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Received 15 Dec 2011
|
Accepted 30 Apr 2012
|
Published 29 may 2012
DOI: 10.1038/ncomms1876
Light propagation through an optical fibre causes a long, non-resonant (true) time delay used
in numerous applications. In contrast to how it is deployed in optical communication systems,
fibre is coiled in these applications to reduce footprint. This is a configuration better suited
for a chip-based waveguide that would improve shock resistance, and afford the possibility
of integration for system-on-a-chip functionality. However, integrated waveguide attenuation
rates lag far behind the corresponding rates of optical fibre, featuring attenuation many orders
larger. Here we demonstrate a monolithic waveguide as long as 27
m (39
m optical path length),
and featuring broadband loss rate values of (0.08
±
0.01) dB
m
− 1
measured over 7
m by optical
backscatter. Resonator measurements show a further reduction of loss to 0.037
dB
m
− 1
, close
to that of optical fibres when first considered a viable technology.
scaling this waveguide to
integrated spans exceeding 250
m and attenuation rates below 0.01
dB
m
− 1
is discussed.
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA. Correspondence and requests for materials
should be addressed to K.J.V. (email: vahala@caltech.edu).
ultra-low-loss optical delay line on a silicon chip
Hansuek Lee
1
, Tong Chen
1
, Jiang Li
1
, oskar Painter
1
& Kerry J. Vahala
1
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F
ibre-optic waveguides for true time delay are used in rotation
sensing, radio frequency photonics, high-stability microwave
oscillators and all-optical signal processing
1–
7
. Transfer of
these applications to a wafer imposes new challenges on microphot
-
onic fabrication. Waveguide loss must be reduced to unprecedented,
low levels and maintained over a broadband spectral region. Also,
the process must scale so as to maintain these low-loss levels in a
continuous waveguide structure over broad areas. Concerning
waveguide loss, the lowest attenuation rates are obtained for a silica-
based or silica-clad guide, and there has been interest in the practi
-
cal limits of optical loss in such structures
8–1
0
. For a pure silica core
waveguide
1
0
the state-of-the-art does not reflect fundamental mate
-
rial limits, but is instead set by interface roughness on the waveguide
itself. Certain processes can heal out this roughness. Laser-induced
reflow of thermal silica has been used to create ultra-high-Q toroi
-
dal-shaped resonators
1
1
, but comparably low attenuation rates have
not been possible in adapting this technique for waveguide fabrica
-
tion
1
2
. Likewise, thermal reflow is possible by introducing dopants
such as phosphor and boron so as to lower the melting point of
silica below that of silicon. However, the doping process has been
observed to increase material optical loss
1
3
.
Characterization of attenuation rate in a very-low-loss integrated
waveguides is complicated by the insertion loss associated with cou
-
pling light into the guide. The most reliable characterization meth
-
ods avoid this problem entirely by using either resonators or optical
backscatter reflectometry. Resonator Q measurements have long
been recognized as a reliable way to characterize spans of waveguide
configured into closed-loop whispering galleries
8
, because the
Q-factor in the under-coupled limit depends only on waveguide
attenuation.
Although this method is an accurate way to test loss over a small
area, the ultimate goal of replacing optical fibre in certain applica
-
tions requires much greater spans of waveguide than has been typical
in photonics. Local testing of either short spans of waveguide or res
-
onators, while important, is not a sufficient test of device uniformity
or fabrication scalability. Over large length spans, optical backscatter
reflectometry provides attenuation versus propagation distance that
captures attenuation variability caused by wafer-scale variation of
the fabrication process
1
4
. Using backscatter reflectometry, an inte
-
grated silica waveguide (length 10
m) with loss of 1.7
dB
m
− 1
and a
silicon nitride in silica guide (length 6
m) with loss of 2.9
dB
m
− 1
have been demonstrated
9,1
0
. Moreover, a silicon nitride waveguide
configured into resonators has produced even better results around
1.1
dB
m
− 1
(ref.
15). A loss of 0.3
dB
m
− 1
has been reported for a
silica guide
1
6
; and recently, loss less than 0.1
dB
m
− 1
at 1,580
nm
(rising to 0.8
dB
m
− 1
at 1,540
nm) has been reported for a 1-m long
silicon nitride waveguide using a backscatter method
1
7
.
