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Laser & Photon. Rev., 1–11 (2008) / DOI
10.1002/lpor.200710032 1
Abstract We describe recent progress in photonic
crystalnanocavity lasers with an emphasis on our recent results
onultrafast pulse generation. These lasers produce pulses on
thepicosecond scale, corresponding to only hundreds of
opticalcycles. We describe laser dynamics in optically pumped
singlecavities and in coupled cavity arrays, at low and room
temper-ature. Such ultrafast, efficient, and compact lasers show
greatpromise for applications in high-speed communications,
infor-mation processing, and on-chip optical interconnects.
© 2008 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Ultrafast photonic crystal lasers
Dirk Englund 1,*, Hatice Altug 2, Bryan Ellis 1, and Jelena
Vučković 1
1 Ginzton Laboratory, Stanford University, Stanford CA 943052
Electrical and Computer Engineering Department, Boston University,
Boston MA 02215
Received: 13 November 2007, Revised: 17 March 2008, Accepted: 13
May 2008Published online: 2 July 2008
Key words: photonic crystal; laser; Purcell effect;
ultrafast
PACS: 42.55.Sa,42.55.Tv,42.50.Ct, 42.70.Qs
1. Introduction
The field of photonics is transitioning towards highly
in-tegrated nanoscale devices. For the first time, researchersare
able to integrate fast low-power optical components onsemiconductor
chips, causing some to draw analogies to thesemiconductor
electronics revolution. The most commer-cially significant
application of such integrated photonicsis optical communications.
Because of low output pow-ers, devices would first find
applications in short-distancecommunication, including high-speed
local networks, andboard-to-board and chip-to-chip interconnects.
Additionalapplications lie in biochemical sensing and data
storage.
One of the most promising architectures for integratednanoscale
devices is the planar photonic crystal (PC). In-plane confinement
is achieved by distributed Bragg reflec-tion using periodic
arrangements of holes, while out-of-plane confinement results from
total internal reflection. Cav-ities, defined by defects in the PC,
can confine light nearthe ultimate volume limit λ/2n in all
dimensions. Withoptimized local geometry, extremely high
confinement ispossible, with quality factors on the order of 104 in
ac-
tive [1–3] and 106 in passive structures [4]. Through
thecombination of a high quality factor (Q) and small modevolume
Vm, such cavities can dramatically increase thevacuum Rabi energy,
enabling cavity quantum electrody-namic effects such as enhanced
spontaneous emission (SE)rate of embedded emitters [5]. This cavity
Purcell effectlowers the lasing threshold through higher SE
couplingefficiency β, far in excess of 50% for even modest
meanPurcell factor [3]. By contrast, β in Vertical Cavity Sur-face
Emitting Lasers (VCSELs) is typically less than 0.1%.The Purcell
effect can also increase the direct modulationspeed [6, 7]. The
photonic on-chip design is ideally suitedfor the integration of
different optical components; e.g.,light sources/detectors and
multiplexers/demultiplexers foroptical communications.
In this paper, we describe recent progress on photoniccrystal
nanocavity lasers. We will focus mainly on ultrafastlaser dynamics
reported in recent work from our group,but will attempt to mention
the major works in the fieldwhere appropriate. Previous studies
investigated the las-ing dynamics indirectly in the frequency
domain [7]; here,we instead focus on direct time-domain
measurements. In
Corresponding author: e-mail: [email protected]
© 2008 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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2 D. Englund, H. Altug, et al.: Ultrafast photonic crystal
lasers
Sect. 2.1, we begin with the designs for single-cavity
andcoupled-cavity devices, then in Sect. 2.2 introduce a modelthat
describes lasing action in our devices. In Sect. 3, wediscuss our
recent work on optically pumped PC lasers,driven by multiple
quantum wells (QWs). These structuresshow extremely fast lasing
action due to fast relaxationdynamics. In the near-IR range, we
demonstrate room tem-perature lasing with large-signal modulation
response onpicosecond time-scales, i.e., with only several hundreds
ofelectric-field oscillations per pulse. A surface
passivationtechnique greatly improves the practicality of the PC
laserby limiting nonradiative (NR) losses. Using a similar de-sign
in the InP/InGaAsP material system, we demonstratelarge-signal
modulation with pulse widths near 10ps in thetelecom band. In Sect.
4, we shift our attention from theQW to quantum dot (QD) gain
medium. In typical cavitieswith Q ≥ 1000 and QD density ≥ 100/µm2,
where thresh-old is determined by material properties, the QD
activematerial reduces lasing threshold because of lower gainarea
and surface recombination losses. We conclude with abrief
discussion of electrical pumping.
2. Small-volume PC lasers
The small-volume, high-Q cavities enabled by photoniccrystals
can decrease turn-on time and lasing threshold [6].This improvement
results when the gain spectrum overlapswith the cavity resonance so
that spontaneous emissioninto the cavity mode exhibits higher
spontaneous emissionrate and spontaneous emission coupling
efficiency β. Theseeffects can decrease turn-on time and lasing
threshold [6].In addition, microcavity lasers can be designed with
verybroad modulation bandwidth because the relaxation oscilla-tion
can be shifted beyond the cavity cutoff frequency [8].
Above threshold, higher pump powers lead to fasterdecay due to
increased stimulated emission rates. Smallmode volume PC cavities
can be used to achieve large pho-ton densities and speed up this
process. Compared to othertypes of lasers such as VCSELs, PC lasers
offer lower driv-ing power (Sec. 3), higher relaxation oscillation
frequency(see Sec. 2.4), and potentially faster electrical
modulationspeed because of the potential for lower device
capacitanceand resistance.
