IEICE TRANS. ELECTRON., VOL.E85–C, NO.4 APRIL 2002

1033

PAPER

Special Issue on Recent Progress of Integrated Photonic Devices

Low Loss Ultra-Small Branches in a Silicon Photonic Wire
Waveguide
Atsushi SAKAI† , Tatsuhiko FUKAZAWA† , Nonmembers,
and Toshihiko BABA†a) , Regular Member

SUMMARY We theoretically and experimentally demonstrate low loss branches in a Si photonic wire waveguide. Approximate calculation by the two-dimensional ﬁnite-diﬀerence timedomain (2-D FDTD) method and detailed design by the 3-D
FDTD method indicate that low excess loss less than 0.2 dB is expected for a µm-size bend-waveguide-type branch at a wavelengthof 1.55 µm. This branch is fabricated in a silicon-on-insulator substrate and the loss is evaluated to be 0.3 dB. This value is smallenough to construct a very compact branching circuit.
key words: integrated optics, optical waveguide, branch circuit,
SOI, FDTD

1.

Introduction

For a dense wavelength division multiplexing system with several hundred channels, the size reduction
and high-density integration of optical circuits suchas wavelength multi/demultiplexers and cross connect
switches are crucial. The most fundamental issue is tominiaturize optical waveguides. However, conventional
silica-based waveguides have small ﬂexibility in opticalwirings because of large bends and branches, each occupying mm2 –cm2 area. To realize a compact opticalcircuit of mm2 in total area, the bend radius must beof µm order. The photonic crystal waveguide [1] is oneof the candidates that clear this issue, so it is attracting much attention. However, it requires a complex
design theory and a ﬁne fabrication process. Anothersimpler solution is an ultra-high ∆ waveguide, where∆ is the relative refractive index diﬀerence deﬁned as(n21 − n22 )/2n21 for core index n1 and cladding index n2 .
A commercially available silicon-on-insulator (SOI)
substrate is usable for such a high-∆ waveguide. The
Si slab (n1 ∼3.5) is used as a core and the SiO2 (n2∼1.45) layer is used as a cladding in the transparent
wavelength range of λ = 1.3–1.55 µm. Therefore, ∆of this waveguide is as large as 45%. Of course, thiswafer is used for electronic circuits. Thus, the SOI substrate can be a platform of functional opto-electronic
circuits. So far, rib-type waveguides in an SOI substrate have been demonstrated with a low propagation
loss less than 0.5 dB/cm [2], [3]. However, the bend
radius was of mm order because of the weak optical
Manuscript received October 9, 2001.
The authors are with Division of Electrical andComputer Engineering, Yokohama National University,
Yokohama-shi, 240-8501 Japan.
a) E-mail: baba@dnj.ynu.ac.jp†

conﬁnement. For µm order bends, Si layer must be thecompletely etched down to be the rectangular shape, as
shown in Fig. 1.
Such rectangular waveguide has also been reported[4]. However, only the propagation loss of the straightwaveguide was discussed, and other components suchas bends and branches have not been investigated yet.
In a previous work, we fabricated this type of waveguide, which satisﬁes the singlemode condition, andshowed that 1) the propagation loss is ∼10 dB/mm at
λ = 1.55 µm and it is dominated by the scattering loss
caused by the high-∆, 2) the group index is larger thanthe material index, and 3) the bend loss can be less than
1 dB, when the bend radius is only 1 µm [5]. Based onthese results, we designed and fabricated ultra-small
branches in an SOI substrate, and demonstrated thelow excess loss in this work. We ﬁrst estimated theexcess loss in several branches by the 2-dimensional (2D) ﬁnite-diﬀerence time-domain (FDTD) method [6].
For two structures showing low loss in this calculation,
we designed the structural detail by the 3-D FDTD
method. Then, we fabricated a bend-waveguide-type
branch, the best structure for low excess loss, and evaluated its characteristics.
2.

2-D FDTD Analysis of Various Branches

The FDTD method is very powerful for simulating electromagnetic properties in arbitrary structure with ahigh index contrast. In a 3-D FDTD calculation, however, a large computer memory and a long CPU time
are required. The 2-D FDTD method with the equivalent index approximation signiﬁcantly reduces the load
SiO2 Cladding
Si CoreLight
Si SubstratexzyFig. 1 Schematic of Si rectangular channel photonic wire
waveguide and the coordinate system.

