Mathematical Modeling of Near-Field Optics

Consider a time-harmonic electromagnetic plane wave incident on a periodic (grating) structure. An inhomogeneous (subwavelength) object is placed inside the periodic structure. The scattering problem is to study the electromagnetic field distributions. The problem arises in the study of near-field optics and has many physical and biological applications. This work is devoted to modeling and analysis of a near-field optics problem. An integral representation approach is presented to solve the problem. It is shown particularly that the perturbation due to the object decays exponentially along the periodic direction of the structure, provided that no surface waves occur. Based on the approach, a general solution method is discussed and the well-posedness of the model problems are established.