Selected Papers

Si-based Photonic Crystal Components: Relationshipbetween Performance and Structural Disorder
Eiichi Kuramochi†, Stephen Hughes, Akihiko Shinya,
and Masaya Notomi
Abstract
We report recent achievements with our Si-based photonic crystal slab components. Using precise
nanofabrication, we made a waveguide with a record low propagation loss (2 dB/cm). We investigatedthe loss mechanism in photonic crystal slab waveguides, where structural disorder plays an importantrole, and found that disorder also degrades the quality factor of photonic nanocavities.

1. Introduction
Photonic crystal (PhC) [1] is attracting widespreadattention because of its novel optical properties andpotential for use in nanophotonics [2]. Although athree-dimensional PhC can ideally achieve optimum
characteristics [1], [3], it is still very difficult to makebecause the structure is too complicated for current
nanofabrication technologies. Recently, photonic
crystal slabs (PhCS) [4] have been actively studied as
an alternative to the three-dimensional PhC. In a
PhCS, three-dimensional light confinement isachieved by the photonic bandgap (PBG) in the inplane direction and by index confinement in the vertical direction. The basic element, namely an array ofvertical air holes or dielectric pillars, is highly compatible with current nanofabrication technologies. It
has been shown that a suitably designed PhCS structure theoretically provides a lossless waveguide and aphotonic nanocavity with a quality factor (Q) of
around 107 [4], [5]. The advantage of the PhCS has
been demonstrated experimentally by the fabricationof very-low-propagation-loss waveguides (6 dB/cm)[6] and ultrahigh (6 × 105) quality factor (Q) cavities
with an ultrasmall modal volume [5], [7]. However,the factors restricting the waveguide loss and cavityQ of actual structures were not well understood.
† NTT Basic Research Laboratories
Atsugi-shi, 243-0198 Japan
E-mail: kuramoti@nttbrl.jp

Vol. 3 No. 12 Dec. 2005

These loss mechanisms must be clarified if we are toenhance PhCS device performance. We have focusedon improving the preciseness of electron beam lithography to reduce fabrication-related disorder, which
may have a considerable effect on PhCS loss characteristics. In this paper, we report our recent development of Si-based PhCS components for the opticalcommunication wavelength regime including PhCS
waveguides with a record low loss. We discuss therole of disorder in detail for the first time by carefully comparing theory and experiment.
2. Low-loss photonic crystal waveguides andfabrication
Our Si-based PhCS fabrication process is shown in
Fig. 1. We fabricated Si PhCSs from commerciallyavailable silicon-on-insulator (SOI) wafers whose Si
and SiO2 thicknesses were 205 and 3000 nm, respectively. Our PhCS structure consisted of a Si slab layer
with triangular lattice of air holes and upper/lower air
cladding. To define the PhCS structure we drew a pattern on a ZEP520 (ZEON) resist with a 100-kV JEOL
electron beam (EB) writer and then transferred theresist pattern to an SOI layer using an inductively
coupled plasma etcher. The SiO2 layer under the
PhCS was removed with buffered hydrofluoric acid.
Here, the most important issue was to reduce the fabrication error. Scanning electron microscope (SEM)
images of a fabricated PhCS are shown in Fig. 2. The
vertical hole sidewalls were achieved by optimizing
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EB resist
Air (n = 1)
SOI (Si, n = 3.46)
SiO2 (n = 1.48)

Air (n = 1)

Si substrate
(a)

(b)

(c)

Fig. 1. Si-based PhCS fabrication process. (a) Patterning of EB resist with an EB writer. (b) Dry etching of SOI layer.
(c) Wet etching of SiO2 layer under-cladding.

ir)

0.29
Light line (a200 nmNormalized frequency ω (a /λ)

0.30

0.28

W1 (even)

0.27

W1 (odd)
W0.65 (even)
0.26
0.0
Γ

0.1

0.2

0.3

Normalized wavevector (2π/a)

0.4

0.5
Κ

Fig. 2. SEM images of PhCS samples.

the dry etching conditions. The surface roughness ofthe hole sidewalls, determined by a statistical analysis of the SEM images, was less than 2 nm (root meansquare (RMS)), namely the detection limit of our
SEM. We believe that the samples fabricated in thisstudy are the best-quality PhCSs reported to date. The
crucial factors for minimizing roughness were optimization of the pattern data and the resist development process and suitable management of the proximity effect during electron beam lithography.
In this study, we investigated two types of linedefect PhCS waveguides: W1 and W0.65. The former
was a simple one-row-missing line defect, and the latter was a width-reduced waveguide [8] whose linedefect width was 65% of the former. The photonic
band structure of the waveguide mode for the two
waveguides is shown in Fig. 3. The x-axis is normalized wavenumber in the Γ–Κ direction and the y-axis
is normalized frequency ω = a/λ (a: lattice constantof photonic crystal, λ: wavelength). There are threeimportant differences between W1 and W0.65. (1) In
70

