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在光纤激光器中也可产生OAM涡旋光,其形成原理是基于光纤内简并模式的叠加,通过控制支持LP11模式的光纤激光器中的偏振态即可获得OAM光束的输出,具体原理阐述如下。通过求解光纤中麦克斯韦方程组,可以得到光纤中矢量模式,也叫本征模式,其具有复杂的电磁场分布。在常规的少模或多模光纤中,纤芯和包层的折射率差在10−3量级,同一模式群内的不同矢量模式间的有效折射率差小于10−4,这导致了矢量模式的简并,此时在光纤输出端得到的是不同矢量模式的组合,也就是标量模式。从本质上讲光纤中涡旋光束的形成可以分为两类:一种是由同阶同偏振标量模式的奇模和偶模附加±π/2相位差产生线偏振OAM涡旋光束,其不携带自旋角动量;另一种是由同一矢量模式的奇模和偶模附加±
$ \pi$ /2相位差产生圆偏振OAM涡旋光束,其携带自旋角动量。(1)线偏振OAM模式
同阶同偏振标量模式的奇模和偶模附加±π/2相位差产生线偏振涡旋光束,如公式(1)所示:
$$\begin{split} \left\{ {\begin{array}{*{20}{c}} {\hat x{L_{ \pm l,m}}} \\ {\hat y{L_{ \pm l,m}}} \end{array}} \right\} =& \left\{ {\begin{array}{*{20}{c}} {LP_{l,m}^{c,x} \pm iLP_{l,m}^{s,x}} \\ {LP_{l,m}^{c,y} \pm iLP_{l,m}^{s,y}} \end{array}} \right\} = {F_{l,m}}(r)\left\{ {\begin{array}{*{20}{c}} {\hat x\exp ( \pm il\varphi )} \\ {\hat y\exp ( \pm il\varphi )} \end{array}} \right\},\\ &(l \geqslant 1)\\ \end{split} $$ (1) 式中:L±l,m表示线偏振涡旋模式,下角标±l,m表示相应的角向和径向模数,其中±表示相位旋转方向;
$\hat x,\hat y$ 表示相应的偏振方向;$LP_{l,m}^{c,x}$ 表示不同的线偏振模式;上角标c,s表示横向场分布遵循cosine函数和sine函数,x,y表示标量场的偏振方向。(2)圆偏振OAM模式
同一矢量模式的奇模和偶模可通过附加±π/2相位差产生圆偏振涡旋光束,如公式(2)所示:
$$\begin{split} \left\{ {\begin{array}{*{20}{c}} {V_{ \pm l,m}^ \pm } \\ {V_{ \pm l,m}^ \mp } \end{array}} \right\} =& \left\{ {\begin{array}{*{20}{c}} {HE_{l + 1,m}^e \pm iHE_{l + 1,m}^o} \\ {EH_{l - 1}^e \pm iEH_{l - 1,m}^o} \end{array}} \right\} =\\ &{F_{l,m}}(r)\left\{ {\begin{array}{*{20}{c}} {{{\hat \sigma }^ \pm }\exp ( \pm il\varphi ),(l \geqslant 1)} \\ {{{\hat \sigma }^ \mp }\exp ( \pm il\varphi ),(l > 1)} \end{array}} \right\} \end{split}$$ (2) 式中:
$V_{ \pm l,m}^ \pm $ 表示圆偏振涡旋模式,其上角标$ \pm $ 表示自旋角动量;上角标e,o分别表示偶模、奇模;${\hat \sigma ^ \pm } = \hat x \pm i\hat y$ 表示左旋或者右旋圆偏振。一般来说,通过光纤激光器产生OAM涡旋光都需要在激光器输出端连接额外的光纤器件和偏振控制元件,但是因为光纤激光器需要通过尾纤输出激光,所以将其归在光纤激光器直接输出OAM涡旋光中。光纤激光器中一般可以通过模式选择耦合(Mode Selective Coupler, MSC)[47],错位熔接联合光纤布拉格光栅[48],长周期光纤光栅[49](括声致光纤光栅[50]及机械式挤压光纤光栅[51]等形式的长周期光纤光栅),光子晶体光纤[52],特殊结构掺杂光纤[53]等方式产生OAM涡旋光的方法。为了实现短脉冲涡旋光输出,一般需要能支持宽光谱的模式转换器件。下面介绍两种主要通过光纤激光器输出超短脉冲OAM涡旋光的方法。
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一种是通过模式选择耦合器联合锁模激光器产生超短OAM涡旋光输出。模式选择耦合器是由单模光纤和少模光纤拉锥形成。该模式耦合器在将激光导出激光腔的同时,也将实现在宽谱范围内光纤中LP01模式向高阶模式(LP11或LP21)的转换。模式耦合器的示意图一般如图6所示。
图 6 模式选择耦合器示意图[57]
Figure 6. Sketch of a fiber mode selective coupler[57]