IEICE TRANS. ELECTRON., VOL.E85–C, NO.4 APRIL 20021034

of calculation and gives a rough but reasonable estimation. In all calculations of this paper, wavelength
λ is ﬁxed to 1.55 µm. In this section, the polarization is ﬁxed to that having the electric ﬁeld parallelto the yz plane and the magnetic ﬁeld in the x direction. This corresponds to the transverse electric (TE)-like polarization in a 3-D channel which will be discussed in Sect. 3. The equivalent index neq of the Si
slab is assumed to be 2.6, and the channel width is
0.3 µm. Lateral claddings are air with an index of 1.0.
They satisfy the singlemode condition at λ = 1.55 µm.
One side of the square Yee cell is 20 nm (∼ λ/30neq ).
The time step is 0.04 fs, which satisﬁes Courant’s stable condition. The magnetic ﬁeld distribution of theanalytically-derived guided mode is continuously excited around the channel. The excess loss of a branch isestimated from the ratio of total power from two waveguides beyond the branch (Pout ≡ Pout1 + Pout2 ) to the
input power observed near the excitation (Pin ). Here,the excitation source locates 18 µm from the branch.
This is long enough to avoid that the reﬂected powerfrom the branch is counted as the input power. To
estimate Pout accurately, two waveguides beyond thebranch are bent, so it looks like a T-branch, as illustrated in Fig. 1. The analytical space is terminatedby Mur’s second-order absorbing boundary condition.
Since the reﬂection at waveguide ends is not perfectly
suppressed even with these boundaries, Pout1 and Pout2
are evaluated at points 16 µm apart from the absorbing boundary. This is distant enough to estimate them
before reﬂected waves reach these points.
Table 1 summarizes various branches modeled.
The excess loss of simple Y branch (a) is estimatedto be 2 dB when the branching angle is 15◦ . Although
the excess loss may be reduced by a smaller angle, it
makes the branch long, so it is not suitable for the purpose of this study. For modiﬁed antenna-coupled-type
branches (b)–(d) [7], [8], the loss is less than 0.5 dB. Especially, (d) marks a minimum value of less than 0.1 dB.
In branch (e), two fans with 0.9-µm-radius are connected to the input waveguide with a small taper. This
structure is similar to a reported one [9], in which twocorner mirrors are used at the branch. However, we
rather employed the fans to avoid the unwanted reﬂection. The minimum loss is 0.3 dB, when guided modes
are eﬃciently coupled to whispering gallery modes ineach fan [10]. In branch (f), two bent waveguides areconnected, so we call it bend-waveguide-type. Whenthe bend radius is 5.85 µm, the loss is less than 0.1 dB.
3.

Design by 3-D FDTD Method

For branches (d) and (f) showing < 0.1 dB loss in
Sect. 2, structural details are designed using the 3-D
FDTD method. The thickness of Si and SiO2 layers
are assumed to be 0.32 µm and 1.0 µm, respectively, tosimulate the SOI wafer used in the experiment. The

Table 1

Various branch structures.

Schematic(a)

Loss
2.0 dB

0.3µm

θ = 150.84µm(b)

0.5 dB
0.42µm(c)

0.5 dB
0.42µm
0.84µm(d)< 0.1 dB

0.9 µm(e)

0.3 dB

5.85 µm(f)< 0.1 dB

air above the Si core and Si substrate below the SiO2
layer are also included in the analytical space. Indexesof Si, SiO2 and air are assumed to be 3.45, 1.44 and
1.0, respectively. One side of the cubic Yee cell ∆x is
enlarged to 40 nm (∼λ/11n1 ) to save the CPU time.
The time step is 0.06 fs, which satisﬁes the Courant’s
stable condition. Although the polarization cannot be
deﬁned rigorously in a 3-D waveguide, the y componentof the electric ﬁeld is excited to simulate the TE-likemode. The waveguide width w is ﬁxed to be 0.44 µm(= 11∆x). This width satisﬁes the singlemode condition at λ = 1.55 µm and the peak of the electric ﬁeldof the guided mode locates just at the center of the
waveguide.
Figure 2 shows the x component of the magnetic
ﬁeld distribution in the antenna-coupled-type branch.
Here, lengths l of the taper in both input and output
waveguides are the same. For l = 0.8 µm, the ﬁeld exhibits the winding motion in the output waveguides.
This motion is smaller for l = 2.8 µm, but it still remains. This indicates that the rapid change of thestructure at the branch excites radiation modes, whichshould be the excess loss, as shown in Fig. 3. The loss
deceases monotonically with increasing l. However, itcannot be less than 1 dB. This result is diﬀerent fromthat for the 2-D model shown in Table 1. We thinkthat this diﬀerence comes from diﬀerent zigzag paths

SAKAI et al.: LOW LOSS ULTRA-SMALL BRANCHES IN A SILICON PHOTONIC WIRE WAVEGUIDE

1035

Hx [a.u.]

z
−2

y

x

−1

0

Hx [a.u.]

z
1

2

∆w

Pout1
Pout1

−2

y

x

−1

0

1

2

Pout2

Pout2
g

r
l
Pin
Pin

w
w

(a)

(b)

10
Excess Loss [dB]Fig. 2 Top view of the 3-D FDTD calculation model and thex component of magnetic ﬁeld in antenna-coupled-type brancheswith w = 0.44 µm. (a) and (b) are for l = 0.8 µm and 2.8 µm,
respectively.

