Tamoxifen-zinc(II) phthalocyanine conjugates for target-based photodynamic therapy and hormone therapy

Article abstract of DOI:10.1142/S108842461950161X

Although photodynamic therapy has been extensively studied in recent years and preclinical studies have shown promising results, strategies for enhancing PDT outcomes and reducing side effects still urgently need to be developed. In this study, a series of Tamoxifen-zinc(II) phthalocyanine conjugates have been designed and synthesized. In these "double-headed" conjugates, photodynamic therapy agent zinc(II) phthalocyanine and hormone therapy drug Tamoxifen were combined via oligoethylene glycol linkers. The conjugates show high specificity, and some of them show cytotoxic effects against the MCF-7 cells overexpressed Estrogen receptor, due to the targeting and cytostatic Tamoxifen moiety. Upon illumination, all these conjugates show high cytotoxicity due to the photosensitizing phthalocyanine unit. Their structure-activity relationship was also assessed. The results show that α-substituted Tamoxifen-zinc(II) phthalocyanine conjugates are highly promising anticancer targeting agents which exhibit additive effects of photodynamic therapy and hormone therapy.

Full text of DOI:10.1142/S108842461950161X

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 25, NO. 6, NOVEMBER/DECEMBER 2019
1900509
Linewidth Enhancement Factor in InAs/GaAs
Quantum Dot Lasers and Its Implication in
Isolator-Free and Narrow Linewidth Applications
Zeyu Zhang , Student Member, IEEE, Daehwan Jung, Member, IEEE, Justin C. Norman , Member, IEEE,
Weng W. Chow, Fellow, IEEE, and John E. Bowers , Fellow, IEEE
where dnꢀ, dnꢀꢀ are the variations in the real and imaginary
Abstract—The linewidth enhancement factor (αH) is an
important parameter for semiconductor lasers. In this paper,
we investigate, both theoretically and experimentally, the key
dN. An identical, yet independently developed, definition of
parameters that affect αH of InAs/GaAs quantum dot lasers.
part of the refractive index for a change in carrier density
the linewidth enhancement factor was shortly after reported by
Both dot uniformity and doping density are found to be critical
Vahala and Yariv [3] in their seminal paper on semiconductor
noise theory. Both [2] and [3] derived the now well recognized
linewidth formula for semiconductor laser:
in achieving small αH in quantum dot lasers. The prospects
for quantum dot lasers in isolator-free and narrow linewidth
applications are also discussed.
Index Terms—Linewidth enhancement factor, quantum dot
laser, feedback sensitivity, narrow linewidth.
Δν = ΔνSꢀ T(1 + αH2 )
(2)
I. INTRODUCTION
where ΔνSꢀ T is the modified Schawlow-Townes linewidth. The
linewidth enhancement factor was soon found to be important
in various aspects of semiconductor laser dynamics. In a laser
feedback sensitivity study, the critical feedback level marking
the onset of coherence collapse [4] was discovered to be strongly
dependent on αH [5], [6] from a stability analysis of the Lang-
Kobayashi rate equation [7].
For quantum well (QW) lasers, αH is normally in the range
of 2-5 [8]–[10] depending on the active region composition
and waveguide design. At these values, QW lasers experience
significant linewidth broadening. The critical feedback level has
been measured to be no larger than 10−4 times the output power
[5]. The broadened linewidth has been proven to be detrimental
to frequency-comb enabled high precision spectroscopy and
optical atomic clock generation [11], [12]. The lack of feedback
tolerance in QW lasers necessitates the introduction of an optical
isolator into the package.
NE of the major differences of semiconductor lasers from
their solid-state counterpart is the existence of a carrier
O
reservoir in addition to the photon reservoir. As a result, the real
and the imaginary part of the complex refractive index in the
active region are coupled as an instantaneous change in carrier
density in the laser active region changes both the material
gain and real refractive index. This phenomenon manifests in
semiconductor lasers as broadened spectral linewidth compared
to what is predicted from the modified Schawlow-Townes
linewidth formula [1]. Henry [2] was the first to properly explain
the linewidth enhancement in semiconductor lasers with the
introduction of the linewidth enhancement factor
dnꢀ/dN
dnꢀꢀ/dN
αH = −
(1)
Manuscript received January 4, 2019; revised March 29, 2019; accepted
May 7, 2019. Date of publication May 22, 2019; date of current version
June 27, 2019. This work was supported in part by the Advanced Research
Projects Agency-Energy under Grant DE-AR000067, by the U.S. Department
of Energy under Contract DE-AC04-94AL85000, and by the American Institute
for Manufacturing Integrated Photonics. (Corresponding author: Zeyu Zhang.)