如果将模式耦合器用于锁模激光器中,就可得到相对应的超短脉冲OAM涡旋光输出。上海大学的曾祥龙教授团队通过将MSC引入到NPR锁模光纤激光器中,首次实现了140 fs的OAM±1和OAM±2涡旋光输出[54],实验装置如图7所示。实验中采用了0.4 m LIEKKI ER80-8/125光纤作为增益光纤,最高输出功率为620 mW的980 nm的半导体激光器为泵源,通过色散补偿光纤将腔内色散控制为0.015 ps2,实现了耗散孤子锁模。实验中通过MSC将LP01模式转换为LP11模式,再通过偏振控制器PC3实现了手性可控的一阶或二阶OAM涡旋光输出。实验测得激光输出中心波长为1545 nm,3 dB谱宽为67.6 nm,锁模脉冲重频为36.10 MHz,一阶涡旋光的脉宽为273 fs,二阶涡旋光的脉宽为140 fs,涡旋光输出的最高脉冲能量为0.36 nJ。
图 7 NPR锁模激光器联合模式选择耦合器实现短脉冲OAM涡旋光输出的实验装置图
Figure 7. Experimental setup of an all-fiber NPR mode locked fiber laser using mode selective coupler
南开大学李乙钢教授团队在非线性环形镜锁模光纤激光器中采用模式耦合器作为输出镜实现了手性可调的超短脉冲OAM涡旋光束出,实验装置如图8所示[55]。实验中采用980 nm LD作为泵源,一段0.65 m长的掺Er光纤作为增益介质。一个2∶8的耦合器两端连接作为非线性环形镜,该光纤环长度为11 m。一个20%的SMF-FMF耦合器作为光纤激光器输出镜以及模式选择器件。锁模激光器输出LP11模式,该模式再通过偏振控制器控制LP11奇偶两分量间的相位,以实现OAM±1涡旋光输出。实验中获得的锁模脉冲重频为10.5 MHz,通过调节光纤激光器的偏振态可实现脉冲宽度为1.098 ps及542 fs的超短脉冲OAM光束输出。
图 8 非线性环形镜锁模光纤激光器联合模式选择耦合器
Figure 8. Nonlinear-loop-mirror mode locked fiber laser using mode selective coupler
随后,模式耦合器还被该团队用在非线性放大环镜(NALM)中用于实现超短脉冲OAM涡旋光的输出,实验装置如图9所示[56]。NALM由一段高掺杂Er光纤,一根100 m长的单模光纤以及一个偏振控制器组成。该NALM的泵源为一个980 nm的半导体激光器LD。5∶5的耦合器联合左边的环形腔起类似于可饱和吸收体的作用以实现锁模输出。通过SMF-FMF模式选择耦合器可实现LP11模式输出。偏振控制器PC1和PC2用来补偿光纤双折射导致的偏振改变。PC3用于控制奇偶LP11模式间的相位用于实现OAM模式输出。通过该装置,最后实现了脉冲重频为1.78 MHz、脉冲宽度为393 fs、中心波长为1567 nm、拓扑荷数为±1的OAM涡旋光输出。
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基于少模光纤的长周期光纤光栅也可作为模式转换器实现锁模超短OAM涡旋光输出。为了通过长周期光纤光栅实现模式转换,需要满足相位匹配条件Λ=λ/(n1 − n2),其中Λ为光栅刻线周期,λ为激光波长,n1−n2为两个模式的有效折射率差。当简并的HE11, x和HE11, y模式通过长周期光纤光栅后,将分别转换为TM01+HE21,even混合模式以及TE01+HE21,odd混合模式。通过偏振控制器可在这两个混合模式间引入±π/2的相位差,实现手性为正或负的涡旋光输出[57]。
西北工业大学赵建林教授团队通过使用声致光纤光栅实现了飞秒OAM涡旋光输出,实验装置如图10所示[58]。通过传播的弯曲声波可以在光纤中产生周期性的微小弯曲,等效于在光纤中形成了一个光栅。实验中先通过碳纳米管可饱和吸收体实现被动锁模Er光纤激光器,获得了脉冲频率为12.5 MHz、脉冲宽度为384 fs、中心波长为1520 nm、谱宽为60 nm的锁模脉冲输出。该飞秒脉冲再通过弯曲声波调制的光纤光栅模式转换器,当加载的声波信号所形成的光栅满足相位匹配条件时,获得了手性可控的飞秒OAM涡旋光输出。
图 10 通过使用声致光纤光栅实现了飞秒OAM涡旋光输出的实验装置图
Figure 10. Experimental setup of femtosecond optical vortex pulse generation based on an acoustically induced fiber grating
李乙钢教授团队通过使用机械挤压形成的长周期光纤光栅联合NPR锁模Er光纤激光器实现了锁模重复频率为27 MHz、脉冲宽度为398 fs、中心波长为1564 nm、谱宽为8 nm的OAM±1涡旋光输出,实验装置如图11所示[59]。NPR锁模激光器通过1∶9耦合器输出的锁模脉冲为LP01模式,该LP01模式通过挤压式长周期光纤光栅后转换为了LP11模式。LP11模式可等效为两个相互垂直的LP11,a和LP11,b模式的叠加。随后,通过挤压少模光纤改变其等效折射率,可以在LP11,a和LP11,b间引入π/2的相位差形成OAM涡旋光输出。
图 11 通过使用机械挤压形成的长周期光纤光栅联合NPR锁模Er光纤激光器
