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Journal of Crystal Growth 514 (2019) 98–102
Contents lists available at ScienceDirect
Journal of Crystal Growth
journal homepage: www.elsevier.com/locate/jcrysgro
Gain measurement of terahertz quantum cascade laser via a masteroscillator power-amplifier configuration
T
Chenren Yua,b, Huan Zhua, Fangfang Wanga, Gaolei Changa,b, Haiqing Zhua,b, Jianxin Chena,
Gangyi Xua, Li Hea
a
b
Key Laboratory of Infrared Imaging Materials and Detectors, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
University of Chinese Academy of Sciences, Beijing 100049, China
A R T I C LE I N FO
A B S T R A C T
Communicated by Dr. C. Charles W. Tu
We report a method to measure the net loss and gain of a terahertz quantum cascade laser (THz-QCL), which is
based on a master-oscillator power-amplifier (MOPA) configuration. In the measurement, the master-oscillator
(MO) section and power-amplifier (PA) section are separately biased. With the fixed seed power from the MO
section, the output power of the device is measured at various bias voltage applied on the PA section, from which
the net loss and gain is deduced as a function of bias. We demonstrate that gain clamping and gain saturation can
be avoided in our measurement, which allow a complete evolution of the loss and gain characteristics. For a THzQCL with the bound-to-continuum active region and the metal–metal waveguide, the measured maximal net
gain is about 13.0–16.5 cm−1 at 2.58 THz at 20 K, which is in qualitative agreement with the theoretical analysis.
Keywords:
A1. Optical gain
B2. Semiconducting III-IV materials
B3. Terahertz quantum cascade laser
B3. Master-oscillator power-amplifier
1. Introduction
Terahertz quantum cascade laser (THz-QCL) is one of the most
promising THz sources, for its wide frequency coverage, high energy
conversion efficiency and compactness [1]. The gain characteristic is
one of the most important parameters of the THz-QCL. It shows crucial
influences on the threshold current, the slope efficiency of the output
power, and the maximum operation temperature of the laser [2]. In
order to optimize the active region design and thus improve the laser
performance, it is essential to accurately measure the gain characteristic of the laser.
There have been several methods for measuring the gain of the
semiconductor laser. The early studies include measuring the ratio
between the peaks and valleys of the individual Fabry-Perot (FP) resonance, which is called the Hakki-Paoli method [3–7], or measuring
the amplified spontaneous emission spectrum of the ridges with different lengths [8,9]. However, due to the extremely weak spontaneous
emission of the THz-QCL below the threshold, it is hard for these approaches to provide gain characteristic with reasonable signal-to-noise
ratio. In addition, the waveguide loss at zero bias or the net gain above
the threshold cannot be extrapolated from the gain sub-threshold
measured using Hakki-Paoli technique in THz-QCLs [10,11]. Recently,
started with the experimental work by Kröll et al. [12], terahertz time-
domain spectroscopy (THz-TDS) was proposed to investigate the gain of
the THz-QCL. Broadband gain spectrum, clamping effect, spatial-holeburning effect, and the dynamic features of the gain in the THz-QCLs
with different kinds of active regions and waveguides have been studied
by means of THz-TDS. All these experiments prove that THz-TDS is a
powerful tool to analyze the gain characteristics of the THz-QCL
[12–18]. However, expensive experimental facilities and complicated
optical alignments are involved in the THz-TDS measurements, which
make the experiment technically challenging and time consuming. A
simple and robust method is still highly desired to measure the gain
characteristic of a THz-QCL as a function of bias, emission frequency,
and operation temperature.
Here we present a simple and reliable method to measure the net
gain (g) of the THz-QCL. The device under test is a THz master-oscillator power-amplifier quantum cascade laser (THz-MOPA-QCL) based
on a metal-metal (MM) waveguide [19,20]. In the THz-MOPA-QCL, the
master-oscillator (MO) and the power-amplifier (PA) sections are
monolithically integrated and share the same active region. The two
sections are electrically separated but optically linked. We fixed the bias
applied on the MO section and measured the output power of the device
as a function of the bias on the PA section. In this way, the net gain was
measured at various bias and operation temperature. Here, the net gain
(g) refers to the difference between the gain caused by the active region
E-mail addresses: lieshang@163.com (C. Yu), zhuhuan@mail.sitp.ac.cn (H. Zhu), wangfangfang@mail.sitp.ac.cn (F. Wang), changgl1610@126.com (G. Chang),
3110101664@zju.edu.cn (H. Zhu), jianxinchen@mail.sitp.ac.cn (J. Chen), gangyi.xu@mail.sitp.ac.cn (G. Xu), lihe@mail.sitp.ac.cn (L. He).
https://doi.org/10.1016/j.jcrysgro.2019.03.001
Available online 02 March 2019
0022-0248/ © 2019 Elsevier B.V. All rights reserved.
