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APPLIED
PHYSICS
Octa
ve-spanning
tunable
infr
ared
par
ametric
oscilla
tors
in
nanophotonics
Luis Ledezma
1,2
, Arkadev
Roy
1
, Luis Costa
1
, Ryoto Sekine
1
, Robert Gray
1
, Qiushi
Guo
1
,
Rajveer Nehra
1
, Ryan M. Briggs
2
, Alireza Marandi
1
*
Widely
tunable
coher
ent
sour
ces
are desir
able
in
nanophotonics
for
a multitude
of
applica
tions
ranging
from
communica
tions
to
sensing.
The
mid-infr
ared
spectr
al
region
(w
avelengths
be
yond
2 μm)
is particularly
impor-
tant
for
applica
tions
relying
on
molecular
spectr
oscopy
. Among
tunable
sour
ces,
optical
par
ametric
oscilla
tors
typically
offer
some
of
the
broades
t tuning
ranges;
ho
wev
er,
their
implementa
tions
in
nanophotonics
ha
ve been
limited
to
narr
ow
tuning
ranges
in
the
infr
ared
or
to
visible
wavelengths.
Her
e,
we surpass
these
limits
in
dis-
persion-engineer
ed
periodically
poled
lithium
nioba
te
nanophotonics
and
demons
trate
ultr
awidely
tunable
optical
par
ametric
oscilla
tors.
Using
100
ns
pulses
near
1 μm,
we gener
ate
output
wavelengths
tunable
from
1.53
μm
to
3.25
μm
in
a single
chip
with
output
po
wers
as
high
as
tens
of
milliw
atts.
Our
results
repr
esent
the
firs
t octa
ve-spanning
tunable
sour
ce
in
nanophotonics
extending
into
the
mid-infr
ared,
which
can
be
useful
for
numer
ous
integr
ated
photonic
applica
tions.
Copyright
© 2023 The
Authors,
some
rights
reserved;
exclusive licensee
American
Associa
tion
for the Advancement
of Science.
No claim to
original
U.S. Government
Works. Distributed
under
a Creative
Commons
Attribution
License
4.0 (CC BY).
INTRODUCTION
Widely
tunable
coher
ent sources are vital for applica
tions
ranging
from multichannel
optical
communica
tions
(
1
) to LiDAR
(
2
). Wide
tunability
in the mid-infr
ared spectr
al range
is especially
desirable
because
of the rich molecular
responses
at wavelengths
longer
than
2 μm (
3
). While
it is possible
to gener
ate light
at these
wavelengths
with
semiconductor
lasers
(
4
), the tuning
ranges
are typically
narrow because
of limited
bandwidth
of semiconductor
gain
(
5
8
). Alterna
tively, optical
parametric
oscilla
tors (OPOs) based
on
quadr
atic nonlinearity
have been
a prominent
example
of sources
with
flexible
and broad tuning
ranges,
which
have commonly
been
realized
using
nonlinear
crystals in bulky
tabletop
setups
(
9
).
Previous
efforts
toward OPO minia
turiza
tion
include
using
lithium
nioba
te
diffused
waveguides
with
fiber
feedba
ck loops
(
10
),
semiconductor
waveguides
with
Bragg mirrors deposited
on
the chip
end facets (
11
),
and whispering-gallery
microresona
tors
(
12
,
13
). However, implementa
tion
of OPOs in nanophotonics
with
subw
avelength
modal
confinement
and low propaga
tion
losses
is highly
desirable because
of opportunities
for dense
integr
a-
tion with other
on-chip
components,
strong nonlinear
interactions,
and dispersion
engineering
(
14
).
Over the past decade,
nanophotonic
OPOs were demons
trated in
the near-infr
ared and visible
ranges
using
materials
with cubic
(3)
]
and quadr
atic [χ
(2)
] nonlinearities
(
15
22
).
However, the main
ad-
vantages
of tabletop
OPOs, namely
, wide
tunability
and mid-infr
a-
red coverage, have not yet been
accessed
in nanophotonics.
A
noteworthy
roadblock
for this is the typical
use of simple
pump
res-
onant
configur
ations
in which
all the interacting
optical
fields
res-
onate simultaneously
in a single
resona
tor. This
leads
to ultralow
OPO thresholds
at the expense
of an overconstrained
wavelength
tunability
. In contr
ast, OPOs with singly
or doubly
resonant
config-
urations
(i.e.,
with
nonresonant
pump)
offer
wide
tunability
and
frequency
stability
(
9
).
Here, we design
and demons
trate ultrawidely
tunable
doubly
resonant
OPOs in lithium
nioba
te nanophotonics.
This is achiev
ed
by combining
dispersion
engineering,
precise
design
of the spectr
al
response
of the cavity, and quasi-phase
matching.
With a pump
tunable
over 30 nm at around
1 μm,
we achiev
e wavelengths
tunable
from 1.53 to 3.25 μm from five OPOs on a single
nanopho-
tonic
chip.
RESULTS
The tuning
concept
of the OPOs is illustrated in Fig. 1A, where
more than
1500
nm of tuning
around
2 μm for the signal
and
idler
is obtained
by tuning
the pump
wavelength
around
1 μm by
less than
30 nm. Such
a tuning
range
for the pump
is already
avail-
able from integr
ated distributed
Bragg reflector
(DBR)
semiconduc-
tor lasers
(
23
).
