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 60 degrees with respect to the waveguide axis, which we have also
confirmed by experiments. We obtained up to 90% coupling efficiency into the
waveguide

Englund, Dirk

Faraon, Andrei

Fushman, Ilya

Vuckovic, Jelena

Waks, Edo

English

arXiv

Coupling of photonic crystal (PC) linear three-hole defect cavities 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. The simulations indicate increased coupling when the cavity is tilted by 60° with respect to the waveguide axis, which was also confirmed by experiments. Up to 90% coupling efficiency into the waveguide was obtained

Vučković, Jelena

Caltech Authors - Main

Efficient photonic crystal cavity-waveguide couplers
Andrei Faraon, Edo Waks, Dirk Englund, Ilya Fushman, and Jelena Vučković 
 
Citation: Appl. Phys. Lett. 90, 073102 (2007); doi: 10.1063/1.2472534 
View online: http://dx.doi.org/10.1063/1.2472534 
View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v90/i7 
Published by the American Institute of Physics. 
 
Related Articles
Terahertz mirage: Deflecting terahertz beams in an inhomogeneous artificial dielectric based on a parallel-plate
waveguide 
Appl. Phys. Lett. 101, 111108 (2012) 
Integrating a plasmonic coupler to photo detector of terahertz frequency 
Appl. Phys. Lett. 101, 091114 (2012) 
Electromagnetically induced transparencies in a closed waveguide with high efficiency and wide frequency band 
Appl. Phys. Lett. 101, 093502 (2012) 
Short-wavelength tunable Bragg reflectors based on coupling of propagating and cutoff waves: Modeling and
experimental studies 
Appl. Phys. Lett. 101, 083507 (2012) 
Resonant transmission of light through ZnO nanowaveguides in a silver film 
Appl. Phys. Lett. 101, 081113 (2012) 
 