Journal of Crystal Growth 514 (2019) 98–102
C. Yu, et al.
The drawback of using a low seed power is probably a poor signal-tonoise ratio. Under correct bias condition, the THz radiation is generated
in the MO section and is injected efficiently into the PA section, where
the THz wave is amplified by the preamplifier and is finally extracted
into the free space by the grating coupler.
Our previous work demonstrates that an optimized structure design
will enable efficient power extraction, and completely suppress the selflasing in the PA section [17,18]. In consequence, the device operates in
the single mode and the output power PMOPA can be expressed as:
PMOPA = PMO × ηPA = PMO × exp (g × Lpre ) × κGC
(1)
where PMO is the seed power from the MO section, ηPA is the total
amplification factor of the PA section, Lpre is the length of the preamplifier. κGC is the coupling efficiency of the grating coupler which
measures the ratio of the total emitted THz power extracted out of the
grating coupler to the power injected into it. κGC is determined by the
structure of the grating coupler and the net gain (g) of the waveguide,
i.e., κGC = κGC(g). Since the structure of the grating coupler is well
defined and can be precisely measured, the relationship between κGC
and g can be calculated by the means of 2D full-wave finite element
method with a commercial solver of COMSOL. The parameters used are
the structure parameters of the devices. The effective refractive index of
the material is 3.57. The absorber boundary is approximated as a perfectly matched layer, and the top and bottom metallization is approximated as a perfect electric conductor. The κGC, as a function of the
net gain/loss is deduced from the ratio of the output power from the
grating coupler to the input power, shown in the Fig. 2.
In the experiments, the total output power of the device (PMOPA) is
measured at different bias voltage applied on the PA section (VPA).
Therefore, in Eq. (1), only the seed power PMO and the net gain (g) are
the unknown parameters, but the former is a constant since the VMO
(bias voltage applied on the MO section) is fixed during the measurement. By comparing the values of PMOPA at different bias VPA, we are
able to deduce the net gain.
Since we will deduce the exact value (NOT the relatively value) of
the net gain, we select the net gain at the threshold bias of the MO
section (Vth) as the reference point. At this reference bias, the net gain
equals to the radiation loss of the MO section (αrad,MO). In our design,
the value of αrad,MO is relatively small and can be calculated by 3D
finite-difference time-domain (FDTD) calculation. With the same
parameters aforementioned, the calculated αrad,MO is about 3 cm−1.
In experiment, we first make VPA equal to the Vth and record the
output power of the whole device (PMOPA = PMOPA,Vth):
Fig. 1. Schematic (a) and SEM picture (b) of the THz-MOPA-QCL used in the
gain measurement. The THz-MOPA-QCL is composed of two sections: the MO
section and the PA section. The MO section is a first-order DFB laser. The PA
section consists of a preamplifier, a grating coupler and an absorbing boundary.
These two sections share the same active region and are electrically separated
by an air gap on the top metallization.
and the waveguide absorption. Since the self-lasing is totally suppressed
in the PA section, gain clamping effect is avoided and the maximum
available gain can be deduced in our measurements.
2. Information of material, device structure and measurement
method
The GaAs/Al0.15Ga0.85As quantum well heterostructure used in this
work was grown by molecular beam epitaxy (MBE), which is based on a
bound-to-continuum design similar to that described in Ref. [21]. The
active region consists of 90 stages with a total thickness of 11.7 μm. The
upper heavily doped GaAs layer is doped at the level of n = 2 × 1018
cm−3. The measured central emission frequency is about 2.5 THz. The
fabrication of the THz-MOPA-QCL is similar to that of the second-order
DFB laser based on the MM waveguide [22]. The frequency of the laser
is approximately 2.58 THz.
