# Which dielectric constant in media?

by swooshfactory
Tags: constant, dielectric, media
 P: 66 Hi, In deriving a complex wave vector for waves in media, an equation D = ε E is typically used. Later though, it is common to relate D and E through a complex ε which is generally written as εcomplex = ε + 4 pi i σ / ω. It seems a contradiction to insert one relationship into the Maxwell equations and then explain how really it's another, where a complex epsilon allows for a phase shift between D and E. I'm also confused whether the σ here is necessarily complex; in the constituitive relation used to derive it, we had j = σ E and from the Dressel Electrodynamics of Solids book and the Wooten online optical solid state book he identifies σ as real. See, for example, http://web.mit.edu/course/6/6.732/www/6.732-pt2.pdf pages 2-3. Thanks!
 Sci Advisor P: 3,596 The definition of D and H, in contrast to E and B, is convention. What is physical is the current density j. Part of it may be expressed as either the divergence of polarization P or rotation of the magnetization M. In different situations different conventions are useful. Nowadays in optics one mostly uses a convention where H=B, see e.g. http://siba.unipv.it/fisica/articoli...06_49_1029.pdf As to your question whether conductivity sigma is real or complex, it is clearly complex in general. That reflects the fact that the current may be out of phase with the electric field.