2.1. PC nanocavity laser design
In designing the PC structure for fast lasing action,
twoconsiderations are weighed: the Q value must be relativelylarge
to achieve SE Purcell enhancement and hence highSE coupling
efficiency; at the same time, the mode energyring-down time τc =
Q/ω should be small as it limitsthe laser’s response time. We
choose Q ≈ 2 · 103, corre-sponding to τ = 1 ps at laser wavelength
λ ≈ 1 µm. Thisvalue of Q is easily achieved with the the
single-defectcavity shown in Fig. 1c, defined in a square-lattice
photonic
(a) B
(c) (d)
z
xy
xy
(b) Bz
|E||E|2
Figure 1 (online color at: www.lpr-journal.org)
Square-latticephotonic crystal laser structures. (a) x-dipole-mode
field pattern(out-of-plane magnetic field Bz). y−dipole is rotated
by 90◦.(b) Quadrupole mode. (c) Single-defect cavity with electric
fieldintensity (inset). (d) Coupled cavity array structure in
GaAs.
crystal. The quadrupole mode, shown in the inset, has aQ ∼ 2000
as predicted by Finite Difference Time Domain(FDTD) simulations
[9].
Because of its small size, the single-defect PC laser hasthe
disadvantage that output power is low – on the order ofa few µW –
and much of this power is lost due to a wide-angle emission
profile. On the other hand, band edge PClasers, which operate in
slow-group velocity regions of thePC dispersion, comprise a greater
gain area, as was shownin the first PC laser demonstrations [10,
11]. They also of-fer greatly improved emission directionality
[12]. However,they entail other drawbacks, such as reduced lateral
confine-ment [13]. A good compromise appears to be combiningthe
strengths of the nanocavity and band edge lasers by ar-ranging
single-cavity lasers into an array [9]. If the cavitiesare
sufficiently close, lasing can be achieved in a commonmode. This PC
nanocavity array laser has far more direc-tional emission and
larger active material than the singlelaser, while providing better
lateral confinement than theband edge laser. The nanocavity array
achieves very lowgroup velocity in any photonic crystal direction
and a veryhigh density of electromagnetic states; in effect, the
struc-ture is the two-dimensional analog of coupled
resonatoroptical waveguides (CROWs) in photonic crystals [14,
15].Though coupled arrays of small numbers of VCSELs werepreviously
investigated [16], coupling between individuallasers is difficult
and requires a rather complicated fabri-cation procedure. Photonic
crystal nanocavity arrays allowprecise control of both the
uniformity and the coupling.
© 2008 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.lpr-journal.org
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Laser & Photon. Rev. (2008) 3
(a) (b)
Figure 2 (online color at: www.lpr-journal.org) Three-hole
de-fect cavity. (a) FDTD design with electric field intensity. (b)
Fab-ricated structure in GaAs with central InAs QD layer.
We investigated two-dimensional cavity arrays withmodes that
couple equally in the different crystal directions(monopole and
quadrupole modes in the square lattice ormonopole and hexapole
modes in the triangular lattice). Weprimarily consider PC cavity
array structures in a squarelattice [9]; this choice was arbitrary
and we would expectsimilar results in the triangular lattice. The
coupled cav-ity array and its dipole and quadrupole field patterns
areshown in Fig. 1a,b. In these modes, the in-plane electricfield
components Ex and Ey, as well as out-of-plane Bz ,are maximized in
the center of the slab. This is commonlycalled the transverse
electric (TE)-like mode.
For QD lasers, we explored higher Purcell factors with
athree-hole defect cavity [17]. Though theoretically limitedto Q ∼
120, 000 in this design, the fabricated structureshown in Fig. 2
has Q ∼ 3000, reduced by fabricationimperfections and material loss
[18].
2.2. Rate equations
A simple rate equations model describes the lasing dynam-ics
well. Material gain is averaged over the full mode as theQW or QD
layers span the full structure. The mode holdsp photons in a volume
Vm. The laser dynamics are mod-eled with three carrier levels: the
excitonic ground state,the pump level carrier number nE (populated
above theGaAs-bandgap using a laser with power Lin), and the
QWlasing level carrier number nG (resonant with the lasingmode
frequency). We then have [19]
dpdt
= g(nG)p+FmnGτr
− pτp
(1)
dnGdt
=nEτE,f
− nG(Fm + FPC
τr+
1τPC,nr
)− g(nG)p
dnEdt
= ηLin~ωp− nE
(1τE,r
+1
τE,nr+
1τE,f
)In the top equation, the cavity photon number is driven
by the QW through stimulated emission (gain term g(nG)p– see
[19]) and SE (at the resonant mode’s Purcell-enhancedrate Fm/τr).
The cavity loses photons at the cavity lossrate 1/τp. The carrier
number nG in the center equation ispumped by carrier relaxation
from the pump level popu-lation nE at rate 1/τE,f . Besides pumping
the cavity, nG
decays through NR channels at rate 1/τPC,nr and PC leakymodes at
rate FPC/τr, where FPC ≈ 0.2 expresses SErate quenching inside the
PC bandgap compared to the SErate 1/τr in the bulk QW (following
simulations in [5]).In the bottom equation, the nE level is pumped
throughabove-band optical excitation with power Lin at
frequencyωp(the first term) and decays through carrier relaxation
tonG, NR recombination, and SE (second term).
In the following text, we will use these rate equationsto model
the lasing action of single and coupled PC lasers,at both room and
low temperature (∼ 10K) and containingQWs or QDs as gain material.