The reduction in active region dimensionality is an effective
way to reduce αH [13], [14]. In atom-like active regions as
seen in quantum dot (QD) lasers, the carriers are confined in
Z. Zhang is with the Department of Electrical and Computer Engineering, spatially separated potential boxes. For this reason, the variation
University of California Santa Barbara, Santa Barbara, CA 93106 USA (e-mail:
z_zhang@ucsb.edu).
D. Jung is with the Materials Department, University of California Santa
in the index or gain in a dot is highly localized and will have
little effect on another QD certain distance away. As pointed
Barbara, Santa Barbara, CA 93106 USA, and also with the Korea Institute of out by [15], the improved symmetry in the gain spectrum of
Science and Technology, Center for Opto-Electronic Materials and Devices,
Seoul 02792, South Korea (e-mail: daehwan.jung.ucsb@gmail.com).
J. Norman is with the Materials Department, University of California Santa
QD laser also plays an important role in achieving smaller αH
compared to QW lasers. Due to the delta-like density of states,
Barbara, Santa Barbara, CA 93106 USA (e-mail: jcnorman223@gmail.com).
W. Chow is with Sandia National Laboratories, Albuquerque, NM 87105 USA
(e-mail: wwchow@sandia.gov).
the ideal inhomogeneously broadened gain spectrum of a QD
laser assumes a perfectly symmetrical gaussian shape. Granted
the peak gain wavelength stays the same, the Kramer-Kronig
J. E. Bowers is with the Department of Electrical and Computer Engineering
and Materials Department, University of California Santa Barbara, Santa relationship dictates a zero gain-peak differential refractive
Barbara, CA 93106 USA (e-mail: bowers@ece.ucsb.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
index and therefore zero αH regardless of carrier density.
In real self-assembled QD lasers, several issues complicate
Digital Object Identifier 10.1109/JSTQE.2019.2916884
the physics behind αH. First, the band-filling effect and
1077-260X © 2019 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution
requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

1900509
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 25, NO. 6, NOVEMBER/DECEMBER 2019
many-body effects cause the gain peak wavelength to shift as
carrier density increases [16]. Therefore, the actual αH at the
gain peak deviates from zero. Secondly, the Stranski-Krastanov
growth of QDs creates dots witha sizevariation, whichtranslates
toaninhomogeneouslybroadenedgainspectrum. Consequently,
the αH at any given wavelength is due to the contribution of
an ensemble of dots, among which the on-resonance and off-
resonancedotscontributedifferently. Furthermore, manyofhigh
performance QD lasers are modulation p-doped for improved
devicelifetime [17], temperaturesensitivity [18] and modulation
speed[19]. Theintroductionof p-typedopingintheactive region
alters the position of the quasi-Fermi levels [20], which greatly
affects αH of QD lasers.
In this work, a many-body gain model is employed to
calculate αH in InAs/GaAs QD lasers. The importance of dot
uniformity and modulation doping density in realizing small
αH will be demonstrated from both theoretical calculation
and measurements. Considering the high feedback insensitivity
of the QD lasers with small αH, the possible application of
these laser in future isolator-free system will be discussed. The
effect of having small αH in different narrow linewidth laser
configurations will also be quantitatively studied.
dφ
dz
ω
(ω) = −
Re (P (ω)) ,
(6)
ε0ncV E (ω)
where ε0 and c are the permittivity and speed of light in
vacuum, n is the background refractive index, E (ω) is the laser
electric field amplitude, ω is its frequency, V is the dot-in-a-well
(DWELL) volume. Details for the formulation and evaluation of
eqs. (3) to (6) are described in the literature [16].
The calculation in (5) and (6) are for a homogeneous
population of QD. For the presence of inhomogeneous
broadening due to QD size fluctuations, we performed a
statistical average over a range of band-gap energy ε:
ꢄ
ꢅ
ꢆ
ꢃ
2
∞
1
ε − εg
√
√
2Δinh
Sinh (ω) = −∞ dε
exp −
S (ω, ε) ,
2πΔinh
(7)
where S refers to either GM or dφ/dz, εg is the InAs band-
gap energy, and we assume a weighting described by a normal
distribution characterized by an inhomogeneous broadening
width Δinh. Following the formal definition of the linewidth
enhancement factor, the αH is then calculated from:
αH = − d(dφ/dz)
.
