Optical EngineeringNanostructures with small and large scale periodic and random rough surfaces and lateral fluctuations in the permittivity and permeability-scattered near fields
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The scattered electromagnetic near fields due to fluctuations in the surface height and/or lateral variations in the electromagnetic medium parameters are evaluated using a full-wave approach. Since the scales of the height and medium fluctuations considered could be significantly smaller or larger than the electromagnetic wavelengths, the familiar perturbation and physical/geometrical optics solutions cannot be used nor is it possible to investigate subwavelength features based on far-field measurements. The full-wave approach employs complete field expansion that includes propagating and evanescent waves as well as lateral waves and surface waves, which are not accounted for in the perturbation and physical optics solutions. Exact boundary conditions for the electric and magnetic fields are imposed at the rough interfaces. The complete modal expansions do not uniformly converge at the irregular boundaries, therefore the interchange of orders of differentiation and summation/integration of the field expansions is avoided. Large-scale and small-scale (relative to electromagnetic wavelength) approximations for the full-wave near-field solutions are expressed as integrals over the complete scattered wave number variables. Random rough surfaces as well as periodic and quasiperiodic structures are also considered.