Time-resolved lasing action from single and coupled photonic crystal nanocavity array lasers emitting in the telecom-band
ABSTRACT We measure the lasing dynamics of single and coupled photonic crystal nanocavity array lasers fabricated in the indium gallium arsenide phosphide material system. Under short optical excitation, single cavity lasers produce pulses as fast as 11 ps (FWHM), while coupled cavity lasers show significantly longer lasing duration which is not explained by a simple rate equations model. A Finite Difference Time Domain simulation including carrier gain and diffusion suggests that asynchronous lasing across the nanocavity array extends the laser's pulse duration.
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ABSTRACT: We theoretically investigate the modulation response of quantum-dot based nanocavity light emitting devices. For high Purcell enhancement factors, our theory predicts the possibility of decreasing the modulation bandwidth with increasing scattering rate into the lasing quantum-dot state. This counterintuitive effect is investigated using a microscopic semiconductor model. The resulting guidelines for possible optimizations of quantum-dot based nanocavity laser devices are given.Applied Physics Letters 11/2010; 97(21):211106-211106-3. · 3.79 Impact Factor
Time-resolved lasing action from single and coupled photonic crystal nanocavity array
lasers emitting in the telecom-band
Department of Applied Physics, Stanford University, Stanford CA 94305
Electrical and Computer Engineering Department, Boston University, Boston MA 02215
Jelena Vuˇ ckovi´ c
Ginzton Laboratory, Stanford University, Stanford CA 94305
We measure the lasing dynamics of single and coupled photonic crystal nanocavity array lasers
fabricated in the indium gallium arsenide phosphide material system. Under short optical excitation,
single cavity lasers produce pulses as fast as 11 ps (FWHM), while coupled cavity lasers show
significantly longer lasing duration which is not explained by a simple rate equations model. A Finite
Difference Time Domain simulation including carrier gain and diffusion suggests that asynchronous
lasing across the nanocavity array extends the laser’s pulse duration.
The ultrasmall mode volume and high quality factor
Q of cavities in photonic crystals (PCs) enables control-
lable light-matter interaction. This control can improve
the performance of lasers by simultaneously increasing
the spontaneous emission rate into the cavity mode while
suppressing emission into other all other modes, result-
ing in a large spontaneous emission coupling efficiency
β [1, 2, 3, 4, 5]. Nanocavity lasers moreover enable very
broad modulation bandwidth as the relaxation oscillation
can be shifted beyond the cavity cutoff frequency. We
recently demonstrated single and coupled PC nanocavity
array lasers in GaAs membranes with InGaAs quantum
wells (QWs), emitting at 940-980nm with pulse duration
shorter than 4 ps (FWHM ) at room temperature[7, 8].
There has been particular interest in PC lasers emitting
in the transparency window of standard telecommunica-
tions fiber near 1550 nm[9, 10, 11]. We have recently ad-
dressed this wavelength band with PC nanocavity array
lasers in the InGaAsP material system, emitting from
1530-1550 nm in quasi-continuous mode operation.
To increase power output from single cavities, we also
described a coupled PC nanocavity array design. In this
letter, we investigate the time-domain lasing character-
istics of such coupled- and single cavity PC lasers in the
InGaAsP material system, to better understand their las-
ing dynamics and potential modulation rates.
optical excitation with 3-ps pulses above the semicon-
ductor’s bandgap energy, we measure lasing response as
fast as 11 ps for the single-cavity structures. This is ex-
plained by a three-level rate equations model. However,
the coupled-cavity array laser has a longer response time,
as long as 25 ps; this is not explained by the rate equa-
tions model. We instead analyze the coupled cavity array
lasers with a finite difference time domain (FDTD) sim-
ulation incorporating a carrier gain model, which sug-
gests that the extended lasing action results from spa-
tially non-uniform optical pumping of nanocavities and
results in asynchronous lasing action near threshold.
