聶芳松，姜美玲，張明偲，曹耀宇，李向平

基于迂回相位的軌道角動量Talbot陣列照明器

聶芳松，姜美玲，張明偲*，曹耀宇*，李向平

暨南大學(xué)光子技術(shù)研究院，廣東省光纖傳感與通信技術(shù)重點實驗室，廣東 廣州 510632

軌道角動量(OAM)光束具有螺旋形相位分布，在信息光學(xué)、光捕獲、光學(xué)操控等領(lǐng)域都有著重要的應(yīng)用。本文設(shè)計了一種可以生成聚焦OAM光束的平面型光學(xué)器件。該器件利用迂回相位的編碼方式，在平板上加載了根據(jù)分?jǐn)?shù)Talbot效應(yīng)計算得到的特定相位分布。使用時域有限差分(FDTD)分別對具有正方形和六邊形周期性結(jié)構(gòu)的光學(xué)器件進行仿真模擬。結(jié)果表明，平面波經(jīng)過此器件可以轉(zhuǎn)化為陣列型聚焦OAM光束。該器件加工方便，容易拼接或復(fù)制，集成度高，可以用來生成高質(zhì)量大面積陣列型OAM光束。

分?jǐn)?shù)Talbot效應(yīng)；軌道角動量；周期性結(jié)構(gòu)；迂回相位

1 引 言

光子和經(jīng)典力學(xué)宏觀粒子一樣，都可以攜帶能量、動量和角動量。光子的角動量又分為自旋角動量(spin angular momentum，SAM)和軌道角動量(orbital angular momentum，OAM)。自旋角動量是光子的內(nèi)稟屬性，每個光子攜帶的自旋角動量為±?，表現(xiàn)為偏振光學(xué)的左旋或者右旋圓偏振光；軌道角動量是指光在傳播過程中，每一個平行的截面上具有exp(i)的螺旋形相位分布，對應(yīng)的每個光子攜帶的軌道角動量為?，代表軌道角動量光束的拓?fù)浜?，在理論上可以取值為任意整?shù)，因此每一個光子理論上可以攜帶無窮種軌道角動量[1]。因此，軌道角動量光束被普遍應(yīng)用于光通信[2-4]、超分辨[5-6]、納米操控[7-10]、激光加工[11]和光存儲[12-15]等領(lǐng)域。隨著光學(xué)微納器件逐步開始由實驗室研究階段發(fā)展為大規(guī)模工業(yè)生產(chǎn)階段，人們對于OAM光束提出了越來越高的要求。

1992年，Allen等人利用兩個柱透鏡，首次在實驗中產(chǎn)生了軌道角動量光束[1]。目前，軌道角動量光束已經(jīng)可以通過多種方式產(chǎn)生，例如：通過螺旋相位片法[16-17]、渦旋波片法[18-20]、全息叉形光柵法[21-22]、空間光調(diào)制器[23-25]等相位調(diào)制方法，都可以在宏觀空間中產(chǎn)生OAM光束；通過環(huán)形角光柵結(jié)構(gòu)的回音壁模式[26]，表面等離子體耦合-解耦合等手段[27-28]，同樣可以在微觀空間內(nèi)產(chǎn)生OAM光束。然而，以上產(chǎn)生OAM光束的方法多用于產(chǎn)生單一OAM光束，無法滿足人們對于多焦點大面積陣列型光場的需求。

本文中，我們根據(jù)分?jǐn)?shù)Talbot效應(yīng)，設(shè)計了一種可以產(chǎn)生大面積陣列型OAM光束的照明器件。該器件利用迂回相位的編碼方式，在平板上加載特定的相位分布。分別討論了四邊形和六邊形周期結(jié)構(gòu)生成聚焦OAM光束的理論基礎(chǔ)和設(shè)計參數(shù)，解析了單色平面波入射下，兩種周期型相位板生成的軌道角動量光斑強度分布。并使用時域有限差分(finite difference time domain，F(xiàn)DTD)仿真模擬方法對設(shè)計的結(jié)構(gòu)進行了進一步的驗證。該器件設(shè)計簡單，具有高集成度，大面積復(fù)制拼接等優(yōu)勢，可以方便產(chǎn)生高質(zhì)量陣列型聚焦OAM光束。

