Wi
W th
i
th in
je
in c
je t
c io
t n
io
y (d
-35
y (d
-3
Magnitude S
sit -60
n -6
nte
-45
-4
In -80
-81550
1552
1
1554
155
1556
1558
1
0
5
10
15
1
20
Wa
W v
a e
v le
e n
le g
n th
g (n
th m
(n )
Fr
F e
r quency
e
(
quency G
( H
G z
H )
m)
z
(a)
(a
(b)
Fig. 1.16. (a) Measured optical spectra at the modulation frequency of 10 GHz. The insets
show the higher resolution spectra. (b) Frequency response of the slave laser at different
wavelength detuning, where the injection optical power is 3.6 mW, and the mode spacing
difference is 0.14 GHz
In addition to the above two main factors, the total optical injection power of the master
laser and FP mode numbers can also affect the injection operation efficiency (Zhu et al.,
2008). The optimal wavelength matching is mainly twofold: first, the close central
wavelengths and more FP modes, and second, the mode spacing difference of several
gigahertz.
518
Optoelectronic Devices and Properties
-15
-1
I
=57
= m
57 A
m
Mas
Ma t
s e
t r
e
-5
-35
) -3
)
)
-55
-5
B -15
-1
(d
-75
-7
21
-15
tensity(dBm -1
tensity(dBm
I
=3
= 1.5m
3
A
1.5m
Sla
Sl v
a e
v
-25
-2
Mast
M
er
ast
in
Mas
Ma t
s e
t r
in
e
-35
-3
ude S
Wi
W th
i ou
th
t
ou in
t je
in c
je t
c ion
t
tical
Less ov
Less erl
ov
a
erl p
tical
a
-35
-3
-55
-5
Fu
F l
u l
l ov
l e
ov r
e lap
r
Op
Magnit
-75
-7
-45
-4
1540
1545
1550
1555
1560
1565
1570
1575
0
5
10
15
20
Wav
Wa e
v l
e e
l n
e g
n t
g h
t (
h n
( m
n )
m
Freq
Fre ue
q n
ue c
n y
c (
y G
( Hz)
G
(a)
(b)
(
Fig. 1.17. (a) Measured optical spectra of the master laser biased at 57 and 31.5 mA,
compared with the measured spectrum of the slave laser. (b) Corresponding frequency
responses of the slave laser, where the injection optical power is 3.9 mW, and the mode
spacing difference is 4 GHz
4.2 Frequency-pushing effect in single-mode diode laser subject to external dual-
beam injection
A frequency-pushing effect can occur for semiconductor laser at positive detuning
frequencies and higher injection ratios. The degree of pushing increases as the detuning
frequency of the injection ratio increases or the external signal decreases (Simpson et al.,
1997). Frequency convertor based on nearly degenerate four-wave mixing (NDFWM) in
injection-locked semiconductor laser has been demonstrated for frequency conversion in
optical communication systems, where two injection lasers are used. NDFWM in an
injection-locked semiconductor laser has been studied in detail by Li and Petermann (Li &
Petermann, 1993). The NDFWM pump signal is provided by a semiconductor laser
frequency-locked through optical injection of an external signal, and another external
injection signal acts as the probe signal. Therefore, a conjugate signal is produced in the
NDFWM process.
The influence of the frequency-pushing effect on dual-beam injection system can be
observed intuitively in Fig. 1.18. Fig. 1.18(a) shows the free-running spectrum consisting of a
single peak and weak relaxation resonance sidebands. The negative detuning frequency
between the slave and the injection light (M1) is fixed out of the locking range as shown in
Fig. 1.18(b). Then, another light (M2) is simultaneously injected at positive detuning
frequency. As shown in Fig. 1.18(c), the spectrum consists of a slave signal and two
regenerative amplified injected signals M1 and M2, and their detuning frequencies are both
out of the locking range. For optical injection at positive detuning frequency, M2 pushes the
slave signal to the negative detuning frequency. While the detuning frequency between M2
and the slave decreases, the degree of the frequency-pushing increases. Therefore, at a
critical point, M1 falls into the locking range of the slave laser, i.e. the slave signal is locked
to M1 as shown in Fig. 1.18(d). A converted signal C1 is observed at the red side of M1. As
M2 continuously moves towards M1, the amplitude of C1 increases at first and then
Optical and Electrical Spectrum Analysis of Optoelectronic Devices
519
decreases as shown in Fig. 1.18(d)-(f). This means that the conversion efficiency has
maximum (Li & Petermann, 1993). In Fig. 1.18(g), the slave light jumps nearby of its free-
running frequency when M2 gets close to M1 because M1 and M2 are both out of the locking
range again.
