Femtojoule, femtosecond all-optical switching in lithium niobate nanophotonics
Qiushi Guo
1
,
∗
, Ryoto Sekine
1
,
∗
, Luis Ledezma
1
,
2
,
∗
, Rajveer Nehra
1
, Devin J.
Dean
3
, Arkadev Roy
1
, Robert M. Gray
1
, Saman Jahani
1
and Alireza Marandi
1
,
†
1
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
2
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA.
3
Department of Applied Physics, Cornell University, Ithaca, New York 14850, USA.
∗
These authors contributed equally to this work.
†
Email: marandi@caltech.edu
(Dated: July 22, 2021)
Optical nonlinear functions are crucial for var-
ious applications in integrated photonics, such as
all-optical information processing, photonic neu-
ral networks and on-chip ultrafast light sources.
Due to the weak nonlinearities in most integrated
photonic platforms, realizing optical nonlinear
functions typically requires large driving ener-
gies in the picojoules level or beyond, thus im-
posing a barrier for most applications. Here, we
tackle this challenge and demonstrate an inte-
grated nonlinear splitter device in lithium niobate
nano-waveguides by simultaneous engineering of
the dispersion and quasi-phase matching. We
achieve non-resonant all-optical switching with
ultra-low energies down to tens of femtojoules,
a near instantaneous switching time of 18 fs, and
a large extinction ratio of more than 5 dB. Our
nonlinear splitter simultaneously realizes switch-
on and -off operations and features a state-of-
the-art switching energy-time product as low as
1
.
4
×
10
−
27
J
·
s. We also show a path toward at-
tojoule level all-optical switching by further op-
timizing the device geometry. Our results can
enable on-chip ultrafast and energy-efficient all-
optical information processing, computing sys-
tems, and light sources.
Photons are known to be excellent information carri-
ers. Yet, the quest for all-optical information process-
ing – a technology that can potentially eliminate the
limitations on the bandwidth and energy consumption
of electronic and opto-electronic systems – is generally
deemed to be challenging because optical nonlinearities
are usually weak. All-optical switching using cubic (
χ
(3)
)
nonlinearities
1,2
and saturable absorption
3–5
in semicon-
ductor materials typically require pulse energies on the
order of picojoules or beyond. Such energy requirements
hinder their widespread utilization for any applications
as they necessiate bulky and power-hungry light sources.
To lower the energy requirement of all-optical switching,
one approach consists of enhancing the optical nonlin-
earity in optical cavities. However, this enhancement is
accompanied by a cavity photon lifetime, which unavoid-
ably increases the switching times and typically leads to
low bandwidths up to 10s of GHz
6–12
. Therefore, all-
optical switching in solid-state photonic platforms faces
a performance trade-off between the energy per bit and
the switching time, making the energy-time product an
apt figure of merit
13
. A promising path toward a bet-
ter energy-time product is the utilization of stronger and
instantaneous nonlinearities, such as the quadratic non-
linearity (
χ
(2)
).
Compared to the
χ
(3)
nonlinearity,
χ
(2)
nonlinearity
in non-centrosymmetric materials requires lower light in-
tensities by many orders of magnitude. When the phase-
matching condition is achieved and in the absence of
significant dispersion, nonlinear optical interactions can
grow substantially as a function of propagation length,
thus circumventing the need of resonant enhancement
and compromising switching speed. Recently, thin-film
lithium niobate (TFLN) has emerged as a promising
integrated photonic platform. TFLN-based nanopho-
tonic waveguides exhibit strong
χ
(2)
nonlinearity and
a high normalized nonlinear frequency conversion effi-
ciency in the continuous wave (CW) regime (
>
1000
%
/W-
cm
2
)
14–17
that is not easily attainable in bulk material
platforms, thanks to the strong spatial confinement of
the waveguide modes as well as quasi-phase matching
(QPM). Additionally, the tight spatial confinement of
the waveguide modes allows dispersion engineering
18–20
,
which enables temporal confinement of interacting waves
over long interaction lengths, leading to further enhance-
ment of the nonlinear processes using ultra-short pulses.
In this work, we engineer the quasi-phase matching in a
TFLN nanophotonic waveguide to achieve non-resonant
all-optical switching in an integrated nonlinear splitter.
