Selected Papers

Photonic Crystals: Towards UltrasmallLightwave Circuits
Masaya Notomi†, Akihiko Shinya, and Eiichi Kuramochi
Abstract
A photonic crystal having photonic band gaps is expected to play a key role in future large-scale photonic integrated circuits. We have been investigating two-dimensional silicon-on-insulator (SOI) photonic crystal slabs and have demonstrated that such a slab is a good candidate for the basic platform ofphotonic-crystal-based circuits. In this paper, we show how to design photonic crystals of this type to
implement various components. As a result of appropriate design and with the help of advanced Si nanofabrication technology, we have successfully made various ultrasmall photonic-band-gap waveguides,
resonators, and functional components in SOI photonic crystal slabs with operating wavelengths covering most of the fiber communication wavelengths.

1. Introduction
A photonic crystal is a structure whose refractive
index is periodically modulated on the scale of an
optical wavelength. Such a crystal is predicted topossess various unique characteristics that cannot be
achieved in conventional materials. This is analogous
to electronic properties in conventional materials.
Various electronic properties—such as conducting,semiconducting, or insulating—arise from electronsin crystals feeling periodic perturbation from the lattices, resulting in the formation of so-called energy
band structures. In a similar way, light propagation inphotonic crystals (PhCs) can be largely controlled
because photons in crystals feel periodic perturbation, resulting in the formation of photonic band
structures. As Fig. 1 shows, the dispersion relationship in conventional materials is fundamentally different from that in PhCs. The former usually exhibitsa photonic band gap (PBG) in which there are no
propagation modes. PhCs within this PBG frequency
range behave as if they were photonic insulators,
which do not exist in nature (for conventional materials). In addition, the curvature of the dispersion curveis also very different from that of conventional mate† NTT Basic Research Laboratories
Atsugi-shi, 243-0198 Japan
E-mail: notomi@nttbrl.jp

36

rials, which means that the traveling speed of light
can be controlled over a wide range.
PhCs with PBGs are expected to be key platforms
for future large-scale optical integrated circuits [1],[2]. Making optical (photonic) ICs or LSIs has been
an important target of photonics technology since it
started several decades ago, but it is still an engineer’s
dream. This is mostly due to the very fundamental
characteristic of light: photons do not interact efficiently with materials or with other photons. This
makes it difficult to confine photons in a tiny space
and also leads to poor controllability. Most opticalcomponents rely on total internal reflection (TIR) to
confine the light, but TIR becomes ineffective forsmall components. (This is because TIR is effective
only for a certain range of propagation directions.)
Actually, optical components are normally significantly larger than the optical wavelength. PhCs with
PBGs give us another mechanism for confining light.
Since the reflection caused by PBGs is effective for
all angles, PBG confinement works even for wavelength-scale components. In PhCs, point defects
function as optical cavities (PBG resonators) whileline defects function as optical waveguides (PBG
waveguides). The coupling of PBG resonators andwaveguides leads to functional devices. Thus, putting
a large number of various functional defects into
PhCs with PBGs (equivalent to creating photonic
insulating substrates) leads to photonic ICs/LSIs
NTT Technical Review

Selected Papers(Fig. 2). Since the size of each component is comparable to the optical wavelength, the total size of circuits will be significantly less than that of conventional optical circuits. In addition, the strong confinement of light in PBGs enhances the interaction

between light and matter, as in amplification and optical nonlinear switching, for example.
In this paper, we describe some design and measurement issues related to PBG waveguides and resonators in two-dimensional (2D) PhC slabs (mainly
Photonic crystal

Conventional material

Frequency ω

ω=ck/nNormalized frequency (ωa/2πc)

0.8

0.6
Photonic band gap
0.4

0.2

T
Z

R
U

Y
0.0

Si/SiO2/air

S

Γ

X

Wavevector kYΓX
Wavevector k

(a)

(b)

S

R

T

U

Z

Γ

Fig. 1. Dispersion relationship of light in (a) conventional dielectrics and (b) typical photonic crystals. (a: the lattice constant)

(a)

(b)

(c)
detector

λ1, λ2, λ3, λ4

λ5, λ6, λ7, λ8
Light source

Switch(d)Fig. 2. Schematics of various components in PhCs. (a) Point defect in a PhC acting as a resonator, (b) line defect in a
PhC acting as a waveguide, (c) coupled defects in a PhC acting as a functional component, and (d) schematic ofa PhC-based circuit.