Additional information on Appl. Phys. Lett.
Journal Homepage: http://apl.aip.org/ 
Journal Information: http://apl.aip.org/about/about_the_journal 
Top downloads: http://apl.aip.org/features/most_downloaded 
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Downloaded 14 Sep 2012 to 131.215.70.169. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
Efficient photonic crystal cavity-waveguide couplers
Andrei Faraon,a Edo Waks,b Dirk Englund, Ilya Fushman, and Jelena Vučković
E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305
Received 13 October 2006; accepted 11 January 2007; published online 12 February 2007
Coupling of photonic crystal PC linear three-hole defect cavities 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. The simulations indicate increased coupling when the cavity is tilted by 60° with respect
to the waveguide axis, which was also confirmed by experiments. Up to 90% coupling efficiency
into the waveguide was obtained. © 2007 American Institute of Physics. DOI: 10.1063/1.2472534
Structures that consist of InGaAs/GaAs quantum dots
QDs coupled to two-dimensional photonic crystal PC
cavities are promising candidates for highly efficient single
photon sources. They represent essential devices for quantum
cryptography and quantum computation.1–4 Efficient imple-
mentation of quantum computation devices requires on-chip
integration of photonic circuits consisting of PC cavities and
waveguides.5 The performance of these circuits is limited by
the cavity-waveguide coupling efficiency. Our work investi-
gates this coupling with the goal of improving the efficiency
of single photon transfer into PC waveguides. The results are
also relevant for channel drop filter applications in optical
telecommunications.
We investigate the waveguide coupling efficiency of the
linear three-hole defect cavities L3.6 The L3 cavities have a
high quality factor Q to mode volume V ratio and provide
good matching between cavity and waveguide field patterns,
which improves in-plane coupling efficiency.7,8 The cavity
mode we work with has magnetic field with even/odd sym-
metry with respect to the x /y axes. This mode Fig. 1a
needs to be coupled to one of the guided modes in the PC
waveguide. Of the possible waveguide bands inside the PC
band gap,7 the best choice for coupling the L3 cavity is the
one with similar symmetry and frequency as the L3 cavity
mode Fig. 1b. For efficient coupling, the cavity and
waveguide modes need to be spatially overlapped and fre-
quency matched. A closer look at the L3 cavity field profile
Fig. 1a reveals that the evanescent field is strongest along
a direction 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 60°
Fig. 1c. The choice of this angle is determined by the
symmetry constraints of the triangular lattice. Directional
couplers with cavity axes nonparallel to waveguide axes
have recently been studied by Kim et al.9 and by Shinya et
al.10,11 In contrast with previous work, we present here opti-
mized designs of couplers as well as detailed theoretical and
experimental data, confirming the advantage of the tilted
configuration for coupling L3 cavities to PC waveguides.
To test the validity of our approach, we compare the
coupling parameters for the tilted cavity configuration Fig.
1c to the standard approach where the cavity and the
waveguide share the same axis straight cavity configuration
Fig. 1d. First, three-dimensional finite difference time do-
main 3D FDTD simulations of coupled cavity-waveguide
systems were performed with both tilted and straight cou-
plers. The frequency of the waveguide band was lowered
with respect to the cavity 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 con-
figurations with spacing of two to five lattice hole separation
between the cavity and the waveguide. The inset of Fig. 2
shows an image of the simulated magnetic field profile for a
tilted cavity coupled to a waveguide with three-hole separa-
tion. In the tilted configuration, the separation between the
cavity and the waveguide is changed along a direction indi-
cated by the arrow in Fig. 1c.
The energy transfer into the waveguide degrades the Q
of the coupled cavity. The total Q of a coupled cavity relates
to the uncoupled cavity quality factor Qc according to
Q−1 = Qc
−1 + Qwg
−1 , 1
where Qwg
−1 is the loss rate into the waveguide.
The coupling strength between the cavity and the wave-
guide is given by 1/Qwg which is proportional to the decay
rate of the cavity field into the waveguide. The quality factor
aElectronic mail: faraon@stanford.edu
bPresent address: Department of Electrical and Computer Engineering, Uni-
versity of Maryland, College Park, MD 20742.
FIG. 1. Color online 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-hole 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-hole separation.
APPLIED PHYSICS LETTERS 90, 073102 2007
0003-6951/2007/907/073102/3/$23.00 © 2007 American Institute of Physics90, 073102-1
Downloaded 14 Sep 2012 to 131.215.70.169. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
Qwg was computed from the 3D FDTD simulations, with
results presented in Fig. 2. For 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 pecu-
liar aspect of the simulations is that for the tilted coupling
configuration, Q is actually larger for four-hole than for five-
hole separation. This is unexpected because it is natural to
assume that reducing the distance between the cavity and
waveguide would improve the overlap integral between the
two modes. However, this increase in the quality factor is
observed under a large variety of different simulation param-
eters, suggesting that it is real, as opposed to a simulation
artifact. We suspect that, at four-hole separation, the antinode
of one of the modes overlaps with the node of the other
resulting in a lower overlap integral. Further investigation is
required in order to conclusively confirm this.
The coupling changes from Qwg500 for the tilted cav-
ity with two-hole separation to Qwg106 for four- and five-
hole separations both configurations. For single photon
sources based on PC cavities with InGaAs QDs operating at
900–1000 nm, the experimental out-of-plane quality factor
is limited to about Qc=10
4 because of material loss and fab-
rication imperfections.12 On the other hand, to get efficient
photon transfer into the waveguide, Qwg needs to be lower
than Qc; therefore, only the coupling configurations with
