36 NTT Technical Review

1. Introduction

A photonic crystal is a structure whose refractiveindex is periodically modulated on the scale of anoptical wavelength. Such a crystal is predicted topossess various unique characteristics that cannot beachieved in conventional materials. This is analogousto electronic properties in conventional materials.Various electronic properties—such as conducting,semiconducting, or insulating—arise from electronsin crystals feeling periodic perturbation from the lat-tices, resulting in the formation of so-called energyband structures. In a similar way, light propagation inphotonic crystals (PhCs) can be largely controlledbecause photons in crystals feel periodic perturba-tion, resulting in the formation of photonic bandstructures. As Fig. 1 shows, the dispersion relation-ship in conventional materials is fundamentally dif-ferent from that in PhCs. The former usually exhibitsa photonic band gap (PBG) in which there are nopropagation modes. PhCs within this PBG frequencyrange behave as if they were photonic insulators,which do not exist in nature (for conventional materi-als). In addition, the curvature of the dispersion curveis also very different from that of conventional mate-

rials, which means that the traveling speed of lightcan be controlled over a wide range.

PhCs with PBGs are expected to be key platformsfor future large-scale optical integrated circuits [1],[2]. Making optical (photonic) ICs or LSIs has beenan important target of photonics technology since itstarted several decades ago, but it is still an engineer’sdream. This is mostly due to the very fundamentalcharacteristic of light: photons do not interact effi-ciently with materials or with other photons. Thismakes it difficult to confine photons in a tiny spaceand also leads to poor controllability. Most opticalcomponents rely on total internal reflection (TIR) toconfine the light, but TIR becomes ineffective forsmall components. (This is because TIR is effectiveonly for a certain range of propagation directions.)Actually, optical components are normally signifi-cantly larger than the optical wavelength. PhCs withPBGs give us another mechanism for confining light.Since the reflection caused by PBGs is effective forall angles, PBG confinement works even for wave-length-scale components. In PhCs, point defectsfunction as optical cavities (PBG resonators) whileline defects function as optical waveguides (PBGwaveguides). The coupling of PBG resonators andwaveguides leads to functional devices. Thus, puttinga large number of various functional defects intoPhCs with PBGs (equivalent to creating photonicinsulating substrates) leads to photonic ICs/LSIs

Selected Papers

Masaya Notomi†, Akihiko Shinya, and Eiichi KuramochiAbstract

A photonic crystal having photonic band gaps is expected to play a key role in future large-scale pho-tonic integrated circuits. We have been investigating two-dimensional silicon-on-insulator (SOI) pho-tonic 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 toimplement various components. As a result of appropriate design and with the help of advanced Si nano-fabrication technology, we have successfully made various ultrasmall photonic-band-gap waveguides,resonators, and functional components in SOI photonic crystal slabs with operating wavelengths cover-ing most of the fiber communication wavelengths.

Photonic Crystals: Towards UltrasmallLightwave Circuits

† NTT Basic Research LaboratoriesAtsugi-shi, 243-0198 JapanE-mail: notomi@nttbrl.jp

Vol. 2 No. 2 Feb. 2004 37

(Fig. 2). Since the size of each component is compa-rable to the optical wavelength, the total size of cir-cuits will be significantly less than that of conven-tional optical circuits. In addition, the strong confine-ment of light in PBGs enhances the interaction

between light and matter, as in amplification and opti-cal nonlinear switching, for example.

In this paper, we describe some design and mea-surement issues related to PBG waveguides and res-onators in two-dimensional (2D) PhC slabs (mainly

Nor

mal

ized

freq

uenc

y (ω

a/2π

c)

Fre

quen

cy ω

ω=ck/n

Conventional material

Wavevector k

Photonic band gap

X

Y S

ZT

UR

Si/SiO2/air

X U Z ΓΓ

Γ

YTRS

Photonic crystal

Wavevector k

(a) (b)

0.8

0.6

0.4

0.2

0.0

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

Light source

detector

Switch

(a) (b)

(d)

(c)

λ5, λ6, λ7, λ8

λ1, λ2, λ3, λ4

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

Selected Papers

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38 NTT Technical Review

SOI PhC slabs). We show that ultrasmall waveguidesand resonators having a small radiation loss can bemade using available lithographic nano-fabricationtechniques. Indeed, some of their unique propertieshave already been observed experimentally. In addi-tion, we discuss various functional elements pro-duced by coupling PBG waveguides and resonators.This final topic is very important for integrated-cir-cuit applications.

2. Two-dimensional SOI photonic crystal slab

It might seem natural to choose 2D PhCs for pho-tonic IC applications because the geometry of anyconventional circuit is basically two-dimensional.Actually, most theoretical studies of PhC-based cir-cuits assumed ideal 2D PhCs, that is, infinitely thick2D crystals. However, such simple 2D crystals are notpractical because light will leak out in the out-of-plane direction due to the lack of vertical confinementmechanisms. Of course, proper implementation ofcircuit elements within 3D PhCs having full PBGsshould solve this problem, but such fabrication is very

challenging. Considering how easy it is to fabricate2D 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 variousmethods. In this paper, we show that such efficient 2DPhCs can be made using silicon-on-insulator (SOI)substrates.

Figure 3 shows schematic figures of the fabricationprocess of SOI PhC slabs and electron micrographsof a bulk PhC and a waveguide within a PhC. Period-ic hole patterns are formed on the top Si layer of anSOI substrate by electron beam lithography and elec-tron-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 uppercladding layer is air. We refer to this structure as aSiO2-clad PhC slab. Sometimes we selectively etchoff the SiO2 layer to form an air-bridge structure. Insuch cases, both cladding layers are air. We call thisan air-clad type PhC slab. PhC slabs are 2D PhCstructures located within high-index-contrast slabwaveguides. In PhC slabs, light waves are confined

Si(0.2 µm)

SiO2(3 µm)

SiO2

(c)

Air

w 0.7w0

1 µm

Si

Si

SiO2orAir

Si sub.

Γ-MΓ-K

(a)

(b)

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-variedwaveguides (discussed in 3.2). ( , where a is the lattice constant.)w a0 3=

Selected Papers

Vol. 2 No. 2 Feb. 2004 39

by a combination of in-plane PBG confinement andvertical TIR confinement. Although we still use TIRin the vertical direction, light waves can be stronglyconfined within ultrasmall waveguides and res-onators in PhC slabs without practical leakage if wedesign their structures appropriately.

So, how can we make meaningful 2D PBGs in these2D PhC slabs? Figure 4(a) shows the photonic bandstructure of Si PhC slabs. The red lines in the graphshow band dispersion calculated by the plane-waveexpansion 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 ofthe cladding are leaky because they overlap withradiation modes in the cladding. PBGs below thelight line can work as meaningful 2D PBG withoutradiation loss. If the refractive index n of the claddingmaterial is not so small, the position of the light line

is lower, leading to a reduction or vanishing of theusable PBG region. In this sense, a large index con-trast (between Si and SiO2) 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 directlymeasured the transmittance of 2D SOI hexagonal air-hole PhCs by using a single-mode tapered fiber and awideband white light source. Figure 4(b) showstransmittance spectra along two crystal axes and thecorresponding photonic band diagram for transverseelectric wave (TE) polarization. We observed a com-mon PBG from 1.23 to 1.58 µm for Γ-K and Γ-Mcrystal-axis orientations, which shows that a full PBGis open in the 2D plane. The experimental resultagrees very well with the 3D finite-difference time-domain (FDTD) calculation [4], [5]. The observedPBG covers the entire wavelength range currentlyused for optical communications. Thus, this resultshows that SOI photonic crystal slabs can be consid-ered as possible platforms for photonic ICs in thiswavelength range.

3. PBG waveguides

3.1 DesignNext, we examine how to make efficient wave-

guides in 2D PhC slabs. Our goal is to make a wide-band single guiding mode that operates within thePBG. In fact, if we use only a straight isolated wave-guide, then the position of the mode relative to thePBG is not a serious matter. However, if we want tomake bends, splitters, or coupling to point-defect cav-ities (which is always the case with practical applica-tions), then we need a PBG in the operating band.Figure 5(a) shows the calculated waveguide disper-sion of typical line-defect waveguides in hexagonalPhC slabs. In Fig. 5(a), there are two modes withinthe PBG: an even mode and an odd mode. Thus, thesingle-mode bandwidth is limited by the existence ofthis second odd mode. In addition to the position ofthe PBG, we must consider the position of the lightline of the cladding material. The TIR confinement inthe vertical direction is lost in the mode above thelight line, and the mode becomes leaky. It should benoted that theoretically the mode below the light lineis a truly guided mode that has no propagation loss.We estimated the loss of the leaky modes just abovethe light line to be about 100 dB/mm [6], which wethink is too large for most applications, althoughleaky modes can be used under certain limited condi-

0.5

0.4

0.3

0.2

0.1

0

–10

–20

–30

1200 1300 1400 1500 1600 1700

Γ Γ

Γ-KΓ-M

M KWavevector

Wavelength (nm)

(a)

(b)

Nor

mal

ized

freq

uenc

y (a

/λ)

Tra

nsm

issi

on (

dB)

PBG

PBG

2D-PhC

LL(air)

LL(SiO2)

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

Selected Papers

40 NTT Technical Review

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 disper-sion curve in the limited wavevector space, a largegroup velocity is preferable. The previous sectionsuggests that we can control the operating wave-length and group velocity of waveguiding modes byappropriately controlling the modes having differentcharacteristics and also by controlling the so-calledanticrossing behavior which we discuss below.

We have already examined this light-line problemin PhC slabs in detail [6], [7]. The following brieflysummarizes the issue. In the case of air-clad PhC slabstructures, a conventional single-missing-hole-linewaveguide (Fig. 5(a)) has a relatively wide single-mode bandwidth. But with SiO2 (or polymer) cladPhC slabs, the same single-missing-hole-line wave-guide has only a very small bandwidth. This happensbecause a TIR-guided mode (with a negative curva-ture) and a PBG-guided mode (with a positive curva-ture) cross each other in the PBG under the light line

of SiO2 in a normal single-missing-hole-line defect,and the anticrossing of two modes with opposite cur-vatures results in a very flat band, namely a verysmall width. The situation is graphically shown inFig. 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 wave-guide 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 (= 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 demonstratedthat this modification produced a wideband transmis-sion window for SiO2-clad PhC slabs as shown inFigs. 6(b) and 6(c). We confirmed that this wave-guide has a very small propagation loss (6 dB/mm),which is comparable to normal single-missing-hole-

3

Air

0.3

0 0.1 0.2 0.3

k

0.4 0.5

0.2

Nor

mal

ized

freq

uenc

y

PB

G0.1

0.3

0 0.1 0.2 0.3

k

(a) (b)

0.4 0.5

0.2

Nor

mal

ized

freq

uenc

y

0.1

Odd

SiO2 light line

Even

Even Gap-guided

Index-guidedEven

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).

Selected Papers

Vol. 2 No. 2 Feb. 2004 41

line defects in air-clad PhC slabs. In fact, a normalsingle-missing-hole-line defect has a relatively smalltruly single-mode condition. Thus, the width-reducedwaveguide also improves the width of the truly sin-gle-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 wave-guides have a large degree of freedom when the dis-persion is tuned, there are many other ways to achievethis in an equally practical manner. Examples of othertuning methods are shown in Fig. 6(a) [7]-[9].

3.2 Group velocity dispersion measurementAs 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 largedispersion over a wide wavelength range, as seen inFig. 5(a), cannot be achieved by other conventionaldielectric waveguides. In addition to simple applica-tions to dispersion-controlled waveguides, such alarge dispersion and good controllability of groupvelocity may prove important for various applicationsrelated to optical nonlinear phenomena. In terms ofphysics, it is well known that light-matter interactionin materials is strongly influenced by the groupvelocity of light.

Here, we describe our experimental study of thegroup velocity dispersion of PBG waveguides in SOIPhC slabs [10]. Since there is some reflection at bothends of our PBG waveguides, we can observe aFabry-Perot interference pattern in the transmissionspectra. This interference pattern is directly related tothe group index of the waveguide, so we can deducethe group index if we know the precise length of thewaveguide. Figure 7 shows the deduced group indexof two different PBG waveguides: a normal single-missing-hole-line waveguide (W=1.0w0) and awidth-reduced waveguide (W=0.65w0). The deducedgroup index shows an extremely large group velocitydispersion. It also shows an extremely large group

Normalized frequency: ω=a/λ

W

(a)

(b)

W=1.0W0

ω=0.265

line defect

line defect

waveguiding modeW=0.7W0

Tran

smitt

ance

(dB

)

Wavelength (nm)

(c)

0.300

–5

–10

–15

–20

–25

–30

–35

Tran

smitt

ance

(dB

)

0

–5

–10

–15

–20

–25

–30

–35

0.28 0.26 0.24

1300 1400 1500 1600 1700

Wavelength (nm)1300 1400 1500 1600 1700

Fig. 6. Structural tuning of PBG waveguides. (a) Variousexamples of structural tuning (width-varied, egg-shaped-hole, and phase-shifted-hole) and (b) and(c) transmission spectra of PBG waveguides in2D SOI PhC slabs with SiO2 cladding, where thewaveguides are normal single-missing-hole linedefect waveguides in (b) and width-reduced linedefect waveguides in (c). a is the lattice constant.

100

80

60

Gro

up in

dex G

roup

inde

x

40

20

01460 1480 1500

1.0w0

0.65w0

1.0w0

1420

15

10

5

01460

λ (nm)1500

Wavelength: λ (nm)

1520

Fig. 7. Group velocity dispersion measurement. Measuredgroup index as a function of wavelength.

Selected Papers

42 NTT Technical Review

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 populationmodulation [12], by controlling the material disper-sion. Such slow modes are expected to provide ulti-mate 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 resultindicates that a PBG waveguide may be another can-didate for enhancing light-matter interaction.

3.3 Coupling to fibersOne of the most frequently addressed problems

concerning PBG waveguides is their poor couplingefficiency with conventional single-mode fibers. Thisis a fundamental problem because the mode size forline-defect waveguides is always very much smallerthan that for silica single-mode fibers. This smallnessis usually considered to be an advantage for PhCs, butit 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 magni-tude smaller than that of a silica single-mode fiber.Moreover, there is a large reflection loss due to thelarge index difference between PBG waveguides and

silica fibers.To solve this problem, we designed an adiabatic

mode connector, which is monolithically integratedin 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 Si-wire waveguide, which was invented by NTTMicrosystem Integration Laboratories [14], and amode-profile converter (MPC), which adiabaticallyconnects a Si-wire waveguide and ii) a photonic-crys-tal waveguide. The mode size and the refractive indexof the polymer waveguide were designed to be thesame as those of a high-∆ single-mode fiber. Themode size in the Si-wire waveguide was designed tobe the same as that in the PBG waveguide. The fabri-cation process is very simple, namely a combinationof a single-stage Si etching process and a convention-al polymer waveguide process.

We fabricated this device and investigated its con-nection loss. The measured connection loss was 3–4dB per port, which is the sum of the connection loss-es for SSC and MPC. Compared with the value of 30dB, we significantly reduced the connection loss.Recently, a connection loss of 0.8 dB per port in anSSC for Si-wire waveguides was reported by NTTMicrosystem Integration Laboratories [14]. If wecombine that with this technology, we believe that wecan further reduce the connection loss for PBG wave-guides.

Spot-size converter

Mode profile converter

Mode size0.2 × 0.3 µm

Photonic-crystal waveguide

Si-wire waveguide

Polymer waveguide

Single-mode fiber

Mode size 9 µm-φ

Fig. 8. Adiabatic mode connector containing a spot-size converter and a mode-profile converter.

Selected Papers

Vol. 2 No. 2 Feb. 2004 43

4. PBG resonators

4.1 DesignWith conventional optical resonators, which rely on

TIR confinement, their quality factor (Q) is limitedby their mode volume. That is, if the mode volume isreduced to a wavelength-scale size, Q will alwaysdecrease to a very small value. This can be intuitive-ly explained as follows. Small-volume modes have abroad distribution in k-space, but TIR confinementonly works for the k component that satisfies the TIRcondition. That is, a broad k distribution results in adecrease in Q. However, PBG confinement does notimpose such a restriction on the k distribution. There-fore, ultimately small-volume and high-Q resonatorsare expected to be achieved by PBG resonators. Suchsmall and high-Q resonators are required for largecavity 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 fundamen-tal requirement because 2D PBG resonators impose asimilar restriction on the k distribution in the out-of-plane direction. In fact, the Q of 2D PBG resonatorsdecreases when the mode size is reduced. It is noteasy to make high-Q resonators in 3D-PBG materialsbecause a high Q requires very high homogeneity ina relatively large volume. Recently, however, therehas been considerable success regarding this matterin 2D PhC slabs. Several strategies have been pro-posed for increasing the Q value of wavelength-scaleresonators 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 ofthe cladding material discussed in 2.2.) It has beennumerically shown that modifications to the symme-try of cavity modes can lead to a fundamentalincrease 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 directionis reduced by destructive interference. Ryu et al.extended their idea [16] and used whispering gallerymodes (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 hexagonalPhC 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

modes in hexagonal PhC slabs. Many kinds of multi-nodal modes can be obtained in a large cavity, but wewant to keep the volume as small as possible. Thesmallest 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, sosuitable multi-nodal modes should have a slightlylarger volume than a dipole mode and a significantlylarger Q value. It is well known that PBG cavities inhexagonal PhCs can have multi-nodal modes whoseangular 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-nodalmodes 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 cav-ities (a) and the electric field distribution of a typicalhexapole mode in real space (b) and k-space (c andd). The real image clearly shows the three-fold rota-tional symmetry of this mode. The k-space distribu-tion shows that the Fourier intensity is largely con-centrated around six M points (one of the symmetrypoints in the reciprocal space for hexagonal lattices).The white circles in (c) and (d) represent the lightcones of air. There is almost no intensity inside thelight cones. This clearly shows that this mode exhibitsvery little radiation into the air. Figure 9(e) shows Qand 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. Theeffective mode volume V is 0.9(λ/n)3, which is slight-ly larger than that of the dipole modes in hexagonalPhCs but still a very small value. It should be notedthat when Q is at its maximum value, V is almost atits minimum in this case. The high Q and small Vmechanisms must be similar to those in the quadru-pole modes in square PhCs. These values (higher Qand smaller V) in hexagonal PhCs compared withthose in square PhCs can be attributed to the largerPBG bandwidth of the hexagonal PhCs and the larg-er 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 vary-ing 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, somode delocalization also contributed to improving

the Q value.

4.2 Coupling between PBG resonators andwaveguides

Isolated resonators themselves may be useful forlaser or light emitting device applications, but res-

onators coupled to other optical elements (wave-guides or other resonators) [20], [21] are more impor-tant because these coupled elements will be key com-ponents in future PhC-based optical circuits. Here weinvestigate 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 out-put). Light from the input waveguide can passthrough the resonator into the output waveguide byresonant tunneling. This tunneling occurs only whenthe light wavelength matches the resonance wave-length of the cavity. That is, this device works as awavelength filter. We call this a (two-port) resonanttunneling filter [22].