Such
magnifica
tion in tuning
range
from the pump
toward the signal
and idler
(a factor of ~12 in frequency
units)
is
obtained
through
a dispersion-engineer
ed quasi-phase
ma
tched
OPO design
with
a spectr
ally selectiv
e cavity
as depicted
in
Fig. 1B. We use wavelength-selectiv
e couplers
that allow the signal
and idler wavelengths
to resona
te in the OPO cavity with a ~10 GHz
free spectr
al range
(FSR)
while
letting
the pump
go only through
the
poled
waveguide
section
(
24
).
This
differs
sharply
from previously
demons
trated fully
resonant
on-chip
OPO designs
in which
the
pump
also needs
to satisfy a resonant
condition
limiting
their
flex-
ibility
and tunability
. A chip
containing
16 OPOs is fabrica
ted, as
shown in Fig. 1C, where we have highlighted
a single
OPO, which
is also
displa
yed in the false
color
optical
microscope
image
of Fig. 1D.
The simula
ted tuning
behavior of four
OPOs with
differ
ent
poling
periods
is shown in Fig. 1E (solid
black lines).
These
are ob-
tained
from conserva
tion of energy
p
= ω
s
+ ω
i
) and momentum
(
k
p
=
k
s
+
k
i
+ 2π/Λ
QPM
), so they can be tailor
ed by engineering
the
waveguide
dispersion
(
25
).
In particular,
the signal
tuning
slope
(
ω
s
/
ω
p
) is given by the ratio of group velocity
differ
ences
(1/
v
i
1/
v
p
)/(1/
v
i
1/
v
s
), while
the gain bandwidth
is inversely
propor-
tional
to 1/
v
i
1/
v
s
. We have engineer
ed the dispersion
of the poled
1
Department
of Electrical
Engineering,
California
Institute of Technology
, Pasade-
na, CA 91125,
USA.
2
Jet Propulsion
Laboratory, California
Institute of Technology
,
Pasadena,
CA 91109,
USA.
*Corresponding
author.
Email:
marandi@caltech.edu
SCIENCE
ADVANCES
|
RESEARCH
ARTICLE
Ledezma
et al.
,
Sci. Adv.
9
, eadf9711
(2023)
26 July 2023
1 of 7
waveguide
to balance
these
effects.
As a result,
a small
change
in the
pump
wavelength
produces
large
changes
in the output
wavelengths
while
maintaining
a predictable
tuning
curve without
substantial
mode
competition
(see fig. S1).
To study
the transient
and steady-s
tate behaviors
of the nano-
photonic
OPOs, we use pulses
that are much
longer
than
the
cavity lifetime
of the OPOs. This
arrangement
also allows us to
use low average powers incident
on the chip
while
maintaining
high
peak
powers. The experimental
setup
is shown in Fig. 2A,
which
is described
in detail
in Materials
and Methods.
The measur
ed OPO on-chip
signal
power at ~1950
nm is shown
in Fig. 2B as a function
of on-chip
pump
power (at 1050
nm).
Only
the signal
(red squar
es) is measur
ed, as the photodetector
is not sen-
sitive to the idler
wave near
2275
nm. The idler
power (purple
circles) is estimated from the output
coupler
response
(see Materials
and Methods).
The solid
black line is a fit based
on a theor
etical
ex-
pression
with an oscilla
tion threshold
of ~30 mW (30 μWof average
power). Figur
e 2C shows the on-chip
conversion
efficiency
, which
has a maximum
value
of ~9%
for the signal
and up to ~15%
when
including
the idler.
This efficiency
is limited
by the escape
efficiency
of the OPO (see Materials
and Methods),
which
is currently
low for
the idler,
and can be enhanced
substantially
with
differ
ent coupler
designs.
Pump
depletion
characterizes
the efficiency
with
which
pump
photons
are converted
into signal
and idler
photons
inside
the OPO (see
Materials
and Methods).
As shown in Fig. 2D,
~75%
is observ
ed, highlighting
the potential
of nanophotonic
OPOs as extremely
efficient
wavelength
conversion
devices.
These
large
pump
depletion
levels are also readily
appar
ent from the os-
cilloscope
traces shown in Fig. 2 (E and F).
Figur
e 3 shows the spectr
al tuning
range
of five OPOs fabrica
ted
on the same
chip.
Figur
e 3 (top)
shows few spectr
a of the signal
and
idler
emission
of the OPOs. This
includes
an OPO (OPO1, red
traces) that can operate at degener
acy (top
trace), and an OPO
(OPO5, orange
traces) that can achiev
e signal
and idler
wavelengths
separ
ated by more than an octave, and with an idler wavelength
well
into the mid-infr
ared.
More spectr
a from the same
OPOs are shown in Fig. 3 (middle),
demons
trating dense
coverage over the entire spectr
al range,
except
for a band
around
~2.8 μm where the SiO
2
buffer
layer exhibits
an
absorption
peak
(
26
).
The tuning
parameter
in all these
cases
was
the pump
wavelength
as illustrated in the vertical
axis of the bottom
panel.
Note
that OPO1 can be tuned
between 1.76 and 2.51 μm
(over 750 nm) by varying
the pump
wavelength
by only 30 nm, cor-
responding
to a tuning
magnifica
tion factor of ~12 in frequency
units.
