Wave Transmission through a One-Dimensional Cantor-Like Fractal Medium
- 15 July 1990
- journal article
- Published by IOP Publishing in Europhysics Letters
- Vol. 12 (6) , 481-485
- https://doi.org/10.1209/0295-5075/12/6/001
Abstract
We consider the transmission of plane waves through a one-dimensional medium whose material parameters differ from those of free space on segments which form a Cantor set. By employing self-similarity, it is shown that the transmission coefficient is obtained as a solution of an infinite recursive relation. The latter is solved numerically by taking the small fractal length limit as an "initial" condition. The results show that the transmission coefficient is not monotonic with increasing slab thickness. For certain values of the normalized (over the wavelength) thickness the fractal medium is practically transparent and for others it totally reflects the incident wave. A physical interpretation of these effects is suggested.Keywords
This publication has 9 references indexed in Scilit:
- Fractals, Multifractals, and ThermodynamicsZeitschrift für Naturforschung A, 1988
- Relating the various scaling exponents used to characterize fat fractals in nonlinear dynamical systemsPhysica D: Nonlinear Phenomena, 1988
- Spatial spectrum of a general family of self-similar arraysPhysical Review A, 1987
- Optical diffraction on fractalsPhysical Review B, 1986
- Scattering by inhomogeneous systems with rough internal surfaces: Porous solids and random-field Ising systemsPhysical Review B, 1985
- Fresnel scattering by a corrugated random surface with fractal slopeJournal of the Optical Society of America, 1982
- Diffractal echoesJournal of Physics A: General Physics, 1981
- DiffractalsJournal of Physics A: General Physics, 1979
- Surface topography as a nonstationary random processNature, 1978