The structures are fabricated in a 280-nm thick
In0.786Ga0.214As0.445P0.555 membrane containing four
9−nm thick In0.78Ga0.22As0.737P0.263 QWs, separated
by 20-nm barriers, as described in Ref. . The mem-
brane rests on an InP substrate. Photonic crystals are
created using electron beam lithography followed by a
combination of wet and dry etching. We fabricated single
cavities (Fig.4(c)) and coupled cavity arrays (Fig.1(a)) in
square lattice PCs with periodicity a = 500nm and hole
radii ranging from 160nm to 230nm. The array contains
9x9 cavities that are spaced by two holes. It supports a
coupled quadrupole mode (Fig.1(c)) that is designed to
overlap with the QW gain.
FIG. 1: (a) Scanning electron micrograph of coupled nanocavity
photonic crystal array. The inset shows the cross-section of the PC
membrane. (b) Far-field radiation pattern of coupled cavity array
mode obtained at a pump power 1.4 above threshold. (c) Electric
field intensity of coupled quadrupole mode
The structures were tested in a confocal microscope
setup at room temperature. The QWs were excited by
pumping with a pulsed Ti:Sapph laser at an 80 MHz
repetition rate with a pulse duration of 3.5 ps pulses and
a center wavelength at 770 nm, above the bandgap en-
ergy of the In0.786Ga0.214As0.445P0.555 membrane. The
emission was measured using an optical spectrum ana-
lyzer and a streak camera (Hamatsu N5716-02) for time-
The lasing response of a typical single-cavity structure
behavior is shown in the light-in/light out (LL) curve in
Fig. 2(a) and indicates a threshold of ?Lin? = 22 µW
time-averaged power (corresponding to ∼ 71mW peak
arXiv:0812.2287v1 [physics.optics] 12 Dec 2008
FIG. 2: (a) LL curve of single-cavity structure under pulsed exci-
tation. (b) Single-cavity laser spectrum at 28µW averaged pump
power in a 3.5 ps pulse). At an average pump power
of ?Lin? = 28µW, we observe a lasing mode with a
FWHM of 0.25 nm at 1511 nm (Fig.2(b)).
camera measurement at 30µW indicates a lasing response
with FWHM ∼ 11ps. This is shown in Fig.3(a). We an-
alyze the lasing dynamics using the rate equations model
described in Ref.. Briefly, this model assumes a ho-
mogeneous distribution of carries across the spatial ex-
tent of the PC structure. The carriers are considered
to be either in the ground, the pump, or in the las-
ing level.Using parameters derived from experiment,
together with literature values for the gain and trans-
parency carrier concentration, the model predicts a
cavity photon number Pfit(t) (convolved with the streak
camera response) which is in good agreement with the
experimental data in Fig.3(a).
To estimate the maximum modulation rate of the
single-cavity laser, we excited the structure with a series
of pulses produced with an etalon setup in the excitation
path. A small angle misalignment in the etalon caused
consecutive pulses to walk off from the excitation path,
so that only two pulses are visible in the streak-camera
measurement of the pump (center panel of Fig.3(c)). The
laser is pumped at 1.4 times above the threshold, where
it showed stable operation. The pulse separation shown
is 21ps and represents the smallest pulse separation that
resulted in two clearly distinguishable lasing response
pulses (bottom panel of Fig.3(c)). This pulse repetition
is longer than the sub- 10ps repetition time reported for
GaAs lasers with InGaAs QWs. The laser turn-on de-
lay is τ1= 11 ps for the first pulse and τ2= 9 ps for the
second pulse. To understand the lasing dynamics, we
again model the system with the rate equations model.
The result is shown in the solid curve Pfit(t) and fits the
data well. It is useful to consider the lasing level con-
centration NG(t) predicted by the model; it is plotted in
the top panel of Fig.3(c), normalized by the carrier trans-
parency concentration Ntr∼ 1.5·1018cm−3. The fraction
of carriers that exceeds the transparency value (shaded
region) is efficiently converted to cavity photons during
the lasing process, since the threshold carrier concentra-
tion roughly equals the transparency concentration; the
remainder recombines primarily through nonradiative re-
combination at the photonic crystal hole boundaries,
with a recombination time given by τnr= r/2S, where r
and S are the hole radius and the surface recombination
velocity, respectively[15, 16]. This decay is also visible
in the spontaneous emission tail in the bottom panel of
Fig.3(c). From separate lifetime measurements, we esti-
mate τnr ≈ 270 ps, which gives S ≈ 3 · 104cm/s. This
value is 2-3 times higher than the value of S ∼ 104cm/s
reported elsewhere for this material system[12, 17], prob-
ably due to the processing of the holes. The slower decay
of carriers that remain after the first lasing pulse (roughly
equal to Ntr in the top panel of Fig.3(c)) strongly im-
pacts the dynamics of the second laser pulse, and would
lead to eye-closing under a pseudo-random bit sequence.
