Please do not remove this page
Width dependence of inherent TM-mode lateral
leakage loss in silicon-on-insulator ridge
waveguides
Webster, Mark; Pafcheck, Robert; Koch, Thomas; Mitchell, Arnan
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Webster, Pafcheck, R., Koch, T., & Mitchell, A. (2007). Width dependence of inherent TM-mode lateral
leakage loss in silicon-on-insulator ridge waveguides. IEEE Photonics Technology Letters, 19(6), 429–431.
https://doi.org/10.1109/lpt.2007.891979
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 6, MARCH 15, 2007 429
Width Dependence of Inherent TM-Mode
Lateral Leakage Loss in Silicon-On-Insulator
Ridge Waveguides
M. A. Webster, Member, IEEE, R. M. Pafchek, A. Mitchell, Member, IEEE, and T. L. Koch, Fellow, IEEE
Abstract—We report the first experimental observation in the
optical domain of a dramatic width-dependent lateral leakage loss
behavior for the TM-like mode of tight vertical confinement ridge
waveguides formed in silicon-on-insulator. The lateral leakage
loss displays a series of sharp cyclic minima at precise waveguide
widths, and appears to be inherent to waveguide geometries of
central importance to a wide variety of active devices in silicon
photonics requiring lateral electrical access. This behavior is not
predicted by the often-used effective-index-based methods, but
is understood phenomenologically and also compared to prior
numerical analysis and predictions of leaky mode behavior. It is
shown that TM-like mode operation, critical to the operation of
some active component designs, will require precision control of
waveguide dimensions to achieve high performance.
Index Terms—Leaky waves, optical losses, optical waveguides,
silicon-on-insulator (SOI) technology.
I. INTRODUCTION
I
N THE rapidly advancing area of silicon photonics, the large
refractive-index-contrast of the silicon-on-insulator (SOI)
material system allows for very tight vertical field confinement
and thus enables greater performance for a wide variety of
important active devices such as modulators and promising
source configurations. The ridge waveguide geometry (inset in
Fig. 1) is often required in SOI photonics for lateral electrical
access to the optical mode region in such active devices. It is
not generally appreciated that the high refractive-index-contrast
and common active device dimensions of these tight vertical
confinement ridge waveguides can make the TM-like mode
inherently leaky in the lateral direction for many waveguide
geometries of great interest.
Here, we present experimental observations in the optical do-
main of the lateral leakage loss behavior for the TM-like mode.
The leakage loss displays a dramatic width dependence with a
series of sharp cyclic minima at very precise waveguide widths
Manuscript received Nov. 27, 2006. This work was supported by National
Science Foundation Grant ECS-0335067, by Pennsylvania BFTDA Grant
ME#21-116- 0014, by the Army Research Laboratory Cooperative Agreement
W911NF-04-2-0015, and by the Bandwidth Foundry Pty Ltd., Australia.
M. A. Webster, R. M. Pafchek, and T. L. Koch are with the Center for
Optical Technologies, Lehigh University, Bethlehem, PA 18015 USA (e-mail:
tlkoch@lehigh.edu).
A. Mitchell is with the School of Electrical and Computer Engineering, RMIT
University, Melbourne, VIC 3001, Australia.
Color versions of one or more of the figures in this letter are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LPT.2007.891979
Fig. 1. Slab mode indexes used in effective index calculations. The modal in-
dexes for the guided TE-like and TM-like modes, respectively, lie intermediate
between their slab values for slab thicknesses
t
and
t
. We use index values of
n
=3
:
475
and
n
=1
:
444
at 1.55-
m wavelength.
[1]. A simple phenomenological model is presented and also
compared to prior numerical analysis and predictions of leaky
mode behavior.
