of 3
Supercontinuum generation in an
on-chip silica waveguide
Dong Yoon Oh,
1
David Sell,
1
Hansuek Lee,
1
Ki Youl Yang,
1
Scott A. Diddams,
2
and Kerry J. Vahala
1,
*
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
2
Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
*Corresponding author: vahala@caltech.edu
Received November 27, 2013; revised January 10, 2014; accepted January 11, 2014;
posted January 14, 2014 (Doc. ID 202054); published February 13, 2014
Supercontinuum generation is demonstrated in an on-chip silica spiral waveguide by launching 180 fs pulses from
an optical parametric oscillator at the center wavelength of 1330 nm. With a coupled pulse energy of 2.17 nJ, the
broadest spectrum in the fundamental TM mode extends from 936 to 1888 nm (162 THz) at
50
dB
from peak. There
is a good agreement between the measured spectrum and a simulation using a generalized nonlinear Schrödinger
equation. © 2014 Optical Society of America
OCIS codes:
(320.6629) Supercontinuum generation; (190.4390) Nonlinear optics, integrated optics.
http://dx.doi.org/10.1364/OL.39.001046
A supercontinuum of light is generated when a narrow-
band pulse undergoes an extreme spectral broadening
due to nonlinear optical processes such as self-phase
modulation, cross-phase modulation, Raman scattering,
soliton fission, dispersive wave generation, four-wave
mixing, and self-steepening [
1
]. Photonic crystal fiber
has been remarkably successful in supercontinuum gen-
eration (SCG) due to the feasibility of controlling the
dispersion and reducing the mode area by engineering
its air-hole geometry [
2
4
]. Interest in SCG has been
driven by applications including frequency combs [
5
,
6
],
optical coherence tomography [
7
], and wavelength divi-
sion multiplexing [
8
,
9
]. In the past few years, SCG has
also been investigated in several chip-based systems, in-
cluding silicon photonic nanowires [
10
12
], chalcogenide
waveguides [
13
,
14
], and silicon nitride (Si
3
N
4
) wave-
guides [
15
,
16
]. These chip-based waveguides for SCG will
become important elements to expanding the functional-
ity of photonic integrated circuits.
In this Letter, we demonstrate SCG using an on-chip
silica (SiO
2
) waveguide. Silica has a relatively small Kerr
coefficient
n
2
of
2
.
6
×
10
20
m
2
W
1
[
17
], which is 10 times
smaller than silicon nitride and more than 100 times
smaller than silicon [
18
]. Compared to other materials,
however, silica has a much lower linear loss, a feature
central to the success of optical-fiber-based SCG devices.
Recently, a chip-based silica waveguide having record-
low optical loss was demonstrated [
19
]. In addition to
its function as an optical delay line, here the possibility
of SCG in the waveguide harnessing its nonlinear inter-
action length is tested.
The silica waveguide used in the experiment has a total
physical path length of 3.5 m and consists of four cas-
caded sections [see Fig.
1(a)
]. Each section contains
two interleaved waveguides configured in the form of
an Archimedean spiral. For example, a lightwave travel-
ing from left to right would enter the far-left spiral of
Fig.
1(a)
at the bottom, take a counterclockwise path
toward the spiral center, execute a turn on an S-shaped
waveguide at the spiral center, and then exit on a clock-
wise path. A connection waveguide then conveys the
lightwave to the next spiral where entry now occurs
on a clockwise path. Each spiral has an outer radius
of 7.0 mm. The chip size is
2
.
5
cm ×
6
.
9
cm. The details
of the fabrication method and waveguide design princi-
ples can be found in [
19
,
20
].
To test spectral broadening using the spiral waveguide,
an optical parametric oscillator (OPO, Spectra-Physics
OPAL) is used to generate an 80 MHz repetition rate
and 180 fs long (FWHM) pulse. The peak power of the
pulse is controlled by a variable neutral density filter
Fig. 1. Low-loss silica-on-silicon waveguide and experimental
setup. (a) Photograph of the sample showing four cascaded
spiral waveguides. (b) Experimental setup for SCG and charac-
terization using the silica waveguide. OPO, optical parametric
oscillator; OSA, optical spectrum analyzer. (c) Close-up view
of the optical coupling stage, imaging objectives, and spiral
waveguide chip.
1046 OPTICS LETTERS / Vol. 39, No. 4 / February 15, 2014
0146-9592/14/041046-03$15.00/0
© 2014 Optical Society of America
and the polarization by a half-wave plate, as shown in
Fig.
1(b)
. Both TE and TM mode SCG were studied
and exhibited qualitatively similar behavior both in the
measurements and modeling. However, only data for
the TM modes are presented as their spectra are slightly
broader on account of a reduced modal, cross-sectional
area relative to the TE modes. An objective lens with
12 mm focal length is mounted on a piezo-controlled
xyz
stage for the coupling of OPO pulses into the wave-
guide. Due to the cleave angle of the front facet of the
waveguide (introduced to minimize back reflection),
the sample is rotated by 35°
40° for efficient coupling.
At the end facet, a cleaved multimode fiber is closely
positioned to receive the light coming out of the wave-
guide. The coupling loss at the input and the output ends
of the waveguide are estimated to be around 3 and 10 dB,
respectively. The other end of the multimode fiber is con-
nected to an OSA. Two OSAs were used to separately
record the spectra in the wavelength ranges 600
1700 nm (Agilent 86141B) and 1200
2400 nm (Yokogawa
AQ6375). As the center wavelength of the input pulse is
varied from 1250 to 1350 nm, the broadest spectrum is
observed near 1330 nm. Measured TM mode spectra
for various coupled pulse energies are presented in Fig.
2
.
At the maximum energy of 2.17 nJ, an octave spanning
continuum extending from 936 to 1888 nm (162 THz)
at
50
dB from peak is generated.
The pulse propagation in the waveguide is modeled
by implementing a generalized nonlinear Schrödinger
equation [
21
]:
~
A
0
z