Vol. 2 No. 2 Feb. 200437

Selected Papers

SOI PhC slabs). We show that ultrasmall waveguides
and resonators having a small radiation loss can bemade using available lithographic nano-fabrication
techniques. Indeed, some of their unique properties
have already been observed experimentally. In addition, we discuss various functional elements produced by coupling PBG waveguides and resonators.
This final topic is very important for integrated-circuit applications.
2. Two-dimensional SOI photonic crystal slab
It might seem natural to choose 2D PhCs for photonic IC applications because the geometry of any
conventional circuit is basically two-dimensional.
Actually, most theoretical studies of PhC-based circuits assumed ideal 2D PhCs, that is, infinitely thick2D crystals. However, such simple 2D crystals are notpractical because light will leak out in the out-ofplane direction due to the lack of vertical confinement
mechanisms. Of course, proper implementation of
circuit elements within 3D PhCs having full PBGs
should solve this problem, but such fabrication is very

challenging. Considering how easy it is to fabricate
2D PhCs, one key issue is how to introduce efficientvertical confinement in 2D PhCs. Recent studies haveshown that it is indeed possible to achieve efficientvertical confinement within 2D PhCs by various
methods. In this paper, we show that such efficient 2D
PhCs can be made using silicon-on-insulator (SOI)
substrates.
Figure 3 shows schematic figures of the fabrication
process of SOI PhC slabs and electron micrographsof a bulk PhC and a waveguide within a PhC. Periodic hole patterns are formed on the top Si layer of an
SOI substrate by electron beam lithography and electron-cyclotron-resonance ion stream dry etching [3].
This patterned Si layer acts as a 2D PhC. The SiO2
layer works as a lower cladding layer, and the upper
cladding layer is air. We refer to this structure as a
SiO2-clad PhC slab. Sometimes we selectively etch
off the SiO2 layer to form an air-bridge structure. In
such cases, both cladding layers are air. We call thisan air-clad type PhC slab. PhC slabs are 2D PhC
structures located within high-index-contrast slab
waveguides. In PhC slabs, light waves are confinedSi(0.2 µm)

Si

SiO2(3 µm)
SiO2

Si sub.

(a)

Γ-M

Γ-K

SiO2
or
Air

Si

w
1 µm

(b)

0.7w0

Air
(c)

Fig. 3. Schematics of the fabrication process. (a) An SOI substrate on which PhCs are to be fabricated. (b) Periodic holepatterns formed by electron beam lithography and dry etching. (c) Electron micrographs of SOI PhC slab and aline-defect waveguide fabricated in a similar structure. The waveguide shown here is an example of width-varied
waveguides (discussed in 3.2). ( w0 = 3a , where a is the lattice constant.)

38

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Selected Papers

by a combination of in-plane PBG confinement andvertical TIR confinement. Although we still use TIR
in the vertical direction, light waves can be strongly
confined within ultrasmall waveguides and resonators in PhC slabs without practical leakage if wedesign their structures appropriately.
So, how can we make meaningful 2D PBGs in these
2D PhC slabs? Figure 4(a) shows the photonic band
structure of Si PhC slabs. The red lines in the graphshow band dispersion calculated by the plane-wave
expansion method, and gray lines are light lines of thecladding material (air and SiO2). The light line isdefined as ω =ck/n, and modes above this light line of
the cladding are leaky because they overlap withradiation modes in the cladding. PBGs below thelight line can work as meaningful 2D PBG without
radiation loss. If the refractive index n of the cladding
material is not so small, the position of the light line

Normalized frequency (a/λ)