II. T
HEORY OF LATERAL-LEAKAGE LOSS
Under an equivalent slab model for the ridge waveguide ge-
ometry (inset in Fig. 1), the lateral leakage loss for the TM-like
mode is due to TM/TE mode conversion at the ridge boundary
[2]–[4]. It should be emphasized that this effect is not caused
by any surface or side-wall roughness. With reference to slab
waveguide dispersion curves in Fig. 1, for the case of TE-like
modes, this mode conversion at the boundary cannot lead to any
propagating field or leakage loss in the lateral cladding since
longitudinal phase-matching requires that any fields generated
at the ridge boundaries will be laterally evanescent in the slab
lateral cladding for both the TE and TM generated fields. How-
ever, in the case of the TM-like mode, while phase-matching
requires that the lateral TM slab mode be evanescent in the lat-
eral cladding, any TE slab field component generated at the
boundary is phase-matched to a laterally propagating TE slab
mode at some angle
in the lateral slab cladding region.
This phase-matching is illustrated in Fig. 2(a). Here
and
represent the propagation constants of the TE-like and
TM-like modes of the ridge waveguide, respectively. This di-
agram illustrates that the propagation constant of the TM-like
mode is much less than that of the TE-like mode, and for many
1041-1135/$25.00 © 2007 IEEE
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Citation: Webster, M, Pafcheck, R, Koch, T and Mitchell, A 2007, 'Width dependence of inherent TM-mode lateral leakage
loss in silicon-on-insulator ridge waveguides', IEEE Photonics Technology Letters, vol. 19, no. 6, pp. 429-431.
430 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 6, MARCH 15, 2007
Fig. 2. Phase-matching diagram showing TM-like waveguide mode
phase-matched to a propagating TE slab mode in the lateral cladding.
practical rib guides may also lie below the propagation constant
of the unguided TE slab mode
. Since this slab mode
is unguided by the rib, it may propagate at any angle and if
, it is possible to rotate by an angle such
that the TE-slab and TM-guided mode are phase-matched in the
direction. Since the guided mode is then phase-matched to a
radiation mode, it is possible that leakage may occur if there is
some means for mode conversion.
For a thin enough lateral slab thickness
, and certainly in
the case of a strip or “wire” waveguide where
, the TE
slab effective index can lie below the TM-like mode effective
index, and hence, avoid this phase-matched leakage. However,
for electrical access, these designs may not be practical, and
thus, this leakage loss must be well understood.
The leakage process is illustrated in Fig. 2(b). Since the
components of all propagation constants are conserved, all
waves develop the same relative phase along the length of guide
and we can discuss phase in the lateral direction only.
Starting at the bottom, a TM mode is guided by the rib and is
represented as the solid ray incident on the right wall, where
the angle of incidence is such that TM total internal reflec-
tion occurs. However, due to the step discontinuity at the rib
wall, mode conversion from TM to TE can occur, and it can be
shown from mode-matching calculations [4] that TE transmitted
and reflected propagating waves are produced that are approxi-
mately equal in magnitude, but are
radians out of phase. The
reflected TE radiation mode traverses across the core as shown
by a dashed line. Upon total internal reflection, the TM mode
experiences a negative phase shift
and the combination of
with the phase from a single traverse of the guide to the
left is zero for the fundamental mode.
At the left rib wall, the TM mode generates additional small
reflected and transmitted TE propagating waves. The new trans-
mitted TE wave, with a relative phase of
radians as noted
above, combines with the previous reflected TE wave that has
traversed the guide with a phase shift of
. Thus, if this
phase shift across a single traverse for the TE in the core is a
multiple of
, the TE waves will interfere destructively. This
Fig. 3. AFM images of waveguide profiles formed by (a) wet-etching and
(b) thermal oxidation.
leads to a width dependence for the leakage minima that satis-
fies a resonance-like condition [3] of
,or
alternatively stated,
(1)
Here,
has a weak dependence, so some care must
be used if precision is required. From this argument, we would
expect to see significant leakage loss for TM propagation, ex-
cept at precise, specific waveguide widths satisfying the reso-
nance condition (1), where the leakage loss would be greatly
reduced due to destructive interference of radiating TE waves.
It is also interesting to note that the next higher order mode will
be lossy at these widths, since the radiated fields add in phase
for this mode. This may allow relatively wide guides with effec-
tively single-mode behavior.
