a b с Consider electromagnetic waves for which the relation γεμ /w² - w² C between wave number k and the angular frequency w holds, for some constant parameter we. (Such waves can actually exist in wave guides.) k(w) = = Give a detailed description of the meaning of the constants E, μ and c which appear in the given expression for k(w). Compute the phase velocity uph as well as the group velocity ugr for such waves. Compare the resulting expression for the product Uph ugr of the phase and the group velocity with the phase velocity of plane electromagnetic waves. Expand the expression for the phase and group velocities found in part b to lowest non-trivial order in the region w >>we. Interpret the result.
a b с Consider electromagnetic waves for which the relation γεμ /w² - w² C between wave number k and the angular frequency w holds, for some constant parameter we. (Such waves can actually exist in wave guides.) k(w) = = Give a detailed description of the meaning of the constants E, μ and c which appear in the given expression for k(w). Compute the phase velocity uph as well as the group velocity ugr for such waves. Compare the resulting expression for the product Uph ugr of the phase and the group velocity with the phase velocity of plane electromagnetic waves. Expand the expression for the phase and group velocities found in part b to lowest non-trivial order in the region w >>we. Interpret the result.
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Transcribed Image Text:a
с
d
Consider electromagnetic
waves for which the relation
εμ
w² - w²
C
between wave number k and the angular frequency w holds, for some constant
parameter wc.
(Such waves can actually exist in wave guides.)
k(w) =
=
Give a detailed description of the meaning of the constants e, μ and c which
appear in the given expression for k(w).
Compute the phase velo up as well as the group velocity Ugr for such
waves.
Compare the resulting expression for the product uph Ugr of the phase and the
group velocity with the phase velocity of plane electromagnetic waves.
Expand the expression for the phase and group velocities found in part b
to lowest non-trivial order in the region w >>> wc.
Interpret the result.
What happens with the phase and group velocity if w approaches the specific
value wc (but still w > wc)?
What happens when w is smaller than we?
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