Figure 10(b) shows scanning electron micrographsof resonant tunneling filters fabricated in SOI PhCslabs with air cladding, where a single point-defectcavity was placed between two line-defect wave-guides in hexagonal PhC slabs. The measurementresults are shown in Fig. 10(c). We observed sharplyresonant transmission within the transmission win-dow of the PBG waveguides. It is important to note

Selected Papers

44 NTT Technical Review

0.1 0.011.0 0.01 E-3 E-4

rrm

M

KΓ

(a) (b)

1.0 0.1 0.01 E-3 E-4

(c) (d)

0.275 0.300 0.325 0.350 0.375100

1000

10,000

100,000

1,000,0000.26a

0.325a

0.3a

0.275a

0.25a

0.225a

rm=0.2a

Resonant frequency [ωa/2πc]

Ver

tical

Q fa

ctor

0.8

1.0

1.2

1.4

1.6

Effe

ctiv

e m

ode

volu

me

[(λ/

n)3 ]

(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, whererm=0.26 a and Q=480,000 in (c) and rm=0.30 a andQ=11,000 in (d), and (e) calculated Q and modevolume (V) of hexapole modes as a function of theresonance frequency.

PBG waveguide PBG resonator PBG waveguide

rd=0.125ard=0.0a

0

–5

1300 1350 1400

Wavelength (nm)

(c)

(a)

(b)

1450 1500

–10T

rans

mitt

ance

(dB

)

–15

–20

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

that the resonant transmission wavelength changed aswe changed the hole radius of the point defect. In thisway, this device functioned as a wavelength-tunablenarrow-band transmission filter. The resonant wave-length can be easily tuned by modifying the geomet-rical shape of the point defects.

The performance of this device is represented bythe transmission Q and transmission intensity. Thetransmission characteristics of these resonancedevices can be analyzed using the coupled-mode the-ory [23]. This analysis confirmed that the transmis-sion 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 crys-tal size is sufficiently large. QH is mainly due to decayinto the waveguides as a result of coupling. Thus, thetotal Q (QT) is given by 1/QT =1/QV+1/QH, and ener-gy transmittance (T) is expressed as T=(QT/QH)2.Thus, to achieve a high QT and a high T simultane-ously, we must carefully design QV and QH to achieveoptimization. The transmittance was very low (a fewpercent) 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=0.65w0)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 res-onator although there is no true PBG in the barrierpart. 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 withSiO2 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. Itshould also be noted that the adiabatic mode connec-tor does not fit PhC slabs with air cladding.

We fabricated this type of resonant tunneling filterwith adiabatic mode connectors as described previ-ously. The adiabatic mode connectors were fabricat-ed using the same process as before. This is the firstPBG resonator device that can be directly connectedto single-mode fibers. Figure 11 shows the transmis-sion spectra of this device. The measured Q and ener-

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Vol. 2 No. 2 Feb. 2004 45

0.65w0

1

0.15

0.1

0

0.05

0.8

Tra

nsm

ittan

ceT

rans

mitt

ance

0.6

0.4

0.2

01480 1490

1480

Nb=2

Nb=3

(b)

(c)(a)1490

0.4w0

0.6w0

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.

gy transmittance values were 408 and 86% for (b)and 1350 and 12% for (c), respectively. Nb is the bar-rier thickness, that is, the number of holes for the0.4w0 waveguide section. We achieved a significantimprovement in the transmittance compared with theresult in Fig. 10(c).

Further improvement of this filter requires animprovement in QH, which means that we must com-bine high-Q PBG cavities with PBG waveguides withan appropriate coupling strength. We recentlyimproved these resonant tunneling filters [24].Instead of single-missing-hole point defects, we usedtwo-point defects to achieve high QV. As a result oftuning the size of nearest-neighbor holes, weobtained QV as high as 28,500. By appropriatelydesigning the barrier between resonators and wave-guides (that is, adjusting QH), we achieved QT=7000and T>70% simultaneously.

In this section, our discussion was limited to two-port devices, but future studies should investigatemore complicated resonator-waveguide coupleddevices, such as devices with four or more ports.

