June 1, 2015 / Vol. 40, No. 11 / OPTICS LETTERS
2493
Degenerate band edge resonances in periodic
silicon ridge waveguides
Michael G. Wood, Justin R. Burr, and Ronald M. Reano*
Electroscience Laboratory, Department of Electrical and Computer Engineering, The Ohio State University, Columbus, Ohio 43212, USA
*Corresponding author: [email protected]
Received March 18, 2015; revised April 27, 2015; accepted April 30, 2015;
posted May 1, 2015 (Doc. ID 236363); published May 20, 2015
We experimentally demonstrate degenerate band edge resonances in periodic Si ridge waveguides that are compatible with carrier injection modulation for active electro-optical devices. The resonant cavities are designed using
a combination of the plane-wave expansion method and the finite difference time domain technique. Measured and
simulated quality factors of the first band edge resonances scale to the fifth power of the number of periods. Quality
factor scaling is determined to be limited by fabrication imperfections. Compared to resonators based on a regular
transmission band edge, degenerate band edge devices can achieve significantly larger quality factors in the same
number of periods. Applications include compact electro-optical switches, modulators, and sensors that benefit
from high-quality factors and large distributed electric fields. © 2015 Optical Society of America
OCIS codes: (230.7370) Waveguides; (250.5300) Photonic integrated circuits; (050.5298) Photonic crystals.
http://dx.doi.org/10.1364/OL.40.002493
Periodic dielectric waveguides with one-dimensional
periodicity provide many of the properties found in structures with higher-dimensional periodicity but with reduced fabrication complexity [1–3]. Ridge waveguides
with periodicity allow for the fabrication of carrier
injection devices where dopants can be placed close
to a resonant cavity, reducing electrical power consumption of switches, modulators, and active sensors [4–10].
Furthermore, dispersion engineering can be used to reduce group velocity, increasing light–matter interaction
for nonlinear optics [11,12] and lasing [13].
Resonators based on periodic dielectric waveguides
can be realized by introducing a defect in the periodicity
or by truncating periodicity to a finite number of periods.
In defect-based resonators, a resonance is created inside
the photonic bandgap [1,2,4–8]. In this Letter, the focus
is on finite-length periodic structures where resonances
are exploited near the photonic band edge [9,13–15].
Finite-length periodic structures consisting of a single
grating have a quadratic dispersion relationship near the
band edge given by ω − ω0 ∝ k − k0 2 where ω is the frequency, k is the wave number, and ω0 and k0 are the corresponding values at the band edge. Quadratic dispersion
gives rise to a regular band edge (RBE) resonance and
quality factor (Q) scaling proportional to N 3 , where N
is the number of periods [16,17]. In contrast, when the
band edge resonator consists of two coupled periodic
gratings, it is possible to engineer a quartic dispersion relationship near the band edge ω − ω0 ∝ k − k0 4 , giving
rise to degenerate band edge (DBE) resonances [18]. On
a DBE resonance, the light intensity inside the cavity
forms a giant slow wave resonance whose maximum amplitude scales as N 4 [16,17]. The quality factor scaling of
DBE resonances is proportional to N 5 [17]. In addition,
DBE resonances can demonstrate near-unity transmission on resonance from the presence of propagating
and evanescent cavity modes [15,17,19]. Devices based
on DBE resonances have applications in low-threshold
all-optical switching [20] and lasing [21].
Initial theoretical studies of DBE resonances were
based on one-dimensional periodic layered structures
with strong birefringence [16] or optical fibers with
0146-9592/15/112493-04$15.00/0
multiple gratings [19,22]. Recently, finite-length coupled
periodic integrated optical waveguides have been studied as a more practical and physically realizable platform
for on-chip devices based on DBE resonances [14,18].
Although coupled periodic strip waveguides have been
shown to demonstrate DBE resonances both theoretically [18,23] and experimentally [14], there has not yet
been a report of DBE resonances in ridge waveguides
required for carrier injection.
In this work, we design, fabricate, and experimentally
demonstrate resonators that exhibit DBE resonances
and are compatible with carrier injection through a cavity design that includes a 40 nm Si slab for ion implantation of dopants. We present a design methodology for
obtaining a DBE resonance along with details of the fabrication process. The resonators are promising candidates for compact devices due to fifth-order Q scaling
with the number of periods. The peak measured quality
factor in demonstrated devices is 16,700, limited by fabrication imperfections.
A schematic of the ridge waveguide cavity designed
for a DBE resonance is shown in Fig. 1. The resonator
consists of a 790 nm wide Si waveguide, w, with a
one-dimensional array of pairs of etched holes with a
period, a, of 370 nm. The ridge waveguide is partially
etched from a height of 205 nm to leave a 40 nm Si slab,
sh , external to the cavity. Two 395 nm wide input and
output Si ridge waveguides are used to couple light into
and out of the cavity. A multimode ridge waveguide region of length zL is included between the Y-junctions of
the input and output waveguides and the cavity to allow
excitation of the cavity modes with light input only on
port 1 and output primarily on port 4 [14].
