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Profile of a dark hollow beam in sub-diffraction -limit imaging is of crucial importance for its spatial resolution when using the coherent anti-Stokes Raman scattering microscopy, as far as the imaging quality is concerned. Therefore, the generation of dark hollow beams through a vortex phase plate will be theoretically analyzed based on the Fresnel diffraction theory. Influences of different incidence conditions on the intensity distribution of the generated dark hollow beams are also investigated. And it is shown that a perfect dark hollow beam could be produced when a Gaussian beam is vertically incident upon a first-order vortex phase plate, with the incident light wavelength equal to that of the phase plate. However, both the circular symmetry of the incident beam's intensity distribution and the alignment between the centers of Gaussian beam and phase plate may affect the intensity distribution of the dark hollow beam, which will almost be in circular symmetry though it may shift some distance from the image center when at a small incident angle. Furthermore, the dark hollow beam's intensity distribution will scarcely change when the central wavelength deviation is very small from the incidence light and the phase plate. These results may be of great value in generation of perfect dark hollow beams in sub-diffraction –limit imaging by coherent anti-Stokes Raman scattering microscopy.
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Keywords:
- dark hollow beam /
- sub-diffraction-limit /
- coherent anti-Stokes Raman scattering microscopy /
- vortex phase plate
[1] Yamanaka M, Smith N I, Fujita K 2014 Microscopy 0 1
[2] Park J, Lee J, Namgung S, Heo K, Lee H, Hohng S, Hong S 2014 Small 10 462
[3] Hess S T, Girirajan T P K, Mason M D 2006 Biophys. J. 91 4258
[4] Rust M J, Bates M, Zhuang X W 2006 Nature Methods 3 793
[5] Hell S W, Wichmann J 1994 Opt. Lett. 19 780
[6] Cheng J X, Xie X S 2003 The J. Phys. Chem. B 108 827
[7] Evans C L, Xie X S 2008 Annu. Rev. Anal. Chem. 1 883
[8] Cheng J X, Jia Y K, Zheng G, Xie X S 2002 Biophys. J. 83 502
[9] Nan X, Potma E O, Xie X S 2006 Biophys. J. 91 728
[10] Beeker W P, GroBP, Lee C J, Cleff C, Offerhaus H L, Fallnich C, Herek J L, Boller K 2009 Opt. Express 17 22632
[11] Beeker W P, Lee C J, Boller K, GroBP, Cleff Cn, Fallnich C, Offerhaus H L, Herek J L 2010 Phys. Rev. A 81 012507
[12] Nikolaenko A, Krishnamachari V V, Potma E O 2009 Phys. Rev. A 79 013823
[13] Hajek K M, Littleton B, Turk D, McIntyre T J, Rubinsztein-Dunlop H 2010 Opt. Express 18 19263
[14] Liu W, Niu H 2011 Phys. Rev. A 83 023830
[15] Liu S L, Chen D N, Liu W, Niu H B 2013 Acta Phys. Sin. 62 184210 (in Chinese) [刘双龙, 陈丹妮, 刘伟, 牛憨笨 2013 物理学报 62 184210]
[16] Liu X, Liu W, Yin J, Qu J L, Lin Z Y, Niu H B 2011 Chin. Phys. Lett. 28 034202
[17] Yin J, Yu L Y, Liu X, Wan H, Lin Z Y, Niu H B 2011 Chin. Phys. B 20 014206
