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

Ref. p. 134] 2.1 Ultrafast solid-state lasers 83
The saturation of the fast absorber then follows directly from (2.1.16):
q (t) =
q 0
1+ I A (t)
I sat,A
, (2.1.17)
whereweusedthefactthatP sat,A = E sat,A /τ A and P (t) /P sat,A = I A (t) /I sat,A . In the linear
regime we can make the following approximation in (2.1.17):
q (t) ≈ q 0 − γ A P (t) with γ A ≡
q 0
I sat,A A A
. (2.1.18)
The total absorber loss coefficient q p , (2.1.10)–(2.1.11), now depends on the pulse form and for
a sech 2 -pulse shape we obtain for an incident pulse fluence F p,A and the linear approximation of
q (t) for weak absorber saturation (2.1.18):
q p (F p,A )= 1
F p,A
∫
q (t) I A (t)dt = q 0
(
1 − 1 3
)
F p,A
. (2.1.19)
τI sat,A
We will later see that we only obtain an analytic solution for fast saturable absorber mode-locking,
if we assume an ideal fast absorber that saturates linearly with pulse intensity (2.1.18) – which in
principle only applies for weak absorber saturation in a real absorber. For a maximum modulation
depth, we then can assume that q 0 = γ A P 0 (assuming an ideal fast absorber over the full modulation
depth). We then obtain with (2.1.19) a residual saturable absorber loss of q 0 /3, which the pulse
experiences to fully saturate the ideal fast saturable absorber.
2.1.4.3 Semiconductor saturable absorbers
2.1.4.3.1 Semiconductor dynamics
Semiconductors are well suited absorber materials for ultrashort pulse generation. In contrast to
saturable absorber mechanisms based on the Kerr effect, ultrafast semiconductor nonlinearities
can be independently optimized from the laser cavity design. In addition, ultrafast semiconductor
spectroscopy techniques [99Sha] provide the basis for many improvements of ultrashort pulse
generation with semiconductor saturable absorbers.
The semiconductor electronic structure gives rise to strong interaction among optical excitations
on ultrafast time scales and very complex dynamics. Despite the complexity of the dynamics,
different time regimes can be distinguished in the evolution of optical excitations in semiconductors.
These different time regimes are schematically illustrated in Fig. 2.1.10, which shows the energy
dispersion diagram of a 2-band bulk semiconductor which is typical for a III–V semiconductor material.
Optical excitation with an ultrafast laser pulse prepares the semiconductor in the coherent
regime (time regime I in Fig. 2.1.10). In this regime, a well-defined phase relation exists between
the optical excitations and the electric field of the laser pulse and among the optical excitations
themselves. The coherence among the excitations in the semiconductor gives rise to a macroscopic
polarization (dipole moment density). Since the macroscopic polarization enters as a source term
in Maxwell’s equations, it leads to an electric field which is experimentally accessible. The magnitude
and decay of the polarization provide information on the properties of the semiconductor
in the coherent regime. The irreversible decay of the polarization is due to scattering processes
(i.e. electron–electron and electron–phonon scattering) and is usually described by the so-called
dephasing or transversal relaxation time. For a mathematical definition of this time constant the
reader is referred to [99Sha, 90Goe, 75All].
Landolt-Börnstein
New Series VIII/1B1