Abstract
We measure and calculate the optical response of a structure consisting of a square array of subwavelength silicon posts on a silicon substrate at telecommunication wavelengths. By the use of the reduced Rayleigh equations and the Fourier modal method (rigorous coupled wave analysis) we calculate the reflectivity of this structure illuminated from vacuum by normally incident light. The calculated reflectivities together with experimentally determined ones, are used to test the accuracy of effective medium theories of the optical properties of structured silicon surfaces, and to estimate the effective refractive index of such surfaces produced by a homogeneous layer model.
Highlights
It has been established that Maxwell's equations are form-invariant under geometrical transformations [1], and that the consequences of a given transformation can be interpreted in terms of modifications of the material properties involved
The concept of a metamaterial is intimately related to the notion of an effective medium; it relies on the idea that when the inclusions or heterogeneities are much smaller than the wavelength, the wave propagates as in a homogeneous medium with some effective optical properties that depend on the geometry and the filling fraction of the inclusions
In the preceding section we found that the reflectivity estimated for our structures by means of the effective medium theories (EMTs) did not agree with the one obtained experimentally
Summary
It has been established that Maxwell's equations are form-invariant under geometrical transformations [1], and that the consequences of a given transformation can be interpreted in terms of modifications of the material properties involved. Regions with homogeneous properties are transformed into regions whose permittivity and permeability are determined by the mathematical nature of the transformation This property has given rise to the field of transformation optics [1], which is an emerging area of optics in which coordinate transformations are used to design structures with novel optical properties. Silicon and Silicon on Insulator (SOI) wafers constitute interesting platforms for experimental tests of transformation optics concepts, and for the implementation of novel designs for silicon photonics. The method is heavier computationally, but does not have the height limitations of the Rayleigh method It is better-suited for calculations with structures that have steep slopes.
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