0.5

0.4

3. PBG waveguides

0.3
PBG
0.2
LL(air)0.1

0

2D-PhCΓ

LL(SiO2)
MΓK
Wavevector(a)–10Transmission (dB)

is lower, leading to a reduction or vanishing of theusable PBG region. In this sense, a large index contrast (between Si and SiO 2) in SOI substrates isadvantageous for large 2D PBGs.
If we wish to construct PhC-based photonic ICs, wemust first confirm whether appropriate PBGs areformed at desired wavelengths. We have directly
measured the transmittance of 2D SOI hexagonal airhole PhCs by using a single-mode tapered fiber and a
wideband white light source. Figure 4(b) showstransmittance spectra along two crystal axes and thecorresponding photonic band diagram for transverse
electric wave (TE) polarization. We observed a common PBG from 1.23 to 1.58 µm for Γ-K and Γ-M
crystal-axis orientations, which shows that a full PBG
is open in the 2D plane. The experimental result
agrees very well with the 3D finite-difference timedomain (FDTD) calculation [4], [5]. The observed
PBG covers the entire wavelength range currently
used for optical communications. Thus, this resultshows that SOI photonic crystal slabs can be considered as possible platforms for photonic ICs in thiswavelength range.

Γ-K

Γ-M
PBG

–20

–30

1200

1300

1400
1500
Wavelength (nm)

1600

1700

(b)

Fig. 4. Bulk properties of SOI PhC slabs. (a) Calculated
photonic band structure of 2D SOI PhC slabs and(b) transmission spectra of SOI PhC slabs.

Vol. 2 No. 2 Feb. 2004

3.1 Design
Next, we examine how to make efficient waveguides in 2D PhC slabs. Our goal is to make a wideband single guiding mode that operates within the
PBG. In fact, if we use only a straight isolated waveguide, then the position of the mode relative to the
PBG is not a serious matter. However, if we want tomake bends, splitters, or coupling to point-defect cavities (which is always the case with practical applications), then we need a PBG in the operating band.
Figure 5(a) shows the calculated waveguide dispersion of typical line-defect waveguides in hexagonal
PhC slabs. In Fig. 5(a), there are two modes within
the PBG: an even mode and an odd mode. Thus, thesingle-mode bandwidth is limited by the existence of
this second odd mode. In addition to the position of
the PBG, we must consider the position of the lightline of the cladding material. The TIR confinement in
the vertical direction is lost in the mode above thelight line, and the mode becomes leaky. It should be
noted that theoretically the mode below the light line
is a truly guided mode that has no propagation loss.
We estimated the loss of the leaky modes just above
the light line to be about 100 dB/mm [6], which we
think is too large for most applications, although
leaky modes can be used under certain limited condi39

Selected Papers

Air

SiO2 light line

Even
Odd

0.3

Normalized frequency

Normalized frequency

PBG

0.3

Even
0.2

0.1

Gap-guided
0.2

0.1

Index-guided

Even

0

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

0.3

k

k

(a)

(b)

0.4

0.5

Fig. 5. Dispersion of PBG waveguides. (a) Theoretical dispersion curves of single-missing-hole line-defect waveguides inhexagonal PhC slabs and (b) intuitive understanding of the same mode as in (a).

tions.
Therefore, we must design a wideband single-mode
condition below the light line within the PBG. Sincea wide bandwidth requires a large slope of the dispersion curve in the limited wavevector space, a large
group velocity is preferable. The previous section
suggests that we can control the operating wavelength and group velocity of waveguiding modes byappropriately controlling the modes having different
characteristics and also by controlling the so-called
anticrossing behavior which we discuss below.
We have already examined this light-line problem
in PhC slabs in detail [6], [7]. The following briefly
summarizes the issue. In the case of air-clad PhC slab
structures, a conventional single-missing-hole-line
waveguide (Fig. 5(a)) has a relatively wide singlemode bandwidth. But with SiO2 (or polymer) clad
PhC slabs, the same single-missing-hole-line waveguide has only a very small bandwidth. This happens
because a TIR-guided mode (with a negative curvature) and a PBG-guided mode (with a positive curvature) cross each other in the PBG under the light line40of SiO2 in a normal single-missing-hole-line defect,
and the anticrossing of two modes with opposite curvatures results in a very flat band, namely a verysmall width. The situation is graphically shown in
Fig. 5(b). Since this anticrossing occurs accidentallyin this position, we can change the situation bychanging the geometrical structure of the defect.
To solve this problem, we introduced a new waveguide structure, namely width-varied line-defectwaveguide. The left diagram of Fig. 6(a) shows awidth-varied line-defect waveguide, in which thewidth W is varied from the normal width w0 (= 3 a,where a is the lattice constant). By reducing thewidth, we created another band with a large groupvelocity that enters the PBG from the lower bandedge. We fabricated a width-reduced PBG waveguideon SOI PhC slabs and experimentally demonstrated
that this modification produced a wideband transmission window for SiO2-clad PhC slabs as shown in
Figs. 6(b) and 6(c). We confirmed that this waveguide has a very small propagation loss (6 dB/mm),
which is comparable to normal single-missing-holeNTT Technical Review

