The Study Of The Characteristic Of The Near-field Diffraction Of Small Aperture And The Different Diffraction Theory

As the basic problem of the optical wave, the diffraction is not avoided in the practicalapplication. Sometimes in order to obtain the specific optical field distribution, we use thediffraction of the barrier to change the transmission of the light beam. Usually, the accurateexpression of the diffraction problem is solved by the Maxwell equations with the help of theelectromagnetic field theory. The rigorous diffraction theory considers the vector of theelectromagnetic field. In general, when the size of the barrier is larger than the opticalwavelength and the transmission distance is farther, we can describe the physical process of theoptical propagation by using the scalar approximation method. However, in the diffraction of thebarrier with small scale, especially the near-field diffraction of the small aperture, the scalardiffraction is not suitable, and we must adopt the vector diffraction theory.Firstly, the thesis introduces the scalar and vector diffraction theory. The scalar diffractiontheory includes Kirchhoff diffraction integral formula, Rayleigh-Sommerfeld diffraction integral,the angular spectrum of the plane wave. And the vector diffraction theory includes the vectorangular spectrum theory, the vector Rayleigh-Sommerfeld diffraction integral andfinite-difference time-domain (FDTD). We not only state the self-consistent of the Kirchhoffdiffraction integral formula, but also briefly prove the equivalence between angular spectrumtheory and Rayleigh-Sommerfeld diffraction integral。In this thesis, the diffraction characteristic of the aperture is analyzed through programming.We study the near-field and far-field diffractions of the circular aperture, and numericallycalculate the diffraction intensity distribution with the help of FDTD. Moreover, we discuss indetail the one-dimensional distributions on the axis, along the boundary shadow and thetransverse direction. We compare the results of the intensity distribution on the axis with theresults obtained according to FA theory and RS diffraction. The research indicates that thenear-field diffraction characteristics of the circular aperture can not be deduced according to theresults in far-field diffraction, and the near-field diffraction of a small hole, even the deep Fresnel diffraction, should be considered by the vector diffraction theory.The angular spectrum has two kinds of forms, including the vector and scalar forms.In thethesis, we study the near-field diffraction of a small aperture by the method of the vector andscalar angular spectrum theory. We discuss the influence on the near-field diffraction by theevanescent wave, and then demarcate the range of influence. We find that the existence of theevanescent wave leads the small aperture to converge the light beam. The results show that therange of influence in the scalar angular spectrum theory is different from that in the vector one.The fluctuation of the boundary effect is more obvious when the electromagnetic vector isconsidered. Moreover, the scalar diffraction theory makes the extreme positions of thelongitudinal diffraction of the small aperture move to the farther transmission distance.The thesis also studies the near-field interference of double hole. It is convenient for us todivide the electromagnetic field into TE wave and TM wave by using FDTD method. Theresearch results indicate that the interference fringes of double hole under two different modesillumination are obviously different. We also discuss the interference of double hole of TM modewith the help of the angular spectrum theory. Comparing the result with the one obtained byFDTD, We can see the mismatched phenomenon of the interference fringe in the near-field.