We use a logarithmic gainmodel for QWs and a linear gain model for
QDs. Underhigh pump power, the rate equations model would
requiremodification to account for QD saturation [20].
2.3. Threshold
Solving Eqs. (1) in steady state gives the lasing
thresholdpower, defined here as the power where the average
photonnumber p = 1 [8]. Assuming that most pump-level popu-lation
drops into the lasing level (τE,f � τE,r, τE,nr), thethreshold is
given by
Lin,th =~ωpτpη
[nG,th
(FPC
τpτr
+τp
τPC,nr
)+ 1
].
In our QW- and QD-driven cavities, the threshold carriernumber
in the active volume Va is approximated using thematerial’s
transparency concentration, nG,th ≈ NtrVa ≈1018 cm−3VmΓ , where the
gain confinement factor Γ ≈0.16 approximates the cavity mode
overlap with the QWregion. Furthermore, with τp ∼ 1 ps, τr ∼ 600
ps, andτPC,nr ∼ 100 ps, it is easy to see that for our laser
structuresthe first term in the brackets dominates, giving
Lin,th ≈~ωpηVaNth
(FPCτr
+1
τPC,nr
)(2)
The threshold is thus determined by the gain
material’stransparency concentrationNtr, radiative loss into
non-lasermodes, and nonradiative recombination. In the
QD-drivendevices, nonradiative recombination is reduced and theterm
FPC/τr dominates. The factor FPC indicates thatthreshold is reduced
by suppression of SE into non-lasingmodes [5]. On the other hand,
in QW-driven devices, thenonradiative term 1/τPC,nr determines
threshold. AlthoughEq. (2.3) was derived for steady-state, we find
that it is alsoa good approximation for pulsed excitation.
2.4. Laser intensity modulation
Two modulation schemes are used in
telecommunications:small-signal and large-signal modulation [21,
22]. In small-signal modulation, the laser is driven at a constant
above-threshold pump power Lin,0 and modulated with a small sig-nal
∆Lin, resulting in differential changes ∆P = ∆(p/Vm)
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KGaA, Weinheim
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4 D. Englund, H. Altug, et al.: Ultrafast photonic crystal
lasers
and ∆NG = ∆(nG/Va) to the steady-state photon densityP0 and
lasing-level carrier densities NG,0. At low drivingpower above
threshold, the differential output power∝ ∆Pabout the steady-state
output P0 is limited by the relaxationoscillation frequency
[6],
ω2R =avgP0τp
+β
τpτr/Fm+
βN0P0τPC,nrτr/Fm
(3)
Here β = Fm/(FPC + Fm), as described in [5], a is
thedifferential gain, and vg the group velocity. In
conventionallasers, only the first term in Eq. (3) is considered as
β issmall [21]. Therefore, to increase bandwidth, P0 and hencethe
driving power is raised. The higher power can resultin thermal
problems [23], though injection locking mayhelp in VCSELs [24]. Eq.
(3) shows that in the high-βlaser, strong cavity effects help to
increase ωR without theneed to increase pump power, opening a new
pathway forincreasing laser modulation bandwidth [8].
In large-signal modulation, the rate equations predictthat the
modulation rate is limited by the pump-level re-laxation time τE,f
and cavity response time τp = Q/ω.An additional turn-on delay
arises as spontaneous emissionbuilds the cavity field to the point
when stimulated emissionbecomes dominant. This delay time is
reduced in the high-Purcell regime through faster SE rate and
higher β. Thisis seen from the turn-on behavior for laser cavities
withdifferent Q in Fig. 3. Here the Purcell factor is calculated
as
Fm = ξ ·3
4π2Q
Vm/(λ/n)3, (4)
where the factor ξ accounts for spatial averaging and is
esti-mated at ξ ≈ 0.18 from the measured Purcell rate enhance-ment
of the coupled cavity array in Sect. 3.2. The figureshows that as
Fm is increased, the turn-on delay asymp-totically decreases to a
value determined by the carrierrelaxation time and the pump power.
The delay decreases
1 2 3 4 5 6
10
P (mW)
0t(ps)
out
pump P
Q=1600, F = 81
Q=800, F = 41
Q=400, F = 20
Q=200, F = 10
Q=100, F = 5
010
0
0
10 0
10010
0in
m
m
m
m
m
Figure 3 (online color at: www.lpr-journal.org) Calculated
lasingpower P (t) · (Vm~ωG/τp) in response to a 3-ps pump pulse
(top),for a range of Q. The turn-on delay drops with increasing Q.
Theexcitation carrier density is 3Ntr per pulse for all plots, and
pumpefficiency η = 1 in this idealized model.
with pulse energy, which is set here to excite a carrier
con-centration of 3×Ntr. As Q is increased from 100 to 1600,the
lasing duration first decreases with faster SE rate, thenextends as
it approaches the cavity ring-down time. De-pending on the driving
conditions, the modulation rate canbe optimized with a Q that
provides high Purcell factor butdoes not excessively slow the
cavity response.
2.5. Rate equations model in FDTD
The three-level rate equations model does not account forspatial
variations in the carrier concentration across the pho-tonic
crystal device. However, we have found that spatialeffects such as
carrier transport from the pump spot to thegain region, or spatial
hole burning effects [25], are impor-tant in understanding lasing
efficiency and time response.For that reason, we have developed a
finite-difference timedomain model that includes carrier
dynamics.
