Numerical Simulation of Anomalous Vortex Beams on Different Fractional Fourier Transform Planes

2014 ◽  
Vol 556-562 ◽  
pp. 3745-3748 ◽  
Author(s):  
Zhi Ping Dai ◽  
Zhen Feng Yang ◽  
Zhen Jun Yang ◽  
Zhao Guang Pang ◽  
Shu Min Zhang
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Fractional Order ◽  
Topological Charge ◽  
Fractional Fourier Transform ◽  
Analytical Expression ◽  
New Type ◽  
Vortex Beams ◽  
Beam Parameters

The properties of fractional Fourier transform of anomalous vortex beams are studied. A new type of analytical expression of fractional Fourier transform for anomolous vortex beams is obtained. The properties of anomolous vortex beams on different fractional Fourier transform planes with different parameters are illustrated. The results show that the anomolous vortex beams always has a doughnut profile, the distribution of intensity on different fractional Fourier transform planes highly depends on the fractional order and the beam parameters, such as the beam order and the topological charge.

Phase Analyse of Non-Vortical and Vortical Beams in Fractional Fourier Transform System

2014 ◽  
Vol 602-605 ◽  
pp. 3648-3651
Author(s):  
Zhi Ping Dai ◽  
Zhen Jun Yang
Keyword(s):  
Fourier Transform ◽  
Intensity Distribution ◽  
Topological Charge ◽  
Fractional Fourier Transform ◽  
Phase Distribution ◽  
Dark Region ◽  
Strong Intensity ◽  
Beam Parameters ◽  
The Fourier Transform ◽  
Phase Analyse

The phase of vortical beams is very different from that of non-vortical beams. The phase of non-vortical and vortical beams in fractional Fourier transform system is investigated by selecting different parameters of the anomalous vortical beam. It is found that although the intensity distribution is similar except nearby the Fourier transform plane for the non-vortical and the vortical beams, the phase distribution is very different even the beam parameters are the same except the topological charge. The different phases bring different intensity distributions especially at the Fourier transform plane, i.e the center of non-vortical beams is a very strong intensity peaks, however the center of vortical beams is a dark region.

Numerical Simulations of Fractional Fourier Transform of Hypergeometric-Gaussian Beam

2013 ◽  
Vol 765-767 ◽  
pp. 780-784 ◽  
Author(s):  
Zhen Feng Yang ◽  
Wen Dan Miao ◽  
Zhen Jun Yang ◽  
Shu Min Zhang
Keyword(s):  
Fourier Transform ◽  
Numerical Simulations ◽  
Gaussian Beam ◽  
Intensity Distribution ◽  
Fractional Fourier Transform ◽  
Focal Length ◽  
Beam Width ◽  
Laser Beams ◽  
New Type ◽  
Lens Focal Length

The fractional Fourier transform (FRFT) of a new type of laser beams called the hypergeometric-Gaussian beam (HyGGB) is investigated in detail. The analytical expression for the FRFT of a HyGGB is derived. The properties of a HyGGB in the FRFT plane with different parameters are illustrated. The results show that the intensity distribution of a HyGGB in the FRFT plane strongly depends on the fractional order, the lens focal length and the initial beam width.

scholarly journals Key Validity Using the Multiple-parameter Fractional Fourier Transform for Image Encryption

2021 ◽  
Author(s):  
Tieyu Zhao ◽  
Yingying Chi
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Information Security ◽  
Theoretical Analysis ◽  
Image Encryption ◽  
Fractional Fourier Transform ◽  
Point Of View ◽  
Multiple Parameter

Abstract Multiple-parameter fractional Fourier transform (MPFRFT) is proposed and applied to image encryption. The MPFRFT with two vector parameters has better security, which becomes the main technical means to protect information security. However, our study found that many keys of the MPFRFT are invalid, which greatly reduces its security. Theoretical analysis and numerical simulation verify our point of view.

Fractional Fourier transform of Lorentz-Gauss vortex beams

2013 ◽  
Vol 56 (8) ◽  
pp. 1487-1494 ◽  
Author(s):  
GuoQuan Zhou ◽  
XiaoGang Wang ◽  
XiuXiang Chu
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Vortex Beams

A feasibility study on elbow erosion monitoring using active sensing approach and fractional Fourier transform

2020 ◽  
pp. 1045389X2096317
Author(s):  
Ning Li ◽  
Furui Wang ◽  
Gangbing Song
Keyword(s):  
Fourier Transform ◽  
Fractional Order ◽  
Stress Wave ◽  
Fractional Fourier Transform ◽  
Damage Index ◽  
Active Sensing ◽  
Thickness Gauge ◽  
Order Energy ◽  
Energy Peak ◽  
Elbow Erosion

Elbow erosion monitoring is of great significance to the safety of pipeline systems and maintenance personnel. This paper proposes a new elbow erosion monitoring method, which combines the PZT (lead zirconate titanate) enabled active sensing with the fractional Fourier transform (FrRT), and takes the fractional-order energy peak of the stress wave signal as the damage index. Three 90°-elbows and three 90°-elbow assemblies were used in the experimental studies. Under different erosion degrees, the mass reduction of the three separate elbows was measured by high-precision electronic scale and the residual thickness of the three elbow assemblies was detected by ultrasonic thickness gauge. Two pieces of PZT patches were respectively used to excite and receive the signals in the active sensing. FrFT was used to distinguish the linear sweep signal components of stress wave signals from the energy of other interference or noise signals, and the fractional-order energy peak was used as the damage index. The results show that there is a one-to-one relationship between mass of erosion loss and damage index. Compared with the traditional time domain signal energy method, the new method has the advantage of eliminating the saturation phenomenon. The proposed method and damage index proposed in this paper will be a promising tool for real-time monitoring of elbow erosion.

Propagation and transformation of four-petal Gaussian vortex beams in fractional Fourier transform optical system

Optik ◽  
2021 ◽  
pp. 167644
Author(s):  
Zhi-Ping Dai ◽  
Yong-Bo Wang ◽  
Qiao Zeng ◽  
Zhao-Guang Pang ◽  
Zhen-Jun Yang
Keyword(s):  
Fourier Transform ◽  
Optical System ◽  
Fractional Fourier Transform ◽  
Vortex Beams
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