OPO1 can also operate at degener
acy by using
a 1060
nm
pump,
as shown in the topmos
t trace of the top panel,
correspond-
ing to the black dot in the bottom
panel.
By tuning
the pump
power level, the OPOs can operate with
a
single
mode,
few modes,
or multiple
mode
clusters, with
examples
shown in Fig. 4. Closer
to threshold,
the OPOs can oscilla
te in a
single
spectr
al mode,
as shown in Fig. 4A. As the pump
power is
increased,
oscilla
tion
in a few modes
can occur,
as shown in
Fig. 4B. Multiple
mode
clusters appear
several times
above thresh-
old, as shown in Fig. 4C. The multimode
behavior is due to the para-
metric
gain bandwidth
being
larger
than
1 THz,
so a large
number
Fig.1.Ultrawidely
tunable
OPOsinnanophotonics.
(
A
) Anarrowlytunable
(<30nm)pump
around1μmleadstoanOPOsignal
andidlertuning
rangeexceeding
1500
nm. (
B
) Schema
tic of the doubly
resonant
parametric
oscillator with a frequency-selectiv
e resonator that provides feedba
ck only to the signal
and idler while enabling
continuous
tuning
of the pump.
(
C
) Image
of the chip highlighting
the area occupied
bya single
OPO. (
D
) False coloroptical
microscope
image
of the OPO (green) and a
straight waveguide
(purple,
used for calibration and phase-ma
tching
verification). Insets
show a two-photon
microscope
image
of the periodic
poling
and a close-up
of
the adiaba
tic output
coupler.
(
E
) Example
of OPO tuning
curves for four different poling
periods
Λ0 to Λ3. The dashed
vertical
lines and the blue stripe are to guide
the
eyes on how continuous
tuning
over an octave can be achieved with four poling
periods
and only 30 nm of pump
tuning.
SCIENCE
ADVANCES
|
RESEARCH
ARTICLE
Ledezma
et al.
,
Sci. Adv.
9
, eadf9711
(2023)
26 July 2023
2 of 7
of modes
(~10
GHz
FSR)
experience
gain.
At the same
time,
wave-
guide
dispersion
causes
a differ
ence in FSR between signal
and idler
wavelengths,
which
produces
cluster effects
in doubly
resonant
OPOs well above threshold
(
27
).
Further
dispersion
and cavity en-
gineering
can be used
for either
suppr
essing
the multimode
effects
or tailoring
it toward gener
ation of frequency
combs
(
28
).
Figur
e 5 shows the tuning
range
and peak
power level of our
OPO chip
in the quasi
continuous
wave (CW)
regime
alongside
previously
reported
tunable
sources in nanophotonics,
which
operate in the CW regime.
Such
notable
performance
is enabled
by our nonresonant
pump
OPO design
combined
with
disper-
sion-engineer
ed, quasi-phase
ma
tched,
directly
etched
waveguides
(see Materials
and Methods).
DISCUSSION
Our results
show that ultrawidely
tunable
infrared sources can be
implemented
on the thin-film
lithium
nioba
te platform,
adding
to
the increasingly
large
set of functionalities
available
in this platform
(
29
) and complementing
the recent
demons
tration of tunable
near-
infrared DBR
lasers
(
23
).
The threshold
and requir
ed pump
tuning
range
of our OPOs are within
the reach of low-cos
t near-infr
ared
laser
diodes.
Additional
engineering
of the cavity design,
waveguide
dispersion,
and quasi-phase
matching
can be used
for tailoring
the
operation toward a multitude
of applica
tions.
For instance,
the
threshold
of the OPOs can be substantially
reduced
by using
a sep-
arate resona
tor for the pump
without
sacrificing
the conversion
ef-
ficiency
and tunability
(unlik
e a triply
resonant
design).
Fig. 2. Transient
and steady-s
tate measur
ements
of on-chip
doubly
resonant
OPOs.
(
A
) Measur
ement
setup.
We use 100 ns pulses
with a 10 kHz repetition
rate to
decrease the average power while keeping
the peak power above the OPO threshold.
ECDL,
external
cavity diode
laser; SOA, semiconductor
optical
amplifier;
YDFA,
ytterbium
doped
fiber amplifier;
FPC, fiber polariza
tion controller; OPO, optical
parametric
oscillator; PD, photodetector;
WDM,
wavelength
division
multiple
xer. (
B
) On-
chip output
power versus pump
power for a signal
wavelength
of 1950 nm and a pump
wavelength
of 1050 nm; the idler and total power are estimated from the signal
(seeMaterials
andMethods).
(
C
) Differentmeasur
edon-chip
efficiencies.
(
D
) Measure
dandexpected
pump
depletion
levelsrepresenting
theconversion
efficiency
within
the OPO. (
E
and
F
) Measur
ed pump
and signal
traces at two different power levels, as indicated by the shaded
gray regions
in (B) to (D).
SCIENCE
ADVANCES
|
RESEARCH
ARTICLE
Ledezma
et al.
,
Sci. Adv.
9
, eadf9711
(2023)
26 July 2023
3 of 7
The maximum
conversion
efficiency
of a doubly
resonant
OPO
is domina
ted by its escape
efficiency
, which
is related to the ratio of
output
coupler
transmittance
to total resona
tor losses
(see Materials
and Methods).