Material gain is implemented in FDTD by an effectiveconductivity
σ, as in references [26, 27]. An auxiliary dif-ferential equation
is used to describe the evolution of thecurrent density J . In
turn, J is related to the carrier densityNG (assumed to be equal
for holes and electrons in theintrinsic semiconductors considered
here). The set of equa-tions obtained when J = σE is substituted
into Maxwell’sequations and is then expressed in the time-domain
anddiscretized, as described in [28]. The resulting nonlinearFDTD
model allows calculation of the carrier drift into thelasing mode,
and is important for explaining the laser timeresponse measurements
covered in Sect. 3.
3. Quantum well photonic crystal lasers
Quantum wells provide large gain when embedded in thecenter of
the PC membrane, where the resonant TE-likemode has the maximum
electric field energy density. Asingle QW in the PC slab center
would see the highestelectric field and hence the highest gain
overlap; however,to optimize the laser current, it is often better
to distributecarriers (or current) across several quantum wells
[29]. AQW-driven PC nanocavity laser was first demonstrated
withfour InGaAsP quantum wells [30] and was soon followedby other
demonstrations employing between three and sixquantum wells
[31,32], all operating in the telecommunica-tions band.
3.1. GaAs/InGaAs structures
We first investigated time-domain characteristics of
PCnanocavity lasers using a streak camera with a Hama-matsu
N5716-03 streak tube. Since the detector responseis limited to
wavelengths below 1 µm, we fabricated PClasers emitting between
900–980 nm. These employ four8-nm In0.2Ga0.8As QWs separated by
8-nm GaAs barri-ers (see illustration in Fig. 4). The top and
bottom QWs
© 2008 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Laser & Photon. Rev. (2008) 5
cryostat
400 500 600 700 800 900 1000
spectrometeror OSA
streak camera
PBSPBSHWPHWP
objectivelens
Ti:Saphpumppulses
MQWs
substrate
Figure 4 (online color at: www.lpr-journal.org) Confocal
micro-scope setup (lens numerical aperture=0.65). The laser
structuresare mounted in a cryostat, which is cooled for some
measurements.Emission is directed to either the streak camera,
spectrometer withcooled Si detector, or optical spectrum analyzer
for IR spectra.Inset: Illustration of coupled cavity array
membrane.
are about 32 nm from the center and still see 89% of thecentral
maximum field intensity. We use compressivelystrained QWs which
have higher differential gain, lowertransparency carrier density
Ntr, and higher coupling to theTE-like-polarized cavity mode than
unstrained QWs [21].We first consider lasers consisting of 172
nm-thick GaAsslabs patterned with 9× 9 arrays of coupled PC
cavitiesin a square-lattice PC (Fig. 1d). The structures are
fabri-cated by electron beam lithography in polymethyl
methacry-late (PMMA), followed by plasma-etch mask transfer
andwet-etch removal of a sacrificial layer beneath the mem-brane.
To reduce nonradiative (NR) surface recombinationon the large QW
area exposed through PC patterning, thesample was passivated in a
(NH4)S solution, which re-sulted in a 3.7-fold reduction in the
lasing threshold [33].We found that surface passivation was
critical in our sam-ples for room-temperature and continuous-wave
(CW) low-temperature operation.
The structures are pumped optically with 3-ps shortpulses at an
80 MHz repetition rate and a wavelength cen-tered at 750 nm using
the confocal microscope as describedin [34] and shown in Fig. 4.
High-resolution lasing spec-tra are measured with the spectrometer,
while time re-sponse is obtained using a streak camera with 3-ps
resolu-tion. At room temperature, the photoluminescence of
theIn0.2Ga0.8As quantum wells peaks at 980 nm. For highergain and
heat dissipation, we first evaluated cooled struc-tures [6].
The PC array laser in Fig. 1d supports a lasing mode atλmode =
950 nm at low temperature (LT) of 10K (Fig. 5a).Because of
fabrication imperfections, PC holes near theedges of the structure
were slightly smaller and cavities
100 200 300 400
5
15
25
5 10 15
5
15
25
10 30 50
20
40
60
80
L (�W)in
(d) 293K,pulsed
(e) 10K,CW
(c) 10K,pulsed
model
model model
L (�W)inL (�W)in
4co
unts
/s 1
0
.
2co
unts
/s 1
0
.
4co
unts
/s 1
0
.
930 950 9700
4
8
12
� (nm)
Inte
nsity
(10
00 c
ount
s)
Q=1520
(a) 10K,pulsed
5 10 15
2
6
10
1410.
4cts
L (�W)in
(f)10K, CW (struct 2)
model
coupled cavity
coupled cavity coupled cavity
coupled cavity single cavity
inte
nsity
(a.
u.)
20 300
unpass-ivated
passivated
10
(b) 10K,pulsed
0
L (�W)in
Figure 5 (online color at: www.lpr-journal.org) QW-driven
PClasing characteristics (passivated structures). (a)
Coupled-cavityarray spectrum below threshold and at low temperature
(10K).The lasing mode consists of an estimated 7–9 cavities. (b)
Low-temperature lasing curve shows threshold reduction after
passiva-tion. (c,d) Low-and room-temperature lasing curves with
pulsedexcitation (3.5-pulses at 80 MHz repetition, passivated
structure).(e,f) Continuous excitation lasing curves for coupled
and singlecavity. Horizontal axes show average pump power. The fits
areby Eqs. (1).
showed a higher resonance wavelength. As a result, weobserved
that coupled cavity modes existed only in a sub-set of the full
array. From optical microscope images, weestimate that the lasing
mode comprises only 7–9 cavities;the pump beam diameter was
adjusted to this size. Fig. 5cshows the lasing curve for pulsed
excitation (3.5 ps at 13 nsrepetition), with an averaged threshold
of 6.5 µW(measuredin front of the objective lens). This corresponds
to a largepeak pump power of ∼ 21mW.