Simultaneously, dispersion engineering of our device al-
lows spatio-temporal confinement of the pulses over the
length of the device, leading to ultra-low energy (fJ)
and ultrafast (fs) all-optical switching with a high ex-
inction ratio. The dispersion- and QPM- engineered
LN nanophotonic waveguide enables nonlinear interac-
tion lengths as long as 70 mm, allowing for attojoule
ultrafast all-optical switching.
The main element of our all-optical switch is a QPM-
engineered LN nanophotonic waveguide. Figure 1 illus-
trates the concept of this QPM-engineering: a uniform
periodically poled LN waveguide (periodicity=
Λ
) is per-
turbed by a “poling defect”, i.e. an isolated ferroelectric
domain of length
L
= Λ
in the middle of the waveguide.
While the poling period is designed for phase-matched
arXiv:2107.09906v1 [physics.optics] 21 Jul 2021
2
a
Intensity
SH
Λ
“Poling defect” L=
Λ
FH
Propagation distance
DOPA
SHG
ω
2
ω
φ
2
ω
–
2
φ
ω
=0
ω
2
ω
φ
2
ω
–
2
φ
ω
=
π
0
1
2
3
4
5
6
0.0
0.5
1.0
1.5
Power (
m
W)
Propagation distance (mm)
FH
SH
0
1
2
3
4
5
6
0
50
100
150
200
250
Power (
m
W)
Propagation distance (mm)
FH
SH
SHG
DOPA
On
-
state
(Strong nonlinear conversion)
e
SHG
DOPA
Off
-
state
SHG
DOPA
c
d
On
-
state
Poling defect
Drop port
Input
Through port
Off
-
state
(Weak nonlinear conversion)
b
Drop port
Through port
Input
Poling defect
FIG. 1.
Device design and operating principle. a
, Illustration of the QPM engineering in PPLN waveguide. The poling
defect (a longer ferroelectric domain with a length
L
= Λ
) shifts the phase difference between the FH and SH by
π
. As a
result, the poling defect switches the SHG to degenerate optical parametric amplification (DOPA) in the second half of the
PPLN waveguide. The insets illustrate the phase relation and the direction of energy transfer between the FH and the SH.
b
,
Schematic of the integrated nonlinear splitter device and its operation in the “off-state” when the input FH pulse energy is low.
c
, Simulated evolution of the FH and SH optical power along the main waveguide for the off-state, in which the transmittance
of the FH is low (15
%
).
d
, Schematic of the integrated nonlinear splitter device and its operation in the “on-state” when the
input pulse energy is high.
e
, Simulated evolution of the FH and SH optical power along the main waveguide for the “on-state”,
in which the transmittance of the FH is high (85
%
). The simulations in
c
and
e
assume an input pulse of 46.2 fs at 2.09
μ
m
and device parameters of a 2.5-mm-long SHG region, a 3.5-mm-long DOPA region, and 85
%
out-coupling of the FH by the
directional coupler.
second-harmonic generation (SHG), the poling defect lo-
cally changes the phase relationship between the first har-
monic (FH) and the second harmonic (SH) waves by the
amount of
∆
φ
=
π
21
. Since the direction of power flow
between the FH and the SH is dependent on the relative
phase between them, the
π
phase shift due to the pol-
ing defect switches the nonlinear process from SHG to
degenerate optical parametric amplification (DOPA), in
which the generated SH serves as the pump to amplify
the FH.