Beyond achieving very low optical loss values, long delay lines
present a new and non-trivial device challenge with respect to opti
-
cal micro-fabrication. The combination of the large field size, sus
-
ceptibility to single-point failure and required low transmission loss,
make them sensitive to process-induced defects and defect density
levels that might otherwise be tolerated in smaller-area, higher-loss
devices. The fabrication process demonstrated here uses only con
-
ventional techniques. Specifically, only conventional lithography
as well as wet and dry etching are performed. This enables visible
defects and voids to be maintained at levels no greater than unity
over areas of 50
cm
2
, ensuring no breaks in transmission. This is an
advantage over techniques such as wafer bonding
1
8
.
In this study, both optical backscatter reflectometry and resonator
Q measurements are used to confirm waveguide loss. Average meas
-
ured waveguide loss of 0.08
±
0.01
dB
m
− 1
in long spirals is inferred
from backscatter measurements over a broad band of wavelengths
in the telecommunications window. Also, narrow-band backscat
-
ter measurements are used to study the wavelength dependence of
the loss and a lower limit of 0.05
±
0.015
dB
m
− 1
is measured.
Moreover, a lower value of 0.037
dB
m
− 1
is obtained with resonator-
based measurements. As a simple application of these new devices, a
data stream is also transmitted through a delay line to illustrate a data
buffer function. The waveguide delay lines reported are the longest,
ultra-low-loss devices demonstrated to date and the ultra-low-loss
window is shown to be broadband, spanning the telecommunica
-
tions window. Moreover, by showing that fields containing long
sections of waveguide can be stitched to create an even longer con
-
tinuous waveguide, the approach is shown to be scalable. Structures
over areas as large as 9.5
cm×9.5
cm are demonstrated and delays as
long as 250
m are feasible.
Results
Fabrication process and waveguide structure
. To fabricate the
waveguide delay line, we have adapted a technique for realization of
high-Q silica whispering-gallery resonators. Therein, disk resonators
with Q factors as high as 50 million (0.5
dB
m
− 1
) have previously
been demonstrated using lithography, followed by a buffered HF
etch and XeF
2
dry etch of the silicon
1
9
. In those devices, a distinctive
wedge profile was applied to isolate the optical mode from the rough
lithographic edge. By creating a small-angle wedge, the mode was
pushed away from the edge, thereby lowering scattering loss and
boosting Q factor. After careful study of this process, we have found
that proper etch control can eliminate the lithographic roughness
altogether. As illustrated in
Fig.
1
, two competing etch fronts regulate
whether the roughness is present. By allowing the etch time to run
longer, a single etch front results and ultra-low-loss structures can
be fabricated over a wide range of angles (8–30°). A long waveguide
based on this wedge geometry was prepared in the form of an
Archimedean whispering-gallery spiral. A cross-section is shown
in
Fig.
1
. In the current design, only one edge of the oxide is used
for waveguiding. As discussed later, a ridge design can enable use
Figure 1 | An SEM micrograph showing a cross-section of the spiral delay
line.
(
a
) silicon pillars support thermal oxide structures, the outer edge
of which guides the optical mode. (
b
) Close-up view of oxide edge that is
formed using a non-optimized etch. Two etch fronts are apparent along
with roughening of the oxide surface. (
c
) Close-up view of oxide edge that
is formed using an optimized etch. Etch duration has been increased to
eliminate one of the etch fronts, resulting in a smooth edge. (
d
) The finite
element simulation of the fundamental optical mode propagating inside the
waveguide. scale bars: (
a
) 100
μ
m; (
b
) 0.5
μ
m; (
c
) 0.5
μ
m; (
d
) 8
μ
m.
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of the inner edge thereby boosting the areal efficiency of the delay
structure. Finally, oxide thickness was increased from previous work
so as to further reduce surface scattering loss. A thickness of 8
μ
m
was used in the present devices.
Backscatter characterization of single-spiral delay lines
. An opti
-
cal backscatter reflectometer (Luna OBR 4400) was used to charac
-
terize each delay line.
Figure 2
a
shows a spiral with a path length of
approximately 7
m. (All path lengths quoted here are physical path
lengths, and optical path lengths are about 1.45 times longer.) The
cleaved facet input is at the lower left corner of the chip and features
a 7° cleave angle so as to reduce Fresnel reflection for backscatter
reflectometer measurements. Optical fibre and index-matching oil
are used for coupling. The waveguide is a single, counter-clockwise
Archimedean spiral that terminates near the centre of the spiral. As
noted in
Fig.
