Nonparaxial Properties Of Schell-model Beams

With the continuous emergence of new light sources,the description of beams in nonparaxial field becomes more and more important.Nonparaxial beams can be generated by solid state lasers or by tightly focusing of paraxial beam with high numerical aperture.In this case,the characteristic of the beam is that its linear size or spatial variation scale is equivalent to or even smaller than the wavelength,In fact,Schell-model light source is a kind of typical light source.In the past,researchers have been committed to studying the propagation properties of different types of Schell-model beams under the paraxial approximation.However,due to the small spot size of the laser beam applied in some fields,such as particle manipulation and tightly focusing,leading to the angle between the beam and the optical axis of the system becomes large,which no longer meets the propagation theory of the beam under the paraxial approximation,so it can not be treated by paraxial approximation.Therefore,it is very necessary to adopt a set of propagation theory with practical significance for in-depth research.After that,various nonparaxial methods,such as perturbation method and angular spectrum representation have been proposed to deal with the propagation of nonparaxial beams.On the other hand,in view of the potential application value of nonparaxial beams in the fields of free space optical communication,high-resolution microscopy and etc,the research on nonparaxial beams is of great significance and has attracted extensive attention of researchers.Due to the different processing methods between paraxial and nonparaxial beams,it is necessary to identify the paraxial characteristic of the beam before studying the beam.In this paper,three kinds of Schell-model light sources are taken as the research objects,the effects of different light source parameters on the degree of paraxiality of light beams which propagating in free space are discussed,and the reasons are analyzed.The specific research contents are as follows:1.Taking the anisotropic hollow multi-Gaussian Schell-model beam as the research model,the analytical expressions of the degree of paraxiality and the square of the tangent of the far-field divergence angle of anisotropic hollow multi-Gaussian Schell-model beam are derived.The effects of different light source parameters(including the anisotropy and boundary characteristics of the light source,the waist width and coherence width of the beam)on the degree of paraxiality and the far-field divergence angle of the beam which propagating in free space are discussed.The results show that the effects of different light source parameters on the degree of paraxiality and the far-field divergence angle are essentially different.2.The research object is changed from scalar field to vector field,so that the definition of the degree of paraxiality is also extended from scalar field to vector field.Taking the electromagnetic fractional multi-Gaussian Schell-model as the research object,the analytical expressions of the degree of paraxiality and the square of the tangent of the far-field divergence angle of electromagnetic fractional multi-Gaussian Schell-model beam are derived.The effects of different light source parameters(including the rms widths of the auto-correlation functions,the truncated parameter,the degree of polarization,and the boundary characteristics of light source)on the degree of paraxiality and the far-field divergence angle of the beam which propagating in free space are analyzed in detail.3.The definition of the degree of paraxiality is extended from stochastic electromagnetic field to twist stochastic electromagnetic field.Taking twist electromagnetic Gaussian Schell-model beam as the research model,the analytical expressions of the degree of paraxiality and the square of the tangent of the far-field divergence angle are deduced.The effects of several light source parameters(including the rms widths of the auto-correlation functions,twist factor and the degree of polarization)on the degree of paraxiality and the far-field divergence angle of twist electromagnetic Gaussian Schell-model beam which propagating in free space are studied and discussed.