Filtering Properties of Optical Cantor Multilayers

Fractals are geometric structures which exhibit invariance property with respect to a change of scale. They can be obtained by repeating a basic operation (generator) on a smaller and smaller scale. Optical Cantor fractal multilayers are structures obtained by applying the fractal Cantor construction to the optical length of the layers of two different dielectrics. Their transmission spectrum can be evaluated using the transmission matrix method. It can be shown that the spectrum exhibits several stop-bands and very narrow transmission peaks and that the self-similarity of the multilayer reflects on the self-scaling property of its electromagnetic response. In this work we show that the stop-bands and the transmission peaks can be shifted by inserting a defect in the fractal structure. The defect is a layer of a dielectric different from the ones constituting the fractal. The extension of the shift of both stop-bands and transmission peaks depends on both the thickness and the refractive index of the defect layer