U.S. Patent

Jan. 11, 2022

Sheet 18 of 22

US 11,221,540 B2

) Ae TTT om tO)

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gp Av = 256.1 THz 301.4 THz Pys dem |
40} 2634 THe

2

Optical spectra (dB)

40
0

2

4g

0

0 7
v= (384 THz

320.2 THz

794TH

458.6 THz

PyaSmW

OT ay =906 TH

Tv

250

300

367.9 THz

380 400

v (THz)
FIG. 18

450

500


US 11,221,540 B2

33

Qn 20F Vinay @

NO

where «, is the pump angular frequency. Q,, and Q,, are the
coupling and loaded quality factors for the pump mode. Q,,
and Q,, are the loaded quality factors for signal and idler
modes. €, is the vacuum permittivity constant. “ny... Vipsps
and Tips, are average index, mode volume, and mode over-
lap for the degenerate four-wave mixing interaction. x,,..,
is calculated from the n value? following x°=4/3n7e,c/n3,
where n is the refractive index and c is the speed of light.

Consider two likely extremes (Q,=Q,=1x10° and
Q,=Q,=1%10%). The mode volume and mode overlap are
extracted from simulations for pump, signal, and idler
around 390 THz, 265 THz, and 515 THz. These values
depend on wavelengths, but are at similar levels for different
OPO signal-idler combinations. With these assumptions in
mind, we estimate the expected thresholds. This range of
estimated thresholds is consistent with those measured in the
experiments.

The device layout in this Example was made with the
Nanolithography Toolbox, a software package developed by
the NIST Center for Nanoscale Science and Technology. The
SiN, layer is deposited by low-pressure chemical vapor
deposition on top of a 3 jum thick thermal SiO, layer ona 100
mm diameter Si wafer. The wavelength-dependent refractive

index and the thickness of the layers are measured using a 3

spectroscopic ellipsometer, with the data fit to an extended
Sellmeier model. The device pattern is created in positive-
tone resist by electron-beam lithography. The pattern is then
transferred to Si,N, by reactive ion etching using a CE,/

CHF, chemistry. The device is chemically cleaned to 3

remove deposited polymer and remnant resist, and then
annealed at 1100° C. in an N, environment for 4 hours. An
oxide lift-off process is performed so that the microrings
have an air cladding on top, while the input/output edge-
coupler waveguides have SiO, on top to form more sym-
metric modes for coupling to optical fibers. The facets of the
chip are then polished for lensed-fiber coupling. After pol-
ishing, the chip is annealed again at 1100° C. in an N,
environment for 4 hours.

Dilute hydrofluoric acid (DHF) etching is used as a
post-processing technique that isotropically removes Si;N,
with sub-nanometer control, providing a level of geometric
control beyond what we achieve through electron-beam
lithography and dry etching. Using a dilution of 100:1
(H,O:HF), a SijN, etch rate of 0.4 nm/min is achieved (the
correspond SiO, etch rate is 8 nm/min). We also note that
DHF etching can also improve resonator quality factor; for
example, >2x improvement in Q values are often observed.

While one or more embodiments have been shown and
described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
limitation, Embodiments herein can be used independently
or can be combined.

All ranges disclosed herein are inclusive of the endpoints,
and the endpoints are independently combinable with each
other. The ranges are continuous and thus contain every
value and subset thereof in the range. Unless otherwise
stated or contextually inapplicable, all percentages, when
expressing a quantity, are weight percentages. The
suffix “(s)” as used herein is intended to include both the

S

2

40

34

singular and the plural of the term that it modifies, thereby
including at least one of that term (e.g., the colorant(s)
includes at least one colorants). “Optional” or “optionally”
means that the subsequently described event or circumstance
can or cannot occur, and that the description includes
instances where the event occurs and instances where it does
not. As used herein, “combination” is inclusive of blends,
mixtures, alloys, reaction products, and the like.

As used herein, “a combination thereof” refers to a
combination comprising at least one of the named constitu-
ents, components, compounds, or elements, optionally
together with one or more of the same class of constituents,
components, compounds, or elements.

All references are incorporated herein by reference.

The use of the terms “a” and “an” and “the” and similar
referents in the context of describing the invention (espe-
cially in the context of the following claims) are to be
construed to cover both the singular and the plural, unless
otherwise indicated herein or clearly contradicted by con-
text. “Or” means “and/or.” It should further be noted that the
terms “first,” “second,” “primary,” “secondary,” and the like
herein do not denote any order, quantity, or importance, but
rather are used to distinguish one element from another. The
modifier “about” used in connection with a quantity is
inclusive of the stated value and has the meaning dictated by
the context (e.g., it includes the degree of error associate ink
objects of a list or alternatives and is not disjunctive: rather
the elements can be used separately or can be combined
together under appropriate circumstances.

What is claimed is:

1. An optical parametric oscillator for producing idler
coherent light and signal coherent light from pump coherent
light by balanced parametric dispersion, the optical para-
metric oscillator comprising:

a substrate cladding;

a microring resonator disposed on the substrate cladding

and comprising:
a Kerr nonlinear medium comprising an annulus with a
radius R, a height H, and a width W that provides a
balanced parametric dispersion;
and that:
receives pump coherent light from a waveguide; and
produces idler coherent light and signal coherent
light from the pump coherent light,

the idler coherent light and signal coherent light
produced according to the balanced parametric
dispersion of the microring resonator;

and

a waveguide disposed on the substrate cladding in optical
communication with the microring resonator and com-
prising a transparent Kerr nonlinear medium and that:
receives pump coherent light; and
communicates the pump coherent light to the microring

resonator for production of the idler coherent light
and the signal coherent light from the pump coherent
light.

2. The optical parametric oscillator of claim 1, further
comprising:

a cover cladding disposed on the waveguide, the micror-
ing resonator, and the substrate cladding such that
microring resonator and the waveguide are interposed
between the substrate cladding and the cover cladding
to encapsulate the microring resonator and the wave-
guide.

3. The optical parametric oscillator of claim 1, further

comprising:



US 11,221,540 B2

25

length can be achieved by various parameters, because the
change in H can usually be compensated by the change in
RW. For widely-separated frequency matching only, the
dispersion design also shows a similar trend although the
design is less trivial. The OPO device is more sensitive in H
than RW as the combination of these two principles is
nontrivial. For the dispersion engineering based on H, we
showcase its sensitivity in FIG. 13(a)-(c). Here all three
devices with H of 490 nm, 500 nm, and 510 nm can satisfy
widely-separated frequency matching similarly, but only the
510 nm device (FIG. 13(c)) can support the normal disper-
sion when the pump is at 322 THz (green). In contrast, the
first two devices, as shown in FIG. 13(a,4), although have
normal dispersion at pump frequencies around 322 THz
(green), do not support frequency matched pairs for widely-
separated OPO for these pump frequencies. Moreover, when
these two devices have such widely-separated matched
pairs, e.g., when pump is around 315 THz (purple), the
dispersion near the pump is quite anomalous. Because of this
anomalous dispersion, these widely-separated OPO,
although in principle allowed, are usually took over by
close-band OPO in practice. We note that this sensitive
dependence on H is quite general in design, although we
have only show one case here. On the other hand, when we
vary the ring width parameter, e.g., (d) 1150 nm, (c) 1160
nm, (ec) 1170 nm, and (f) 1180 nm in FIG. 13, both
widely-separated modes and normal dispersion around the
pump are simultaneously obtainable. although the optimized
pump frequency shifts slightly as (d) 324 THz, (c) 322 THz,

(e) 320 THz, and (f) 318 THz, respectively. We note that the 3

device is sensitive to RR as well, because the bending
dispersion also contributes to the overall dispersion design,
particularly for the widely-separated case.

The device layout was done with the Nanolithography

Toolbox, a free software package developed by the NIST 3

Center for Nanoscale Science and Technology. The Si;Ny
layer is deposited by low-pressure chemical vapor deposi-
tion on top of a 3-m thick thermal SiO, layer on a 100 mm
diameter Si wafer. The wavelength-dependent refractive
index and the thickness of the layers are measured using a
spectroscopic ellipsometer, with the data fit to an extended
Sellmeier model. The device pattern is created in positive-
tone resist by electron-beam lithography. The pattern is then
transferred to Si,N, by reactive ion etching using a CE,/
CHF, chemistry. The device is chemically cleaned to
remove deposited polymer and remnant resist, and then
annealed at 1100° C. in an N, environment for 4 hours. An
oxide lift-off process is performed so that the microrings
have an air cladding on top while the input/output edge-
coupler waveguides have SiO, on top to form more sym-
metric modes for coupling to optical fibers. The facets of the
chip are then polished for lensed-fiber coupling. After pol-
ishing, the chip is annealed again at 1100° C. in an N,
environment for 4 hours.

The relative coupling of the pump and signal/idler OPO
modes can be used to suppress the close-band OPOs. In FIG.
12(d), we showed that the pulley coupling can be optimized
to particular pump and signal frequencies. Here, we show
that when changing the gap of such pulley coupling from
230 nm to 210 nm in 10 nm increments, the change in Q. is
spectrally non-uniform, as shown in FIG. 14(a). We calcu-
late the suppression ratio (VQIsQU/Q,,, in these cases, where
Qin (M=P,8,i) is given by Qin,=QomtQem: Quem iS extracted
from the simulation (FIG. S4(a)) and Q,,,, is assumed to be
2.5x10° (inset of FIG. $4(a) shows a fitting of a typical
pump transmission recorded experimentally). The suppres-
sion ratio is therefore estimated to be 1.31, 1.38 and 1.45 for

S

20

2

40

&

26

the gap of 230 nm (blue), 220 nm (yellow), and 210 nm
(red). These values suggest that we can have more suppres-
sion for the close-band OPO while decreasing the coupling
gap, and the trend is clearly observable experimentally in
FIG, 14(6). In the 230 nm device, only close-band OPOs are
observed. In the 220 nm device, both close-band OPO and
widely-separated OPO are observed, which indicates that
these two OPO cases have similar power thresholds. In the
210 nm device, however, only the widely-separated OPO is
observed. We want to emphasize that these devices have the
same geometry except for the coupling gap, and are adjacent
to each other on the chip so that unintended difference in
geometry (e.g., film thickness) are expected to be negligible.

We present experimental data for the thermal dependence
and pump power dependence. FIG. 15(a) shows that the
OPO frequency is stable over 10° C. temperature tuning,
This temperature stability allows our device to operate
reasonably stable in the environment, also we have not
tested the device in extreme temperatures. For the power
dependence, we notice that at higher power above the
threshold, the device OPO blueshifts to higher frequency as
the power increase. The effect can be explained by FIG.
11(c). When the power is so high that the phase change of
the intra-cavity energy is larger than the natural cavity
mismatch, we use red detuning of the pump, which is usually
not directly accessible due to thermal bistability. Therefore,
a close mode set with larger natural cavity mismatch
becomes the optimized OPO. Here we show that the OPO
can be tuned ata rate of 1 FSR (1 THz for 23 jum device) per
0.3 mW and that the number of FSRs can be adjusted by
device radius, in principle.

Example 2

On-Chip Optical Parametric Oscillation into the
Visible: Generating Red, Orange, Yellow, and
Green from a Near-Infrared Pump

The on-chip generation of coherent, single-frequency
laser light that can be tuned across the visible spectrum
would help enable a variety of applications in spectroscopy,
metrology, and quantum science. Third-order optical para-
metric oscillation (OPO) in a microresonator has shown
great promise as an efficient and scalable approach towards
this end. However, considering visible light generation, so
far only red light at <420 THz (near the edge of the visible
band) has been reported. In this work, we overcome strong
material dispersion at visible wavelengths and demonstrate
on-chip OPO in a Si,N,, microresonator covering >130 THz
of the visible spectrum, including red, orange, yellow, and
green wavelengths. In particular, using an input pump laser
that is scanned 5 THz in the near-infrared from 386 THz to
391 THz, the OPO output signal is tuned from the near-
infrared at 395 THz to the visible at 528 THz, while the OPO

‘5 output idler is tuned from the near-infrared at 378 THz to the

infrared at 254 THz. The widest signal-idler separation of
274 THz is more than an octave in span and is the widest
demonstrated for a nanophotonic OPO to date. This
Example shows how nonlinear nanophotonics can transform
light from readily accessible compact near-infrared lasers to
targeted visible wavelengths of interest.

On-chip generation of coherent visible light is important
for scalable manufacturing and field-level deployment of
many applications in spectroscopy, metrology, and quantum

5 optics. For example, many wavelength references and opti-

cal clocks are based on visible lasers stabilized to atomic
systems. Moreover, many quantum systems suitable for


US 11,221,540 B2

Sheet 12 of 22

Jan. 11, 2022

U.S. Patent

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U.S. Patent Jan. 11, 2022 Sheet 22 of 22 US 11,221,540 B2

2BmW | 300TH 930x106 40x105 tx 108 041x108 20 266ym3 0.94 —330x10-2F dive
2BmW | 300TH 300x108 4.0x908 t0x708 410x108 20 2b6umd 094 399x121 mee

FIG, 22


US 11,221,540 B2

35

a second waveguide in optical communication with the
microring resonator and comprising a transparent mate-
rial and that:
receives the idler coherent light and the signal coherent

light from the microring resonator.

4. The optical parametric oscillator of claim 1, wherein
the substrate cladding comprises silicon dioxide.

5. The optical parametric oscillator of claim 1, wherein
the radius R of the microring resonator is from 100 nm to 1
cm.

6. The optical parametric oscillator of claim 1, wherein
the height H of the microring resonator is from 10 nm to 5
jum.

7. The optical parametric oscillator of claim 1, wherein
the width W of the microring resonator is from 10 nm to 10
jum.

8. The optical parametric oscillator of claim 1, wherein a
frequency of the pump coherent light is from 100 THz to 800
THz.

9. The optical parametric oscillator of claim 1, wherein a
frequency of the idler coherent light is from 50 THz to 400
THz.

10. The optical parametric oscillator of claim 1, wherein
a frequency of the signal coherent light is from 100 THz to
1000 THz.

11. The optical parametric oscillator of claim 1, wherein
the balanced parametric dispersion is in accord with the
threshold relationship given below:

Pin =

(-)-(5)]
2 2 yewm ayy

12. The optical parametric oscillator of claim 1, wherein

the balanced parametric dispersion comprises:
a pump frequency node at a pump frequency v, and
comprising a parametric dispersion that is zero;
an idler frequency node at an idler frequency v, and
comprising a parametric dispersion that is zero;
an idler normal dispersion minimum interposed at a
frequency between the pump frequency v, and the idler
frequency v, and comprising a normal parametric dis-
persion;
an idler anomalous dispersion frequency at a frequency
that is less than the idler frequency v, and comprising
an anomalous parametric dispersion;
a signal frequency node at a signal frequency v, and
comprising a parametric dispersion that is zero;
a signal normal dispersion minimum interposed at a
frequency between the pump frequency v, and the
signal frequency v, and comprising a normal paramet-
ric dispersion; and
a signal anomalous dispersion frequency at a frequency
that is greater than the signal frequency v, and com-
prising an anomalous parametric dispersion;
wherein:
the balanced parametric dispersion consists essentially
of the normal parametric dispersion between the
idler frequency node and the pump frequency node;
and

the balanced parametric dispersion consists essentially
of the normal parametric dispersion between the
pump frequency node and the signal frequency node.

op 2 Yew

25

45

35

60

36

13. The optical parametric oscillator of claim 1, wherein
a central wavelength of the idler coherent light and a central
wavelength of the pump coherent light are separated by 50
THz to 300 THz.

14. The optical parametric oscillator of claim 1, wherein
a central wavelength of the signal coherent light and a
central wavelength of the pump coherent light are separated
by 50 THz to 300 THz.