1
, waveguiding occurs on the outer edge of the silica.
The undercut to the silica must therefore be sufficient to eliminate
scattering of the fundamental guided mode with the silicon pillar.
Both calculation and measurement (see discussion of
Fig. 2
c
) show
that an undercut of 60
μ
m is sufficient to lower this silicon pillar
interaction to levels below that caused by silica surface scattering. In
backscatter measurements, however, the presence of a few higher-
order radial modes will produce an enhanced backscatter signal
due to their stronger interaction with the silicon pillar. For the
same reason, these modes also show higher waveguide attenuation,
masking the underlying fundamental-mode optical loss. To pre
-
vent this masking effect, the undercut in
Fig. 2
a
has been increased
somewhat beyond what is necessary for the fundamental mode. By
doing this, even higher-order radial modes excited by the input fibre
will experience a negligible level of pillar scattering. This behaviour
is observed by monitoring backscatter signal in spirals of increasing
undercut. The backscatter decay rate is observed to steadily decrease
and finally plateau at around 75
μ
m of undercut.
Backscatter data in
Fig. 2
b
are obtained for such a deeper under
-
cut spiral. With the exception of the narrow-band spectral study
in
Fig.
5
, all backscatter data are taken using a broadband setting
(approximately 90
nm span in the 1,550
nm band)
1
4
. The data show
a linear decrease (on the log scale) over nearly the full 7
m of the spi
-
ral path. The inferred loss rate from this data is 0.05
±
0.01
dB
m
− 1
and provides a lower bound on the waveguide attenuation rate. This
value accounts for the optical return, which increases the observed
backscatter attenuation rate by twofold. To further refine the esti
-
mate, the impact of the varying backscatter signal caused by the
changing radius of curvature is accounted for in the measurement.
For this calibration, we first note that bending loss data in
Fig. 3
,
when compared with attenuation calculation based on atomic force
microscope (AFM) roughness data, show that surface roughness
scattering is the principle source of attenuation to diameters at least
as large as about 1
cm. By assuming that backscatter strength is pro
-
portional to attenuation, a simple differential equation relates the
0
1
2
3
4
5
6
7
−125
−122.5
−120
−117.5
−115
Amplitude (dB mm
–1
)
Length (m)
0
0.05
0.1
0.15
0.2
Local loss (dB
m
–1
)
2.13
a
c
b
d
1.97
1.79
1.59
1.37
1.10
0.71
Radius (cm)
0
5
10
15
20
25
−125
−120
−115
−110
−105
−100
Amplitude (dB mm
–1
)
Length (m)
Figure 2 | Optical micrographs and backscatter reflectometer data for a single spiral and a monolithic spiral cascade.
(
a
) An optical micrograph of a
7-m physical path length, counter-clockwise spiral. This spiral has a diameter of 4.3
cm. (
b
) optical backscatter reflectometer measurement of the spiral
waveguide shown in
a
. on account of the return path, the backscatter decay rate is increased twofold. The blue curve is a fit to the backscatter level,
while the green curve gives a fit to the local backscatter decay rate and the red curve uses a model to infer the actual local waveguide attenuation, which
is approximately 0.08
dB
m
− 1
over most of the spiral. The upper axis gives the radius from centre, while the lower axis gives the physical path length.
(
c
) optical micrograph of a cascaded, four-spiral waveguide having a physical path length of 27
m. The input port is in the upper left of the image, and
the waveguides connecting neighbouring spiral delays are visible. The entire chip is 9.5
cm×9.5
cm and consists of four, separately exposed and stitched
lithography fields. (
d
) optical backscatter reflectometer measurement of the spiral waveguide delay line shown in
c
. The periodic singularities (blue
circles) in the backscatter signal correspond to the optical wave transiting the inner adiabatic coupling region of each spiral. other discontinuities (green
squares) in backscatter occur when the optical wave transfers between the spirals and result from higher-order transverse modes being mode filtered. The
inset to
d
is a magnified view of the adiabatic coupling section, which is approximately 1
mm in diameter. scale bars: (
a
) 1
cm; (
c
) 2
cm; (
d
) 500
μ
m.