To arrive at a design for the periodic region, the impact
of changes in the hole radius (r), longitudinal offset (z0 ),
and lateral offset (x0 ) on the band diagram are simulated
by the three-dimensional plane-wave expansion method
[24,25]. We use a refractive index of 3.48 for the silicon
ridge, 1.41 for the spin-on glass (FOx-15), and 1.45 for
the buried oxide (BOX) and plasma-enhanced chemical
vapor deposition (PECVD) SiO2 claddings surrounding
the ridge. The design methodology is presented in
© 2015 Optical Society of America
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OPTICS LETTERS / Vol. 40, No. 11 / June 1, 2015
Fig. 1. Schematic of the resonant cavity designed to exhibit
a DBE resonance in a ridge waveguide. (a) Top view of the complete cavity; (b) top view of the coupling region; (c) crosssectional view. The oxide top cladding is not shown in
(a) and (b) for clarity.
Fig. 2. First, as shown in Fig. 2(a), the hole radius and
lateral offset are swept for a fixed longitudinal offset
of 0 nm to maximize the size of the bandgap between
the second (red) and third (green) quasi-TE modes (dominant electric field component E x ) and to position the
peak of the second band near the design frequency.
Next, as shown in Fig. 2(b), the longitudinal offset is
increased until the second band takes on the desired
quartic form. As shown in Fig. 2(c), continuing to increase the longitudinal offset results in a split band edge
(SBE) in which the band diagram is no longer quartic and
the group velocity reaches zero away from the band
edge [23,26].
The quartic dispersion relationship and N 5 Q scaling
corresponding to a DBE resonance occur only in a small
parameter space with significant deviation resulting in either an RBE or SBE resonance. Once the periodic region
is designed, finite-difference time-domain (FDTD) simulations (Lumerical FDTD, Vancouver, Canada) are performed on finite-length periodic structures to confirm
that the Q of the first resonances scales to the fifth power
with an increasing number of periods. FDTD results are
presented alongside measurements. Additional FDTD
simulations are used to design zL so that the input port
1 to output port 4 transmission is maximized at the first
resonance. Length zL is set to the same value on both
sides of the periodic structure. The final design parameters are w 790 nm, h 165 nm, sh 40 nm, sw 20 μm, a 370 nm, r 130 nm, z0 115 nm, x0 380 nm, and zL 750 nm.
The devices are fabricated on a silicon-on-insulator
wafer with a silicon device layer of 210 nm and BOX
thickness of 1 μm. Electron beam lithography (EBL) is
used to pattern waveguides and alignment markers with
Fig. 2. Tuning longitudinal hole offset, z0 , to achieve a
DBE resonance. (a) No offset, z0 0 nm; (b) z0 115 nm;
(c) z0 150 nm. Left column: band diagram. Center column:
group velocity of the second mode. Right column: simulated
geometry with colors corresponding to Fig. 1. The blue, red,
and green curves of the band diagram are the guided TE modes
of the structure. The light line, black, corresponds to the lowestorder mode of the Si slab [25]. The green band in (a) moves
above the light line as z0 is increased in (b) and (c).
a hydrogen silsesquioxane (HSQ) mask [27]. Ridge waveguides are patterned with inductively coupled plasma
reactive ion etching (ICP-RIE) with a Cl2 ∕O2 chemistry,
leaving a 60 nm Si slab.
Next, EBL is used with negative-tone maN-2403 resist
to pattern the Si slab. The maN-2403 mask is 20 μm wide
around the DBE cavity and 3 μm wide around the input
and output waveguides. The maN-2403 is not exposed
directly above the DBE cavity to allow etching of the
holes to the BOX layer. The HSQ serves as an etch mask
for the Si ridge. The Si slab width is tapered to connect
the slab surrounding the cavity to the input and output
ridge waveguides, as seen in Fig. 1(a). Away from the
cavity, a second set of tapers converts the input and
output ridge waveguides to strip waveguides. Strip waveguides are needed for fiber-to-chip coupling with cantilever couplers [28,29]. ICP-RIE with Cl2 ∕O2 is used to
completely etch the Si slab outside of the patterned regions. Images of fabricated devices after the slab patterning etch are given in Fig. 3. Patterning the slab layer
electrically isolates nearby devices [30].
Dry thermal oxidation is then performed to reduce the
sidewall roughness, decreasing propagation loss [31].
