置一个检偏器,通过检偏器的光场经透镜成像在CCD上。
当相位延迟分别为2π, 3π/2, π, π/2时,通过对(2)式化简,可以计算出不同相位延迟下出射光的琼斯矩阵。当电压为25V时,液晶q波片的相位延迟为2π,此时出射光的琼斯矩阵如下式所示:
$ {\mathit{\boldsymbol{E}}_{{\rm{out}}}} = - \frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} 1\\ { - {\rm{i}}} \end{array}} \right] $
(3) 出射光与入射光保持一致,为左旋圆偏光。当转动检偏器时,光斑形状与光强几乎无变化。如图 6a所示。
Figure 6. States of polarization, phase fronts and intensity distributions at four different phase delays
当电压为16.8V时,液晶q波片的相位延迟为3π/2,出射光的琼斯矩阵如下式所示:
$ {\mathit{\boldsymbol{E}}_{{\rm{out}}}} = \exp ( - {\rm{i}}\varphi )\exp ({\rm{i}}3{\rm{ \mathsf{ π} }}/4)\left[ {\begin{array}{*{20}{c}} {\cos (\varphi + {\rm{ \mathsf{ π} }}/7)}\\ {\sin (\varphi + {\rm{ \mathsf{ π} }}/4)} \end{array}} \right] $
(4) 出射光为既具有轴对称偏振分布又具有螺旋相位分布的矢量涡旋光,用(p, φ0, l)来表示,其中p表示偏振阶数,φ0表示初始偏振角度,l表示拓扑荷数。由(4)式可知,当q波片相位延迟为3π/2时,出射(p=1, φ0=π/4, l=-1)的矢量涡旋光场。转动检偏器时,消光位置跟着一起旋转,如图 6b所示。
当电压为10.4V时,液晶q波片的相位延迟为,由下式分析:
$ {\mathit{\boldsymbol{E}}_{{\rm{out}}}} = {\rm{i}} \times {{\rm{e}}^{ - {\rm{i}}2\varphi }} \times \frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} 1\\ { - {\rm{i}}} \end{array}} \right] $
(5) 出射光为拓扑荷数l=-2的涡旋光。转动检偏器时,光斑始终是亮环,如图 6c所示。
当电压为6.8V时,液晶q波片的相位延迟为π/2,出射光的琼斯矩阵如下式:
$ \begin{array}{*{20}{c}} {{\mathit{\boldsymbol{E}}_{{\rm{out}}}} = \exp ( - {\rm{i}}\varphi ) \times }\\ {\exp ({\rm{i \mathsf{ π} }}/4)\frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} {\cos (\varphi - {\rm{ \mathsf{ π} }}/4)}\\ {\sin (\varphi - {\rm{ \mathsf{ π} }}/4)} \end{array}} \right]} \end{array} $
(6) 出射光与第2种情况类似,是矢量涡旋光场(p=1, φ0=-π/4, l=-1)。转动检偏器时,消光位置与理论分析的偏振分布一致。如图 6d所示。
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通过波片组可以实现不同偏振分布的矢量涡旋光之间的转换,实验光路如图 7所示。在液晶q波片后面加入一对λ/2波片(2HWP),通过调节两个波片快轴之间的夹角θ,可实现对矢量涡旋光场空间每一点偏振方向旋转2θ。以相位延迟为3π/2矢量涡旋光为例,调节两个λ/2波片的夹角分别为22.5°和67.5°,则光波横截面上任意位置的偏振方向都分别发生了45°和135°的旋转,最终分别产生了如图 8所示的角向矢量涡旋光场(p=1, φ0=π/2, l=-1)和径向矢量涡旋光场(p=1, φ0=0, l=-1)。
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自旋角动量(spin angular momentum, SAM)到轨道角动量(orbital angular momentum,OAM)的转换(SAM-to-OAM conversion,STOC),其转换效率RSTOC可用来表征液晶q波片对入射光的能量利用率[38-39]。由前面分析可知,当以左旋圆偏光入射时,经过液晶q波片后的出射光可用(2)式表示。其中第1项为保留项,表示出射光仍为左旋圆偏光,第2项为转换项,表示出射光的自旋角动量发生反转变为右旋,并且携带有轨道角动量。利用如图 9a所示的光路,在液晶q波片后加入由λ/4波片(QWP)和偏振分光棱镜(polarizing beam splitter, PBS)构成的圆偏光检偏器将出射光场中的保留项和转换项分开,并用功率计分别测量它们的功率[40-43]:
Figure 9. a—setup for measuring STOC efficiency b—relationship between STOC efficiency and the applied voltage
$ \left\{ {\begin{array}{*{20}{l}} {{P_1} = {P_0}{{\sin }^2}\left( {\frac{\delta }{2}} \right)}\\ {{P_2} = {P_0}{{\cos }^2}\left( {\frac{\delta }{2}} \right)}\\ {{R_{{\rm{STOC}}}} = \frac{{{P_1}}}{{{P_1} + {P_2}}}} \end{array}} \right. $
(7) 式中,P0=TPin是透过液晶q波片后的光总功率; T表示液晶q波片的透过率; Pin表示入射到液晶q波片的光功率; P1表示转换项的光功率; P2表示保留项的光功率。
实验中调节液晶q波片两端施加的电压,测得P1, P2随电压实时变化的数据,并通过MATLAB对数据进行处理,可得如图 9b所示的P1, P2随电压的变化曲线以及STOC转换效率随电压变化曲线,该液晶q波片的STOC转换效率最高可达85%。
大孔径液晶q波片的制备及性能研究
Preparation and characteristics of large aperture liquid crystal q-wave-plates
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摘要: 为了解决液晶q波片制备过程中重复性差、方法繁琐、孔径限制的问题, 采用了一种基于紫外掩模曝光法和液晶面外区域定向技术的液晶q波片制备方法, 进行了理论分析和实验验证。搭建了紫外曝光系统, 制备了直径为2.54cm, q=1, 夹角α0=0的大孔径液晶q波片。结果表明, 紫外掩模法构建的大孔径液晶q波片的自旋角动量-轨道角动量的转换效率可达到85%;利用该波片实现了涡旋光、矢量涡旋光的产生和转换。基于紫外掩模法构建大孔径液晶q波片的方法具有成本低廉、制备工艺简单、速度快等优点, 可实现液晶q波片的批量化制作, 有利于液晶q波片走向商业化。Abstract: In order to solve the problems of poor repeatability, cumbersome methods and aperture limitation in the preparation of liquid crystal q-wave-plates, a preparation method of liquid crystal q-wave-plates was adopted based on ultraviolet mask exposure and liquid crystal out-of-plane orientation technology. Theoretical analysis and experimental verification were carried out. The ultraviolet exposure system was built. Large aperture liquid crystal q-wave-plates were prepared with diameter of 2.54cm, topological charges q of 1 and initial angle of 0.The results show that the conversion efficiency of spin angular momentum to orbital angular momentum of the large aperture liquid crystal q-wave-plates constructed by ultraviolet mask method can reach 85%. By using the wave plate, the generation and conversion of vortices and vector vortices are realized. The method of constructing large aperture liquid crystal q-wave-plates based on ultraviolet mask has advantages of low cost, simple preparation process and fast speed. It can realize batch fabrication of liquid crystal q-wave-plates. It is conducive to the commercialization of liquid crystal q-wave-plates.
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Key words:
- optical devices /
- liquid crystal q-wave-plate /
- specific light field /
- vortex beam /
- Jones matrix
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