III. E
XPERIMENTAL
RESULTS
We fabricated a series of ridge waveguides with widths
varying from 0.5 to 1.8
m in 50-nm increments with thickness
nm and nm (i.e., a 15-nm ridge height) on
an SOI wafer with a 2-
m buried oxide layer thickness. These
waveguides were formed by wet-etching, and as previously
measured at a wavelength of 1.55
m for the TE-like mode,
have low propagation losses of about 0.7 dB/cm [5].
We also fabricated waveguides using a thermal oxida-
tion process that results in smoother and rounded sidewalls.
Fig. 3(a) and (b) shows atomic force microscope (AFM) pro-
files of the waveguide surfaces.
The total relative transmitted fiber-coupled power was mea-
sured as a function of waveguide width for both the TE and
TM input polarizations and is presented in Fig. 4. Here each
data point corresponds to the measured power averaged over ten
nominally identical waveguides with a length of 1.5 cm. It can
be readily observed that the TE-like mode has a net loss weakly
dependent upon waveguide width, whereas the TM-like mode
has large loss except at precise values of width.
A simple effective index model was used to calculate the TE
and TM modal effective indices. These were then substituted
into (1) to obtain predicted widths of 0.72 and 1.44
m for the
first two resonances which are in excellent agreement with the
measured results, as shown in Fig. 4.
The data of Fig. 4(b) show that the waveguides with a smooth
rounded sidewall still display the TM-like mode lateral leakage
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WEBSTER et al.: WIDTH DEPENDENCE OF INHERENT TM-MODE LATERAL LEAKAGE LOSS IN SOI 431
Fig. 4. Experimentally measured transmission losses (log scale) for the fun-
damental TE-like and TM-like modes for SOI waveguides formed by (a) wet-
etching and (b) thermal oxidation. Note dramatic width dependence of TM-like
mode loss, and sharp reduction in losses at very precise values of waveguide
width, in excellent agreement with predictions of (1).
loss, but show a broader width dependence at the loss minima.
This is believed to be due to a weaker TM/TE conversion at the
ridge boundaries.
IV. D
ISCUSSION
The characteristics presented in Fig. 4 exhibit some subtle
features that warrant further discussion. First, it should be noted
that the resonant leakage cancellation is not perfect. This is par-
ticularly evident for the first peak of Fig. 4(a). This imperfect
cancellation was predicted [4] and can be explained by the fact
that near cutoff, close to the critical angle, the magnitudes of the
transmitted and reflected TE waves produced by an incident TM
wave are not exactly equal. This imbalance reduces as the angle
approaches glancing, and thus, we see improved resonant can-
cellation for stronger guiding with the wider rib. It should also
be noted that the leakage loss in general reduces with increasing
rib width. This was also predicted [3], [4] and can be explained
to the reduced mode conversion from TM to TE as the incident
angle approaches 90
(where the conversion drops to zero).
Also of significant interest is the reduced leakage behavior
exhibited by the oxidized samples in Fig. 4(b). Here the narrow
rib exhibits almost the same loss as the TE guided mode and
the wider rib appears to possibly provide even lower propaga-
tion loss in the TM mode. The resonances are also significantly
broader than the rectangular etched ribs. This suggests that engi-
neering of the leakage behavior to broaden the range of low-loss
widths may be possible. Optimal designs and effective simula-
tion strategies for investigating these designs are currently under
investigation.
This demonstration of design requirements to realize low-loss
TM mode guidance will have significant consequences for the
practicality of TM-based devices, including slot waveguide with
a very thin horizontal low-index layer that provide large slot-
layer confinement factor [6], [7]. Successful engineering of TM
guides that are both low-loss and fabrication tolerant will be an
important technology for this branch of Si photonics.
V. C
ONCLUSION
We have presented the first experimental observation of un-
usual cyclic leaky mode behavior for the TM-like mode in the
optical domain, and in an SOI waveguide. This compares well
with theoretical predictions. Experimental observations of non-
rectangular geometries suggest that engineering for improved
TM leakage properties may be possible.
R
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