In addition to the QPM-engineered main waveguide,
our all-optical switch is composed of a neighboring linear
directional coupler, as sketched in Fig. 1b and d. The
linear directional coupler evenescently couples out most
(85
%
) of the FH, while leaving most of SH freely propa-
gating in the main waveguide. This whole device exhibits
a strongly intensity-dependent splitting ratio. When the
input FH intensity is low (in the “off-state” shown in
Fig. 1b), most of the input FH does not convert to SH,
and hence is directed by the linear coupler to the drop
port. This is illustrated by the simulated power evolu-
tion of both the FH and the SH in the main waveguide in
Fig. 1c. In this “off-state”, the transmittance of the FH
in the main waveguide (through port) is low. However,
when the input FH intensity is high (or in the “on-state”
as shown in Fig. 1d, e), due to the efficient SHG at the
beginning of the waveguide, most of the FH can con-
vert to the SH, which remains in the main waveguide
after passing through the coupler, and negligible FH is
directed to the drop port. In the second half of the main
waveguide, the poling defect switches the SHG process to
the DOPA, through which most of the SH converts back
to the FH. As shown in Fig. 1e, in the “on-state”, the
device favors transmission of the FH to the through port
3
800
1000
1200
1400
1600
1800
2000
2200
2400
0
20
40
60
80
100
Simulation
Measurement
Coupling Ratio (%)
Wavelength (nm)
85% at 2090 nm
5% at 1045 nm
Poling defect
a
b
800
1000
1200
1400
1600
1800
2000
2200
2400
-50
0
50
100
150
200
250
GVM
GVM (fs/mm)
Wavelength
(
nm
)
-100
0
100
200
300
400
500
GVD
GVD (fs
2
/mm)
d
e
b
c
FIG. 2.
Integrated nonlinear splitter and its linear optical characteristics. a
, SEM image of the fabricated nonlinear
splitter. Scale bar: 20
μ
m. The device has a 2.5-mm-long SHG region and a 3.5-mm-long DOPA region. The directional coupler
has a coupling length of 70
μ
m and a gap of 650 nm between the waveguide top surfaces.
b
, 2D AFM scan on LN waveguide.
c
, Second harmonic microscope image showing the inverted domains and the poling defect along the waveguides.
d
, Simulated
group velocity mismatch (GVM, red) between the FH and the SH and group velocity dispersion (GVD, blue) for the quasi-TE
modes of the dispersion-engineered LN waveguide. The optimized waveguide has a top width of 1650 nm, an etching depth of
350 nm and a total thin-film thickness of 700 nm. The waveguide exhibits low (0.4 fs/mm) GVM between the pump at 1045
nm and the signal around 2090 nm, and low GVD for both wavelengths. Inset: Electric field distributions of the fundamental
quasi-TE modes for the dispersion-engineered waveguide at 1045 nm and 2090 nm. The black dashed line denotes the zero
GVM.
e
, Measured (red symbols) and simulated (blue solid curve) out-coupling ratio of the directional coupler as a function
of the wavelength. In
d
and
e
, the dotted lines correspond to the regime where mode crossing between the fundamental TE
mode and the second order TM mode occurs, which is distant enough from the SH central wavelength and is not expected to
affect the device operation.
since most of input pulse energy can be “stored” in (i.e.
converted to) the SH, which is unaffected by the linear
coupler. Since the FH transmission strongly depends on
the input pulse energy of the FH, the intensity-dependent
nonlinear splitter functions as an all-optical switch.
It is worth noting that our design is in sharp contrast
with the previously demonstrated nonlinear directional
couplers in micro-wavguides which required picojoules of
energy
22
. In those devices, quadratic nonlinearity per-
turbs the evanescent coupling as the switching mecha-
nism, while in our device the switching mechanism arises
from the wavelength conversion in the QPM-engineered
waveguide and the evanescent coupler remains a linear
spectrally-selective splitter. Our nonlinear splitter shares
similarities in operation with bulk nonlinear mirrors used
in some mode-locked lasers
23
.
We fabricated the nonlinear splitter on a 700-nm-thick
X-cut magnesium-oxide (MgO) doped LN thin film on a
2-
μ
m-thick silicon dioxide layer on top of a LN substrate
(NANOLN). The details about the periodic poling, the
waveguide patterning and etching can be found in the
Methods. As shown in the scanning electron microscope
image (Fig. 2a) and the atomic force microscope im-
age (Fig. 2b), the Ar-based dry etching process yields
smooth waveguide sidewalls (with surface roughness
∼
1
nm) and a sidewall angle of
∼
60
◦
. The top width of
the main waveguide and the etching depth are measured
to be 1650 nm and 350 nm, respectively, with an error
of
±
5
nm. The inverted ferroelectric domains and the
poling defect along the main waveguide are shown in the
second-harmonic image in Fig. 2c. The device has a 2.5-
mm-long SHG region and a 3.5-mm-long DOPA region.