For our device,
this ratio is ~9% at 1950
nm, indica
t-
ing that the output
coupling
is small
compar
ed to the total losses
in
the resona
tor. This could
be caused
in part by the little transmission
of the output
coupler,
particularly
at mid-infr
ared wavelengths,
and
in part by intrinsic
resona
tor losses
and losses
at the input
coupler.
Fine tuning
of the coupler
designs
and reducing
the cavity loss can
lead to substantial
improvement
of efficiency
. We used
adiaba
tic
couplers
in this work
since
they provide a simple
means
to approx-
imately achiev
e our requir
ements
of high
signal
and idler
coupling
together
with
low pump
coupling.
However, the input
coupler
should,
ideally
, have 100%
coupling
at signal
and idler
frequencies
since
any transmission
in this coupler
behaves as additional
resona-
tor loss, leading
to higher
thresholds
and lower efficiencies.
Simultaneously
, the input
coupler
should
provide very low cou-
pling
at the pump
wavelength,
since
any coupling
just leaks
pump
power into the unused
port,
and also provides
an undesir
ed feed-
back path for the pump.
These
characteris
tics may be achievable
through
more advanced
coupler
designs,
for instance,
those
ob-
tained
by inverse design
methods
(
30
).
The tuning
range
of a single
OPO can be further
enhanced
by
implementing
multiple
poling
periods
on the same
OPO. Moreover,
since
the wavelength
coverage of the OPO appears
to be limited
by
the loss of the SiO
2
buffer
layer, a similar
design
with
a differ
ent
buffer
layer material
can allow operation
toward the entire
lithium
nioba
te transpar
ency
windo
w (
31
).
The OPO design
we
demons
trate here can also be readily
applied
to other
emerging
non-
linear
photonic
platforms
with
transpar
ency
windo
ws deeper
into
the mid-infr
ared (
32
).
The measur
ements
presented
in Fig. 3 only
exploit
the depen-
dence
of the output
wavelength
on pump
wavelength.
Two addi-
tional
degrees of freedom
are the temper
ature and the resona
tor
s
FSR (which
could
be varied,
for instance,
by electr
o-optic
modula-
tion of the resona
tor
s feedba
ck arm).
These
three variables
com-
bined
can
facilitate precise
and
fast tuning
of the output
wavelengths
over a much
broader
spectr
al range
(
26
),
especially
when
an integr
ated pump
laser
is used.
Singly
resonant
OPOs offer
even smoother
tunability
and stabil-
ity characteris
tics at the expense
of higher
threshold
powers. While
pure singly
resonant
behavior can be obtained
by changing
the
coupler
response
so that only
the signal
or idler
resona
tes, we
note
that the transition
between doubly
and
singly
resonant
designs
is smooth
(
33
) and we have evidence
that our OPOs can
operate in this regime
(see fig. S2). This could
enable
fast and ultrab-
road wavelength
synthesis
on-chip
with
potential
mode-hop
free
operation.
In summary
, we have demons
trated on-chip
doubly
resonant
OPOs that can be tuned
over an octave up to 3.25 μm. Our OPOs
are based
on an innovative on-chip
doubly
resonant
design
that
avoids many
of the challenges
present
in triply
resonant
configur
a-
tions
and linear
cavity oscilla
tors,
and can be easily
extended
to
singly
resonant
configur
ations.
Further
dispersion
engineering
Fig. 3. Wavelength
tuning
of nanophotonic
OPOs.
(
T op
) Examples
of output
spectra for a few OPOs on the same chip exhibiting
an octave-wide
tuning
range. Each
color represents
a different OPO. (
Middle
)
Many more output
spectra from the same OPOs. (
Bottom
)
All measure
d data (colored dots) with the corresponding
pump
wavelength
on the vertical
axes along
with the theoretical tuning
curves (solid lines).
SCIENCE
ADVANCES
|
RESEARCH
ARTICLE
Ledezma
et al.
,
Sci. Adv.
9
, eadf9711
(2023)
26 July 2023
4 of 7
may lead to femtosecond
synchr
onously
pumped
OPOs in nano-
photonics
and the numer
ous applica
tions
they unlock
(
34
).
MATERIALS
AND METHODS
Device
design
We use adiaba
tic couplers
to create the wavelength
selectiv
e cavity
(see fig. S1A).
The input
and output
couplers
are identical
and are
designed
so that signal
and idler wavelengths
(λ > 1.8 μm) have large
coupling
factors
(>80%),
while
pump
wavelengths
near
1 μm are
only
slightly
coupled
(<10%).
The residual
coupling
of the pump
leads
to round-trip
feedba
ck factors
of less than
1% that produce
negligible
modula
tions
of the pump
intensity
as a function
of fre-
quency
, allowing
continuous
tuning
of the pump
wavelength.
When
designing
a tunable
OPO, it is desirable to have a large
tuning
slope
so a small
change
in pump
wavelength
produces
large
changes
in the output
wavelengths.
At the same
time,
a
small
gain bandwidth
is preferable to limit
the number
of resona
tor
modes
experiencing
gain.
To achiev
e a balance
between these
two
behaviors,
we engineer
the dispersion
of the waveguide
using
its ge-
ometry
, resulting
in 2.5-μm-wide
waveguides
on a 700-nm-thick
lithium
nioba
te layer and 250 nm of etching
depth.
