2.1 Ultrafast solid-state lasers - ETH - the Keller Group

Ref. p. 134] 2.1 Ultrafast solid-state lasers 95
Table 2.1.8. Examples of material dispersions calculated from the Sellmeier equations given in Table 2.1.6
and the equations given in Table 2.1.7.
Material
Refractive index n
at a center wavelength of 800 nm
Propagation constant k n
at a center wavelength of 800 nm
Fused quartz n (0.8 μm) = 1.45332
∂n
∂λ∣ = −0.017 1
800 nm
μm
∣
∂ 2 n ∣∣∣800 1
=0.04
∂λ 2 nm
μm 2
∣
∂ 3 n ∣∣∣800 1
= −0.24
∂λ 3 nm
μm 3
∂k n
∂ω
∣ =4.84 × 10 −9
800 nm
s ns
=4.84
m m
∣
∂ 2 k n ∣∣∣800
=3.61 × 10 −26 s 2 fs2
=36.1
∂ω 2 nm
m mm
∣
∂ 3 k n ∣∣∣800
=2.74 × 10 −41 s 3 fs3
=27.4
∂ω 3 nm
m mm
SF10 glass n (0.8 μm) = 1.71125
∂n
∂λ∣ = −0.0496 1
800 nm
μm
∣
∂ 2 n ∣∣∣800 1
=0.176
∂λ 2 nm
μm 2
∣
∂ 3 n ∣∣∣800 1
= −0.997
∂λ 3 nm
μm 3
∂k n
∂ω
∣ =5.70 × 10 −9
800 nm
s ns
=5.70
m m
∣
∂ 2 k n ∣∣∣800
=1.59 × 10 −25 s 2 fs2
= 159
∂ω 2 nm
m mm
∣
∂ 3 k n ∣∣∣800
=1.04 × 10 −40 s 3 fs3
= 104
∂ω 3 nm
m mm
Sapphire n (0.8 μm) = 1.76019
∂n
∂λ∣ = −0.0268 1
800 nm
μm
∣
∂ 2 n ∣∣∣800 1
=0.064
∂λ 2 nm
μm 2
∣
∂ 3 n ∣∣∣800 1
= −0.377
∂λ 3 nm
μm 3
∂k n
∂ω
∣ =5.87 × 10 −9
800 nm
s ns
=5.87
m m
∣
∂ 2 k n ∣∣∣800
=5.80 × 10 −26 s 2 fs2
=58
∂ω 2 nm
m mm
∣
∂ 3 k n ∣∣∣800
=4.21 × 10 −41 s 3 fs3
=42.1
∂ω 3 nm
m mm
can be exploited. Usually, one requires sources of negative GDD, and in addition appropriate higherorder
dispersion for shorter pulses. The most important techniques for dispersion compensation
are discussed in the following subsections. Different optical elements that introduce wavelengthdependent
refraction (i.e. prism pairs, Sect. 2.1.5.2.3) or wavelength-dependent diffraction (i.e.
grating pairs, Sect. 2.1.5.2.2) can be used to introduce an additional wavelength dependence to the
round-trip phase and thus contribute to the overall dispersion. A wavelength-dependent round-trip
phase can also be introduced with GTIs (Sect. 2.1.5.2.1) and chirped mirrors (Sect. 2.1.5.2.4).
The challenge in ultrashort pulse generation is dispersion compensation over a large bandwidth
to compensate for the dispersive pulse broadening that is occurring in the gain material and other
elements inside the laser cavity. Dispersion compensation is important because for example, a 10-fs
(1-fs) Gaussian pulse at the center wavelength of 800 nm is broadened to 100 fs (1 ps) after only
1 cm of fused quartz due to second-order dispersion. This follows from (2.1.21) for the regime of
strong pulse broadening and Tables 2.1.6–2.1.8. In addition, in femtosecond lasers the pulses are
ideally soliton pulses for which a constant negative dispersion over the full spectral width of the
pulse balances the chirp of the self-phase modulation. The necessary negative dispersion required
for a certain pulse duration follows from (2.1.74). It is required that all higher-order dispersion
terms are negligibly small.
Landolt-Börnstein
New Series VIII/1B1