Eur. Phys. J. B 36, 431–443 (2003) DOI: 10.1140/epjb/e2004-00001-9 T HE EUROPEAN P HYSICAL JOURNAL B Interferential polychromatic filters M. Kanzari a , A. Bouzidi, and B. Rezig Laboratoire de Photovolta¨ ıque et Mat´ eriaux Semiconducteurs (LPMS), ´ Ecole Nationale d’ing´ enieurs de Tunis-BP 37 le Belv´ ed` ere 1002 Tunis, Tunisia Received 10 July 2003 Published online 30 January 2004 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2004 Abstract. The reflection properties of one-dimensional generalized Cantor-like multilayer (GCLM) are investigated numerically in the visible range. Strong correlation between the stack geometry and the properties of the optical reflection spectra is found, namely spectral scalability and sequential splitting. The construction of multilayer systems according to the definite Cantor distribution brings improvements to the reflection properties. In particular, the widening of the band gap and the thin peak appearance in the reflection spectra whose number increases with the division number in the (GCLM). Optical properties of (GCLM) inserted between two periodic stacks are numerically investigated. We chose SiO2(L) and TiO2 (H) as two elementary layers. The study configuration is H(LH) 5 [GCLM] P H(LH) 5 which forms an effective interferential filter in the visible spectral range. We show that the number of resonator peaks is dependent on the repetition of the number P of the (GCLM). The best performances are obtained in particular for the symmetrical configurations of the (GCLM) and especially for P an odd number. PACS. 61.44.Br Quasicrystals – 42.70.Qs Photonic bandgap materials – 42.79.Ci Filters, zone plates, and polarizers 1 Introduction During the last decade, one dimensional dielectric struc- tures, referred to as photonic crystals, have been exten- sively studied both theoretically and experimentally [1–7]. Photonic band gap (PBG) crystals are usually composed of altering layers having a high refractive index say n H , and a low refractive index say n L , in an arrangement that gives rise to a series of forbidden wavelength gaps. That is, light is almost completely reflected by the crystal, while a series of wavelength pass bands form [8]. It has been shown that for a suitable choice of high and low refractive indices n H , and n L , periodic struc- tures strongly reflect at frequencies and angles of inci- dence corresponding to photonic band gap [9]. On the other hand, PBGs have been extended to photonic quasi- periodic structures [10–12] such as Cantor and Fibonacci multilayer. This work deals with the use of quasiperiodic struc- tures for novel optical components. We first report a nu- merical simulation of the reflection properties of multilayer films, built according to the asymmetrical Cantor mode proposed here. The construction of multilayer systems ac- cording to the Cantor distribution brings improvements in the reflection properties. Indeed, this model will allow the construction of fractal multilayer structures with the aim a e-mail: mounir.kanzari@ipeit.rnu.tn of getting more interesting optical properties by compar- ison with the results obtained with classic periodic PBG structures. Secondly, we intend to study an interferential filter based on the generalized Cantor-like multilayer. The generalized Cantor-like multilayer represents an interest polychromatic filter when is sandwiched between two pe- riodic stacks [13]. 2 Generalized Cantor-like multilayer To built multilayer structures according to this model, we start from an initiator of length l and of high re- fractive index n H , we subdivide it into m unities of equal length (l/m), the first layer of length a(l/m) is a layer of high refractive index n H , the second layer of length b(l/m) is a layer of low refractive index n L and the last layer of length [l - (a + b)l/m] is of high re- fractive index n H . Where a and b are integer, m the ho- mothetic ratio. If m = 2 the interferential mirror is a periodic multilayer. When m> 2, we have to consider different cases according to the algebraic properties of the homothetic ratio. This is the first step (N = 1) of the model. In the second iteration (N = 2), we subdivide into m units of equal length a(l/m 2 ), the first layer and take a segment of length a 2 (l/m 2 ) as a layer of high re- fractive index n H , the second layer of length ba(l/m 2 ) is a layer of low refractive index n L and the last layer of