430 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 5, MAY 2001
Measurement of Linewidth Enhancement Factor of
Semiconductor Lasers Using an Injection-Locking
Technique
G. Liu, X. Jin, and S. L. Chuang, Fellow, IEEE
Abstract—A new method for measuring the linewidth enhance-
ment factor of semiconductor lasers using the injection-locking
technique is presented. This idea is based on the relation between
the upper and lower bounds of the locked and unlocked regimes
when the detuning of the pump and slave laser is plotted as a
function of the injection power. Our results are confirmed with an
independent measurement using amplified spontaneous emission
(ASE) spectroscopy as well as our theory, which takes account of
the realistic quantum-well (QW) band structure and many-body
effects. This method provides a new approach to measure the
linewidth enhancement factor above laser threshold.
Index Terms—Linewidth enhancement factor, optical injection,
semiconductor laser.
T
HE LINEWIDTH enhancement factor ( ) is one of the
key parameters for semiconductor lasers. The linewidth
enhancement factor characterizes the linewidth broadening and
chirp due to fluctuation in the carrier density, which are detri-
mental sources for high-speed performance. Several methods
have been proposed to measure
, such as interferometric
measurement [1], RF-modulation measurement [2], injec-
tion-locking method [3], and amplified spontaneous emission
(ASE) method [4]. In this letter, a new method for the determi-
nation of the linewidth enhancement factor of a semiconductor
Fabry-Perot (FP) laser is performed by measuring the injection
locking range of the laser. In the past, it was proposed that
can be obtained by measuring the optical power change of an
injection-locked laser [3]. In this method, the injection level
should be low to satisfy the assumption for the
calculation.
At the same time, it is difficult to injection-lock the laser and
measure the power variation at low injection levels accurately.
Our method does not require any fitting parameters, which
would bring uncertainty for different laser systems. Meanwhile,
our results are in excellent agreement with our independent
measurement based on ASE spectroscopy. Both experimental
results are confirmed with our theory, which takes account of
realistic band structure with the valence band-mixing effect and
many-body effects.
In an optical injection-locked laser system, which consists
of a master laser (stable laser oscillation) and a test laser, the
locking properties of the test laser depend on its linewidth en-
hancement factor
. The locking range is asymmetric when
Manuscript received December 15, 2000; revised January 25, 2001.
The authors are with the Department of Electrical and Computer Engineering,
University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA.
Publisher Item Identifier S 1041-1135(01)03766-1.
Fig. 1. Experimental setup for measuring the linewidth enhancement factor
of semiconductor FP lasers using injection locking technique.
, and the value of the linewidth enhancement factor can
be evaluated from this asymmetry.
Fig. 1 shows the experimental setup. The test laser is a buried
heterostructure FP laser with five
compressively
strained quantum wells (QWs) made of
materials with a lasing wavelength at 1550 nm [5]. The test
laser has a threshold current of 11.7 mA, and is operated at a
bias current of 25 mA and a heat sink temperature of 25
C. The
master lasers are selected from a group of single wavelength
DFB lasers with sidemode suppression ratios greater than 40
dB and lasing wavelengths ranging from 1520 nm to 1580
nm. The master laser is mounted on a heat sink. The heat
sink temperature is used to control the lasing wavelength of
the master laser with a tunability of about 1 nm. The light is
coupled into an optical fiber by a laser optical-fiber interface
(LOFI) and fed into an erbium-doped fiber amplifier (EDFA).
In this way, the wavelength and optical power of the injection
laser light can be controlled independently. The 1% output of a
1
2 fiber coupler ( ) is connected to an optical power
meter in order to monitor the injected light power. The light
then is injected into the test laser. An optical spectrum analyzer
(OSA) is used to monitor the spectrum of the test laser.
Fig. 2 shows the optical power spectra of the test laser. The
master laser used in this figure lases at 1534.2 nm, which is
close to one of the free-running FP modes of the test laser
(1534.35 nm). The injection power in this figure represents
the master laser power measured before being coupled into
the test laser. The long dashed line shows the free-running
laser emission spectrum of the test laser. When the external
master laser light is injected into the test laser, which is biased
above threshold, the injected light competes with the optical
gain of the test laser for amplification. At a given detuning
between the external laser light frequency and one of the FP
mode frequencies of the test laser, when the optical power of
1041–1135/01$10.00 ©2001 IEEE
431 LIU et al.: MEASUREMENT OF LINEWIDTH ENHANCEMENT FACTOR OF SEMICONDUCTOR LASERS
Fig. 2. Optical spectra of the free-running state (long dashed line), the
unlocked state (biased at 25 mA, 25
C under an injection optical power of
2.9 mW (short dashed line), and the injection-locked state under an injection
optical power of 4.4 mW (solid line) for the test laser.
the injected light is weak, the light at the injection wavelength
is barely amplified. When the injected optical power is strong
enough and close to the FP mode of the test laser (1534.35
nm), the injection-locked state of the test laser is achieved. The
injection-locked state is determined by the observations that
the test laser lases at the injection laser wavelength and all the
other free-running sidemodes are greatly suppressed. Once an
injection-locking state is reached, almost all of the power of
the test laser is emitted at the optical frequency of the master
laser, as shown by the solid line in Fig. 2. In contrast to this,
when the injected optical power is not strong enough to lock
the test laser, the spectrum of the unlocked test laser injection
(short dashed line in Fig. 2) shows that the optical spectrum
of the test laser and the master laser are approximately added
together. The frequencies of the cavity mode of the test laser
shift very little by the external signal. The conditions which
allow the injection-locking occur will enable us to measure the
linewidth enhancement factor for the test laser accurately.
