Filtering properties of defect-bearing periodic and triadic cantor multilayers q Francesco Chiadini a , Vincenzo Fiumara b, * , Ilaria Gallina c , Innocenzo M. Pinto c , Antonio Scaglione a a Department of Electrical and Information Engineering, University of Salerno, via Ponte Don Melillo, Fisciano (SA) 84084, Italy b Department of Environmental Engineering and Physics, University of Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy c The Waves Group, Department of Engineering, University of Sannio, Corso Garibaldi 107, Benevento 82100, Italy Received 8 June 2007; received in revised form 5 October 2007; accepted 10 October 2007 Abstract Defect-bearing periodic as well as pre-fractal dielectric multilayers can be designed to operate as narrow-band filters. For the same dielectric constituents and the same (or closest to same) number of layers, pre-fractal structures are remarkably better than the periodic ones, both in terms of filter bandwidth and transmittance peak, and are less sensitive to variations in the defect thickness. For structures having about 30 layers, optical losses do not significantly affect the filtering features of both morphologies if the loss tangent of the con- stituent materials is less than 10 5 . Ó 2007 Elsevier B.V. All rights reserved. PACS: 42.70.Qs; 42.79.e; 42.79.Ci Keywords: Dielectric multilayers; Filters; Fractals 1. Introduction Inserting an extra dielectric layer (called a defect layer) in a truncated-periodic dielectric multilayer makes this structure behave as a narrow-band filter [1,2]. The center frequency, width and depth of the transmission peak can be controlled to some extent by varying the thickness and/or the refractive index of the defect layer, and its location. In [3] we showed that defect-bearing pre-fractal dielec- tric multilayers can also be designed to work as narrow- band filters. By themselves, pre-fractal multilayers can be viewed as (truncated) periodic multilayers with defects [4], therefore exhibiting narrow transmission peaks in their spectral response. The center frequency, width and depth of these peaks can also be controlled to some extent by varying the thickness and/or the refractive index of the defect layer. In this paper we present a comparison of the filtering properties of defect-bearing truncated–periodic (henceforth TP) and triadic Cantor pre-fractal (henceforth TCPF) dielectric multilayers in terms of suitable performance fig- ures, for the case of a normally incident plane wave. To make the comparison fair, we use the same dielectric con- stituents and the same (or closest to same) total number of layers for both morphologies. The paper is organized as follows. In Sections 2–4, defect-bearing TP, TCPF, and defect-bearing TCPF dielec- tric multilayers are introduced, respectively. Comparison between the filtering features of the two morphologies 0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.10.022 q This work has been sponsored in part by the Italian Ministry of University and Research (PRIN 2006, Study and Realization of Metam- aterials for Electronics and TLC applications). * Corresponding author. E-mail addresses: fchiadini@unisa.it (F. Chiadini), vfiumara@unibas.it (V. Fiumara), ilaria.gallina@unisannio.it (I. Gallina), pinto@sa.infn.it (I. M. Pinto), ascaglione@unisa.it (A. Scaglione). www.elsevier.com/locate/optcom Available online at www.sciencedirect.com Optics Communications 281 (2008) 633–639