Selected Papers

W

100Group index(a)Transmittance (dB)

0

0.30

Normalized frequency: ω=a/λ
0.28
0.26

0.65w0
10
5
0

1.0w0
1420

40

1460
λ (nm)

1500

W=1.0W0

–5
–10
–15

20

line defect

1.0w0

–20
–25
–30
–35

0
1460
1300

1400
1500
Wavelength (nm)(b)

0Transmittance (dB)

0.24

60

Group index

1580

W=0.7W0

–5

1600

1700

line defect–20–25
ω=0.265

–30
–35

1300

1400
1500
Wavelength (nm)
(c)

1600

1700

Fig. 6. Structural tuning of PBG waveguides. (a) Various
examples of structural tuning (width-varied, eggshaped-hole, and phase-shifted-hole) and (b) and(c) transmission spectra of PBG waveguides in
2D SOI PhC slabs with SiO2 cladding, where thewaveguides are normal single-missing-hole line
defect waveguides in (b) and width-reduced line
defect waveguides in (c). a is the lattice constant.

line defects in air-clad PhC slabs. In fact, a normal
single-missing-hole-line defect has a relatively small
truly single-mode condition. Thus, the width-reduced
waveguide also improves the width of the truly single-mode condition even for air-clad PhC slabs.
Width reduction is not the only way to solve theproblem for SiO2-clad PhC slabs. Because PBG waveguides have a large degree of freedom when the dispersion is tuned, there are many other ways to achieve
this in an equally practical manner. Examples of othertuning methods are shown in Fig. 6(a) [7]-[9].

Vol. 2 No. 2 Feb. 2004

1500

1520

Wavelength: λ (nm)Fig. 7. Group velocity dispersion measurement. Measured
group index as a function of wavelength.

waveguiding mode

–10
–15

1480

3.2 Group velocity dispersion measurement
As discussed in the previous section, the dispersion
can be tuned over a wide range in PBG waveguides,
which is one of their most important features. A large
dispersion over a wide wavelength range, as seen in
Fig. 5(a), cannot be achieved by other conventional
dielectric waveguides. In addition to simple applications to dispersion-controlled waveguides, such alarge dispersion and good controllability of groupvelocity may prove important for various applications
related to optical nonlinear phenomena. In terms ofphysics, it is well known that light-matter interaction
in materials is strongly influenced by the groupvelocity of light.
Here, we describe our experimental study of thegroup velocity dispersion of PBG waveguides in SOI
PhC slabs [10]. Since there is some reflection at bothends of our PBG waveguides, we can observe a
Fabry-Perot interference pattern in the transmission
spectra. This interference pattern is directly related to
the group index of the waveguide, so we can deduce
the group index if we know the precise length of the
waveguide. Figure 7 shows the deduced group index
of two different PBG waveguides: a normal singlemissing-hole-line waveguide (W=1.0w 0 ) and awidth-reduced waveguide (W=0.65w0). The deducedgroup index shows an extremely large group velocity
dispersion. It also shows an extremely large group41

Selected Papers

index that reaches almost 100 in the vicinity of themode gap.
This large group index value means that the groupvelocity in this waveguide is very small. Recently,
slow light modes in materials have been observed invarious phenomena including electromagneticallyinduced transparency [11] and coherent population
modulation [12], by controlling the material dispersion. Such slow modes are expected to provide ultimate control of the light-matter interaction with avery small light intensity. The origin of the slow lightmodes in Fig. 7 is very different (it is purely due tocontrol of the structural dispersion), but this result
indicates that a PBG waveguide may be another candidate for enhancing light-matter interaction.

