The Theory Of Hermitian-Gaussian-correlated Schell-mode Beams Propagating In Gradient Fibers And Free-space Self-repairing Theory And Experimental Verification

A special function correlated partial coherence beam has many special abilities and be utilized in many research area.It is important in regulation of light field.A Hemite-Gaussian correlated Schell-model(HGCSM)beam is self-split in free space propagation.Researchers pay attention to the properties in free space propagation,but have not focus on propagation in media.A partial coherence beam is able to self-healing in propagation in free space,but many researchers analyzed the properties.But the opaque obstacle is set at the source place.To qualify the self-healing process between the original beam and the beam propagation with obstacle,many definitions of the degree of similarity have been suggested.The paper focuses on two chapters.We analysis the statistics property of a HGCSM beam propagation in gradient-index fiber by Collins formula,calculate the propagation factor.We find the distribution of intensity and coherence in a gradient-index fiber repeat at the same distance periodical.The properties of a HGCSMl beam are not influenced by the character of a gradient fiber.We discuss the properties of self-healing of a HGCSM beam with an opaque obstacle in propagation.To compare the beam with and without obstacle,we fix the distance between source plane and obstacle plane to modify the distance between observer plane and source plane.Another way is fixing the distance between observer plane and source plane to modify the distance between source plane and obstacle plane.It is clear that the obstacle doesn't influence the coherence of a beam,and the properties of a HGCSM beam are the key of self-healing.The paper suggests a new definition of the similarity degree of self-healing and discusses the properties of a well definition.Numerical similarity and experiment results fit wel.The paper analysis the properties of a HGCSM beam in gradient fiber and self-healing in free space.It means that the beam could be utilized in anti-interference,communication,micromanipulation,microscopy imaging and so on.The paper make a little work in special correlated partial beam and self-healing.A HGCSM beam is still worth to find more properties and the similarity degree of self-healing is waiting to be expanded more.