i
γ

z;
ω

e
L

z;
ω

z
×
F

A

z; T

Z
R

T
0
j
A

z; T
T
0
j
2
d
T
0

;
(1)
A

z; T

is the pulse envelope in a frame of reference mov-
ing along the
z
direction at the group velocity at the pump
frequency
ω
0
,
~
A

z;
ω
ω
0

is its Fourier transform
(
F
), and
~
A
0

z;
ω
ω
0

is defined as
~
A

z;
ω
ω
0

e
L

z;
ω

z
.
The function
L

z;
ω

P
M
k

2

β
k

z;
ω
0

k
!

ω
ω
0

k

α

z;
ω

2

has contributions from the dispersion (first
term) and the optical loss (second term), where
β
is the
propagation constant and
β
k

k
β
∕∂
ω
k
. Once
β
2

z;
ω

is known, then
β
k

z;
ω
0

for
k
3
can beobtained by fitting
β
2

z;
ω

to a polynomial in
Δ
ω

ω
ω
0
. In the simulation,
the fitting is taken to 13th order in the summation. Last,
γ

z;
ω

is the frequency-dependent nonlinearity and
R

T

is the nonlinear response function, which has an in-
stantaneous electronic contribution and a contribution
from the delayed Raman response [
22
].
The dispersion, nonlinearity, and scattering loss of the
waveguide as functions of waveguide radius in the spiral
are calculated using a finite element solver. In Fig.
3
, the
group velocity dispersion (

2
π
c
λ
2

β
2
) and nonlinearity
at selected values of waveguide radius
r
are shown. The
outermost part (at
r

7
.
0
mm) of a spiral waveguide
has a 8
μ
m thick, 20° wedge-shaped cross section. It
has a zero-dispersion wavelength of 1230 nm and a non-
linearity of
0
.
001
0
.
010
W
1
m
1
over the wavelength
range 600
1700 nm. As the waveguide spirals inside,
the zero-dispersion wavelength increases up to 1510 nm
because of the more negative geometric dispersion of the
waveguide at smaller radius. Proceeding further inside
(
r<
0
.
7
mm), the wave experiences a drop of the zero-
dispersion wavelength due to a tapering of the waveguide
for the minimization of the transition loss over the
S-shaped waveguide at the spiral center. At
r

