Need some help regarding phase and group velocity of a wave

AI Thread Summary
The discussion centers on the relationship between group velocity (v_g) and phase velocity (v_p) in the context of lasers and fiber optics. The formula v_g = v_p * sin(A) is presented, where A is the incident angle, suggesting a trigonometric basis for understanding these velocities. The user questions whether this interpretation aligns with the conventional definition of group velocity as the speed of the amplitude wave in a wave packet. Clarification is sought on whether there are multiple meanings of group velocity or if the presented formula accurately represents its general concept. The conversation emphasizes the importance of understanding how group velocity relates to energy flow in fiber optics.
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I'm currently working with lasers and in relation to that, fiber optics. In the book I'm reading there's a section regarding modes and their "group velocity". The text claims that there is the following relation:
v_g=v_p * sin(A)
where v_g is the group velocity and
where v_p is the phase velocity and A is the incident angel as showed on the picture, although denoted as theta there.
From the picture you can see that the relation is reached by using trigonometry, and v_g is in this case simply the velocity in the direction along the fiber. My question is, if this is the general idea of group velocity? I thought group velocity was the velocity of the "amplitude wave" in a wave packet? Am I wrong, or are there just different meanings of group velocity?
 
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Here is the picture!
 

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v_g found that way would be the velocity of the envelope of a wave packet.
It is the velocity of energy flow along the fiber direction.
 
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