ultrafast photonic crystal lasers - stanford university2 d. englund, h. altug, et al.: ultrafast...

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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

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

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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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



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-



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-



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.



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



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.).



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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