Figure 11. Experimental setup of femtosecond vortex laser based on NPR mode-locking and mechanical LPG
近期,上海大学曾祥龙教授团队开展了在窄线宽锁模激光器中的涡旋光模式转换过程的实时监控研究[60],实验装置如图12所示。实验采用线性腔结构,增益光纤为掺Er光纤,通过可饱和吸收体SESAM实现被动锁模。采用声致光纤光栅实现模式转换,通过加载不同的声波频率,将改变等效光栅周期,实现LP01模式到相互垂直的简并LP11,a及LP11,b模式的转变。LP11,a或LP11,b模式可通过调控偏振控制器PC2旋转45°,并由PC2引入的压力改变少模光纤的等效尺寸,获得±π/2的相位差,实现锁模涡旋光输出。实验中通过改变加载在光纤上的声波,可实现LP01,OAM+1,OAM−1模式可调锁模脉冲输出,脉冲的重复频率为4.835 MHz,脉冲宽度均约为400 ps。实验中还观察了模式改变的动态过程中锁模脉冲建立的时域变化过程,发现在不同模式转变过程中锁模脉冲建立过程不同。该发现为研究锁模脉冲建立过程提供了新的维度。
Research progress on direct generation of ultrashort pulse OAM vortex beams (Invited)
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摘要: 轨道角动量(OAM)涡旋光是一种具有相位孤立奇点的光场,其相位波前呈螺旋分布,光场复振幅包含螺旋相位项exp(ilθ)。近年来,OAM涡旋光被广泛地应用在光学操控、成像、通信、传感等方面。超短脉冲OAM涡旋光同时具有涡旋光和超短脉冲的优点,可应用于手性材料加工、远距离传输、强场物理研究,非线性频率转换研究等方面。通过激光器直接产生OAM涡旋光具有系统整体简便性高和光束质量好等优势,对国内外基于有源方法产生超短OAM涡旋光的方法进行了总结。目前,通过有源方式产生的超短OAM涡旋光的脉冲宽度还局限于几百飞秒,如何通过直接输出的方法获得百飞秒以内甚至是少周期脉冲涡旋光输出将是未来研究的一个重要方向。Abstract: Orbital angular momentum (OAM) vortex beam has a phase singularity with a twisted wave-front, whose complex amplitude comprises the helical term exp (ilθ). OAM vortex beam has been widely used in optical manipulation, imaging, optical communication, sensing and so on. Ultra-short pulse OAM vortex beams have the advantages of both vortex beams and ultra-short pulses, and can be applied to chiral material processing, long distance transmission, strong field physics and nonlinear frequency conversion. Direct generation of ultra-short OAM vortex beams has the advantages of compact and simple system and good beam quality. The research progress on direct generation of ultra-short OAM vortex beams was summarized. At present, the pulse width of the ultra-short OAM vortex beam generated by the active method is still limited to a few hundred femtoseconds. How to obtain the pulsed vortex beam output within 100 femtoseconds or even with a few cycles through the direct output method will be an important future development direction.
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Key words:
- vortex beam /
- ultrashort pulse /
- direct generation
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图 6 模式选择耦合器示意图[57]
Figure 6. Sketch of a fiber mode selective coupler[57]
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