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图 3a是系统输出光束的总强度分布, 图 3b~图 3e是通过不同角度的检偏器后的强度分布。每个箭头代表检偏器透射轴的方向,即0°, 45°, 90°和135°。由于组合线偏振片只有4个分块,当检偏器偏振方向位于水平或竖直时,光斑分布不变但强度减弱,如图 3b和图 3d所示。当检偏器旋转到或时,光斑分布为两侧都是扇形的亮斑,且两侧扇形的角平分线和检偏器的偏振方向一致,如图 3c和图 3e所示。该结果很好地反映了系统输出光束的偏振分布。
任何光的偏振态都可以用4个斯托克斯参量(S0, S1, S2, S3)来表征[21],通过这4个参量能够得到非常全面的偏振特性参量,例如偏振度、偏振方向、椭圆率和偏振类型等,图 4是用经典斯托克斯参量测量法测量径向偏振光纯度的示意图。不插入λ/4波片,并使线偏振片偏振方向分别为0°, 45°和90°时,可以得到前3个参量S0,S1和S2; 当线偏振片处于45°偏转,同时插入快轴方向沿水平的λ/4波片得到第4个参量S3,就能得到光的偏振方向ψ和椭圆率角χ:ψ=arctan(S2/S1)/2, χ=arcsin(S3/S0)/2。
光束波面上任意一点的径向分量表达式为:
$ {E_{\rm{r}}} = {E_x}\text{cos}\varphi + {E_y}\text{sin}\varphi $
(1) 式中,Ex, Ey, φ分别为该点振幅的水平分量、竖直分量和在波面上的方位角。对于径向偏振光而言,偏振纯度指沿径向的光束能量与总能量的比值,可以表示为:
$ \begin{array}{*{20}{c}} {\eta = \frac{{\smallint {{\left| {{E_{\rm{r}}}} \right|}^2}{\rm{d}}S}}{{\smallint {{\left| \boldsymbol{E} \right|}^2}{\rm{d}}S}} = }\\ {\frac{{\smallint [{E_x}^2{\rm{co}}{{\rm{s}}^2}\varphi + {E_y}^2{\rm{si}}{{\rm{n}}^2}\varphi + {\rm{Re}}({E_x}^*{E_y}){\rm{sin}}(2\varphi )]{\rm{d}}\varphi }}{{\smallint {S_0}{\rm{d}}S}} = }\\ {\frac{{\smallint [({S_0} + {S_1}){\rm{co}}{{\rm{s}}^2}\varphi + ({S_0} - {S_1}){\rm{si}}{{\rm{n}}^2}\varphi + {S_2}{\rm{sin}}(2\varphi )]{\rm{d}}\varphi }}{{2\smallint {S_0}{\rm{d}}S}}} \end{array} $
(2) 式中, S是面积,E为电场矢量。从表 1可知,当组合线偏振片的分块数为4时,理论偏振纯度为81.8%。根据CCD接收到的图像可以得到光截面上每个像素点的斯托克斯参量,进而计算出实际径向偏振光的纯度为80.5%,与理论值十分接近。
Table 1. Polarized purity at different numbers of C-PL
numbers of C-PL 4 8 16 N polarized purity 81.8% 95.0% 98.8% 使用旋转检偏器法和经典斯托克斯参量测量法都能检测出径向偏振光是局部线偏振的,但是它们并不能检测出在同一时刻t时径向偏振光对称区域的相位关系。图 5是基于马赫-曾德尔干涉原理对系统输出光束进行相位延迟检测的原理图。但实际上,由于组合半波片和组合线偏振片的工艺问题导致输出光束的偏振角度略有偏移,同时滤波系统也无法完全消除胶合位置引入的衍射效应(如图 3a所示)。为了避免这些衍射条纹对相位延迟检测的实验现象的干扰,最终使用了图 6中的测量方案。
马赫-曾德尔干涉仪上臂的透射光场上下两部分可以分别表示为:
$ \left\{ \begin{array}{l} {E_{{\rm{up}}}} = {E_0}{\rm{exp}}[{\rm{j}}(k{z_1} - \omega t)]\\ {E_{{\rm{down}}}} = {E_0}{\rm{exp}}[{\rm{j}}(k{z_1} - \omega t + {\rm{ \mathit{ π} }})] \end{array} \right. $
(3) 马赫-曾德尔干涉仪下臂的透射光场也分割成上下两部分用于计算,表达式为:
$ \begin{array}{*{20}{c}} {E' = {E_0}{\rm{exp}}\{ {\rm{j}}[k({z_2}{\rm{cos}}\alpha + x{\rm{sin}}\alpha ) - \omega t]\} \approx }\\ {{E_0}{\rm{exp}}[{\rm{j}}(k{z_2} + kx\alpha - \omega t)]} \end{array} $
(4) 式中, E0,k,ω分别表示振幅、波数、频率; z1和z2分别为分束镜(beam splitter, BS)BS1沿干涉仪上臂和下臂到CCD接收面的距离; x为CCD接收面的横坐标(如图 7b箭头所示); α为干涉仪上下臂两束光的夹角。通过光波叠加可以得出合束后的光场上下两部分光强表达式分别为:
