Diffraction Effects in the Near Field

Abstract

This dissertation is concerned with understanding and analyzing some of the effects of diffraction in the near field. The contributions of homogeneous and of evanescent waves to two-dimensional near-field diffraction patterns of scalar fields are examined in detail. Exact relations are obtained for calculating these contributions for arbitrary propagation distances, along with approximate expressions for the near field. The behavior of the two contributions is illustrated for the case of a plane wave diffracted by a slit in an opaque screen. The finite-difference time-domain (FD-TD) method is used examine the influence of exact boundary values on the near field for the case of a slit in a thin perfectly conducting screen. The FD-TD numerical results are displayed in color images that illustrate the intricate behavior of the amplitude and the phase of the field in the vicinity of the slit. These numerical results are compared with the predictions of approximate theories. Some new methods for determining near-fields in rigorous diffraction problems involving thin screens are discussed. Specifically, new approximate theories of diffraction are introduced for both scalar and electromagnetic fields and an iterative Fourier-based algorithm is proposed for solving the rigorous boundary value problem. In order to understand the effects of an optical vortex on diffraction, the field emerging from a spiral phase plate illuminated by a Gaussian beam is examined. It is shown that the amplitude profile of the emerging field changes appreciably over propagation distances that are much smaller than the Rayleigh range.