Fig. 4 Top view of the 3-D calculation model and the x component of magnetic ﬁeld in bend-waveguide-type branch with r= 1.78 µm, w = 0.44 µm, g = 0.28 µm, and ∆w = 0 µm.

Excess Loss [dB]

10
8
6

8
6
4
2

4

0
0

2
0

0

1.0

2.0
3.0
l [µm]

4.0

0.5 1.0 1.5 2.0 2.5
Bend Radius r [µm]3.0Fig. 5 Excess loss with bend radius r in bend-waveguide-type
branch with w = 0.44 µm, which is calculated by 3-D FDTD
method.

of light in the waveguide, which give diﬀerent groupindexes, i.e., 4–5 for 3-D model [5], while ∼3 for the
2-D model. The diﬀerent zigzag paths cause diﬀerent
excitations of multimodes at the branch and results in
diﬀerent optimum structures.
The x component of the magnetic ﬁeld distribution in the bend-waveguide-type is shown in Fig. 4. The
light is smoothly separated without any serious scattering at the branch and winding motion in output waveguides. The excess loss calculated with bend radius r isshown in Fig. 5. A similar 3-D calculation indicates thatthe bend loss is estimated to be 0.2–0.4 dB for radius
assumed in Fig. 5. This ﬁgure shows the excess loss
including the bend loss at the bend. It is estimatedto be less than 0.4 dB for all radius assumed, and theminimum value is 0.20 dB for r = 1.38 µm.
We investigated the inﬂuence of asymmetry in thebend-waveguide-type. Figure 6 shows the change ofthe power branching ratio Pout1 /Pout calculated with

Pout1 / Pout

Fig. 3 Excess loss with taper length l in antenna coupled typewith w = 0.44 µm, which is calculated by the 3-D FDTD method.

1.0

g=
1.64
1.44

0.8

1.24

0.6

1.04
0.84

0.4

0.68
0.52

0.2

0.36
0.20

0

0

10

20

30
40
∆w/w [%]

50

Fig. 6 Branching ratio with normalized shift ∆w/w of input
waveguide for parameter g in bent-waveguide-type branch withr = 2.18 µm and w = 0.44 µm.

the normalized shift ∆w/w of input waveguide measured from the center axis. The power branching ratio is strongly inﬂuenced by overlapping length g. For

IEICE TRANS. ELECTRON., VOL.E85–C, NO.4 APRIL 2002

1036

1.2

MonitorExcess Loss

1.0

VidiconCamera

0.8

Laser
Diode

0.6
0.4

Polarization
Controller

H
E

0.2
0

0

10

20
30
∆w/w [%]

40

SampleSinglemode Fiber Polarization
Maintaining Cleaved Facet
Fiber

50

Fig. 7 Change of excess loss with ∆w/w in bend-waveguidetype branch with r = 2.18 µm, w = 0.44 µm and g = 0.32 µm.

Fig. 9Measurement setup of light propagation characteristics.

Si CoreSiO2 Cladding

Fig. 8SEM view of fabricated Si rectangular channel.

g ≤ 0.68 µm, Pout1 /Pout decreases as ∆w/w increases.
On the other hand, for g ≥ 0.84 µm, it increases as∆w/w increases. The critical point giving Pout1 /Pout= 0.5 for any ∆w/w can be expected for g ∼ 0.80 µm.
The loss change with ∆w/w is shown in Fig. 7. It is relatively insensitive to ∆w/w, e.g., the loss is still 0.3 dB
for ∆w/w = 20%.
4.

