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The generation and application of the vortex beams are part of the hot topics in the optical field. In this paper, the phase structure of the four-step phase plates, analyzed by Fourier series expansion method, is composed of a series of spiral phase plates. When the phase plate is directly irradiated by linearly polarized light, multi-order diffraction waves with different topological charge numbers are generated. Unlike vortex waves, the intensity distribution of the multi-order diffraction has a deviation from the axial symmetry due to the interference with each other. On this basis, a new scheme is proposed to generate vortex beams by the four-step phase plates. With the help of Mach-Zehnder interferometer, the diffraction waves generated by two pieces of the four-step phase plates overlap each other. By adjusting the phase difference of the Mach-Zehnder interferometer, some orders of diffraction waves generate destructive interference while the others generate constructive interference. Thus the linear polarized light can be converted into vortex beams. The diffraction intensity and angular momentum distributions of the four-step phase plates with different cycle numbers are numerically simulated and compared with the spiral phase plates, we can provethat the vortex beams can be obtained by simple four-step phase plates which are the same as those obtained by spiral phase plates. In addition, the four-step phase plates with a small cycle number can generate vortex beams with a large topological charge number and the fabrication difficulty of the phase plates is reduced.
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Keywords:
- vortex beams /
- the four-step phase plate /
- the spiral phase plate /
- orbital angular momentum
[1] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
[2] Prabhakar S, Kumar A, Banerji J, Singh R P 2011 Opt. Lett. 36 4398
[3] Simpson N, Dholakia K, Allen L, Padgett M 1997 Opt. Lett. 22 52
[4] Li X, Cao Y, Gu M 2011 Opt. Lett. 36 2510
[5] Chen Z Y, Pu J X, Zhao D M 2011 Phys. Lett. A 375 2958
[6] Fickler R, Lapkiewicz R, Plick W N, Krenn M, Schaeff C, Ramelow S, Zeilinger A 2012 Science 338 640
[7] Gecevičius M, Drevinskas R, Beresna M 2014 Appl. Phys. Lett. 104 231110
[8] Chen C R, Yeh C H, Shih M F 2014 Opt. Express 22 3180
[9] Rodenburg B, Mirhosseini M, Malik M 2014 N. J. Phys. 16 033020
[10] Zhou Z H, Guo Y K, Zhu L 2014 Chin. Phys. B 23 044201
[11] Colin J R S 2014 Opt. Express 22 18128
[12] Qian X M, Zhu W Y, Rao R Z 2015 Chin. Phys. B 24 044201
[13] Beijersbergen M W, Allen L, Vanderveen H E L O, Woerdman J P 1993 Opt. Commun. 96 123
[14] Remy P, Fabrice D, Mathieu C 2008 Opt. Express 16 7134
[15] Guo C S, Liu X, He J L, Wang H T 2004 Opt. Express 12 4625
[16] Kotlyar V V, Khonina S N, Kovalev A A 2006 Opt. Lett. 31 1597
[17] Cottrell D M, Davis J A, Hernandez T J 2011 Opt. Express 19 12873
[18] Yang Y J, Dong Y, Zhao C L, Cai Y J 2013 Opt. Lett. 38 5418
[19] Kotlyar V V, Kovalev A A, Stafeev S S, Nalimov A G 2013 J. Opt. 15 025712
[20] Schemmel P, Pisano G, Maffei B 2014 Opt. Express 22 14712
[21] Ostrovsky A S, Parrao P C, Arrizon V 2013 Opt. Lett. 38 534
[22] Rumala Y S, Leanhardt A E 2013 J. Opt. Soc. Am. B 30 615
[23] Rumala Y S 2014 J. Opt. Soc. Am. B 31 A6
[24] Huang S J, Gu T T, Miao Z, He C, Wang T Y 2014 Acta Phys. Sin. 63 244103(in Chinese) [黄素娟, 谷婷婷, 缪庄, 贺超, 王廷云 2014 63 244103]
[25] Wang Y D, Gan X T, Ju P, Pang Y, Yuan L G, Zhao J L 2015 Acta Phys. Sin. 64 034204(in Chinese) [王亚东, 甘雪涛, 俱沛, 庞燕, 袁林光, 赵建林 2015 64 034204]
[26] Liang K M 2010 Methods of Mathematical Physics (Beijing: Higher Education Press) p72 (in Chinese) [梁昆淼 2010 数学物理方法 (北京: 高等教育出版社)第72页]
[27] Ji X M, Mu R W, Yin J P 2005 Acta Phys. Sin. 54 5109(in Chinese) [纪宪明, 沐仁旺, 印建平 2005 54 5109]
[28] Allen L, Padgett M J, Babiker M 1999 Prog. Opt. 39 291
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[1] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
[2] Prabhakar S, Kumar A, Banerji J, Singh R P 2011 Opt. Lett. 36 4398
[3] Simpson N, Dholakia K, Allen L, Padgett M 1997 Opt. Lett. 22 52
[4] Li X, Cao Y, Gu M 2011 Opt. Lett. 36 2510
[5] Chen Z Y, Pu J X, Zhao D M 2011 Phys. Lett. A 375 2958
[6] Fickler R, Lapkiewicz R, Plick W N, Krenn M, Schaeff C, Ramelow S, Zeilinger A 2012 Science 338 640
[7] Gecevičius M, Drevinskas R, Beresna M 2014 Appl. Phys. Lett. 104 231110
[8] Chen C R, Yeh C H, Shih M F 2014 Opt. Express 22 3180
[9] Rodenburg B, Mirhosseini M, Malik M 2014 N. J. Phys. 16 033020
[10] Zhou Z H, Guo Y K, Zhu L 2014 Chin. Phys. B 23 044201
[11] Colin J R S 2014 Opt. Express 22 18128
[12] Qian X M, Zhu W Y, Rao R Z 2015 Chin. Phys. B 24 044201
[13] Beijersbergen M W, Allen L, Vanderveen H E L O, Woerdman J P 1993 Opt. Commun. 96 123
[14] Remy P, Fabrice D, Mathieu C 2008 Opt. Express 16 7134
[15] Guo C S, Liu X, He J L, Wang H T 2004 Opt. Express 12 4625
[16] Kotlyar V V, Khonina S N, Kovalev A A 2006 Opt. Lett. 31 1597
[17] Cottrell D M, Davis J A, Hernandez T J 2011 Opt. Express 19 12873
[18] Yang Y J, Dong Y, Zhao C L, Cai Y J 2013 Opt. Lett. 38 5418
[19] Kotlyar V V, Kovalev A A, Stafeev S S, Nalimov A G 2013 J. Opt. 15 025712
[20] Schemmel P, Pisano G, Maffei B 2014 Opt. Express 22 14712
[21] Ostrovsky A S, Parrao P C, Arrizon V 2013 Opt. Lett. 38 534
[22] Rumala Y S, Leanhardt A E 2013 J. Opt. Soc. Am. B 30 615
[23] Rumala Y S 2014 J. Opt. Soc. Am. B 31 A6
[24] Huang S J, Gu T T, Miao Z, He C, Wang T Y 2014 Acta Phys. Sin. 63 244103(in Chinese) [黄素娟, 谷婷婷, 缪庄, 贺超, 王廷云 2014 63 244103]
[25] Wang Y D, Gan X T, Ju P, Pang Y, Yuan L G, Zhao J L 2015 Acta Phys. Sin. 64 034204(in Chinese) [王亚东, 甘雪涛, 俱沛, 庞燕, 袁林光, 赵建林 2015 64 034204]
[26] Liang K M 2010 Methods of Mathematical Physics (Beijing: Higher Education Press) p72 (in Chinese) [梁昆淼 2010 数学物理方法 (北京: 高等教育出版社)第72页]
[27] Ji X M, Mu R W, Yin J P 2005 Acta Phys. Sin. 54 5109(in Chinese) [纪宪明, 沐仁旺, 印建平 2005 54 5109]
[28] Allen L, Padgett M J, Babiker M 1999 Prog. Opt. 39 291
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