General solution for TEM, TE, and TM waves in fractional dimensional space and its application in rectangular waveguide filled with fractional space

Abstract

This work presents general solution to the Maxwell’s equations inside a waveguide or transmission line where space is assumed to be of noninteger dimensions. The solution is a generalization of wave equation inside a waveguide or transmission line from integer dimensional space to fractional dimensional space. General analytical expressions for TE, TM, and TEM waves in fractal medium are also developed from the obtained general solution. Using the same notion, wave propagation inside rectangular waveguide is mathematically modeled and analyzed when it is filled fractal medium. The results obtained are analyzed and compared with the waveguide filled with nonfractal medium and substantial changes are observed to be present between the two cases. It is also observed that the classical results are recovered from all our results by considering integer dimensional space.