Question

Problem 4.4- Suppose n o and n e are given. In (a) you only need to find the magnitude of the group velocity. Problem #2 in HW 10 may be helpful. You can also directly use the definition of group velocity, i.e., v g = triangle k w (k), taking into account the equation of the wave normal surface.

4.4- Group Velocity and Phase Velocity

a.) Derive an expression for the group velocity of the extraordinary wave in a uniaxial crystal as a function of the polar angle 0 of the propagation vector.

b.) Derive an expression for the angle a between the phase velocity and the group velocity. This angle is also the angle between the field vectors E and D.

c.) Show that a = 0 when 0 = 0, ½ pi. Find the angle at which a is maximized and obtain an expression for a max. Calculate this angle a max for quartz with n o = 1.554, n e = 1.553.

d.) Show that for no or ne, the maximum angular separation a max occurs at 0 = 45 degrees; show that a max is proportional to [ n o – n e].