Fig. 3. Calculated band structure of waveguide mode for
Si PhCS. The colored area is above the light line
where the waveguide is leaky.

the vicinity of the low frequency limit (mode edge),
W1 has a “slow light mode” where the group velocity of light can be smaller than c/100 (c: velocity oflight in vacuum) [9], [10], corresponding to the nearly flat band in Fig. 3. (2) W0.65 has a broader lowloss transmission band than W1 considering the significant loss increase above the light line. (3) W1 hasanother waveguide mode with odd symmetry above
the fundamental mode (even symmetry), whereas
W0.65 has only one even mode with a high-frequency mode edge. We fabricated W1 (a = 432 nm) andW0.65 waveguides (a = 400 nm), where the holeradius was about 0.25a and the slab thickness was
0.48a. We measured the loss spectrum by comparing
the transmittance of different length waveguides (cutback method). The loss plot for W1 at a wavelengthof 1550 nm is shown in Fig. 4(a). The evaluated propagation loss was 2 dB/cm [11], which is the best value
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100(a)Loss: 2 dB/cm (λ = 1550 nm)

–2

–3

0

1
2
Waveguide length L (mm)

3

1000

Loss (dB/cm)

L(ω)vgL(ω)vg2

10

1

0.1
0.270

(b)

W1
W0.65

0.275

0.280

0.285

ω (a /λ)Fig. 5. Comparison of the frequency dependence of
waveguide loss for vg and vg2. In the shaded area,
the dependence is approximately (1/vg)2.

100

10

1

Product value (a.u.)Transmittance (dB)

–1

1500

1550

1600

Wavelength (nm)Fig. 4. (a) Loss plot of W1 waveguides at a wavelength
length of 1550 nm. (b) Loss spectrum of W1 andW0.65 waveguides.

yet reported for a PhC waveguide. Note that there was
no increase in loss even at the longest waveguide (3mm), which demonstrates that there is no technicalbarrier for millimeter-order PhCS waveguides. The
loss spectra for W1 and W0.65 are shown in Fig.
4(b). Both waveguides had a finite low loss bandwidth and that of W0.65 was the broader of the two,
as suggested by Fig. 3. The loss of W0.65 (approx. 15
dB/cm) was much higher than that of W1, probably
because there was considerable field seepage into theholes surrounding the waveguide, which increases
the loss due to sidewall fluctuation among holes [12].
3. Loss mechanism of photonic crystal
waveguides
We clarified that the loss spectra in Fig. 4 were
determined by rich and complex loss physics. It has
been predicted that out-of-plane loss (not related toscattering) takes place above the light line, but wefound that the main loss factor in Fig. 4(b) was disorder-related scattering. Applying Fermi’s golden ruleVol. 3 No. 12 Dec. 2005

to the scattering process, we derived a formula thatshows that the loss depends on the local density ofstates (LDOS) of both the initial and final states [12].
Since the LDOS of the waveguide mode is proportional to 1/vg (vg: group velocity), the loss depends on
1/vg for out-of-plane scattering and on (1/v g)2 forbackscattering. The products of loss L(ω) × vg andL(ω) × vg2 for W1 are compared in Fig. 5 [13]. We
found that the loss was more closely proportional to(1/vg)2 than to 1/vg in the vicinity of the low-frequency mode edge, which means that backscattering was
dominant in this regime where vg was very small.
Although out-of-plane scattering loss has alreadybeen reported, this is the first report of the large contribution of backscattering in the slow light mode [9],[10]. This is important because low loss for slow lightmode is essential for device applications such as an
optical delay line. Inter-mode scattering in the multimode region was another reason for the increase inloss for W1 in the high frequency region because theupper odd mode had a large LDOS and a large loss
due to the larger field distribution. Our physical concept also includes the idea that loss depends on thesquare of the RMS sidewall roughness [12]. Thismeans that the waveguide was lossless if there was no
disorder. Thus, we clarified that the complex loss
characteristics of actual PhCS waveguides are determined by disorder, LDOS, and vg. We even foundVan-Hove-singularity-like loss peaks corresponding
to the mode edge of waveguide mode [13].
We calculated the theoretical loss using the formula mentioned above [12] and compared the resultswith experimental loss spectra for an actual sample.
Figure 6 shows this comparison for a W1 sample
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1000

a = 420 nm, r = 0.275a, slab thick = 0.5asr = 0.5r, shift = 0.25a

Experimental

W1

Loss (dB/cm)

Calculated

100
B

C

D

0.285

0.290

10
A

0.270

0.275

0.280
ω (a /λ)Fig. 7. The 4-point defect structure model used for FDTD
simulation.