Fig. 1(a) shows the schematic structure of a THz-MOPA-QCL for
gain measurement, and Fig. 1(b) presents an SEM picture of a typical
device. The device is based on the MM waveguide. The device ridge is
150 μm in width. The MO section is a first-order distributed feedback
(DFB) laser in which the DFB grating is defined by forming air slits in
the top metallization. The periodicity of DFB grating (ΛDFB) is 20.6 μm.
The DFB contains 30 periodic air slits whose width (WDFB) is 5 μm. On
the top metallization, there is an 8-μm-wide air gap between the MO
and the PA in order to separately pump these two sections. The PA
section consists of a preamplifier, a grating coupler and an absorbing
boundary. The preamplifier is essentially an MM waveguide, 500-μmlong. The grating coupler consists of periodic air slits in the top metallization, which couples the THz radiation into the free space in an
oblique direction. It contains of 20 periods with a grating periodicity
(ΛGC) of 50 μm. The width of the air slits (WGC) in the grating coupler is
15 μm. The uncovered heavily doped GaAs contact layer acts as the
absorbing boundary, which completely absorbs the THz wave transmitted through the grating coupler. The absorbing boundary is 300-μmlong. The mode mismatch is very low at the interface between the MM
waveguide and the bare heavily doped semiconductor waveguide,
where the calculated reflectivity is ∼0.9%. In our recent study, the selflasing of the PA section is suppressed, so the frequency is only decided
by the MO section [19]. Therefore, the net gain in the PA section is
completely exploited to amplify the seed radiation, without suffering
the effect of gain clamping. Since the MO section and the PA section are
separated by an air gap on the top metallization (shown in Fig. 1(a) and
(b)), the seed power from the MO section is independently controllable.
That means, even for the devices with high gain, we can keep the seed
power from the MO section sufficiently low to avoid the gain saturation.
PMOPA, Vth = Pout , MO × exp (gVth × Lpre ) × κGC (gVth )
(2)
In subsequence we measure the output power PMOPA with various
VPA:
Fig. 2. Calculation result of the coupling efficiency of the grating coupler κGC as
a function of the net gain/loss of the waveguide. The grating coupler contains
20 periods. The periodicity of the grating coupler and the width of the air slit
are 50 μm, 15 μm, respectively.
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Journal of Crystal Growth 514 (2019) 98–102
C. Yu, et al.
Fig. 3. (a) Spectra of the THz-MOPA-QCL at different VPA while VMO is fixed at 4.2 V. (b) Light-current–voltage (LIV) characteristics of the THz-MOPA-QCL, measured
at different temperature of 20 K, 40 K and 60 K.
Fig. 4. The measured output power of the THz-MOPA-QCL as a function of VPA (a) and the deduced net gain/loss (g(V)) (b), while VMO is fixed in various values, at
20 K.
Fig. 5. (a) and (b) show respectively the measured output power of the THz-MOPA-QCL as a function of VPA and the deduced net gain/loss while VMO is fixed in
various values at the temperature of 40 K. (c) and (d) plot the related results at the temperature of 60 K.
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Journal of Crystal Growth 514 (2019) 98–102
C. Yu, et al.
temperature. Fig. 3(b) shows the light–current-voltage (LIV) curves of
the THz-MOPA-QCL when the MO and PA sections are equally biased,
measured at different operation temperatures. The results illustrate that
the threshold bias voltages are 3.55 V, 3.67 V, and 4.00 V at 20 K, 40 K,
and 60 K, respectively. We assume that the material and radiation losses
of the device do not change with temperature, so the net gain of the
waveguide at the threshold bias (gth) equals to approximately 3 cm−1.
Fig. 4(a) plots PMOPA as a function of VPA when the MO section is
biased at 3.6 V, 4.0 V and 4.2 V, respectively. The measurement is
carried out at 20 K. For the MO section, the threshold bias is 3.55 V, and
the seed power peaks at the bias of 4.2 V. Fig. 4(a) illustrates when the
PA bias below 3.0 V, the PA section is lossy and the total output power
PMOPA is very weak. When VPA > 3.0 V, the energy subbands in the
active region start to be aligned. In this case, more electrons are injected into the upper laser subband and population inversion is built up.
The gain of the waveguide is thus converted from negative to positive
gradually, and PMOPA rises rapidly. When the PA section is biased at
4.25 V, the optimized alignments between the related energy subbands
are achieved, giving rise to maximized population inversion. The net
gain and PMOPA also reach the maxima. With VPA further increasing, the
energy subbands re-staggered, and the gain of the waveguide transforms from positive to negative gradually.
