The Comparison And Study Of Vectorial Diffraction Theories And Its Application

It is well known that the light wave is electromagnetic wave and to solve the diffraction problem can not be separated from the classic electromagnetic theory which based on the a Maxwell equations. The electromagnetic fidld is vector field so the strict diffraction theory shoud be vectorial diffraction theory. To the majority optics diffraction and the light beam transmission actual problem, the scalar diffraction theory all is extremely precise, but along with the development of near-field optics and the gradually increased using of small-scale but large divergence angle light, the scalar approximation of diffraction theory is no longer useful and vector diffraction theory must be applied .This research has studied the paraxial theory is not of self-consistency and the two typical research methods of non-paraxial vector diffraction: the vectorial diffraction theory of the angular spectrum representation a Rayleigh-Sommerfeld diffraction theory, also proved the equivalence of the two methods.Based on the angular spectrum represenatation of the vector diffraction,exact solution of space maps of transverse component , vector diffraction field vertical component of exact solutions, exact light intensity of vectorial field. But the vertical component of vectorial field is exist so the optical field distribution is not axial symmetry,only stduy a adirection(such as x-axis directions)of light can not completely description light field. We studied the vector and scalar theory in the three-dimensional space in Matlab,pointed out that vector correction to the scalar approximatio of near field are necessary and the validity of the scalar diffraction theory is studied.In this thesis, we take the Gauss beam diffracted at a small circular aperture's vector diffraction theory as an example,shown that non-paraxial approximate solution apply to describe the beam waist width and linear dimensions of the aperture are very small when nonparaxial Gauss beam diffracted in the near-field. In this paper ,detailed numerical calculations for the series expansion solution ,non-paraxial approximation solution of vectorial Gaussian beams diffracted at a small circular aperture depends on the waist width ,aperture and propagation distance,and they are compensated mutually.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,only when the waist width aperture aren very bigger than the wavelength the scalar diffraction theory is exactly. When the beam waist is much smaller than aperture, it can be transited to the Gaussian biam transmis in the free-space ,. When the beam waist is much bigger than aperture ,it can be transited to the plane wave's Diffraction,and the field strength is basically with the plan wave.