682
23 Electricity-to-Light Conversion
(a)
20
15
10
5
0
Frequency (GHz)
1
2
3
4
5
0
P (mW )
1/2
1/2
f 3dB
f RO
(In,Ga)/(As,P)
(b)
10
8
6
4
2
0
f
(GHz )
RO
2
2
Power (mW)
0
0.5
1.0
1.5
2.0
InAs QD
Fig. 23.61 a Dependence of small-signal 3 dB cutoff frequency f 3dB (filled symbols) and relaxation oscillation frequency
f RO (empty symbols) on the square root of the output power P for a DFB-laser. Adapted from [2013]. b Relaxation
oscillation frequency f 2
RO versus power for an InAs/GaAs QD laser. The solid line is a model including gain compression
(P sat = 3.3 mW), the dashed line is the linear relation (23.44) for small power. Adapted from [2014]
exhibits so-called relaxation oscillations (RO) before the steady-state (cw) intensity level is reached
(Fig. 23.60b).
In the laser, first the carrier density is built up. It surpasses the threshold density that leads to a
build-up of the photon density. The laser pulse depletes the carrier density faster below threshold than
the current can supply further carriers. Therefore, the laser intensity drops below the cw level. From
the solution of the coupled rate equations for the electron and photon densities n and S (23.40a,b), the
frequency of the relaxation oscillations is found as
f RO =
1
2π
v g g
S 0
τ ph
1/2
,
(23.44)
where
is the differential modal gain as defined in (23.41) and S 0 is the steady-state photon density
per volume that is proportional to the laser power P. The dependence f RO ∝ S
1/2
0
is also found
experimentally (Fig. 23.61a). For higher power the relation f
2
RO ∝ S 0 becomes non-linear (Fig. 23.61b)
due to gain compression; in this case S 0 is replaced with S 0 /(1 + S S 0 ) ∝ P/(1 + P/P sat ), with P sat
being the saturation power.
Pattern Response
For digital data transmission, the laser is driven with pulse sequences (bit patterns). The response to a
random bit pattern is called an ‘eye pattern’ and is shown in Fig. 23.62. The pattern consists of traces
of the type shown in Fig. 23.60b. A clear distinction with well-defined trigger thresholds between ‘on’and ‘off’-states can only be made if the eye formed by the overlay of all possible traces remains open.
From the eye patterns in Fig. 23.62, it can be seen that the RO overshoot can be suppressed by driving
the laser with a dc offset current well above threshold.
Small-Signal Modulation
In small-signal modulation, the injection current I is varied periodically by a small amount δ I with
δ I I in the lasing regime. The current modulation leads to a corresponding variation of the output
intensity. The frequency response is limited by the differential gain and the gain compression coefficient.
The frequency response shifts to higher frequency with increasing laser power as shown in Fig. 23.63b.
23 Electricity-to-Light Conversion
(a)
20
15
10
5
0
Frequency (GHz)
1
2
3
4
5
0
P (mW )
1/2
1/2
f 3dB
f RO
(In,Ga)/(As,P)
(b)
10
8
6
4
2
0
f
(GHz )
RO
2
2
Power (mW)
0
0.5
1.0
1.5
2.0
InAs QD
Fig. 23.61 a Dependence of small-signal 3 dB cutoff frequency f 3dB (filled symbols) and relaxation oscillation frequency
f RO (empty symbols) on the square root of the output power P for a DFB-laser. Adapted from [2013]. b Relaxation
oscillation frequency f 2
RO versus power for an InAs/GaAs QD laser. The solid line is a model including gain compression
(P sat = 3.3 mW), the dashed line is the linear relation (23.44) for small power. Adapted from [2014]
exhibits so-called relaxation oscillations (RO) before the steady-state (cw) intensity level is reached
(Fig. 23.60b).
In the laser, first the carrier density is built up. It surpasses the threshold density that leads to a
build-up of the photon density. The laser pulse depletes the carrier density faster below threshold than
the current can supply further carriers. Therefore, the laser intensity drops below the cw level. From
the solution of the coupled rate equations for the electron and photon densities n and S (23.40a,b), the
frequency of the relaxation oscillations is found as
f RO =
1
2π
v g g
S 0
τ ph
1/2
,
(23.44)
where
is the differential modal gain as defined in (23.41) and S 0 is the steady-state photon density
per volume that is proportional to the laser power P. The dependence f RO ∝ S
1/2
0
is also found
experimentally (Fig. 23.61a). For higher power the relation f
2
RO ∝ S 0 becomes non-linear (Fig. 23.61b)
due to gain compression; in this case S 0 is replaced with S 0 /(1 + S S 0 ) ∝ P/(1 + P/P sat ), with P sat
being the saturation power.
Pattern Response
For digital data transmission, the laser is driven with pulse sequences (bit patterns). The response to a
random bit pattern is called an ‘eye pattern’ and is shown in Fig. 23.62. The pattern consists of traces
of the type shown in Fig. 23.60b. A clear distinction with well-defined trigger thresholds between ‘on’and ‘off’-states can only be made if the eye formed by the overlay of all possible traces remains open.
From the eye patterns in Fig. 23.62, it can be seen that the RO overshoot can be suppressed by driving
the laser with a dc offset current well above threshold.
Small-Signal Modulation
In small-signal modulation, the injection current I is varied periodically by a small amount δ I with
δ I I in the lasing regime. The current modulation leads to a corresponding variation of the output
intensity. The frequency response is limited by the differential gain and the gain compression coefficient.
The frequency response shifts to higher frequency with increasing laser power as shown in Fig. 23.63b.