In an anisotropic medium, permittivity varies with electric field direction, and is a property seen in most crystals. Consider a uniform plane wave propagating in the z direction in such a medium, and which enters the material with equal field components along the x and y axes. The field phasor will take the form:

E_s (z) = E₀(a_x + a_y e^jΔβz) e^−jβz

where  β = β_x − β_y is the difference in phase constants for waves that are linearly polarized in the x and y directions. Find distances into the material (in terms of  β) at which the field is

(a) Linearly polarized

(b) Circularly polarized.

(c) Assume intrinsic impedance η that is approximately constant with field orientation and find H_s and < S >.