To get a deep insight of this process, we explain it on the viewpoint of medium-gain. Firstly
we consider a single-beam injection system. Since the external injection light enhances the
stimulated emission inside the cavity, the carrier population gets depleted faster, which
results in a reduction of the gain and the carrier density in the laser cavity. This gain
reduction induced by external light injection (blue line) is illustrated in Fig. 1.19 by showing
the gain spectrum and the loss spectrum. Furthermore, this gain reduction through ß (the
linewidth enhancement factor) changes the slave laser cavity frequency. The amount of
cavity resonance shift is: Δλcav ( N)=－ (λ02/2πc) ßgΔN/2 (Zhao et al., 2006), where g is the differential gain, N is the carrier density and c is the speed of light. Since ΔN is always
negative, the cavity resonance is red-shifted and Δλcav (N) is increased as the injection power
increased.
Under the optical injection at positive detuning frequencies, the cavity resonance shift
exhibits a frequency-pushing effect, which can be related to the medium-gain spectrum of
the slave laser. For an injection wavelength far from the cavity resonance, the medium gain
is small, and the amount of stimulated emission (regenerative amplified master light)
caused by injection light is also small. Thus, the cavity resonance shift as well as the carrier
density reduction is small. The injection light experiences more cavity gain as it getting
closer to the cavity resonance under a fixed injection power, leading to a further reduced
carrier density and a further red-shifted cavity resonance. In this process, the regenerative
amplified master light is amplified by the cavity gain and the cavity resonance mode is
suppressed. Finally, the slave laser gain is smaller than its threshold value, the master laser
compensates this reduction and the slave laser is lasting at the master wavelength when it is
injection locked. This process is illustrated in Fig. 1.19(a)-(d).
For optical injection at negative detuning frequencies (Fig. 1.19(e)), the cavity resonance shift
exhibits a frequency pulling effect towards the injected light. As the frequency detuning
between the maser and slave light is decreased at a critical point (Fig. 1.19(f)), the cavity
resonance shifts automatically and continually to the frequency of the injection light until
injection locking. It can be explained as follows: at the critical point (the margin of the
locking range), the negative detuning injection light pulls the cavity resonance to the red
side by a little amount, thus, the injection light can experience more cavity gain, which
results in a further reducing of the carrier density and a more red-shifted cavity resonance.
The red-shifted cavity resonance makes the injection light experience even more cavity gain.
This process repeats automatically until the slave laser gain is smaller than its threshold
value, leading to injection locking as shown in Fig. 1.19(f)-(h). The physically process in Fig.
1.19 is important in understanding the frequency-pushing effect in dual masters-slave
system.
The gain and optical spectra in Fig. 1.20(a)-(f) correspond to the process in Fig. 1.18(b)-(g).
The slave laser gets sufficient push when M2 moves closer (Fig. 1.20(b)), as explained in Fig.
1.19(a)-(c), and then it falls into the locking range of M1. Thus, the slave light is locked to the
frequency of M1 just like the process illustrated in Fig. 1.19(f)-(h). NDFWM between the
M2and injection-locked slave accounts for the converted signal C1 and C2 as shown in Fig.
1.20(c). When the converted signal C1 coincides with the red-shifted cavity resonance
(amplified spontaneous emission), C1 is amplified by the cavity resonance as shown in Fig.