15. A process for producing idler coherent light and signal
coherent light from pump coherent light with the optical
parametric oscillator of claim 1, the process comprising:

receiving the pump coherent light by the waveguide:

communicating the pump coherent light from the wave-
guide to the microring resonator; and

producing the idler coherent light and the signal coherent

light from the pump coherent light according to the
balanced parametric dispersion of the microring reso-
nator.

16. The process of claim 15, farther comprising:

receiving, by a second waveguide in optical communica-

tion with the microring resonator and comprising a
broadly transparent medium, the idler coherent light
and the signal coherent light from the microring reso-
nator.

17. The process of claim 15, wherein the balanced para-
metric dispersion is in accord with

Pn =

int ( aml (fey

Top 2 yeww (2 2 Yewar

18. The process of claim 15, wherein the balanced para-
metric dispersion comprises:

a pump frequency node at a pump frequency v, and

comprising a parametric dispersion that is zero;

an idler frequency node at an idler frequency v, and

comprising a parametric dispersion that is zero;

an idler normal dispersion minimum interposed at a

frequency between the pump frequency v,, and the idler
frequency v, and comprising a normal parametric dis-
persion;

an idler anomalous dispersion frequency at a frequency

that is less than the idler frequency v, and comprising
an anomalous parametric dispersion;
signal frequency node at a signal frequency v, and
comprising a parametric dispersion that is zero;
signal normal dispersion minimum interposed at a
frequency between the pump frequency v, and the
signal frequency v, and comprising a normal paramet-
ric dispersion; and
signal anomalous dispersion frequency at a frequency
that is greater than the signal frequency v, and com-
prising an anomalous parametric dispersion;

wherein:

the balanced parametric dispersion consists essentially
of the normal parametric dispersion between the
idler frequency node and the pump frequency node;
and

the balanced parametric dispersion consists essentially of

the normal parametric dispersion between the pump
frequency node and the signal frequency node.

19. The process of claim 15, wherein a central wavelength
of the idler coherent light and a central wavelength of the
pump coherent light are separated by 50 THz to 300 THz.

20. The process of claim 15, wherein a central wavelength
of the signal coherent light and a central wavelength of the
pump coherent light are separated by 50 THz to 300 THz.

+ ke ee

.

2

2



U.S. Patent Jan. 11, 2022 Sheet 3 of 22 US 11,221,540 B2

(A) 205 (B) 206 205 207
/ mA / /
pump ' idler A signal
' {
|
1 i f |
laser input OPO output
@)
iam}
on 14001200 1000800 800 700 600
a H=600nm
Re 1440 nm 7
¥pe 204 THe
|
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4 8 L L £ L | 4 i
200 250 300 380 400 480 500
| v(t
26 205, 208 207


US 11,221,540 B2

21
when inside the microring, manifests itself as a shift of
cavity frequencies as shown in FIG. 11(4). The third-order
nonlinear (~“) effects, including SPM, XPM, and FWM,
are described by the cavity nonlinear parameter given by the
following equation generally:

(85)

3th ray

Ac ot ay Ves

Yinmus = (with m,n,u, v= ps, i),

which is a positive real parameter. 1,,,,,,.,. characterizes the
spatial overlap of interacting optical modes given by:

[eeVenereves EuEaksE, 60)

Nee = 7

fare lEnl' fedv etal! fidvez

Weal Laver

where fi,,, represents the dominant electric field components
of the m=p.s.i mode. This mode is related to A,, in that
U,-lA,P=fvTM e,,|B,,|?. Here the approximation is made
possible when the other electric field components are much
smaller than the dominant one, for example, |F.,1, If,1«IE,|
for transverse-electric-like (TE) modes. %®,,,,,, 18 short for
XO (O23, @,) and represents the third-order

ne Days

nonlinearity at @,, With the inputs at Oy. %. © Apna >

represents average linear refractive index — figima=
(n,.n,n,n,)"4, Likewise, Vj. Fepresents average mode
volume Vonnn—WnV,Vu¥,)', where individual mode

volume is given by:

(s?)

The last term in Eq. (S1) is the source term that represents.
the pump laser that is coupled into the cavity. The coupling
rate [,,, is given by Eq. S4 and the input field S*,, is
normalized in such a way that |S~,,|?=P,,, represents the input
power in the waveguide (FIG. 11).

Terms representing phenomena such as nonlinear absorp-
tion and free carrier effects are not considered in Egs.
(S1-$3), as silicon nitride (Si,N,) is a wide bandgap material
and does not have such effects in the frequency ranges of
interest in this work. Moreover, quantum fluctuation of the
signal and idler bands are not included because we are only
interested in the classical regime, when the OPO is near and
above parametric threshold.

We first study the near-threshold case of the OPO process
for Eqs. (S1-S3). When the signal and idler intra-cavity
energies are small (U,, U,“U,), their nonlinear contribution
can be neglected. The equations are then reduced to

aA, (88)
GE = lilberp + YpUp) — Vip /2Ap + inf Tep Sin

dA, . tee (89)
Gp = Wes + 27.9 p) Vin DAs + fying

20

0

35

60

6:

22
-continued
dA; ; g2ae (S10)
Ge = Hilden + 2yp Up) — Pa IIA: + trey,

where SPM and XPM terms, now combined with the linear
detuning terms, effectively create nonlinear detunings for all
three intra-cavity light fields. If we assume that signal and
idler fields are nonzero (1A,|, |A,|#0), in steady-state these
equations yield

[(A0, 40,2 +0 2? Te Pine (su)

(A0,424,,U, TAO 424, ULE gs (S12)

(Nip Nepiel isp Uy +2 tap A OMY; AO, JU +
AOA HT },/2)(Fy/2)=0,

(S13)

where aforementioned energy and power normalizations are
used. Here Eq. (S11) describes the relation of pump thresh-
old power in the waveguide and the intra-cavity threshold
energy. Eq. (S12) indicates that the ratios of overall detun-
ings to the cavity linewidths are identical. This equation is
related to the coherence of the OPO. Eq. S13 is the equation
leads to the intra-cavity threshold energy, which needs to
have a positive solution for OPO to occur. At this point, it is
important to recall the requirements for detunings:

040-200,-N04N0,-2400, 409, 4Og-20g-0, (si4)

We consider the case that frequency matching can be
matched for signal and idler, that is, Aw,=-2y,,U, and
Aw,=-24,,U,, which is clearly a solution for Eq. ($12). The
frequency matching for pump. however, is not guaranteed to
be matched automatically and needs to be adjusted by laser
detuning. Such detuning needs to consider both the natural
frequency mismatch and also the nonlinear cavity shilling
due to phase modulation (FIG. 11(6)). For simplicity, we
define At,=09,-+(,-2009,, Which is related to the frequency
mismatch (Av) in the main text by Aw,=2xAv, where when
close to pump, positive values correspond to anomalous
dispersion and negative values correspond to normal dis-
persion. We also define PeVTDy. YewsVopp¥ pap
Wer VepHips and YpyAlypHip-Yp Eqs. (S13, S14) then
reduces to

yh! (S15)
POD yews
Seo Tr Yew (si6)
Aw, = -
2 2 yew

We bring these into Eq. (S11), and the pump threshold power
is therefore given by:

Pre

it 1 | Aw Ti yer P (Te) a)
st ee +{2] |.
3 tim eal

We can see that the threshold power critically depends on
frequency matching. For example, an OPO with an overall
detuning of 31, would require 10x higher threshold power
than the ideal case, if all other parameters are the same. In
the main text, we search for devices that have zero frequency
mismatch (Aw,=0) for the natural cavity frequencies for
convenience. However, this dispersion condition is not opti-
mized for the threshold power. In fact, it is I,I',/T?,,41

2 2 yews


US 11,221,540 B2

Sheet 19 of 22

Jan. 11, 2022

U.S. Patent

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US 11,221,540 B2

5

stable for pump power from 2.46 mW to 3.70 mW. When the
pump power is further increased, the OPO signal blueshifis
1 FSR for 0.3 mW increase. The measurements are carried
out at T=31.1° C.;

FIG. 16 shows optical parametric oscillation transforms a
near-infrared pump into visible wavelength light. (a) Device
and (b) scheme of the OPO process to generate signal and
idler in the visible and infrared, respectively, using a pump
in the near-infrared. When the pump shifis by only a few
THz, the OPO outputs shift by ~100 THz. This advantage
makes OPO unique for light generation over broad spectral
bands. (c) Top panel shows the comparison of widely-
separated single signal-idler pair OPO in miniaturized/on-
chip photonic devices. Most of these works are pumped by
infrared lasers either at ~193.5 THz (1.55 jum) for MgF2 and
SiO2 whispering gallery mode resonators (WGMRs) or at
~150 THz (2 um) in an AIN microring, where the represen-
tative data with the widest span (y axis) are shown by the
brown lines. An OPO work in SiN, uses a near-infrared
pump at ~330 THz (910 nm) to generate red light at the edge
of the visible at ~420 THz (714 nm), as shown by the dashed
line, and the OPO herein can go deeper into the visible,
where material dispersion is much larger (e.g.. SiN, dis-
persion curve in the bottom panel), covering from red
(bottom) to green (top), using only a few THz of pump
tuning around =385 THz (780 nm). In particular, the top line
shows the case where the OPO is octave-spanning, with idler
and signal bridging infrared and green wavelengths. An
experimental result and simulation (273.7 THz) results were

consistent. (d) Top view microscope images of devices 3

exhibiting OPO, showing the scattering of generated visible
light in the red, orange, and green. These images are taken
without ambient illumination, using a camera that is insen-
sitive to the pump and generated idler wavelengths. The
device is a Si,N,, microring with an outer radius of 25 um.
The 20 ym scale bar in the top right corner applies to all
three images. Two waveguides are designed for each micror-
ing, as evident from the scattered light in the images, but
only the bottom waveguide is used to effectively couple
pump, signal, and idler light, as depicted in (a).

FIG. 17 shows a dispersion design for visible light gen-
eration. (a) Cross-section view of the device shows two
geometric parameters, ring width (RW) and film thickness/
height (H), that provide dispersion engineering. (b) Simu-
lation shows the frequency matching profiles that support
the OPO spectral separations. Frequency mismatch (y axis)
is plotted for phase matched mode sets (m,+m,-2m,-0),
where the pump is shifted from 380 THz (bottom) to 385
THy (top) by a step of 1 THz. In the top panel, when the
pump is at 385 THz (black), the device dispersion is too
large to support any OPO. When the pump is decreased to
384 THz (green), the device supports octave-spanning OPO
with idler and signal at 247.5 THz and 520.5 THz, respec-
tively. A further decrease in the pump frequency leads to a
smaller frequency span with different colors for the visible
wavelength signal (e.g., yellow, orange, and red). The device
has a radius of 25 um, a thickness of 500 nm, and a radius
of 825 nm.

FIG. 18 shows widely-separated OPO in an exemplary
device, (a) Normalized transmission of a pump mode (fun-
damental transverse-electric mode, whose electric field pro-
file is in the inset) shows an intrinsic Q of (1.67#0.15)x10°,
where the uncertainty is a one standard deviation value
Obtained from the fitting of the doublet resonance. (b) When.
the pump frequency shifts by ~5 THz, the signal and idler
frequencies shift by 123 THz and 113 THz, respectively. The
ratio of the signal/idler spectral tuning to that of pump is

2

6

~26:1. (c) Three optical spectra are shown with pump
frequency of 391.1 THz, 389.4 THz, and 387.7 THz, from
top to bottom, respectively. Pump power dropped into the
cavity can be larger when OPO span is larger. The spectra
were clean without noise or competitive processes. In the
bottom spectrum, a second pair of OPO sidebands emerges
and is much weaker (~20 dB) than the primary pair, and is
commonly observed for OPO that is close to pump. The
device has a radius of 25 jm, a thickness of 500 nm, and a
nominal ring width of 826 nm. The resonator free spectral
range is ~0.9 THz.

FIG. 19 shows OPO output light from red to green. (a) A
collection of signal (red), pump (violet), and idler (blue)
frequencies plotted versus the OPO span (Av) for a series of
devices in which the geometry (and hence dispersion) is

5 slightly varied. The pump laser is scanned from 386 THz to

391 THz, and its span in use is only 5 THz. The OPO signal
frequencies span>130 THz, corresponding to a 26 times
amplification. Data is shown from six devices with ring
widths from 824 nm to 830 nm before and after a dilute
hydrofluoric acid (DHF) dip. The DHF dip isotropically
removes <1 nm of Si,N,, which enables the corresponding
tuning of the OPO output wavelengths with a resolution
beyond what we achieve through lithography and dry etch-
ing alone. The overall frequency span covers red, orange,

yellow, and green signal wavelengths. In particular, OPO

frequencies with Av from 256.1 THz to 273.7 THz are
accessed by pump power tuning in a device with nominal
RW of 826 nm after DHF dip. (b) Representative OPO
spectra for signal output light in the green at 527.8 THz
(568.4 nm), yellow at 513.9 THz (583.7 nm), orange at
491.6 THz (610.3 nm), and red at 450.6 THz (665.8 nm)
from top to bottom, respectively. The trace corresponds to
the widest OPO achieved by pump power tuning in (a). The
coupling of signal (visible) light is 10 dB-20 dB smaller than
the coupling of idler (near infrared or infrared) light because
of the evanescent-coupling nature of the waveguide. Optical
microscope images (with illumination) show the corre-
sponding colors that are generated. The scale bars represent
20 um in these four images:

FIG. 20 shows tuning of OPO frequencies with pump
power. When the dropped pump power (Pd=P(1-T), where
Pis the laser power in the waveguide and T is the normalized
cavity transmission of the pump mode that can be adjusted
by laser-cavity detuning) increases from 22 mW to 37 mW,

5 the pump frequency (vp) is adjusted to follow the thereto-

optical shift of the pump mode;

FIG. 21 shows %2) versus x° OPO for visible light
generation. (a) The comparison of two schemes of OPO to
achieve the result we have shown in this work. Third-order
OPO requires an infrared pump at 768 nm, while second-
order OPO would require an ultra-violet pump at 384 nm.
(b) The material dispersion is much larger at shorter wave-
lengths. For example, silicon nitride’s dispersion is 11 times
larger at 384 nm than at 768 nm; and

FIG. 22 shows parameters to estimate threshold power of
widely-separated OPO. Q.,, and Q,, are estimated values
from experiments, where Q,,~1.5x10° and the cavity mode
is undercoupled (Q.,>Qo,). Threshold power depends on Q,,
and Q, values and is ~2.8 mW for signal and idler modes
with similar Q (10%) to the pump. Mode volume and mode
overlap are from finite-element-method simulation.

DETAILED DESCRIPTION

A detailed description of one or more embodiments is
presented herein by way of exemplification and not limita-
tion.


