Question

1. (50 points) A plane electromagnetic (EM) wave, of angular frequency = 2Tx5.1x1014 rad/s, propagates inside a birefringent calcite crystal whose principal refractive indices are 1.65836 and ne- 1.48641 no Dt)= De.F-t) BF)-B.F) When using a given set of principal axes reference, the orientation of the wave-vector k is specified by k=(1, 1, 1)/ V3 As we know, when choosing an alternative and appropriate system of reference, the propagation of an ORDINARY wave and an EXTRAORDINARY wave of independent polarization are clearly identified. In the questions below, use such an alternative system of reference to provide your answers. 1.A Use the Maxwell Eqs. to justify analytically the orientation of the ORDINARY EM fields E, E, D, 3, as well as T. Sketch a corresponding diagram. Provide the three components of each vector E, B, D, 3, and k. (You may want to give the three components of each unit vectors.) 1.B Use the Maxwell Eqs. to justify analytically the orientation of the EXTRAORDINARY EM fields E, B,D, 3, as well as k. Sketch a corresponding diagram. Provide the three components of each vector E,B, D, 3, and . (You may want to give the three components of each unit vectors.) Hint: no n=ng V& VEO Along principal axes: D Ex E D,= &y E, D,- & E Poynting vector S 1 ExB Sin Y 1 Cos . 2 wave, You may want to use diagram like the following to illustrate your answer. But alternative sketches are allowed.

Answer 1

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