To achieve ultra-low-energy and ultrafast operation,
we engineer the dispersion of the LN ridge waveguide
and minimize both the group velocity dispersion (GVD)
and the group velocity mismatch (GVM) between the
FH and the SH
19
. Negligible GVD at the FH and SH
wavelengths preserves the temporal confinement of these
pulses and hence their high peak intensities along the wa-
veguide, thereby ensuring efficient short-pulse and low-
energy SHG and DOPA. Additionally, negligible GVM
between the FH and the SH waves guarantees that both
FH and SH pulses travel together along the waveguide.
As shown in Fig. 2d, in the dispersion-engineered wave-
guide, the fundamental quasi-TE modes at the FH (2090
nm) and SH (1045 nm) have a very low GVM of 0.4
fs/mm. In addition, the GVD for both the FH and SH
waves are as low as 40 fs
2
/mm and 114 fs
2
/mm, respec-
4
0
100
200
300
400
500
600
0
20
40
60
80
100
120
0
25
50
75
100
125
150
-1
0
1
2
3
4
5
6
7
Simulation
Experiment
P
out
(
m
W)
P
in
(
m
W)
Normalized transmission (dB)
Input pulse energy
(fJ)
0
100
200
300
400
500
600
0
10
20
30
40
0
25
50
75
100
125
150
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
P
out
(
m
W)
Simulation
Experiment
P
in
(
m
W)
Normalized transmittance (dB)
Input pulse energy
(fJ)
a
b
-40
-20
0
Normalized Power (dBm)
1600
1800
2000
2200
2400
-40
-20
0
Wavelength (nm)
through port
drop port
sech
2
1600
1800
2000
2200
2400
-40
-20
0
through port
drop port
sech
2
Wavelength (nm)
-40
-20
0
Normalized Power (dBm)
c
d
On
-
state
(E
in
=500
fJ
)
Off
-
state
(E
in
=7
fJ
)
On
-
state
(E
in
=500
fJ
)
Off
-
state
(E
in
=7
fJ
)
FIG. 3.
Ultra-low energy nonlinear optical transmission in the integrated nonlinear splitter. a
, Upper panel:
average on-chip output power of 2.09
μ
m FH from the drop port as a function of on-chip input average power/pulse energy.
Lower panel: normalized transmittance (
10 log(
T/T
P
in
→
0
)
) of the FH from the drop port.
b
, Upper panel: average output
power of FH from the through port as a function of input average power/pulse energy. Lower panel: normalized transmittance
(
10 log(
T/T
P
in
→
0
)
) of the FH from the through port. In both
a
and
b
, the blue solid lines are the simulation results. The
black symbols are the measured data. The insets illustrate the ports at which we collected the data.
c
, Measured output FH
spectra at the through port (blue) and the drop port (red) in the “on-state” (upper panel) and the “off-state” (lower panel).
The input FH pulse energy is 500 fJ for the “on-state” and 7 fJ for the “off-state”. In the “on-state”, the dip in the spectrum
of the drop port, which does not persist in the through port or in the “off-state”, is another strong experimental evidence for
the interplay of SHG and DOPA in the switching mechanism.
d
, Simulated output FH spectra at the through port (blue) and
the drop port (red) in the “on-state” (upper panel) and the “off-state” (lower panel), corresponding to the measurements in
(c). In both (c) and (d), the spectral dips are labeled by the red arrows.
tively. For a 35-fs-long input pulse at 2.09
μ
m, the op-
timized waveguide has a dispersion length of more than
50 mm and a walk-off length of 115 mm.
To ensure that the coupling ratio of the directional
coupler is resilient to fabrication errors, we adopt an adi-
abatic design in which the main waveguide is uniform
with a fixed width, while the coupler waveguide width
is adiabatically tapered
24
. The detailed geometry of the
directional coupler is discussed in the Supplementary In-
formation Section I. Figure 2e shows the wavelength de-
pendent coupling ratio, which is the ratio between the
output power at the drop port over the input power. Due
to the large mode area difference between the fundemen-
tal TE modes at 2090 nm and 1045 nm, the 70-
μ
m-long
directional coupler exhibits a large coupling ratio of over
85
%
for wavelengths beyond 2090 nm and a small cou-
pling ratio of less than 5
%
for wavelengths below 1045
nm. The measured (red symbols) result agrees well with
the simulation result (blue solid curve).
