arXiv:physics/0610105v1 [physics.optics] 13 Oct 2006
Efficient Photonic Crystal Cavity-Waveguide Couplers
Andrei Faraon, Dirk Englund, Ilya Fushman, Jelena Vuˇ ckovi´ c
E. L. Ginzton Laboratory, Stanford University, Stanford, CA, 94305
Department of Electrical and Computer Engineering,
University of Maryland, College Park, MD, 20742
(Dated: October 12, 2006)
Coupling of photonic crystal (PC) linear three-hole defect cavities (L3) to PC waveguides is
theoretically and experimentally investigated. The systems are designed to increase the overlap
between the evanescent cavity field and the waveguide mode, and to operate in the linear dispersion
region of the waveguide. Our simulations indicate increased coupling when the cavity is tilted by
60owith respect to the waveguide axis, which we have also confirmed by experiments. We obtained
up to 90% coupling efficiency into the waveguide.
Structures that consist of InGaAs/GaAs quantum
dots (QDs) coupled to two-dimensional PC cavities are
promising candidates for highly efficient single photon
sources. They represent essential devices for quantum
cryptography and quantum computation [1, 2, 3, 4].
Efficient implementation of quantum computation de-
vices requires integration of photonic circuits directly
on the chip. These circuits consist of single photon
sources (SPSs) that inject single photons into the waveg-
uides, which subsequently redirect them to other quan-
tum nodes, i.e. other PC cavities containing QDs. Once
the necessary quantum operations have been performed,
photons need to be outcoupled from the waveguide ei-
ther out-of-plane for vertical collection (e.g., by coupling
the photons back into an “output cavity” that scatters
them out of plane), or collected in the PC plane (e.g., by
outcoupling to a fiber). The performance of this kind of
circuit is limited by the coupling efficiency between the
cavities and the waveguides. Our work investigates this
coupling with the goal of improving the efficiency of sin-
gle photon transmission from one cavity to another. The
results are also relevant for channel drop filter applica-
tions in optical telecommunications.
In this paper we investigate the coupling of linear
three-hole cavities (L3)  into PC waveguides.
choose the L3 cavities for their high quality factor(Q) to
mode volume (V) ratio and good matching between cav-
ity and waveguide field patterns, which improves in-plane
coupling efficiency [6, 7]. The cavity mode we work with
has magnetic field with even/odd symmetry with respect
to the x/y axes. This mode, whose magnetic field con-
figuration is depicted in Fig. 1(a), needs to be coupled to
one of the guided modes in the PC waveguide. The field is
computed using three-dimensional finite difference time
domain simulations (3D FDTD). Of the possible waveg-
uide bands inside the PC band gap  the best choice for
coupling the L3 cavity is the one with similar symmetry
and frequency as the L3 cavity mode (Fig. 1(b)). To
get efficient coupling, the cavity and waveguide modes
need to be spatially overlapped and frequency matched.
A closer look at the L3 cavity field profile (Fig. 1(a))
reveals that the evanescent field is strongest along a di-
rection tilted with respect to the cavity axis and is weak
along the cavity axis. A good approach for obtaining a
larger overlap between the cavity and waveguide mode is
to tilt the cavity with respect to the waveguide axis by
an angle of 60o(Fig. 1(c)). The choice of this angle is de-
termined by the symmetry constraints of the triangular
lattice. Directional couplers with cavity axes non-parallel
to waveguide axes have recently been studied by Kim et
al  for coupling the hexapole modes of single hole de-
fect cavities and by Shinya et al for coupling L3 and L4
cavities . In contrast with previous work, we present
here optimized designs of couplers as well as detailed the-
oretical and experimental data, confirming the advantage
of the tilted configuration for coupling L3 cavities to PC
FIG. 1: (a) Magnetic field (Bz component) for the mode with
the highest quality factor in a L3 cavity. (b) Magnetic field
pattern of the even mode in a PC waveguide. (c) Fabricated
tilted cavity coupled to a waveguide (four holes separation).
