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According to the diffraction integral theory of vector field and the pupil filtering method with a discrete complex amplitude, we present a tunable pupil filter to achieve and manipulate the focused vector fields with ultra-long depth of focus. The filter consists of a polarization rotator with two /2 wave plates and a discrete complex amplitude filter with six zones. Amplitude transmissions of these zones are different and increase along the radial direction. And every two adjacent transmitted zones have the opposed phases 0 and . With optimized cylindrical polarization (0 =52) and discrete amplitude, the generalized cylindrical vector field can be tightly focused into a three-dimensional (3D) flat-top field with an extended depth of focus (～10 ) by a high numerical aperture lens. For the main outermost zone and the other five inner zones, we analyze the intensity distributions of the three polarized components and the total polarized component in the focal region. We find that the axially and azimuthally polarized components are the major contributors. The outermost zone offers the central field of the focused field while the other five zones affect the side lobe more obviously. Through adjusting the included angle between the double wave plates, we can change the polarization states of the incident vector field and alter the structures of the focused fields among the 3D flat-top focused field, needle-like field, tube-like field and the other fields with intermediate form. Result obtained is superior to that of the past research for the adjustable freedom between these forms, and it reveals the dynamic relation between the evolved vectorial form of incident field and the vector structure of the focused field. Our work paves a way to achieve the controlled dynamical focused field with a long depth of focus. The needle-like field, tube-like field and the well-matched 3D flat-top focused field will meet the demand of applications in optical microscope, optical micro-manipulating, optical micromachining and so on.
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Keywords:
- polarization /
- vector field /
- focusing /
- pupil filter
[1] Zhan Q W 2009 Adv. Opt. Photon. 1 1
[2] Beckley A M, Brown T G 2010 Opt. Express 18 10777
[3] Wang X L, Ding J, Ni W J, Guo C S, Wang H T 2007 Opt. Lett. 32 3549
[4] Youngworth K S, Brown T G 2000 Opt. Express 7 77
[5] Zhan Q W, Leger J R 2002 Opt. Express 10 324
[6] Dorn R, Quabis S, Leuchs G 2003 Phys. Rev. Lett. 91 233901
[7] Chen W B, Zhan Q W 2006 Opt. Commun. 265 411
[8] Wang H F, Shi L P, Luk'yanchuk B, Sheppard C, Chong C T 2008 Nat. Photon. 2 501
[9] Wang J M, Chen W B, Zhan Q W 2010 Opt. Express 18 21965
[10] Du F R, Zhou Z H, Tan Q F, Yang C X, Zhang X Q, Zhu L Q 2013 Chin. Phys. B 22 064202
[11] Zhou Z H, Zhu L Q 2015 Chin. Phys. B 24 028704
[12] Liu J L, Chen Z Y, Zhang L, Pu J X 2015 Acta Phys. Sin. 64 064201 (in Chinese) [刘绩林, 陈子阳, 张磊, 蒲继雄 2015 64 064201]
[13] Chang Q, Yang Y F, He Y, Liu H G, Liu J 2013 Acta Phys. Sin. 62 104202 (in Chinese) [常强, 杨艳芳, 何英, 刘海港, 刘键 2013 62 104202]
[14] Han W, Yang Y F, Cheng W, Zhan Q W 2013 Opt. Express 21 20692
[15] Yun M J, Liu L R, Sun J F, Liu D A 2005 J. Opt. Soc. Am. A 22 272