The mode
profile for a set of representa
tive wavelengths
is shown in fig. S1B,
illustrating that the modal
overlap
remains
substantial
despite
the
large
frequency
differ
ence.
Fig. 4. Spectral structur
es of free-running
OPOs.
The generated spectrum
of our OPOs can vary from (
A
) single-mode
emission,
to (
B
) emission
in a few modes
sep-
arated by several FSRs, to (
C
) emission
in several mode
clusters. Insets
show close-up
of spectra with dashed
vertical
lines separated by the resonator
s FSR, which
is
approximately equal to the 10 GHz OSA resolution
bandwidth.
SCIENCE
ADVANCES
|
RESEARCH
ARTICLE
Ledezma
et al.
,
Sci. Adv.
9
, eadf9711
(2023)
26 July 2023
5 of 7
Device
fabrica
tion
We fabrica
te our devices
using
a commer
cial wafer (NANOLN)
with
an x-cut,
700-nm-thick
MgO-doped
lithium
nioba
te layer
and a SiO
2
buffer
layer. We provide quasi-phase
matching
in a 5-
mm-long
region
through
periodic
poling
(inset
of Fig. 1B shows a
second-harmonic
microscope
image
of a typical
poled
section).
The
waveguides
are patterned
by e-beam
lithogr
aphy
and dry etched
with
Ar
+
plasma
to a depth
of 250 nm. All the OPOs have the
same
waveguide
geometry
obtained
from dispersion
engineering,
with
2.3-μm-wide
input
and
output
waveguides
that taper
(through
the adiaba
tic couplers)
to 2.5-μm-wide
waveguides
inside
the resona
tor. To maximize
the spectr
al range
covered on a
single
chip,
we fabrica
ted OPOs with
poling
periods
ranging
from
5.55 to 5.7 μm in 10-nm
steps.
We include
a straight
waveguide
next
to each OPO for calibr
ation and quasi-phase
matching
verifica
tion
(color
ed purple
in Fig. 1B).
Device
characteriza
tion
We characterize
our OPOs using
the experimental
setup
shown in
Fig. 2A, which
consis
ts of a tunable
CW 1 μm laser
amplified
by a
semiconductor
optical
amplifier,
which
is modula
ted to gener
ate
100-ns-long
(full-width-half-maximum)
pulses
with 10-kHz
repeti-
tion rate. These
pulses
are further
amplified
by an ytterbium-doped
fiber
amplifier
and coupled
into the chip using
a single-mode
1 μm
lensed
fiber
(~10
dB coupling
loss).
The OPO output
is collected
by
either
a 2 μm lensed
fiber
or a cleaved InF3
fiber
and sent to an
optical
spectrum
analyzer
(OSA)
or to an InAsSb
detector
connect-
ed to an oscilloscope.
Awavelength
division
multiple
xer allows us to
monitor
the depleted
pump
and signal
output
simultaneously
.
To estimate propaga
tion losses
in our waveguides,
we fabrica
ted
chips
with
arrays of critically
coupled
resona
tors and extracted
quality
factors
~6 × 10
5
, which
transla
te to losses
below 0.3 dB/
cm for waveguides
without
poling.
Detailed
inspection
of the peri-
odically
poled
waveguide
inside
the resona
tor reveals periodic
roughness
of the waveguide
sidewalls, likely from the polariza-
tion-dependent
etch
rate of lithium
nioba
te. More studies
are
needed
to improve the resona
tor quality
factor.
To estimate input
and output
coupling
losses,
we use single-
mode
lensed
fibers
to couple
into and out of the chip
and then
divide
the total
throughput
loss equally
between both
interfa
ces.
We do this on several unpoled
straight
waveguides
and obtain
a
coupling
coefficient
varying
from 10 to 13 dB, with
10 dB giving
the most conserva
tive estimate for on-chip
input
power. When
using
an asymmetric
setup
(lensed
fiber
at input,
cleaved fiber
at
output),
we assume
that the input
coupling
remains
at 10 dB and
calcula
te the output
coupling
from the throughput
loss. Comparing
transmission
of straight
waveguides
to that of OPOs allows us to es-
timate a total
loss factor of 0.929
per coupler
at the pump
wave-
length,
reasonably
close
to the simula
ted value
of 0.95 (fig. S1A).
The plots
of Fig. 2 (B to D) are obtained
from oscilloscope
traces
like those
in Fig. 2 (E and F) by first converting
voltage
to power,
integr
ating them
to find the energy
, and then
dividing
them
by the
100 ns pulse
width
to obtain
the average peak
power.
Efficiency
and idler power estimation
The efficiency
of an OPO (η) can be written
as the product
of two
efficiencies,
η = η
0
η
e
. The internal
efficiency
0
) measur
es how ef-
ficiently
pump
photons
are converted
into signal
and idler
photons,
while
the escape
efficiency
e
) measur
es the fraction
of the gener-
ated signal
and idler
photons
available
at the output
of the OPO.
The differ
ence
between the pump
power at the beginning
and end
of the gain section
is
P
p
=
P
p
(0)
P
p
(
L
g
). The internal
efficiency
is
just the pump
depletion
η
0
=
P
p
/
P
p
(0) shown in Fig. 2D.