silica fibers.
To solve this problem, we designed an adiabatic
mode connector, which is monolithically integrated
in an SOI PhC slab chip [13]. As schematicallyshown in Fig. 8, the connector consists of two parts:i) a spot-size converter (SSC), which adiabaticallyconnects a polymer single-mode waveguide, a Siwire waveguide, which was invented by NTT
Microsystem Integration Laboratories [14], and amode-profile converter (MPC), which adiabaticallyconnects a Si-wire waveguide and ii) a photonic-crystal waveguide. The mode size and the refractive index
of the polymer waveguide were designed to be thesame as those of a high-∆ single-mode fiber. The
mode size in the Si-wire waveguide was designed tobe the same as that in the PBG waveguide. The fabrication process is very simple, namely a combinationof a single-stage Si etching process and a conventional polymer waveguide process.
We fabricated this device and investigated its connection loss. The measured connection loss was 3–4
dB per port, which is the sum of the connection losses for SSC and MPC. Compared with the value of 30
dB, we significantly reduced the connection loss.
Recently, a connection loss of 0.8 dB per port in an
SSC for Si-wire waveguides was reported by NTT
Microsystem Integration Laboratories [14]. If we
combine that with this technology, we believe that we
can further reduce the connection loss for PBG waveguides.

3.3 Coupling to fibers
One of the most frequently addressed problems
concerning PBG waveguides is their poor coupling
efficiency with conventional single-mode fibers. Thisis a fundamental problem because the mode size forline-defect waveguides is always very much smaller
than that for silica single-mode fibers. This smallness
is usually considered to be an advantage for PhCs, but
it is a fatal disadvantage for coupling. The typicalcross-sectional size of a PBG waveguide is 0.4 × 0.2µm2, which is approximately three orders of magnitude smaller than that of a silica single-mode fiber.
Moreover, there is a large reflection loss due to thelarge index difference between PBG waveguides andPhotonic-crystal waveguide
Mode size
0.2 × 0.3 µm
Si-wire waveguide

Polymer waveguide

Mode profile converter
Single-mode fiber

Spot-size converter

Mode size 9 µm-φFig. 8. Adiabatic mode connector containing a spot-size converter and a mode-profile converter.

42

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Selected Papers

4. PBG resonators
4.1 Design
With conventional optical resonators, which rely on
TIR confinement, their quality factor (Q) is limitedby their mode volume. That is, if the mode volume is
reduced to a wavelength-scale size, Q will always
decrease to a very small value. This can be intuitively explained as follows. Small-volume modes have abroad distribution in k-space, but TIR confinement
only works for the k component that satisfies the TIR
condition. That is, a broad k distribution results in adecrease in Q. However, PBG confinement does not
impose such a restriction on the k distribution. Therefore, ultimately small-volume and high-Q resonators
are expected to be achieved by PBG resonators. Suchsmall and high-Q resonators are required for large
cavity quantum electrodynamics (cavity-QED)
effects in the solid state and are also important forvarious applications, such as lasers, emitters, andswitching devices. This is the most important featureof PBG resonators.
In this context, a 3D PBG seems to be a fundamental requirement because 2D PBG resonators impose asimilar restriction on the k distribution in the out-ofplane direction. In fact, the Q of 2D PBG resonators
decreases when the mode size is reduced. It is noteasy to make high-Q resonators in 3D-PBG materials
because a high Q requires very high homogeneity ina relatively large volume. Recently, however, there
has been considerable success regarding this matterin 2D PhC slabs. Several strategies have been proposed for increasing the Q value of wavelength-scale
resonators in 2D PhC slabs. They are all intended tominimize the k distribution inside the radiation coneof the 2D PhC slabs (which is simply the light cone of
the cladding material discussed in 2.2.) It has been
numerically shown that modifications to the symmetry of cavity modes can lead to a fundamental
increase in the Q of 2D PBG resonators. Johnson etal. [15] proposed using multi-nodal modes in a squarelattice in which the radiation in the vertical direction
is reduced by destructive interference. Ryu et al.
extended their idea [16] and used whispering gallery
modes (quadrupole modes) in square PhC slabs.
Vuckovic et al. [17] showed that the introduction ofedge dislocations in the center of the dipole modes inhexagonal PhC slabs increased Q.
We investigated multi-nodal modes in hexagonal
PhC slabs. High-Q resonators in hexagonal PhCs arevery important because they have the largest 2D PBG[18]. First, we must look for suitable multi-nodal
Vol. 2 No. 2 Feb. 2004