In this experiment we shift the cavity with respect to the
waveguide along the direction indicated by the arrow. (d)
Fabricated straight cavity coupled to a waveguide (three holes
To test the validity of our approach, we compare the
coupling parameters for the tilted cavity configuration
(Fig. 1(c)) to the standard approach where the cavity
and the waveguide share the same axis (straight cavity
configuration) (Fig. 1(d)). First, 3D FDTD simulations
of coupled cavity waveguide systems were performed with
both tilted and straight couplers. The frequency of the
waveguide band was lowered with respect to the cav-
ity frequency by reducing the size of the PC holes that
bound the waveguide. In this way, coupling occurs in the
dispersion-free linear region of the waveguide band. We
directly simulated tilted and straight coupler configura-
tions with spacing of two-to-five lattice holes separation
between the cavity and the waveguide. An image of the
simulated magnetic field profile for a tilted cavity coupled
to a waveguide with three-hole separation is depicted in
Fig. 2(inset) . In the tilted configuration, the separation
between the cavity and the waveguide is changed along
a direction indicated by the arrow in Fig. 1(c).
pling expressed in terms of the quality factor. The coupling
strength is proportional to (1/Qwg).
field of a cavity-waveguide coupler in tilted configuration with
three hole separation (inset).
Simulation results for the cavity waveguide cou-
The energy transfer into the waveguide degrades the
Q of the coupled cavity. The total Q of a coupled cav-
ity relates to the uncoupled cavity quality factor (Qc)
Qtot−1= Qc−1+ Qwg−1, (1)
Different applications require different coupling. For
high-efficiency single photon transfer, the in-plane cou-
pling into the waveguide modes needs to be dominant
so Qwg should be lower than Qc. On the other hand,
the advanced single photon sources  require cavities
with a quality factor on the order of thousands, which
implies Qwgshould also be in the same range. For other
applications, single photons need to be scattered out of
plane from a PC waveguide through an output cavity. To
achieve high transfer efficiency from waveguides to the
output cavities, the cavity-waveguide system needs to be
wgis the loss rate into the waveguide.
in the critical coupling regime defined by Qwg= Qc. In
that case, we do not need the output cavity to have a
high quality factor.
The coupling strength between the cavity and the
waveguide is given by 1/Qwgwhich is proportional to the
decay rate of the cavity field into the waveguide. The
quality factor Qwg was computed from the 3D FDTD
simulations, with results presented in Fig.
the same cavity-waveguide separation, Qwg is generally
smaller for the tilted than for the straight configuration.
This is an indication of better cavity-waveguide coupling
obtained by tilting the cavity. One peculiar aspect of the
simulations is that for the tilted coupling configuration,
the Q is actually larger for four-holes than for five-holes
separation. This is unexpected because it is natural to
assume that reducing the distance between the cavity and
waveguide should improve the overlap integral between
the two modes. However, this increase in the quality
factor is observed under a large variety of different simu-
lation parameters, suggesting that it is real, as opposed
to a simulation artifact. We suspect that, at four hole
separation, the anti-node of one of the modes overlaps
with the node of the other resulting in an lower over-
lap integral. Further investigation is required in order to
conclusively confirm this.
The coupling changes from Qwg ≈ 500 for the tilted
cavity with two-hole separation to Qwg≈ 106for four and
five-holes separation (both configurations).
photon sources based on PC cavities with InGaAs QDs
operating at 900nm− 1000nm, the experimental out-of-
plane quality factor is limited to about Qc = 104be-
cause of material loss and fabrication imperfections .
On the other hand, to get efficient photon transfer into
the waveguide, Qwgneeds to be lower than Qctherefore,
only the coupling configurations with two- and three-hole
separation represent good options. Experimentally we
expect the total Q to be independent of the waveguide
coupling in the case of four and five holes separation.
