The Physical Feature Of Lorentz Beams

In this work we present a new kind of diffraction-free and three-dimensional scalar optical beams, Gawhary named this beams as Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions. He derive a closed-form expression of free-space propagation under the paraxial approximation.We study the diffraction-free distance of Lorentz beams in free-space and its non-diffrating features, and point out its perfect pseudo non-diffrating features. Also, we derive the analytical expression of interference with Lorentz beams. Study its interference features.Moreover, in this work we introduce a new kind of rectangularly symmetric optical beams, also is three-dimensional scalar beams. This beam has been called as Super-Lorentzian beams because it is on the basis of Lorentz beams, so Super-Lorentz beams are also belong to the foresaid Lorentz beams.We derive its closed-form expression of free-space propagation under the paraxial approximation too. And with the space of polynomials, we constitute a family of mutually orthogonal paraxial optical fields on the basis of Lorentz beams with a related new class of orthogonal polynomials. Since it was shown, that there exist some sources that produce fields with special shape, require different models than the ubiquitous TEM 00Gaussian beam.With the help of paraxial wave equation, that in tridimensional space, there also exist Lorentz-Gaussian beams and Super Lorentz-Gaussian beams. These two beams obtained by multiplying the original Lorentz beam and Super-Lorentz beams to a Gaussian envelope function respectively, and they also exist under paraxial limit.By using the MATLAB programming language, we simulate the propagations of the Lorentz beams and Gaussian beams in free-space, and the interference of traveling Lorentz beams. The simulations are also including Lorentz-Gaussian beams and Super-Lorentz beams. We study the features of these Lorentz beams and by the comparison of Lorentz beams and Gassian beams. We make the conclusion that the Lorentz beams is the kind of perfect non- diffrating beams, and can be very useful in practical application.