Let the half space z 0 be filled with a magnetic crystal where H 1 B The inverse permeability matrix 1 is (rows and columns labeled by x, y, z) Assume that 0 inside the crystal and that the real, dimensionless matrix elements satisfy m m ' 0 (a) Show that (k, ) ck m m ' sin 2 for a wave E x E 0 exp...

To show that k ck m m sin2 for a wave E x E0 expik r t inside the crystal with k ky sin z cos well start by considering Maxwells equations for the electric field E and the magnetic field H in the pres ...

Let the half-space z 0 be filled with a magnetic crystal where H = 1

Question:

Let the half-space z ≥ 0 be filled with a magnetic crystal where H = μ⁻¹ · B. The inverse permeability matrix μ⁻¹ is (rows and columns labeled by x, y, z)

Assume that ε = ε₀ inside the crystal and that the real, dimensionless matrix elements satisfy m > m' > 0.

(a) Show that ω(k, θ) = ck √m − m' sin 2θ for a wave E = x̂ E₀ exp[i(k · r − ωt)] inside the crystal when k = k(ŷ sin θ + ẑ cos θ).
(b) A plane wave E = x̂E₀exp[i(kz − ωt)] is incident on this crystal from the vacuum (z

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