中国物理B ›› 2010, Vol. 19 ›› Issue (1): 10308-010308.doi: 10.1088/1674-1056/19/1/010308

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Optical scaled Fresnel--Fourier transform obtained via intermediate coordinate-- momentum representation

李迟生, 罗汉文   

  1. Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200030, China
  • 收稿日期:2009-04-25 修回日期:2009-06-19 出版日期:2010-01-15 发布日期:2010-01-15

Optical scaled Fresnel--Fourier transform obtained via intermediate coordinate-- momentum representation

Li Chi-Sheng(李迟生)† and Luo Han-Wen(罗汉文)   

  1. Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200030, China
  • Received:2009-04-25 Revised:2009-06-19 Online:2010-01-15 Published:2010-01-15

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摘要： Using the intermediate coordinate--momentum representation |x>s,r, we introduce a new Hadamard transform. It is found that the operator U corresponding to this transform can be considered as a combination of the Fresnel operator F(r,s) and the Fourier transform operator F by decomposing U. We also find that the matrix element s,r< x| U|f> just corresponds to an optical scaled Fresnel--Fourier transform.

Abstract: Using the intermediate coordinate--momentum representation $|x\rangle_{s,r}$, we introduce a new Hadamard transform. It is found that the operator U corresponding to this transform can be considered as a combination of the Fresnel operator $F(r,s)$   and the Fourier transform operator $\mathcal{F}$ by decomposing U. We also find that the matrix element ${}_{s,r}\langle x|U|f\rangle$ just corresponds to an optical scaled Fresnel--Fourier transform.

Key words: Fresnel transform, Fresnel operator, Fourier transform, intermediate coordinate--momentum representation

中图分类号:  (Quantum optics)

  • 42.50.-p
02.30.Nw (Fourier analysis) 02.30.Uu (Integral transforms)