two- and three-hole separations represent good options. Ex-
perimentally we expect the total Q to be independent of the
waveguide coupling in the case of four- and five-hole sepa-
rations.
To test the validity of our simulation results, the couplers
were fabricated on a 165 nm thick freestanding GaAs mem-
brane containing an InGaAs QD layer. Structures with two-
to five-hole separation in both tilted and straight configura-
tions Figs. 1c and 1d were fabricated. We made seven
structures of each kind. The spectrum of each cavity was
measured using the InGaAs QDs embedded in the GaAs
membrane as an internal light source. The fabrication and
measurement procedures are similar with those reported in
Ref. 3. The mean value of the quality factor for each con-
figuration is plotted in Fig. 3a, where the error bars are
given by the standard deviation in Q due to fabrication fluc-
tuations 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 con-
figuration. This result is a consequence of higher coupling
for tilted cavities.
Since a more efficient coupling between the cavity and
the waveguide degrades the cavity quality factor, when de-
signing a PC network one should choose the configuration
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 disper-
sion relation. To test the position of the cavity with respect to
the waveguide band, we fabricated longer waveguides closed
at the ends. These waveguides act as Fabry-Pérot resonators.
Fringes can be observed using the broad distribution of the
QDs.13 In the linear region of the dispersion relation the
fringes are equally spaced and get closer together as the fre-
quency 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 Fig.
3d.
For a direct comparison between simulation and experi-
ment, Qc of the uncoupled cavity needs to be known. The
upper bound for Qc is limited by fabrication imperfections
and material loss. Our simulation results indicate that in the
case of coupled cavities with four-hole separation, the cou-
pling into the waveguide is very small so the total Q is well
approximated by Qc. For this reason, the average value of the
measured Q for the tilted configuration with four-hole sepa-
ration, was used as Qc. By plugging Qc and the simulated
value for Qwg into expression 1, the predicted value for the
total Q Qtot was computed. The values for Q inferred from
simulations are plotted in Fig. 3b and show good agree-
ment with the experimental data Fig. 3a. Some inconsis-
FIG. 2. Color online Simulation results for the cavity-waveguide coupling
expressed in terms of the quality factor. The coupling strength is propor-
tional to 1/Qwg. Simulated magnetic field of a cavity-waveguide coupler in
tilted configuration with three-hole separation inset.
FIG. 3. Color online Comparison between simulations and experimental
data for cavity-waveguide couplers. a Measured value of total cavity Q
mean. b Value of total Q inferred from simulations by combining simu-
lated Qwg and measured Qc. c Coupling efficiency from the PC cavity into
the PC waveguide. d Measured spectrum of a closed waveguide coupled to
a L3 cavity. The Fabry-Pérot fringes are equidistant in the linear region of
the waveguide dispersion relation where the cavity is also located and they
get closer next to the waveguide band edge 970 nm.
073102-2 Faraon et al. Appl. Phys. Lett. 90, 073102 2007
Downloaded 14 Sep 2012 to 131.215.70.169. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
tency 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. 3c. The coupling efficiency is up to 40% in the
case of straight configuration with two-hole separation and
up to 90% for tilted configuration with two-hole separa-
tion. Because of the coupling to the waveguide, the total
cavity Q dropped to Q500 for the 90% coupling efficiency
case. However, the small mode volume of the L3 cavity still
enables large Purcell factors F50. With 90% and F
50 an efficient waveguide coupled single photon source
with repetition rate of tens of gigahertz can be built. As dis-
cussed in Ref. 14, these are two parameters that in addition
to multiphoton probability suppression which is unaffected
by the cavity determine the quality of a single photon source
for most applications; a higher Q cavity will not improve
these properties, as the repetition rate will still be limited to
tens of gigahertz by the carrier capture time.
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 improved by tilting
the cavity with respect to the waveguide. The coupling is
more efficient because the evanescent tails of the cavity field
are not oriented along the cavity axis but at a 30° angle.
Understanding and controlling the coupling mechanism are
essential for on-chip single photon transfer and the imple-
mentation of on-chip quantum networks.
Financial support was provided by the MURI Center for
Photonic Quantum Information Systems ARO/DTO Pro-
gram No. DAAD19-03-1-0199, ONR Young Investigator
Award, and NSF Grant No. CCF-0507295.
1J. Vučković, D. Fattal, C. Santori, G. S. Solomon, and Y. Yamamoto,
Appl. Phys. Lett. 82, 2374 2003.
2E. Waks and J. Vučković, Phys. Rev. Lett. 96, 153601 2006.
3D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y.
Arakawa, Y. Yamamoto, and J. Vučković, Phys. Rev. Lett. 95, 013904
2005.
4B. Sanders, J. Vučković, and P. Grangier, Europhys. News 36, 56 2005.
5D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vučković, e-print
arXiv/ quant-ph/0609053.
6Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature London 425,
944 2003.
7D. Englund, I. Fushman, and J. Vučković, Opt. Express 12, 5961 2005.
8E. Waks and J. Vučković, Opt. Express 13, 5064 2005.
9G. H. Kim, Y. H. Lee, A. Shinya, and M. Notomi, Opt. Express 12, 6624
2004.
10A. Shinya, S. Mitsugi, T. Tanabe, M. Notomi, I. Yokohama, H. Takara,
and S. Kawanishi, Opt. Express 14, 1230 2006.
11A. Shinya, S. Mitsugi, E. Kuramochi, and M. Notomi, Opt. Express 13
2005.
12D. Englund and J. Vučković, Opt. Express 14, 3472 2006.
13X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romero, P. Viktorovitch, M. Le
Vassor d’Yerville, D. Cassagne, and C. Jouanin, Appl. Phys. Lett. 79,
2312 2001.
14J. Vučković, D. Englund, D. Fattal, E. Waks, and Y. Yamamoto, Physica E
Amsterdam 31 2006.
073102-3 Faraon et al. Appl. Phys. Lett. 90, 073102 2007
Downloaded 14 Sep 2012 to 131.215.70.169. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions


Efficient photonic crystal cavity-waveguide couplers

Andrei Faraon

Edo Waks

Dirk Englund

Ilya Fushman

Jelena Vučković

Crossref

Efficient photonic crystal cavity-waveguide couplers
Andrei Faraon, Edo Waks, Dirk Englund, Ilya Fushman, and Jelena Vučković 
 
Citation: Appl. Phys. Lett. 90, 073102 (2007); doi: 10.1063/1.2472534 
View online: http://dx.doi.org/10.1063/1.2472534 
View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v90/i7 
Published by the American Institute of Physics. 
 
Related Articles
Terahertz mirage: Deflecting terahertz beams in an inhomogeneous artificial dielectric based on a parallel-plate
waveguide 
Appl. Phys. Lett. 101, 111108 (2012) 
Integrating a plasmonic coupler to photo detector of terahertz frequency 
Appl. Phys. Lett. 101, 091114 (2012) 
Electromagnetically induced transparencies in a closed waveguide with high efficiency and wide frequency band 
Appl. Phys. Lett. 101, 093502 (2012) 
Short-wavelength tunable Bragg reflectors based on coupling of propagating and cutoff waves: Modeling and
experimental studies 
Appl. Phys. Lett. 101, 083507 (2012) 
Resonant transmission of light through ZnO nanowaveguides in a silver film 
Appl. Phys. Lett. 101, 081113 (2012) 
 