The escape
efficiency
is given by η
e
= (ω/ω
p
)
T
(ω)/[1
L
(ω)],
wher
e
T
(ω)
is the power transmission
coefficient
of the output
coupler,
while
L
(ω)
is the total
round-trip
power loss factor of the
resona
tor, i.e.,
L
(ω)
= [1
T
(ω)]
2
exp(
L
),
where α is the field
propaga
tion loss,
assumed
constant,
and the squar
e term
comes
from considering
identical
input
and output
couplers.
Since
the
output
power can
be calcula
ted
from
the
efficiency
as
P
out
(ω) = η
0
η
e
(ω)
P
p
(0), the idler
power can be estimated from the
signal
power and the simula
ted coupler
response,
T
(ω),
as
P
out
ð
ω
i
Þ�
η
e
ð
ω
i
Þ
η
e
ð
ω
s
Þ
P
out
ð
ω
s
Þ¼
ω
i
ω
s
T
ð
ω
i
Þ
T
ð
ω
s
Þ
1
L
ð
ω
s
Þ
1
L
ð
ω
i
Þ
Supplementary
Materials
This PDF file includes:
Figs. S1 and S2
REFERENCES
AND NOTES
1. A. E. Willner,
Optical
Fiber
Telecommunica
tions
VII
(Academic
Press, 2020).
2. Y.Jiang,S. Karpf, B.Jalali,
Time-str
etchLiDAR
asa spectrallyscanned
time-of-flight
ranging
camera.
Nat. Photonics
14
, 14
18
(2020).
3. I. E. Gordon,
L. S. Rothman,
R. J. Hargreaves, R. Hashemi,
E. V. Karlovets, F. M. Skinner,
E. K. Conway, C. Hill, R. V. Kochano
v, Y. Tan, P. Wcisło,
A. A. Finenk
o, K. Nelson,
P. F. Bernath,
M. Birk, V. Boudon,
A. Campargue,
K. V. Chance,
A. Coustenis, B. J. Drouin
, J. -M. Flaud,
R. R. Gamache, J. T. Hodges,
D. Jacquemart,
E. J. Mlawer, A. V. Nikitin,
V. I. Perevalov,
M. Rotger,
J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, E. M. Adkins,
A. Baker, A. Barbe,
E. Canè, A. G. Császár,
A. Dudaryono
k, O. Egorov, A. J. Fleisher,
H. Fleurbaey
, A. Foltyno
wicz,
T. Furtenba
cher, J. J. Harrison,
J. -M. Hartmann,
V.-M. Horneman,
X. Huang,
T. Karman,
J. Karns,
S. Kassi, I. Kleiner,
V. Kofman,
F. Kwabia-Tchana,
N. N. Lavrentieva,
T. J. Lee,
D. A. Long, A. A. Lukashevska
ya, O. M. Lyulin,
V. Y. Makhnev,
W. Matt, S. T. Massie,
M. Melosso,
S. N. Mikhailenk
o, D. Mondelain,
H. S. P. Müller,
O. V. Naumenk
o, A. Perrin,
O. L. Polyansky, E. Raddaoui,
P. L. Raston, Z. D. Reed, M. Rey, C. Richard,
R. Tóbiás,
I. Sadiek,
D.W.Schwenke,E.Stariko
va, K.Sung,F.Tamassia,
S. A.Tashkun,
J.V.Auwera,I.A.Vasilenko,
A. A. Vigasin,
G. L. Villanueva,
B. Vispoel,
G. Wagner,
A. Yachmenev,
S. N. Yurchenko, The
HITRAN2020
molecular
spectros
copic database.
J. Quant.
Spectr
osc. Radia
t. Transf.
277
,
107949
(2022).
4. Y. Yao, A. J. Hoffman,
C. F. Gmachl, Mid-infr
ared quantum
cascade
lasers.
Nat. Photonics
6
,
432
439
(2012).
Fig. 5. Comparison
of the on-chip
output
powerand wavelength
coverage of
ouron-chip
OPOswithotherintegra
tedtunable
sources.
Thepowerlevelisthe
sum of signal
and idler for all OPOs.
SCIENCE
ADVANCES
|
RESEARCH
ARTICLE
Ledezma
et al.
,
Sci. Adv.
9
, eadf9711
(2023)
26 July 2023
6 of 7
5. E. Shim, A. Gil-Molina,
O. Westreich, Y. Dikmelik,
K. Lascola,
A. L. Gaeta,
M. Lipson,
Tunable
single-mode
chip-scale
mid-infr
ared laser.
Commun.
Phys.
4
, 268 (2021).
6. Y. Han, Y. Han, X. Zhang,
X. Zhang,
R. Ma, M. Xu, H. Tan, J. Liu, R. Wang, S. Yu, X. Cai, Widely
tunable
O-band
lithium
niobite/III-V
transmitter.
Opt. Express
30
, 35478
35485
(2022).
7. M. Li, L. Chang,
L. Wu, J. Staffa,
J. Ling, U. A. Javid, S. Xue, Y. He, R. Lopez-Rios,
T. J. Morin,
H. Wang, B. Shen, S. Zeng, L. Zhu, K. J. Vahala, J. E. Bowers, Q. Lin, Integrated pockels laser.
Nat. Commun.
13
, 5344 (2022).
