MHB Group Velocity and Phase Velocity

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The discussion focuses on deriving expressions for group velocity and phase velocity in uniaxial crystals, specifically for extraordinary waves. Participants seek clarification on how to approach Problem 4.4, which involves calculating the group velocity as a function of the polar angle and determining the angle between phase and group velocities. The need for additional information and definitions regarding phase and group velocity is emphasized, as well as the relevance of previous homework problems for context. The conversation highlights the complexity of the topic and the necessity for clear definitions to facilitate understanding.
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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].
 
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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"?
 
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