We characterized the nonlinear optical behavior of the
device using 46-fs-long pulses at 2.09
μ
m from a syn-
chronously pumped degenerate optical parametric oscil-
lator (OPO) with a repetition frequency of 250 MHz.
The characterization of the 2.09
μ
m pulses is elaborated
in Supplementary Information Section II. By measuring
the nonlinear splitter devices with different poling peri-
ods, we found that 5.11
μ
m is the optimal poling period
for realizing QPM, which is in good agreement with the
theoretical period of 5.08
μ
m. The experimental details
of optimizing the QPM condition are discussed in Meth-
ods and the Supplementary Information Section IV. At
the optimum QPM condition, we measured the output
power of the FH both at the through port and the drop
port. The detailed calibration of the input/outout cou-
pling loss of our waveguide is discussed in the Supple-
mentary Information Section V.
As shown in Fig. 3a, the normalized transmit-
tance from the input to the drop port, defined as
10 log(
T/T
P
in
→
0
)
, shows a clear reduction (~7 dB) when
the on-chip input FH pulse energy increases from 0 to
600 fJ. This behavior is well captured by the simulation
(blue solid line). Such a reduction in the transmittance
is a result of the strong depletion of FH waves during the
SHG process, since the directional coupler only couples
5
out the FH in the first half of the main waveguide. The
time-domain nonlinear dynamics of the SHG process is
elaborated in the Supplementary Information Section VI.
Based on the measured depletion of the FH shown in Fig.
3a and assuming that the propagation loss of the FH is
far less than its depletion, we estimated that 600 fJ input
FH pulse energy in the waveguide converts to a SH pulse
energy of 500 fJ.
The normalized transmittance of the FH from the in-
put port to the through port increases by more than 5
dB as the input pulse energy increases, as shown in Fig.
3b. This behavior is the opposite of the transmittance
to the drop port, which confirms that the poling defect
indeed switches the SHG to the DOPA process in the sec-
ond half of the main waveguide, thereby converting the
generated SH back into the FH. The experimental result
agrees well with the simulation (blue solid line), despite
showing a slightly lower peak transmittance, which can
be ascribed to the slightly lower SHG efficiency in the
first half of the device or the imperfect phase shift im-
posed by the poling defect. Based on the results shown in
Fig. 3a and b, we can deduce that the largest paramet-
ric gain in the DOPA region is more than 12 dB at 600
fJ input FH pulse energy, which translates to a gain per
unit length of 34 dB/cm given that the DOPA region is
3.5-mm-long. Notably, this result is consistent with our
recent parametric gain measurement on a similar QPM
LN waveguide, which exhibits a gain per unit length of 35
dB/cm pumped with 500 fJ 1.045
μ
m pulses
19
. Moreover,
the measured output FH power from the main waveguide
agrees well with the simulation.
The interplay of SHG and DOPA in the all-optical
switching mechanism is also evident from the output
spectra. In Fig. 3c, we compare the measured output FH
spectra at the drop port and the through port. When the
device is subjected to 500 fJ of input pulse energy (in the
“on-state”), the output spectrum at the drop port (red)
deviates from the initial sech
2
spectral shape, showing
spectral dips around 1920 nm and 2250 nm which indi-
cate a strong depletion of the FH. However, the output
spectrum at the through port (blue) does not show such
dips at high input pulse energies and has a spectral shape
similar to the sech
2
, which indicates the recovery of the
FH power. When the device is in the “off-state” (Fig. 3c
lower panel), the output spectra measured at the through
port and the drop port both have sech
2
shapes, because
of the weak nonlinear conversion in the “off-state”. Sim-
ilar behaviors can also be seen in the simulated output
spectra for the “on-state” (Fig. 3d upper panel) and the
“off-state” (Fig. 3d lower panel). In the Supplementary
Information Section VI, we provide a detailed analysis
of the nonlinear dynamics that explains the origin of the
spectral dips. We also explain how the spectral dips are
indicative of the power flow direction. It is worth not-
ing that when the input pulse energy exceeds 600 fJ, the
input FH exhibits significant spectral broadening during
the SHG
25
and the phase relation between the FH and
SH changes. This leads to a lower parametric gain of
the DOPA (see Supplementary Information Section VI
for details).
