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

doi:10.1088/1674-1056/19/1/010308

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.

Keywords: Fresnel transform Fresnel operator Fourier transform intermediate coordinate--momentum representation

Received: 25 April 2009
Revised: 19 June 2009
Accepted manuscript online:

PACS:	42.50.-p	(Quantum optics)
	02.30.Nw	(Fourier analysis)
	02.30.Uu	(Integral transforms)

Cite this article:

Li Chi-Sheng(李迟生) and Luo Han-Wen(罗汉文) Optical scaled Fresnel--Fourier transform obtained via intermediate coordinate-- momentum representation 2010 Chin. Phys. B 19 010308

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

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