8. C. O. de Beeck,
F. M. Mayor, S. Cuyvers, S. Poelman,
J. F. Herrmann,
O. Atalar,
T. P. McKenna,
B. Haq, W. Jiang, J. D. Witmer,
G. Roelkens, A. H. Safavi-Naeini, R. V. Laer, B. Kuyken, III/V-on-
lithium
niobate
amplifiers
and lasers.
Optica
8
, 1288
1289
(2021).
9. M. H. Dunn,
M. Ebrahim-Zadeh,
Parametric
generation of tunable
light from continuous
wave to femtosecond
pulses.
Science
286
, 1513
1518
(1999).
10. C. Langrock, M. M. Fejer, Fiber-feedba
ck continuous-wa
ve and synchronously
pumped
singly-r
esonant
ring optical
parametric
oscillato
rs using reverse-pr
oton-e
xchanged
peri-
odically-poled
lithium
niobate waveguides.
Opt. Lett.
32
, 2263
2265
(2007).
11. M. Savanier,
C. Ozanam,
L. Lanco,
X. Lafosse, A. Andronico,
I. Favero, S. Ducci,
G. Leo, Near-
infrared optical
parametric
oscillator in a III-V semiconductor
waveguide.
Appl.
Phys.
Lett.
103
, 261105
(2013).
12. N. Amiune,
D. N. Puzyre
v, V. V. Pankratov, D. V. Skryabin, K. Buse, I. Breunig,
Optical
para-
metric-oscilla
tion-based
χ(2) frequency
comb
in a lithium
niobat
e microresonator.
Opt.
Express
29
, 41378
41387
(2021).
13. N. L. B. Sayson, T. Bi, V. Ng, H. Pham,
L. S. Trainor,
H. G. L. Schwe
fel, S. Coen, M. Erkintalo,
S. G. Murdoch,
Octave-spanning
tunable
parametric
oscillation
in crystalline
Kerr micro-
resonators.
Nat. Photonics
13
, 701
706
(2019).
14. C. Wang, C. Langrock,
A. Marandi, M. Jankowski, M. Zhang,
B. Desiatov, M. M. Fejer,
M.Loncar,
Ultrahigh-efficiency
wavelength
conversion
innanophotonic
periodically
poled
lithium
niobate waveguides.
Optica
5
, 1438
1441
(2018).
15. L. Razzari,
D. Duchesne,
M. Ferrera, R. Moran
dotti, S. Chu, B. E. Little, D. J. Moss,
CMOS-
compa
tible integrated optical
hyper-par
ametric
oscillator.
Nat. Photonics
4
, 41
45
(2010).
16. X. Lu, G. Moille,
A. Singh,
Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles,
S. B. Papp,
K. Srinivasan,
Milliwatt-threshold
visible
telecom
optical
parametric
oscillatio
n using
silicon
nanophotonics.
Optica
6
, 1535
1541
(2019).
17. X. Lu, G. Moille,
A. Rao, D. A. Westly, K. Srinivasan,
On-chip
optical
parametric
oscillation
into the visible:
Generating red, orange, yellow, and green from a near-infr
ared pump.
Optica
7
, 1417
1425
(2020).
18. Y. Tang, Z. Gong,
X. Liu, H. X. Tang, Widely separated optical
Kerr parametric
oscillation in
AlN microrings.
Opt. Lett.
45
, 1124
1127
(2020).
19. J. R. Stone,
X. Lu, G. Moille,
K. Srinivasan,
Efficient
chip-based
optical
parametric
oscillators
from 590 to 1150 nm.
APL Photonics
7
, 121301
(2022).
20. A. W. Bruch,
X. Liu, J. B. Surya, C.-L. Zou, H. X. Tang, On-chip
χ
(2)
microring optical
para-
metric
oscillator.
Optica
6
, 1361
1366
(2019).
21. J. Lu, A. A. Sayem, Z. Gong,
J. B. Surya, C.-L. Zou, H. X. Tang, Ultralow-thre
shold thin-film
lithium
niobate optical
parametric
oscillator
.
Optica
8
, 539
544
(2021).
22. T. P. McKenna,
H. S. Stokowski, V. Ansari,
J. Mishra, M. Jankowski, C. J. Sarabalis,
J. F. Herrmann,
C. Langrock, M. M. Fejer, A. H. Safavi-Naeini,
Ultra-low-pow
er second-order
nonlinear
optics
on a chip.
Nat. Commun.
13
, 4532 (2022).
23. P. A. Verrinder,
L. Wang, J. Fridlander,
F. Sang, V. Rosborough,
M. Nickerson,
G. Yang,
M. Stephen,
L. Coldren, J. Klamkin,
Gallium
arsenide
photonic
integrated circuit platform
for tunable
laser applica
tions.
IEEE J. Sel.
28
, 1
9 (2022).
24. A. Marandi, L. Ledezma,
Y. Xu, R. M. Briggs,
Thin-film
optical
parametric
oscillator
s. U.S.
Patent 11,226,538
(2022).
25. L. Ledezma,
R. Sekine,
Q. Guo, R. Nehra, S. Jahani,
A. Marandi, Intense
optical
parametric
amplificati
on in dispersion-engineer
ed nanophotonic
lithium
niobate
waveguides.
Optica
9
, 303
308
(2022).
