Please wait a minute...
Chin. Phys. B, 2009, Vol. 18(2): 611-615    DOI: 10.1088/1674-1056/18/2/037
CLASSICAL AREAS OF PHENOMENOLOGY Prev   Next  

Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field

Fan Hong-Yi(范洪义) and Hu Li-Yun(胡利云)
Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
Abstract  This paper proves a new theorem on the relationship between optical field Wigner function's two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ(x) propagates through an optical [D(B)(C)A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D,B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A,C.
Keywords:  Fresnel transform      two-parameter Radon transform      Wigner function  
Received:  21 August 2008      Revised:  11 September 2008      Accepted manuscript online: 
PACS:  42.50.-p (Quantum optics)  
  02.30.Uu (Integral transforms)  
  42.30.Kq (Fourier optics)  
  42.79.Sz (Optical communication systems, multiplexers, and demultiplexers?)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174).

Cite this article: 

Fan Hong-Yi(范洪义) and Hu Li-Yun(胡利云) Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field 2009 Chin. Phys. B 18 611

[1] Margolus-Levitin speed limit across quantum to classical regimes based on trace distance
Shao-Xiong Wu(武少雄), Chang-Shui Yu(于长水). Chin. Phys. B, 2020, 29(5): 050302.
[2] Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system
Haiyun Bi(毕海云), Guoyuan Qi(齐国元), Jianbing Hu(胡建兵), Qiliang Wu(吴启亮). Chin. Phys. B, 2020, 29(2): 020502.
[3] Wigner function for squeezed negative binomial state and evolution of density operator for amplitude decay
Heng-Yun Lv(吕恒云), Ji-Suo Wang(王继锁), Xiao-Yan Zhang(张晓燕), Meng-Yan Wu(吴孟艳), Bao-Long Liang(梁宝龙), Xiang-Guo Meng(孟祥国). Chin. Phys. B, 2019, 28(9): 090302.
[4] Negativity of Wigner function and phase sensitivity of an SU(1,1) interferometer
Chun-Li Liu(刘春丽), Li-Li Guo(郭丽丽), Zhi-Ming Zhang(张智明), Ya-Fei Yu(於亚飞). Chin. Phys. B, 2019, 28(6): 060704.
[5] Analytical and numerical investigations of displaced thermal state evolutions in a laser process
Chuan-Xun Du(杜传勋), Xiang-Guo Meng(孟祥国), Ran Zhang(张冉), Ji-Suo Wang(王继锁). Chin. Phys. B, 2017, 26(12): 120301.
[6] Quantum statistical properties of photon-added spin coherent states
G Honarasa. Chin. Phys. B, 2017, 26(11): 114202.
[7] Quantum metrology with two-mode squeezed thermal state: Parity detection and phase sensitivity
Heng-Mei Li(李恒梅), Xue-Xiang Xu(徐学翔), Hong-Chun Yuan(袁洪春), Zhen Wang(王震). Chin. Phys. B, 2016, 25(10): 104203.
[8] Algebraic and group treatments to nonlinear displaced number statesand their nonclassicality features: A new approach
N Asili Firouzabadi, M K Tavassoly, M J Faghihi. Chin. Phys. B, 2015, 24(6): 064204.
[9] Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states:Non-classical and non-Gaussian properties
Xu Xue-Xiang (徐学翔), Yuan Hong-Chun (袁洪春), Wang Yan (王燕). Chin. Phys. B, 2014, 23(7): 070301.
[10] New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function
Meng Xiang-Guo (孟祥国), Wang Ji-Suo (王继锁), Liang Bao-Long (梁宝龙). Chin. Phys. B, 2013, 22(3): 030307.
[11] Nonclassicality and decoherence of coherent superposition operation of photon subtraction and photon addition on squeezed state
Xu Li-Juan (徐莉娟), Tan Guo-Bin (谭国斌), Ma Shan-Jun (马善钧), Guo Qin (郭琴). Chin. Phys. B, 2013, 22(3): 030311.
[12] A new type of photon-added squeezed coherent state and its statistical properties
Zhou Jun(周军), Fan Hong-Yi(范洪义), and Song Jun(宋军) . Chin. Phys. B, 2012, 21(7): 070301.
[13] Quantum phase distribution and the number–phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems
G. R. Honarasa, M. K. Tavassoly, and M. Hatami . Chin. Phys. B, 2012, 21(5): 054208.
[14] Nonclassicality of a two-variable Hermite polynomial state
Tan Guo-Bin(谭国斌), Xu Li-Juan(徐莉娟), and Ma Shan-Jun(马善钧) . Chin. Phys. B, 2012, 21(4): 044210.
[15] The Wigner distribution functions of coherent and partially coherent Bessel–Gaussian beams
Zhu Kai-Cheng(朱开成), Li Shao-Xin(李绍新), Tang Ying(唐英), Yu Yan(余燕), and Tang Hui-Qin(唐慧琴) . Chin. Phys. B, 2012, 21(3): 034201.
No Suggested Reading articles found!