LP to CP conversion by an anisotropic crystal. Repeat MATLAB Exercise 7.30 but for a...

LP to CP conversion by an anisotropic crystal. Repeat MATLAB Exercise 7.30 but for a linearly polarized time-harmonic uniform plane electromagnetic wave propagating, with the free-space wavelength of λ₀ = 1 μm, in the positive z direction and entering the crustal. The electric field intensity vector of the wave, E, is at 45 ° to x and y directions. The length of the crystal (along the z axis) is such that the wave emerging on the other side of it is circularly polarized, and out of many possible such lengths the shortest one is chosen. Also, determine the handedness (RH or LH) of the output CP wave. (ME7 32.m on IR) H

HINT:

The vector E of the input wave can be decomposed onto Ex and Ey components that have equal amplitudes (equal to the amplitude of E times cos 45) and are in phase with respect to each other (δ = 0). Therefore, the two field components will be exactly 90? out of phase, which is circular polarization, Eq.(7.24), at the output of the crystal if the acquired δ_a due to material anisotropy, in Eq.(7.28), amounts to δ_a = π/2 (the smallest value) – note that δ_a > 0 for the given permittivities of the material, in Eqs.(7.27).