The threshold power is much lower under continuouspumping at low
temperature. Fig. 5e displays the lasingcurve of the passivated
structure, indicating onset of lasingat only∼ 9 µW. For a single
cavity, threshold is even lower,near 2 µW, shown in Fig. 5f. This
threshold and a similarlylow value recently reported with
GaInAsP/InP QWs [35]are lower than in previous low-threshold QW
lasers [36,37].
We believe that three main factors reduce threshold inCW
operation. First, carrier radiative efficiency is higher
insteady-state lasing as stimulated emission outpaces
othernonradiative recombination processes, which are more sig-
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KGaA, Weinheim
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6 D. Englund, H. Altug, et al.: Ultrafast photonic crystal
lasers
0t(ps)
(a)
0 10 20 30 40
t(ps)2
4
6
810
1017.
conc
entr
atio
n (1
/cm
)3
NGN E
pumppump
efficient carrier conversion
threshold
0 10 20 30 40 50 60
1
(b)
pump
cou
nts
(n
orm
aliz
ed
) RT LTexperimenttheory
P(t) 5.laser response:
Figure 6 (online color at: www.lpr-journal.org) Laser time
re-sponse. (a) Experimental data shows response nearly followingthe
excitation pulse at room temperature; data at both temperaturesare
acquired at 2× lasing threshold. (b) Illustration of pump
inef-ficiency in pulsed operation. Pump energy is efficiently
channeledinto the cavity mode only during lasing (shaded area under
P (t)curve, amplified here 5× for visibility); much of the
remainingpump energy is wasted to SE and NR losses.
nificant in pulsed operation (see illustration in Fig.
6b).Second, for the same average pump power, the peak powerof the
pulsed beam is thousands of times larger and resultsin a higher
temperature of photoexcited carriers. The fasterdiffusion of the
high-temperature carriers results in a largereffective pump spot
(observed in photoluminescence) withlower gain overlap. Third, we
estimate that CW operationis made even more efficient by carrier
drift into cavity. Thisdrift results from a carrier density
gradient caused by spatialhole burning in the cavity mode (see Fig.
10a). It is expectedto be insignificant for the higher-temperature
pumping inpulsed operation [34].
These contributions are quantified by applying the ratemodel of
Eqs. (1)(see fits in Fig. 5). All recombination ratesare estimated
from time-resolved measurements on non-lasing structures. The model
indicates that pump CW ab-sorption efficiency η ∼ 0.055 is far
better than in pulsedoperation, where η = 1.3 · 10−3 [34]. The
comparisonof CW and pulsed excitation regimes indicates that
thereis significant room for improving pumping efficiency inpulsed
mode at low temperature.
At room temperature (RT), threshold is higher. The las-ing curve
in Fig. 5d indicates a lasing threshold of 68 µWaverage power. The
larger threshold results in part from ahigher transparency
concentration, smaller optical gain [21],and larger NR surface
recombination rate [33]. These ef-
fects are furthermore exaggerated by heating due to
higherthreshold pump power. Because of larger thermal velocityand
diffusion, the above-mentioned carrier drift into thelasing cavity
will be reduced. The larger threshold causesheating in the
suspended membrane structures that limitsthe maximum output power,
as can be seen in the fall-off in Fig. 5d at ∼ 350 µW. Because of
this heating, weachieved only quasi-CW operation at RT. This
required achopper wheel that provided 1 ms-long pulses at a 17
Hzrepetition rate. Heat dissipation can be greatly improvedin
RT-operation by fabricating the PC laser structures ontop of
low-index substrates such as sapphire or silicon ox-ide [31, 32,
38–40], or by replacing QWs with QDs whichhave lower nonradiative
loss and carrier transparency [41].We have also found that capping
the photonic crystal mem-brane in PMMA improves heat dissipation by
up to 20×,based on measurements of the maximum pump power be-fore
the structure is damaged. The capping method alsohelps prevent
re-oxidation of passivated structures.
Because of faster carrier dynamics, RT operation resultsin
faster modulation speed. This is seen in Fig. 6a compar-ing RT and
LT lasing response to 3.4-ps-long pump pulses(13 ns repetition).
Both measurements were obtained withpump powers roughly 2× above
threshold, correspondingto averaged pump powers of 13 µW and 136 µW
at low-androom temperature, respectively. We measured
significantlyfaster lasing response at room temperature, with the
lasingpulses roughly following the 3.4-ps pump duration. Fre-quency
chirp was less than the cavity linewidth up to ∼ 2×threshold pump
power.
The speed-up results primarily because the intrabandrelaxation
time is shorter at RT; we measured τE,f < 1 ps[34], which agrees
with previous reports for III-V quan-tum wells [25, 42, 43]. This
behavior is captured well bythe three-level rate equations model
(fits in Fig. 6a) whosecalculated response is convolved with a
filter that takes intoaccount the 3-ps response time (FWHM) of the
streak cam-era [33]. Based on the model, lasing response
approachesFWHM = 1.2 ps at 2× threshold pump power whenpumped with
shorter 1-ps laser pulses, implying that modu-lation rates in the
THz regime would be possible. The delaycan be decreased with higher
pump power, but is ultimatelylimited by the carrier relaxation time
τE,f .