Substitute the measured data of Fig. 4(a) into Eq. (4), and adopt the
calculated gth and κGC, we can deduce the net gain of the waveguide as
a function of the bias. The results are given in Fig. 4(b). At 20 K, the net
loss of the waveguide is about 77 cm−1 at zero-bias voltage. The net
loss of the waveguide is not constant. Instead, it decreases as the bias
rises. When VPA is 3.47 V, the net loss is 0, where the waveguide is
transparent for the THz wave. With increasing the PA bias, the waveguide exhibits the property of gain. The peak net gain is about
16.5 cm−1 at VPA = 4.25 V. When the bias voltage is further increased,
the energy subbands are misaligned again. The net gain gradually decreases and eventually transforms to a net loss. It is worth noting that
the values of the net gain deduced from the measured data with different VMO are in highly consistent with each other. The results coincide
with the principle of our method, expressed by Eq. (4), that the net gain
is independent of the seed power from the MO section. In addition, the
results also indicate that gain saturation does not happen in our measurement, because the deduced get gain almost keeps constant when
the seed power increases by a facet of 4 as VMO increases from 3.6 V to
4.2 V.
Fig. 5(a) and (b) show respectively the measured PMOPA as a function of VPA, and the deduced net gain when the operation temperature
of the device is 40 K. Fig. 5(c) and (d) plot the related results when the
operation temperature is 60 K. At low bias, the net loss of the waveguide is similar at different operation temperatures. The reason is that
the loss mechanisms of the waveguide – including the Ohmic loss of the
metallization, the absorption of free electrons in the heavily doped
layers, and the light absorption via intersubband transition – are temperature insensitive. However, as the temperature rises, the maximum
of the net gain falls regularly from 16.5 cm−1 at 20 K to 6.6 cm−1 at
60 K. The most important reason is that the electron-LO phonon scattering is enhanced significantly as temperature increases, which
Fig. 6. The net gain/loss as a function of VPA while VMO is fixed in 4.2 V for
different lasers, at 20 K. The structure of the grating couplers of these three
lasers are the same. Here, ΛDFB, WDFB, ΛGC, WGC, NGC are 20.6 μm, 5 μm, 50 μm,
15 μm and 20, respectively. The number of the periods of the DFB grating
(NDFB) and the length of the preamplifier (Lpre) of these devices are marked in
the Figure.
PMOPA, VPA = Pout , MO × exp (g × Lpre ) × κGC (gVPA)
(3)
Keep in mind that Pout,MO is constant since we fix the value of VMO.
So, the ratio of Eq. (2) to Eq. (3) equals to
κGC (gVth )
PMOPA, Vth
= exp [(gVth − g ) × Lpre ] ×
κGC (gVPA )
PMOPA, VPA
(4)
In Eq. (4), the net gain (g) is the only unknown parameter and can be
easily deduced by measuring the output power at different bias VPA.
3. Results and discussion
We first confirm that in the PA section self-lasing is suppressed and
all the gain is exploited to amplify the THz wave generated in the MO
section. Measurements were implemented in pulsed mode with a repeated frequency of 25 kHz and a pulse width of 1 μs. Fig. 3(a) presents
the emission spectra of the THz-MOPA-QCL measured at 20 K. During
the measurement, VMO is fixed at 4.2 V which corresponds to the
maximal seed power, and VPA changes from 0 to 4.5 V so that the PA
section varies from a loss medium to a gain medium. Fig. 3(a) shows
that the device keeps single mode emission with constant emission
frequency in the whole range of VPA. It demonstrates that emission
frequency is determined by the periodicity of the DFB grating in the MO
section, and self-lasing in the PA section is completely suppressed in the
whole dynamic range. These phenomena maintain at different operation temperature, and are consistent with our previous work [19]. The
phenomena reveal that the net gain in the PA section is completely
exploited to amplify the seed radiation.
We then specify the threshold bias (Vth) for the device at different
Fig. 7. Schematic of optimized structure used to measure gain/loss of the lasers. Two THz-MOPA-QCLs are back to back, sharing one MO section. The DFB laser,
preamplifiers and grating couplers are separated by the air gaps, pumped independently. The geometric parameters of the grating couplers are the same. The only
difference between two PA sections is the length of the preamplifiers, marked as L1 and L2 in the figure, respectively.