0
.
2
mm where the wave enters the S-shaped waveguide
that couples light between clockwise and counterclock-
wise spirals, the waveguide has a triangular cross section
with 1.4
μ
m thickness. There, the zero-dispersion wave-
length is as short as 720 nm and nonlinearity is as high
as
0
.
0313
0
.
145
W
1
m
1
over the wavelength range
600
1700 nm. Since the length of the tapered section is
Fig. 2. Spectral broadening in the fundamental TM mode
measured at a series of pulse energies. The blue solid curves
are measured spectra, and the dashed curves in light blue
are spectra from the simulation.
Fig. 3. Calculated dispersion and nonlinearity of the funda-
mental TM mode at a series of radii that occur at the inner
and outer waveguides within each spiral.
February 15, 2014 / Vol. 39, No. 4 / OPTICS LETTERS 1047
negligible, however, most of the spectral broadening
occurs in the nontapered outer region of the spiral.
On account of the radial dependences in Fig.
3
, there is
a corresponding
z
dependence for quantities within
Eq. (
1
), which is accounted for as follows. The equation
for an Archimedean spiral is
r

b
θ

r
c
in polar coordi-
nates where
r
is the waveguide radius,
θ
is the rotational
angle, and the origin is taken to be the spiral center.
The parameter
b

0
.
056
mm is the distance between
successive turnings divided by
2
π
, and
r
c

0
.
2
mm is
the radius at which the spiral ends and the S-shaped
waveguide starts near the center. Defining
r
0

7
.
0
mm
as the radius at the waveguide entrance (
z

0
),
the radius of the waveguide at the inward propagation
length
z
is
r

z


r
2
0
2
bz
q
. Outward propagation is
modeled in a similar way. Quantities in Eq. (
1
) are then
evaluated at 22 chosen values of radii directly from finite
element modeling simulations and interpolated at all the
other radii encountered in the waveguide. The resulting
spectra from a simulation match well with the measured
ones (see Fig.
2
).
In conclusion, we have experimentally demonstrated a
supercontinuum using an on-chip silica waveguide
pumped by femtosecond pulses from an OPO. An octave
spanning spectrum in the telecommunication band is
generated in the fundamental TM mode. The modeling
of the pulse propagation in the spiral waveguide is dis-
cussed and a good agreement between the measured
spectrum and a simulation is found. With further
dispersion engineering and tighter modal confinement,
a silica waveguide is expected to be a viable platform
for nonlinear optics on a chip.
The authors gratefully acknowledge financial support
from the DARPA QuASAR program, NASA, and the Kavli
Nanoscience Institute.
References
1. G. P. Agrawal,
Nonlinear Fiber Optics
(Academic, 1995).
2. J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett.
25
,25
(2000).
3. P. Russell, Science
299
, 358 (2003).
4. J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys.
78
,
1135 (2006).
5. S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K.
Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W.
Hänsch, Phys. Rev. Lett.
84
, 5102 (2000).
6. D.J.Jones,S.A.Diddams,J.K.Ranka,A.Stentz,R.S.Windeler,
J. L. Hall, and S. T. Cundiff, Science
288
, 635 (2000).
7. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G.
Fujimoto, J. K. Ranka, and R. S. Windeler, Opt. Lett.
26
, 608
(2001).
8. T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K.
Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M.
Yamada, T. Kanamori, and H. Ono, Electron. Lett.
32
,
906 (1996).
9. S. Kawanishi, H. Takara, K. Uchiyama, I. Shake, and K.
Mori, Electron. Lett.
35
, 826 (1999).
10. I. W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C. Y.
Chou, F. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood,
Opt. Express
15
, 15242 (2007).
11. Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express
15
,
16604 (2007).
12. L. Yin, Q. Lin, and G. P. Agrawal, Opt. Lett.
32
, 391
(2007).
13. M. R. Lamont, B. L. Davies, D. Y. Choi, S. Madden, and B. J.
Eggleton, Opt. Express
16
, 14938 (2008).
14. A. C. Judge, S. A. Dekker, R. Pant, C. M. Sterke, and B. J.
Eggleton, Opt. Express
18
, 14960 (2010).
15. L. Zhang, Y. Yan, Y. Yue, Q. Lin, O. J. Painter, R. G. Beausoleil,
and A. E. Willner, Opt. Express
19
, 11584 (2011).
16. R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson,
and A. L. Gaeta, Opt. Lett.
37
, 1685 (2012).
17. D. Milam, Appl. Opt.
37
, 546 (1998).
18. D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, Nat.
Photonics
7
, 597 (2013).
19. H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, Nat.
Commun.
3
, 867 (2012).
20. T. Chen, H. Lee, J. Li, and K. J. Vahala, Opt. Express
20
,
22819 (2012).
21. J. M. Dudley and J. R. Taylor,
Supercontinuum Generation
in Optical Fibers
(Cambridge University, 2010).
22. Q. Lin and G. P. Agrawal, Opt. Lett.
31
, 3086 (2006).
1048 OPTICS LETTERS / Vol. 39, No. 4 / February 15, 2014