Therefore, return-to-zero signaling would be problematic
at a modulation rate exceeding ∼ 1/τNRunless the laser
is pumped far above threshold where the remaining car-
rier concentration Ntrbecomes insignificant. In our sus-
pended structures, thermal problems made it difficult to
achieve stable lasing action above ∼ 1.6 times the thresh-
old power. Heat dissipation can be improved by fabricat-
ing the PC laser structures on top of low-index substrates
such as sapphire or silicon oxide[10, 11, 18, 19, 20].
We next turn to the 9x9 photonic crystal nanocav-
ity array. At a pump power of 2 times above threshold
and below, we measured significantly longer lasing du-
ration. For a pump intensity of 1.4 times above thresh-
old, where we achieved stable operation, we measured
FWHM≈ 19 ps (Fig.3(b)). This longer response time is
not adequately explained by the rate equations model, as
shown in the poor match of the best fit to the data.
255075 100 125
255075 100 125
N (t)/N (model)
FIG. 3: (a) Single-cavity lasing response (dots) and rate equations
fit Pfit. Pump power ?Lin? = 31 µW. All plots are normalized to
the maximum intensity. (b) Coupled-cavity array lasing response
(?Lin? = 1.4× threshold). The rate equations model does not ade-
quately explain the long lasing duration. (c) Single-cavity response
to excitation by two pulses: top, lasing level concentration; center,
measured excitation sequence; bottom, observed intensity and rate
We believe that the poor fit to the rate equations model
arises in large part because it does not account for spatial
variations in the carrier concentration across the photonic
crystal device. It was found previously that the spatial
profile significantly impacts lasing dynamics, for exam-
ple through spatial hole burning, and is important
in understanding lasing threshold. To understand its
role in the laser time response, we have implemented car-
rier dynamics in our finite-difference time domain model.
Such nonlinear FDTD implementations have been used
previously to model the dynamics in PC lasers. Mate-
rial gain is implemented in FDTD by an effective conduc-
tivity σ, as in references [23, 24]. An auxiliary differential
equation is used to describe the evolution of the current
density?J. In turn,?J is related to the carrier density
NG(assumed here to be equal for holes and electrons).
The set of equations obtained when?J = σ?E is substi-
tuted into Maxwell’s equations is then expressed in the
time-domain and discretized as described in .
∆ y /a
∆ y /a
∆ y /a
FIG. 4: (a) Lasing-level carrier concentration (1 ps after injec-
tion) showing density gradient towards lasing cavity. Spatial hole
burning results from the fast stimulated recombination during the
lasing pulse. Pump power is 2 × Ntr at the center of the gaussian
spot with radius 2a, where a is the PC lattice period. (b) Carrier
concentration in PC array, 1 ps after injection. Pump energy cor-
responds to 1.4 × Ntr. Small inhomogeneities in the pump spot
(radius 6a) and coupled cavity mode can result in a spreading of
lasing onset times, contributing to longer total pulse duration. (c)
SEM of single-cavity InP laser structure. (d) Out-of-plane mag-
netic field of lasing mode, 1ps after carrier injection.