[16] Wang J M, Liu L R, Yun M J, Liu D A, Liu X M 2005 J. Opt. A 7 748
[17] Yun M J, Wan Y, Kong W J, Wang M, Liu J H, Liang W 2008 Acta Phys. Sin. 57 194 (in Chinese) [云茂金, 万勇, 孔伟金, 王美, 刘均海, 梁伟 2008 57 194]
[18] Kyoko K, Kyosuke S, Susumu N 2010 Opt. Express 18 4518
[19] Jabbour T, Kuebler S 2006 Opt. Express 14 1033
[20] Wang J M, Liu Q L, Liu Y W, Chen W B, Zhan Q W 2011 Proc. SPIE 8097 809722
[21] Sheppard C J R, Mehta S 2012 Opt. Express 20 27212
[22] Chen L L, Wang J M, He C J, Liu Y W, Yun M J, Kong W J 2013 J. Mod. Opt. 60 391
[23] Guo H M, Weng X Y, Jiang M, Zhao Y H, Sui G R, Hu Q, Wang Y, Zhuang S L 2013 Opt. Express 21 5363
[24] Lin J, Chen R, Yu H C 2014 J. Opt. Soc. Am. A 31 1395
[25] Wang J M, Chen W B, Zhan Q W 2011 Opt. Commun. 284 2668
[26] Huang K, Shi P, Kang X L, Zhang X, Li Y P 2010 Opt. Lett. 35 965
[27] Weng X Y, Guo H M, Sui G R, Hu Q, Zheng J H, Wang Y, Zhuang S L 2013 Opt. Commun. 311 117
[28] Nie Z G, Shi G, Zhang X R, Wang Y X, Song Y L 2014 Opt. Commun. 331 87
[29] Liu T, Tan J B, Liu J, Wang H G 2013 Opt. Lett. 38 2742
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[1] Zhan Q W 2009 Adv. Opt. Photon. 1 1
[2] Beckley A M, Brown T G 2010 Opt. Express 18 10777
[3] Wang X L, Ding J, Ni W J, Guo C S, Wang H T 2007 Opt. Lett. 32 3549
[4] Youngworth K S, Brown T G 2000 Opt. Express 7 77
[5] Zhan Q W, Leger J R 2002 Opt. Express 10 324
[6] Dorn R, Quabis S, Leuchs G 2003 Phys. Rev. Lett. 91 233901
[7] Chen W B, Zhan Q W 2006 Opt. Commun. 265 411
[8] Wang H F, Shi L P, Luk'yanchuk B, Sheppard C, Chong C T 2008 Nat. Photon. 2 501
[9] Wang J M, Chen W B, Zhan Q W 2010 Opt. Express 18 21965
[10] Du F R, Zhou Z H, Tan Q F, Yang C X, Zhang X Q, Zhu L Q 2013 Chin. Phys. B 22 064202
[11] Zhou Z H, Zhu L Q 2015 Chin. Phys. B 24 028704
[12] Liu J L, Chen Z Y, Zhang L, Pu J X 2015 Acta Phys. Sin. 64 064201 (in Chinese) [刘绩林, 陈子阳, 张磊, 蒲继雄 2015 64 064201]
[13] Chang Q, Yang Y F, He Y, Liu H G, Liu J 2013 Acta Phys. Sin. 62 104202 (in Chinese) [常强, 杨艳芳, 何英, 刘海港, 刘键 2013 62 104202]
[14] Han W, Yang Y F, Cheng W, Zhan Q W 2013 Opt. Express 21 20692
[15] Yun M J, Liu L R, Sun J F, Liu D A 2005 J. Opt. Soc. Am. A 22 272
[16] Wang J M, Liu L R, Yun M J, Liu D A, Liu X M 2005 J. Opt. A 7 748
[17] Yun M J, Wan Y, Kong W J, Wang M, Liu J H, Liang W 2008 Acta Phys. Sin. 57 194 (in Chinese) [云茂金, 万勇, 孔伟金, 王美, 刘均海, 梁伟 2008 57 194]
[18] Kyoko K, Kyosuke S, Susumu N 2010 Opt. Express 18 4518
[19] Jabbour T, Kuebler S 2006 Opt. Express 14 1033
[20] Wang J M, Liu Q L, Liu Y W, Chen W B, Zhan Q W 2011 Proc. SPIE 8097 809722
[21] Sheppard C J R, Mehta S 2012 Opt. Express 20 27212
[22] Chen L L, Wang J M, He C J, Liu Y W, Yun M J, Kong W J 2013 J. Mod. Opt. 60 391
[23] Guo H M, Weng X Y, Jiang M, Zhao Y H, Sui G R, Hu Q, Wang Y, Zhuang S L 2013 Opt. Express 21 5363
[24] Lin J, Chen R, Yu H C 2014 J. Opt. Soc. Am. A 31 1395
[25] Wang J M, Chen W B, Zhan Q W 2011 Opt. Commun. 284 2668
[26] Huang K, Shi P, Kang X L, Zhang X, Li Y P 2010 Opt. Lett. 35 965
[27] Weng X Y, Guo H M, Sui G R, Hu Q, Zheng J H, Wang Y, Zhuang S L 2013 Opt. Commun. 311 117
[28] Nie Z G, Shi G, Zhang X R, Wang Y X, Song Y L 2014 Opt. Commun. 331 87
[29] Liu T, Tan J B, Liu J, Wang H G 2013 Opt. Lett. 38 2742
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