Analysis of a Line-Defect Waveguide

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 22, NO. 12, DECEMBER 2004 2787

Analysis of a Line-Defect Waveguide ona Silicon-on-Insulator Two-Dimensional

Photonic-Crystal SlabYoshinori Tanaka, Takashi Asano, Ranko Hatsuta, and Susumu Noda, Member, IEEE

AbstractThis paper describes the investigation of the wave-guide properties of a silicon-on-insulator (SOI)-based two-dimen-sional photonic-crystal slab. It is found that coupling betweentransverse-electric (TE)-like defect modes and transverse-mag-netic (TM)-like slab modes occurs in some frequency range dueto structural asymmetries in the vertical direction. This TETMcoupling, together with the smaller refractive-index contrastbetween the slab and dielectric cladding, results in propagationlosses for a line-defect waveguide in an SOI structure. The paperalso presents optimization methods for obtaining a wide losslesspropagation band using such a line defect.

Index TermsLine-defect waveguide, photonic-crystal slab,propagation loss, silicon-on-insulator, TETM coupling.

I. INTRODUCTION

PHOTONIC CRYSTALS (PC) [1], [2], which have periodic

refractive-index modulations, are a new optical material.

The most characteristic feature of a PC is the existence of

a photonic bandgap (PBG) where photons cannot propagate

into the PC. Artificial defects introduced into PCs can control

the photons with a large degree of freedom. Among various

possible PC structures, the two-dimensional (2-D) PC slab,which consists of a thin dielectric slab with cladding layers

processed to form a 2-D PC structure, has attracted much

attention. Such structures can be fabricated relatively easily and

can realize strong optical confinement. Photons are controlled

by the PBG effect for the in-plane direction and by the large

refractive-index contrast between the slab and the cladding

layers in the vertical direction. Line defects introduced in a 2-D

PC slab can be utilized as waveguides, and point defects can

be utilized as ultrasmall cavities. Various device applications

such as ultrasmall surface-emitting channel add/drop filters

[3], [4] and other optical circuits have been developed by the

use of defects in 2-D PC slabs.Careful selection of the cladding material is important for the

utilization of 2-D PC slabs, as the refractive-index contrast de-

termines optical confinement in the vertical direction. When the

Manuscript received October 9, 2003; revised June 2, 2004. This work is sup-ported in part by CREST, the Japan Science and Technology Corporation, andby the Ministry of Education, Culture, Sports, Science and Technology of Japanunder a Grant-in-Aid for Scientific Research.

Y. Tanaka, T. Asano, and S. Noda are with the Department of ElectronicScience and Engineering, Kyoto University, Kyoto 615-8510, Japan (e-mail:[email protected]; [email protected]).

R. Hatsuta is with the R&D Center, TDK Corporation, Chiba 272-8558,Japan.

Digital Object Identifier 10.1109/JLT.2004.833290

Fig. 1. Schematic of an SOI 2-D PC-slab waveguide.

slab has air cladding on both sides, strong confinement can be

achieved because of the large refractive-index contrast. In this

case, an air-bridge structure is typically utilized to support the

slab. In addition, a slab having dielectric cladding on one side

and air cladding on the other [5] is also interesting. The mechan-

ical robustness of such structures is improved by the existence of

the supporting dielectric material under the slab, although this

results in weaker optical confinement due to the reduced refrac-tive-index contrast. It should be noted that a 2-D PC slab on

dielectric cladding exhibits an asymmetric refractive-index dis-

tribution for the vertical direction. To the authors knowledge,

there have been no reports specifically discussing vertical asym-

metries of such structures, except for our previous short paper

[6]. In this present paper, detailed consideration is given to the

effects of one-sided cladding on the line-defect waveguides by

employing a typical 2-D PC structure fabricated using a sil-

icon-on-insulator (SOI) substrate.

In Section II, the properties of SOI 2-D slab waveguides is

theoretically discussed, and a new concept, the TM-slab line,

is demonstrated. In Section III, the waveguide properties are

investigated experimentally and compared with theoretical re-

sults. Section IV discusses the optimal structure for the realiza-

tion of a wide propagation band in the SOI 2-D PC waveguide.

The findings are summarized in Section V.

