Integral equations applied to wave propagation in two dimensions: modeling the tip of a near-field scanning optical microscope

We present a Green’s-function/Green’s-theorem integral equation approach to numerically modeling two-dimensional, s-polarized, wave propagation problems effectively for a variety of geometries. The model accurately calculates both near fields and far fields because of the minimal assumptions made on the behavior of the scattered radiation. The method was applied to modeling light emission from a near-field scanning optical microscope fiber tip. Several convergence and energy tests were used to give confidence in the results. The behavior of intensity and power near the tip was investigated. The effects of changing the dielectric constant of a sample material located below the tip were also examined.