We further characterize the all-optical switching dy-
namics and the switching energy of the nonlinear splitter
device using a degenerate pump–probe technique, similar
to the measurement technique used in Ref.
13
As shown
in Fig. 4a, the beam containing ~46-fs-long pulses cen-
tered at 2090 nm generated from a table-top degenerate
optical parametric oscillator
26
is split into two beams by
a beam splitter in a Michelson interferometer. One beam
with a weak optical fluence (3 fJ, 770 nW on chip aver-
age power) is used as the probe beam, and another beam
with a high/tunable optical fluence and adjustable time
delay (controlled by a motorized delay stage) is used as
the pump beam. In the measurement, we couple the out-
put of the Michelson interferometer which contains both
the pump and the probe beams to our chip, and switch
the transmission of the probe signal by controlling the
power of the pump pulse. To suppress the interferences
between the pump and the probe beams, we use a piezo-
electric transducer (PZT) in the optical path of the probe
and modulate the phase of the probe pulses at 350 Hz,
which is much faster than the measurement bandwidth.
Additionally, we employ the lock-in modulation and de-
modulation scheme at 80 Hz to acquire the output probe
signal only, rather than acquiring both the pump and
probe signals.
The dynamics of the “on-state” for the probe signal is
measured at the through port and the drop port as plot-
ted in Fig. 4 b and 4c, respectively. At the through port,
we observe that the probe pulse is clearly appearing when
the pump pulse temporally overlaps with it, whereas at
the drop port the probe pulse is eliminated. To extract
the rise and fall times of the switching mechanism, we
fitted the data with exponential growth and decay func-
tions for relative time delays
∆
τ
< 0 fs and
∆
τ
> 0 fs,
respectively, convolved with the autocorrelation of the in-
put pulse, which was approximated by a Gaussian profile
with a FWHM of 65.2 fs. (see Supplementary Informa-
tion II for details) For the measurement at the through
port (Fig. 4b), the best fit yields a switching rise time of
(5.1
±
1) fs and a fall time of (18.1
±
2.9) fs. The mea-
surement at the drop port shows a switching rise time of
(1.75
±
0.86) fs and a fall time of (11.0
±
2.15) fs. The
measured ultrafast dynamics confirms that the all-optical
switching mechanism is indeed the result of instantaneous
quadratic nonlinearity without the contribution of other
slow nonlinearities. However, the entire all-optical switch
still has a finite response time due to the non-zero GVM,
GVD and the finite phase matching bandwidth, which
make switching for pulses shorter than 20 fs challenging.
We have confirmed with numerical simulations that the
asymmetry in the switching dynamics could be caused
by the interplay of several dispersion mechanisms such
as the GVM and the GVD.
The measured ultrafast switching also indicates that
the slow carrier dynamics that are commonly observed in
LN and other materials, such as photorefractive effect
27
6
a
1045 nm
Mode
-
locked laser
LPF
PZT
MM
OPO
75 fs
250 MHz
BS
LIA
TEC
LPF
2 um
PD
OBJ
OBJ
NDF
NDF
Time delay
Pump
Probe
0
20
40
60
80
100
120
0
80
160
240
320
400
480
-10
-8
-6
-4
-2
0
Probe signal (dB)
P
pump
(
m
W)
Pump pulse energy
(fJ)
3 dB switching energy=20 fJ
0
20
40
60
80
100
120
0
80
160
240
320
400
480
0
1
2
3
4
5
6
Probe signal (dB)
P
pump
(
m
W)
Pump pulse energy (fJ)
3 dB switching energy=80 fJ
b
c
d
e
-300
-200
-100
0
100
200
300
0.1
0.2
0.3
Probe signal (mV)
Estimated switching
fall time=18.1 ± 2.9 fs
Estimated switching
rise time=5.07 ± 1 fs
Time delay (fs)
E
pump
= 80 fJ
-300
-200
-100
0
100
200
300
0.5
1.0
1.5
Probe signal (mV)
Time delay (fs)
Estimated switching
fall time=11.0 ± 2.15 fs
Estimated switching
rise time=1.75 ± 0.86 fs
E
pump
= 20 fJ
FIG. 4.
