where the second form is composed of two factors, the sinusoidal wave at the mean wavenumber, vary-
ing rapidly in space at k
0
, and an envelope function, varying slowly in space at Δk. e rapid sinusoids
travel at the phase velocity
v
k
c
n
p
==
ω
0
0
whereas the envelope travels at the group velocity
v
k
ckn
k
c
n
ck
n
n
k
c
n
nn
kk
g
()
===−
=−
∆
∆
∆
∆
∆
∆
∆
∆
ω/
/
/
2
1
=+
c
n
nn
1
∆
∆
/
/λλ
Referring to Figure 1.2 for the case of silica int glass, we see that
λ
λ
λ
=−
∆
==
=−
∆
400500
100
450
0222
163166
nm,
,
.
..n
n
n
==
−
=−
003
1645
0207
.
.
.
and thus
vv
v
c
n
c
gp
p
=
==
0918
061
.
.
So in this case of normal dispersion, the group velocity of the packet is slower ...
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