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Ultrafast photonic crystal nanocavity laser
HATICE ALTUG
1
*, DIRK ENGLUND
1
AND JELENA VU
ˇ
CKOVI
´
C
2
1
Applied Physics Department, Stanford University, Stanford, California 94305, USA
2
Electrical Engineering Department, Stanford University, Stanford, California 94305, USA
*
e-m a il: altug@s tan fo rd .e d u
Published online: 1 July 2006; doi:10.1038/nphys343
Spontaneous emission is not inherent to an emitter, but
rather depends o n its electromagnetic environm ent. In
a microcavity, the spontaneous emission rate can be
greatly enhanced com pared with that in free space. This
so-called Purcell effect can dramatically increase laser
mo d u la tio n spee d s, althoug h to date no time -d o main
measurem ents have demonstrated this. Here we show
extremely fast photonic crystal nanocavity lasers with
response tim es as short as a few picoseconds resulting
from 75-fold spontaneous emission rate enhancement
in th e cavity. We d e mo n s tra te dire c t mod u la tio n spee d s
far exceeding 100 GHz (limited by the detector response
time), alr eady more than an order of magnitude above
the fastest semiconductor lasers. Such ultrafast, efficient,
and compact lasers show great promise for applications in
high-speed comm unications, inform ation processing, and
on-chip optical interconnects.
T
he spontaneous emission (SE) rate in a microcavity is
enhanced by the Purcell factor
1
(F), proportional to the ratio
of the cavity quality factor
(Q) to mode volume (V
mode
).
Until now, the advantages of large SE rate enhancement have
not been fully explored in lasers because of their large mode
volumes. Thus, their SE properties have been dictated by the
intrinsic radiative lifetime of the bulk material. With the recent
advances in semiconductor fabrication and crystal growth, it
has become possible to produce high-quality photonic crystals.
These are structures of alternating refractive index
2,3
that provide
unprecedented control over the electromagnetic environment.
Cavities introduced into the photonic crystal can have extremely
high
Q/V
mode
ratios, and therefore can enable large Purcell
factors. So far, such nanocavities have been used for cavity
quantum electrodynamic (QED) experiments
4–12
such as SE rate
enhancement
4,5,9–11
and suppression
4
, and also for single-photon
sources
4,12
and lower-threshold lasers
13–17
. Here, we demonstrate
extremely fast photonic crystal nanocavity lasers with response
times below the 2 ps detection limit of our measurement apparatus.
The turn-on delay times are measured as near 1 ps, more than an
order of magnitude faster than previous measurements
18,19
.
There are two important laser modulation schemes: small-
and large-signal modulation. We analyse the laser dynamics
by solving the laser rate equations
20
for photon and carrier
densities. Communication systems use both small- and large-
signal modulation
20–22
. In the small-signal regime, the laser is
driven with an above-threshold d.c. pump power
L
in,0
and
modulated with a small time-varying (a.c.) signal
L
in
.The
carrier and photon densities follow the pump with d.c. and a.c.
components
N
0
+ N and P
0
+ P, respectively. The modulation
response is given by
P/N. At low d.c. driving power above
threshold, the bandwidth of the laser is limited by the relaxation
oscillation frequency:
ω
2
R
=
aν
g
P
0
τ
p
+
β
(τ
p
τ
r0
/F)
+
βN
0
(τ
r0
/F)P
0
1
τ
total
−
1
τ
r0
/F
.
(1)
Here, the parameters are as follows: τ
r0
is the intrinsic carrier
radiative lifetime of the bulk material,
a is the differential gain, v
g
is the group velocity, τ
p
(=Q/ω
l
) is the photon lifetime, ω
l
is the
lasing frequency,
β is the SE-coupling factor, τ
nr
is the non-radiative
lifetime, and 1
/τ
total
= F/τ
r0
+ 1/τ
nr
.
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a
b
1 μm
2 μm
Figure 1 Scanning electron micrographs of fabricated structures.
a, Single-defect photonic crystal cavity laser with six PhC confining layers around
the defect. b, Coupled-cavity array laser consisting of a 9 × 9 array in the described
GaAs material system. The periodicity of the holes is fixed at 315 nm, and the hole
radius is tuned from 105 to 130 nm to change the resonance frequency of
the cavities.
In conventional semiconductor lasers, the fraction of
spontaneously emitted photons that is coupled into a single-
cavity mode (denoted by
β) is small due to the small F factor
20
.
Therefore, only the first term in equation (1) is considered
20
.The
standard way to improve modulation bandwidth is to increase the
photon density
(P
0
) with stronger pumping. However, this causes
significant thermal problems and practically limits the modulation
speeds to below 20 GHz (ref.
