Electromagnetic waves in non-integer dimensional spaces and fractals. (December 2015)

• Record Type: Journal Article
• Authors: Tarasov, Vasily E.
• Is Part Of: Chaos, solitons and fractals. Volume 81:Part A(2015)
• Page Start: 38
• Page End: 42
• Publication Date: 2015-12
• Subjects: Fractal media -- Non-integer dimensional space -- Electromagnetic -- Waves -- Effective refractive index; 64.60.Ak -- 45.10.Hj; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2015.08.017
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: Electromagnetic waves in non-integer dimensional spaces are considered in the framework of continuous models of fractal media and fields. Using the recently suggested vector calculus for non-integer dimensional space, we consider electromagnetic fields in isotropic case. This D-dimensional calculus allows us to describe fractal properties by continuous models with non-integer dimensional spaces. We prove that the wave equation for non-integer dimensional space is similar to equation of waves in non-fractal medium with heterogeneity of power-law type. The speed of electromagnetic waves and the effective refractive index of non-integer dimensional spaces and fractals are discussed.