(8)
inh
dN
d(GM
dN
)
inh
II. THEORETICAL MODEL AND MEASUREMENT TECHNIQUE
The experimental characterization of αH involves directly
measuring the change of real and imaginary parts of the
complex refractive index. After Fabry-Perot (FP) laser sample
preparation, amplified spontaneous emission (ASE) spectra are
measured at different current injection levels under pulsed
conditions. The mode-sum method [23] is then employed to
extract the change of gain (Δg) and thereby the change of the
imaginary part of the index (nꢀꢀ) from the ASE spectra. The
change of the real part of the index (nꢀ) can be extracted by
tracking the wavelength shift of the peaks of the FP modes
(Δλm). αH can then be extracted based on
Three batches of QD lasers with unintentionally doped (UID),
5 × 1017 cm−3, and 1 × 1018 cm−3 p-type dopant concentration
in the active region are grown and fabricated. These doping
concentrations correspond to, on average, 0, 10, and 20 extra
holes per QD. The lasers are otherwise the same as the ones
reported before [21].
The theoretical modeling of QD active region starts from
solving the equation of motion for the electron-hole polarization
amplitude pαβ
:
ꢀ
ꢁ
dpαβ
c−p
c−c
,
αβ
= iωαβpαβ − iΩαβ neα + nβh − 1 + S
+ S
λꢀ Δλm
αβ
= − n
= −
.
(9)
dnꢀ/dN
dnꢀꢀ/dN
4πnꢀ Δλm
λ2 Δg
dt
(3)
αH = −
λ
4π Δg
where ωαβ and Ωαβ are the renormalized transition and Rabi
frequencies, nα and nβ are the electron and hole populations in
states α and β. Dephasing contributions from carrier-phonon
III. RESULTS AND DISCUSSION
c−p
c−c
and carrier-carrier scattering are given by S
and S
,
The simulated homogeneously broadened spectra of GM and
dφ/dz are shown in Fig. 1(a)(b), respectively. The nonzero gain
bandwidth in (a) is due to the many-body collisions represented
αβ
αβ
respectively. The input to the calculations are the electron
and hole energy levels, as well as the optical dipole matrix
elements, computed using a Schrödinger-Poisson solver [22].
To connect the microscopic polarization amplitude pαβ with the
macroscopic complex dielectric polarization amplitude P (ω),
we utilize the relationship:
c−p
c−c
by S
and S
in (3). These collisions result in a finite
αβ
αβ
life time of carriers at certain energy state. Through quantum
mechanics, the finite life time is translated to full-width-at-
half-maximum (FWHM) of ∼5 meV in the homogeneously
broadened gain spectrum of the QD laser. The red-shifted
emission energy is due to bandgap renormalization from
Coulomb coupling between discrete QD states and continuum
states in the QW [24], [25].
Due to the small gain bandwidth in the homogeneous QD
population, the carrier induced phase change shows strong
wavelength dependence (Fig. 1(b)). At photon energy more than
10 meV away from gain peak, the refractive index decreases
with increasing carrier injection. Such dependence on the carrier
density gives rise to positive αH and is commonly observed
ꢂ ꢂ
1
P (ω) =
μαβpαβ
,
(4)
h
α
β
where h is the Planck constant and μαβ is the dipole matrix
element. The summation in (4) is over all QD and QW states.
The material gain GM and carrier induced phased change per
distance dφ/dz is then directly proportional to P (ω) based on:
ω
GM (ω) = −
Im (P (ω)) ,
(5)
ε0ncV E (ω)

ZHANG et al.: LINEWIDTH ENHANCEMENT FACTOR IN InAs/GaAs QUANTUM DOT LASERS
1900509
Fig. 1. (a)(b) Simulated homogeneously broadened spectra of GM and dφ/dz at ground state in an undoped QD laser active region at carrier density from
2 × 1011 cm−2 to 3 × 1011 cm−2. The area dot density is 1 × 1010 cm−2. The arrows in (b) points to the direction of increasing carrier density. (c)(d) Schematic
representations of how the inhomogeneous broadened gain spectrum of a QD laser is composed of contribution of dot groups with different emission energy. In
(c), Δinh = 10 meV. In (d), Δinh = 20 meV.
in QW lasers [26]. In addition, since the differential gain at QD groups within the 10 meV detuning range will dominate the
the tail of the gain spectra is very small, the absolute value behavior of αH of the laser. The QD active region satisfying this
of αH at said wavelength regime becomes fairly large. At the condition is expected to show close to zero or even negative
gain peak wavelength, however, the refractive index increases αH. The calculated αH of an undoped QD active region at
with increasing carrier injection. This is due to bandgap different Δinh is shown in Fig. 2. The effects of detuned dot
renormalization that red shifts the peak emission wavelength. groups on the gain-peak αH can be clearly seen in Fig. 2(a).