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Journal of Crystal Growth 514 (2019) 98–102
C. Yu, et al.
gain/loss is derived from the relationship between the output power of
the device and the bias applied on the power-amplifier section. The
limitations of gain clamping and gain saturation can be avoided in our
measurement, so the complete evolution of the gain/loss characteristic
as a function of bias and operation temperature can be deduced. Our
measurements present a simple and reliable way to optimize the design
of the THz-QCL active region. At the end, we propose an optimized
scheme to assess more reliable values of the net gain/loss.
severely degrades the population inversion.
To prove the reliability of our method and the consistency of the
results, we provide the results of multiple lasers with the same active
region. Fig. 6 shows the net gain as a function of the voltage for different devices, whose lasing modes are the same at 20 K. The material
and geometric parameters of these three devices are the same except for
the number of the periods of the DFB grating (NDFB) and the length of
the preamplifier (Lpre). The details are marked in the figure. The measured peak net gain is about 13.0–16.5 cm−1. The values of the net gain
are qualitatively comparable with each other. However, the losses of
the devices are different with the bias below 3 V or upon 5 V. The
possible reason for the disparities is the output power and the signal-tonoise ratio is too low to be measured accurately in those bias ranges.
It is hard to compare directly our measurement results with those by
the THz-TDS method, not only because the gain characteristics are very
sensitive to the active region design, but also because the target parameters measured are different. In the THz-TDS method, what measured
is the spectral gain defined as the ratio of the transmitted electric field
with the QCL on to that with the QCL off [15]. Here, the optical gain is
separated from the waveguide loss, and the latter is assumed to be a
constant and not related to the bias condition. In our work, the parameter we deduced is the net gain which defined by the difference between the gain created by the active region and the waveguide loss, and
both of which varies with the bias condition.
We therefore compare our measurement results with the theoretical
analysis in which the same active region is considered [23]. The calculation results by Schrottke et al. point out that the peak gain of the
active region is about 33 cm−1 at low temperature. Taking into account
the loss of metal-metal waveguide loss which is about 15–20 cm−1, the
calculated net gain is around 18–13 cm−1, which is in good agreement
with our measured value (13.0–16.5 cm−1 at 20 K). We note, at zerobias voltage, the net loss deduced by our measurement is relatively high
(77 cm−1) which may be caused by the bound-to-continuum design of
the active region. At zero-bias, such active region will form a miniband
in the injection region of each stage which is partially doped, and the
intra-miniband transitions of electrons will induce high loss. More
systematical study is necessary to explain the measurement results,
which is out of the scope of this work.
Since our method relies on the theoretical calculations of the αrad,MO
and κGC, we propose an optimized design of measuring to improve the
accuracy, as shown in Fig. 7. Essentially, there are two THz-MOPAQCLs sharing one MO section. The DFB laser, preamplifiers and grating
couplers are electrically insulated by the air gaps. The only difference
between two PA sections on each side of the DFB laser is the length of
the preamplifiers, marked as L1 and L2, respectively. During the measurement we keep the two grating couplers zero-biased, fix the bias on
the common MO section and therefore provide a constant and equal
seed power from each export of the MO section. We then measure the
output power from each grating coupler (respectively P1 and P2), as a
function of the bias on the related preamplifier. From Eq. (1), we know
that Pi = PMO × exp (g (V ) × Li ) × κGC , where i equals 1 or 2. In this
expression, PMO and κGC are unknown but unchanged values. Then we
can immediately get the ratio of P1 to P2 to be
P1/ P2 = exp[(L2 − L1) × α w (VPA)]. The gain/loss will be deduced:
α w (VPA) = ln(P1/ P2)/(L2 − L1) . During the measurement, no theoretically assisted parameter is needed, which make the measured values
more solid and reliable.
Acknowledgment
This work is supported by the Key Project of Chinese National
Programs
for
Research
and
Development
(Grant
Nos.
2016YFB0402303), the National Natural Science Foundation of China
(Grant Nos. 61574149 and 61734006), the Shanghai Science and
Technology Committee (16JC1403500), and “The Hundred Talents
Program” of CAS.
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25 (2010) 045025, https://doi.org/10.1088/0268-1242/25/4/045025.
4. Summary
In conclusion, we have demonstrated a method to measure the net
gain/loss of a THz-QCL based on the MOPA configuration. The net
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