5. Summary

Future PhC-based photonic integrated circuits willbe based on a combination of PBG waveguides andPBG resonators. In this paper, we investigated vari-ous PBG waveguides and resonators in 2D PhC slabs,especially 2D SOI PhC slabs, which can be made oncommercially available SOI substrates using existingmature Si nano-fabrication technology. Thus, 2DPhC slabs have a great advantage over other forms ofPhC, but there is a severe limitation to 2D PhCsbecause they have a PBG only in the in-plane direc-tion. In this study, we showed how this limitationaffects the performance of PBG waveguides and res-onators and demonstrated how we can design wave-guides and resonators to overcome this limitation.

With appropriate design, it is possible to achieveefficient PBG waveguides in PhC slabs that includeair and SiO2 cladding. We fabricated various types ofPBG waveguide in SOI PhC slabs. An extremelylarge group dispersion, which is one of the most inter-esting features of PBG waveguides, was experimen-tally confirmed for the fabricated waveguides. Wemade PBG waveguides with adiabatic mode connec-tors, which greatly improved the connection efficien-cy between PBG waveguides and single-mode fibers.

The effect of incomplete PBGs in PhC slabs is moresevere for PBG resonators. However, we can alsoovercome this problem by using an appropriate

design. We used 3D FDTD simulation to show thatultrahigh-Q and small-volume resonators can bemade in hexagonal PhC slabs. Finally, we investigat-ed one of the simplest forms of resonator-waveguidecoupled devices in PhC slabs, namely resonant tun-neling filters. We fabricated resonant tunneling filtersin SOI PhC slabs and studied how to design high-Qand high-transmittance devices. We made resonanttunneling mode-gap filters with adiabatic mode con-nectors and demonstrated that relatively high-Q andhigh-transmittance filters can be made.

These studies show that PBG waveguides and res-onators in 2D PhC slabs have various promising fea-tures that overcome the fundamental limitations of2D PhCs. We believe that the future direction of PhC-based photonic integration lies in the directiondescribed in this paper. More complicated coupleddevices and components will be studied in the futurewithin a similar context.

References

[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-statephysics and electronics,” Phys. Rev. Lett., Vol. 58, pp. 2059-2062,1987.

[2] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic Crys-tals,” Princeton University Press, 1995.

[3] C. Takahashi, J. Takahashi, M. Notomi, and I. Yokohama, “Accuratedry etching with fluorinated gas for two-dimensional Si photoniccrystals,” MRS Proceedings Vol. 637, E1.8, 2000.

[4] I. Yokohama, M. Notomi, A. Shinya, C. Takahashi, and T. Tamamu-ra, OECC, Makuhari, Chiba, Jul. 2000.

[5] A. Shinya, M. Notomi, I. Yokohama, C. Takahashi, J. Takahashi, andT. Tamamura, “Two-dimensional Si photonic crystals on oxide usingSOI substrate,” Optical and Quantum Electronics, Vol. 34, No. 1-3,pp. 113-121, 2002.

[6] M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I.Yokohama, “Single-mode transmission within the photonic bandgapof width-varied single-line-defect photonic crystal waveguides onSOI substrates,” Electron. Lett., Vol.37, pp.243-244, 2001.

[7] M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I.Yokohama, “Structural tuning of guiding modes of line-defect wave-guides of SOI photonic crystal slabs,” IEEE J. Quantum Electron.,Vol. 38, No. 7, pp. 736-742, 2002.

[8] A. Shinya, M. Notomi, K. Yamada, C. Takahashi, J. Takahashi, and I.Yokohama, “Two-dimensional Si-photonic crystal single modewaveguide on SiO2 substrate which functions above the light line,”OSA Topical Meeting of Integrated Photonic Research (IPR 2001),IMD4, Monterey, U.S.A., Jun. 2001.

[9] A. Shinya, M. Notomi, and E. Kuramochi, “Single-mode Transmis-sion in Commensurate Width-Varied Line-Defect SOI Photonic Crys-tal Waveguides,” SPIE Photonics West, Optoelectronics 2003, SanJose, 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. 87,253902, 2001.

[11] L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature, “Lightspeed reduction to 17 metres per second in an ultracold atomic gas,”Vol. 397, pp. 594-596, 1999.

