Photonic crystal nanocavity laser in an optically
very thick slab
Se-Heon Kim,
1,2,
* Jingqing Huang,
1,2
and Axel Scherer
1,2
1
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125, USA
2
Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
*Corresponding author: seheon@caltech.edu
Received November 15, 2011; accepted December 9, 2011;
posted December 15, 2011 (Doc. ID 158271); published February 6, 2012
A photonic crystal (PhC) nanocavity formed in an optically
very thick
slab can support reasonably high-
Q
modes for
lasing. Experimentally, we demonstrate room-temperature pulsed lasing operation from the PhC dipole mode emit-
ting at 1324 nm, which is fabricated in an InGaAsP slab with thickness (
T
) of 606 nm. Numerical simulation reveals
that when
T
≥
800
nm
, over 90% of the laser output power couples to the PhC slab modes, suggesting a new route
toward an efficient in-plane laser for photonic integrated circuits. © 2012 Optical Society of America
OCIS codes:
230.5298, 250.5960.
An optically
thin
dielectric slab with photonic crystal
(PhC) air holes has been a versatile platform for design-
ing various high-
Q
cavities [
1
]. Thickness (
T
) of the PhC
slab is often chosen to maximize the size of the photonic
band gap (PBG) [
2
], which is approximately equal to half
the effective wavelength of the cavity resonance. For de-
signing a PhC slab laser emitting at 1.3
μ
m, this thickness
consideration requires that
T
should be about 250 nm.
In this Letter, we show that even a
very thick
slab can
support sufficiently high-
Q
cavity modes for lasing. Once
we are free from the thickness constraint, design of a cur-
rent-injection type laser becomes more feasible; we can
employ a vertically varying p-i-n structure along with a
current confinement aperture, as has been done for ver-
tical-cavity surface-emitting lasers [
3
]. Furthermore, as
will be shown below, we can build an efficient
in-plane
emitting laser, where most of the laser emission couples
to the two-dimensional (2D) Bloch modes [
2
] in the
PhC slab.
We begin with numerical simulations using the finite-
difference time-domain (FDTD) method. We adopt the
widely used modified single-cell cavity design [
4
] and in-
vestigate the PhC dipole mode as shown in Fig.
1
.We
assume
T
and the lattice constant (
a
) are 2000 and
305 nm, respectively. The refractive index of the slab
is assumed to be 3.4. Other structural parameters are
as follows [
4
]: the background hole radius
R
0
.
35
a
,
the modified hole radius
Rm
0
.
25
a
, and the hole ra-
dius perturbation
Rp
0
.
05
a
. It should be noted that
the in-plane PBG [
2
] is completely closed at
T
≈
1
.
5
a
for a PhC slab with
R
0
.
35
a
. However, it is interesting
that we can still find several resonant modes that seem to
be well confined within the defect region, as shown in
Figs.
1(b),(c)
. In fact, these modes have the same
trans-
verse
mode profile, while the number of intensity lobes
along the
z
direction varies from one to three. Therefore,
these modes originate from the slab resonance between
the top and bottom surfaces, which can act as reflectors
due to the relatively high refractive index of the slab. We
summarize various optical characteristics of the dipole
modes in a slab with
T
2
;
000
nm, including
Q
, emis-
sion wavelength
λ
, and mode volume
V
, in Table
1
[
4
].
In particular,
Q
tot
[
5
] of the fundamental mode is over
5000. It should be noted that a similar thick slab design
was proposed by Tandaechanurat
et al.
with a special
focus on a PhC cavity in a
T
1
.
4
a
slab [
6
].
To gain further insight into the loss mechanism, in
Fig.
2
, we calculate
Q
tot
,
Q
vert
, and
Q
horz
[
1
,
5
] as a function
of
T
, where
a
is varied to keep the emission wavelength
at 1.3
μ
m. First, let us focus on
Q
vert
. In the case of a
thin
slab PhC cavity,
Q
vert
depends strongly on
Rm
and
Rp
[
7
]
and the
Q
vert
of the dipole mode can be as high as
∼
15
;
000
[
4
]. Indeed, when
T
≤
400
nm,
Q
vert
is in the
range of 10,000. However, when
T
≥
500
nm,
Q
vert
in-
creases almost exponentially as
T
increases. We obtain
a surprisingly high
Q
vert
of
6
×
10
5
at
T
2
;
000
nm, im-
plying the existence of a certain highly efficient vertical
confinement mechanism, which will be clarified later. On
the other hand, the in-plane confinement mechanism is
not very effective, as expected, because the PBG is
closed for
T>
∼
450
nm. However,
Q
horz
can be brought
up to
∼
5500
at
T
2
;
000
nm, and
Q
tot
is usually limited
by
Q
horz
at large
T
. This large difference between
Q
vert
Fig. 1. (Color online) (a) Design of the modified dipole cavity,
(b), (c) FDTD simulations for the dipole mode in a PhC slab
with
T
2
;
000
nm: (b) top-down view of the electric-field in-
tensity (
j
E
j
2
) profile and (c) cross-sectional views of
j
E
j
2
of the
fundamental, first-order, and second-order slab modes.