U.S. Patent Jan. 11, 2022 Sheet 21 of 22 US 11,221,540 B2

al voy
thid-order OPO 4 4 A
secont-order OPO 4 | i 4
Tinhared | | ghra-violet
Iam | | *384nm
(b) ; +
' |
4
Ee |
Ez l
2 |
Sl Winesdgesie r
$000

‘oS
v(THe)

FIG, 21


US 11,221,540 B2

23

times of the ideal case, if we assume the nonlinear param-
eters are similar for phase matching (y,,, ¥,,> Y,) and four
wave mixing (Y.,;p5 Yipsp)- We still use the natural frequency
mismatch for two reasons. First, this factor (I,1',/T?,,-1) is
typically within 2 and therefore does not make a very
significant difference. Second, it is difficult in practice to
estimate the phase modulation terms accurately a priori

The overall detuning should be zero to minimize the
threshold power. In another words, the natural frequency
mismatch should be a positive value that matches the
difference of the SPM and XPM (Aw =~ jypyirway» In
such case, the threshold power is reduced to

Tp? 1 AQ. eon estor? sip Gis)

LT, 2 = Sp Qip __Poltpltasttoi spin
r= 34) sam = GVO: Ongrl ror

This equation can give some important hints for OPO
competition besides frequency matching. First, only pump
frequency, but not signal and idler frequencies, is present in
this equation, which implies that widely-separated OPOs are
no different than closeband OPOs and therefore can be as
effective when optimized. Second, this equation suggests
that we can suppress the close-band OPO by controlling the
coupling Q. We notice that for the close-band OPOs, Q,,.
Q,-Q,, in general, because both intrinsic and coupling Q
values are similar. Therefore, the Q dependence of the
threshold power for the close-band OPO is Q.,/Q*,». com-
pared to Q.,/(@,, VQSQH) for the widely-separated OPO.
We define the suppression ratio to be the ratio of these two
values, i.c., WQISQU/Q,,. To suppress the close-band OPO
relative to widely-separated OPO, we need to increase Q,,,

Q,, and decrease Q,,. Moreover, Eq. S18 suggests that the ,

S

threshold power is minimized when the pump is critically ”

coupled (Q.,=Qo,), and signal and idler extremely under
coupled (Q..=Q.=®). In this case, the threshold power is
reduced to

(S19)

Gp eam teasttos? sip

Py = 5
20 V O20 Bngiy) Xone inp

While it is difficult to achieve different coupling for pump,
signal and idler modes in the close-band OPOs, it is possible
to design such coupling for the widely-separated OPOs, as
signal and idler frequencies are separated far way. Moreover,
we notice that such configuration of Q factors not only yields
the optimized threshold power for the widely-separated
OPO, but also naturally suppresses the close-band OPO
processes over widely-separated OPO processes. The sup-
pression ratio is 2 /QOp, and is ~2 assuming Q,.,
QoQo,- The suppression ratio can be further increased
when the pump modes are overcoupled, at a price of
increased threshold power. Although the coupling effects are
generally difficult to isolate to confirm such a suppression
ratio in practice, and we show some experimental data
supporting this argument.

In Eq. (S19), the parameters to optimize (besides fre-
quency matching and coupling Q engineering) appear in the
right term. The refractive indices and mode volumes of the
three modes together have a minor difference on the thresh-
old power (<10%) for the widely-separated case and the
close-band case (the frequency dependence of ¥ is not
studied in this paper, and requires further examination). In

45

60

24

particular, mode overlap (7,»,,) guarantees that the widely-
separated OPO process be in consideration when competing
processes are also potentially realizable. In our case, because
all the modes are single fundamental transverse-electric
(TE1) modes, the mode overlap is 90% of the perfect case
(ie., close-band OPOs), even when signal and idler are
separated =200 THz away.

In summary, analysis of the equations presented in this
section shows that widely-separated OPOs can operate at
similar threshold powers as close-band OPOs when opti-
mized. We find that, besides dispersion design for frequency
matching, coupling quality factor engineering (i.e., through
the coupling design) can also be used to optimize the
wide-band OPO process, by suppressing the dose-band

5 OPOs (see Section V for details) and/or minimizing the

threshold power of the wide-band process.

We used designs to demonstrate widely-separated OPOs
and summarize the devices parameters in FIG. 12 for several
designs. Design I generates OPO at 700 nm and 1300 nm by
920 nm pump. Design II generates OPO at 780 nm and 1500
nm by 1020 nm pump. The device parameters are labeled in
FIG. 12(a) and their typical values are summarized in FIG.
12(b). There are three parameters for the device disper-
sion—thickness (H), ring radius (RR), and ring width (RW)

s. The dispersion engineering has been already been discussed

in detail for design I in the main text. Here we provide
further data for design II in Fig. $2(c), where the pump is
tuned from 289 THz to 299 THz. The device has a radius of
23 um and the free spectral range (FSR) is close to 1 THz.
When the pump is below 291 THz, we can see that the
overall dispersion is anomalous, which is only suited for
close-band OPO generation. When the pump frequency is
between 292 THz to 294 THz, the dispersion around the
pump is normal and the signal and idler are widely separated
in frequency. While our simulation range is too small to
conclude for the 295 THz case, for pump frequencies above
296 THz, the device seems to be too normal to support any
frequency and phase matched modes. The overall trend is
similar to design I, but there are only one pair of widely
separated modes supported by this design.

In terms of the coupling, we use two waveguides to
couple pump, signal, and idler modes, because it is very
challenging to couple widely-separated signal and idler
within one waveguide. For example, we provide coupling
data for design I in FIG. 12(d). We use a straight waveguide
to couple the idler mode that has the largest wavelength.
Because of the evanescent coupling nature, pump and signal
modes are more confined within microring and waveguide
and therefore are not coupled efficiently by such a wave-
guide. We also use a pulley waveguide, which is a wave-
guide with a constant width (PW) wrapped around the
microring with a constant gap (PG) for a certain coupling
length (PL). Such a structure can efficiently couple pump
and signal despite the limited evanescent overlap, because of

5. the increased coupling length, while the waveguide width is

chosen so that it is cut off slightly below the idler wave-
length and therefore does not couple the idler mode. In FIG.
12(d), we show the calculated wavelength-dependent cou-
pling behavior of our pulley designs. The coupling curves
each have two dips (optimal coupling rates) at 325 THz (950
nm) and 450 THz (714 nm) for design I, and 285 THz (1050
nm) and 380 THz. (790 nm) for design Il, respectively.
Two dispersion design principles for widely-separated
POs include phase and frequency matching for the widely-

5 separated mode set and normal dispersion at the pump mode.

These two design principles, when separated, have both
been achieved previously. Normal dispersion at one wave-


U.S. Patent Jan. 11, 2022 Sheet 16 of 22 US 11,221,540 B2

a
oa
(a) () ~ 400TH Blew THe ~ 00TH
fe | dy thy |
pump ts : ty H
puny signal 4 Ht
waveguide 4 \ i
( | Ag
300
_-, Ob
=m
2 16F
& ih (sSOgWONR, oy
_ A 7/ I16] $id WEMR
50} (20) AIN microring
fo .
OT al
2
= dr
“Brgy [7 NaF AN
S ‘ot 7 SOp_ SiN
va) 10015020015) OAD
y (THz)

FIG. 16


U.S. Patent

Jan. 11, 2022

a
10 SS

Sst

= i a “> Roa,

Ba SI ao

eb 1D Poop
SH) | SS

10
31436 38 300 302 Sk 38 308 20

v (Thy) 05 i
S14 346 348 320 322 324 328 328

Sheet 8 of 22

{
if
on
i
{

t vp (Tha)
iam}
0 1300 1200 1100 1000900 800 100
7 t RW= 1150 om vp S2t4 THe 4
i

8

3

OPO spectra (dB)

sZss. 8858. 8888a

a \ paiaemaaas

RW= 1150 om vy 3280 THe 4
—_——aA

RW= 1150 nm | wpe ShITHZ

L We 150ne Y= del Te
t RW = 115000 vp? 0066 THz
i | ee ee)
v(t
FIG. 8

US 11,221,540 B2


US 11,221,540 B2

17

zero-dispersion frequency (ZDF) is at ~321 THz. The dis-
persion is anomalous for smaller frequencies and normal for
larger frequencies. The frequency mismatch (Av) is plotted
[FIG. 7(d)] with pump frequency (v,) ranging from 314 THz
to 328 THz. When v,=322 THz, nearby modes show an
overall small normal dispersion, and there are two widely
separated mode pairs that are frequency matched (Av=0). In
contrast, larger values of vp have large normal dispersion
and do not lead to widely separated OPO, Smaller v, may
allow widely separated OPO (e.g., 319 THz case), but the
anomalous dispersion around the pump results in several
close-band competitive OPO processes, making widely
separated OPO unavailable in general.

We also simulate devices that have different RW but the
same RR and H, with the dispersion plotted in FIG. 8a),
When RW increases from 1140 nm to 1160 nm, the ZDF red
shifts from 325 THz to 321 THz, remaining within our laser
scanning range. We thus have a prescription for geometries
to experimentally observe the transition from close-band to
widely separated OPO processes.

We fabricate devices as described below with fixed H and
varying RW, and characterize them as a function of v, near
the ZDF. The results are summarized in FIG. 8(6) and FIG.
8(c). The output OPO spectra are recorded by an optical
spectrum analyzer (OSA), while the pump is scanned for
modes that transit from anomalous to normal dispersion,
with an example in FIG. 8(c) for fixed RW=1150 nm. The
OPO signal and idler frequencies for all RW and v,, are then
plotted in FIG. 8(6), v, for OPO with the widest separation

red shifts from 327.8 THz (RW=1160 nm) to 325.7 THz 3

(RW=1150 nm) and 323.8 THz (RW=1140 nm), following
the shift in device dispersion. Focusing again on the
RW=1150 nm spectra for several different v, [FIG. 8(c)}, we
clearly observe the trend predicted previously when tuning

y, from anomalous to normal. When the pump dispersion is 3

anomalous, OPO signal and idler bands are closely spaced
around the pump [top panel in FIG. 8(c)]. When the pump
dispersion is slightly normal, the OPO signal and idler have
increasingly large spectral separation as v,, increases [second
to fourth panels in FIG. 8(c)]. However, when the pump
dispersion is too normal, no widely separated OPO is
observed, and only very close-band OPO is seen [bottom
panel in FIG. 8(c)]. The RW=1160 nm device [red in FIG.
8(b)| has a similar trend but fewer pumping modes in the
transition to the slightly normal region. This trend agrees
with the prediction in FIG. 7(d), although the experimental
v, is 2 THz larger than predicted, which is likely due to
uncertainties in device fabrication.

We focus on the RW=1160 nm device and study its power
dependence at v,=322 THz in FIG. 9. The OPO signal and
idler have a spectral separation that is too large for a single
waveguide [FIG. 7(a)] to out-couple both frequencies efli-
ciently. We therefore use two waveguides to separate the
coupling tasks, as shown in FIG. 9(a). The bottom pulley
waveguide couples the pump and signal light together, while
being cutoff at telecom wavelengths. The top waveguide
couples telecom light efficiently, but does not couple the
pump and signal light due to a limited spatial overlap that
prevents effective evanescent coupling. The combined cou-
pling geometry is designed to have coupling Q=(1-2)x10°
for pump, signal, and idler modes. In experiment, we verify
that the fabricated device has intrinsic Q=(2-3)x10° and
loaded Q=1x10° for TE1 modes in the pump band, which
corresponds to loaded cavity linewidths of ~300 MHz. With
such high Q, the device shows large thermal bistability at
milliwatt pump powers, as shown in FIG. 9(6). For each
pump power, we situate the pump detuning near the dip of

20

2

40

&

g

18

the cavity resonance and measure the generated OPO spec-
trum. Three representative spectra are shown in FIG. 9(e),
with pump detuning indicated by the open circles in FIG.
9(6). For 1 mW pump power at v,=323.8 THz (926.5 nm),
the top panel in FIG. 9(e) shows that a widely separated
OPO is generated with signal at 419.8 THz (714.6 nm) and
idler at 227.8 THz (1317 nm). The signal-idler separation is
192 THz, comparable to the largest reported value for WGM
resonators (~230 THz), where the idler frequency was
inferred (signal and idler were both in the infrared). With an
increased pump power of 1.6 mW, an additional pair is
generated at 388.8 THz (771.6 nm) and 258.8 THz (1187
nm), as shown in the middle panel in FIG. 9(e). With a
further increase in pump power to 2.5 mW, clustered combs

5 are generated around the second signal-idler pair, while the

first pair remains unaccompanied by other spectral tones
[bottom panel in FIG. 9(e)].

These two OPO pairs measured in experiment agree quite
well with the theoretical predictions [FIG. 9(d)]. where pair
Tis predicted to be at 423 THz (I-s) and 221 THz (I-i) and
pair II at 389 THz (II-s) and 255 THz (II-i). The m numbers
of these modes are {420, 383, 310, 237, 200} for {I-s, II-s,
p. Ili, I-i} [labeling scheme in FIG. 9(d)]. These mode
numbers clearly satisfy phase matching (Am=0). Moreover,

the fact that the clustered comb is generated in the I pair, but

not in the I pair, is not coincidental and can be explained as
follows. All the mode pairs satisfying phase matching are
plotted in FIG. 9(d). Each mode is represented by an open
circle, and the cavity free spectral range (FSR) is ~1 THz.
Although both I and II satisfy frequency matching, the
densities of mode pairs (within a given range of frequency
mismatch) around | and II are different. Because material
dispersion is much larger at higher frequencies, the I pair
exhibits larger dispersion and has sparser modes in the
neighborhood of the tolerated frequency mismatch, which
can be estimated by the cavity linewidth (300 MHz). In
other words, the modes near II are preferred for clustered
comb generation considering both mode density and fre-
quency matching. Moreover, because of the normal disper-
sion around the pump, there are no competitive processes in
the pump band even at higher pump power [FIG. 9(e)]. A
power-dependence study [FIG. 9(c)] indicates a threshold of
(0.9+0.1) mW for the first set of OPO lines. The second OPO
has a threshold of (1.5+0.2) mW, while its subsequent

5 clustered frequency comb has a threshold near 2.5 mW.

For applications, the delivered output power of the OPO
is an important metric. In our devices, the typical OPO
signal and idler fields are 10 dB to 20 dB lower than the
pump [FIG. 9(e)]. While this is actually better than previous
widely separated OPO works (where the signal and idler are
30 dB to 50 dB lower than the pump [20,21]) and not
uncommon for microcavity OPOs regardless of spectral
separation (e.g., ~15 dB difference in Ref. [32]), improving
the conversion from pump to signal is nevertheless impor-

5 tant. To do so, we anticipate that more advanced coupling

engineering is needed to increase the out-coupling effi-
ciency. While this will generally result in a higher threshold
power, depending on the application, an appropriate balance
can be struck between output power (e.g., for the visible
wavelength signal) and overall power efficiency.

Although close-band OPO with spectral tones near the
pump are successfully suppressed, the generation of two
OPO pairs with pair II eventually exhibiting a cluster of
tones might be unwanted in applications. Here, we show

5 how the ring geometry can be tuned to achieve a dispersion

that supports only one single set of widely separated OPO
tones.


US 11,221,540 B2

11

ear phase shifts are small then OPO at low power can be
achieved with a natural cavity mismatch Aw,=0.

It should be appreciated that optical parametric oscillator
200 is a chip-integrated optical parametric oscillator with
signal and idler output fields as idler coherent light 206 and
signal coherent light 207 that are widely separated in fre-
quency and that are produced from silicon nanophotonics. In
an embodiment, optical parametric oscillator 200 includes
microring resonator 204 with integrated waveguide 203
on-chip for coupling pump coherent light 205 into microring
resonator 204 and extracting generated light (206, 207) out
of microring resonator 204. Microring resonator 204 and
waveguide 203 are defined in a thin film (sub-micrometer)
of a Kerr nonlinear medium such as silicon nitride (Si;N,)
that is disposed on a lower cladding (substrate cladding 201)
of silicon dioxide (SiO,) and can be grown using low
pressure chemical vapor deposition techniques on a silicon
substrate.

In optical parametric oscillator 200, the optical parametric
oscillation mechanism is based on cavity-enhanced degen-
erate four-wave mixing, a nonlinear optical process in which
pump coherent light 205 is injected at a pump wavelength (at
pump frequency v,) that is converted to signal and idler
wavelengths (respectively at signal frequency v, and idler
frequency v,), subject to energy and momentum conserva-
tion. The process for producing idler coherent light 206 and
signal coherent light 207 from pump coherent light 205 by
optical parametric oscillator 200 that has balanced paramet-
ric dispersion 210 involves dispersion of microring resona-
tor 204 (cavity and resonator are used interchangeably here)
to support a pair of widely-separated signal and idler wave-
lengths (for idler coherent light 206 and signal coherent light
207). The choice of wavelengths can be broadly tuned by
adjusting the geometry (cross-section of microring resonator
204) and the pump wavelength of pump coherent light 205.
The nanophotonic microring resonator 204 has high optical
quality factors (low loss) and small modal volumes (strong
optical field confinement), which together provide a thresh-
old power less than or equal to the one milliwatt level.

Optical parametric oscillator 200 can be made by scalable
manufacturing based on silicon photonics so that pump
coherent light 205 produces outputs (206, 207) that are
widely separated. Optical parametric oscillator 200 covered
visible and telecommunications wavelengths using a near-
infrared pump with coarse tuning and fine tuning of wave-
lengths of output occur by adjustment to geometry of
microring resonator 204. Moreover, optical parametric oscil-
lator 200 is very power efficient. The threshold power of
pump coherent light 205 for producing idler coherent light
206 and signal coherent light 207 is at the sub-mW level,
which is 50 times smaller than conventional devices. With
such small power consumption, optical parametric oscillator
200 can be directly integrated with on-chip or compact
pump lasers that provide pump coherent light 205 that can
operate in the near-infrared. Further, optical parametric
oscillator 200 produces idler coherent light 206 and signal
coherent light 207 with sub-mW power of pump coherent
light 205 in an absence of an intermediate amplifier as a
considerable practical benefit.

Optical parametric oscillator 200 solves the problem of
on-chip generation of coherent laser light at frequencies for
which suitable laser gain media do not exist or do not
perform very well. Optical parametric oscillator 200 has
relevance in context of integrated photonics, where technol-
ogy is being built to enable routing and manipulation of light
on a chip, including at visible wavelengths for atomic
systems used as wavelength references and clocks. Spec-

30

40

&

12

troscopy and sensing of biochemical systems on a chip that
is an area of use for optical parametric oscillator 200 in
which optical parametric oscillator 200 is combined with
integrated photonics and microfluidics. Advantageously,
optical parametric oscillator 200 converts near-infrared or
telecom wavelengths to visible light and retains coherence
properties associated with lasers while operating at a wave-
length relevant to the aforementioned applications.

Optical parametric oscillator 200 can be made in various
ways. In an embodiment, a process for making optical
parametric oscillator 200 includes: depositing substrate
cladding 201, e.g., forming 3-um thick silicon dioxide by
thermal oxidation of a silicon wafer. Optionally, substrate
cladding 201 can be provided by a uniform material of
properties described earlier, e.g., a fused silica or quartz
substrate. The process also includes depositing the material
including microring resonator 204 and waveguide 203, e.g.,
stoichiometric silicon nitride (Si;N,) via low pressure
chemical vapor deposition; spin coating and patterning of
electron-beam resist via electron beam lithography to create
the resonator and waveguide shapes in the electron-beam
resist layer: transferring of pattern from electron-beam resist
into the microring 204 and waveguide 203 material via
reaction ion etching; removing electron-beam resist; clean-
ing of sample using solvents (e.g., acetone, methanol, iso-
propanol) or acids (e.g., sulfuric acid, hydrogen peroxide) as
selected; depositing cover cladding layer as desired; and
optionally separating starting substrate into chips and pre-
paring facets (e.g., via cleaving, reactive ion etching, or
dicing and polishing) to enable edge coupling via optical
fibers.

The process for making optical parametric oscillator 200
also can include wet etching to thin microring 204 or
waveguide core layer 203 to a select thickness. Trimming
can occur after initial film deposition or after dry etching and
resist removal, e.g., prior to depositing cover cladding 202.
Post-fabrication annealing in an N, or O, environment at
1100° C. for 3 hours can occur to limit absorption losses in
the deposited materials. This can be performed prior to
deposition of the cover cladding layer or after deposition of
the cover cladding layer. Electron-beam lithography can be
substituted by photolithography with adequate resolution to
define the desired features, e.g., 193 nm or 248 nm deep UV
lithography, often provided by a step and repeat tool, which
is referred to as a stepper.

In an embodiment, a process for producing idler coherent
light 206 and signal coherent light 207 from pump coherent
light 205 using optical parametric oscillator 200 includes
using a pump laser source whose frequency matches pump
frequency 214, wherein a laser linewidth is narrower than
the optical cavity mode linewidth in the pump frequency
band; confirming that pump laser light is coupled into a
mode of the cavity by tuning the pump laser frequency to
produce a dip in pump transmission signal carried by

5 waveguide 203; adjusting the frequency of the pump laser to

be within the pump transmission dip; increasing the pump
power to be greater than the threshold value P,,, such that if
conditions for balanced parametric dispersion and threshold
are satisfied, optical parametric oscillator 200 produce idler
coherent light 206 and signal coherent light 207; and option-
ally optimizing the pump frequency based on maximizing
generated signal coherent light 207.

Optical parametric oscillator 200 has numerous advanta-
geous and unexpected benefits and uses. In an embodiment,

5 a process producing idler coherent light 206 and signal

coherent light 207 from pump coherent light 205 with
optical parametric oscillator 200 includes: receiving pump


US 11,221,540 B2

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US 11,221,540 B2

1
OPTICAL PARAMETRIC OSCILLATOR AND
PRODUCING IDLER COHERENT LIGHT
AND SIGNAL COHERENT LIGHT FROM
PUMP COHERENT LIGHT

CROSS REFERENCE TO RELATED
APPLICATIONS

The application claims priority to U.S. Provisional Patent
Application Ser. No. 62/901,456, filed Sep. 17, 2019, the
disclosure of which is incorporated herein by reference in its
entirety,

STATEMENT REGARDING FEDERALLY
SPONSORED RESEARCH

This invention was made with United States Government
support from the National Institute of Standards and Tech-
nology (NIST), an agency of the United States Department
of Commerce, under Agreement No. 70NANB10H193 and
the Defense Advanced Research Projects Agency (DARPA),
an agency of the United States Department of Defense. The
Government has certain rights in the invention. Licensing
inquiries may be directed to the Technology Partnerships
Office, NIST, Gaithersburg, Md., 20899; voice (301) 301-
975-2573; email tpo@nist.gov; reference NIST Docket
Number 19-052US1.

BRIEF DESCRIPTION

Disclosed is an optical parametric oscillator for producing
idler coherent light and signal coherent light from pump
coherent light by balanced parametric dispersion, the optical
parametric oscillator comprising: substrate cladding; a

microring resonator disposed on the substrate cladding and 3

comprising: a Kerr nonlinear medium shaped into a micror-
ing with a radius R, a height H, and a width W that provides
a balanced parametric dispersion: and that: receives pump
coherent light from a waveguide; and produces idler coher-
ent light and signal coherent light from the pump coherent
light, the idler coherent light and signal coherent light
produced according to the balanced parametric dispersion of
the microring resonator; and the waveguide disposed on the
substrate cladding in optical communication with the
microring resonator and comprising a Kerr nonlinear
medium and that: receives pump coherent light; and com-
municates the pump coherent light to the microring resona-
tor for production of the idler coherent light and the signal
coherent light from the pump coherent light.

Disclosed is a process for producing idler coherent light
and signal coherent light from pump coherent light with the
optical parametric oscillator of claim 1, the process com-
prising: receiving the pump coherent light by the waveguide;
communicating the pump coherent light from the waveguide
to the microring resonator; and producing the idler coherent
light and the signal coherent light from the pump coherent
light according to the balanced parametric dispersion of the
microring resonator.

BRIEF DESCRIPTION OF THE DRAWINGS

The following description should not be considered lim-
iting in any way. With reference to the accompanying
drawings, like elements are numbered alike.

FIG. 1 shows an optical parametric oscillator in perspec-
tive view (panel A), top view (panel B), and cross-section
(panel C) along line A-A shown in panel B;

40

&

2

FIG. 2 shows an optical parametric oscillator in perspec-
tive view (panel A), top view (panel B), and cross-section
(panel C) along line A-A shown in panel B;

FIG. 3 shows laser input for optical parametric oscillator
in panel A, output from the optical parametric oscillator in
panel B, and a parametric dispersion curve of the optical
parametric oscillator that has balanced parametric dispersion
in panel C;

FIG. 4 shows a parametric dispersion curve for an optical
parametric oscillator that has balanced parametric disper-
sion;

FIG. 5 shows a plurality of parametric dispersion curves
compared with balanced parametric dispersion;

FIG. 6 shows a plurality of parametric dispersion curves
that have balanced parametric dispersion;

FIG. 7 shows a nanophotonic visible-telecom optical
parametric oscillator. (a) Schematic indicating that the
microring device uses cavity-enhanced degenerate four-
wave mixing (dFWM) to generate signal and idler light that
have frequencies widely separated from the input pump. All
interacting modes (pump, signal, and idler) are fundamental
transverse-electric modes (TE1), with their dominant elec-
tric field components shown in insets. The input pump and
the output signal and idler are all coupled with the same
waveguide in this scheme. (b) Cross-section view of the
microring shows the air cladding and silicon dioxide sub-
strate, and two key geometric parameters, ring width (RW)
and height (H). These two parameters, together with the ring
outer radius (R), unambiguously determine the microring
dispersion. (c) Dispersion curve (D) of a typical geometry,
with R=23 um, RW=1160 nm, and H=510 nm. D=0 when
the pump frequency v, is ~321.7 THz (932.5 nm), as shown
in the zoomed-in inset. The dispersion is anomalous (D>0)
when v, is smaller, and normal (D<0) when v, is larger. (d)
Frequency mismatch (Av) for dFWM for the geometry in (c)
at various values of v,. When the pump is slightly normal at
322 THz (red), there are two cases in which signal and idler
modes are phase/frequency matched, with both suitable for
widely separated OPO. Av is calculated for specific mode
number (m) sets, because dF WM requires the phase-match-
ing condition to be satisfied, i.e., m,+m,-2m,. The mode
frequency for each mode number is calculated for the
geometry in (c) by the finite-element method;

FIG. 8 shows OPO frequencies critically depend on ring
width (RW) and pumping frequency (v,). (a) Simulated
dispersion (D) curves for different RW. The zero-dispersion
frequency (ZDF) blue shifts with decreasing RW. (b) Experi-
mentally recorded OPO output (signal and idler) frequencies
(left axis, v, and v,) and wavelengths (right axis, 4, and 2,)
of the aforementioned geometries when v,, is varied around
the ZDF. Widely separated OPO occurs when the dispersion
is slightly normal because potential close-band OPO pro-
cesses are inhibited. (c) OPO spectra for the RW=1150 nm
device when v,, is varied. When scanning v, from a mode in

5 the anomalous region to one in the normal region, the

spectral separation of the OPO signal and idler increases
from 9 THz to 37 THz, 61 THz, and 178 THz, and finally
decreases to 7 THz (from top to bottom). On the y axis, 0 dB
is referenced to 1 mW, i.e., dBm;

FIG. 9 shows power dependence of the visible telecom
OPO. (a) When the OPO frequencies are separated widely
into the visible-telecom regime, two waveguides are needed
to couple the visible and telecom light efficiently. The
straight waveguide (top) is used for out-coupling the tele-

5 com (idler), and the pulley waveguide (bottom) is for

out-coupling the visible (signal). (b) Transmission (T) traces
for v,~322 THz show bistabilities with various pump pow-


a2 United States Patent

Srinivasan et al.

US011221540B2

US 11,221,540 B2
Jan. 11, 2022

(10) Patent No.:
(45) Date of Patent:

(54)

(29)

(72)

(73)

(*)

(21)
(22)
(65)

(60)

GD

(52)

(58)

OPTICAL PARAMETRIC OSCILLATOR AND
PRODUCING IDLER COHERENT LIGHT
AND SIGNAL COHERENT LIGHT FROM
PUMP COHERENT LIGHT

Applicant: Government of the United States of
America, as represented by the
Secretary of Commerce, Gaithersburg,
MD (US)

Inventors: Kartik Arvind Srinivasan, Rockville,

MD (US); Xiyuan Lu, Montgomery

Village, MD (US)

GOVERNMENT OF THE UNITED
STATES OF AMERICA, AS
REPRESENTED BY THE
SECRETARY OF COMMERCE,
Gaithersburg, MD (US)

Assignee:

Notice: Subject to any disclaimer, the term of this

patent is extended or adjusted under 35
U.S.C. 154(b) by 0 days.

Appl. No.: 17/023,732
Filed: Sep. 17, 2020

Prior Publication Data
US 2021/0080805 Al Mar. 18, 2021

Related U.S. Application Data

Provisional application No. 62/901,456, filed on Sep.
17, 2019.

Int. Cl.

GO2F 139 (2006.01)

GO2F 135 (2006.01)

US. Cl.

CPC . G0O2F 1/395 (2013.01); GO2F 1/3501

(2013.01); GO2F 1/3509 (2021.01)
Field of Classification Search
CPC veessntenenenenennanaieneeenene GOQF 1/395
See application file for complete search history.

(56) References Cited

U.S. PATENT DOCUMENTS

9,490,605 B2* 11/2016 Gaeta
10,261,391 B2* 4/2019 Casale

(Continued)

HOIS 5/5054
GO2B 6/29338,

OTHER PUBLICATIONS

J. A. Black, S. Yu, R. Streater, J. R. Stone, X. Lu, G. Moille, K.
Srinivasan, and S. B. Papp, “Optical synthesis by spectral transla-
tion ,”in Conference on Lasersand Electro-Optics, OSA Technical
Digest (Optical Society of America, 2020), paper STu3H.1. (Year:
2020).*

(Continued)

Primary Examiner — Rhonda $ Peace
(74) Attorney, Agent, or Firm — Ofiice of Chief Counsel
for National Institute of Standards and Technology

(7) ABSTRACT

An optical parametric oscillator for producing idler coherent
light and signal coherent light from pump coherent light by
balanced parametric dispersion includes: substrate cladding;
a microring resonator disposed on the substrate cladding and
including: a broadly transparent Kerr nonlinear medium
including a annulus with a radius R, a height H, and a width
W that provides a balanced parametric dispersion: and that:
receives pump coherent light from a waveguide; and pro-
duces idler coherent light and signal coherent light from the
pump coherent light, the idler coherent light and signal
coherent light produced according to the balanced paramet-
ric dispersion of the microring resonator; and the waveguide
disposed on the substrate cladding in optical communication
with the microring resonator and comprising a broadly
transparent medium such as silicon nitride and that: receives
pump coherent light; and communicates the pump coherent
light to the microring resonator for production of the idler
coherent light and the signal coherent light from the pump
coherent light.

20 Claims, 22 Drawing Sheets



U.S. Patent Jan. 11, 2022 Sheet 10 of 22 US 11,221,540 B2

=

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4600 1400, 1200, = 1000 900 700 600

at
tt <n r :
| [fH 6am
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ss

20) 250 300 380 400 450 00

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FIG. 10


US 11,221,540 B2

Sheet 9 of 22

Jan. 11, 2022

U.S. Patent

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US 11,221,540 B2

15

using III-V semiconductors, but the wavelength coverage is
limited by the available gain media and requires nontrivial
heterogeneous integration to be compatible with a silicon
chip. Another approach is to use nonlinear optics to create
light at new frequencies from existing lasers. There are
many second/third-order (yy) nonlinear optical pro-
cesses for this purpose, including optical parametric oscil-
lation (OPO), second/third-harmonic generation (SHG/
THG), sum frequency generation (SFG), and stimulated
four-wave mixing/optical parametric amplification
(StFWM/OPA). Among these processes, OPO is uniquely
suitable to generate coherent light over a wide spectral
range, because the generated light is not limited to harmon-
ics of pump frequencies (unlike SHG/THG), and only one
pump laser is required (unlike SFG/StF WM/OPA). Histori-
cally, x OPO has been particularly efficient in creating
coherent light across wide spectral ranges. Half a century
ago, coherent OPO light from 970 nm to 1150 nm was
generated by a 529 nm pump laser in a LiNbO, crystal.
Later, the OPO signal wavelength was brought into the
visible (from 537 nm to 720 nm) by a 308 nm pump laser in
a BaB,O, crystal. Nowadays, %° OPO systems have
become a laboratory workhorse tool in the generation of
coherent, tunable visible light, particularly when pumped by
a Ti:sapphire laser. However, nanophotonic implementa-
tions of OPO that can reach visible wavelengths are still
lacking.

In this Example, a nanophotonic ¥°) OPO for on-chip
visible light generation is described. We use % rather than
© for two important reasons. First, x
© processes, are naturally compatible with silicon photon-
ics. Second, as the x’ OPO consumes two pump photons
for each generated signal/idler pair, visible wavelengths can
be reached through an easily available infrared pump laser,

in contrast to a x? OPO, which needs a UV pump laser. 3

Although ideas for how to achieve widely separated

OPO have been demonstrated in photonic-crystal-fib
based systems and then introduced to silicon nanophotonics
theoretically over a decade ago, because of the challenging
dispersion engineering requirements, such nanophotonic
OPO has not been experimentally demonstrated. This is in
contrast to other wide-band nonlinear processes, ¢.g., nano-
photonic SHG/THG, which have been extensively reported.
Recently, widely separated OPO has been achieved in whis-
pering-gallery mode (WGM) platforms with larger foot-
prints, including crystalline MgF, microcavities and SiO,
microtoroids, but the threshold powers are relatively large,
and the spectra of the OPO output have been restricted to the
infrared.

To demonstrate nanophotonic visible telecom OPO, we
use the silicon nitride (Si,N.,) platform, whose advantageous
characteristics for silicon-based nonlinear nanophotonics,
including octave-spanning frequency combs, frequency con-
version/spectral translation, entanglement generation and
clustered frequency comb generation, have by now been
well established. Here we show, for the first time, on-chip
OPO with signal and idler at visible and telecom frequen-
cies, e.g., 419.8 THz (714.6 nm) and 227.8 THz (1316.9
nm), respectively. The OPO process is power efficient due to
nanophotonic confinement and strong spatial mode overlap,
and has an ultra-low threshold power of (0.9+0.1) mW. In
contrast to recent microresonator OPO works that use
between 50 mW and 380 mW of pump power to achieve
widely separated signal and idler in the infrared, our devices
use only milliwatt-level power, without intermediate optical
amplifiers, to achieve widely separated signal and idler in
the visible and telecom, respectively. We further show that

processes, unlike 3

S

0

3

40

16

the OPO frequencies can be readily controlled by changing
the device geometry. In particular, we demonstrate OPO
with signal and idler at 383.9 THz (781.4 nm) and 202.1
THz (1484 nm), respectively, by pumping at 293.0 THz
(1024 nm). This signal wavelength is suitable for rubidium
vapor, and the pump wavelength is accessible from compact
semiconductor chip lasers.

Our OPO devices are based on cavity-enhanced degen-
erate FWM (dFWM), which involve conservation of both
momentum and energy for the interacting optical modes. For
the same mode family, momentum conservation is simpli-
fied to conservation of the azimuthal mode number, i.e.,
Am=m,+m,-2m,=0, where the subscripts s,i,p denote signal,
idler, and pump, respectively. Energy conservation requires
the central frequencies of the cavity modes to have a
mismatch (Av-v,+v,-2v,) within the cavity linewidths, ie.,
IAvi<v,/Q,, where k=s, i, p, and Q, is the loaded quality
factor for the k mode. We note that achieving such phase and
frequency matching across visible and telecom bands has
been demonstrated in silicon nanophotonics only for photon-
pair generation and spectral translation, where a mode-
splitting approach enables the identification of specific azi-
muthal modes separated by hundreds of THz. We employ a
similar approach here, focusing on fundamental transverse
electric (TE1) modes only, which have high-Q, strong modal
confinement (V-), and good mode overlap (7). These attri-
butes are involved for achieving low-threshold operation.

However, the above design principles do not guarantee
that the targeted wide-band OPO process will occur. The
process also can win over all other competing processes that
are matched in phase and frequency, including OPO in the
pump band, clustered frequency combs in the signal and
idler bands, and other nonlinear processes (e.g., stimulated
Raman scattering and THG). Some report telecom-to-visible
spectral translation via stimulated dFWM did not exhibit
widely separated OPO, because without the seed telecom
light, close-to-pump OPO processes dominate. Thus, unlike
previous work in wide-band silicon nonlinear nanophoton-
ics, visible-telecom OPO faces a more stringent requirement
not only on enhancing the process of interest, but also on
suppressing all competing processes at the same time.

In particular, OPO in the pump band can be suppressed if
the pump modes are in the normal dispersion regime, which
corresponds to a negative dispersion parameter (D).

where c, 2, and n~ represent the speed of light, vacuum
wavelength, and effective mode index, respectively. D<0 is
equivalent to Av<0 when the signal and idler modes are near
the pump mode. Therefore, we need to design the device to

5 have Av<0 when signal and idler are near the pump, and

Av=0 when signal and idler are widely separated.

We use the aforementioned design principles to guide
numerical simulations for the widely separated OPO. FIG.
7(b) shows a cross-sectional view of the microring. The
Si,N, core has a rectangular cross section, described by ring
width (RW), thickness (H), and ring radius (RR). We use
these parameters to tailor the geometric contribution to the
dispersion. We note that self-/cross-phase modulation is
negligible in our device, so that we can use the natural cavity

5 frequencies to design our OPO.

FIG. 7(c) shows the dispersion parameter of a device with
RW=1160 nm, H=511.0 nm, and RR=23 pm, where the


US 11,221,540 B2

13

coherent light 205 by waveguide 203: communicating pump
coherent light 205 from waveguide 203 to microring reso-
nator 204; and producing idler coherent light 206 and signal
coherent light 207 from pump coherent light 205 according
to balanced parametric dispersion 210 of microring resona-
tor 204. According to an embodiment, the process further
includes receiving, by second waveguide 203.2 in optical
communication with microring resonator 204 and including
silicon nitride, idler coherent light 206 and signal coherent
light 207 from microring resonator 204.

‘Additional steps can be performed in producing idler
coherent light 206 and signal coherent light 207 with optical
parametric oscillator 200. Such steps can include injection
locking of a pump laser producing coherent pump light 205.
Here, a chip-based Fabry-Perot laser diode is butt-coupled to
the optical parametric oscillator chip. Optical feedback
provided by resonant backscattering from the microring will
injection lock the pump laser at a frequency matching the
microring resonator pump mode frequency, thereby select-
ing a single frequency output from the multimode Fabry-
Perot laser that is automatically aligned with the microring
resonator pump mode. This process alleviates the need to
fine tune the pump laser frequency to match the microring
resonator pump mode frequency.

It should be appreciated that idler coherent light 206 and
signal coherent light 207 can be used for applications such
as spectroscopy of visible wavelength atomic or atomic-like
systems, including warm atomic vapors, cold atom systems,
quantum dots, nitrogen vacancy centers in diamond, and

semiconductor quantum dots. Here, the microring resonator 3

dispersion is chosen to create optical parametric oscillator
200 in which either idler coherent light 206 or signal
coherent light 207 is spectrally resonant with the known
optical transition frequency of one of the above systems.

Feedback to the optical parametric oscillator to tune the 35

signal coherent light 207 or idler coherent light 206 and lock
its frequency to the atomic or atomic-like transition can be
achieved through temperature control of the optical para-
metric oscillator chip.

Optical parametric oscillator 200 and processes disclosed
herein have numerous beneficial uses that include producing
output optical frequencies (i.e., idler coherent light 206 and
signal coherent light 207) that can be situated anywhere
within an exceptionally broad range of frequencies that is
fundamentally only limited by energy conservation required
by the underlying four-wave mixing process. It is contem-
plated that a Kerr nonlinear resonator pumped at a frequency
of 380 THz can produce signal frequencies anywhere
between slightly above 380 THz and as high as almost 760
THz. Material constraints (e.g., absorption at certain wave-
lengths) can limit a maximum output frequency to 650 THz
under certain conditions. Actual frequencies produced can
depend on the balanced dispersion profile and in particular
the positions of the zero crossing points, nodes (216, 219),
which are adjustable based on microring 204 geometry
(thickness H, width W, and radius R). Coherent light can be
generated over a range of frequencies that is much broader
than conventional semiconductor laser materials. In an
embodiment, a single chip is fabricated with optical para-
metric oscillator devices made of a single material and that
produces green, yellow, orange, and red colors. It should be
appreciated that such is not provided with conventional
semiconductor laser technologies. Advantageously, optical
parametric oscillator 200 overcomes limitations of technical
deficiencies of conventional compositions such as the afore-
mentioned semiconductor lasers and optical parametric
oscillator based on the second-order optical nonlinearity.

2

40

&

14

The former produces coherent light in a wavelength range
dictated by their electronic bandgap such that multiple
materials are combined for a wide wavelength range to be
covered. The latter requires a pump frequency that is equal
to the sum of the signal frequency and idler frequency,
which can be at ultraviolet wavelengths for which many
Kerr nonlinear media are absorbing.

Conventional direct laser generation on-chip is limited by
availability and spectral bandwidth of laser gain media,
which is overcome by optical parametric oscillator 200
Various types of chip-integrated visible wavelength lasers
are available but are not as broadly tunable as optical
parametric oscillator 200. Moreover, conventional optical
parametric oscillator technology lack wide spectral separa-
tion between signal and idler as compared with optical
parametric oscillator 200 even though the conventional
technology is based on silicon photonics. Because silicon is
a technologically mature fabrication platform accessible
through foundry facilities, optical parametric oscillator 200
has a relatively low cost of production and enjoys scalable
fabrication processes with integration into systems. Optical
parametric oscillator 200 can include sub-mW pump power
for on-chip or compact integration with a near-infrared
pump laser. Integration with a compact near-infrared pump
laser provides near readily available conversion of near
infrared light to visible with optical parametric oscillator
200.

Optical parametric oscillator 200 and processes herein
generate coherent light at optical frequencies that are not
commonly available in integrated photonic chip platforms
For example, visible coherent light can be generated from a
near-infrared coherent pump.

The articles and processes herein are illustrated further by
the following Examples, which are non-limiting,

EXAMPLES
Example 1

Milliwatt-Threshold Visible-Telecom Optical
Parametric Oscillation Using Silicon Nanophotonics

The on-chip creation of coherent light at visible wave-
lengths is crucial to field-level deployment of spectroscopy
and metrology systems. Although on-chip lasers have been
implemented in specific cases, a general solution that is not
restricted by limitations of specific gain media has not been
reported, to the best of our knowledge. Here, we propose
creating visible light from an infrared pump by widely
separated optical parametric oscillation (OPO) using silicon
nanophotonics. The OPO creates signal and idler light in the
700 nm and 1300 nm bands, respectively, with a 900 nm
pump. It operates at a threshold power of (0.9+0.1) mW,
over 50x smaller than other widely separated microcavity
OPO works, which have been reported only in the infrared.
This low threshold enables direct pumping without need of
an intermediate optical amplifier. We further show how the
device design can be modified to generate 780 nm and 1500
nm light with a similar power efficiency. Our nanophotonic
OPO shows distinct advantages in power efficiency, opera-
tion stability, and device scalability, and is a major advance
towards flexible on-chip generation of coherent visible light
On-chip generation of coherent light at visible frequencies
is critical for miniaturization and field-level deployment for
spectroscopy and metrology, e.g., wavelength-stabilized ref-
erence lasers based on atomic vapors and optical atomic
clocks. One approach is to develop on-chip lasers directly


U.S. Patent Jan. 11, 2022 Sheet 6 of 22 US 11,221,540 B2

Se no OPO vp? 385 THz 4
0
5 4
bE Ave 03TH2 vprdiTte
0 — eee <
LL — a ee _ |
—_ _—
; RO * yy2380TH2 /
_ Av=230TH2 ps8 THe /
= 0 b os <= &
oa NS a ° ig oA
= 5 L L L i 4 4.
x [ T T T T T d T d
a? X y= 193 THz /
\ 4.
0 \ a SN y)
ak Non S07" Fil
1F cn v= {60TH ; |
i oS aaa $
4b Son" mo" vgs 081TH
O46 \ Av=04 THz ? 7
Q wF On ?
4 Sov So” vp 380TH 7
250 300 360 400 450 500 580
y (THz

FIG. 6


U.S. Patent Jan. 11, 2022 Sheet 20 of 22 US 11,221,540 B2

ab me 7
= “Om ‘p
ob “BQ,
~~
L L i 3S.
528 + Te
UP +t
“
526 F a ~| 266
“
LL “ON ~| 264
re 524 3 . a .
2 iow y 4+
522 F SS. a =
“4 SS ~| 260
520 Yo NS
S Sy ~| 28
BP a + 26
st C n fl nl TM“S 7 254
20 iB 0 6 ry
Pa (mit)

FIG. 20


US 11,221,540 B2

29

parameters that define the cross-section of the microring
(FIG. 17(a)), its ring width (RW) and thickness (H), have the
strongest influence on the resonator dispersion, we focus our
search on these parameters. In FIG. 17(4), we show the
results of such a search. Here, we first consider the azimuthal
mode numbers (m) and corresponding simulated frequencies
(vm) of TE] modes using the finite-element method for a
device with ring radius (RR) of 25 jum (corresponding free
spectral range, or FSR, of 0.9 THz), H=500 nm, and
RW=825 nm. For each configuration that satisfies phase
matching, i.e. m,+m,-2m,=0, the frequency mismatch is
plotted. When the pump laser is at np=385 THz, while the
pump is situated in normal dispersion, no modes are fre-
quency and phase matched for OPO. When the pump laser
is situated below 385 THz, the conditions for widely-
separated OPO start to become fulfilled, with the pump
remaining in normal dispersion while only a single pair of
widely-separated modes is frequency matched. The span
(separation between signal and idler mode frequencies)
decreases as the pump frequency decreases, and the signal
mode frequency moves from about 525 THz to 425 THz. For
the widest OPO, the span is ~273 THz, with the signal
predicted to be in the green.

As noted above, with this design all of the aforementioned
pump frequencies are in the normal dispersion regime, that
is, “U,#Uj-2'v,<0 when “v, and “v, are close to “v,. Such
dispersion prohibits close-to-pump OPO because any Kerr
shift further decreases this frequency mismatch (more nega-
tive for OPO) when pump power is injected into the cavity.

Therefore, we expect that our visible-infrared OPO devices 3

should be free from competition due to close-to-pump GPO.
Finally, we note that in FIG. 17, the resonator geometry is
kept fixed and only the pump frequency is varied (in one
FSR steps). Doing so results in relatively coarse jumps in

OPO output signal and idler frequencies. However, we note 3

that the device geometry itself can be varied—ultimately it
is the dispersion of the resonator relative to the pump
frequency that is important. As we shall show in the upcom-
ing sections, varying both pump frequency and resonator
geometry can lead to a finer coverage of the broad spectral
range predicted in FIG. 17.