22). On the other hand, in nanocavity
lasers with large Purcell effect,
β can approach unity while the
intrinsic radiative lifetime is reduced dramatically (that is,
F is
large). This makes the additional terms in (1) significant. Thus,
these cavity-QED effects open a fundamentally new pathway for
improving laser modulation bandwidth
23
.
In the st rong-pumping reg ime, the bandwidth is determined
by the cavity ring-down time
τ
p
. Although the cavity effects
could be increased with higher
Q, the longer photon lifetime
would still limit modulation speeds significantly. For example,
for
Q = 10
6
(τ
p
∼ 50 ps), the modulation speed is only 20 GHz.
Thus, ultrahigh
Q cavities
24
(such as microdiscs) alone cannot
achieve higher modulation speeds. In contrast, photonic crystal
nanocavities enable very large Purcell effects, even with moderate
Q values, because of their ultrasmall cavity mode volumes, below
(l/n) (ref. 3). In our lasers with large Purcell factor, the Q values
can be as small as several thousand, allowing fast cavity ring-down
times
(τ
p
< 1ps).
4
3
2
1
920 930 940 950 960 970
3.0
2.5
2.0
1.5
1.0
0.5
0
900 950 1,000
5
0
Intensity (a.u.)
Intensity (a.u.) Intensity (a.u.)
850 1,050
(nm)
(nm)
1.6
2.5
2.0
1.5
1.0
0.5
0
02040
1.4
1.2
1.0
0.8
0.6
0.4
935 937 939
Averaged P
in
(μW)
P
out
(a.u.)
a
b
λ
(nm)
λ
λ
Figure 2 Spectra of the single-defect photonic crystal laser . a, Spectrum below
lasing threshold. The dashed rectangle indicates the cavity mode, and the inset
shows the lorentzian fit (red) for its Q-factor estimation. b, Spectrum above
threshold. The inset shows the lasing curve, that is, the input pump power versus
output power.
In large-signal modulation, where the laser is turned on and
off completely, our QED-enhanced lasers offer particularly striking
advantages. For this modulation scheme, an important parameter
is the turn-on delay time
18–20
, which is the time delay between the
pump and laser peak responses. Turn-on delay times severely limit
laser speeds. The delay time can be significantly decreased if the
stimulated emission process is faster, w hich can be achieved in a
cavity with large
β value and large SE rate enhancement. Increasing
pump power can also reduce the delay time
18
at the expense of
thermal problems, reduced laser reliability and significant chirp.
This delay time is limited to a few tens of picoseconds in fast
semiconductor lasers
18,19
, but it is reduced more than an order of
magnitude in our QED-enhanced nanocavity lasers even at power
levels near lasing threshold. We have measured delay t imes as small
as 1.5 ps for pump powers only 1.3 times above lasing threshold.
Besides the dramatically enhanced small- and large-signal
modulation speeds, the QED-enhanced lasers can also significantly
improve power consumption
13–17,23
and associated thermal
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4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0
0.2
0
20
40
60
80
100
120
140
160
500 1,000 1,5000 880 900 920 940 960 980 20 40 60 80 100 120 1402,000
Time (ps) (nm)
0 160
Time (ps)
4.5
0
Intensity (a.u.)
Intensity (a.u.)
Time (ps)
Coupled
Uncoupled
coupled
~17 ps
bulk
~640 ps
uncoupled
~31 ps
a
b
c
τ
τ
τ
λ
Figure 3 Time-resolved photolum inescence decay curves measured by streak camera. a,FortheIn
02
Ga
0.8
As MQW structure in bulk (unpatterned MQW region) with an
exponential fit (red). b, For the photonic crystal coupled-cavity array laser below lasing threshold. The lobes at the longer (943 nm) and shorter (925 nm) wavelengths
correspond to coupled and uncoupled carriers to the cavity mode, respectively. c, The decay curves of carriers shown with dashed rectangles in b with exponential fits.
problems. The large β reduces the threshold power of the laser
23
.
In addition, the use of small mode volume cavities increases the
photon density, so the modulation speed can be increased without
increasing the pump power.
Our nanocavity laser is based on a 2D photonic crystal
slab patterned with a square lattice. Lattice defects in the form
of missing holes act as cavities to confine light. Both single-
and coupled-nanocavity array structures
25,26
are fabricated on a
172-nm-thick GaAs layer by a combination of electron beam
lithography, and dry and wet etching
4
(Fig. 1). The slab contains
a gain medium consisting of four 8-nm In
0.2
Ga
0.8
As multiple
quantum wells (MQW) separated by 8-nm GaAs barriers.
