Electromagnetics in deterministic and stochastic bianisotropic media

Time-harmonic Problems – The Interior Problem
The Bohren decomposition – Beltrami fields
Introducing the fields
we note that (25) is written as
where
Q L := i η −1 E + H , Q R := E + i η H ,
curlQ L = γ L Q L,
curlQ R = −γ R Q R,
γ L := k(1 − kβ) −1 , γ R := k(1 + kβ) −1 .
Note that γ 2 = γ Lγ R. Q L and Q R satisfy the vector Helmholtz equation
∆Q λ + γ 2 λQ λ = 0, λ = L, R ,
(26)
and γ L, γ R are the wave numbers of the Beltrami fields Q L, Q R, respectively.
If E, H are divergence free, the same holds for Q L, Q R, as well.
I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 32 / 95