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According to the stochastic behavior of the continuous phase plate (CPP) surface shape distribution, the autocorrelation function and the correlation length are used to analyze its surface shape characteristics. A Gaussian random distribution function is used to derive the analytic relation between the correlation length and the far-field distribution of CPP. Numerical algorithm is used to calculate the variance and the energy usage rate of CPP's far-field distribution, and also the specific influence of correlation length on far-field distribution of CPP. The conclusion is that the smaller the correlation length, the better the homogeneity of far-field distribution is, and the closer to the target spot the shape of the focal spot will be, and at the same time the higher the energy usage rate will be.
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Keywords:
- continuous phase plate /
- autocorrelation function /
- correlation length /
- far-field distribution
[1] Zhao Z Q, He W H, Wang J, Hao Y D, Cao L F, Gu Y Q, Zhang B H 2013 Chin. Phys. B 22 104202
[2] Ye W H, Zhang W Y, He X T 2000 Acta Phys. Sin. 49 762 (in Chinese) [叶文华, 张维岩, 贺贤土 2000 49 762]
[3] L S Y, L B D 2009 Chin. Phys. B 18 3883
[4] Lin Z Q, Lei A L, Fan W, Zhou S L, Wang L 2013 High Power Laser Sci. Eng. 1 110
[5] Kilkenny J D, Glendinning S G, Haan S W, Hammel B A, Lindl J D, Munro D, Remington B A, Weber S V, Knauer J P, Verdon C P 1994 Phys. Plasmas 1 1379
[6] Huang X X, Gao F H, Yuan Q, Hu D X, Zhang K, Zhou W, Dai W J, Deng X W 2013 Acta. Phys. Sin. 62 205206 (in Chinese) [黄小霞, 高福华, 袁强, 胡东霞, 张崑, 周维, 代万俊, 邓学伟 2013 62 205206]
[7] Rothenberg J E, Auerbach J M, Dixit S N, Haan S W, Pollaine S M, Williams W H 1998 Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion (Monterey: SPIE) SUPL65
[8] Li J L, L B D 2008 Chin. Phys. B 17 1840
[9] Wang Y Y, Liu Z J, Liao Q H, Liu S T 2010 Chin. Phys. B 19 054204
[10] Yao X, Gao F H, Zhang Y X, Wen S L, Guo Y K, Lin X D 2009 Acta Phys. Sin. 58 3130 (in Chinese) [姚欣, 高福华, 张怡霄, 温圣林, 郭永康, 林祥棣 2009 58 3130]
[11] Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M 1984 Phys. Rev. Lett. 53 1057
[12] Dixit S N, Lawson J K, Manes K R, Powell H T, Nugent K A 1994 Opt. Lett. 19 417
[13] Lin Y, Kessler T J, Lawrence G N 1995 Opt. Lett. 20 764
[14] Lin Y, Kessler T J, Lawrence G N 1996 Opt. Lett. 21 1703
[15] Yang C L, Yan H, Wang J, Zhang R Z 2013 Opt. Express 21 11171
[16] Feng Y J, Lin Z X, Zhang R Z 2011 Acta Phys. Sin. 60 104202 (in Chinese) [冯友君, 林中校, 张蓉竹 2011 60 104202]
[17] Lin Z X, Zhang R Z, Yang C L, Xu Q 2010 High Power Laser Paticle Beams 22 2634 (in Chinese) [林中校, 张蓉竹, 杨春林, 许乔 2010 强激光与粒子束 22 2634]
[18] Wang Y D, Wang J 2006 Stochastic Signal Analysis (2nd ed.) (Beijing: Publishing House of Electronics Industry) pp77-85 (in Chinese) [王永德, 王军 2006 随机信号分析基础 (第二版) (北京: 电子工业出版社) 第77–85页]
[19] Yang C L, Zhang R Z, Xu Q, Ma P 2007 Appl. Opt. 47 1465
[20] Oppenheim A V, Willsky A S (translated by Liu S T) 1998 Signals and Systems (Xi'an: Xi'an Jiaotong University Press) p223 (in Chinese) [奥本海姆 A V, 威尔斯基 A S著 (刘树棠译) 1998 信号与系统 (西安: 西安交通大学出版社) 第223页]
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[1] Zhao Z Q, He W H, Wang J, Hao Y D, Cao L F, Gu Y Q, Zhang B H 2013 Chin. Phys. B 22 104202
[2] Ye W H, Zhang W Y, He X T 2000 Acta Phys. Sin. 49 762 (in Chinese) [叶文华, 张维岩, 贺贤土 2000 49 762]
[3] L S Y, L B D 2009 Chin. Phys. B 18 3883
[4] Lin Z Q, Lei A L, Fan W, Zhou S L, Wang L 2013 High Power Laser Sci. Eng. 1 110
[5] Kilkenny J D, Glendinning S G, Haan S W, Hammel B A, Lindl J D, Munro D, Remington B A, Weber S V, Knauer J P, Verdon C P 1994 Phys. Plasmas 1 1379
[6] Huang X X, Gao F H, Yuan Q, Hu D X, Zhang K, Zhou W, Dai W J, Deng X W 2013 Acta. Phys. Sin. 62 205206 (in Chinese) [黄小霞, 高福华, 袁强, 胡东霞, 张崑, 周维, 代万俊, 邓学伟 2013 62 205206]
[7] Rothenberg J E, Auerbach J M, Dixit S N, Haan S W, Pollaine S M, Williams W H 1998 Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion (Monterey: SPIE) SUPL65
[8] Li J L, L B D 2008 Chin. Phys. B 17 1840
[9] Wang Y Y, Liu Z J, Liao Q H, Liu S T 2010 Chin. Phys. B 19 054204
[10] Yao X, Gao F H, Zhang Y X, Wen S L, Guo Y K, Lin X D 2009 Acta Phys. Sin. 58 3130 (in Chinese) [姚欣, 高福华, 张怡霄, 温圣林, 郭永康, 林祥棣 2009 58 3130]
[11] Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M 1984 Phys. Rev. Lett. 53 1057
[12] Dixit S N, Lawson J K, Manes K R, Powell H T, Nugent K A 1994 Opt. Lett. 19 417
[13] Lin Y, Kessler T J, Lawrence G N 1995 Opt. Lett. 20 764
[14] Lin Y, Kessler T J, Lawrence G N 1996 Opt. Lett. 21 1703
[15] Yang C L, Yan H, Wang J, Zhang R Z 2013 Opt. Express 21 11171
[16] Feng Y J, Lin Z X, Zhang R Z 2011 Acta Phys. Sin. 60 104202 (in Chinese) [冯友君, 林中校, 张蓉竹 2011 60 104202]
[17] Lin Z X, Zhang R Z, Yang C L, Xu Q 2010 High Power Laser Paticle Beams 22 2634 (in Chinese) [林中校, 张蓉竹, 杨春林, 许乔 2010 强激光与粒子束 22 2634]
[18] Wang Y D, Wang J 2006 Stochastic Signal Analysis (2nd ed.) (Beijing: Publishing House of Electronics Industry) pp77-85 (in Chinese) [王永德, 王军 2006 随机信号分析基础 (第二版) (北京: 电子工业出版社) 第77–85页]
[19] Yang C L, Zhang R Z, Xu Q, Ma P 2007 Appl. Opt. 47 1465
[20] Oppenheim A V, Willsky A S (translated by Liu S T) 1998 Signals and Systems (Xi'an: Xi'an Jiaotong University Press) p223 (in Chinese) [奥本海姆 A V, 威尔斯基 A S著 (刘树棠译) 1998 信号与系统 (西安: 西安交通大学出版社) 第223页]
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