To test the validity of our simulation results, the cou-
plers were fabricated on a 165 nm thick freestanding
GaAs membrane containing a InGaAs QD layer. Struc-
tures with two- to five-hole separation in both tilted and
straight configuration (Fig. 1(c, d)) were fabricated. We
made seven structures of each kind. The spectrum of
each cavity was measured using the InGaAs QDs embed-
ded in the GaAs membrane as an internal light source.
The fabrication and measurement procedures are similar
with those reported in . The mean value of the qual-
ity factor for each configuration is plotted in Fig. 3(a),
where the error bars are given by the standard deviation
in Q due to fabrication fluctuations between the seven
structures of each kind.
As expected from simulations, the experimental data
show that for the same cavity-waveguide separation, the
total quality factor is lower for the tilted than for the
straight configuration. This result is a consequence of
higher coupling for tilted cavities.
Since a more efficient coupling between the cavity and
data for cavity-waveguide couplers. (a) The measured value
of total Q (mean) (b) The value of Q inferred from simula-
tions by combining simulated Qwg and measured Qc. (c) The
coupling efficiency from the PC cavity into the PC waveguide.
(d) Measured spectrum of a closed waveguide coupled to a L3
cavity. The Fabry-Perot fringes are equidistant in the linear
region of the waveguide dispersion relation (where the cav-
ity is also located) and they get closer next to the waveguide
Comparison between simulations and experimental
the waveguide degrades the cavity quality factor, when
designing a PC network one should choose the configu-
ration that gives the optimum trade-off between transfer
efficiency and high Q. One advantage of using the tilted
cavity is that the same set of parameters can be obtained
with the cavity further spaced from the waveguide.
As mentioned before, the cavity coupling was designed
to couple in the linear region of the waveguide-band
dispersion relation. To test the position of the cav-
ity with respect to the waveguide band, we fabricated
longer waveguides closed at the ends. These waveguides
act as Fabry-Perot resonators. Fringes can be observed
using the broad distribution of the QDs .
linear region of the dispersion relation the fringes are
equally spaced, and get closer together as the frequency
approaches the band edge. Since the cavity resonance
was positioned in the region with equidistant fringes, we
concluded that the coupling occurs in the linear region
For a direct comparison between simulation and ex-
periment, Qcof the uncoupled cavity needs to be known.
The upper bound for Qcis limited by fabrication imper-
fections and material loss. Our simulation results indi-
cate that in the case of coupled cavities with four hole
separation the coupling into the waveguide is very small
so the total Q is well approximated by Qc. For this rea-
son, the average value of the measured Q for the tilted
configuration with four hole separation was used as Qc.
By plugging Qcand the simulated value for Qwginto ex-
pression (1), the predicted value for the total Q (Qtot)
was computed. The values for the Q inferred from simu-
lations are plotted in Fig. 3(b) and show good agreement
with the experimental data (Fig. 3(a)). Some incon-
sistency is observed in the case of five-hole separation.
These inconsistencies result from fabrication errors.
The coupling efficiency into the waveguide was com-
puted by taking the ratio Q/Qwg and the results are
plotted in Fig. 3(c). The coupling efficiency is up to
90% in the case of tilted configuration with two holes
separation and up to 40% for straight configuration with
two holes separation.
In conclusion we have designed PC cavity-waveguide
couplers with optimized coupling efficiency and operating
in the linear waveguide dispersion region. We have shown
both theoretically and experimentally that the coupling
between a L3 PC cavity and PC waveguides can be im-
proved by tilting the cavity with respect to the waveg-
uide. The coupling is more efficient because the evanes-
cent tails of the cavity field are not oriented along the
cavity axis but at a 30oangle. Understanding and con-
trolling the coupling mechanism is essential for on-chip
single photon transfer and the implementation of on-chip
Financial support was provided by the MURI Center
for photonic quantum information systems (ARO/DTO
program No. DAAD19-03-1-0199), ONR Young Investi-
gator Award and NSF Grant No. CCF-0507295.
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