Fig. 6. Comparison of experimental and theoretical loss
spectra of W1 waveguide.

200000r
Vertical Q[13]. The main loss mechanisms were: backscattering(A), out-of-plane scattering (B), intermode scattering(even to odd) (C), and intrinsic out-of-plane loss
above the light line (D). Because the comparison was
performed for an old sample whose RMS sidewallroughness was 3 nm, the loss (5 dB/cm) was slightly
larger than the values shown in Fig. 4. We found that
there was surprisingly good agreement between thecalculation and experiment. Such good agreement
was also obtained for a waveguide with a different
structure without using a fitting parameter. This is thefirst demonstration of the precise quantitative calculation of the loss of PhCS waveguides. It should be
noted that the good agreement was also assisted by
the small uniform disorder in our samples.

250000150000100000

50000

0

0

1

2

3

4

5

Disorder of r (nm, RMS)

Fig. 8. Disorder dependence of cavity-Q as a function of
the RMS hole radius obtained by FDTD.

4. Disorder in photonic nanocavities
It was not understood until recently why the experimental Q of a PhCS nanocavity is much less (about
one order of magnitude) than its theoretical Q. The
theoretical calculations were usually performed for
ideal structures without disorder, so we thought thatthe disorder reduced the cavity-Q by increasing theloss in the same way as with waveguide loss. We performed a numerical study of the way in which theinter-hole disorder restricts the Q of PhCS nanocavities [11], [14]. We considered a four-point-defect cavity with a smaller, shifted hole (radius: 50%, shift:
0.25a) at each end of the defect [15] (Fig. 7). We calculated the Q of the cavity using the three-dimensional finite-difference time-domain (FDTD) method72

with an in-plane calculation area of 19 × 28 periods.
The calculated vertical Q was 210,000 without disorder. We used a simple disorder model characterized
by only the RMS deviation of the hole radii; i.e.,
intra- and inter-hole correlations were disregarded.
The disorder dependence of cavity-Q as a function of
the RMS of the hole radius obtained by FDTD isshown in Fig. 8. We found that for 3-nm inter-holedisorder, the vertical Q was reduced to as little as half
the value without disorder, which is not far from theexperimental Q (maximum: 70,000). This suggeststhat inter-hole disorder has a great influence on the Qof nanocavities. We were the first to report the large
effect of inter-hole disorder although another group
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started to study disorder before us. Although we have
not yet studied this issue in detail, perhaps the same
scattering mechanisms that cause waveguide loss also
reduce the Q values of nanocavities.
5. Conclusion
We have already obtained PhCS waveguides withdB/cm-order loss, which is sufficiently low for mm2order PhCS integrated circuits. Very recently, wedeveloped a PhCS nanocavity with a new design
whose experimental Q was over 106 for the first time[16]. This substantially increased Q value will enable
us to reduce the coupling loss at cavities, reduce thechannel interval for wavelength division multiplication devices, extend the light trapping time for opticalmemory operation, and decrease the operating power
needed for optical switches. Although we must still
overcome polarization dependence and chip-to-fiber
coupling loss, the waveguide loss and cavity-Q nolonger represent bottlenecks for photonic component
applications. Our study of the loss mechanism
revealed that the performance of PhCS components
can be further improved by reducing structural disorder, which indicates that a PhCS is a promising candidate for a nanophotonics platform.
References
[1]
[2]

[3]

[4]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic Crystals,” Princeton University Press, 1995.
M. Notomi, A. Shinya, and E. Kuramochi, “Photonic Crystals:
Towards Ultrasmall Lightwave Circuits,” NTT Technical Review,Vol. 2, No. 2, pp. 36-47, 2004.
E. Yablonovitch, “Inhibited spontaneous emission in solid-statephysics and electronics,” Phys. Rev. Lett., Vol. 58, pp. 2059-2062,
1987.
S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulous, and L.
A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys.
Rev. B, Vol. 60, pp. 5751-5758, 1999.