26. R.A.Soref,S. J.Emelett,
W.R.Buchwal
d, Silicon
waveguided
components
for thelongwave
infrared region.
J. Optics
A
8
, 840
848
(2006).
27. R. C. Eckardt,
C. D. Nabors,
W. J. Kozlovsky, R. L. Byer, Optical
parametric
oscillator
fre-
quency
tuning
and control.
J. Opt. Soc. Am. B
8
, 646 (1991).
28. S. Mosca,
M. Parisi, I. Ricciardi,
F. Leo, T. Hansson,
M. Erkintalo,
P. Maddaloni,
P. De Natale,
S. Wabnitz,
M. De Rosa, Modula
tion instability
induced
frequency
comb
generation in a
continuously
pumped
optical
parametric
oscillator
.
Phys.
Rev. Lett.
121
, 093903
(2018).
29. D.Zhu,L.Shao,M.Yu,R.Cheng,
B.Desiatov,C.J.Xin,Y.Hu,J.Holzgr
afe,S.Ghosh,
A.Shams-
Ansari,
E. Puma,
N. Sinclair,
C. Reimer, M. Zhang,
M. Loncar,
Integrated photonics
on thin-
film lithium
niobate
.
Adv. Opt. Photon.
13
, 242
352
(2021).
30. S. Molesky
, Z. Lin, A. Y. Piggott,
W. Jin, J. Vuckovic, A. W. Rodriguez,
Inverse design
in
nanophotonics.
Nat. Photonics
12
, 659
670
(2018).
31. J. Mishra, T. P. McKenna,
E. Ng, H. S. Stokowski, M. Jankowski, C. Langrock, D. Heydari,
H. Mabuchi,
M. M. Fejer, A. H. Safavi-Naeini,
Mid-infr
ared nonlinear
optics
in thin-film
lithium
niobate on sapphir
e.
Optica
8
, 921
924
(2021).
32. R. Bechek
er, M. Bailly, S. Idlahcen,
T. Godin,
B. Gerard, H. Delaha
ye, G. Granger,
S. Fevrier,
A. Grisard,
E. Lallier,
A. Hideur,
Optical
parametric
generation in OP-GaAs
waveguides
pumped
by a femtosecond
fluoride
fiber laser.
Opt. Lett.
47
, 886
889
(2022).
33. S. T. Yang, R. C. Eckardt,
R. L. Byer, Power and spectra
l characteristics of continuous-w
ave
parametric
oscillat
ors: The doubly
to singly
resonant
transition.
J. Opt. Soc. Am. B
10
,
1684
1695
(1993).
34. Y. Kobayashi, K. Torizuka,
A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang,
D. T. Reid,
Femtosecond
optical
parametric
oscillator
frequency
combs.
J. Optics
17
, 094010
(2015).
Acknowledgments:
The device
nanofabrica
tion was performed
at the Kavli Nanoscience
Institute (KNI) at Caltech.
Part of this research was carried
out at the Jet Propulsion
Laboratory,
California
Institute of Technology
, under
acontract with NASA.
We thank NTT Research for their
financial
and technical
support.
Funding:
The authors
gratefully
acknow
ledge
support
from
Army Research Office
grant no. W911NF-23-1-0048
(A.M.),
National
Science
Founda
tion grant
no. 1846273
(A.M.),
National Science
Founda
tion grant no. 1918549
(A.M.),
and Air Force Office
of Scientific
Research award FA9550-20-1-0040
(A.M.).
This work was supported
by a NASA
Space Technology
Graduate Research Opportunities
Award.
Author
contributions:
Conceptualiza
tion: A.M. and L.L. Methodology:
L.L. designed
the devices.
L.L. fabrica
ted the
chip with assistance from R.S. and Q.G. L.L. characterized
the devices
with assistance from A.R.,
L.C., R.G., R.N., and R.M.B.
Supervision:
A.M. Writing
original
draft: L.L. Writing
re
view and
editing:
A.M., L.L., and A.R.
Competing
interests:
L.L., R.M.B.,
and A.M. are inventors
on granted
U.S. patent 11,226,538
held by California
Institute ofTechnology
and filed on 7 March 2019 that
coversthin-film
optical
parametric
oscillators.L.L.,A.M.,A.R.,R.S.,andR.G.areinventors
onaU.S.
provisional
patent applica
tion filed by the California
Institute of Technology
(applica
tion
number
63/466,188)
on 12 May 2023. L.L., A.M., and R.G. are inventors on a U.S. provisional
patent applica
tion filed by the California
Institute of Technology
(applica
tion number
63/
434,015)
on 20 December
2022. L.L. and A.M. are involved in developing
photonic
integrated
nonlinear
circuits at PINC Technologies
Inc. L.L. and A.M. have an equity
interest in PINC
Technologies
Inc. The other authors
declare that they have no competing
interests.
Data and
materials
availability:
All data needed
to evalua
te the conclusions
in the paper
are present in
the paper
and/or
the Supplementary
Materials.
Submitted
23 November
2022
Accepted
22 June 2023
Published
26 July 2023
10.1126/sciadv.adf9711
SCIENCE
ADVANCES
|
RESEARCH
ARTICLE
Ledezma
et al.
,
Sci. Adv.
9
, eadf9711
(2023)
26 July 2023
7 of 7