3.2. Spontaneous emission rate modification
We measure the Purcell factor Fm directly from
lifetimemeasurements of the cavity array pumped below thresh-old,
compared to emission lifetime in the unpatterned(bulk) sample [6].
Decay times for the passivated cav-ity array structure are
estimated from Fig. 7b,c, indicatingτuncoupled ≈ 142 ps and
τcoupled ≈ 19 ps. Then the centerequation of (1) is used to
calculate the underlying recom-bination rates (with p = 0). For the
bulk and PC regionsat times far after the excitation pulse (when nE
∼ 0), thelaser level carrier number nG and its measured
photolumi-
© 2008 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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-
Laser & Photon. Rev. (2008) 7
intensity
(a) bulk
(b) PC, uncoupled
(c) cavity
unpassivated, !=618ps
passivated, !=605ps
unpassivated """"""""""!=34 ps
passivated""""""""""!=142ps
intensity
intensity
0 250 500 750 1000 1250 1500 1750 2000t(ps)
0.2
0.4
0.6
0.8
1
0 25 50 75 100 125 150 175 200t(ps)
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50
0.2
0.4
0.6
0.8
1
t(ps)
passivated"""""!=19ps
Figure 7 (online color at: www.lpr-journal.org)
Microphotolumi-nescence from bulk quantum well, PC (uncoupled to
cavity arraymode), and non-lasing PC cavity array at 1/2 threshold
power(Pin = 12 µW before objective lens for original and 12 µW
forpassivated structures, pulse length 3.5 ps with 80 MHz
repetition).Measurements at 10K. Solid fits are by Eqs. (1); dashed
fits showexponential decay approximations.
nescence signal decay according to
1τcoupled
=Fm + FPC
τr+
1τPC,nr
1τuncoupled
=FPCτr
+1
τPC,nr
1τbulk
=1τr
+1
τbulk,nr
(5)
From bulk measurements, we estimate the natural radia-tive
lifetime τr ∼ 605 ps, assuming τbulk,nr � τr. Eqs. (5)then give Fm
≈ 28. Repeating these measurements for anunpassivated single-defect
cavity gives a spatially averagedFm ≈ 81 [6]. The high Purcell
factor for single cavitiesis not surprising as they are expected to
have a maximum
(a)
(b)(c)
Time (ps)
Inte
nsity
(a.u
.)
Pum
p la
ser
PhC
lase
r
0
0.5
1.0
1.5
2.0
2.5
05 10 15 20 25
delay ~1.5 ps
wavelen
gth
Figure 8 (online color at: www.lpr-journal.org)
Large-signallasing response in QW-driven PC laser. (a) Response to
excitationpulses at (i) 9 ± 0.5 and (ii) 15 ps. (b) Excitation
pulse traincreated by etalon setup. Imperfect mirror arrangement
causesan exponential decrease in pulse power and only the first
threepulses exceed the photonic crystal lasing threshold. (c)
Lasingresponse delay.
F of 165 for the cavity with this set of Q and Vm [5],
in-dicating that spatial averaging over the mode reduced Fmby ∼ 2×.
Baba et al. previously estimated SE lifetime en-hancement exceeding
16 (detector response limited) forsimilar structures in GaInAsP PC
nanocavities [25].
3.3. Delay time
As we indicated above, an important parameter in the
large-signal modulation scheme is the delay time, which de-creases
in high Purcell-factor cavities. We measured the de-lay time at
100K (with 890-nm pump wavelength) as 1.5 ps(Fig. 8c). This delay
time is nearly two orders of magnitudeshorter than in previous
measurements for VCSELs [44].
3.4. Large-signal modulation
To further demonstrate high-speed characteristics, we di-rectly
modulate single-defect cavity lasers at high speedsby pumping with
a series of 170-fs pulses generated usinga Fabry-Perot etalon [6].
Fig. 8a,b shows the results fordirect modulation of a nanocavity at
low temperature. Thismeasurement shows that in principle,
large-signal modula-tion well in excess of 100 GHz is indeed
possible. Fasteroperation at room temperature is expected, but the
etalonmeasurements were not repeated in the passivated
structure.
www.lpr-journal.org © 2008 by WILEY-VCH Verlag GmbH & Co.
KGaA, Weinheim
-
8 D. Englund, H. Altug, et al.: Ultrafast photonic crystal
lasers
1500 1510 1520 15300
0.2
0.4
0.6
0.8
1
! (nm)
Inte
nsity
(nor
mal
ized
)In
tens
ity (n
orm
aliz
ed)
"!=0.25nm
0 20 40 600
0.2
0.4
0.6
0.8
1
Lin(# W)Int
ensi
ty (n
orm
’d)
0
0.5
1
Inte
nsity
(nor
mal
ized
)
-20 -10 0 10 20 30 400
0.5
1
t(ps)
(b)
(c)
(a) single cavity
coupled cavity array
Figure 9 (online color at: www.lpr-journal.org) PC laser in
InPwith InGaAsP multiple QWs. (a) Lasing mode (2× threshold)and
light-in, light-out curve (inset) for single-cavity structure.(b)
Single-cavity lasing response (Lin = 45 µW) (c) Coupled-cavity
array time response (Lin = 2× threshold).
3.5. Surface passivation
Quantum wells have a major drawback as gain media inphotonic
crystal devices. Nonradiative surface recombina-tion rate is very
large because the QW has a large surfacearea exposed to air at the
hole walls. We have reduced theNR recombination problem, for the
first time in a PC laserstructure, by applying a surface
passivation treatment [33].The (NH4)S-mediated treatment reduced
the NR recom-bination rate by more than four times (Fig. 7b) and
ledto a fourfold reduction of lasing threshold, as shown inFig.
5(b). The increased efficiency extends the operatingrange from
cryogenic to practical regimes, enabling theabove-mentioned
room-temperature and ultra-low thresh-old CW operation.
3.6. Telecom wavelength laser
Lasers operating near 1500 nm are particularly interestingfor
applications in optical telecommunications [30–32]. Forthis reason,
we investigated the time-domain characteristicsof PC nanocavity
lasers in InP with InGaAsP quantumwell gain [45,46]. The structure
was tested with the setupin Fig. 4 (configured for 1550 nm with
detector N5716-02). The coupled cavity designs are identical to the
GaAsstructures presented earlier, though scaled up for the
longeroperating wavelength.
The single-cavity InP structure is shown in Fig. 10c. Itslasing
behavior is shown in Fig. 9a and indicates a thresh-old of 22 µW
when pumped with 3-ps above-band (750 nm)excitation pulses. We
measure large-signal response withFWHM ≈ 10 ps, at 2× above
threshold.
In a 9× 9 photonic crystal cavity array, we measuredFWHM≈ 19 ps,
also at 2× above threshold. We believethat the longer pulse
duration results from inhomogeneityin the pump beam, leading to
different gain in different cav-ities.
To analyze the pulse duration more closely, we modeledthe lasing
action using the nonlinear FDTD simulations
! x/a
! y /a
"5 0 5
"5
0
5
NG
0.2
0.6
1
1.4
1.8
2.2x 1018
carrier concentration
! x/a
! y /a
"4 0 4
"4
0
4
2"m
(c) SEM
! x/a
! y /a
"4 0 4
"4
0
4
(a) (b)
(d) B
carrier concentration
z
Figure 10 (online color at: www.lpr-journal.org) (a)
Lasing-level carrier concentration (1 ps after injection) showing
densitygradient towards lasing cavity. Spatial hole burning results
fromthe fast stimulated recombination during the lasing pulse.
Pumppower is 2 × Ntr at the center of the gaussian spot with
radius2a (lattice periods). (b) Carrier concentration in PC array,
1 psafter injection. Just beyond threshold, small inhomogeneities
inthe pump spot (radius 6a) and coupled cavity mode can result in
aspreading of lasing onset times, contributing to longer total
pulseduration. (c) SEM of single-cavity InP laser structure. (d)
Out-of-plane magnetic field of lasing mode, 1 ps after carrier
injection.
discussed in Sect. 2.5. Optical pumping with a finite-sizedbeam
results in inhomogeneous gain and uneven lasingaction, spreading
out the total pulse duration. This is seenfrom the lasing level
concentration NG and lasing fieldsin Fig. 10b,d, recorded here 1 ps
after injecting carriersat a two-fold transparency concentration.
The cavities arein different stages of lasing action. As a result,
the totalresponse time is extended. Experimentally we find that
athigher powers, the pulse response becomes shorter.
Thisobservation supports our model, as all cavities would befurther
above threshold and lase in a closer timeframe. Thisresult shows
that phase-locking on the ultrafast time scalerequires homogeneous
pumping across the array.
4. Quantum dot photonic crystal lasers
We now consider PC lasers that use QDs for gain. Thesepermit
lower threshold due to lower carrier transparencyand nonradiative
surface recombination, and greater tem-perature stability and
differential gain. Their speed is setby the smaller of relaxation
rate 1/τE,f and relaxationoscillation rate ωR. In high-Q photonic
crystal nanocav-ities, the lasing response is sped up through the
Purcell
© 2008 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.lpr-journal.org
-
Laser & Photon. Rev. (2008) 9
Inte
nsity
(a.u
.)
L (!W)in t(ps)
t(ps)t(ps)
(a) (b)
(c) (d)
Inte
nsity
(a.u
.)
experiment*theory
pump
response
Inte
nsity
(a.u
.)In
tens
ity (a
.u.)
Figure 11 (online color at: www.lpr-journal.org) GaAs PC
laserwith InAs QD gain. (a) Measured lasing curve and fit by Eq.
(1).(b) The measured turn-on delay between pump (first peak)
andlaser response (second peak) is limited by carrier
relaxation.(c) Measured large-signal modulation speed increases
with pumppower. (d) Corresponding fit by rate equations.
effect, while large β and thus higher efficiency and
lowerthreshold are achieved. We investigated these aspects inthe
135 nm thick GaAs PC membrane shown in Fig. 2(a),containing a
high-density (600 µm−2) of InAs QDs. Theseself-assembled dots have
shallow confinement and operateonly at cryogenic temperature with
an emission wavelengthof 940 nm and inhomogeneous linewidth of 20
nm. Lower-energy QDs allow laser operation at room temperature
inpulsed [47] and CW modes [41].
The y-polarized fundamental mode (Fig. 2(b)) is reso-nant in the
structure near 920 nm, with cold-cavity Q ∼3000(τp ∼ 1.5 ps). We
measure a gradual onset of lasingnear 1 µW, as shown in Fig. 11a.
