Welcome to our community

Be a part of something great, join today!

Group Velocity and Phase Velocity

Joystar1977

Active member
Jul 24, 2013
119
I have no idea how to do this or where to start. Can someone please help me?

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].
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
I'm afraid no one is going to be able to help you without more information. Certainly no one here knows what "problem #2 in HW 10" is!

What are you using as the definitions of "phase velocity" and "group velocity"?