Femtosecond, femtojoule all-optical switching. a
, Experimental setup for femtosecond all optical switching
measurement. 46-fs pulses at 2.09
μ
m generated from a free-space optical parametric oscillator (OPO) was used to characterize
the device. A pump and probe field with relative time delay
∆
τ
are injected into the waveguide via the objective lens. Probe
transmission depends on whether the two pulses excite the device simultaneously or at different times. LPF: long-pass filter;
MM: motorized mirror; PZT: piezoelectric transducer; NDF: neutral density filter; BS: beam splitter; OBJ: objective lens; LIA:
lock-in amplifier; PD: photodetector.
b
, Measured dynamics of the “on-state” at the through port. The input pump pulse
energy (
E
pump
) is 80 fJ.
c
, Measured dynamics of the “on-state” at the drop port. The
E
pump
is 20 fJ. The insets illustrate the
ports at which we collected the data.
d
, relative probe signal power at the through port as a function of the pump pulse power
(energy).
e
, relative probe signal power at the drop port as a function of the pump pulse power (energy). The 3 dB switching
energies at the through port and the drop port are 80 fJ and 20 fJ, respectively.
and photothermal effect
28
are absent, primarily due to
the low photon energies of the input FH and the gener-
ated SH, the ultra-low input pulse energy and the non-
resonant nature of the switch. We have also ruled out
the intensity-dependent index change (Kerr effect) of the
LN waveguide as the possible mechanism for the switch-
ing and nonlinear transmission characteristics
29
, given
the fact that no switching behavior and power-dependent
transmission was observed on a similar device without
poling in the main waveguide.
Figure 4d and e show the extinction ratio between the
“on-” and “off-” states of the switch for both output ports
at
∆
τ
= 0. We estimated a switching pump energy of
80 fJ (20 fJ) for the through port (the drop port) at the
3-dB contrast level. Within 500 fJ of input pulse energy,
we obtain a switching contrast over 5 dB in the through
port and a switching contrast over 8 dB in the drop port.
Such a high switching contrast is difficult to realize us-
ing the saturable absorption in semiconductors
5
and low-
dimensional materials
30–32
without coupling them to op-
tical cavities, since it, in general, requires very high op-
tical fluence to excite a significant portion of electrons
from the valence band to the conduction band.
In summary, we demonstrate on-chip all-optical
switching based on the strong instantaneous nonlinear
response of an LN nano-waveguide, with simultaneous
dispersion and QPM engineering. Our on-chip device
features the state-of-the-art switching energy-time prod-
uct of
1
.
4
×
10
−
27
J
·
s, which is an order of magnitude
improvement over the previous all-optical switch based
on graphene-loaded plasmonic waveguides
13
. This non-
linear splitter also enables the simultaneous realizations
of switch-on and -off operations as well as a large extinc-
tion ratio of over 5 dB when subjected to less than 500 fJ
7
of input pulse energy. Moreover, due to the exceptionally
low GVM and GVD of our dispersion-engineered LN wa-
veguide, we can further improve the performance limit of
the device by simply prolonging the poled region in the
main waveguide. Our numerical simulation (see Supple-
mentary Information section VII for details) has revealed
that with the same dispersion characteristics and input
pulse configuration of 45 fs at 2.09
μ
m, a 70-mm-long-
main waveguide (containing a 20-mm-long SHG and a
50-mm-long DOPA regions) yields a 2 dB switching con-
trast at a switching energy of 800 aJ. We envision that the
low required switching energy (on the order of 10s of fJ)
and the THz bandwidth of our all-optical switch make it
amenable to directly interfacing with recently developed
LN-based on-chip pulsed light sources, such as Kerr soli-
ton micro-combs
33–35
and electro-optical (EO) combs
36
,
towards on-chip ultrafast information processing
37
and
time-multiplexed photonic networks
38
.
METHODS
Device fabrication.