The devices are fabricated (see Supplement 1 for details)
according to the design shown in FIG. 2, with nominally
fixed thickness and ring radius (H=500 nm, RR=25 pm)
while varying the ring width (RW=820 nm to 830 nm).
Dilute hydrofluoric acid (DHF) etching is incorporated as a
key step to post-process the devices and achieve fine control
of geometry at the sub-nanometer level, which in turn
controls frequency- and phase-matching of the resonator
modes. Moreover, in some cases DHF etching improves the
modes’ optical quality factors. After fabrication, devices are
characterized as a function of np near the simulated near-
infrared frequencies around 385 THz. For example, the
characterization of widely-separated OPO in a device with
nominal RW of 826 nm is shown in FIG. 18.

The pump mode has intrinsic Q in the range of 1x10°-
2x10° and loaded Q=1x10°. For example, we show in FIG.
18(a) a pump mode at 385.8 THz (777.7 nm), which is a
fundamental transverse-electric mode (TE1) whose simu-
lated field profile is shown in the inset (the resonance
doublet is likely due to backscattering resulting from side-
wall roughness, and seems to have a random amplitude in
our devices). The output OPO spectra are recorded by an
optical spectrum analyzer (OSA) as the pump is tuned over
modes that support widely-separated OPO with normal
dispersion around the pump, whose frequency is adjusted
between 387 THz and 391 THz (FIG. 18(6)). When the

S

3

40

&

3!

30

pump frequency is >391 THz, no widely-separated OPO is
observed. When the pump frequency is at 391 THz, the OPO
device has its widest span of 256.1 THz (the top panel of
FIG. 3(c)). The signal is at 519.2 THz (577.8 nm), which is
yellow in color, and the idler is at 254.1 THz (1140 nm) in
the infrared. A further decrease in the pump frequency shifts
the signal to red at 458.6 THz (654.1 nm) and then towards
the near-infrared at 407.5 THz (736.2 nm), with the corre-
sponding idler shifting from within the infrared at 320.2 THz
(936.9 nm) to the near-infrared at 367.9 THz (815.4 nm), as
shown in the bottom two panels of FIG. 18(c).

With this device, a mere ~5 THz pump shift leads to a 123
THz shift of the signal and a 113 THz shift of the idler. Such
large amplification in the output tuning range relative to the

5 pump tuning range comes from the large dispersion of the

nanophotonic resonator in the targeted frequency matching
bands, and is particularly useful when wide spectral cover-
age is needed. In the next section, we will describe how finer
steps in this spectral coverage can be achieved.

The required pump power (P,), specified in FIG. 18(c).
has a dependence on the OPO span. P=P(1-T) represents
the pump power that is coupled into the microring, where P
is the input pump power in the waveguide and T is the
normalized cavity transmission of the pump laser mode. For

s example, in the top panel, an OPO spanning 256.1 THz

requires a pump power of P=42 mW in the waveguide, of
which P,~22 mW is dropped into microring to excite the
OPO above threshold. In the middle and bottom panel,
where the OPO span is 54% and 15% of the widest span, the
required dropped power is 36% and 18% of that in the top
panel. Such power dependence may come from lower Q of
the cavity resonances at higher frequencies.

The wavelengths at which light is generated are very
sensitive to the device geometry because of the large ampli-
fication of the frequency span relative to the pump detuning
from its nominal position. As shown in the previous section,
even a change in pump mode of one free spectral range
(ESR~0.9 THz) leads to a >20 THz change in the frequency
of the visible signal. Similarly, a small change in device
dimension, even on the order of 1 nm, can lead to a different
color of light generated in the visible band. In this section,
we will focus on how we can use this dispersion sensitivity
alongside the previously used pump tuning to more finely
cover the very larger range of OPO output frequencies

5 possible in this platform. While each of our devices is

fabricated with its own bus waveguide, we note that multiple
individually addressable devices can be fabricated with the
same bus waveguide, as has been shown for second har-
monic generation, for example.

In FIG. 19(a), we collect the pump, signal, and idler
frequencies from different pumping modes in six devices
with ring widths from 824 nm to 830 nm. We can see that
within a 5 THz pump scan in the near-infrared (violet
symbols), the OPO outputs of these devices taken together
cover >270 THz, spanning from the infrared and near-
infrared to the visible, and exceeds (by nearly 20 THz) the
widest span shown in the previous section. The tuning of the
signal and idler frequencies, although still discrete, is much
finer in step than that of the single device shown in FIG.
18(6). In particular, this set of devices covers >130 THz of
the visible band, including red, orange, yellow, and green
colors (see the right color bar in FIG. 19(a)), and the average
step in frequency tuning for the signal is a few THz, in
comparison to the >20 THZ step shown in the previous

3 section.

We next present four optical spectra showing the genera-
tion of green, yellow, orange, and red light in FIG. 19(6). In


US 11,221,540 B2

31

each case, the OPO spectrum shows no noise or competitive
nonlinear processes, and its color is confirmed by optical
microscope images when the device is in operation, showing
red, orange, yellow, and green light generated in the micror-
ing. In particular, in a device with RW=826 nm, when the
pump mode is at 391.0 THz (the top panel), we observe the
widest OPO with a span of 273.7 THz, which is very close
to the simulated value (273 THz). The pump mode fre-
quency is ~7 THz larger than the simulation (384 THz),
which is likely due to a combination of uncertainty in the
refractive index model chosen for Si;N,, and in the fidelity
of the fabricated device dimensions relative to design. This
octave-spanning OPO has a 527.8 THz (568.4 nm) signal
and a 254.1 THz (1181 nm) idler.

We note that the threshold power increases from a few
milliwatts to a few tens of milliwatts as the OPO output
signal and idler becomes more widely separated (FIGS.
18(c) and 19(6)). This is likely due to a decrease in optical
quality factors of the signal and/or idler modes. A rough
estimate assuming Q values around 10° and 10° yields
threshold powers of 28 mW and 2.8 mW, respectively.

The ability to realize continuous spectral coverage would
complement the above demonstration of broad spectral
coverage using the widely-separated OPO process. The
broad coverage is made possible by the dispersion properties
of the resonator, which results in an amplification of the
signal tuning range relative to the pump laser tuning range
of =26:1 (FIG. 19(a)). Of course, the resonant nature of the
device is such that the pump laser is not tuned continuously,

but instead in jumps across different pump modes separated 3

by the resonator FSR~0.9 THz. As a result, the output
spectral coverage, though broad in overall extent, is sampled
with both signal and idler frequencies varying in jumps of
multiple FSRs, as shown in FIG. 19(a) when both pump

frequency tuning and varying geometric dispersion are 3

employed. In comparison, larger devices used in other OPO
works in the infrared*!*!>"° obtain a finer step in output
frequency. In this section, we show that we can achieve
1-FSR tuning steps for the signal and idler in the visible and
infrared bands, respectively, by shifting one pump mode
continuously through pump power tuning.

An example of this coverage is shown in FIG. 20. This
device generates green light as shown in the top panels of
FIG. 18(c) and FIG. 19(4). The OPO frequencies depend on
the pump power dropped into the microring (P,), which
results in a thereto-optical shift that linearly depends on P,.
We plot the pump (violet), signal (red), and idler (blue)
frequencies versus P, in FIG. 20. When P, is 22 mW, the
idler is at 263.1 THz and signal is at 519.2 THz (the top
panel of FIG. 18(c)). When P, increases to 37 mW, the idler
frequency decreases to 254.1 THz and signal frequency
increases to 527.8 THz (the top panel of FIG. 19(b)). The
visible frequency shifis by 8.6 THz, while the pump fre-
quency shifts by <0.2. THz. Therefore, such thermo-optic
tuning method can be used to improve the spectral coverage
in the visible band, bringing the multiple-FSR jumps down
to about 1 FSR. Going forward, further improvement in the
output tuning resolution may require using larger devices
with smaller FSRs, though this will come at the cost of
increased threshold power and also an increased chance of
competing or additional four-wave mixing processes (for
example clusters of phase- and frequency-matched modes).
The dispersion profile also needs to be adjusted and vali-
dated for larger devices.

We have demonstrated functional for applications, that is,
using widely-separated OPO in Si,N,, as a flexible platform
for realizing on-chip visible laser light sources and have

0

2

40

&

0

32

shown the generation of light up to 527.8 THz, covering red,
orange, yellow, and part of green. However, there are several
applications for which accessing to higher frequencies,
including the blue and violet, would be desirable.

The output visible power in some devices can include 30
dB to 40 dB below the pump power. A challenge is associ-
ated with efficient resonator-waveguide coupling, where we
can see from FIG. 19(6) that idler light (with longer wave-
length and hence improved spatial overlap between the
waveguide and resonator modes) is coupled 10 dB to 15 dB
better than the signal light. The coupling of visible light can
be optimized by appropriately designed pulley couplers
Such couplers have to be designed for specific wavelength
bands, and universal coupling across broad spectra, particu-
larly for short wavelengths, is challenging due to the cor-
responding small dimensions required. Besides this coupling
issue, at higher conversion efficiency levels, a clearer physi-
cal understanding of the pump depletion level to accurately
predict both the intracavity and external signal/idler powers
is needed. Finally, a frequency matching design is centered
around a regime in which Kerr frequency shifts due to self-
and cross-phase modulation are limited. Depending on the
application, one may instead seek to operate in a higher
pump power regime (to enable higher absolute output pow-
ers), in which case these Kerr shifts can be included in the
design.

We use a fiber-coupled external cavity tunable diode laser
at 780 nm to pump the devices. As noted earlier, there are
several paths to more compact and integrated pumping
solutions, including the use of commercial DFB and DBR
laser solutions, hybrid integration of compact gain/laser
chips to create full OPO modules, and heterogeneous inte-
gration of gain with Si;N, photonics.

The level of wavelength tuning needed depends on the
application. We have shown access to a broad range of
output wavelengths between 568 nm and 1180 nm by
varying the pump wavelength and device geometry, sug-
gesting the ability to access a number of different spectral
bands in a common photonics platform. Tuning from one
output wavelength to another is discrete, however, and the
finest tuning we have demonstrated is at the 1 FSR level. To
move beyond this and improve the continuity of tuning, we
note that thermal tuning has been implemented in both
crystalline resonators and on-chip microrings. Such thermal
tuning, taken together with the incorporation of many dif-
ferent resonator geometries (and corresponding dispersion
profiles) on a common bus waveguide, may provide a first
step to realizing both ultra-wide wavelength coverage and
fine wavelength tuning.

Nanophotonic OPO devices have output frequencies (in-
cluding both the signal and idler) that cover a range from
527.8 THz to 254.1 THz, which encompasses the green,
yellow, orange. and red parts of the visible spectrum, as well
as the near-infrared and a portion of the infrared spectrum.
The OPO magnifies the frequency tuning span of the near-
infrared pump source by ~25 times in the generated output
frequency ranges for both the infrared idler and visible
signal light. Devices whose dispersion supports the widest
separation in signal and idler frequencies exhibit octave-
spanning OPO at <30 mW threshold power. We further show
a tuning method to achieve 1-FSR output tuning steps. The

5 OPO provides coherent on-chip sources of visible light.

‘The threshold of ax OPO in microring can be estimated
by', assuming perfect frequency and phase matching,


US 11,221,540 B2

7

Ithas been discovered that an optical parametric oscillator
(OPO) and processes described herein produce coherent
light on-chip that fulfills a long-felt need that was recog-
nized, persistent, and not solved by others in frequency
ranges for which conventional laser gain media do not exist
or do not perform well. The OPO and processes described
herein provide a nanophotonic article with output coherent
light that are widely spectrally separated and that operate
with ultra-low pump power using silicon nanophotonics.
The OPO and processes described herein provide advan-
tages in power efficiency with low sub-mW threshold power,
device scalability, and access to a broad range of output
wavelengths. Furthermore, OPO and processes described
herein can directly integrate compact chip-based lasers
without an intermediate amplifier.

Optical parametric oscillator 200 produces idler coherent
light 206 and signal coherent light 207 from pump coherent
light 205 by balanced parametric dispersion 210 of micror-
ing resonator 204. In an embodiment, with reference to FIG.
1 and FIG. 2, optical parametric oscillator 200 includes:
substrate cladding 201; microring resonator 204 disposed on
substrate cladding 201 and including: Kerr nonlinear
medium fashioned into a ring geometry with radius R, height
H, and width W that provides balanced parametric disper-
sion 210; and that: receives pump coherent light 205 from
waveguide 203; and produces idler coherent light 206 and
signal coherent light 207 from pump coherent light 205,
idler coherent light 206 and signal coherent light 207
produced according to balanced parametric dispersion 210

of microring resonator 204; and waveguide 203 disposed on 3

substrate cladding 201 in optical communication with
microring resonator 204 and including the Kerr nonlinear
medium and that: receives pump coherent light 205; and
communicates pump coherent light 205 to microring reso-

nator 204 for production of idler coherent light 206 and 3

signal coherent light 207 from pump coherent light 205.

In an embodiment, optical parametric oscillator 200 fur-
ther includes: cover cladding 202 disposed on waveguide
203, microring resonator 204, and substrate cladding 201
such that microring resonator 204 and waveguide 203 are
interposed between substrate cladding 201 and cover clad-
ding 202 to encapsulate microring resonator 204 and wave-
guide 203.

In an embodiment, optical parametric oscillator 200 fur-
ther includes: second waveguide 203 in optical communi-
cation with microring resonator 204 and including a Kerr
nonlinear medium and that receives idler coherent light 206
and signal coherent light 207 from microring resonator 204.

Components of optical parametric oscillator 200 can be
made from and include various materials. Substrate cladding
201 has a lower refractive index than microring resonator
204 and waveguide 203 and supports broadband optical
transparency that spans a wavelength range inclusive pump
coherent light 205, idler coherent light 206, and signal
coherent light 207. The substrate cladding can include a
plurality of layers that can be disposed, e.g., immediately
under microring resonator 204 and that can be a lower
refractive index than microring resonator 204. Substrate
cladding 201 provides a lower refractive index medium to
support guided optical modes of waveguide 203 and micror-
ing resonator 204 as well as a mechanical structure for
disposition of other elements of optical parametric oscillator
200 thereon. Substrate cladding 201 can include silicon
dioxide in proximity to microring resonator 204 and silicon
underneath the silicon dioxide, but the silicon dioxide can
also be substituted by other materials with similar refractive
indices such as sapphire, quartz, or MgF2. A thickness of

8

2

40

&

8

substrate cladding 201 can be from 500 nm to 5 mm,
specifically from 1 pm to 1 mm, and more specifically from
1 um to 10 um. It is contemplated that the thickness of the
low refractive index layer (e.g., silicon dioxide) within
substrate cladding 201 can be from 500 nm to 5 mm,
specifically from 1 jum to 10 um, and more specifically from
1 pm to 1 mm. In an embodiment, substrate cladding 201 is
silicon dioxide.

Cover cladding 202 can, in combination with substrate
cladding 201, cover and encapsulate waveguide 203 and
microring resonator 204 between cover cladding 202 and
substrate cladding 201. Cover cladding 202 has a lower
refractive index than microring resonator 204 and wave-
guide 203 and supports broadband optical transparency that

5 spans a wavelength range inclusive of pump coherent light

205, idler coherent light 206, and signal coherent light 207.
‘The cover cladding can include a plurality of layers that can
be disposed, e.g., immediately above microring resonator
204 and can have a lower refractive index than microring
resonator 204. Cover cladding 202 can include silicon
dioxide or also can be substituted by other materials with
similar refractive indices such as photoresist or electron
beam resist, doped glasses, or intermediate refractive index
materials (i.e., materials with a refractive index higher than

silicon dioxide but lower than that of microring resonator

204) such as silicon oxynitride. A thickness of cover clad-
ding 202 can be from 1 nm to 1 cm, specifically from 1 um
to I mm, and more specifically from 1 1m to 3 wm. In an
embodiment, cover cladding 202 is silicon dioxide.
Waveguide 203 receives pump coherent light 205 and
communicates pump coherent light 205 to pump coherent
light 204 via evanescent coupling. Waveguide 203 can
include a core material that has a refractive index greater
than that of substrate cladding layer 201 and that supports
broadband optical transparency that spans the wavelength
range of pump coherent light 205, idler coherent light 206,
and signal coherent light 207. Waveguide 203 can include a
material such as silicon nitride, silicon oxynitride, or a
combination including at least one of the materials. Optical
parametric oscillator 200 can include a plurality of wave-
guides 203 (e.g., 203.1, 203.2 shown in FIG. 2), wherein a
number of waveguides 203 can be selected to communicate
independently or in combination pump coherent light 205,
idler coherent light 206, or signal coherent light 207. In an

5 embodiment, waveguide 203 communicates pump coherent

light 205, idler coherent light 206, and signal coherent light
207. In an embodiment, first waveguide 203.1 communi-
cates pump coherent light 205 and idler coherent light 206,
and second waveguide 203.2 communicates signal coherent
light 207. In an embodiment, first waveguide 203.1 com-
municates pump coherent light 205 and signal coherent light
207, and second waveguide 203.2 communicates idler
coherent light 206. In an embodiment, first waveguide 203.1
communicates pump coherent light 205; second waveguide

5 203.2 communicates idler coherent light 206, and third

waveguide 203.3 communicates signal coherent light 207
Distance R1 from a center of microring resonator 204 to a
closest portion of waveguide 203 can be from 100 nm to 1
om, specifically from 1 ym to 1 mm, and more specifically
from 10 jun to 100 um. A separation distance between
microring resonator 204 to a closest portion of waveguide
203 can be from 100 nm to 1 cm, specifically from 1 jum to
1 mm, and more specifically from 10 jum to 100 um. A width
W and height H of waveguide 203 can be from 100 nm to
10 um, specifically from 100 nm to 5 pm, and more
specifically from 100 nm to 2 pm. In an embodiment,
waveguide 203 is silicon nitride.


U.S. Patent Jan. 11, 2022 Sheet 2 of 22 US 11,221,540 B2

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U.S. Patent Jan. 11, 2022 Sheet 1 of 22 US 11,221,540 B2

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US 11,221,540 B2

27

local storage and manipulation of quantum information,
including trapped ions, atoms, and spins in crystals, have
optical transitions that require visible pump lasers for opera-
tion. A direct approach is to develop on-chip lasers based on
III-V semiconductors, e.g., indium gallium nitride lasers, but >
spectral coverage is typically limited by the available gain
media. Achieving spectral coverage via direct optical tran-
sitions over a wide range of wavelengths is challenging, and
integrating such a laser into a mature photonic integrated
circuit platform is also nontrivial.

Nonlinear optics is another route to visible light genera-
tion. While optical harmonic generation enables access to
visible wavelengths via a near-infrared pump. the output
frequency tuning range is limited to a small multiple of the
input frequency tuning range. In contrast, optical parametric
oscillation (OPO) provides a mechanism by which output
light with wide spectral coverage can be obtained using only
limited tuning of a single pump laser. Over the past few
decades, table-top OPO has been extensively studied for
visible light generation, and has been a major workhorse for
laboratory purposes, Such table-top OPO provides a versa-
tile source of high-power tunable laser light, but is also
bulky, expensive, and lacks the miniaturization and scalabil-
ity for field-level deployment in many applications. 2

On-chip OPO based on both the second-order (x) and
third-order (y) nonlinearity has been intensely studied in
microphotonic and nanophotonic resonators. While both
processes can be successful, we note that the pump laser
requirements are very different. For x° OPO, the energy 3
conservation criterion requires v,-v,+v,, where p, s, i
represent pump, signal, idler respectively. As a result, gen-
eration of a visible wavelength signal will require a pump
laser in the blue to ultra-violet region (depending on how
short an output wavelength is desired). In contrast, for x°) 3:
OPO, the energy conservation criterion is 2v,-v,+u,
Because two pump photons now contribute to the process,
visible wavelength output is accessible from a near-infrared
pump laser. Such lasers are commercially available in com-
pact forms, including distributed feedback (DFB) and dis-
tributed Bragg reflector (DBR) geometries.

We describe widely-separated OPO based on the third-
order nonlinearity in a silicon nitride (SijN,) microring
(FIG. 16(a)). Our OPO devices address ~34% (130 THz) of
the visible spectrum, including red, orange, yellow, and 45
green colors, through a small change in the pump laser
frequency (FIG. 16(4)). Our approach enables octave-span-
ning OPO to be observed, with a 527.8 THz (568.4 nm)
signal in the green and a 254.1 THz (1181 nm) idler in the
infrared. The corresponding span of 273.7 THz is the widest
on-chip OPO reported so far—it is >40 THz larger than the
previous record set for an infrared OPO—despite the sub-
stantial increase in material dispersion at visible wave-
lengths (FIG. 16(c)). We further show that through power
tuning, the visible output signal can be tuned in a finer 5:
fashion, similar to devices with larger footprints. The device
described here uses nonlinear nanophotonics to access
desired wavelengths in the visible spectrum (FIG. 16(d)) and
has numerous applications in spectroscopy, metrology, and
quantum science.

A benefits of the Si,N, OPO platform is pump laser
integration. Such activities, which could include edge cou-
pling of semiconductor gain media to the OPO chip, are
being increasingly pursued in the context of microresonator
frequency combs. More intimate and scalable integration of 6:
pump lasers and Si,N, nonlinear nanophotonics is also
possible, and we note the substantial recent efforts on

2

40

60

28

heterogeneous integration of III-V gain media on Si,N4.
including the demonstration of electrically-injected lasing at
wavelengths below 1 um.

The physical process to support widely-separated OPO is
cavity-enhanced degenerate four-wave mixing. To achieve
such a nonlinear optical process, both the momentum and
energy for the interacting cavity modes have to be con-
served. For the whispering gallery modes of a microring
resonator, when modes from the same mode family (e.g., the
fundamental transverse-electric mode TE1 in this work) are
used, the momentum in question is in the azimuthal direc-
tion, and momentum conservation reduces to a simple
equation, m,+m,-2m,=0, where the subscripts s; i; p denote
signal, idler, and pump, respectively, and m is the azimuthal

5s mode number. Energy conservation requires frequency

matching, and for the energy-conserving frequencies gener-
ated by the four-wave mixing process to match the corre-
sponding cavity modes, we need ‘v,+v,-2'v, (where “vy
represents the center resonance frequency of k-mode) needs
to be approximately within the cavity linewidths (‘v,=Q,.
where Q, is the loaded quality factor for the k mode). While
the above criteria are involved for efficient four-wave mix-
ing between this set of cavity modes, they are not sufficient

In particular, as four-wave mixing can occur across multiple
sets of modes simultaneously, another factor in device
design is that all other signal and idler mode sets do not
simultaneously realize frequency and phase matching. For
example, close-to-pump OPO has been a competitive pro-
cess for widely-separated OPO when the device exhibits
anomalous dispersion around the pump. In brief, we require
the device dispersion to be such that only a single set of
widely-spaced signal, idler, and pump modes be phase- and
frequency-matched.

Achieving such conditions can be especially challenging
at visible wavelengths, due to the increased dispersion of the
constituent materials. The bottom panel of FIG. 16(¢) sum-
marizes the first main challenge that our design space must
address, which is the strong dispersion associated with
Si,N, in the visible, as quantified by its group velocity
dispersion (GVD), which at 600 nm (500 THz) is many
times the values at 1500 nm (200 THz). Other common
microresonator OPO materials like SiO,, AIN, and MgF,
exhibit similar trends, though the problem is most acute for
Si,N,. A second challenge is in how flexible the OPO design
is in reaching wavelengths of interest. Ideally, we would
prefer a design in which small changes in the pump fre-
quency can results in large changes in the generated signal
and idler frequencies, as schematically depicted in FIG.
16(6). Such a design would enable a broad range of output
frequencies to be accessed from the narrow tuning ranges
available from distributed feedback or distributed Bragg
reflector pump lasers, for example. We note that the full
desired spectral range does not necessarily need to be
covered within one device (as multiple devices can be
fabricated on the same chip in parallel), and as a result
variations in the device’s in-plane geometry (ring width and
ring radius) can be considered, but the device layer thick-
ness, which is more difficult to systematically control across
a chip, should ideally remain the same.

We determine a Si;N, microring geometry with three
dispersion characteristics to satisfy the above criteria: (1)
phase- and frequency-matching of a single set of widely-
separated modes, with signal in the visible and idler in the
infrared; (2) normal dispersion around the pump, to elimi-
nate the possibility of close-to-pump OPO in which phase-
matching is mediated by nonlinear frequency shifts; and (3)
flexible tuning of the OPO output wavelengths. As the two


US 11,221,540 B2

3

ers (P). The open circles specify the laser detuning at various
powers for the OSA spectra in (e). (c) OPO threshold power
is only (0.90.1) mW, measured by the power dependence of
the OPO signal peak amplitudes. I-s and II-s denote signal
peaks of two OPO tones at 419.8 THz and 388.7 THz in (e).
Here, on the y axis, 0 dB is referenced to 1 mW, i.e., dBm.
Error bars are one standard deviation values due to fluctua-
tions in optical path losses. The quoted pump power is
on-chip, with the facet loss typically between 2 dB and 3 dB.
(@) Zoom-in frequency mismatch curve for two phase-/
frequency-matched cases, where the signal/idler frequencies
are labeled as I-s/I-i and II-s/II-i, respectively. The pump
frequency is labeled as p (around 322 THz). (e) OPO spectra
as a function of pump power. When the pump power is 1.0
mW, OPO I is above threshold and OPO II is below
threshold, with I-s and I-i located around 419.8 THz (714.6
nm) and 227.8 THz (1316.9 nm), respectively, correspond-
ing to a spectral separation of 192 THz. Next, when the
pump power is 1.6 mW, both OPO I and II are above
threshold and observable in the spectrum. II-s and II-i are
located around 388.7 THz (771.8 nm) and 258.8 THz
(1159.2 nm), respectively. The frequencies of both OPO V/II
agree reasonably well with the theoretical prediction in (d).
Finally, when the pump power is 2.5 mW, close-band FWM
adjacent to OPO II is excited, because the modes adjacent to
II have smaller frequency mismatch compared to those
around I, as indicated by (d). On the yy axis, 0 dB is
referenced to 1 mW, ie., dBm;

FIG. 10 shows OPO ona single widely separated pair. (a)

Top panel shows a microring design with only one phase-/ 3

frequency-matched widely separated OPO pair. The micror-
ing has parameters of H=600 nm and RW=1440 nm. When
the pump laser frequency v,=293.5 THz, the generated OPO
is predicted to have only a single pair with frequencies of

205 THz and 382 THz. The bottom panel shows the experi- 3

mental optical spectrum, which confirms that only a single
widely separated pair is generated at 202.1 THz (1484 nm)
and 383.9 THz (781.4 nm) when vp=293.0 THz vp=293.0
THz (1024 nm). Due to the large spectral separation, the
device needs two waveguides to couple the OPO signal and
idler, with spectra shown in red and blue, respectively. (b)
Threshold study of the OPO pair with various dropped pump
powers Pd=P(1-T), where transmission (T) is changed by
the laser-cavity detuning (A), as shown in the inset. The
threshold power is (1.30.1) mW. (c) Dispersion is normal
near the pump, as shown in (a), thereby disfavoring close-
band OPO. However, when the pump power is sufficiently
above threshold, the close-band OPO process begins to
appear. This competitive OPO is much less efficient than the
widely separated OPO, but nevertheless needs further sup-
pression for ideal operation. In the yy axes of (b) and (c), 0
dB is referenced to 1 mW, dBm;

FIG. 11 shows a configuration for optical parametric
oscillator. (a) Nanophotonic OPO scheme. The pump laser
with a power of Pin is coupled at a rate T'cp into the
microring resonator. The intra-cavity pump energy Up is
resonantly enhanced by an amount proportional to the
photon lifetime in the microring. When the pump energy
reaches the threshold value, that is, the four-wave mixing
generation rates are larger than the cavity losses for signal
and idler modes, intra-cavity OPO (Us, Ui) can be built up
coherently. Each mode has two decay paths in total and the
total decay is represented by Itm (m=p,s.i). One decay path
is through intrinsic loss of the cavity '0m sidewall scatter-
ing) and the other path is through coupling out to the
waveguide em. (b) Nonlinear resonance shifts of the cavity
modes, The intense intra-cavity pump field yields self-phase

0

40

&

0

0

4

modulation (SPM) of the pump mode and cross-phase
modulation (XPM) of the signal and idler mode, and red-
shifis the cavity resonances from their natural resonance
frequencies 0m (m=p,s.i). The cavity linewidths remain
unchanged and the full-wave-half-maximum (FWHM) val-
ues are given by I'tm. (c) Frequency diagram of the OPO
process. The OPO process requires pump detuning to com-
pensate the overall frequency mismatch, including natural
cavity frequency mismatch and the differences of the SPM
and XPM shifts. Here the detunings follow the previous
definition Aom=om-w0m (m=p,s,i). The natural frequency
mismatch is given by Am0=«0s+0i-200p, which is related
to Av in the main text by a factor of 2x;

FIG. 12 shows (a) device blueprint for widely separated

5 OPO, wherein two waveguides are used to couple pump.

signal, and idler light. The top straight waveguide couples
idler light. The bottom pulley waveguide couples pump and
signal light. Three parameters control the dispersion of the
microring: thickness (H), microring width (RW), and
microring radius (R). Two more parameters are needed for
defining the coupling to the straight waveguide (wg.): wave-
guide width (SW) and gap (SG). Additionally, three param-
eters are needed to describe pulley wg. coupling: pulley
width (PW), pulley gap (PG), and pulley length (PL). (b) A

s parameter table for two typical geometries studied in the

main text. (c) The simulated frequency mismatch (Av) of
design II with different pump frequencies. The data of the
widely-separated OPO studied in the main text are high-
lighted in red. (d) The simulated frequency-dependent cou-
pling Q (Qc) of the pulley waveguides in design I and II. We
tailor the pulley coupling so that the pulley resonances (dips
in coupling Q) fit the pump and visible frequencies for each
design;

FIG. 13 shows dispersion sensitivity of the frequency
match (Av) on thickness (H) and ring width (RW). (panels
a-c) Dispersion sensitivity on H. The widely-separated OPO
is very sensitive to H. For example, for a fixed RW of 1160
nm, a design with H=510 nm shows widely-separated phase
and frequency matched modes with normal dispersion at the
pump (c), while designs with H=500 nm and H=490 nm
show no widely-separated modes for OPO. vp changes from
312 THz to 327 THz (from top to bottom) with =0.9 THz
FSR. The bold green lines indicate vp=322 THz, which is
close to what is investigated in experiment. (panels d-f)
Dispersion sensitivity on RW. The sensitivity of the disper-
sion to RW is significantly less when compared with H. For
example, (d,c,e.f) show devices with RW of (1150 nm, 1160
nm, 1170 nm, 1180 nm), respectively. All devices show
widely-separated frequency matched modes, with vp of 324
THz, 322 THz, 320 THz, and 318 THz, respectively. Here all
parameters other than H and RW are given in the previous
section (design I):

FIG. 14 shows effect of waveguide-microring coupling on
competition between OPO processes. (a) Coupling Qs for

5 pulley gaps of 230 nm, 220 nm, and 210 nm (from top to

bottom). The device inset shows a typical optical mode at the
pump band. The fitting indicates an intrinsic Q of (2.6+0.1)x
10°. Dashed lines indicate the targeted idler, pump, and
signal frequencies, from left to right, respectively. (b) OPO
generation for various pulley gaps. For a closer gap, the
Close-band OPOs are suppressed because the pump band is
more over-coupled in relative to signal and idler band:
FIG. 15 shows thermal and power effects on widely-
separated OPOs. (a) Thermal stability of the OPO. At the

5 same pump power level, that is, P=2.46 mW, the device

outputs are stable in frequency when temperature (T)
changes from 21.5° C, to 31.1° C. (b) The OPO outputs are


US 11,221,540 B2

Page 2
(56) References Cited
U.S. PATENT DOCUMENTS

10,268,100 B2* 4/2019 Sciancalepore GO2F 1/365
11,016,363 B2* 5/2021 Lin GO2F 1/3551
11,063,402 B2* 7/2021 Wong HOLS 3/1608
2014/0193155 Al* 7/2014 Popovic GO2F 1/395
398/82
2021/0080805 Al* 3/2021 Srinivasan GO2F 1/3501

OTHER PUBLICATIONS

X. Lu, G, Moille, A. Singh, Q. Li, D. Westly, A. Rao, S. Yu, T. C.
Briles, T. Drake, S. B. Papp, and K. Srinivasan, “Efficient widely-
separated optical parametric oscillation,” in Conference on Lasers
and Electro-Optics, OSA Technical Digest (Optical Society of
America, 2020), paper SF2B.7. (Year: 2020).*

Lu, X., et al., “Milliwatt-threshold visible-telecom optical paramet-
ric oscillation using silicon nanophotonics”, Optica, 2019, p. 1535-
1541, vol. 6 No. 12

Lu, X., et al., “On-chip optical parametric oscillation into the
visible: generating red, orange, yellow, and green from a near
infrared pump”, Physics Optics, 2020, doi: https://arxiv.org/pdf!
2003.12177 pdf.

