Download Lecture Notes on Poynting Theorem for Dispersive and Lossy Media | OPTI 6104 and more Study notes Guiding Electromagnetic Systems in PDF only on Docsity!
(Reading) JAK::3.1.G (Reading) JDJ::6.8; the 2nd edition of this book is reversed in lib. optional resources: ch2, Electromagnetic Metamaterials, Caloz & Itoh) (you can come to borrow a copy from me;) For linear dispersive media with losses, constitutive relations are easier defined in the frequency domains rather than time domain, as did in the situation like vacuum. For a more enlightening discussion on constitutive relation, see P.N. Butcher & D. Cotter, "The Elements of Nonlinear Optics," chapter 2. Cambridge 1990.
"Linearity" and "isotropy" mandate: "Reality" mandate: Fourier decomposition of E- and D-fields (the same for H- & B-fields): (generic) Poynting theorem with real fields:
Poynting theorem for dispersive & lossy media
Saturday, January 19, 2008 10:48 PM
The 1st term on the RHS becomes:
This function can be expressed in a slightly different way by involving symmetry:
From the above two identity, we can rewrite the result:
Before we move on, we like to generalize a useful expression from the above
conclusion which we will need it again later on:
Assume the bandwidth of the wave is small compared to the bandwidth of the system, which is in turn much less than the carrier frequency of the light; The above condition is in general true. For example, Ti:Sapphire lasers offer extremely short pulses. With a center frequency around 800 nm, the bandwidth corresponding 100 fs is around 10 nm only. And typically the material response bandwidth is large, if not considering sharp transition such as atomic resonance.
- Let us know examine how to simplify eq.(1). The right-hand side (RHS) becomes: And the 2nd term at RHS is simplified following eq. (2);
The first two terms on RHS become: Time-average Poynting theorem in linear, isotropic, dispersive media with losses becomes: a. 1 st^ term LHS: energy input to the system from currents; b. 1 st^ term RHS: time rate of change of the stored E&M energy density; c. 2 nd^ term RHS: energy flow out of locality; Physical meaning of various terms: These two terms become:
