Need some help regarding phase and group velocity of a wave

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SUMMARY

The discussion centers on the relationship between group velocity (v_g) and phase velocity (v_p) in the context of fiber optics and laser applications. The formula presented, v_g = v_p * sin(A), where A represents the incident angle, illustrates how group velocity is derived using trigonometric principles. The participants clarify that group velocity refers to the velocity of the envelope of a wave packet, which is indeed the velocity of energy flow along the fiber. This understanding aligns with established definitions in wave mechanics.

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  • Knowledge of trigonometry as applied to physics
  • Basic concepts of laser technology
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Physicists, optical engineers, and students studying fiber optics or wave mechanics will benefit from this discussion, particularly those interested in the dynamics of wave propagation and energy transfer in optical systems.

ehj
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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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