* cited by examiner


US 11,221,540 B2

19

We calculate the device dispersion and OPO frequency
mismatch for various ring widths using mode frequencies
from finite-element method (FEM) simulations. The top
panel in FIG. 10(a) shows the key result where the device
with RW=1440 nm is predicted to generate a visible telecom
OPO with signal and idler located at 384 THz (781 nm) and
204 THz (1470 nm), respectively, for a pump at 294 THz
(1020 nm). This H=600 nm design has widely separated
frequency-/phase-matching mode pairs and normal disper-
sion near the pump, similar to the previous H=510 nm
design [FIG. 9(d)]. However, the H=600 nm design supports
only one widely separated OPO pair, and is also ~5x more
dispersive in the frequency bands of interest. These two
properties together make this design better in suppressing
competitive OPO processes. In the measured optical spec-
trum [bottom panel in FIG. 10(a)], the fabricated device
generates OPO with signal and idler at 383.9 THz (781.5
nm) and 202.1 THz (1484 nm), respectively, when pumping
at 293.0 THz (1023.9 nm) with 1.3 mW pump drop power.
The measured frequencies agree with theoretical prediction
within 2 THz for all three modes. Moreover, only one pair
of widely separated tones is generated, as the simulation
predicts. We note that the short wavelength OPO output is
suited for spectroscopy of rubidium vapor (1.5 nm wave-
length tuning needed), and the telecom OPO output makes
such a device potentially suitable for spectral translation. We
also note that in FIG. 10(c), a small close-to-pump OPO is
generated at 1.5 mW pump drop power. Such close-band
OPO is ~10 dB smaller than the widely separated OPO and

occurs when the pump is depleted. The pump depletion 3

effectively broadens the cavity linewidth (acts as another
effective loss channel), thereby enabling the close-band
OPO to occur.

One property of our device is its operation stability, ie.,

OPO works at a continuous detuning of the pump. This 3

stability has not been demonstrated in prior works, where
large pump power is used to assist phase matching, and clean
OPO pairs typically require sensitive pump detuning. In
some conventional devices, a cluster frequency comb is
clearly in competition with the clean OPO pair when the
detuning changes. In contrast, our OPO has stable output
frequencies. We study this stability by recording the peak
amplitude of the 781.5 nm signal versus the pump power
dropped inside the microring [FIG. 10(4), inset]. The pump
threshold power is (1.3+0.1) mW, similar to, but slightly
larger than, that of the previous design. In particular, we
observe only one widely separated OPO pair throughout this
detuning process, until at the highest dropped powers, one
close-band OPO occurs [FIG. 10(c)]. Importantly, such
close-band OPO, although affecting the output power for the
targeted widely-separated OPO, does not come with clus-
tered frequency combs near the signal and idler. We note that
some coupling designs can suppress the close-band OPO.
The stability can be attributed to three factors. First, our
device has a smaller size and thus an FSR of ~1 THz that
conventional devices that can have larger size and an
FSR of ~100 GHz to 300 GHz. Second, because of the larger
material dispersion at the visible wavelength and larger
geometric dispersion of the nanophotonic devices, the
modes around OPO pairs are more dispersive and therefore
less prone to clustered frequency combs. Our devices have
smaller operation powers and thus smaller parametric gain
bandwidths, which further limits the allowable number of
competitive OPO processes. Such superior power efliciency
and operation stability comes with a sacrifice of frequency
tunability. For example, our results typically show only a
few pump modes that can generate widely separated OPO,

3

40

20

as shown in FIG. 8(6), while conventional works can
possess ~10x more pump modes for such operation. We note
that the frequency tunability can be aided with pump power
tuning but not temperature tuning.

In summary, the visible telecom OPO had silicon nano-
photonics, with a signal-idler spectral separation of ~190
THz, and a sub-mW threshold power that is two orders of
magnitudes smaller than conventional infrared OPO. Our
demonstration represents an advance for on-chip generation
of coherent visible light. Compatibility with silicon photon-
ics and its accompanying potential for low-cost, scalable
fabrication make our approach particularly promising for
integrated photonics applications.

Optical parametric oscillation (OPO) in high-Q microre-

5  sonators are considered with an estimate of threshold power

as a function of the cavity decay rates and effective nonlin-
earity including mode overlap. In particular, cases where
signal, pump, and idler can be quite different in frequency
are considered. In high-Q microresonators, because light
propagates many round trips before being lost (e.g. scatter-
ing or absorption) or appreciably coupled out from the
cavity, we can treat the loss and coupling as if they are
uniformly distributed in time and space. The slowly varying
light fields satisfy the following equations.

day : (sv)
Gp = (Bey —Tp Dp +

ip Up + 2ypsU0 + 2ypiUi)Ap + iy ppiA,
day : : (82)
SE = (eas — Vial DAs + HU + 279Up + 27a UDAL +
da a (83)

A 3 ; a2ye
a = (Boog Vg DA: + IU; + 2ypUp + WU IA: + ive, Al,

wherein A,, (m=p,s,i) are the intra-cavity light fields for
pump, signal, and idler modes, sitting on the fast-oscillating
background of e~"””, where «,, is the angular frequency of
the light. Frequency conservation requires @,+0,—20,,
which is assumed in deducing the equations. Our convention
is to define the higher and lower frequency OPO outputs as
signal and idler, respectively. The cavity fields are normal-
ized so that |A,,|?=U,,, (m=p.s.i), which represents the intra-
cavity energy. The first terms in Eqs. (S1-S3) describe the
free cavity evolution (without sources or nonlinear effects),
where Aw,, (m=p,s,i) represents the detuning of laser/light
frequency (,,) from the natural cavity frequency (09,,), i.€.,
AW,,=0,,-Oo,,- U, describes the decay of the intra-cavity
energy U,,. which includes the intrinsic cavity loss and the
out-coupling to waveguide, T’,,,=T,,+T".,,. Here the decay
term T,,,, is related to optical quality factor Q,,, by

om

Qin

(84)

Tin = SO, crm = psi).

We use I’ instead of Q so that it is more straightforward
to describe the physics of the cavity, as shown in FIG.
11(ad). The second and third terms in Eqs. (S1-S3) describe
selfcross-phase modulations (SPM/XPM) and four-wave
mixing (FWM) of the cavity fields, respectively. For SPM,
Ym iS short fOr Y,,..mm (m=p,s,i) and describes the phase

5 modulation of the in mode on itself. For XPM, y,,,, is short

fF Youn (M,N=P.s.i, men) and describes the phase modu-
lation of the m mode by the n mode. The phase modulation,



US 11,221,540 B2

9

Microring resonator 204 receives pump coherent light 205
from waveguide 203 and produces pump coherent light 205
to pump coherent light 205 from pump coherent light 205.
Microring resonator 204 can include a core material that has
a refractive index that is greater than that of substrate
cladding 201 and that supports broadband optical transpar-
ency that spans the wavelength range of pump coherent light
205, idler coherent light 206, and signal coherent light 207
The materials also support a Kerr nonlinearity (also known
as a third-order optical nonlinearity). Microring resonator
204 can include a material that satisfies the above criteria,
such as silicon nitride, silicon oxynitride, tantalum pentox-
ide, aluminum nitride, lithium niobate, gallium phosphide,
gallium nitride, aluminum gallium arsenide, or a combina-
tion including at least one of the foregoing materials. A
radius R of microring resonator 204 can be from 100 nm to
1 cm, specifically from 1 1m to 5 mm, and more specifically
from 10 jum to 500 um. A width W and height H of microring
resonator 204 can be from 100 nm to 10 jm, specifically
from 100 nm to 5 um, and more specifically from 100 nm to
2 wm. In an embodiment, microring resonator 204 is silicon
nitride.

For production of idler coherent light 206 and signal
coherent light 207 from pump coherent light 205, pump
coherent light 205 has balanced parametric dispersion 210 as
shown in FIG. 3 and FIG. 4 for the parametric dispersion of
pump coherent light 205 as a function of frequency, referred
to as a parametric dispersion curve. Balanced parametric
dispersion 210 includes pump frequency node 214 at pump

frequency v, and including a parametric dispersion that is 3

zero; idler frequency node 216 at idler frequency v, and
inchiding a parametric dispersion that is zero; idler normal
dispersion minimum 215 interposed at a frequency between
pump frequency v,, and idler frequency v, and including a

normal parametri¢ dispersion; idler anomalous dispersion 3

frequency 217 at a frequency that is less than idler frequency
vy, and including an anomalous parametric dispersion; signal
frequency node 219 at signal frequency v, and including a
parametric dispersion that is zero: signal normal dispersion
minimum 218 interposed at a frequency between pump
frequency v, and signal frequency v, and including a normal
parametric dispersion; and signal anomalous dispersion fre-
quency 220 at a frequency that is greater than signal fre-
quency v, and including an anomalous parametric disper-
sion; wherein: balanced parametric dispersion 210 consists
essentially of normal parametric dispersion between idler
frequency node 216 and pump frequency node 214: and
balanced parametric dispersion 210 consists essentially of
normal parametric dispersion between pump frequency node
214 and signal frequency node 219. Without wishing to be
bound by theory, it is believed that balanced parametric
dispersion 210 is a consequence of the material composition
of microring resonator 204, substrate cladding 201, and
cover cladding 202 (if present), and in particular, the wave-
length-dependence of the refractive index or indices of their
constituent materials, in combination with the physical
dimension (radius R, height H, width W) of microring
resonator 204. In this regard, balanced parametric dispersion
results from the combined effect of the dispersion of the
constituent materials (i.e., the variation in their refractive
indices as a function of wavelength/frequency) and the
geometric dispersion associated with the optical confine-
ment provided by the microring resonator.

As used herein, parametric dispersion Av refers to
Av-v,+v,-2v,, wherein v, is the frequency of signal coher-
ent light 207: y, is the frequency of idler coherent light 206,
and v, is the frequency of pump coherent light 205. Further,

S

2

40

&

10
a node in a parametric dispersion curve has parametric
dispersion that is zero, i.e, Av-O. Normal parametric dis-
persion has a negative parametric dispersion, i.e., Av<0.
Anomalous parametric dispersion has a positive parametric
dispersion, i.c., AV>0.

In contrast to balanced parametric dispersion 210 shown
in FIG, 4 that characterizes microring resonator 204, con-
ventional resonators can have a parametric dispersion curve
shown in FIG. 5 (except for balanced parametric dispersion
210 that is shown for comparison) that include negative
parametric dispersion 211, concave parametric dispersion
212, and convex parametric dispersion 213 that lack nodes,
normal parametric dispersion, and anomalous parametric

5 dispersion of balanced parametric dispersion 210. Again, it

is noted that balanced parametric dispersion 210 is included
in FIG. 5 for comparison of negative parametric dispersion
211, concave parametric dispersion 212, and convex para-
metric dispersion 213.

Pump coherent light 205 can have a frequency selected so
that microring resonator 204 produces desired frequencies of
idler coherent light 206 and signal coherent light 207. It is
contemplated that the frequency of pump coherent light 205
is from 100 THz to 800 THz, specifically 150 THz to 600

'S THz, and more specifically from 200 THz to 400 THz. A

frequency of idler coherent light 206 can be from 50 THz to
800 THz, specifically 50 THz to 400 THz, and more spe-
cifically from 50 THz to 300 THz. A frequency of signal
coherent light 207 can be from 100 THz to 1000 THz,
specifically 200 THz to 800 THz, and more specifically from
400 THz to 750 THz. In an embodiment, a central wave-
length of idler coherent light 206 and a central wavelength
of pump coherent light 205 can be separated by a frequency
difference from 50 THz to 750 THz, specifically 100 THz to
600 THz, and more specifically from 150 THz to 300 THz.
According to an embodiment, a central wavelength of signal
coherent light 207 and a central wavelength of pump coher-
ent light 205 can be separated by a frequency difference
from 50 THz to 750 THz, specifically 100 THz to 600 THz,
and more specifically from 150 THz to 300 THz.

A power of pump coherent light 205 injected into wave-
guide 203 and received by microring resonator 204 that
satisfies balanced parametric dispersion 210 so that micror-
ing resonator 204 can produce idler coherent light 206 and

5 signal coherent light 207 through nonlinear processes is in

accord with the threshold power relationship:

LT, 1 [(Ae@o Te yew
DT” 2 yew

nea)

wherein P,,, is a power of pump coherent light 205 injected
into waveguide 203; I, is the geometric mean of the micror-

‘5 ing resonator total energy loss rate at the signal and idler

frequencies; I’, is the microring resonator total energy loss
rate at the pump frequency; I’, is the coupling rate between
microring resonator 204 and waveguide 203; Ypyay is the
effective four-wave mixing nonlinear parameter and Yp,, is
the effective nonlinear parameter associated with the differ-
ence between cross-phase modulation and self-phase modu-
lation. Awa is the natural cavity mismatch and is 27 times the
parametric dispersion Av=v,+v,-2v,. It should be appreci-
ated that the threshold power is minimized when the natural

5 cavity mismatch Aw, is a positive value that matches dif-

ference between the effects of self-phase and cross-phase
modulation, ic., A@o=V'yondYtrnar However, when nonlin-


U.S. Patent Jan. 11, 2022 Sheet 11 of 22 US 11,221,540 B2

a waveguide

microring

b SPHIXPM



U.S. Patent

a

Jan. 11, 2022

Sheet 14 of 22 US 11,221,540 B2

48

4gbe

407 E

on \ ;
4 qi WA nat if \ va 7q
a oe
' “Ri! \ oe a4
NT

il 09 A
08 /
ayoo7 i]

0050 0510 /
Aon) fj

GLE ne

rig

OPO spectra (dBm)

250

700

280
v (THz)

500

PG = 200m +

T t T T

PG=220nm

i)

20

30080
vith)

FIG. 14