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On the Scaled Fractional Fourier Transformation Operator

Fan Hong‐Yi, Liyun Hu

Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched.

Chinese Physics LettersFeb 1, 200810 citations

Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation

Qian Qian, Xiaoqing, Song +1 more

我们为多国参加的纠缠的州的表示推出纠缠的部分 Fourier 转变(EFFT ) ，它最新互相与二被构造 conjugaten 模式在 n 模式 Fock 空格纠缠了连续统变量的状态。我们为量建立形式主义 ofEFFT 机械波浪工作，它提供我们导出某波浪的一个方便方法工作。我们发现 EFFT 的 eigenmode 与平常的 Hermite 多项式不同。Wealso 导出 n 模式的 EFFT 挤压的状态。

理论物理通讯：英文版Jan 1, 20060 citations

Heisenberg’s uncertainty principle for N -dimensional fractional Fourier transform of complex-valued functions

Zhichao Zhang, Puyu Han, Yun Ping Sun +6 more

OptikApr 26, 20218 citations

On the core of the fractional Fourier transform and its role in composing complex fractional Fourier transformations and Fresnel transformations

Hong-Yi Fan, Junhua Chen

By a quantum mechanical analysis of the additive rule F α[F β[f]]=F α+β[f], which the fractional Fourier transformation (FrFT) F α[f] should satisfy, we reveal that the position-momentum mutual-transformation operator is the core element for constructing the integration kernel of FrFT. Based on this observation and the two mutually conjugate entangled-state representations, we then derive a core operator for enabling a complex fractional Fourier transformation (CFrFT), which also obeys the additive rule. In a similar manner, we also reveal the fractional transformation property for a type of Fresnel operator.By a quantum mechanical analysis of the additive rule F α[F β[f]]=F α+β[f], which the fractional Fourier transformation (FrFT) F α[f] should satisfy, we reveal that the position-momentum mutual-transformation operator is the core element for constructing the integration kernel of FrFT. Based on this observation and the two mutually conjugate entangled-state representations, we then derive a core operator for enabling a complex fractional Fourier transformation (CFrFT), which also obeys the additive rule. In a similar manner, we also reveal the fractional transformation property for a type of Fresnel operator.

Frontiers of PhysicsSep 13, 201414 citations

On the Scaled Fractional Fourier Transformation Operator

范洪义, 胡利云

基于我们的以前的学习[下巴。Phys。Lett。24 (2007 ) 2238 ] 在哪个相应于古典夫累Ｘ尔变换的夫累Ｘ尔操作员被介绍，我们导出部分 Fourier 转变操作员，和光操作员方法然后被充实。

Chinese Physics LettersJan 1, 20080 citations

Eigenfunctions of the complex fractional Fourier transform obtained in the context of quantum optics

Hong-Yi Fan, Liyun Hu, Ji‐Suo Wang

We employ the recently established basis (the two-variable Hermite-Gaussian function) of the generalized Bargmann space (BGBS) [Phys. Lett. A303, 311 (2002)] to study the generalized form of the fractional Fourier transform (FRFT). By using the technique of integration within an ordered product of operators and the bipartite entangled-state representations, we derive the generalized generating function of the BGBS with which the undecomposable kernel of the two-dimensional FRFT [also named complex fractional Fourier transform (CFRFT)] is obtained. This approach naturally shows that the BGBS is just the eigenfunction of the CFRFT.We employ the recently established basis (the two-variable Hermite-Gaussian function) of the generalized Bargmann space (BGBS) [Phys. Lett. A303, 311 (2002)] to study the generalized form of the fractional Fourier transform (FRFT). By using the technique of integration within an ordered product of operators and the bipartite entangled-state representations, we derive the generalized generating function of the BGBS with which the undecomposable kernel of the two-dimensional FRFT [also named complex fractional Fourier transform (CFRFT)] is obtained. This approach naturally shows that the BGBS is just the eigenfunction of the CFRFT.

Journal of the Optical Society of America AMar 26, 200814 citations

On the core of the fractional Fourier transform and its role in composing complex fractional Fourier transformations and Fresnel transformations

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On the core of the fractional Fourier transform and its role in composing complex fractional Fourier transformations and Fresnel transformations

Abstract

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