The overall locking range of a semiconductor laser is deter-
mined by both detuning (
) and the external in-
jection power. From the rate equations, an asymmetric locking
bandwidth can be obtained [6]
(1)
where
injected optical power;
test laser optical power;
refractive index;
laser cavity length;
speed of light.
Outside this region is the unlocked region, where the injec-
tion level is too low or the detuning is too high to reach in-
jection-locking condition. A detailed stability analysis can be
found in [7], which also calculates a self-pulsation zone (a Hopf
bifurcation), chaotic zone, and a coherence collapse zone. In
this letter, we focus on the stable locking regime. As a note,
our experiment is carefully controlled to make sure that the in-
jected power is not strong enough to cause self pulsation. Also,
the effect due to the nonlinear gain suppression is controlled
Fig. 3. The upper and lower detuning ranges are plotted as functions of the
square root of the injected optical power for the boundaries between the locked
and unlocked states. The ratio of the two slopes, which is independent of the
optical powers, is used to calculate the linewidth enhancement factor.
Fig. 4. The linewidth enhancement factor is plotted as a function of the
wavelength for the test laser. The solid squares are the experimental results
using the injection locking technique, the dots are the experimental data using
the ASE spectroscopy. The theoretical linewidth enhancement factor is plotted
for the interband contribution (short dashed line), the plasma effect contribution
(long dashed line), and their total (solid line).
to be less than 3% ( ). The incomplete
locked regime (as discussed in [6]), in which the energy is dis-
tributed in the free-running and locked modes, is considered the
unlocked regime so that (1) can be applied. From (1), as shown
in Fig. 3, the upper and lower detuning ranges are plotted for the
conditions that the injection-locking occurs at the wavelength
of 1534.35 nm (one of the free-running FP modes of the test
laser). The horizontal axis is the square root of the injected op-
tical power. From the ratio of the two slopes for the boundaries
of the locking ranges (least square fit), which is independent of
the optical powers, the linewidth enhancement factor of the test
laser can be found to be
. Such experiments are per-
formed over wavelengths ranging from 1520 to 1580 nm with
different DFB lasers as the master laser. The linewidth enhance-
ment factor is plotted in square symbols in Fig. 4.
In order to verify the above results, we also perform measure-
ment of the linewidth enhancement factor using the ASE spec-
troscopy. The ASE spectrum of the test laser is measured for two
close currents below lasing threshold at
C. The peak
wavelength of each FP mode in the ASE spectrum is a function
of the effective refractive index
. The change in the effec-
tive index can be calculated from [8]
(2)
432
where is the wavelength shift of an FP mode due to a
change in injected carriers at two bias currents.
is the mode
spacing of two adjacent FP peaks.
can then be extracted using
(3)
where
is change of the net modal gain [5]. The results
are plotted as dots in Fig. 4, and they are in excellent agreement
with our results using the injection-locking technique. When
using the ASE spectroscopy method, the linewidth enhancement
factor is measured near threshold condition. On the other hand,
using the injection locking method, the linewidth enhancement
factor is measured above threshold and lasing condition. For
high-speed modulation applications, the linewidth enhancement
factor measured at the lasing condition will be more important.
The results show that the linewidth enhancement factor does not
change too much near threshold and at lasing conditions.
To model the
QW lasers, the band struc-
tures of the quantum wells are calculated using a block-diago-
nalized 3
3 Hamiltonian based on the method for valence
subbands and a simple isotropic parabolic band model for con-
duction subbands. Once the band structure is known, the optical
gain
based on a non-Markovian gain model using a spon-
taneous-emission transformation method is given in[5], and the
induced change in the refractive index
due to interband
transition is given by
(4)
where definitions of symbols can be found in [5]. In addition,
there is a contribution from the free carrier plasma effect [9] for
TE polarization.
(5)
where
carrier concentration;
refractive index of the QW layer;
reduced effective mass for electrons and holes.
The linewidth enhancement factor due to the interband transi-
tion is then obtained by
(6)
where the total refractive index change is
for the TE mode, which is the domi-
IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 5, MAY 2001
nant optical mode for the compressively strained QW laser as
verified by the experiment.
We have fitted the optical gain for this laser in [5]. Using
the same fitting parameters, the change of the refractive index
change due to the interband transition is calculated. In Fig. 4,
the linewidth enhancement factor due to the interband transi-
tion (short-dashed line), the plasma effect (long-dashed line),
and their sum are plotted. The theoretical curve (interband plus
plasma effects) agree with the experiment very well. Both the
interband transition and the plasma effect contribute to the total
linewidth enhancement factor significantly for the laser studied.
At the laser wavelength of 1550 nm, the linewidth enhancement
factor is 3.0. This value agrees with typical value of long wave-
length strained QW lasers. The experimental uncertainty from
both experiments is about 15%.
The injection-locking technique itself has a great potential
for increasing the laser modulation bandwidth, decreasing
the chirp, and measuring many fundamental parameters of
semiconductor lasers [10], [11]. Here, we explored the appli-
cation of this technique for measuring
of a long-wavelength
strained QW laser. Without the absolute
values of the injection level, the value of
can be evaluated
from the detuning ranges of the injection locking. Our theory
shows good agreement with experimental results.
R
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