The Study Of Vectorial Diffraction Theories For Plane Waves Diffracted At A Rectangular Hole

Light field,as a vector field,when the dimension of aperture is so large compared to the wavelength that the coupling relationship between each component can be ignored,can be treated as a scalar field.Conventional scalar diffraction theorem is efficiently applied to solve the propagation of light waves under the approximation of paraxial and far field.But when the dimensions of apertures or obstacles is compared to wavelength or the observation took from a big angle away from the axial,particularly the diffraction occured in the near field and through small apertures,or the medium is inhomogeneous,there exists error with the result calculated by the scalar theorem.Processing the propagation of light wave under these situations needs a strict vector theorem.Wave equation can be converted into Helmholtz equation by pluging the complex amplitude vector expression of light waves into the original vector wave equation.The vector diffraction theory of Kirchhoff vector diffraction integral formula and RayleighSommerfeld vector diffraction integral formula is derived by solving the vector Helmholtz equation drawing on the vector Green theorem and vector analysis theory,and their physical meaning is illustrated.Applying the Fresnel approximation and the Fraunhofer approximation into Rayleigh Sommerfeld vector diffraction integral formula contributes to get the vector Fresnel diffraction integral formula and the vector Fraunhofer diffraction integral formula.Comparison and analysis has been made applying vector diffraction formula and scalar diffraction formula under those two approximation.Computer simulation identifies the feasibility and the reliability of the conclusion and implies the scope and working condition of these theory.The conclusion is contributed to the study of near field optics and vector diffraction theory and enriches the content of whole diffraction theory.