A Wavelength Converter Integrated with a Discretely Tunable Laser ...

3.2 Amplification in SOAs 21
Table 3.1: Density of states in different types of active layers. denotes the thickness of
the quantum well, and is the effective mass of the carrier.
Material Bulk Quantum Well
Dimension 3D 2D
Density
of states
¦
¦ ¦
A transition from the conduction band to the valence band, or visa versa, is restricted by the
conservation of both energy and momentum (k-selection rule),
or ¦
, which is indicated in the figure by the vertical transition line. Combining
Eq. 3.3 and 3.4 we find for the photon energy
¦
¦ ¦
¦ (3.4)
where denotes the reduced mass. The density of transition pairs, i.e. the reduced density of
states, , follows from
E FN
E 2
E c
E v
E 1
EFP E g
E ph
E
conduction band
E+dE
E
valence band
k
¤
number of
states= ρ(E)dE
¤
E
a) b)
¤
ρc
MQW
(3.5)
ρ
ρcbulk
ρv
MQW
Figure 3.1: a) Energy of the electron states as a function of their momentum. The shaded
areas indicate the energy levels for which the probability that the state is occupied by an
electron is more than 50%. b) Density of states versus energy for bulk and MQW material
The shaded areas denote the states in bulk that are occupied with a probability of more than
50%.
eV
E FN
E c
E F
E v
E FP
ρv
bulk