中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60302-060302.doi: 10.1088/1674-1056/22/6/060302

• GENERAL • 上一篇    下一篇

New decomposition of the Fresnel operator corresponding to optical transformation in ABCD-systems

杜建明a, 范洪义b   

  1. a Department of Physics and Electronic Information, Huainan Normal University, Huainan 232001, China;
    b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2012-08-15 修回日期:2012-11-21 出版日期:2013-05-01 发布日期:2013-05-01
  • 基金资助:
    Project supported by the University Natural Science Foundation of Anhui Province, China (Grant No. KJ2011Z339) and the National Natural Science Foundation of China (Grant No. 10874174).

New decomposition of the Fresnel operator corresponding to optical transformation in ABCD-systems

Du Jian-Ming (杜建明)a, Fan Hong-Yi (范洪义)b   

  1. a Department of Physics and Electronic Information, Huainan Normal University, Huainan 232001, China;
    b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2012-08-15 Revised:2012-11-21 Online:2013-05-01 Published:2013-05-01
  • Contact: Du Jian-Ming E-mail:jmdu@hnnu.edu.cn
  • Supported by:
    Project supported by the University Natural Science Foundation of Anhui Province, China (Grant No. KJ2011Z339) and the National Natural Science Foundation of China (Grant No. 10874174).

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摘要： By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property, we obtain new decomposition of the Fresnel operator as the product of quadratic phase operator, squeezing operator, and fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems. The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.

关键词: Fresnel operator, integration within an ordered product technique, optical transformation

Abstract: By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property, we obtain new decomposition of the Fresnel operator as the product of quadratic phase operator, squeezing operator, and fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems. The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.

Key words: Fresnel operator, integration within an ordered product technique, optical transformation

中图分类号:  (Quantum mechanics)

  • 03.65.-w
42.50.-p (Quantum optics)