Therefore, the model predicts a negative αH at wavelengths A homogeneous dot group originally shows negative alpha at
around gain peak in homogeneous QD population.
the gain peak. As the dot size variation worsens, αH at the
Since the inhomogeneously broadened gain spectrum is the gain peak increases due to large αH at tails of the detuned dot
weighted sum of homogeneoussly broadened spectra of QD groups. For Δinh larger than 10 meV, the gain-peak αH begins
with different sizes, in a realistic QD active region αH at to be dominated by the behavior of the detuned dot groups. The
any wavelength is also the weighted sum of its homogeneous dependence of gain-peak αH on carrier density at different Δinh
counterparts. Fig. 1(c)(d) provide insightful illustration on how is shown in Fig. 2(b). It can be seen that dot size variation not
dot size variation (Δinh) affects αH at gain peak in QD lasers. only modifies the gain-peak αH, it also alters the trends of αH
In both Fig. 1(c)(d), the peak gain of QD active region mainly versus carrier density. By comparing the gain bandwidth of the
comes from the contribution of a homogeneous QD group calculated inhomomogeous broadened gain spectrum with that
with highest dot density. Due to the small homogeneous gain of the measured gain spectrum extracted from ASE spectrum,
bandwidth, QD groups more than 10 meV detuned from the laser the Δinh in our lasers is determined to be ∼10 meV [21]. The
gain peak barely contributes to the peak gain, in spite of their high dot uniformity in these lasers enables the gain-peak Δinh
significant population. However, the same detuned QD groups, to be less affected by the detuned dot group.
as pointed out before, also show large positive αH at the peak
When p-type doping is introduced in the QD active region,
of the inhomogeneously broadened laser gain spectrum (the tail the quasi-Fermi levels in the conduction and valence band
of their own homogeneously broadened spectra). Comparing will be shifted down to lower energy. The movement of the
Fig. 1(c) and (d), it can be seen that the larger Δinh is, the more quasi-Fermi levels causes a reduced transparent carrier density
the contribution from these detuned QD group to αH at gain and increased differential gain in the laser active region [20],
peak. As dot uniformity in the QD active region improves, the [27]. The effects of p-type dopants on the material gain and

1900509
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 25, NO. 6, NOVEMBER/DECEMBER 2019
Fig. 2. (a) Calculated spectra of αH at the ground state of an undoped QD active region under different inhomogeneous broadening at carrier density of
1 × 1011 cm−2. The red circles mark αH at the gain peak wavelength under each inhomogeneous broadening condition. (b) Calculated gain-peak αH as a function
of carrier density and inhomogeneous broadening. The traces from bottom up are for Δinh = 0, 5, 10, 15 and 20 meV.
Fig. 3. (a)(b) Simulated inhomogeneously broadened spectra of GM and dφ/dz at the ground state in QD laser active regions with different p doping levels.
The blue, pink and red lines in (a) and (b) represent doping density of on average 0, 10 and 20 extra holes per dot. The calculation in both (a) and (b) are done at
a carrier density of 1.7 × 1011 cm−2 and Δinh of 10 meV. (c)(d) Calculated and measured gain-peak αH of the QD active region with Δinh of 10 meV. UID:
unintentionally doped.
refractiveindexoftheQDactiveregionareshowninFig. 3(a)(b). going through transparency at said carrier density. Due to the
Due to lower transparency and higher differential gain, the p aforementioned changes in GM and dφ/dz with doping density,
doped QD active region shows significantly higher material both the calculation and measurement indicates decreased gain-
gain (Fig. 3(a)). The additional holes from the dopants also peak αH with increasing doping density. Despite the similar
further decreases the refractive index compared to the undoped dependence on carrier density and doping density, the measured
case(Fig. 3(b)). The calculated and measured gain-peak αH are αH is larger compared to the calculated counterpart. This is
shown in Fig. 3(c)(d). For the UID laser, the sharp increase in probably due to the fact that the model only calculates αH in
αH close to 1.3 × 1011 cm−2 results from the QD active region a single layer of DWELL, while the measured αH is from the

ZHANG et al.: LINEWIDTH ENHANCEMENT FACTOR IN InAs/GaAs QUANTUM DOT LASERS
1900509
extracted changes in gain and refractive index experienced by
the entire optical mode. For this reason, any build up of carrier
in regions other than the DWELL active region could cause the
model to underestimate αH. Nevertheless, the measured αH in
doped samples is still significantly smaller than what has been
observed in QW lasers. More importantly, p doping in QD lasers
provides a way to engineer the αH with the additional benefits
of improved modulation speed [19] and device reliability [17].
