680
23 Electricity-to-Light Conversion
(a)
(b)
Fig. 23.58 a Tuning curves of two sampled gratings DBR mirrors for the front and back mirror current. b 27 wavelength
channels (1531.12 to 1551.72 nm) with a channel separation of 1 nm. Adapted from [2009]
For direct modulation, small- and large-signal modulation are distinguished. Detailed treatments of
laser dynamics and modulation can be found in [1993, 2010, 2011].
Laser Dynamics
The dynamical properties of the laser are described by the coupled rate equations for the carrier density
n and the photon density (per volume) S (for a single mode):
dn
dt
=
j
e d
−
n
τ (n)
− g(n, S) v g S
(23.40a)
dS
dt
= g(n, S) v g S + β B n
2
−
S
τ ph
.
(23.40b)
The first term in (23.40a) describes the electrical injection
23 (= I /(e V )), the second one the recombination (all channels) and the third one the carrier conversion to photons through stimulated emission
via the gain g. In the photon dynamics (23.40b), the first term represents the gain term, the second one
the photons in the laser mode from the recombination (spontaneous emission, cmp. Sect. 23.4.7) and
the third term the photon loss (due to internal losses and the mirrors). The recombination rate n/τ (n)
is typically given by (23.24). The photon lifetime τ ph is given by (23.28). If several optical modes are
present, (23.40b) must be written down for each mode S i and (23.40a) must be summed over all modes.
For the gain, various models are used. A simple one, going beyond (23.13), considering gain
compression due to spectral hole burning, i.e. depletion of carriers due to stimulated emission, is
g(n, S) = g
n − n thr
1 + S S
,
(23.41)
g
being the differential gain, g
= ∂g/∂n| S=0 , and S being the gain compression coefficient.
23 This term can be multiplied by the injection efficiency η inj to account for leakage currents.
23 Electricity-to-Light Conversion
(a)
(b)
Fig. 23.58 a Tuning curves of two sampled gratings DBR mirrors for the front and back mirror current. b 27 wavelength
channels (1531.12 to 1551.72 nm) with a channel separation of 1 nm. Adapted from [2009]
For direct modulation, small- and large-signal modulation are distinguished. Detailed treatments of
laser dynamics and modulation can be found in [1993, 2010, 2011].
Laser Dynamics
The dynamical properties of the laser are described by the coupled rate equations for the carrier density
n and the photon density (per volume) S (for a single mode):
dn
dt
=
j
e d
−
n
τ (n)
− g(n, S) v g S
(23.40a)
dS
dt
= g(n, S) v g S + β B n
2
−
S
τ ph
.
(23.40b)
The first term in (23.40a) describes the electrical injection
23 (= I /(e V )), the second one the recombination (all channels) and the third one the carrier conversion to photons through stimulated emission
via the gain g. In the photon dynamics (23.40b), the first term represents the gain term, the second one
the photons in the laser mode from the recombination (spontaneous emission, cmp. Sect. 23.4.7) and
the third term the photon loss (due to internal losses and the mirrors). The recombination rate n/τ (n)
is typically given by (23.24). The photon lifetime τ ph is given by (23.28). If several optical modes are
present, (23.40b) must be written down for each mode S i and (23.40a) must be summed over all modes.
For the gain, various models are used. A simple one, going beyond (23.13), considering gain
compression due to spectral hole burning, i.e. depletion of carriers due to stimulated emission, is
g(n, S) = g
n − n thr
1 + S S
,
(23.41)
g
being the differential gain, g
= ∂g/∂n| S=0 , and S being the gain compression coefficient.
23 This term can be multiplied by the injection efficiency η inj to account for leakage currents.