[12] M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation ofultraslow light propagation in a ruby crystal at room temperature,”

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46 NTT Technical Review

Phys. Rev. Lett., Vol. 90, 113903, 2003. [13] A. Shinya, M. Notomi, E. Kuramochi, T. Shoji, T. Watanabe, T.

Tsuchizawa, K. Yamada, and H. Morita, “Functional Components inSOI Photonic Crystal Slabs,” SPIE Proc. Vol. 5000, 21, pp. 104-117,2003.

[14] T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita,“Low loss mode size converter from 0.3 µm square Si wire wave-guides to single mode fibers,” Electron. Lett., Vol. 38, pp. 1669-1670,2002.

[15] S. G. Johnson, A. Mekis, S. Fan, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a com-plete photonic band gap,” Appl. Phys. Lett., Vol. 78, pp. 3388-3390,2001.

[16] H-Y. Ryu, S-H. Kim, H-G. Park, J-K. Hwang, Y-H. Lee, and J-S.Kim, “Square-lattice photonic band-gap single-cell laser operating inthe lowest-order whispering gallery mode,” Appl. Phys. Lett., Vol.80, pp. 3883-3885, 2002.

[17] J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimizationof the Q factor in photonic crystal microcavities,” IEEE J. QuantumElectron., Vol. 38, No. 7, pp. 850-856, 2002.

[18] H-Y. Ryu, M. Notomi, Y-H. Lee, “High quality factor and small vol-ume hexapole modes in photonic crystal nanocavities,” Appl. Phys.Lett., Vol. 83, No. 21, pp. 4294-4296, 2003.

[19] R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E.Yablonovitch, “Smallest possible electromagnetic mode volume in adielectric cavity,” IEE Proc. Optoelectron., Vol. 145, No. 06, pp. 391-397, 1998.

[20] S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Chan-nel drop tunneling through localized states,” Phys. Rev. Lett., Vol. 80,pp. 960-963, 1998.

[21] S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of pho-tons by a single defect in a photonic bandgap structure,” Nature, Vol.407, pp. 608-611, 2000.

[22] M. Notomi, “Photonic-band-gap waveguides and resonators,” LEOS2003, Tucson, Arizona, U.S.A., pp. 212-213, Oct. 2003.

[23] C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, andJ. D. Joannopoulos, “Coupling of modes analysis of resonant channeladd-drop filters,” IEEE J. Quantum Electron., Vol. 35, No. 9 , pp. 1322-1331, 1999.

[24] 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,” LEOS 2003,Tucson, Arizona, U.S.A., pp. 214-215, Oct. 2003.

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Vol. 2 No. 2 Feb. 2004 47

Masaya NotomiDistinguished Technical Member, Senior

Research Scientist, Supervisor, Physical ScienceLaboratory, 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, respec-tively. In 1988, he joined NTT OptoelectronicsLaboratories. Since then, his research interest hasbeen to control the optical properties of materialsand devices by using artificial nanostructures,and he has been researching semiconductorquantum wires/dots and photonic crystal struc-tures. In 1996-1997, he was at Linköping Uni-versity, Sweden as a visiting researcher. Since2002, 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 ShinyaPhysical Science Laboratory, NTT Basic

Research Laboratories. He received the B.E., M.E., and Dr. Eng.

degrees in electrical engineering from Tokushi-ma University, Tokushima in 1994, 1996, and1999, respectively. In 1999, he joined the NTTBasic Research Laboratories. He has beenengaged in R&D of photonic crystal devices. Heis a member of JSAP.

Eiichi KuramochiResearch Scientist, Physical Science Laborato-

ry, NTT Basic Research Laboratories.He received the B.E. and M.E. degrees in elec-

trical engineering from Waseda University,Tokyo in 1989 and 1991, respectively. In 1991,he joined NTT Optoelectronics Laboratories,where he engaged in research on semiconductornanostructures for photonic devices. He is cur-rently researching photonic crystals. He is amember of JSAP.