The lasers are optically pumped by 170-fs short pulses with
a repetition rate at 80 MHz and wavelength centred at 750 nm
using a confocal microscope
4
. The spectrum and time response
of the PhC lasers are measured with a spectrometer and a streak
camera, respectively. The streak-camera time response is limited to
3–4 ps linewidth, as measured with a 170-fs laser pulse. Because
the spectral response of the streak camera drops rapidly below
950 nm, we chose the GaAs-based laser material system. At room
temperature, the peak photoluminescence emission wavelength of
the quantum wells is at 980 nm. We cooled the sample in a cryostat
to 7–150 K to improve overlap between the cavity resonances and
the MQW gain. The cooling also improved heat dissipation from
the photonic crystal membranes, although we also observed high-
speed lasing at room temperature at lower repetition rates.
We observed single-mode lasing from both single- and
coupled-cavity array st ructures. Figure 2 shows the single-cavity
spectra below and above threshold. The below-threshold spectrum
indicates a
Q value of 1,200 from a lorentzian fit (Fig. 2a, inset).
The resonant mode has dipole polarization symmetry. Its mode
volume is calculated as 0
.55 (l/n)
3
. The same set of measurements
on coupled-cavity array structures yielded
Q values near 900. From
their threshold ratio, we estimate the mode volume of coupled-
cavity array laser to be nearly 10 times larger than that of single
cavity
26
. Therefore single cavities, by having larger Q/V
mode
ratios,
should achieve much larger Purcell factors.
To estimate the cavity Purcell factor
F, we measured the decay
rates of the carr i ers in the bulk (unpatterned MQW region) and in
the photonic crystal for cavity-coupled and uncoupled cases. These
rates obey the following equations:
1
τ
bulk
=
1
τ
r0
+
1
τ
bulk,nr
;
1
τ
coupled
=
F
τ
r0
+
1
τ
PhC,nr
;
1
τ
uncoupled
=
1
τ
r0
+
1
τ
PhC,nr
. (2)
We estimate the decay times for the cavity array structure from
Fig. 3. The radiative bulk carrier lifetime
(τ
r0
) is at least 640 ps
(Fig. 3a). For bulk, we can neglect non-radiative processes
(τ
bulk,nr
)
as they are much slower than the radiative processes. The radiative
decay rates for cavity-coupled and uncoupled carrier emission
in the PhC-patterned region are
τ
coupled
∼ 17 ps and τ
uncoupled
∼
31 ps (Fig. 3b,c). Uncoupled emission is faster than bulk carrier
lifetime because of the increased non-radiative recombination rate
(1/τ
PhC,nr
) owing to the enhanced surface recombination in the
patterned structures. The cavity-coupled emission is even faster
as the Purcell-enhanced radiative emission rate
(F/τ
r0
) outpaces
non-radiative recombination. By solving (2) with these measured
values, we estimated the in-plane-averaged SE rate enhancement
(F) for the cavity array structure to be 17. The inclusion of SE rate
suppression
4
of uncoupled carriers in photonic crystal (which is
neglected here) will further increase
F. Such high Purcell factors
in coupled array lasers enable both fast laser response, as well as
high output powers with single-mode operation
26
. Repeating these
measurements for the single-defect cavity, we obtained
τ
coupled
∼
6.7ps,τ
uncoupled
∼ 33 ps, and in-plane-averaged F as 76. The hig h
Purcell factor for single cavities
4
is not surprising as they are
expected to have a maximum
F of 165 for the cavity with this set
of
Q and V
mode
.
Above lasing threshold, the decay time is reduced another
order of magnitude due to stimulated emission. Figure 4a,b shows
the time data for the single-defect cavity and coupled-cavity
array lasers, respectively. The decays for both lasers are fitted
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Time (ps)
Time (ps)
Time (ps)
Intensity (a.u.) Intensity (a.u.)
Intensity (a.u.)
Pump laser
PhC laser
0 5.0 10.0 15.02.5 7.5 12.5 0 5.0 10.0 15.02.5 7.5 12.5
0
0.2
0.4
0.6
0.8
1.0
1.2
0
0.5
1.0
1.5
2.0
2.5
Photon number (a.u.)
0.2
0.4
0.6
0.8
1.0
1.4
1.2
0
0 5 10 15 20 25
Time (ps)
24681012140
0
0.2
0.4
0.6
0.8
1.0
1.2
single
~ 2.13 ps
delay
~ 1.5 ps
coupled array
~ 2.18 ps
a
b
c
d
τ
τ
τ
Laser response
Convolved response
Figure 4 Response of photonic crystal laser . Decay rates above lasing threshold. a,b, Time response (blue) of a single-defect cavity (a) and coupled-cavity array (b) laser at
7 K with an exponential fit (red). c, Delay-time measurement of a single cavity laser (blue) with respect to pump laser (red). The cryostat temperature was raised from 7 to
100 K to increase the relaxation rate of carriers from upper quantum-well levels to the lowest level by increasing phonon population. At 7 K, the delay time wa s 3–4 ps,
whereas at 100 K, the delay time decreased to 1.5 ps. d, Simulated photon number as a function of time for a single-defect cavity laser (red line). The simulation result is
convolved with a gaussian of 4-ps width (blue line) to take into account streak-cam era response.