A simulation of optical pumping with a gaussian-
shaped beam results in inhomogeneous gain and asyn-
chronous lasing action, spreading out the total pulse du-
ration. This is seen from the lasing level concentration
NGand cavity field in Fig. 4(b,d), recorded here 1ps after
injecting carriers at 1.4 times the transparency concen-
tration in the center. The cavities are in different stages
of the lasing cycle: in some cavities, the gain has already
been used up (dark cavities in (b)), while other cavities
are still at the onset of lasing (bright cavities in (b)). The
corresponding cavity fields are shown in the Bzcompo-
nent of the field in (d).The carrier concentration in
(b) is blurred through carrier diffusion with a ambipolar
diffusion constant of 7cm2/s. As a result of the asyn-
chronous lasing action across the coupled-cavities array,
the nanocavities are not phase-locked together, and the
total response time is broadened. This hypothesis is sup-
ported by the CCD image in Fig.1(b), which shows that
the laser emission at 1.4× threshold is not uniform across
the structure. Experimentally it appears that at higher
pump power, the pulse response becomes shorter; un-
fortunately, the lasing response becomes unstable when
the pump power exceeds roughly 1.4 times the threshold
power, so we were not able to acquire reliable data on the
streak camera, probably due to heating problems. Nev-
ertheless, this observation would support our model, as
all cavities would reach lasing threshold more rapidly.
In conclusion, we have measured time-resolved lasing
action of single and coupled nanocavity lasers in the
InGaAsP/InP material system and emitting near the
telecommunications band. Single-cavity lasers show las-
ing response as fast as 11 ps (FWHM) at 1.5× above
threshold power, but their modulation rate appears ∼ 2×
slower than that of InGaAs/GaAs PC lasers, probably
due to slower nonradiative recombination. The signif-
icantly longer response time of the coupled cavity ar-
ray structure indicates that under excitation with short
pulses, it is difficult to excite the full photonic crystal
structure uniformly to achieve phase-locking across all
nanocavities. This result suggests that large-signal mod-
ulation of the coupled cavity array laser requires atten-
tion to uniform injection current.
This work was supported by the MARCO Interconnect
Focus Center and the NSF.
 Masayuki Fujita, Shigeki Takahashi, Yoshinori Tanaka,
Takashi Asano, and Susumu Noda. Simultaneous Inhibi-
tion and Redistribution of Spontaneous Light Emission in
Photonic Crystals. Science, 308(5726):1296–1298, 2005.
 D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang,
T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuˇ ckovi´ c.
Controlling the Spontaneous Emission Rate of Single
Quantum Dots in a Two-Dimensional Photonic Crystal.
Phys. Rev. Lett., 95:013904, July 2005.
 S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi,
A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff,
and D. Bouwmeester. Self-tuned quantum dot gain in
photonic crystal lasers. Phys. Rev. Lett., 96(12):127404,
 S. Noda, M. Fujita, and T. Asano. Spontaneous-emission
control by photonic crystals and nanocavities. Nature
Photonics, 1:449 – 458, 2007.
 Kengo Nozaki, Shota Kita, and Toshihiko Baba. Room
temperature continuous wave operation and controlled
spontaneous emission in ultrasmall photonic crystal
nanolaser. Opt. Express, 15(12):7506–7514, 2007.
 G. Bjork and Y. Yamamoto. Analysis of semiconductor
microcavity lasers using rate equations. IEEE Journal of
Quantum Electonics, 27(11):2386–96, November 1991.
 D. Englund, H. Altug, I. Fushman, and J. Vuˇ ckovi´ c.
Efficient Terahertz Room-Temperature Photonic Crys-
tal Nanocavity Laser. Appl. Phys. Lett., 91:071126, July
 H. Altug, D. Englund, and J. Vuˇ ckovi´ c. Ultrafast pho-
tonic crystal nanocavity laser. Nature Physics, 2:484–488,
 O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O’Brien,
P.D. Dapkus, and I. Kim. Two-Dimensional Photonic
Band-Gap Defect Mode Laser. Science, 284:1819–1821,
 Jeong-Ki Hwang, Han-Youl Ryu, Dae-Sung Song, Il-
Young Han, Hyun-Woo Song, Hong-Kyu Park, Yong-
Hee Lee, and Dong-Hoon Jang.
triangular-lattice two-dimensional photonic band gap
lasers operating at 1.54 mu m.