2 基本原理

周期性結(jié)構(gòu)在單色平面波照射下，由于光的衍射，可以產(chǎn)生自成像現(xiàn)象，即Talbot效應(yīng)[29-30]。簡單來說，Talbot效應(yīng)可以理解為橫向周期為的光場，在傳播過程中，產(chǎn)生周期為T=22/的縱向周期性；縱向周期T即為Talbot距離，為單色光波長。當(dāng)周期性光場的占空比為1/時，在周期性結(jié)構(gòu)后方Z=T/2的位置，可以產(chǎn)生一個均勻振幅面，即在這個平面上，光場的強度都是相等的，每個像素之間僅存在相位的差別，這個效應(yīng)又稱之為分?jǐn)?shù)Talbot效應(yīng)，T/2又稱為分?jǐn)?shù)Talbot距離。對于邊長為的二維正方形周期性結(jié)構(gòu)，具有類似于一維周期結(jié)構(gòu)的特點。和一維周期結(jié)構(gòu)相似，二維周期結(jié)構(gòu)的Talbot距離T=22/。因此，根據(jù)分?jǐn)?shù)Talbot效應(yīng)，我們設(shè)計一種15′15的正方形陣列結(jié)構(gòu)作為周期單元，將15′15空間的入射光聚焦到中心點1′1像素上，即=15；每一個正方形像素基元的邊長為unit，根據(jù)分?jǐn)?shù)Talbot距離的定義，得到：

如圖1(c)所示。對于多元相位分布的Talbot相位板，每一個不同的相位，代表著具有不同光程，也就是不同厚度的電介質(zhì)結(jié)構(gòu)單元，相位板的厚度分布示意圖如圖1(d)所示。顯然，上述相位板結(jié)構(gòu)具有非常復(fù)雜的多階結(jié)構(gòu)，這種結(jié)構(gòu)難以通過傳統(tǒng)的激光直寫或者離子刻蝕技術(shù)加工而成。

3 結(jié)構(gòu)設(shè)計和計算分析

圖1 (a), (b) 正方形單周期Talbot相位板的(a)相位分布和(b) l = 1的螺旋相位分布；(c), (d) 疊加軌道角動量的Talbot相位板的(c)總相位分布和其相應(yīng)的(d)三維立體結(jié)構(gòu)。

圖2 (a), (b) 迂回相位編碼Talbot陣列照明器的正方形1′1像素(a)基元結(jié)構(gòu)(其中d(m,n)為0相位中心位置偏移量，O1和O2分別對應(yīng)基元中心和0相位中心)和(b)位置偏移；(c), (d) 迂回相位編碼Talbot陣列照明器的(c)單周期和(d)3′3周期陣列結(jié)構(gòu)

圖3 (a), (b) 迂回相位編碼的正方形Talbot陣列照明器的(a) l=0和(b) l=+1的電場強度分布；(c), (d) 分別是l=0和l=+1的FDTD模擬仿真計算結(jié)果；(e) l=+1的陣列型電場強度分布

當(dāng)光瞳函數(shù)更接近圓域函數(shù)，光斑的分布也就更加接近圓形分布。為了進一步優(yōu)化軌道角動量光斑質(zhì)量，可以將正四邊形的周期性結(jié)構(gòu)替換為正六邊形的周期性結(jié)構(gòu)。定義邊長為的六邊形的光瞳函數(shù)為

根據(jù)倒格子理論，六邊形的Talbot參數(shù)不完全和四邊形等同。對于邊長為′unit(表示每一個邊都由個像素基元構(gòu)成)的六邊形Talbot陣列照明器，特定的六邊形Talbot距離為