by exponentials with a decay constant of 2 ps. To understand
the dynamics, we used the laser rate equations to simulate the
photon and carrier densities as functions of time. Initially, the
photon and carrier densities are taken as zero and above the
transparency condition, respectively. The simulated photon density
is also convolved with a gaussian of 4-ps width to take into
account streak-camera response. The simulation results are shown
in Fig. 4d. The bare photon response (unconvolved data) shows
that when the laser is pumped above threshold, the photon density
decays with the cavity decay time
(τ
p
). For both the single- and
coupled-cavit y arr ay lasers, this is 0.5 ps (for
Q of 1,000), which
is below the resolution limit of our streak camera. The convolved
photon response shows a decay time of 2 ps, which agrees well with
our experimental results.
As we indicated above, an important parameter in this type of
laser modulation scheme is the delay time, which decreases in high
Purcell-factor cavities. We measured this delay time at 100 K (with
890-nm pump wavelength) as 1.5 ps (shown in Fig. 4c), close to the
streak-camera resolution limit. The delay time is nearly two orders
of magnitude shorter than the previous measurements
18,19
.
These results already show that single-defect cavity and
coupled-cavity array lasers, with
τ
p
near 0.5 ps and delay time
of 1 ps, can be modulated at rates approaching THz. To further
demonstrate high-speed characteristics, we directly modulate
single-defect cavity lasers at very high speeds by pumping w ith
a series of femtosecond pulses that we generate using a Fabry–
Perot etalon. The spacing of the pulse train is controlled by the
mirror separation. Only the first three pump pulses have sufficient
power to turn on the nanocavity laser. Figure 5 shows the results
for the direct modulation of a nanocavity laser above 100 GHz.
The response of the laser nicely follows the pump, whose peaks
are separated by
∼9 ± 0.5 ps (a slight non-periodicity in the time
separation between the consecutive pump pulses results from
slight angular deviations of consecutive pulses from the etalon).
This modulation speed is already an order of magnitude higher
than the fastest semiconductor lasers reported to date. The figure
also shows the laser response to a 15-ps-repetition pump, where
the streak-camera resolution more clearly separates the pulses.
For practical applications, electrical pumping will be important.
Recently, electrical pumping of the nanocavity lasers has been
demonstrated
15
. For high-speed electrical modulation, the RC time
constants of the lasers have to be small enough, where
C and R
are the capacitance and resistance of the laser. We belie ve that very
fast electrical pumping of nanocavity lasers is possible, as a recent
experiment achieved time constants below 10 ps using micron-scale
contacts with sub-fF capacitance
27
. In addition, photonic crystal
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Time (ps)
Wavelength
Intensity of PhC laser
Intensity of pump laser
Time (ps)
0
10
20
30
40
50
60
70
0 5 10 15 20 25 30 35 40
a
b
(i)
(ii)
Figure 5 Direct modulation of a single-defect photonic crystal nanocavity laser.
a, The direct modulation was carried out with the repetition periods of 9 ± 0.5ps(i)
and 15 ps (ii). b, A series of femtosecond pump pulses separated by 9 ± 0.5ps
(usedtopumpiina), obtained by an etalon. The transmitted power of consecutive
pulses from the etalon drops geometrically with the ratio R
1
R
2
of the mirror
reflectivities. Only the first three pump pulses had sufficient power to turn on the
laser. Both the femtosecond pump pulses and the laser output pulses are broader as
a result of the slow response time of the streak camera.
nanocavity lasers do not require highly resistive Bragg mirror layers,
which also limit electrical modulation speeds in fast vertical cavity
surface-emitting lasers.
These novel types of nanocavity lasers, built to exploit cavity-
QED effects for high speed and lower pump power, could lead to a
new generation of lasers with applications in communications and
computing. The easy integrability of nanocavity lasers with other
photonic components, such as with photonic crystal waveguides,
also promises to advance photonic integrated circuits significantly.
Received 24 April 2006; accepted 1 June 2006; published 1 July 2006.
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Acknowledgements
This work has been supported by the MARCO IFC Center, NSF Grant Nos ECS-0424080 and
ECS-0421483, the MURI Center for Photonic Quantum Information Systems (ARO/DTO Program
No. DAAD19-03-1-0199), as well as Intel (H.A.) and NDSEG (D.E.) Fellowships.
Correspondence and requests for materials should be addressed to H.A.
Competing financial interests
The authors declare that they have no competing financial interests.
Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/
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