Superlattices and Microstructures, Vol. 9, No. 1, 1991 115 INFLUENCE OF OPTIC PHONONS AND PLASMONS ON LIGHT PROPAGATION IN FIBONACCI SEMICONDUCTOR SUPERLATTICES M. Singh and M.G. Cottam Physics Department, University of Western Ontario, London, Ontario, Canada N6A 3K7 (Received 13 August 1990) A theoretical study is presented for the optical reflection and transmission coefficients in finite-thickness Fibonacci semiconductor superlattices. The materials are characterized by complex frequency- dependent dielectric functions, and we employ a general oblique-angle geometry. Numerical examples are given for particular choices of semiconductors, and effects due to interaction of the light with optical phonons and plasmons are considered. 1. Introduction There is considerable interest at present in the electronic, vibrational and optical properties of one-dimensional ~ID) Fibonacci systems. I Recently Merlin et al- have fabric- ated semiconductor superlattices of GaAs/A£As with the layers of GaAs and A~As arranged in a Fibonacci sequence. Also metallic Fibonacci superlattices of Cu/Nb have been fabricated by Hu et al. 3 Fibonacci superlattices have a 1D structure that is quasi-periodic alon E the growth direction. The structural properties and the various spectral properties of plasmons, phonons and electrons can be very different in quasi-periodic structures compared to those in periodic structures. I Many physical properties of Fibonacci superlattices have already been studied experimentally and theoretically including among others the ' 4-6 ' transmission of TE-polarized light and the acoustic phonons.7'8 The aim of this paper is to report some theoretical results for the propagation of electromagnetic waves for both TE and TM polarizations in finite Fibonacci semiconductor super lat rices. In particular, we employ dielectric functions that are frequency dependent and complex to study effects due to interactions of photons with plasmons and optic phonons. We calculate the frequency dependence of the electromagnetic reflection and trans- mission coefficients for a general oblique- angle geometry. 2. Theory We consider a multilayer system consisting of two different kinds of layers A and B, having frequency-dependent dielectric functions CA(U) and CB(a), and thicknesses d A and d B , respectively. The A and B layers occur in a Fibonacci sequence defined by the recursion relation: s I = B, s2 = A, sj = s.j_is.j_Z for integer j z 3. We consider that an electro- magnetic wave is sent from medium C (typically air or vacuum with real dielectric constant e C) at incident angle 8 with respect to the normal (the z axis) to the Fibonacci superlattice. The plane of propagation is taken to be in the yz plane. The electric field within each homogeneous layer can be expressed as the sum of an incident and reflected plane wave. Within a transfer-matrix formalism (e.g., see Refs. 9-11) the complex amplitudes of these waves constitute the components of a column vector. Thus the electric field components in any layer (~ = A, B or C) can be represented by [a~ 1 . b ~ (1) The y and z components of the wave vector k ~ in medium a can be straightforwardly written down. From the proper~y of t~nslational symmetry in the xy plane, k- and k- are real and both are equal to kC Y ~Y = ~(c C) sin8 for a nonmagnetic Y medium, whereas k ~ (~ = A,B) are complex in z general (due to optical absorption): We examine two different cases of the electric- fieid polarizations, namely TE and TN. In the case of TE waves (electric field vector E perpendicular to the yz plane), the 0749-6036/91/010115+04 S02.00/0 © 1991 Academic Press Limited