Research On The Spatial Coherence Of The Finite Energy Airy Beam

One of the main topics of the theoretical research on laser is coherence.The coherence is one of the important indexes to evaluate the quality of laser and the laser with suitable coherence has broad application prospects in holography,lithography,and other fields.Meanwhile,the finite energy Airy beam is one of hot issues in laser researches because of its particular properties of no-diffracting,self-accelerating and self-healing in free-space transmission,which makes itself occupies extremely important position in application fields such as optical,measurement and the laser communication.Based on the above two points,this article researches the spatial coherence characteristics of finite energy Airy beam,of which the main work is as follows:Firstly,the coherence of the source Gaussian beam generating the finite energy Airy beam(SGB),the finite energy Airy beam(FEAB)and the Gaussian beam fitted by the main lobe of the finite energy Airy beam(FGB)has been studied.The result is as follows briefly: The three kinds of spatial coherent function are all Gaussian function of transverse difference,which are related to decay factor.When the decay factor increases from 0 to 1,the spatial coherence width of SGB becomes narrower,the spatial coherence of SGB gets weaker.On the contrary,the spatial coherence width of FEAB becomes wider,of which the spatial coherence gets stronger.When a(28)0.5,the two coherence widths are equal to each other.Moreover,along with the rising of the decay factor,the spatial coherence width of FEAB keeps increasing until highly close to,but never reach to,that of FGB.That's because the side lobes of FEAB inhibits its spatial coherence.Secondly,the spatial coherence evolution of FEAB imposed nonlinear phase has been analyzed.It shows that the spatial coherent function of this kind of beam is no longer a Gaussian function but relates to the decay factor,free space transmission distance and nonlinear phase.With the increasing of decay factor and the value of Bintegration,the coherence width of this beam becomes narrower and narrower,leading to the spatial coherence getting worse and worse.At the same time,with the increasing of transmission distance,the situation is inverse,which means the spatial coherence width is getting wider and wider,the spatial coherence is becoming better and better.This research brings out a new method,coherence width,to define the beam width of the FEAB,and the spatial coherence of FEAB has been analyzed detail by using the generalized Van Cittert-Zernike theorem,which will offer a certain reference value to the later research related to the Airy beam.