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 $\psi\left( x^{\prime }\right) $ propagates through an optical $\left[ D\left( -B\right) \left( -C\right) A\right] $ 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!