對應(yīng)的分?jǐn)?shù)Talbot距離為

圖4 (a) 六邊形單周期Talbot相位板的相位分布；(b) l=+1的螺旋相位分布；(c) 迂回相位編碼六邊形Talbot陣列照明器的1′1像素基元結(jié)構(gòu)；(d) 迂回相位編碼的六邊形Talbot陣列照明器

圖5給出了邊長為=15的六邊形Talbot照明器上加載不同的螺旋相位時，生成OAM光束的FDTD模擬仿真結(jié)果。=0時，聚焦的光斑不攜帶軌道角動量，是一個中心強度為極大值的實心光斑，半高全寬為0.63 μm，如圖5(a)所示；=±1時，聚焦光斑都表現(xiàn)為一個六個強度均勻的“熱點”組成的準(zhǔn)空心光斑，每個“熱點”光斑與坐標(biāo)原點的距離都是1.0 μm，半高全寬為0.62 μm，環(huán)繞一周相位的變化分別為±2π，分別如圖5(b)，5(c)所示；=+2時，聚焦光斑仍然由六個“熱點”組成，每個“熱點”光斑中心與坐標(biāo)原點的距離仍然是1.0 μm，半高全寬為0.67 μm，環(huán)繞一周相位的變化為4π，如圖5(d)所示。圖5(e)是=+1時的陣列型電場強度分布。和正方形Talbot陣列照明器相比，六邊形Talbot陣列照明器生成的光斑更接近于圓形，同時相位分布也更加均勻。因此，使用六邊形Talbot陣列照明器，可以生成更高質(zhì)量的大面積陣列型OAM光束，以滿足大規(guī)模工業(yè)生產(chǎn)的需要。

4 結(jié) 論

本文在分析分?jǐn)?shù)Talbot效應(yīng)的理論基礎(chǔ)上，利用迂回相位編碼方法，設(shè)計了一種可生成聚焦OAM光束的平面光學(xué)器件。通過使用FDTD仿真模擬表明平面波經(jīng)過此器件可以轉(zhuǎn)化為大面積周期性聚焦OAM光束陣列，焦點尺寸與單像素基元相近。隨著決定相位分布的像素基元排布從正方形向六邊形變化，具有渦旋相位的焦點強度對稱性也相應(yīng)改變。具有較高中心對稱性的像素基元排布有利于實現(xiàn)更均勻的照明。該器件設(shè)計簡單，加工方便，集成度高，可以大面積地復(fù)制拼接，在光捕獲、光操控、光學(xué)加工等領(lǐng)域有很好的潛在應(yīng)用。

圖5 (a) ~(d) 迂回相位編碼的六邊形Talbot陣列照明器的(a) l=0, (b) l=+1, (c) l=-1和(d) l=+2的歸一化電場強度分布；(e) l=+1的陣列型電場強度分布

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Orbital angular momentum Talbot array illuminator based on detour phase encoding

Nie Fangsong, Jiang Meiling, Zhang Mingsi*, Cao Yaoyu*, Li Xiangping

Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Institute of Photonics Technology, Jinan University, Guangzhou, Guangdong 510632, China

(a) The unit cell and (b) one period of hexagonal Talbot array illuminator based on detour phase encoding; (c) Normalized electric field intensity distribution of= +1 for hexagonal Talbot array illuminator