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measured backscatter power,
B
(
z
), to local waveguide attenuation,
α
(
z
). The equation is given by,
1
2
1
B z
dB
z
dz
z
z
d
z
dz
( )
( )
( )
( )
( )
=−
−
a
a
a
This equation shows that when the attenuation rate is changing
with distance (in the present case on account of the slowly changing
radius of the waveguide), there is a slight correction to the loss as
inferred from the backscatter rate. Inward spiraling waves produce
a backscatter signal that attenuates more slowly on account of this
term, while outward spiraling waves appear to decay more quickly.
By using the measured backscatter data as input to the above
equation, a corrected value of 0.08
±
0.01
dB
m
− 1
for the loss of
the device, in
Fig. 2a
,
is obtained.
Backscatter characterization of cascaded-spiral delay lines
.
Figure 2
c
shows four spirals cascaded on a single wafer to create
a 27
m (physical length) waveguide. Each spiral is approximately
4 cm in diameter. The lithography for the spirals involved exposure
and stitching of four distinct lithography fields using a Canon FPA
3000
iW stepper tool. The angle-cleaved input facet is in the upper
left corner of
Fig. 2
c
. Each spiral features inward and outward, inter
-
laced Archimedean-shaped waveguides that are connected at the
spiral centre by an adiabatic coupler. The adiabatic coupler features
a completely undercut silica guide that is designed so as to maintain
propagation in the fundamental transverse mode through the clock
-
wise to counter-clockwise turn. As shown below, the adiabatic cou
-
pler introduces about 0.1
dB insertion loss. In the present design, the
constraints imposed on this completely undercut adiabatic coupler
when combined with etch non-uniformity over the 9.5
cm×9.5
cm
wafer area limits the silicon undercut to about 60
μ
m. This causes
significant interaction of non-fundamental, radial modes with the
silicon pillar as noted above. As a result, the backscatter data in
Fig. 2
d
show an apparent increased loss as light propagates through
the first two spirals. Moreover, the higher-order modes cause a dis
-
continuity in the backscatter at the large radii, waveguide intercon
-
nection between spirals. These conclusions are confirmed through
(1)
(1)
measurements on smaller area, cascaded spiral designs in which a
progression of deeper undercuts completely removes the disconti
-
nuity and reduces the apparent loss in the entrance spirals. They
are also confirmed by the apparent reduction of attenuation in the
third and fourth spirals (see
Fig. 2
d
), wherein we believe propaga
-
tion is primarily in the fundamental mode as a result of high-order
mode filtering provided by spirals one and two as well as their inter
-
connections. It is also significant that the backscatter discontinuity
between spirals three and four is weak, also reflecting propagation
primarily in the fundamental mode.
Analysis of waveguide attenuation in any of the spirals of
Fig. 2
c
is performed by plotting the ratio of out-going to in-going
backscatter strength at equidistant points from the spiral centre.
Such a plot for spiral 3 is shown in
Fig.
4
. The slope of the linear
fit gives approximately 0.1
dB
m
− 1
loss for the waveguide, while
the intercept gives an insertion loss for the adiabatic coupler of less
than 0.1
dB. A similar value is obtained for spiral 4, while spirals 1
and 2 show an apparent waveguide loss of 0.2
dB
m
− 1
, presumably
because of the presence of higher-order radial modes. The small dif
-
ference in optical loss (0.08 versus 0.1
dB
m
− 1
) for the spirals shown
in
Fig. 2a and
c
might reflect slight process variation in the fabrica
-
tion of these devices.
The adiabatic transition used to connect the clockwise and
counter-clockwise Archimedean spirals was designed by applying a
variational analysis to the following functional.
E
s
s
ds
z
z
=
∂
∂
∫
0
1
2
k
( )
where
κ
(
s
) is the curvature of the waveguide and
s
is the arc-length.
Variation of this equation minimizes the adiabaticity condition over
the waveguide. By applying the variation to a third-order polyno
-
mial subject to boundary conditions of smooth connection up to
the first-order derivative of curvature with the Archimedean spi
-
ral, a numerical function for the ‘S-shape’ bend was generated.
(2)
(2)
1
25
25
0
2,500
Q (Million)
0.1
0.01
Loss (dB
m
–1
)
0
2
4
6
8
10
Bending diameter (mm)
Figure 3 | Bending loss data plotted versus the bending diameter.