$ \left\{ \begin{array}{l} {I_{{\rm{up}}}} = 4{I_0}{\rm{co}}{{\rm{s}}^2}\left( {\frac{{{\delta _1}}}{2}} \right)\\ {I_{{\rm{down}}}} = 4{I_0}{\rm{co}}{{\rm{s}}^2}\left( {\frac{{{\delta _2}}}{2}} \right) \end{array} \right. $
(5) 式中,I0=|E0|2,是单个光波的强度; δ1=k(z2-z1)+kxα,是上半部分两光波的位相差; δ2=δ1+π,是下半部分两光波的位相差。
当δ1=2mπ(m为整数)时,可得:
$ \left\{ \begin{array}{l} {I_{{\rm{up}}}} = 4{I_0}\\ {I_{{\rm{down}}}} = 0 \end{array} \right. $
(6) 当δ1=(2m+1)π时,可得:
$ \left\{ \begin{array}{l} {I_{{\rm{up}}}} = 0\\ {I_{{\rm{down}}}} = 4{I_0} \end{array} \right. $
(7) (6) 式和(7)式表明, 输出光束上下两部分光斑的干涉增强点和干涉相消点恰好是相反的,即上下两部分的干涉条纹明暗相对。图 7是一般马赫-曾德尔干涉和实际π相位延迟检测的光束输出图像。
一种径向偏振光的产生方法
A method for generating radially polarized beams
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摘要: 为了产生径向偏振光,采用组合半波片和组合线偏振片在腔外对线偏振光做极化整形的方法,进行了理论分析和实验验证。为检测该径向偏振光产生系统的性能,采用旋转检偏器法对输出光束的偏振分布进行了检测,并用经典斯托克斯参量测量法计算了偏振纯度,最后基于马赫-曾德尔干涉的原理,检测了径向偏振光对称区域的线偏振相位关系。结果表明,当组合线偏振片为4个分块时,获得了偏振纯度为80.5%的径向偏振光,并检测出光斑对称区域的线偏振相位差为π。这一结果对在低成本条件下产生高纯度的径向偏振光是有帮助的。Abstract: In order to generate radially polarized beams, a method of polarization shaping of linearly polarized beams outside the cavity by a combined half-wave-plates and a combined linear polarizer was put forward. In order to detect the performance of the generating system, the polarization distribution of the output beam was detected by the rotary polarizer method, and its polarization purity was calculated by the classical stokes parameters measurement method. Finally, based on the Mach-Zehnder interference principle, the linear polarization phase relationship of the symmetric region of the radially polarized beams was detected. The results show that when the combined linearly polarizer is divided into four segments, the radially polarized beams with a polarization purity of 80.5% is obtained, and the linear polarization phase difference of the symmetric region is π. The result is helpful to produce the radially polarized light with high purity at low cost.
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Table 1. Polarized purity at different numbers of C-PL
numbers of C-PL 4 8 16 N polarized purity 81.8% 95.0% 98.8% -
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