Fractal diffraction gratings built through rectangular domains

Two-dimensional fractal gratings with variable structure and their diffraction

An impedance model is used to solve the reflection problem from a multilayer with periodic and Cantor bar fractal distributions. It is based on the calculation of the input surface impedance of such a structure. The method consists of replacing the multilayer reflection problem by a simple reflection problem on a single surface. This approach has the additional advantage that only the fields above the surface should be taken into account. Numerical calculation leads to an iterative method which can be implemented for each polarization mode. The results for the input impedance function of the system and for the reflectance are presented for different iteration states. Also to quantify the comparison between both types of structures we introduce a self-similarity function which correlates orders or states of the same type.

Beam reflection from multilayers with periodic and fractal distributions

Talbot effect with Cantor transmittances

Superposition of planar Cantor gratings and directional self-similarity I: General considerations

The Fraunhofer region of one-dimensional fractal diffraction grating is studied when this grating is defined using a set of scaled periodical (and rectangular) functions. The fractal structure is obtained through a Cantor density function, which is defined from an incremental product of such periodical components. Each of these components can be filtered individually and so, the corresponding intensity pattern can be evaluated. A mathematical foundation for such decomposition is developed using the concept of characteristic (or indicator) function of a set. Graphic results are shown and the partial self-similarity of lateral intensity distribution calculated in any transversal plane to the optical axis for a certain value of magnification. With these results, fractal, periodical and intrinsic periodical domains can be distinguished to characterize the intensity patterns. The self-similarity of intensity distributions and the contrast of that function are calculated for different states of the Cantor transmittance.

Diffraction by a Fractal Transmittance Obtained from a Multiplicative Superposition of Periodical Rectangular Functions

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Diffraction by a Fractal Transmittance Obtained from a Multiplicative Superposition of Periodical Rectangular Functions