From fits to the lasingcurve, we estimate a SE coupling factor β ∼
0.2. Streakcamera measurements of the rise time of
photolumines-cence from quantum dots in bulk GaAs indicate that the
car-rier relaxation time τE,f ∼ 10 ps for a wide range of
pumppowers. We also find that resonant pumping of
higher-orderconfined states of the QDs (such as p-level states)
doesnot appreciably lower τE,f . Because the carrier capturetime is
longer than the cavity photon lifetime, it ultimatelydetermines the
maximum modulation bandwidth. This iswhat we observe in Fig. 11b
which shows a delay of 13.5 ps(at five times threshold) and does
not drop below 12 ps forhigher powers. Simulations with Eqs. (1)
support this ob-servation as rise time is limited by the carrier
capture time.In our cavity-QED-enhanced structure, the
relaxation-timelimit is rapidly reached in the high-β case. In
contrast, innon-PC quantum dot lasers not employing strong
cavityeffects, far higher pump power is needed to reach this
limit.
Once lasing is reached, stimulated emission causes fastcarrier
recombination. We measured a decay time of 8.5 psat pump powers
around five times the threshold (Fig. 11c).
For higher pump powers the laser response appears
largelyunchanged, presumably due to carrier saturation. We
againmodel the system with Eqs. (1), employing a linear gainmodel
and parameters given in [48]. Fig. 11d shows thesimulated laser
response at various pump powers, demon-strating good agreement
between theory and experiment.
The present work predicts that large-signal modulationin present
PC lasers employing conventional self-assembledIn(Ga)As QDs is
limited to ∼ 30 GHz due to relaxationdynamics. While there is also
evidence to suggest thatcarrier relaxation and hence maximum
modulation rateactually further slows at increased temperature
[49], re-cent advances in QD growth can open the way to
higherperformance. QDs driven through phonon-assisted tunnel-ing
show very short relaxation time, with τE,f ∼ 2 ps atroom
temperature [50], and were recently demonstrated inridge waveguide
lasers with 25 GHz small-signal modula-tion bandwidth [50]. This
bandwidth may be significantlyimproved using a PC laser cavity. In
addition, reduction inthe inhomogenous linewidth broadening and
reduction inhot-carrier effects and associated gain compression
[51],will improve PC QD laser efficiency and speed. P-typedoping of
quantum dots also promises to speed up car-rier dynamics [52].
5. Conclusions and future directions
Photonic crystal lasers provide unprecedented speed, reach-ing
pulses on picosecond scales. They also show verylow threshold,
lasing at only several microwatts of pumppower. Their planar design
makes them ideal on-chip in-tegration. But for practical
applications, PC lasers willneed to be pumped electrically. Many
groups are currentlypursuing this goal, and electrically driven
single-cavityPC lasers have been demonstrated in free-standing
mem-branes [53, 54] and band-edge laser structures [55].
Forhigh-speed electrical modulation in extended structuressuch as
band edge and nanocavity array lasers, it will beimportant that the
structure be uniformly pumped, as thespatial modeling of carrier
dynamics in Sect. 3.6 suggests.A further challenge for any PC laser
will be keeping RCtime constants small, where C and R are the
capacitanceand resistance of the laser. Compared to VCSELs, PC
laserspromise far lower capacitance due to small a footprint
andlower resistance because of thin intrinsic material
betweenelectrodes. A promising recent step demonstrated time
con-stants below 10 ps using micron-scale contacts with
sub-fFcapacitance [56]. With recent advances in integration,
elec-trical pumping, and ultrafast operation, PC crystal
laserspromise to fill a growing need for integrated, ultrafast
opti-cal communication.
Acknowledgements This work was supported by the MARCOIFC Center,
NSF Grants ECS-0424080 and ECS-0421483, theMURI Center (ARO/DTO
Program No. DAAD19-03-1-0199), aswell as NDSEG & NSF
Fellowships (D.E.) and Stanford GraduateFellowship (B.E.).
www.lpr-journal.org © 2008 by WILEY-VCH Verlag GmbH & Co.
KGaA, Weinheim
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10 D. Englund, H. Altug, et al.: Ultrafast photonic crystal
lasers
Dirk Englund is a graduate studentin applied physics at Stanford
Uni-versity. He received his Bachelor’sof Science degree in physics
fromthe California Institute of Technol-ogy in 2002. He is a
recipient ofthe NSF, NDSEG, Stanford GraduateMayfield, and U.S.
Fulbright fellow-ships. His research focuses on quan-
tum photonic devices.
Hatice Altug received the B.S. de-gree in Physics from Bilkent
Univer-sity, Turkey in 2000. She receivedthe M.S. and Ph.D. degree
in electri-cal engineering and applied physicsfrom Stanford
University in 2006.Currently, she is a Peter Paul CareerDevelopment
Professor in Electricaland Computer Engineering Depart-
ment at Boston University. Her research involves de-sign and
implementation of high performance and ultra-compact nano-photonic
devices and sensors includinglasers and all-photonic switches and
their large-scale on-chip integration for communication and
bio-sensing ap-plications.
Bryan Ellis was born in Denver, Col-orado in 1983. He received
the B.S.Edegree in electrical engineering fromPrinceton University
in 2005. He iscurrently working towards a Ph.D.degree in electrical
engineering fromStanford University. His research in-terests
include nanophotonic devicesemploying optical microcavities for
use in optical communications and optical intercon-nect
technologies.
Jelena Vuckovic received the PhD de-gree from Caltech in 2002,
and hasbeen working at Stanford Universityas a faculty since 2003.
Her researchfocuses on nano- and quantum pho-tonic devices and
circuits. She is anauthor of more than 60 publicationsin refereed
journals, more than 70invited and plenary talks, five book
chapters, five issued and several pending U.S. patents,and a
recipient of numerous awards, including the Of-fice of Naval
Research Young Investigator Award andthe Frederick Terman
Fellowship, given to the mostpromising young faculty in sciences
and engineeringat Stanford.
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