Electric field diffraction by a semi-infinite perfectly conducting plane of small thickness:: Application to near-field microscopy

A perfectly conducting halfplane of finite thickness much smaller than the wavelength of the incident electromagnetic wave is investigated The geometry of the structure is defined according to a transformation which is a particular case of the Schwarz-Christoffel transformation, representing a step with a slightly concave edge instead of the usual straight one. The solutions of the partial differential equations describing the structure are given for specific ranges of the variables, and the results obtained with this method are compared to those obtained with an independent numerical method for a step with a straight edge. Good agreement is obtained between the two sets of results, except right around the edges of the steps in the two structures, due to the different shapes involved. It is shown that the width of the structure has but a slight influence on the value of the electric field, while the angle of incidence of the incoming wave has a strong influence on this value. (C) 1999 John Wiley & Sons, Inc.