Question

3. When using a reference constituted by the principal axes of a birefringent crystal, the electric field components of a plane wave (E. E E) = E(7,1)= Ë, e(k.F - ct) propagating in the direction (siny, 0, cosu), satisfy the following set of equations, 2 -Cos') E Sin'P CosY E 0 wave.k 21 -1) E = 0 wave & 2 ne Sin y) E, 0 SINY Cos'Y E + n where is the angle between the wave-vector k and the optical axis Z The Y-axis has been chosen perpendicular to the plane formed by the optical axis Z and k The index of refraction "seen" by this wave is still unknown. wave, & 3.A Show that the phase velocity v; = c/n of the extraordinary wave is determined by the following two equations: no -Cos ) E Sin'P CosP E = 0 + 2 n wave A ne Sin Y) E = 0 Sin'Y Cos E wave & is determined by 3.B Show that n wave, & Sin Y Cos Y 1 n wwve, k

Answer 1

e k nyY kyo, kz z co3y 1 + n ce E 2 huve Sin guasy Ex two inde pendleut ro " ae enuiion aud E E = Jirst gol E o,v pnuide 2 wove epardrdos ound hawe (m'a') Apere ppagatun 2 C aye naavek Ex 2 n. narair E hoth ah equating -ny my

2 2- 2 2. 4- 2 ne 2 2 ne nwen emby 2