1
Supplementary Note 1
Waveguide arrays are fabricated on (100) prime-grade float-zone silicon wafers. The initial oxide layer is thermally
grown at 1000
◦
C with 2
μ
m thickness. The photoresist is patterned on the oxide layer (Fig. 2a), and acts as etch mask
during hydrofluoric acid (HF) immersion. HF wet-etching creates the wedge surfaces at the edge of the photoresist
pattern, and the further wet-etching results in the triangular-cross-section ridge stripe of silica as the two angled
wedge surfaces meet each other (Fig. 2b). The wet-etching duration is around 45 min. Then, an additional thermal
oxidation creates an under-layer of silica (Fig. 2c). The waveguide chips used for data in the manuscript had the
under-layer thickness of either 310 nm or 450 nm. Striped openings (Fig. 2d) are etched after a second lithography
step (Fig. 2e). As a final step, the silicon under the oxide structure is isotropically etched (Fig. 2f). Both numerical
calculation and measurement confirmed that an undercut of 10
μ
m is sufficient to eliminate the silicon structure
interaction as a result of modal confinement. The average spacing between two waveguides is about 35
μ
m, and 725
waveguides per inch can be fabricated in an array.
Dimension (
P
m)
Mask width (
P
m)
b
a
w
H
w
H
13
14
15
16
0
1
2
3
4
5
Supplementary Figure 1: Dependence of ridge dimension on mask width
(
a
) SEM images of a series of
ridges in a fabricated silica waveguide array. The thickness of the base silica layer is 0.45
μ
m. Scale bar is 1
μ
m.
The definition of ridge height (H) and ridge width (w) is shown in the panel. (
b
) Measured ridge dimensions based
on SEM images as a function of mask width. Here, the mask width is the width of the red rectangular strip pat-
terned on photoresist in Fig. 2a of the manuscript. The ridge height (H) and width (w) increase by about 0.5
μ
m
and 1
μ
m, respectively, as the mask width increases by 1
μ
m. The ability to lithographically define the ridge di-
mension enables precise control of waveguide dispersion, and, in turn, precise tuning of the dispersive-wave wave-
length.
2
1.5
2
2.5
3
3.5
4
600
700
800
900
1000
1100
Pump wavelength (nm)
Ridge width (
P
m)
500
200
300
400
500
600
700
DW
(nm)
ZDW,1
ZDW,2
O
O
O
Supplementary Figure 2: Phase-matching dispersive wave wavelength in a waveguide array.
Calcu-
lated TM dispersive wave wavelength given as a colour map (
λ
DW
) as a function of pump wavelength and ridge
width for the waveguide array chip used in Fig. 1e. The black lines are the zero crossing of the group velocity dis-
persion (
λ
ZDW
,
1
and
λ
ZDW
,
2
). The white regions are pump wavelengths where dispersive wave generation is not
possible. For waveguides with
w <
2
.
19
μ
m, there is a second zero crossing (
λ
ZDW
,
2
), allowing for formation of a
second dispersive wave. However, a second dispersive wave was not observed in our experiment due to the loss of
modal confinement at long wavelengths for the waveguides with small mode area. An upper bound on
λ
DW
for a
given ridge width is provided by
λ
ZDW
,
1
.
λ
DW
will approach this wavelength as the pump wavelength approaches
λ
ZDW
,
1
. On the other hand, a lower bound on
λ
DW
is determined by the longest pump wavelength possible in the
anomalous dispersion regime (coloured region).
λ
DW
shifts toward shorter wavelength as the pump wavelength
increases. This is understood from the phase-matching condition. At longer pump wavelengths, the group veloc-
ity is smaller, and hence the propagation constant of the dispersive wave must be larger (shorter wavelength) for
the phase-matching to occur. The upper bound on the pump wavelength in the anomalous dispersion regime is
given by
λ
ZDW
,
2
if it exists. The calculation is consistent with our demonstration of dispersive wave generation at
wavelength
λ
DW
<
300 nm using a 1064 nm pump wavelength as compared to the shortest
λ
DW
of 310 nm gen-
erated using an 830 nm pump wavelength. Lastly, smaller mode area results in smaller
λ
DW
and can be achieved
with smaller ridge widths. However, there is a threshold value of ridge width below which the mode area increases
because of weak modal confinement. For the array waveguide chip with lower silica layer thickness 0.45
μ
m, the
threshold ridge width is 1.47
μ
m using the 830 nm pump.