September 2006
Intermediate to advanced
680 pages
22h 22m
English
book
Ultrashort Laser Pulse Phenomena, 2nd Edition
by Jean-Claude Professor Diels, Jean-Claude Diels, Wolfgang Rudolph
Content preview from Ultrashort Laser Pulse Phenomena, 2nd Edition
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50 Fundamentals
Table 1.2
Comparison of dispersion and diffraction.
Gaussian pulse Gaussian beam
Bandwidth-limited pulse at z = 0 Beam waist at z = 0
(unchirped pulse) (plane phase fronts)
˜
E
0
(t) ∝ e
−(t/τ
G0
)
2
˜
E
0
() ∝ e
−(τ
G0
/2)
2
˜u
0
(x) ∝ e
−(x/w
0
)
2
˜u
0
(k
x
) ∝ e
−(k
x
w
0
/2)
2
Propagation through a medium of Free space propagation over
length L (dispersion) distance L (diffraction)
˜
E(, L) ∝ exp
−
τ
G0
2
2
− i
k
L
2
2
˜
E(t, L) ∝ exp
−(1 + i ¯a)
t
τ
G
2
∝ exp
iω
t
2
2˜p(L)
¯a = L/L
d
τ
G
(L) = τ
G0
1 +¯a
2
˜u(k
x
, L) ∝ exp
−
w
0
k
x
2
2
+ i
Lk
x
2
2k
˜u(x , L) ∝ exp
−(1 + i
¯
b)
x
w
2
∝ exp
−ik
x
2
2˜q(L)
¯
b = L/ρ
0
w(L) = w
0
1 +
¯
b
2
Chirp coefficient (slope) Wavefront curvature
¨ϕ =
2¯a
1+¯a
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