The Comparison And Study Of Non-paraxial Diffraction Theories

To the majority optics diffraction and the light beam transmission actual problem, the scalar Kirchhoff diffraction theory and the first ,the second kind of Rayleigh-Sommerfeld diffraction theory all is extremely precise; when propagation distance z is comparable with wave length Just in the near field region ,because the boundary diffracted wave cannot be neglected ,there are much difference between the three kinds of diffraction theories.In this thesis, we take the Gauss beam diffracted at a small circular aperture as an example. Detailed numerical calculation and comparison research are performed with the series solution and non-paraxial approximate solution and exact solution in vector diffraction field. The result indicated Gauss beam after circular aperture the applicable range of the series solution and non-paraxial approximate solution depends on the beam waist width, linear dimensions of the aperture and propagation distance. The applicable range also depends its order. It is found that for hard-edged aperture diffractions, the contribution due to the high-frequency components cannot be neglected, so its applicable range is very limited; Applicable range of scalar approximation of Gauss beam diffracted at a circular aperture is discussed.The traditional definition of the light intensity is expressed as the square of an absolute value, which is only suitable to the paraxial-scalar diffraction light field. Considering the vectorial property of the time -average energy flow density, a new extensive definition of the light intensity has been proposed. The energy flux density vector is introduced as the accurate formula of the light intensity for nonparaxial scalar beams. In the vectorial diffraction theory, the time-average energy flow density which crosses in a unit time and a unit area can be applied to measuring quantity of the light intensity at any curved surface. In this thesis, based on the vectorial diffraction theory of the angular spectrum representation and taken the circular aperture diffraction as an example, the formulae for three different kinds of light intensity are obtained. Detailed numerical calculation is performed and illustrated. The different results are compared. It is pointed out that vectorial property of the light field must be taken into account in order to analyze the diffracting behavior in near-field region or for small apertures or small waist width. The result can be applied to the research on second intensity moments and optical beam quality of the vectorial light beams.