We fabricated the nonlinear
splitter devices on a 700-nm-thick X-cut MgO-doped
LN thin-film on 2-
μ
m-thick SiO
2
on top of a LN
substrate (NANOLN). We first patterned the poling
electrodes (15 nm Cr/55 nm Au) with varied electrode
finger periodicities using e-beam lithography. Then the
electrodes were formed by e-beam evaporation and metal
lift-off. We performed the ferroelectric domain inversion
(periodic poling) by applying several 380 V, 5-ms-long
pulses at room temperature with the sample submerged
in oil. We visually inspected the poling quality using
a second harmonic microscope. Next, we removed the
electrodes by wet chemical etching, and patterned the
waveguides using the e-beam lithography. The pattern
was transferred to the LN layer by Ar
+
plasma etching.
Finally, the waveguide facets were polished to enable
good light coupling efficiencies.
Optical measurements.
For the linear and nonlinear
optical measurements, we employed a free-space light
coupling setup shown in Fig. 4a. The 1045 nm source
is a 1 W Yb mode-locked laser that produces nearly
transform-limited 75-fs-long pulses at a 250 MHz repeti-
tion rate (Menlo Systems Orange). The output 1045 nm
beam was fed into a near-synchronously pumped degen-
erate OPO
25
to produce
∼
46
-fs-long pulses centered at
2090 nm. The detailed characterization of the 2090 nm
pulses is discussed in the Supplementary Information
Section II. The output 2090 nm beam was split into two
beams by a beam splitter in a Michelson interferometer.
Then the two beams were recombined and coupled
into the nonlinear splitter chip by a reflective objective
(Newport 50102-02). The average off-chip input power
was calibrated by a thermal power meter (Thorlabs
PM16-401). The input/output coupling losses at 2090
nm were estimated to be 21.6 dB/4 dB. For the power
dependent transmittance measurements in Fig. 3, only
one output beam from the Michelson interferometer
was used. The chip was placed on a thermoelectric
cooling stage (TEC). For adjusting the QPM condition,
temperature tuning and thin organic materials were
used (see Supplementary Information Section IV for
details). For the results in Fig. 3 a and b, the output
power was measured by an optical spectrum analyzer
(OSA) covering 1200-2400 nm (Yokogawa AQ6375B)
with a 2 nm resolution bandwidth. For the result in Fig.
4b-e, the output power was measured by an IR 2-
μ
m
photoreceiver (Newport 2034).
Numerical simulations.
We used a commercial soft-
ware (Lumerical Inc.) to solve for the waveguide modes
as well as to obtain the dispersion characteristics shown
in Fig. 2c. In the simulation, the anisotropic index of the
LN was modeled by the Sellmeier equations
39
. For the
nonlinear optical simulation, we solved an analytical non-
linear envelope equation (NEE) in the frequency domain
using a split-step Fourier technique to simulate the pulse
propagation and nonlinear dynamics in the waveguide
40
.
The nonlinear step was solved with a fourth-order Runge-
Kutta method. The details regarding the single-envelope
simulation can be found in Supplementary Information
Section III.
DATA AVAILABILITY
The data that support the plots within this paper and
other findings of this study are available from the corre-
sponding author upon reasonable request.
CODE AVAILABILITY
The computer code used to perform the nonlinear sim-
ulations in this paper is available from the corresponding
author upon reasonable request.
ACKNOWLEDGEMENTS
The device nanofabrication was performed at the Kavli
Nanoscience Institute (KNI) at Caltech. The authors
thank Prof. Kerry Vahala and Prof. Changhuei Yang for
loaning equipment. The authors gratefully acknowledge
support from ARO grant no. W911NF-18-1-0285, NSF
grant no. 1846273 and 1918549, AFOSR award FA9550-
20-1-0040, and NASA/JPL. The authors wish to thank
NTT Research for their financial and technical support.
AUTHORS CONTRIBUTIONS
Q.G. and A.M. conceived the project; Q.G. fabricated
the devices and performed the measurements with assis-
8
tance from R.S, R.N., S.J. and R.M.G. L.L. developed the
single-envelope simulation tool. L.L., D.J.D. and A.R.
contributed to the design of the device; Q.G. and L.L.
analyzed the experimental results and performed the sim-
ulations. L.L. performed the periodic poling; Q.G. wrote
the manuscript with input from all other authors. A.M.
supervised the project.
COMPETING INTERESTS
The authors declare no competing interests.
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