modes in hexagonal PhC slabs. Many kinds of multinodal modes can be obtained in a large cavity, but wewant to keep the volume as small as possible. The
smallest volume mode is known to be a dipole modein a single point defect cavity [19], which is notfavorable in terms of achieving a high Q value, so
suitable multi-nodal modes should have a slightly
larger volume than a dipole mode and a significantly
larger Q value. It is well known that PBG cavities inhexagonal PhCs can have multi-nodal modes whose
angular momentum numbers are M=1, 2, 4, 6, 12, etc.
Of these, the most suitable candidate is the hexapolemode because it is the smallest order of multi-nodal
modes whose symmetry matches the symmetry of thecrystal lattice. To eliminate the vertical radiation loss,
a very delicate balance is required. Thus, othermodes, such as quadrupole modes, are inferior interms of obtaining a small volume and a large Q.
In Fig. 9, we plot our design of hexapole mode cavities (a) and the electric field distribution of a typical
hexapole mode in real space (b) and k-space (c andd). The real image clearly shows the three-fold rotational symmetry of this mode. The k-space distribution shows that the Fourier intensity is largely concentrated around six M points (one of the symmetry
points in the reciprocal space for hexagonal lattices).
The white circles in (c) and (d) represent the light
cones of air. There is almost no intensity inside thelight cones. This clearly shows that this mode exhibits
very little radiation into the air. Figure 9(e) shows Q
and V as a function of the resonance frequency (thevaried parameter is rm). Here the hole radius r of thecrystal is kept constant at 0.35a. A significantly highQ value of 5 × 105 is obtained when rm=0.26 a. The
effective mode volume V is 0.9(λ/n)3, which is slightly larger than that of the dipole modes in hexagonal
PhCs but still a very small value. It should be notedthat when Q is at its maximum value, V is almost at
its minimum in this case. The high Q and small V
mechanisms must be similar to those in the quadrupole modes in square PhCs. These values (higher Q
and smaller V) in hexagonal PhCs compared withthose in square PhCs can be attributed to the larger
PBG bandwidth of the hexagonal PhCs and the larger azimuthal mode number (=3) of the hexapolemodes. The achieved Q is already much larger thanthose of other high-Q cavities in PhC slabs. But wefound that further improvement was possible by varying the radius of the crystal. When r=0.275a, a Q of 2
× 106 was achieved at rm=0.26a. In this condition, theresonance frequency approached the band edge, so
mode delocalization also contributed to improving
43Selected Papersrmr

PBG waveguide

PBG resonator PBG waveguide(a)rd=0.0a

M
K

Γ

1.0

0.1

(a)

0.01 E-3

rd=0.125a

E-4

(b)

Transmittance (dB)

(b)

1.0

0.01 E-3

0.1

(c)

E-4
(d)

Vertical Q factor

10,0000.25a

0.225arm=0.2a1.2
0.3a0.325a

1000

100

1.4

0.275a0.275 0.300 0.325 0.350 0.375

1.0

0.8

Resonant frequency [ωa/2πc](e)Fig. 9. High-Q PBG resonator: (a) hexapole single-defectPBG resonator in hexagonal PhC slabs, (b)electric-field distribution in real space, (c) and (d)electric-field distribution in Fourier space, where
rm=0.26 a and Q=480,000 in (c) and rm=0.30 a and
Q=11,000 in (d), and (e) calculated Q and mode
volume (V) of hexapole modes as a function of theresonance frequency.