Overview:Orbital angular momentum (OAM) beam with helical phase distribution has demonstrated important applications in information optics, optical storage, laser processing, super-resolution, optical trapping, and optical manipulation. These exceptional achievements heavily rely on the development of OAM micro-devices that can precisely manipulate optical fields of demand. As such functional components gradually reach out to large-scale production for practical applications from the laboratory-scale researches, more requirements are raised for producing OAM beams with equal properties in batches. At present, there are varied methods to generate OAM beams, for example, spiral phase plate method, variable spiral plate method, hologram folk grating method, and spatial light modulator method. However, the above methods are mostly focused on generating a single OAM beam, which overlooks the needs of fostering multi-focus array light field that is highly desirable for novel functions in numerous studies. How to readily realize focused OAM arrays beams over a large area remains a tough challenge from concept to implementation. In this paper, based on fractional Talbot effect, we have designed a planar optical device which can generate periodic array of focused orbital angular momentum beam. The phase distribution of the devised structure contains two parts: the focusing lens phase distribution and the spiral vortex phase distribution. According to detour phase encoding, the phase distribution calculated by fractional Talbot effect is implemented on the planar optical device by discretizing the phase distribution with arrayed phase-control units. The multi-level phase distribution is transformed to the lateral displacement of the rectangular bars from the center of each unit cell, which is proportioned to the phase shift as designed. The focusing property of this optical device with periodic square and hexagonal structures are simulated by finite difference time domain (FDTD). The intensity distribution and phase profile of each single focused light beam in the illumination plane are virtually identical. With changing the arrangement of the phase-regulation unit from square to hexagonal Talbot array, the symmetry of the intensity distribution for the focused light spot with vortex phase distribution changes accordingly. The symmetry of the hexagonal Talbot array is higher than the square counterpart. This optical device with explicit advantages of being easy to fabricate, splice, duplicate, and integrate can efficiently prop up the generation of high-quality large-area array-type OAM beams for widely spreading applications in optical trapping, optical manipulation, optical fabrication, and other fields.

Citation: Nie F S, Jiang M L, Zhang M S,Orbital angular momentum Talbot array illuminator based on detour phase encoding[J]., 2020, 47(6): 200093

Orbital angular momentum Talbot array illuminator based on detour phase encoding

Nie Fangsong, Jiang Meiling, Zhang Mingsi*, Cao Yaoyu*, Li Xiangping

Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Institute of Photonics Technology, Jinan University, Guangzhou, Guangdong 510632, China

Orbital angular momentum (OAM) beam with helical phase distribution has demonstrated important applications in information optics, optical trapping, and optical manipulation. In this paper, we designed a planar optical device which can generate a periodic array of focused orbital angular momentum beams. Based on detour phase encoding, the phase distribution calculated by fractional Talbot effect is implemented on this planar optical device. The property of this optical device with periodic square and hexagonal structures is simulated by finite difference time domain (FDTD) respectively. The optical device with explicit advantages of being easy to fabricate, splice, duplicate, and integrate can efficiently prop up the generation of high-quality large-area array-type OAM beams.

fractional Talbot effect; orbital angular momentum; periodic structure; detour phase

TM923

A

10.12086/oee.2020.200093

: Nie F S, Jiang M L, Zhang M S,. Orbital angular momentum Talbot array illuminator based on detour phase encoding[J]., 2020,47(6): 200093

聶芳松，姜美玲，張明偲，等. 基于迂回相位的軌道角動量Talbot陣列照明器[J]. 光電工程，2020，47(6): 200093

Supported by National Natural Science Foundation of China (61605061, 61875073), the Natural Science Foundation of Guangdong Province (2016A030313088), and Guangdong Provincial Innovation and Entrepreneurship Project (2016ZT06D081)

* E-mail: mszhang@jnu.edu.cn; yaoyucao@jnu.edu.cn

2020-03-19；

2020-05-09

國家自然科學(xué)基金資助項目(61605061，61875073)；廣東省自然科學(xué)基金資助項目(2016A030313088)；廣東省創(chuàng)新創(chuàng)業(yè)資助項目(2016ZT06D081)

聶芳松(1994-)，男，碩士研究生，主要從事激光加工微納結(jié)構(gòu)方面的研究。E-mail：315737726@qq.com

張明偲(1990-)，男，博士，主要從事表面等離子體方面的研究。E-mail：mszhang@jnu.edu.cn曹耀宇(1981-)，男，博士，主要從事超分辨光學(xué)技術(shù)與應(yīng)用的研究。E-mail：yaoyucao@jnu.edu.cn