520
Optoelectronic Devices and Properties
1.20(d). This explains the maximum of conversion efficiency from Fig. 1.18(d) to Fig. 1.18(f).
In Fig. 1.20(f), the injection signals are out of the locking range of the slave laser. The
interaction between the injected lights and the slave gain is very weak. Thus, the slave laser
is lasing near its free-running frequency.
-20 (a)
free-running slave
-40
-60
-80
-20
slave
M1
(b)
-40
-60
-80
-20
M2
slave
(c)
M1
-40
-60
-80
(dBm)
-20
locking to M1
(d)
M2
tra -40
ec
C1
-60
-80
al sp
-20 (e)
M2
locking to M1
Optic -40
C1
C2
-60
-80
-20
(f)
M2
locking to M1
-40
C1
-60
C2
-80
-20
slave
M2
M1
(g)
-40
-60
-80
1546.0
1546.2
1546.4
1546.6
1546.8
1547.0
1547.2
Wavelength (nm)
Fig. 1.18. Measured optical spectra in the process: M2 moves towards the slave signal from
positive detuning frequency with a fixed optical power (-15.37 dB) while M1 is fixed at an
operating point (-13.73 dB, -12.59 GHz)
The further influence of the frequency-pushing effect on dual-beam injection system is
shown in Fig. 1.21(a). Firstly, the conventional stable locking diagram is generated in a
single master-beam injection system. The locking boundary is marked by open circles and
dashed curve as shown in Fig. 1.21(a). Next, another injection signal from M2 injects
simultaneously at a fixed operating point (-10.12 dB, 12.08 GHz). A pushed locking range is
observed in this case due to the frequency-pushing effect, whose boundary is indicated by
Optical and Electrical Spectrum Analysis of Optoelectronic Devices
521
red open triangles and dashed curve. The direction of pushing is indicated by a blue arrow,
i.e. towards negative detuning frequency and low injection ratio. This is mainly because the
injection of M2 pushes the slave frequency to the negative detuning frequency and
suppresses its optical power by decreasing the slave gain.
Positive
v detuning
Ne
N ga
e
ti
t ve
v de
e
tu
de ning
Gain
Ga Sp
in
ec
Sp t
ec r
t a
Opti
p cal Sp
l S ec
p tra
r
Gai
Ga n Sp
n
ec
Sp t
ec ra
Opti
Op ca
c l Spec
l Spe tra
r
(a)
Stimul
St
at
imul e
at d
(e)
Gain
Emissio
Emis
n
sio
(cav
(
ity
cav
f
ity r
f equen
r
c
equen y)
y
Am
A plifi
p
e
lifi d
Inje
j ctio
t n
Spon
Spo ta
t neous
Loss
neou
s
Light
Emissio
Emis
n
sio
(fixed power)
(b)
(f)
(f
Master
Mast
Sla
Sl ve
v
(c)
(g)
(g
<10 ns
<
Ampl
p if
i ied
(d)
(d
(h)
Spontaneous
Emissio
Emis
n
sio
(cav
(
ity
cav
f
ity r
f eque
equ nc
n y)
Locking
y)
Lo
L cking
Wave
Wav l
e ength
ngt
Fig. 1.19. Schematic showing the processes of frequency pushing and injection locking by
medium-gain and optical spectra changing at positive and negative detuning frequencies
with a fixed injection power in single-beam injection system
Fig. 1.21(b) gives the locking bandwidth as a function of power injection ratio under single-
beam injection (curve a) and dual-beam injection (curve b). It is obvious that the locking
bandwidth varies with the power injection ratio. The variation of the locking bandwidth
before and after injecting another beam is also shown in Fig. 1.21(b) (curve c= curve b-curve
a). The horizontal dashed grey line as a reference indicates the identical locking bandwidths
before and after injecting another beam. Under dual-beam injection, it can be seen that the
frequency-pushing effect results in an increased locking bandwidth at most injection ratios