Fabrication and Measurement

We prepared a unibond-type SOI wafer (SOI TECInc.), which had a SiO2 layer of 1.0-µm-thickness anda top p-type Si layer of 0.32 µm thickness. The ﬂuctuation in the Si thickness was less than 20 nm insidea 7 × 7 mm2 cleaved piece. The free carrier absorption
loss is negligible compared with the scattering loss atrough sidewalls, since the resistivity of the Si layer is
as high as 14 Ωcm. We used a ﬁeld-emission-type electron beam (EB) lithography and CF4 -based inductively
coupled plasma (ICP) etching to fabricate the Si rectangular channel. After the EB-drawn pattern of thepositive resist was transferred to a metal mask, the top
Si layer was completely etched down by the ICP etching. Figure 8 is a scanning electron micrograph (SEM)of a cleaved end facet of the waveguide. Considering theretreat of the mask, the pattern width was designed toFig. 10 Top view and NFP of light output for sample withr = 2.75 µm, w = 0.47 µm and g = 0.4 µm.

be 0.5 µm. The fabricated one is 0.47 µm, which is close
to the modeled value in Sect. 3. The sidewall angle of
the waveguide is over 85◦ and the sidewall roughness is
20 nm in maximum value and 11 nm in deviation. For
the Si layer in the unibond-type SOI wafer, the perfect
crystal facet cannot be obtained by the cleavage. As
shown in Fig. 8, however, the waveguide facet is smoothenough due to small cross sectional area.
The measurement setup is shown in Fig. 9. The
light of λ = 1.55 µm from a semiconductor laser is controlled to be TE-polarized and focused on the waveguide facet. The output end of the waveguide is terminated inside the wafer by the lithography and theetching. The light from this output end is detected bya vidicon camera from the top of the waveguide. Figure 10 shows the near ﬁeld pattern (NFP) of the light

SAKAI et al.: LOW LOSS ULTRA-SMALL BRANCHES IN A SILICON PHOTONIC WIRE WAVEGUIDE

1037

1.0

3

2

Pout1 / Pout

Excess Loss [dB]

0.8

1

0.6
0.4
0.2

0

0

0.2

0.4
0.6
g [µm]

0.8

1.0

Fig. 11 Measured excess loss for r = 2.75 µm (circle) andcalculated results for r = 2.78 µm (curves).

output from the bend-waveguide-type branch with r =2.75 µm. As expected from the FDTD calculation, thelight passes through the branch and is extracted fromtwo output ends. Such NFP can be observed from the
top without any irregular scattering at waveguide ends,
since the mode size in the Si waveguide is smaller thanthe diﬀraction limit in air, and the radiation angle ofthe light output is over 180◦ [11]. This allows the evaluation of relative output power by the vidicon camera with the compensation of its nonlinearity. First,
the waveguide loss was evaluated to be ∼10 dB/mm bycomparing output powers from diﬀerent length straightwaveguides. This value is almost the same as that evaluated previously by the Fabry-Perot resonance method[7]. Next, the excess loss at the branch was speciﬁed bycomparing the output power from a simple bent waveguide and that from the branch, as shown in Fig. 11.
Here, r is ﬁxed to be 2.75 µm and the overlap lengthof two output waveguides g is changed. The loss takes
the minimum value 0.3 dB for g = 0.4 µm. This result
almost agrees with the 3-D FDTD calculation. The
0.3-dB-loss is small enough and diﬃcult to explain its
origin. One reason considered is the reﬂection at the
input end of the branch. We expect a further low loss
less than 0.1 dB by the slight modiﬁcation of the input
end.
Measured and calculated branching ratio are plotted with length g in Fig. 12. Nearly 60% data lienear
Pout1 /Pout = 0.5. Other data show larger values 0.7–
0.8. This is thought to be due to the complex dependence of the branching ratio on ∆w/w and g.
5.

Conclusion

Ultra-small branches in a Si photonic wire waveguidewere studied theoretically and experimentally. From
the FDTD calculation, it was shown that the bendwaveguide-type branch achieved a low excess loss of
0.2 dB under the singlemode condition at λ = 1.55 µm.
This branch was fabricated into an SOI wafer, and theexcess loss was evaluated to be as low as 0.3 dB. This

0

0

0.5

1.0
g [µm]

1.5

2.0

Fig. 12 Measured branching ratio for ∆w/w = 0–13% (circle)
and 16–22% (square) with r = 2.75 µm. Calculated results for∆w/w = 0% (solid curve), 9% (dashed curve) and 18% (dottedcurve) are also shown with r = 2.78 µm.