Through further improvement in dot uniformity, reduction of
laser threshold through high reflective (HR) coating, or having
more doping density in the QD active region, closer to zero [28]
or even negative αH could be achieved.
IV. ISOLATOR-FREE OPERATION WITH QUANTUM DOT LASERS
Now that the ingredients for obtaining small αH in QD
semiconductor lasers are well understood, it is necessary
to consider the practical implementations of these lasers in
applications where small αH is crucial to proper performance.
The first type of applications to be considered here are diode
laser packages requiring low optical feedback sensitivity. In
almost all commercial butterfly packaged tunable lasers or
narrow linewidth lasers, co-packaged optical isolators can be
found to ensure larger than 30 dB optical isolation [29], [30].
These isolators must be installed because the QW lasers in
these package typically only tolerate feedback level up to 10−4
times the output power [5]. The inclusion of optical isolators
Fig. 4. (a) Calculated modulation response of a QW laser and a p-doped QD
laser in this work. Both lasers are in-plane Fabry-Perot lasers. The transport
effects and the interaction between the ground state and excited state of the
QD active region are not considered in the calculation. More involved dynamic
analysis can be found in [34]. (b) Estimated critical feedback level of the QW and
QD lasers under discussion. The stars marks the possible operation points of the
lasers above threshold. 0 dB represents 100% reflection. (10) is an approximated
solution in the regime of small αH. The exact solution gives even higher fcrit
for αH < 1 [6].
in the laser assembly increases the packaging complexity and
the overall cost of the product. It is therefore highly desired to
eliminate the co-package optical isolator yet still maintain the
feedback tolerance of the product.
In semiconductor stability analysis, when the ratio of laser
power reflected back into the laser cavity reaches above a certain
threshold, the laser will operate in the regime of coherence
collapse marked by severely broadened laser linewidth and
rapidly deteriorated laser relative intensity noise (RIN) [4]. The
threshold for the feedback power ratio is called critical feedback
level (fcrit). From a small signal analysis of the Lang-Kobayashi
rate equation [7], fcrit manifests as the feedback level where the
system just starts to acquire an unstable pole. fcrit turns out to
be a strong function of αH especially when αH is smaller than
1, as in the case of a QD laser. The relationship between fcrit
and αH can be described by [5], [31]:
solution from the Lang-Kobayashi equation, and for this reason
is applicable to practically all feedback intensity and αH [5], [6].
In (10), the quantities related to the intrinsic properties of the
laser active region are γ and αH. Therefore, both damping of the
relaxation oscillations and αH affect the fcrit of semiconductor
lasers. The laser modulation response along with the relationship
between fcrit and αH are plotted in Fig. 4(a)(b) for a QW and
a QD laser. The QD laser parameters used in the calculation
in Fig. 4 are extracted from experiment. The key parameters
and extraction procedure are discussed in Appendix A. The
QW laser considered here assumes the same cavity design and
τL2(Kfr2 + γ0)2 1 + αH2
fcrit
=
,
(10)
16C2
αH4
where τL is the round-trip time in the laser cavity, fr is relaxation oscillation frequency as the QD laser but different
√
the relaxation oscillation rate, and C = (1 − R)/2 R is the K-factor. In a diode laser, fr2 and γ are linearly related by the
coupling strength from the laser main cavity to the external proportionality factor K, which depends on how the laser gain
cavity from a laser facet with reflectivity R. The term Kfr2 + is compressed by the photon density in the cavity. In a QD
γ0 is known as the damping factor γ, in which K is the lasers, the gain compression factor is reported to be at least
proportionality factor between γ and fr2 and γ0 is the damping 10 times that in a typical QW laser [35]. Consequently, the
factor offset. Alternative forms of the critical feedback level lowest K-factor reported in QD lasers is in the range of 0.7–
have been proposed in the literature [32], [33]. However, they 0.9 ns [36], [37], while the lowest K-factor in QW lasers is
are limited in the range of applicable feedback intensity and αH. in the range of 0.2–0.3 ns [38], [39]. The significant damping
(10)ischosenheresinceitbestapproximatestheexactnumerical in QD lasers causes most modulation experiments to show a

1900509
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 25, NO. 6, NOVEMBER/DECEMBER 2019
lack of pronounced relaxation oscillation peaks as shown in
Fig. 4(a). When feedback is presented in the system, the laser
relaxation oscillation response will be superimposed with strong
parasitic oscillation that distablizes the laser [6]. The roughly
3 times higher K-factor in QD lasers reduces the impact of
such parasitic oscillation and makes QD lasers to be ∼10 dB
better than QW lasers based on (10), granted that all other
parameters are the same. In addition, the much smaller αH
in QD lasers further enhances the tolerance to feedback. The
smallest αH at threshold observed in our experiment is ∼0.5 as
shown in Fig. 3(d). Considering the nonpinned carrier density
above threshold in QD laser [40], αH increases significantly
above threshold [28]. Assuming four-fold increase in αH above
threshold, the QD laser is still predicted to tolerate up to 20% of
optical feedback (Fig. 4(b)). Such behavior has been recently
observed in feedback sensitivity experiments [41]. Feedback
tolerance at this level is more than sufficient to warrant the future
application of QD lasers in isolator-free laser packages.