The
blue squares are data points obtained from Q measurement on resonators
of varying diameters. The black curve is a fit to the data using roughness
data provided in the text and obtained using an AF
m. The principle source
of roughness is the lower interface, and an estimate of the bending loss
in case this surface can be smoothed to the level of the upper surface is
provided as the red curve. The inset shows a modified version of the spiral
design in which a waveguide ridge is created so as to provide both interior
and exterior guiding in the spiral. The two colour-graded regions give the
mode intensity profile.
0
1
2
3
4
5
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Length (m
)
Loss (dB)
Figure 4 | Analysis of waveguide loss and adiabatic coupler insertion
loss using backscatter data.
Green data points are generated by taking the
ratio of backscatter signals at symmetrically offset distances away from the
adiabatic coupler in spiral 3 of
Fig. 2
c
. The intercept reveals the insertion
loss of the coupler as given by a range of possible values falling within a
confidence interval. The fitted line (red solid line) slope of about 0.1
dB
m
− 1
provides a measure of the waveguide attenuation rate and is in reasonable
agreement with the spiral in
Fig. 2
a
. The dotted red lines provide the 95%
confidence interval.
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The S-waveguide width used in the variation was selected so as to
allow full undercut of the silica on etching.
Loss spectrum and bending loss
. The backscatter reflectometer
measurement is based on a frequency sweep method. By degrad
-
ing spatial resolution, narrower spectral scans are possible so that
spectral variation of the waveguide loss can be measured. In
Fig.
5
,
spectral data of waveguide loss in a 7-m spiral is presented with the
measurement window set to 5
nm (spatial resolution of 200
μ
m). A
minimum value of 0.05
±
0.015
dB
m
− 1
is measured near 1,595
nm.
There is, overall, a weak variation in the apparent loss rate. None of
the features seem to be associated with molecular absorption.
To obtain the dependence of attenuation on waveguide bending,
the Q factor of disk resonators of varying diameters is measured.
Optical attenuation as low is 0.037
dB
m
− 1
is attained (see F
ig.
3
),
corresponding to an optical Q factor of 670 million. AFM meas
-
urement of the upper, wedge and lower surfaces have also been
performed on these resonators giving corresponding root mean
squared roughness variances of 0.15 and 0.48
nm with correlation
length of approximately 200
nm for the upper and wedge surfaces,
respectively. The roughness of the lower surface is as large as 1–2
nm
in amplitude, but occurs in concentric ring patterns, suggesting that
a complex surface interaction takes place during undercut of the
silicon. The lower side roughness (assuming a 200
nm correlation
length) has been used as a fitting parameter to model the loss ver
-
sus diameter in
Fig.
3
(see Methods for discussion of model). Also,
a projection of the predicted loss is given assuming that the lower
surface roughness could be reduced to that of the upper oxide
surface. In the current design, loss levels lower than 0.01
dB
m
− 1
could be realized. Significantly, the AFM data in conjunction with
the optical attenuation data show that thermal oxide is an excellent
optical material. Indeed, 0.037
dB
m
− 1
is a loss value that is close
to that of the first technologically successful optical fibre
2
0
. Con
-
cerning the stability of this result, based on early work in silica
microspheres
2
1
, it is not expected that water adsorption will
impact Q stability for the larger resonator diameters studied here.
Indeed, neither resonators nor spiral waveguides experienced any
measurable degradation over measurement periods that lasted for
several days.
Optical buffer demonstration
. As a simple test of the delay line
such as might occur in optical buffering, a 13.5-m double spiral was
used to delay a 2.5
Gb
s
− 1
data stream. For this, the light output
from an external-cavity semiconductor laser (New Focus, Velocity
6300) was modulated using a lithium niobate modulator (EOspace,
intensity modulator AZ-OK5-10) and coupled into the delay line.
The delay line was mounted onto a six-axis aligner and the input
and output fibres were coupled using precision six-axis aligners. The
output was passed through a variable attenuator and detected using
a high-speed photo-detector (New Focus, model 1554). Eye pat
-
terns of the detected input and output streams were averaged over
10
s with no visible degradation or change in the structure of the eye
pattern. In this specific test, the optical delay line stored ~170 bits.
At 10
Gb
s
− 1
, it would contain 680 bits. Both the setup and the
eye-pattern data are presented in
Fig.
6
.