488 OPTICS LETTERS / Vol. 37, No. 4 / February 15, 2012
0146-9592/12/040488-03$15.00/0
© 2012 Optical Society of America
and
Q
horz
implies that most of the photons generated
inside the cavity will leak into the PhC slab; at
T
2
;
000
nm, over 99% (horizontal emission efficiency,
η
horz
1
−
Q
tot
∕
Q
vert
) of the total number of photons will
be funneled through the PhC slab.
η
horz
is over 90% when
T
≥
800
nm. This behavior is completely opposite to the
case of a
thin
slab cavity, where
Q
horz
can increase inde-
finitely by simply adding more layers of PhC barriers;
therefore,
Q
tot
is limited by
Q
vert
.
To better understand the highly effective vertical con-
finement mechanism, let us now consider a hypothetical
PhC slab cavity with
T
∞
. The resulting structure may
be viewed as a PhC fiber [
8
], and thus one can define a
waveguide dispersion in the
z
direction. In Fig.
3(a)
,we
show the waveguide dispersion of the dipole mode. It
should be noted that these modes are not PBG-guided
except for the
k
z
0
point, because a nonzero wave vec-
tor (
k
z
>
0
) breaks the TE/TM symmetry, and the original
2D PhC structure with
R
0
.
35
a
cannot have a complete
PBG for both TE and TM [
8
]. Thus, the guided modes
with
k
z
>
0
are
inherently
lossy. Now we will show that
the observed three resonant modes in Fig.
1(c)
originate
from these guided modes. In Fig.
3(a)
, we show intersec-
tion points between the dispersion curve and the three
normalized frequencies (
ω
n
a
∕
λ
) of the resonant
modes. We find that these points are almost equally
arranged in the
k
space, where
Δ
k
z
indeed satisfies
the Fabry
–
Perot resonance condition,
Δ
k
z
π
∕
T
;
Δ
k
z
∕
2
π
∕
a
a
∕
2
T
≈
0
.
076
[
9
]. Note that the group velocity
(
V
g
≡
d
ω
∕
dk
) of the fundamental dipole mode will ap-
proach zero as
T
→
∞
and
k
z
→
0
[See Fig.
3(b)
].
In view of this waveguide model, the
Q
tot
of the funda-
mental dipole mode can be written as the sum of wave-
guide propagation loss and scattering loss at the two
mirror facets such that [
9
,
10
]
1
Q
tot
V
g
ω
α
1
T
log
1
r
2
0
:
(1)
Here,
ω
is the angular frequency of the resonant mode
and
α
is the waveguide propagation loss coefficient [
11
]
describing the imperfect horizontal photon confinement
due to both the finite
x
–
y
domain size and coupling into
the higher-order slab modes [
2
]. As shown in Fig.
3(b)
,
α
varies as a function of
k
z
; it tends to diverge as
k
z
→
0
due
to the presence of a zero group velocity at
k
z
0
[
12
].
r
0
is a reflection coefficient, and
1
∕
T
log
1
∕
r
2
0
describes
the scattering loss at the two mirror facets. Thus,
V
g
α
∕
ω
and
V
g
log
1
∕
r
2
0
∕
T
ω
can be rewritten as
1
∕
Q
horz
and
1
∕
Q
vert
, respectively [
5
]. Now it is straightforward to
show that the
Q
vert
of the fundamental slab mode will
grow indefinitely as
T
→
∞
and
V
g
→
0
. The fact that
the slow group velocity can enhance the
Q
of a resonant
mode has been emphasized by Kim
et al.
[
9
], who ana-
lyzed the ultra-high-
Q
mode in a PhC linear cavity, and
by Ibanescu
et al.
[
13
], who used the anomalous zero
group velocity point in an axially uniform waveguide to
design a high-
Q
∕
V
cavity on a dielectric substrate. How-
ever,
Q
horz
will be bound by a finite value as
k
z
→
0
;
Q
horz
will approach the
Q
of an ideal 2D dipole cavity (TE
mode). Therefore, this simple analysis based on wave-
guide dispersion can explain major features in
Q
behav-
ior observed in Fig.