Additional information on Appl. Phys. Lett.
Journal Homepage: http://apl.aip.org/ 
Journal Information: http://apl.aip.org/about/about_the_journal 
Top downloads: http://apl.aip.org/features/most_downloaded 
Information for Authors: http://apl.aip.org/authors 
Downloaded 14 Sep 2012 to 131.215.70.169. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
Efficient photonic crystal cavity-waveguide couplers
Andrei Faraon,a Edo Waks,b Dirk Englund, Ilya Fushman, and Jelena Vučković
E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305
Received 13 October 2006; accepted 11 January 2007; published online 12 February 2007
Coupling of photonic crystal PC linear three-hole defect cavities 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. The simulations indicate increased coupling when the cavity is tilted by 60° with respect
to the waveguide axis, which was also confirmed by experiments. Up to 90% coupling efficiency
into the waveguide was obtained. © 2007 American Institute of Physics. DOI: 10.1063/1.2472534
Structures that consist of InGaAs/GaAs quantum dots
QDs coupled to two-dimensional photonic crystal PC
cavities are promising candidates for highly efficient single
photon sources. They represent essential devices for quantum
cryptography and quantum computation.1–4 Efficient imple-
mentation of quantum computation devices requires on-chip
integration of photonic circuits consisting of PC cavities and
waveguides.5 The performance of these circuits is limited by
the cavity-waveguide coupling efficiency. Our work investi-
gates this coupling with the goal of improving the efficiency
of single photon transfer into PC waveguides. The results are
also relevant for channel drop filter applications in optical
telecommunications.
We investigate the waveguide coupling efficiency of the
linear three-hole defect cavities L3.6 The L3 cavities have a
high quality factor Q to mode volume V ratio and provide
good matching between cavity and waveguide field patterns,
which improves in-plane coupling efficiency.7,8 The cavity
mode we work with has magnetic field with even/odd sym-
metry with respect to the x /y axes. This mode Fig. 1a
needs to be coupled to one of the guided modes in the PC
waveguide. Of the possible waveguide bands inside the PC
band gap,7 the best choice for coupling the L3 cavity is the
one with similar symmetry and frequency as the L3 cavity
mode Fig. 1b. For efficient coupling, the cavity and
waveguide modes need to be spatially overlapped and fre-
quency matched. A closer look at the L3 cavity field profile
Fig. 1a reveals that the evanescent field is strongest along
a direction 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 60°
Fig. 1c. The choice of this angle is determined by the
symmetry constraints of the triangular lattice. Directional
couplers with cavity axes nonparallel to waveguide axes
have recently been studied by Kim et al.9 and by Shinya et
al.10,11 In contrast with previous work, we present here opti-
mized designs of couplers as well as detailed theoretical and
experimental data, confirming the advantage of the tilted
configuration for coupling L3 cavities to PC waveguides.
To test the validity of our approach, we compare the
coupling parameters for the tilted cavity configuration Fig.
1c to the standard approach where the cavity and the
waveguide share the same axis straight cavity configuration
Fig. 1d. First, three-dimensional finite difference time do-
main 3D FDTD simulations of coupled cavity-waveguide
systems were performed with both tilted and straight cou-
plers. The frequency of the waveguide band was lowered
with respect to the cavity 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 con-
figurations with spacing of two to five lattice hole separation
between the cavity and the waveguide. The inset of Fig. 2
shows an image of the simulated magnetic field profile for a
tilted cavity coupled to a waveguide with three-hole separa-
tion. In the tilted configuration, the separation between the
cavity and the waveguide is changed along a direction indi-
cated by the arrow in Fig. 1c.
The energy transfer into the waveguide degrades the Q
of the coupled cavity. The total Q of a coupled cavity relates
to the uncoupled cavity quality factor Qc according to
Q−1 = Qc−1 + Qwg−1 , 1
where Qwg−1 is the loss rate into the waveguide.
The coupling strength between the cavity and the wave-
guide is given by 1/Qwg which is proportional to the decay
rate of the cavity field into the waveguide. The quality factor
aElectronic mail: faraon@stanford.edu
bPresent address: Department of Electrical and Computer Engineering, Uni-
versity of Maryland, College Park, MD 20742.
FIG. 1. Color online 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-hole 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-hole separation.
APPLIED PHYSICS LETTERS 90, 073102 2007
0003-6951/2007/907/073102/3/$23.00 © 2007 American Institute of Physics90, 073102-1
Downloaded 14 Sep 2012 to 131.215.70.169. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
Qwg was computed from the 3D FDTD simulations, with
results presented in Fig. 2. For 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 pecu-
liar aspect of the simulations is that for the tilted coupling
configuration, Q is actually larger for four-hole than for five-
hole separation. This is unexpected because it is natural to
assume that reducing the distance between the cavity and
waveguide would improve the overlap integral between the
two modes. However, this increase in the quality factor is
observed under a large variety of different simulation param-
eters, suggesting that it is real, as opposed to a simulation
artifact. We suspect that, at four-hole separation, the antinode
of one of the modes overlaps with the node of the other