V. QUANTUM DOT LASERS IN NARROW-LINEWIDTH
APPLICATIONS
The discovery and naming of αH is closely tied to the optical
linewidth of semiconductor lasers [1]. Knowing the ultra-low
αH in QD lasers, perhaps the most obvious applications of these
laser are in systems with stringent linewidth requirement. In
the receiver of a coherent communication system, for example,
narrow linewidth lasers as low noise local oscillators are crucial
in restoring the information encoded in the phase quadrature.
Narrow linewidth operation of semiconductor lasers has been
achieved through coupling with high-Q resonators in external
cavity [42] or lateral confinement engineering in heterogeneous
laser cross-section [43]. In the latter case, the dependence of
laser linewidth on αH follows (2). In the former case, due to the
presence of the external cavity, the laser linewidth formula is
modified as:
Fig. 5. (a) Existing laser designs to achieve narrow linewidth operation in
semiconductor lasers. I: DFB laser. II: DBR laser with passive waveguide
grating. III: external cavity laser with two high-Q ring resonators in one of the
loop mirrors. SOA: semiconductor optical amplifier. (b) Dependence of laser
linewidth on linewidth enhancement factor in each laser design. The calculated
linewidth is normalized with respect to 0 αH scenario. The detailed calculation
procedure and parameters can be found in Appendix B.
to look into the overall effect of αH on the laser linewidth.
Fig. 5(a) illustrates three designs to achieve narrow linewidth
operation in a semiconductor laser. The first design is that of a
distributed feedback (DFB) laser. In a heterogeneous integration
platform, laser linewidth of 18 kHz has been achieved [43]. The
second design is that of a distributed Bragg reflector (DBR) laser.
By having long DBR mirrors in the external cavity in low loss
silicon or silicon nitride platforms, the longitudinal confinement
factor can be significantly reduced to have a large A factor. The
third design involves forming high-Q resonators in a waveguide
loop mirror in the external cavity. Not only does the high Q factor
in the ring resonator enhance the A factor, the sharp filtering
1 + αH2
F2
Δν = ΔνSꢀ T
,
(11)
where F is the linewidth reduction factor due to the external
cavity. It is defined as:
F = 1 + A + B
(12)
(13)
1 dφext
τext
τL
A =
B =
=
τL dω
αH 1 drext
.
(14)
τL rext dω
In (13) and (14), φext and rext are the phase and magnitude response of these resonators results in a large B factor. Using
of the effective mirror response of the external cavity. (13) realistic external cavity design parameters, the normalized laser
denotes the reduction of longitudinal confinement of light due linewidth as a function αH is shown in 5(b) for each of the laser
to external cavity. This is accomplished by the introduction design in 5(a).
of high-Q passive resonator or long delay line in the external
In all three cases, a smaller αH corresponds to narrower
cavity. (14) represents the contribution of the detuned loading linewidth. In a DFB laser the dependence of linewidth on
effect, which arises from the coupling of gain and refractive αH follows strictly the 1 + αH2 relationship in (2). Assuming
index through carrier density in semiconductor laser [44]. the same αH for QW and QD lasers as used in the feedback
Interestingly, a high αH is desirable in order to maximize the sensitivity analysis, the linewidth in QD DFB lasers should be
linewidth reduction from the external cavity. Since αH appears 13% of that in a monolithic QW DFB laser, which typically
on both the numerator and denominator of (11), it is informative exhibits linewidth of a few MHz. In comparison, intrinsic

ZHANG et al.: LINEWIDTH ENHANCEMENT FACTOR IN InAs/GaAs QUANTUM DOT LASERS
1900509
TABLE I
SIMULATION PARAMETERS USED FOR FIG. 4
linewidth as low as 80 kHz has been reported in QD DFB lasers
[45], [46]. For external cavity DBR lasers, the majority of F is
from A due to the relatively flat mirror response at peak mirror
reflection. Consequently, F is a weak function of αH, making
the overall dependence on αH similar to that in the DFB laser.