the Q value.
4.2 Coupling between PBG resonators andwaveguides
Isolated resonators themselves may be useful for
laser or light emitting device applications, but res44

–15
–20
1300

1350

1400

1450

1500

(c)

1.6
0.26a

100,000–5–10

Wavelength (nm)

Effective mode volume [(λ/n)3]

1,000,000

0Fig. 10. Resonant tunneling filter. (a) Schematic view, (b)scanning electron micrographs of the devices,and (c) transmission spectra.

onators coupled to other optical elements (waveguides or other resonators) [20], [21] are more important because these coupled elements will be key components in future PhC-based optical circuits. Here we
investigate an example of such a coupled element, asshown in Fig. 10(a). In this device, a single resonatoris coupled to two straight waveguides (input and output). Light from the input waveguide can passthrough the resonator into the output waveguide byresonant tunneling. This tunneling occurs only when
the light wavelength matches the resonance wavelength of the cavity. That is, this device works as awavelength filter. We call this a (two-port) resonant
tunneling filter [22].
Figure 10(b) shows scanning electron micrographsof resonant tunneling filters fabricated in SOI PhC
slabs with air cladding, where a single point-defectcavity was placed between two line-defect waveguides in hexagonal PhC slabs. The measurement
results are shown in Fig. 10(c). We observed sharply
resonant transmission within the transmission window of the PBG waveguides. It is important to note
NTT Technical Review

Selected Papers

that the resonant transmission wavelength changed as
we changed the hole radius of the point defect. In thisway, this device functioned as a wavelength-tunable
narrow-band transmission filter. The resonant wavelength can be easily tuned by modifying the geometrical shape of the point defects.
The performance of this device is represented by
the transmission Q and transmission intensity. The
transmission characteristics of these resonancedevices can be analyzed using the coupled-mode theory [23]. This analysis confirmed that the transmission characteristics can be explained by vertical Q(QV) and horizontal (in-plane) Q (QH). The QV ismainly due to decay into the radiation loss from thecavity, that is, the Q of the isolated cavity, if the crystal size is sufficiently large. QH is mainly due to decay
into the waveguides as a result of coupling. Thus, thetotal Q (QT) is given by 1/QT =1/QV+1/QH, and energy transmittance (T) is expressed as T=(QT/QH)2.
Thus, to achieve a high QT and a high T simultaneously, we must carefully design QV and QH to achieve
optimization. The transmittance was very low (a few
percent) in the result shown in Fig. 9(c), because QH
is too high compared with QV.
With this in mind, we designed another resonant
tunneling filter, as shown in Fig. 11(a). The basic

structure consists of a width-reduced (W=0.65w 0)
waveguide, but the radius of the nearest-neighborholes was slightly varied in the barrier region (thispart is equivalent to a 0.40w0 waveguide). Since themode gap of 0.40w0 waveguides is located within thetransmission window of 0.60w0 waveguides, the lightfield is confined in this mode gap wavelength region.
That is, the center part (cavity part) functions as a resonator although there is no true PBG in the barrier
part. This design has two advantages. One is that it iseasy to change QH continuously by changing thewidth of the barrier part. This continuous tunabilityof QH is effective in achieving a high transmittance.
Another advantage is that this device can work with
SiO2 cladding and also adiabatic mode connectors.
This is not the case for the structure shown in Fig.
10(a), where 1.0w0 PBG waveguides are used. It
should also be noted that the adiabatic mode connector does not fit PhC slabs with air cladding.
We fabricated this type of resonant tunneling filter
with adiabatic mode connectors as described previously. The adiabatic mode connectors were fabricated using the same process as before. This is the first
PBG resonator device that can be directly connected
to single-mode fibers. Figure 11 shows the transmission spectra of this device. The measured Q and ener1

0.65w0Transmittance

0.8

Nb=2

0.6
0.4
0.2

0.4w0

0

1480

1490
(b)

0.6w0
0.15

Transmittance

Nb=3
0.1

0.05

0
(a)

1490

1480
(c)

Fig. 11. Mode-gap resonant tunneling filter with adiabatic mode connector. (a) Schematic view and (b) and (c)experimental transmission spectra for two values of Nb (number of holes for the 0.4w0 waveguide section, i.e.,the barrier thickness). Solid lines are Lorentzian-fitted curves.