Vol. 3 No. 12 Dec. 2005

[5]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Materials, Vol. 4,
pp. 207-210, 2005.
[6] M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H-Y. Ryu,
“Waveguides, resonators and their coupled elements in photonic crystal slabs,” Optics Express, Vol. 12, pp. 1551-1561, 2004.
[7] H-Y. Ryu, M. Notomi, and Y-H. Lee, “High quality factor and small
volume hexapole modes in photonic crystal nanocavities,” Appl.
Phys. Lett., Vol. 83, No. 21, pp. 4294-4296, 2003.
[8] M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I.
Yokohama, “Structural tuning of guiding modes of line-defect waveguides of SOI photonic crystal slabs,” IEEE J. Quantum Electron.,Vol. 38, No. 7, pp. 736-742, 2002.
[9] M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I.
Yokohama, “Extremely large group velocity dispersion of line-defectwaveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902,
2001.
[10] H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik,
N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-Space Observation of Ultraslow Light in Photonic Crystal Waveguides,” Phys. Rev.
Lett. 94, 073903, 2005.
[11] E. Kuramochi, M. Notomi, S. Hughes, G. Kira, L. Ramunno, A.
Shinya, and T. Watanabe, “Optical Properties of Photonic Crystal
Slab Components: Role of Disorder,” International Symposium on
Photonic and Electromagnetic Crystal Structures (PECS-VI), PTu-59,
Aghia Pelaghia, Crete, Greece, June 2005.
[12] S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic Optical Scattering Loss in Photonic Crystal Waveguides: Role of Fabrication Disorder and Photon Group Velocity,” Phys. Rev. Lett., Vol. 94,
Art. No. 033903, 2005.
[13] E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and
L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B72, 161318 (R), 2005.
[14] E. Kuramochi, M. Notomi, S. Hughes, L. Ramunno, G. Kira, S. Mitsugi, A. Shinya, and T. Watanabe, “Scattering Loss of Photonic Crystal Waveguides and Nanocavities Induced by Structural Disorder,”International Quantum Electronics Conference, 2005 and the Pacific
Rim Conference on Lasers and Electro-Optics, 2005 (IQEC/CLEOPR 2005), CTuE1-1, Tokyo, Japan, July 2005.
[15] S. Mitsugi, A. Shinya, E. Kuramochi, M. Notomi, T. Tsuchizawa, andT. Watanabe, “Resonant tunneling wavelength filters with high Q andhigh transmittance based on photonic crystal slabs,” The 16th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS
2003), Tucson, Arizona, U.S.A., TuE3, Oct. 2003.
[16] E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T.
Watanabe, “Photonic Crystal Nanocavity Formed by Local Width
Modulation of Line-defect with Q of One Million,” The 18th Annual
Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2005),
Sydney, Australia, October, 2005, PD1.1.

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74

Eiichi Kuramochi

Akihiko Shinya

Senior Research Scientist, Optical Science
Laboratory, NTT Basic Research Laboratories.
He received the B.E., M.E., and Ph.D degrees
in electrical engineering from Waseda University, Tokyo in 1989, 1991, and 2004, respectively.
In 1991, he joined NTT Optoelectronics Laboratories, where he engaged in research on semiconductor nanostructures for photonic devices. From
1998, he engaged in research on photonic crystals at NTT Basic Research Laboratories. He
received the Poster Award at the PECS-VI conference in 2005. He is a member of the Japan
Society of Applied Physics (JSAP).

Research Scientist, Optical Science Laboratory, NTT Basic Research Laboratories.
He received the B.E., M.E., and Dr.Eng.
degrees in electrical engineering from Tokushima University, Tokushima in 1994, 1996, and1999, respectively. In 1999, he joined the NTT
Basic Research Laboratories. He is engaged in
the R&D of photonic crystal devices. He is amember of JSAP.

Stephen Hughes

Masaya Notomi

Associate Professor, the Department of
Physics, Queen’s University, Canada.
He received the B.Sc and Ph.D. degrees inphysics from Heriot-Watt University, Edinburgh
in 1991 and 1995, respectively. Following Postdoctoral Fellowships at Philipps-University Marburg (Germany), the University of Tokyo(Japan), and Washington State University(USA), in which he studied a variety of theoretical activities in semiconductor optics and ultrafast light-matter interactions, he returned to the
UK in 1999 as a Lecturer of Physics at the University of Surrey. In 2001 he joined the first photonics start-up company to explore the commercialization of planar photonic crystals, Galian
Photonics Inc. in Vancouver, BC, Canada. Subsequently he co-founded a new optical software
company, Lumerical Solutions Inc., and spent 2
years at NTT Basic Research Laboratories,
Japan, as a Research Specialist. His group in the
Department of Physics at Queen’s University in
Canada, is working on the theory, computation,
and application of light-matter interactions in
nanophotonic and quantum optical materials.

Distinguished Technical Member and Group
Leader, Optical Science Laboratory, NTT Basic
Research Laboratories.
He received the B.E., M.E., and Dr.Eng.
degrees in applied physics from the University ofTokyo, Tokyo in 1986, 1988, and 1997, respectively. In 1988, he joined NTT Optoelectronics
Laboratories. Since then, his research interest has
been to control the optical properties of materials
and devices by using artificial nanostructures,and he has been researching semiconductor
quantum wires/dots and photonic crystal structures. In 1996-1997, he was at Linköping University, Sweden as a visiting researcher. Since
2002, he has also been a guest associate professor at the Tokyo Institute of Technology, Japan.
He is a member of JSAP and the American Physical Society.

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