For an external cavity laser with high-Q resonators as part of
the waveguide mirror, the B factor dominates F because of the
sharp filter responses of the resonators. Only 50% reduction in
linewidth can be achieved by replacing the QW active region
with the QD counterpart. However, the lowest linewidth in
diode lasers by far is reported for lasers integrated with high-Q
resonator. Further reduction in linewidth with QD active region
is still invaluable.
VI. CONCLUSION
Fig. 6. (a) Effective mirror response of the external cavity laser in Fig. 5(a) III.
In this simulation, K = 0.1, α = 3 m−1, Ra = 300 μm and Rb = 310 μm.
(b) The linewidth reduction factor for the same laser design calculated based on
(12)–(14).
We have shown experimentally and theoretically the critical
role dot uniformity plays in achieving ultra small αH in QD
lasers. In addition, the introduction of modulation p doping in the
QD active region further reduces αH. By adjusting the amount
of p-doping in the QD active region, one can even engineer αH
to suit the target application. With small αH and high damping
frequency, QD lasers have been shown to exhibit much higher
feedback tolerance compared to QW lasers. The ultra-stable
operation of QD lasers make it possible to construction laser
systems without co-packaged optical isolators. Last but not least,
the small αH in QD lasers has been shown to significantly reduce
laser linewidth compared to QW lasers in all existing narrow
linewidth laser designs.
similarly to the one detailed in [48]. The parameters used for
Fig. 4 are listed in Table I.
APPENDIX B
LINEWIDTH REDUCTION FACTOR CALCULATION
This section will give an example of how linewidth reduction
factor is calculated for an external cavity laser. The vernier
ring external cavity laser design in Fig. 5(a) will be analyzed
here. In this laser, both waveguide loop mirrors are broadband
and offer little wavelength selectivity. Therefore, the mirror
response is described by the transmission over the two high-Q
ring resonators:
APPENDIX A
QUANTUM DOT LASER PARAMETER EXTRACTION
After measuring the ASE spectra of the QD lasers, the net
modal gain as a function of current is measured using the
mode-sum method [23]. Laser transparency is then measured
at the gain-peak wavelength using the Andrekson method [47],
which enables the extraction of total optical loss (threshold
gain) of the laser [17]. Since the calculated material gain is
κ∗a1κa∗2ηa0.5 κb∗1κ∗b2ηb0.5
1 − ηat∗a1ta∗2 1 − ηbtb∗1tb∗2
r1 = TraTrb
=
(15)
ηa = e−(jβ+α)2πR
(16)
(17)
a
ηb = e−(jβ+α)2πR
b
obtained at different carrier density, comparing the measured where κin and tin are the cross-coupled and through-coupled
material gain with the simulation results allows the extraction field coefficients for ring i and port n, ηi is the round-trip phase
of carrier recombination coefficients. The key parameters in the and loss accumulation in ring i, Ri is the radius for ring i, β
laser modulation response including differential gain, photon is the wave number, α is the field attenuation coefficient in the
life time, and differential carrier life time can then be calculated waveguide and j is the imaginary unit. The computed effective
from the extracted quantities. The laser relaxation oscillation mirror response and the corresponding linewidth reduction
is modeled using a compact rate equation model implemented factor are shown in Fig. 6. As expected from the physical

1900509
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 25, NO. 6, NOVEMBER/DECEMBER 2019
interpretation of A and B, the maxima of A occur at the [21] D. Jung et al., “Highly reliable low-threshold InAs quantum dot lasers
on on-axis (001) Si with 87% injection efficiency,” ACS Photon., vol. 5,
resonance wavelength of the resonators while the maxima of
no. 3, pp. 1094–1100, 2017.
B are detuned to the red side of each resonance peak. Since
F is dominated by B, the maxima of F are detuned from the
resonance peaks of the ring resonators as well.
[22] “Nextnano3.” [Online]. Available: http://www.nextnano.com/nextnano3/.
Accessed: Apr. 18, 2018.
[23] D. T. Cassidy, “Technique for measurement of the gain spectra of
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3099, 1984.