 C. Monat, C. Seassal, X. Letartre, P. Viktorovitch,
P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger,
E. Jalaguier, S. Pocas, and B. Aspar. InP 2d photonic
crystal microlasers on silicon wafer: room temperature
operation at 1.55 um. Electronics Letters, 37(12):764–
766, 7 Jun 2001.
 H. Altug and J. Vuˇ ckovi´ c. Photonic crystal nanocavity
array laser. Opt. Express, 13(22):8819–8828, 2005.
 H. Altug. Physics and Applications of Photonic Crystal
Nanocavities. PhD thesis, Stanford University, December
 D. Englund, H. Altug, Bryan Ellis, and J. Vuckovic. Ul-
trafast photonic crystal lasers. Laser & Photonics Re-
views, pages 1863–8880, 2008.
 K. Tai, T. R. Hayes, S. L. McCall, and W. T. Tsang. Op-
tical measurement of surface recombination in InGaAs
quantum well mesa structures.
53(4):302–303, July 1988.
 D. Englund, H. Altug, and J. Vuˇ ckovi´ c. Low-Threshold
Surface-Passivated Photonic Crystal Nanocavity Laser.
Appl. Phys. Lett., 91:071124, July 2007.
 Hiroyuki Ichikawa, Kyoji Inoshita, and Toshihiko Baba.
Reduction in surface recombination of gainasp micro-
columns by ch[sub 4] plasma irradiation. Applied Physics
Letters, 78(15):2119–2121, 2001.
 C.Monat, C.Seassal,
M. Gendry, P. Rojo Romeo, P. Viktorovitch, M. Le Vas-
sor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier,
S. Pocas, and B. Aspar.
shaped microcavities formed in a two-dimensional pho-
tonic crystal on an InP membrane. Journal of Applied
Appl. Phys. Lett.,
Appl. Phys. Lett.,
Physics, 93(1):23–31, 2003.
 G. Vecchi, F. Raineri, I. Sagnes, A. Yacomotti, P. Mon-
nier, T. J. Karle, K.-H. Lee, R. Braive, L. Le Gratiet,
S. Guilet, G. Beaudoin, A. Taneau, S. Bouchoule, A. Lev-
enson, and R. Raj. Continuous-wave operation of pho-
tonic band-edge laser near 1.55 um on silicon wafer. Opt.
Express, 15(12):7551–7556, 2007.
 B. B. Bakir, C. Seassal, X. Letartre, P. Regreny,
M. Gendry, P. Viktorovitch, M. Zussy, L. Di Cioccio, and
J.-M. Fedeli. Room-temperature InAs/InP quantum dots
laser operation based on heterogeneous “2.5 d” photonic
crystal. Opt. Express, 14(20):9269–9276, 2006.
 T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and
F. Koyama. Observation of fast spontaneous emission
decay in gainasp photonic crystal point defect nanocavity
at room temperature. Appl. Phys. Lett., 85(18):3989–
 W. H. Pernice, F. P. Payne, and D. F. Gallagher. Numer-
ical investigation of field enhancement by metal nano-
particles using a hybrid FDTD-PSTD algorithm. Opt.
Express, 15(18):11433–11443, 2007.
 M. Kretschmann and A. A. Maradudin. Lasing action in
waveguide systems and the influence of rough walls. J.
Opt. Soc. Amer. B, Opt. Phys., 21:150158, January 2004.
 S. C. Hagness, R. M. Joseph, and A. Taflove. Subpi-
cosecond electrodynamics of distributed Bragg reflector
microlasers: Results from finite difference time domain
simulations. Radio Sci, 31(4):931941, 1996.
 D. Marshall, A. Miller, and C.C. Button. In-well am-
bipolar diffusion in room-temperature ingaasp multiple
quantum wells. Quantum Electronics, IEEE Journal of,
36(9):1013–1015, Sep 2000.
 L. A. Coldren and S. W. Corzine. Diode Lasers and Pho-
tonic Integrated Circuits. Wiley, New York, 1995.
 Gain is modeled as g(nG)
Va =active material volume, g0 ≈ 1500/cm, group veloc-
ity vg = c/neff,neff = 2.6,Ntr ≈ 1.5 · 1018cm−3(from
); gain confinement factor Γ ≈ 0.159