II. ANALYSIS OF WAVEGUIDE PROPERTIES

AND THE TM-SLAB LINE

First, we investigate the properties of a line-defect waveguide

formed in the SOI 2-D PC structure. A schematic of the assumed

SOI 2-D PC structure is given in Fig. 1, showing a triangular lat-

ticeof air holes of lattice constant and radius , formedin anSi

slab of thickness on SiO cladding. The line-defect waveguide

0733-8724/04$20.00 2004 IEEE


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TANAKA et al.: ANALYSIS OF A LINE-DEFECT WAVEGUIDE ON AN SOI 2-D PC SLAB 2789

Fig. 3. Electromagnetic-field distribution across the 2-D PC-slab waveguideat the center of the slab: (a)

H

and (b)E

.

structure. It is seen in the figures that there is no propagation

loss under the SiO light line, demonstrating that a TM-slab line

does not exist in such vertically symmetric structures.

III. EXPERIMENTAL VERIFICATION OF THE TM-SLAB LINE

We have shown in Section II that TETM coupling due to the

vertical asymmetry of the structure results in large propagation

losses and that a TM-slab line should be considered for the re-

alization of lossless propagation. To confirm these theoretical

results, we experimentally investigate the transmission spectra

of SOI 2-D PC-slab waveguides.

The structure was fabricated using an SOI substrate, and the

PC patterns were introduced on the Si layer. Electron-beam

lithography and induction-coupling plasma-reactive-ion etching

techniques were utilized for the fabrication. Both edges of the

2-D PC waveguide were cleaved. A scanning electron micro-

scope image of the fabricated sample is shown in Fig. 4(a).

The lattice constant, air-hole radius, waveguide width, and

slab thickness of the fabricated sample were measured to be0.41 m, , and , respectively. The

waveguide length was 250 m ( ), which was long enough

to investigate the influence of the TETM coupling.

The dispersion curve was calculated for the fabricated struc-

ture using the 3-D FDTD method and is shown in Fig. 4(b),

which indicates that the waveguide modefrequency range

under the TM-slab line is about 23 nm (15471570 nm). The

transmission spectrum of a waveguide with the same length

as the sample (250 m) was also calculated from the loss

factor and is shown in Fig. 5(a). This clearly illustrates that

the propagation band is limited by the TM-slab line instead

of the SiO light line in waveguides long enough for practicalapplications. The transmittance spectrum for wavelengths

longer than 1570 nm, where no waveguide mode exists, cannot

be calculated directly using these methods; however, the trans-

mittance should be zero, as incident light cannot couple into

any TE-like waveguide modes.

Next, the transmission spectrum of the waveguide was mea-

sured. Incident light was injected from free space into one facet

of the waveguide, and light transmitted through the waveguide

and emitted from the other facet was measured. The obtained

spectrum is plotted in Fig. 5(b), which shows that the width of

the high-transmission band is 24 nm (15281552 nm), consis-

tent with the calculated results [Fig. 5(a)], except that the wave-

guide-mode frequency is shifted to longer wavelengths. Thisshift is considered to be due to uncertainty in the fabrication

Fig. 4. (a)SEM image of thefabricated SOI2-D PC waveguide. (b)Calculateddispersion curve of fabricated waveguide.

Fig. 5. Transmittance spectra of the fabricated sample: (a) calculation resultand (b) experimental result.

process. The oscillations observed in the experimental spectrum

are FabryProt interference fringes due to reflections at the

cleaved facets of the waveguide. The results show that the prop-agation band of an SOI 2-D PC waveguide is determined by the

TM-slab line, not by the clad light line, and clearly indicate the

existence of TETM coupling.

IV. OPTIMIZATION OF THE STRUCTURE FOR SOI 2-D

PC-SLAB WAVEGUIDE

There are some discussions regarding structural optimization

of SOI 2-D PC-slab waveguides, which take into account the

SiO light line [5]. However, we have shown in Sections II and

III that large propagation losses occur on an SOI 2-D PC-slab

waveguide due to coupling between the TE-like waveguide

mode and the TM-like slab modes, resulting in a TM-slab linethat should be taken into account when designing a line-defect


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2790 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 22, NO. 12, DECEMBER 2004

Fig. 6. Dispersion curves for PC waveguides with slab thicknesses of (a)0 : 4

, (b)0 : 5

, and (c)0 : 6 a

.

waveguide in an SOI 2-D PC slab. Further discussions re-

garding the optimal waveguide structure are therefore needed,

with the TM-slab line taken into account. Here, we discuss

optimal structures for a broader lossless propagation band,

where TE-like waveguide modes and TM-like slab modes donot overlap.

