Beryl is a hexagonal

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Condensed Matter, Materials & Soft Matter · Polarisation and anisotropic media

What an Instrument Can See, Ch Anisotropic media: the dielectric tensor and the index ellipsoid

Problem

Beryl is a hexagonal, uniaxial crystal. At 590 nm its principal indices are

n_o = 1.602

and

n_e = 1.557

(negative uniaxial:

n_e < n_o

). It is transparent and shows no optical activity at this wavelength. ((a)) Write the dielectric tensor

\epsilon_{ij}

in the crystal's principal axes, with the optic axis along

z

. ((b)) A plane wave travels at

60^\circ

to the optic axis. Find the index

n(60^\circ)

of the extraordinary eigenmode.