Approximately 20 nm of Si is consumed in both slab regions and along the sidewalls. Oxidation is slower in the
vertical dimension in the ridge waveguide, since residual
50 nm HSQ on top of the Si core acts as a partial oxidation mask. The top cladding consists of FOx-15 and
PECVD SiO2 [14]. The FOx-15 is used to completely fill
the periodic holes without leaving air voids. After spin
coating, the FOx-15 is baked for 1 h in a N 2 ambient
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Fig. 3. Images of fabricated ridge waveguide DBE devices:
(a) optical micrograph; (b) angled-view scanning electron
microscope (SEM) micrograph of the cavity region. Insets: left,
zoom-in top-down SEM micrograph of the periodic ridge waveguide; right, angled-view cross-section SEM of a Si companion
sample cleaved along the dashed line in the left inset.
at 400°C, resulting in a film thickness of 545 nm. PECVD
SiO2 is then deposited to give a total oxide cladding thickness of 1 μm. Finally, compact cantilever couplers are
patterned for low-loss fiber-to-chip coupling.
Devices are characterized by optical transmission measurements. Linearly polarized TE light from an IR tunable
laser source (1460–1580 nm) is coupled into the device
via a single-mode tapered fiber butt coupled to a compact
cantilever coupler on port 1. Output light is coupled
from port 4 to another tapered single-mode fiber and
measured with a photodetector and power meter.
Ports 2 and 3 are terminated with inverse width tapered
waveguides but are not released from the substrate with
cantilever couplers like ports 1 and 4. Any light scattered
to ports 2 and 3 is radiated into the oxide cladding away
from the cavity and is not collected by the input or output
tapered fibers. Figures 4(a) and 4(b) present the measurement results for devices with 30 and 40 periods,
respectively, along with Fano resonance fitting [14,32].
Q scaling of the first resonance, closest to the bandgap,
for both measured (blue) and simulated (red) devices is
shown in Fig. 4(c). In both cases, Q scales proportional to
N 5 for N > 20, which is a defining characteristic of a DBE
resonance with two propagating and two evanescent
modes [17,18]. While the simulated Q continues scaling
for an increasing number of periods, measured Q drops
off of N 5 scaling after 40 periods or a Q of 13,000. The
peak measured Q of 16,700 occurs for 50 periods.
To understand why Q stops increasing after 40 periods,
we use the model established in [33], in which fabrication
imperfections such as nonuniform hole radius, sloped
sidewalls, and roughness of the Si slab are described
by a quality factor, QImperfections , as
−1
−1
Q−1
Exp QDesign QImperfections ;
Fig. 4. Measurement results: transmission spectra for devices
with (a) 30 and (b) 40 periods, with an optical power of 0 dBm
at the chip input facet. A constant term has been added to the
sum of Fano fits to match the finite reflectivity measured in the
bandgap. (c) Quality factor scaling of the first resonance peak
on the long wavelength side of the photonic bandgap.
average value, 17,200, is close to the peak of QExp .
Fifth-power Q scaling of QExp stops as the measured values approach QImperfections .
Based on SEM inspection of the etched holes and the
analysis of fabricated devices in [33,36,37], we expect
(1)
where QExp is the experimental measurement and QDesign
is obtained from FDTD modeling. The filter-diagonalization method for harmonic inversion is used to extract
QDesign from FDTD simulations of the cavity with excitation from a broadband (1.3–1.7 μm) source [34,35]. The
quality factors from Eq. (1) are plotted in Fig. 5. The
QImperfections term shows no clear trend with N, and its
Fig. 5. Analysis of measured quality factor and impact of
fabrication imperfections as a limitation.
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that the largest contributions to QImperfections are variation
in the hole radius, sidewall roughness, and the slope of
the hole sidewalls. Improvements to fabrication processes of photonic crystal slabs with two-dimensional
periodicity have demonstrated an increase in QImperfections
and a corresponding increase in QExp [38]. Theoretical
studies have also shown that DBE resonances are more
sensitive to fabrication imperfections than RBE resonances [39]. The design of future active ridge waveguide
DBE resonators based on carrier injection modulation
must also account for the changing complex refractive
index with the density of injected carriers. Significant
changes to the Si refractive index will alter the dispersion
relationship from the target quartic form of the DBE.
Modifications of the initial cavity design could potentially
be used to give quartic dispersion when under bias.
In summary, we have designed and experimentally
demonstrated DBE resonances in periodic Si ridge waveguides. The N 5 Q scaling of these resonances is enabling
for future compact electro-optic devices. We expect
that improvements to the fabrication process will lead
to higher absolute Q, since devices are currently limited
by fabrication imperfections rather than a fundamental
limit of the design. Electro-optically active DBE resonances have applications in low-power-consumption modulators, distributed area sensors, and on-chip light
emitters.
This work was supported by the National Science
Foundation under award number 0954996 and the
National Aeronautics and Space Administration Ohio
Space Grant Consortium under award number
NNX10AI39H.
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