A. Slab Thickness

Firstly, we investigate the relation between the lossless prop-

agation band and slab thickness. Fig. 6 shows the calculated

dispersion of PC-slab waveguides of slab thicknesses , ,

and . The air-hole radius and waveguide width are fixed at

and , respectively. As the slab becomes thin,

the frequencies of both the TE-like waveguide mode and the

TM-like slab modes increase due to the decrease of the equiva-lent refractive index. As the electric-field intensity of the lowest

order TM-like modes at the slab surface is generally stronger

than that of the lowest order TE-like mode due to the difference

in the boundary condition, the mode frequency of the former

changes more rapidly than that of the latter when the slab thick-

ness is varied. Therefore, the lossless propagation band becomes

broader as the slab narrows, as shown in Fig. 6. It should also

be noted that the lossless propagation bandwidth does not vary

greatly when the slab thicknesses is varied from to

[Fig. 6(a) and (b)]. As the region under the SiO light line be-

comes small in the high-frequency region, a wide propagation

band cannot be obtained for a very thin slab. This suggests that

a slab thickness of optimizes the width of the losslesspropagation band.

B. Waveguide Width

Next, we investigate the relation between the lossless

propagation band and the waveguide width. Fig. 7(a)(c)

shows calculated dispersion relations for waveguide widths of, , and , respectively. The air-hole

radius and slab thickness were fixed at and , re-

spectively. The figure shows that the frequency of the TE-like

waveguide mode decreases as the waveguide becomes wider,

whereas the frequency of the slab modes remains constant. As

a result, a broader lossless propagation band can be obtained as

the waveguide becomes wider.

Here, it should be observed that, for the widest ( )

waveguides [Fig. 7(c)], the low-frequency side of the propaga-

tion band does not remain within the PBG. Even in this case,

the mode is considered to show lossless propagation, as there

are no TE-like slab modes that directly overlap with the wave-

guide mode. However, this is likely to become a serious problemwhen point-defect resonators and/or waveguide bends are in-

troduced. Therefore, it is important that the waveguide modes

remain within the PBG region when applications to optical cir-

cuits are considered.

C. Radius of Air Holes

Finally, we investigate the relation between the lossless prop-

agation band and the air-hole radius. Fig. 8(a)(c) shows the

calculated dispersion relations for waveguides with an air-hole

radii of , , and , respectively. The slab thickness

and waveguide width were fixed at and ,

respectively. A decrease in the air-hole radius corresponds toan increase in the effective refractive index of the slab for the


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[5] M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I.Yokohama, Structural tuning of guiding modes of line-defect waveg-uides of silicon-on-insulator photonic crystal slabs, IEEE J. Quantum

Electron., vol. 38, pp. 736742, July 2002.[6] Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, Theoretical

investigation of a two-dimensional photonic crystal slab with truncatedcone air holes, Appl. Phys. Lett., vol. 82, pp. 16611663, 2003.

[7] A. Chutinan and S. Noda, Waveguides and waveguide bends in two-

dimensional photonic crystal slabs, Phys. Rev. B, Condens. Matter, vol.62, pp. 44884492, 2000.[8] K. S. Yee, Numerical solution of initial boundary value problems in-

volving Maxwells equations in isotropic media,IEEE Trans. AntennasPropagat., vol. 14, pp. 302307, May 1966.

[9] J. P. Berenger, A perfectly matched layer for the absorption of electro-magnetic waves, J. Comput. Phys., vol. 114, pp. 185200, 1994.

[10] T. Ochiai and K. Sakoda, Dispersion relation and optical transmittanceof a hexagonal photonic crystal slab, Phys. Rev. B, Condens. Matter,vol. 63, p. 125 107, 2001.

Yoshinori Tanaka, photograph and biography not available at the time ofpublication.

Takashi Asano, photograph and biography not available at the time ofpublication.

Ranko Hatsuta, photograph and biography not available at the time ofpublication.

Susumu Noda (M92), photograph and biography not available at the time ofpublication.

Analysis of a Line-Defect Waveguide

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