[18] Parekh S H, Lee Y J, Aamer K A, Cicerone M T 2010 Biophys. J. 99 2695
[19] Paulsen H N, Hilligse K M, Thøgersen J, Keiding S R, Larsen J J 2003 Opt. Lett. 28 1123
[20] Liu W, Chen D N, Liu S L, Niu H B 2013 Acta Phys. Sin. 62 164202 (in Chinese) [刘伟, 陈丹妮, 刘双龙, 牛憨笨 2013 物理学报 62 164202]
[21] Cai Y, Lu X, Lin Q 2003 Opt. Lett. 28 1084
[22] Zhang Q A, Wu F T, Zheng W T, Ma L 2011 Acta Phys. Sin. 60 094201 (in Chinese) [张前安, 吴逢铁, 郑维涛, 马亮 2011 物理学报 60 094201]
[23] Lee H S, Stewart B W, Choi K, Fenichel H 1994 Phys. Rev. A 49 4923
[24] Zhang M Y, Li S G, Yao Y Y, Fu B, Zhang L 2010 Chin. Phys.B 19 047103
[25] Yin J P, Gao W J, Wang H F, Long Q, Wang Y Z 2002 Chin. Phys. 11 1157
[26] Watanabe T, Fujii M, Watanabe Y, Toyama N, Iketaki Y 2004 Rev. Sci. Instrum. 75 5131
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[1] Yamanaka M, Smith N I, Fujita K 2014 Microscopy 0 1
[2] Park J, Lee J, Namgung S, Heo K, Lee H, Hohng S, Hong S 2014 Small 10 462
[3] Hess S T, Girirajan T P K, Mason M D 2006 Biophys. J. 91 4258
[4] Rust M J, Bates M, Zhuang X W 2006 Nature Methods 3 793
[5] Hell S W, Wichmann J 1994 Opt. Lett. 19 780
[6] Cheng J X, Xie X S 2003 The J. Phys. Chem. B 108 827
[7] Evans C L, Xie X S 2008 Annu. Rev. Anal. Chem. 1 883
[8] Cheng J X, Jia Y K, Zheng G, Xie X S 2002 Biophys. J. 83 502
[9] Nan X, Potma E O, Xie X S 2006 Biophys. J. 91 728
[10] Beeker W P, GroBP, Lee C J, Cleff C, Offerhaus H L, Fallnich C, Herek J L, Boller K 2009 Opt. Express 17 22632
[11] Beeker W P, Lee C J, Boller K, GroBP, Cleff Cn, Fallnich C, Offerhaus H L, Herek J L 2010 Phys. Rev. A 81 012507
[12] Nikolaenko A, Krishnamachari V V, Potma E O 2009 Phys. Rev. A 79 013823
[13] Hajek K M, Littleton B, Turk D, McIntyre T J, Rubinsztein-Dunlop H 2010 Opt. Express 18 19263
[14] Liu W, Niu H 2011 Phys. Rev. A 83 023830
[15] Liu S L, Chen D N, Liu W, Niu H B 2013 Acta Phys. Sin. 62 184210 (in Chinese) [刘双龙, 陈丹妮, 刘伟, 牛憨笨 2013 物理学报 62 184210]
[16] Liu X, Liu W, Yin J, Qu J L, Lin Z Y, Niu H B 2011 Chin. Phys. Lett. 28 034202
[17] Yin J, Yu L Y, Liu X, Wan H, Lin Z Y, Niu H B 2011 Chin. Phys. B 20 014206
[18] Parekh S H, Lee Y J, Aamer K A, Cicerone M T 2010 Biophys. J. 99 2695
[19] Paulsen H N, Hilligse K M, Thøgersen J, Keiding S R, Larsen J J 2003 Opt. Lett. 28 1123
[20] Liu W, Chen D N, Liu S L, Niu H B 2013 Acta Phys. Sin. 62 164202 (in Chinese) [刘伟, 陈丹妮, 刘双龙, 牛憨笨 2013 物理学报 62 164202]
[21] Cai Y, Lu X, Lin Q 2003 Opt. Lett. 28 1084
[22] Zhang Q A, Wu F T, Zheng W T, Ma L 2011 Acta Phys. Sin. 60 094201 (in Chinese) [张前安, 吴逢铁, 郑维涛, 马亮 2011 物理学报 60 094201]
[23] Lee H S, Stewart B W, Choi K, Fenichel H 1994 Phys. Rev. A 49 4923
[24] Zhang M Y, Li S G, Yao Y Y, Fu B, Zhang L 2010 Chin. Phys.B 19 047103
[25] Yin J P, Gao W J, Wang H F, Long Q, Wang Y Z 2002 Chin. Phys. 11 1157
[26] Watanabe T, Fujii M, Watanabe Y, Toyama N, Iketaki Y 2004 Rev. Sci. Instrum. 75 5131
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