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

120 2.1.6 Mode-locking techniques [Ref. p. 134
Nonlinear reflectivity [%]
100.0
99.8
99.6
99.4
99.2
99.0
R ns
R
R ns,eff
no ISA
with ISA
R eff
1 10 100
Saturation parameter S=
F p / F sat,A
0.1 2 4 6 8 2 4 6 8 2 4 6 8
Fig. 2.1.18. Nonlinear reflectivity as function of
saturation parameter S which is equal to F p/F sat,A.
F p is the pulse fluence incident on the absorber
mirror (i.e. pulse energy density) and F sat,A is
the saturation fluence of the absorber mirror. Inverse
saturable absorption decreases the reflectivity
at higher pulse energies such that a “roll-over”
is observed. This decreases the effective modulation
depth and increases the effective nonsaturable
absorption. However, it improves the Q-switching
mode-locking threshold.
For F 2 →∞(i.e. without induced nonlinear losses) we retrieve the simpler equation (2.1.77). F 2 is
the inverse slope of the induced absorption effect and can be determined from nonlinear SESAM
reflectivity measurements (Fig. 2.1.18) [05Gra2, 04Hai]:
R ISA (F p )=R (F p ) − F p
, (2.1.81)
F 2
where F p is the pulse fluence incident on the SESAM (i.e. pulse energy density), R(F p ) the measured
nonlinear reflectivity without Inverse Saturable Absorption (ISA) and R ISA (F p ) the measured
reflectivity with inverse saturable absorption. The smaller the inverse slope of the roll-over F 2 ,the
stronger is the roll-over. The stronger the roll-over, the smaller the maximum modulation depth
of the SESAM.
2.1.6.9 External pulse compression
SPM generates extra frequency components. The superposition with the other frequency components
in the pulse can spectrally broaden the pulse (i.e. for positively chirped pulses assuming
n 2 > 0). SPM alone does not modify the pulse width, but with proper dispersion compensation
a much shorter pulse can be generated with the extra bandwidth [80Mol]. The positively chirped
spectrally broadened pulse then can be compressed with appropriate negative dispersion compensation,
where the “blue” spectral components have to be advanced relative to the “red” ones. A
careful balance between a nonlinear spectral broadening process and negative dispersion is needed
for efficient compression of a pulse. Typically, self-phase modulation in a single-mode fiber with
optimized length was used to linearly chirp the pulse, which is then compressed with a grating pair
compressor [84Tom].
Ultimately, uncompensated higher-order dispersion and higher-order nonlinearities limit compression
schemes. For pulses shorter than 100 fs, compression is typically limited to factors of
less than 10. Compression of amplified CPM dye laser pulses with 50 fs duration produced the
long-standing world record of 6 fs [87For]. Similar concepts have been used for external pulse
compression of 13-fs pulses from a cavity-dumped Ti:sapphire laser [97Bal] and of 20-fs pulses
from a Ti:sapphire laser amplifier [97Nis] resulting, in both cases, in approximately 4.5-fs pulses.
In the latter case, the use of a noble-gas-filled hollow fiber instead of a normal fiber allows for
much higher pulse energies. For example, pulse energies of about 0.5 mJ with 5.2-fs pulses and a
peak power of 0.1 TW [97Sar]. More recently, adaptive pulse compression of a super-continuum
produced in two cascaded hollow fibers generated 3.8-fs pulses with energies of up to 15 μJ [03Sch].
Further improvements resulted in 3.4-fs pulses but with only 500 nJ pulse energies [03Yam]. The
pulse duration was fully characterized by Spectral-Phase Interferometry for Direct Electric-field
Reconstruction (SPIDER) (Sect. 2.1.7.3). This is currently the world record in the visible and
near-infrared spectral regime.
Landolt-Börnstein
New Series VIII/1B1