Results 291 to 300 of about 101,618 (327)

Fractional Fourier Transforms

2003
In the next few lectures we provide a brief overview of Fourier analysis and how it has been used to model lin- ear physical phenomena, particularly the reversible propagation of scalar waves in homogeneous media and the irreversible diffusion of one molecular species within another.
Bruce J. West, Mauro Bologna, Paolo Grigolini   +2 more
openaire   +1 more source

Fractional Fourier–Kravchuk transform

Journal of the Optical Society of America A, 1997
We introduce a model of multimodal waveguides with a finite number of sensor points. This is a finite oscillator whose eigenstates are Kravchuk functions, which are orthonormal on a finite set of points and satisfy a physically important difference equation.
Natig M. Atakishiyev, Kurt Bernardo Wolf
openaire   +1 more source

Extended fractional Fourier transforms

Journal of the Optical Society of America A, 1997
The concept of an extended fractional Fourier transform (FRT) is suggested. Previous FRT’s and complex FRT’s are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple ...
Jianwen Hua, Liren Liu, Guoqiang Li
openaire   +1 more source

Generalized fractional Fourier transforms

Journal of Physics A: Mathematical and General, 1997
Summary: We generalize the definition of the fractional Fourier transform (FRT) by expanding the new definition proposed by Shih to the original definition. The generalized FRT is shown to have \(k\)-periodic eigenvalues with respect to the order of Hermite-Gaussian functions and will be reduced to the original FRT and Shih's FRT at the two limits with
Liu, Shutian, Jiang, Jiuxing, Zhang, Yan, Zhang, Jingde   +3 more
openaire   +1 more source

Fractional Fourier transform reflectometry

SPIE Proceedings, 2014
In some OFDR implementations it is advantageous to use sinusoidal frequency tuning and to work in the linear range of the sinusoid. For a given scan frequency this limits the maximum length of the interrogated fiber. We propose a new method which allows exceedingly large delays while maintaining high scan rates.
Lihi Shiloh, Avishay Eyal
openaire   +1 more source

Quantum Fractional Fourier Transform

Frontiers in Optics / Laser Science, 2018
Fourier transform has taken place in different areas and applications, in this paper has been revised an important new form of application in the paradigm of quantum computing. Quantum Fourier transforms have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology [2]. In the Shor’s Algorithm it is used for find
Yesid Madrid, Martha Molina, Rafael Torres   +2 more
openaire   +1 more source

Double-lens extended fractional Fourier transform

Applied Optics, 2006
A double-lens extended fractional Fourier transform (EFRT) is proposed. In the double-lens setup, arbitrary-order EFRTs including real orders and complex orders can be carried out. To verify that the single-lens EFRT and the double-lens EFRT are equivalent, numerical simulations and optical experiments for the real-order EFRT and the complex-order EFRT
Caijie, Yan, Weimin, Jin
openaire   +2 more sources

Beam analysis by fractional Fourier transform

Optics Letters, 2001
A method of spatial modal decomposition for optical beams by fractional Fourier transform, and its practical implementation with reduced complexity by use of modal interleavers, are discussed.
X, Xue, H, Wei, A G, Kirk
openaire   +2 more sources

Wavelet-fractional Fourier transforms

Chinese Physics B, 2008
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite–Gaussian functions. The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
openaire   +1 more source

Improved fast fractional-Fourier-transform algorithm

Journal of the Optical Society of America A, 2004
Through the optimization of the main interval of the fractional order, an improved fast algorithm for numerical calculation of the fractional Fourier transforms is proposed. With this improved algorithm, the fractional Fourier transforms of a rectangular function and a Gaussian function are calculated.
Xingpeng, Yang, Qiaofeng, Tan, Xiaofeng, Wei, Yong, Xiang, Yingbai, Yan, Guofan, Jin   +5 more
openaire   +2 more sources