resulting in a lower overlap integral. Further investigation is
required in order to conclusively confirm this.
The coupling changes from Qwg500 for the tilted cav-
ity with two-hole separation to Qwg106 for four- and five-
hole separations both configurations. For single photon
sources based on PC cavities with InGaAs QDs operating at
900–1000 nm, the experimental out-of-plane quality factor
is limited to about Qc=104 because of material loss and fab-
rication imperfections.12 On the other hand, to get efficient
photon transfer into the waveguide, Qwg needs to be lower
than Qc; therefore, only the coupling configurations with
two- and three-hole separations represent good options. Ex-
perimentally we expect the total Q to be independent of the
waveguide coupling in the case of four- and five-hole sepa-
rations.
To test the validity of our simulation results, the couplers
were fabricated on a 165 nm thick freestanding GaAs mem-
brane containing an InGaAs QD layer. Structures with two-
to five-hole separation in both tilted and straight configura-
tions Figs. 1c and 1d were fabricated. We made seven
structures of each kind. The spectrum of each cavity was
measured using the InGaAs QDs embedded in the GaAs
membrane as an internal light source. The fabrication and
measurement procedures are similar with those reported in
Ref. 3. The mean value of the quality factor for each con-
figuration is plotted in Fig. 3a, where the error bars are
given by the standard deviation in Q due to fabrication fluc-
tuations 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 con-
figuration. This result is a consequence of higher coupling
for tilted cavities.
Since a more efficient coupling between the cavity and
the waveguide degrades the cavity quality factor, when de-
signing a PC network one should choose the configuration
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 disper-
sion relation. To test the position of the cavity with respect to
the waveguide band, we fabricated longer waveguides closed
at the ends. These waveguides act as Fabry-Pérot resonators.
Fringes can be observed using the broad distribution of the
QDs.13 In the linear region of the dispersion relation the
fringes are equally spaced and get closer together as the fre-
quency 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 Fig.
3d.
For a direct comparison between simulation and experi-
ment, Qc of the uncoupled cavity needs to be known. The
upper bound for Qc is limited by fabrication imperfections
and material loss. Our simulation results indicate that in the
case of coupled cavities with four-hole separation, the cou-
pling into the waveguide is very small so the total Q is well
approximated by Qc. For this reason, the average value of the
measured Q for the tilted configuration with four-hole sepa-
ration, was used as Qc. By plugging Qc and the simulated
value for Qwg into expression 1, the predicted value for the
total Q Qtot was computed. The values for Q inferred from
simulations are plotted in Fig. 3b and show good agree-
ment with the experimental data Fig. 3a. Some inconsis-
FIG. 2. Color online Simulation results for the cavity-waveguide coupling
expressed in terms of the quality factor. The coupling strength is propor-
tional to 1/Qwg. Simulated magnetic field of a cavity-waveguide coupler in
tilted configuration with three-hole separation inset.
FIG. 3. Color online Comparison between simulations and experimental
data for cavity-waveguide couplers. a Measured value of total cavity Q
mean. b Value of total Q inferred from simulations by combining simu-
lated Qwg and measured Qc. c Coupling efficiency from the PC cavity into
the PC waveguide. d Measured spectrum of a closed waveguide coupled to
a L3 cavity. The Fabry-Pérot fringes are equidistant in the linear region of
the waveguide dispersion relation where the cavity is also located and they
get closer next to the waveguide band edge 970 nm.
073102-2 Faraon et al. Appl. Phys. Lett. 90, 073102 2007
Downloaded 14 Sep 2012 to 131.215.70.169. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
tency 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. 3c. The coupling efficiency is up to 40% in the
case of straight configuration with two-hole separation and
up to 90% for tilted configuration with two-hole separa-
tion. Because of the coupling to the waveguide, the total
cavity Q dropped to Q500 for the 90% coupling efficiency
case. However, the small mode volume of the L3 cavity still
enables large Purcell factors F50. With 90% and F
50 an efficient waveguide coupled single photon source
with repetition rate of tens of gigahertz can be built. As dis-
cussed in Ref. 14, these are two parameters that in addition
to multiphoton probability suppression which is unaffected
by the cavity determine the quality of a single photon source
for most applications; a higher Q cavity will not improve
these properties, as the repetition rate will still be limited to
tens of gigahertz by the carrier capture time.
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 improved by tilting
the cavity with respect to the waveguide. The coupling is
more efficient because the evanescent tails of the cavity field
are not oriented along the cavity axis but at a 30° angle.
Understanding and controlling the coupling mechanism are
essential for on-chip single photon transfer and the imple-
mentation of on-chip quantum networks.
Financial support was provided by the MURI Center for
Photonic Quantum Information Systems ARO/DTO Pro-
gram No. DAAD19-03-1-0199, ONR Young Investigator
Award, and NSF Grant No. CCF-0507295.
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Efficient Photonic Crystal Cavity-Waveguide Couplers

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