Physica 148A (1988) 343-355 North-Holland, Amsterdam ELECTROMAGNETIC WAVE PROPAGATION IN QUASIPERIODICALLY STRATIFIED MEDIA D. WÜRTZ*, T. SCHNEIDER and M.P. SOERENSEN** IBM Research Division, Zurich Research Laboratory, 8803 Rüschlikon, Switzerland Received 19 June 1987 We explore the wave number dependence of the transmission of electromagnetic waves in quasiperiodic dielectric multilayers. Using the transfer-matrix technique, we also establish the connection to the tight-binding Schrödinger problem. As an example, we consider a multilayer constructed according to the Fibonacci inflation rule. In contrast to the periodic case, we find a highly fragmented distribution of stop bands and self-similar structure in the wave number dependence of transmission. 1. Introduction Recently, the one-dimensional Schrödinger equation with quasiperiodic potential evoked considerable interest 1 - 6 ). This equation displays fragmented eigenvalue spectra because a quasiperiodic potential is intermediate between a random one, yielding exponentially localized wave functions 7 ), and the periodic potentials, leading to energy bands and gaps. Moreover, the new ability to produce semiconductor heterostructures with control of each layer allows experimental realizations of these structures 8 ). Here, the one-dimen- sional Schrödinger equation models the properties of the heterostructure perpendicular to the layers. In this work, we explore a related problem, electromagnetic wave propaga- tion in layered and quasiperiodic dielectric media. The regular counterpart, periodically stratified media, has a long history9) and many important applica- tions, ranging from optical filters to reftectors, solid-state lasers and optical fibers 10 ). In analogy to the Schrödinger problem, one expects quasiperiodic stratified media to represent an intermediate case between the periodic and *Permanent address: Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-6900 Heidelberg, Fed. Rep. Germany. **Permanent address: Laboratory of Applied Mathematical Physics, Tcchnical University of Denmark, Building 303, DK-2800 Lyngby, Denmark. 0378-4371 /88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)