branch was constructed by 2.75-µm-radius bends, so
the total area of the branch occupied only (5 µm)2 area.
We can expect this waveguide and branch to drastically miniaturize some optical circuits such as H-tree
branches.
Acknowledgement
We would like to thank Prof. Y. Kokubun, Prof.
Y. Hirose and Associate Prof. H. Arai, Yokohama
National University, and Prof. K. Iga and Prof.
F. Koyama, Tokyo Institute of Technology, for valuable
discussions.
References[1] T. Baba, N. Fukaya, and J. Yonekura, “Observation oflight propagation in photonic crystal optical waveguides
with bends,” Electron. Lett., vol.35, no.8, pp.654–655, April
1999.
[2] J. Schmidtchen, A. Splett, B. Schuppert, and K.
Petermann, “Low loss single mode optical waveguides withlarge cross-section in silicon-on-insulator,” Electron. Lett.,vol.27, no.16, pp.1486–1488, Aug. 1991.
[3] A.G. Rickman and G.T. Reed, “Silicon-on-insulator opticalrib waveguides: Loss, mode characteristics, bends and yjunctions,” IEE Proc. Optoelectron., vol.141, no.6, pp.391–
393, Dec. 1994.
[4] K.K. Lee, D.R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, andL.C. Kimerling, “Eﬀect of size and roughness on light transmission in Si/SiO2 waveguide: Experiments and model,”Appl. Phys. Lett., vol.77, no.11, pp.1617–1619, Sept. 2000.
[5] A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-D optical waveguide on silicon-on-insulator
substrate,” Jpn. J. Appl. Phys., vol.40, no.4B, pp.L383–
L385, April 2001.
[6] A. Taﬂove and S.C. Hagness, Computational electrodynamics: the ﬁnite-diﬀerence time-domain method, Second ed.,
Artech House Publishers, Boston, 2000.
[7] M. Rangaraj, M. Minakata, and S. Kawakami, “Low loss
integrated optical Y-branch,” J. Lightwave Technol., vol.7,
no.5, pp.753–758, May 1989.

IEICE TRANS. ELECTRON., VOL.E85–C, NO.4 APRIL 2002

1038

[8] M.H. Hu, J.Z. Huang, R. Scarmozzino, M. Levy, and R.M.
Osgood Jr., “A low-loss and compact waveguide Y-branchusing refractive-index tapering,” IEEE Photon. Technol.
Lett., vol.9, no.2, pp.203–205, Feb. 1997.
[9] C. Manolatou, S.G. Jhonson, S. Fan, P.R. Villeneuve, H.A.
Haus, and J.D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol., vol.17, no.9, pp.1682–1692,
Sept. 1999.
[10] A. Sakai and T. Baba, “FDTD simulation of photonic devices and circuits based on circular and fan-shaped microdisks,” J. Lightwave Technol., vol.17, no.8, pp.1493–
1499, Aug. 1999.
[11] T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe,and A. Sakai, “Light propagation characteristics of straightsingle line defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Select.
Topics Quantum Electron. (2002, to be published).

Atsushi Sakai
was born in Saitama
Prefecture, Japan, on September 4, 1970.
He received the B.E. and M.E. degrees
from the Division of Electrical and Computer Engineering, Yokohama National
University, Japan, in 1997 and 1999, respectively, and is currently working toward the Ph.D. degree at Yokohama National University, conducting the research
focused on micro-photonic devices andcircuits by high refractive index diﬀerence.

Tatsuhiko Fukazawa
was born in
Iwate Prefecture, Japan, on October 23,
1977. He is currently working toward
the B.E. degree at Yokohama National
University, conducting the research focused on design and fabrication of microphotonic devices based on SOI substrate.

Toshihiko Baba
was born in Nagano
Prefecture, Japan, on November 12, 1962.
He received the B.E., M.E., and Ph.D. degrees from the Division of Electrical andComputer Engineering, Yokohama National University, Japan, in 1985, 1987,
and 1990, respectively. During Ph.D.
work, he had been engaged in antiresonant reﬂecting optical waveguides (ARROW’s) and integrated lightwave circuits.
From 1990, he has joined the Precision
and Intelligence Laboratory, Tokyo Institute of Technology, asa research associate, and started the research on vertical cavity
surface emitting lasers (VCSEL’s). In 1991, he reported the ﬁrst
calculation of spontaneous emission factor in VCSEL’s. In 1993,
he achieved the ﬁrst RT CW operation of a long wavelength VCSEL. In 1994, he became an associate professor at Yokohama
National University. He had also held a guest associate professor
at Tokyo Institute of Technology, from 1994 to 1999. His current
interests are microcavity lasers, photonic band crystals, spontaneous emission control, micromechanical optics, nonlinear optics
and optical computing. Dr. Baba is a member of the Japan Society of Applied Physics, and the American Institute of Physics.
He received the Niwa Memorial Prize in 1991, the Best Paper
Award of Microoptic Conference in 1993 and 1999, and the Paper Award and the Academic Encouragement Award from the
IEICE in 1994.