[24] W. W. Chow and S. W. Koch, “Theory of semiconductor quantum-dot
laser dynamics,” IEEE J. Quantum Electron., vol. 41, no. 4, pp. 495–505,
Apr. 2005.
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dispersion in quantum-dot active media,” Phys. Rev. B, vol. 66, no. 4,
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in quantum dot and quantum well lasers,” Appl. Phys. Lett., vol. 84, no. 7,
pp. 1058–1060, 2004.
ACKNOWLEDGMENT
The authors are thankful to Frédéric Grillot for meaningful
discussions and M. J. Kennedy for device fabrication. Stella
Meng and Yoyo Meng offered a great deal of moral support
throughout the duration of this project.
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Weng W. Chow (F’09) received the Ph.D. degree in
physics from the University of Arizona, Tucson, AZ,
USA, on research involving fluctuation phenomena
in quantum optics. He is currently a Technical
Staff Member with Sandia National Laboratories,
Albuquerque, NM, USA, where his primary
research involves applying microscopic theory to
semiconductor laser development. Some of this work
is described in two texts—Semiconductor Laser
Physics and Semiconductor Laser Fundamentals:
Physics of the Gain Materials.
Jul. 2017.
He is also the Honorary Professor of physics with Cardiff University, Cardiff,
U.K., and a Fellow with the Institute for Quantum Science and Engineering at
Texas A&M University. He is a Fellow of the Optical Society of America. He
is the recipient of the Department of Energy, Basic Energy Science/Material
Science Award, the J. J. Thompson Premium, the LEOS Distinguished Lecturer
Award, the Alexander von Humboldt Senior Scientist Award, and the IEEE
Photonics Society Quantum Electronics Award.
Zeyu Zhang (S’17) received the B.S. degree in
electrical engineering from Clemson University,
Clemson, SC, USA, in 2015. He is currently working
toward the Ph.D. degree with the University of
California Santa Barbara, Santa Barbara, CA, USA.
His research interests include characterization and
modeling of quantum dot laser epitaxially grown
on silicon as well as passive–active integration of
photonic devices with quantum dot active region on
monolithic III–V on silicon platforms.
Daehwan Jung (M’16) received the Ph.D. degree
in electrical engineering from Yale University, New
Haven, CT, USA, in 2016. He is currently with the
Korea Institute of Science and Technology, Center for
Opto-Electronic Materials and Devices, Seoul, South
Korea.
His primary research interest is to study
novel III–V materials growth for high-performance
optoelectronic and photonic devices. His current
research project is to develop highly reliable, high-
performance quantum dot lasers epitaxially grown on
silicon for communication applications.
John E. Bowers (F’93) received the M.S. and
Ph.D. degrees from Stanford University, Stanford,
CA, USA. He is currently the Fred Kavli Chair
in Nanotechnology, the Director of the Institute
for Energy Efficiency, and a Professor with the
Department of Electrical and Computer Engineering
and Materials Department, University of California
Santa Barbara (UCSB), Santa Barbara, CA, USA.
He is a Co-Founder of Aurrion, Aerius Photonics,
and Calient Networks. He was with AT&T Bell
Laboratories and Honeywell before joining UCSB.
Justin Norman (S’14) received B.S. degree in
chemicalengineeringandphysicsfromtheUniversity
of Arkansas at Fayetteville, Fayetteville, AR, USA,
in 2013, and the Ph.D. degree in materials from
the University of California Santa Barbara, Santa His research is primarily in optoelectronics and photonic integrated circuits. He
Barbara, CA, USA, in 2018. Heistherecipientofboth
the National Science Foundation Graduate Research
has authored/coauthored ten book chapters, 600 journal papers, 900 conference
papers, and has received 54 patents. He is a member of the National Academy
Fellowship and the Frenkel Foundation Fellowship. of Engineering and a Fellow of the Optical Society of America (OSA) and the
He is currently with the University of California Santa
Barbara, as a Postdoctoral Researcher.
American Physical Society. He is a recipient of the OSA/IEEE Tyndall Award,
the OSA Holonyak Prize, the IEEE LEOS William Streifer Award, and the
South Coast Business and Technology Entrepreneur of the Year Award. He and
his coworkers received the EE Times Annual Creativity in Electronics (ACE)
Award for Most Promising Technology for the heterogeneous silicon laser in
2007.
His research interests are in the growth of InAs
quantum dots via molecular beam epitaxy for applications in photonics and
quantum electrodynamics. He also works on the heteroepitaxy of III–V materials
on Si for photonic integration.