Fractional‐Calculus‐Based Electromagnetic Tool to Study Pulse Propagation in Arbitrary Dispersive Dielectrics. Issue 3 (29th October 2018)

• Record Type: Journal Article
• Authors: Mescia, Luciano; Bia, Pietro; Caratelli, Diego
• Other Names: Mescia Luciano guestEditor.; Cannas Marco guestEditor.; Agnello Simonpietro guestEditor.; Gelardi Franco Mario guestEditor.
• Is Part Of: Physica status solidi. Volume 216:Issue 3(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-10-29
• Subjects: computational algorithm -- dielectric relaxation -- dispersive media -- fractional derivative -- propagation model; Solid state physics -- Periodicals; Solids -- Industrial applications -- Periodicals; 530.41
• DOI: 10.1002/pssa.201800557
• Languages: English
• ISSNs: 1862-6300

Abstract

Abstract : Fractional calculus is a fruitful field of research in science and engineering. The concept of fractional exponents is an outgrowth of exponents with integer value. In the same way, fractional order of integration is a generalization of the mathematical operations of differentiation and integration to arbitrary, general, noninteger order. Although it better models the higher complexity by nature, it is still fairly easy to physically represent its meaning. However, taking in consideration that the study of fractional calculus theory opens the mind to entirely new branches of thought, in this feature article the authors illustrate as such concept can be an interesting and useful tools in electromagnetic theory to solve specific electromagnetic problems regarding the wave propagation and radiation in arbitrary dispersive dielectric materials. In particular, time fractional Maxwell's equations for media with power‐law frequency dispersions are illustrated focusing the attention on the mathematical and computational topics. Moreover, practical examples highlighting their usefulness for understanding a variety of electromagnetic phenomena are provided. Abstract : Fractional calculus is successfully applied in electrodynamics. In this paper the authors show a novel electromagnetic solver based on the incorporation of the fractional time derivatives into Maxwell's equations. The illustrated numerical technique could be successfully used to predict new electromagnetic phenomena further applied in microwave, antenna, and optical engineering.