2
.
In our experiment, PhC dipole mode cavities are fabri-
cated in an InGaAsP slab with
T
606
nm. Seven 60 Å
thick compressive-strained (1.0%) InGaAsP quantum
wells emitting near 1.3
μ
m are embedded at the center
Table 1. Optical Properties of the Higher-Order Slab
Modes
λ
(nm)
Q
tot
Q
vert
V
λ
∕
n
3
Fundamental
1324
5392
6
.
5
×
10
5
2.45
First order
1305
1582
41,600
2.65
Second order
1275
755
27,900
2.86
Fig. 2. (Color online)
Q
of the fundamental dipole mode as a
function of slab thickness, where we fix the
x
–
y
simulation
domain size to be
16
a
×
16
a
.
Fig. 3. (Color online) (a) Waveguide dispersion along the
z
direction for the dipole mode. The normalized frequencies of the three
dipole resonant modes shown in Fig.
1(c)
are overlaid on the dispersion curve. (b) Group velocity (
V
g
) and waveguide propagation
loss coefficient,
α
, simulated by FDTD.
V
g
and
α
are normalized by
c
(speed of light) and
2
π
∕
a
, respectively.
February 15, 2012 / Vol. 37, No. 4 / OPTICS LETTERS 489
of the slab, with 120 Å thick tensile-strained (
−
0
.
3
%
)
1.12
μ
m InGaAsP barriers in between. 240 nm thick un-
strained 1.12
μ
m InGaAsP is on the top and bottom of
the active layer and serves as a cladding. We use standard
nanofabrication processes including electron-beam litho-
graphy (using hydrogen silsesquioxane as the resist), dry
etching to drill the PhC air holes, and selective wet-
chemical etching to undercut the InP sacrificial layer.
To define deep and vertical air holes, we use high-
temperature (190 °C) Ar
∕
Cl
2
chemically assisted ion-
beam etching (CAIBE). As shown in Figs.
4(a)
and
(b)
,
our optimized CAIBE system produces very deep
(
>
3
μ
m) and vertical sidewalls, which are requisites to
experimentally realize a theoretical
Q
tot
of
2000
–
3000
.
Figs.
4(b)
and
(c)
show scanning electron microscope
(SEM) images of fabricated laser devices.
The fabricated lasers are photopumped at room tem-
perature with an 830 nm laser diode. The repetition rate
of the pump laser is 1 MHz with a duty cycle of 2%. We
use a
100
× objective lens to focus the pump laser on to
the cavity region. The same objective lens is used to col-
lect the emitted laser light, which is fed into an optical
spectrum analyzer. In Fig.
4(d)
, we present a light-in ver-
sus light-out (
L-L
) curve and a lasing spectrum for one
example laser device. We confirm that the laser emission
indeed comes from one of the degeneracy-split dipole
modes [
1
] by comparing the emission wavelength
(1323.7 nm) with that obtained by FDTD simulation.
Assuming that about 20% of the actual incident pump
power is absorbed in the slab, the effective threshold
peak pump power is estimated to be 78
μ
W.
Though the present work merely demonstrates an op-
tically pumped device, it is our hope that the thick slab
PhC cavity design will provide versatile routes toward a
current-injection PhC laser. One feasible plan is to place
the whole PhC slab cavity onto a metal substrate, where
the metal may serve as both an electrical current path-
way and a heat sink [
14
]. An alternative is to take advan-
tage of the increased slab thickness, which enables more
flexible design of the p-i-n doped layers and a current
aperture structure.
The authors would like to acknowledge support from
the Defense Advanced Research Projects Agency under
the Nanoscale Architecture for Coherent Hyperoptical
Sources program under grant #W911NF-07-1-0277 and
from the National Science Foundation through NSF
CIAN ERC under grant #EEC-0812072.
References and Notes
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Q
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U
t
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exp
−
ω
t
∕
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(
∼
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∕
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tot
) can be decomposed into power radiated into the
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∼
1
∕
Q
horz
) and power radiated in the out-of plane
direction (
∼
1
∕
Q
vert
); therefore,
1
∕
Q
tot
1
∕
Q
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1
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Fig. 4. (Color online) (a)
–
(c) SEM images of PhC dipole lasers
formed in a 606 nm InGaAsP slab. (a) Our dry-etching capability
enables very deep (
>
3
μ
m) and vertical etching; (b) a tilted im-
age taken after selective wet-chemical etching; (c) a top view of
the fabricated laser device. (d) Characteristics of the laser
device.
490 OPTICS LETTERS / Vol. 37, No. 4 / February 15, 2012