Discussion
There has been no attempt to reduce footprint in this study, as the
emphasis has been on reduction of attenuation rate and demonstra
-
tion of scalability. However, a modification of the current design
is shown in
Fig.
3
as an inset. This design uses a ridge geometry
produced by a second wet etch to locally confine the mode to both
sides of the spiral and leads to a considerable improvement in the
area utilization of the wafer. By using the surface roughness meas
-
urements described above, we estimate that a comparably low-loss,
100-m long structure could be fabricated in the same footprint as
the cascaded spiral in
Fig. 2
c
. Specifically, in the current design
~200
μ
m per waveguide is used in the Archimedean spiral. In the
ridge design, this could be reduced to 70
μ
m per waveguide. By
extension of the stitching method already demonstrated here, it
would then be possible to lithographically stitch 10 spiral fields onto
an 8 in wafer for a total path length of 250
m.
Finally, the integration of this optical delay with an optical
circuit is also under study. By using a silicon nitride taper design
it is possible to adiabatically and selectively couple a single-mode
nitride waveguide to the fundamental mode of the spiral structures
described here. This is possible because the fundamental transverse
mode of the delay line features the largest effective index (as it has
the largest propagation constant
β
). As such, a silicon nitride (refrac
-
tive index 2.0) waveguide taper of thickness ~200
nm can be tapered
so as to reduce its effective index to the point of coupling with only
the fundamental transverse mode. Using input and output silicon-
nitride adiabatic couplers, the delay-line would function essentially
as a single transverse mode device, and could be interfaced directly
to conventional photonic circuits on silicon.
Methods
Fabrication of spiral waveguide
. Waveguides and disks were fabricated on (100)
prime grade float zone silicon wafers. The oxide was prepared using the following
procedure. An overall 8
μ
m oxide film was grown by wet oxidation process. Finally, a
dry oxidation process was performed for 24
h. The temperature for all the oxidation
processes was 1,000 °C. Photo-resist was patterned using a GCA 6300 stepper for disks
and Canon FPA 3000
iW stepper for spiral waveguides. Post-exposure bake followed
in order to cure the surface roughness of the photo-resist pattern, which acted as an
etch mask during immersion in buffered hydrofluoric (HF) solution (Transene, buffer
HF improved). The isotropic and uniform etching characteristic of buffered HF solu
-
tion resulted in oxide disks and waveguides having very smooth wedge profile. The
reproducibility of the etch is excellent. Specifically, waveguide width control studies for
waveguides on the same wafer show a
±
0.25
μ
m variation in width. After the conven
-
tional cleaning process to remove photo-resist and organics, the silicon under the oxide
structures was isotropically etched by xenon difluoride to create an air-cladding
whispering-gallery waveguide. Buffer patterns were introduced around the waveguide
to prevent non-uniform undercut by loading effect during the xenon difluoride etching.
Scattering loss modelling
. In the waveguide, transmission loss results from two
sources: the absorptive material losses and scattering loss due to the surface rough
-
ness. Through Q versus resonator diameter studies, we conclude that scattering
losses are the dominant source of loss in the structures tested (
Fig.
3
). To model
these losses, we adapted a general approach reported elsewhere
9,22,2
3
. The rough
interface induced radiation loss is calculated via an equivalent volume density,
which could be evaluated from the roughness profile and surface electric field
J r
i
n
n E
r
r
( )
(
)
( )
(
)
=−
−
∈
we
d
0
0
2
1
2
interfac
e
where
ω
is the radial frequency of the light,
ε
0
is the free space permittivity,
n
0
and
n
1
are the refractive index of waveguide and cladding, respectively, and
(3)
(3)
0.16
0.14
0.12
0.10
0.08
0.06
0.04
1,530
1,540
1,550
1,560
Central
wav
elength (nm)
1,570
1,580
1,590
1,600
1,610
Av
erage loss (dB
m
–1
)
Figure 5 | The wavelength dependence of waveguide loss.
The loss is
measured with backscatter reflectometry over a wavelength range of
1,528 to 1,608
nm in a 7-m long spiral waveguide. The minimum loss
measured is 0.05
±
0.015
dB
m
− 1
near a wavelength of 1,595
nm. The
values plotted have been calibrated for spiral curvature using equation (1).
A measurement window of 5
nm is applied
14,1
7
. Error bars are included
on each point and have been computed by standard deviation of three
independent measurements.