Vol. 2 No. 2 Feb. 200445

Selected Papers

gy transmittance values were 408 and 86% for (b)and 1350 and 12% for (c), respectively. Nb is the barrier thickness, that is, the number of holes for the
0.4w0 waveguide section. We achieved a significant
improvement in the transmittance compared with theresult in Fig. 10(c).
Further improvement of this filter requires animprovement in QH, which means that we must combine high-Q PBG cavities with PBG waveguides with
an appropriate coupling strength. We recently
improved these resonant tunneling filters [24].
Instead of single-missing-hole point defects, we used
two-point defects to achieve high QV. As a result oftuning the size of nearest-neighbor holes, we
obtained QV as high as 28,500. By appropriately
designing the barrier between resonators and waveguides (that is, adjusting QH), we achieved QT=7000
and T>70% simultaneously.
In this section, our discussion was limited to twoport devices, but future studies should investigate
more complicated resonator-waveguide coupleddevices, such as devices with four or more ports.

design. We used 3D FDTD simulation to show thatultrahigh-Q and small-volume resonators can bemade in hexagonal PhC slabs. Finally, we investigated one of the simplest forms of resonator-waveguide
coupled devices in PhC slabs, namely resonant tunneling filters. We fabricated resonant tunneling filters
in SOI PhC slabs and studied how to design high-Q
and high-transmittance devices. We made resonant
tunneling mode-gap filters with adiabatic mode connectors and demonstrated that relatively high-Q andhigh-transmittance filters can be made.
These studies show that PBG waveguides and resonators in 2D PhC slabs have various promising features that overcome the fundamental limitations of
2D PhCs. We believe that the future direction of PhCbased photonic integration lies in the direction
described in this paper. More complicated coupleddevices and components will be studied in the future
within a similar context.
References[1]

5. Summary
Future PhC-based photonic integrated circuits will
be based on a combination of PBG waveguides and
PBG resonators. In this paper, we investigated various PBG waveguides and resonators in 2D PhC slabs,
especially 2D SOI PhC slabs, which can be made oncommercially available SOI substrates using existing
mature Si nano-fabrication technology. Thus, 2D
PhC slabs have a great advantage over other forms of
PhC, but there is a severe limitation to 2D PhCs
because they have a PBG only in the in-plane direction. In this study, we showed how this limitation
affects the performance of PBG waveguides and resonators and demonstrated how we can design waveguides and resonators to overcome this limitation.
With appropriate design, it is possible to achieve
efficient PBG waveguides in PhC slabs that include
air and SiO2 cladding. We fabricated various types of
PBG waveguide in SOI PhC slabs. An extremely
large group dispersion, which is one of the most interesting features of PBG waveguides, was experimentally confirmed for the fabricated waveguides. We
made PBG waveguides with adiabatic mode connectors, which greatly improved the connection efficiency between PBG waveguides and single-mode fibers.
The effect of incomplete PBGs in PhC slabs is more
severe for PBG resonators. However, we can also
overcome this problem by using an appropriate
46

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Jose, U.S.A., Jan. 2003.
[10] 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., Vol. 87,
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NTT Technical Review

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Vol. 2 No. 2 Feb. 2004

Masaya Notomi
Distinguished Technical Member, SeniorResearch Scientist, Supervisor, Physical 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 professorof Tokyo Institute of Technology, Japan. He is amember of the Japan Society of Applied Physics(JSAP) and the American Physical Society.

Akihiko Shinya
Physical 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 has been
engaged in R&D of photonic crystal devices. He
is a member of JSAP.

Eiichi Kuramochi
Research Scientist, Physical Science Laboratory, NTT Basic Research Laboratories.
He received the B.E. and M.E. degrees in electrical engineering from Waseda University,
Tokyo in 1989 and 1991, respectively. In 1991,
he joined NTT Optoelectronics Laboratories,
where he engaged in research on semiconductor
nanostructures for photonic devices. He is currently researching photonic crystals. He is amember of JSAP.

47