US 2022/0390760 Al

to transmit a portion of light of the first beam of light
as a spatially-expanding optical beam, defined by a
non-zero order of diffraction of light at the first
optical system, to a plane in which a distribution of
irradiance of said spatially-expanding optical beam
is substantially different from a Gaussian distribu-
tion; and

‘a second optical system disposed at the plane and con-

figured to transform said spatially-expanding optical
beam incident thereon into a plurality of return optical
beams, each of which overlaps with each of the plu-
rality of return optical beams and the spatially-expand-
ing optical beam within the same volume of space,

wherein the optical apparatus is configured as a part of a

magneto-optical trap for an atom.

15. The optical apparatus according to claim 14, config-
ured to form the spatially-expanding optical beam such that
‘a cross-sectional area of the spatially-expanding optical
beam, measured at the plane, exceeds a cross-section of the
first beam of light at the planar optical waveguide compo-
nent by at least a coefficient of 10*, and wherein said
distribution of irradiance is a substantially spatially-uniform
distribution.

16. The optical apparatus according to claim 14, wherein
the first optical system includes

a birefringent substantially planar metasurface that is

dimensioned to transform light incident thereon into
light having a circular polarization and a phase profile
component corresponding to a phase shift that is intro-
duced by a lens with a negative optical power into light
propagating through such lens;

and/or

an optical retarder, disposed between the birefringent

substantially planar metasurface and the planar wave-
guide component, wherein the birefringent substan-
tially planar metasurface is configured to change a first
state of polarization of the light incident thereon, which
light has been outcoupled from the planar optical
waveguide component and that has traversed the opti-
cal retarder, to a second state of polarization that is
orthogonal to the first state of polarization.

Dec. 8, 2022
12

17. The optical apparatus according to claim 16, wherein
the birefringent substantially planar metasurface includes
only surface features each of which is a half-wave optical
retarder at a wavelength of the first beam of light.

18. The optical apparatus according to claim 14,

wherein the planar optical waveguide component is con-

figured to outcouple light propagating therein as the
first beam of light directed transversely to a normal
drawn to the outer surface, and

wherein the first optical system includes a substantially

planar metasurface configured to transmit said light
therethrough to form said spatially-expanding optical
beam propagating at a non-zero angle with respect to
said normal.

19. A method for controlling parameters of a beam of
light, the method comprising:

during a process of forming a magneto-optical trap

(MOT) for an atom with the use of a first beam of light

outcoupled from a planar photonic integrated circuit

(PIC) element:

transforming the first beam of light by having the first
beam of light interact with a first optical system to
produce a second beam of light having a substan
tially non-Gaussian profile at a pre-defined distance
from the PIC element

while, at the same time,

defining a cross-sectional area of the second beam at
the pre-defined distance to be at least 10* times larger
than that of the first beam of light at the PIC element,
wherein the pre-defined distance is within a range
from about 1 mm to about 200 mm.

20. The method according to claim 19, further compris-
ing:

spatially separating, at the first optical system, a zeroth

order of diffraction of the first beam from a non-zeroth
order of diffraction of the first beam, and

delivering light from the non-zeroth order of diffraction as

said second beam of light to a second optical system,
disposed at said pre-defined distance, to form the MOT.

ee Ree


US 2022/0390760 Al

the EMC 112. FIG. 1D is a scanning electron micrograph of
the 2D-array 160 of MS pillars 164 configured to generate
apolarization-dependent phase profile of the beam 124. FIG.
1E is an optical image of a specific implementation of the
planar structural layer IV in the form of a three-segment
grating chip (alternatively, an array of spatially distinct
grating chips can be employed); a ruled region has a 22 mm
diameter. FIG. 1F schematically presents a cross-section of
the schematic of FIG. 1A with some detail of geometry of
the system 100. Dotted lines 150, 154 indicate a Gaussian
spatial profile of intensity/irradiance of a beam 108 emanat-
ing from the PIC 104 and a substantially flat-top profile of
the beam 124 at the structural layer IV, respectively. Star
point indicates GMOT position. Inset to FIG. 1F shows
atomic fluorescence at 780 nm from the GMOT and the
laser-cooling beams at Rb partial pressure of ~1x10~* Pa.
[0025] The skilled person will readily appreciate, there-
fore, that an embodiment of an optical apparatus includes a
planar optical waveguide component having an outer sur-
face; a first optical system; and a second optical system. The
first optical system is a planar optical system that is config-
ured to accept a first beam of light, outcoupled from the
planar optical waveguide component transversely to the
outer surface, and to transmit a portion of light of the first
beam of light as a spatially-expanding optical beam, defined
by a non-zero order of diffraction of light at the first optical
system, to a target plane in which a distribution of irradiance
of the spatially-expanding optical beam is substantially
uniform. The second optical system is disposed in the target
plane and configured to transform the spatially-expanding
optical beam incident thereon into a plurality of return
optical beams, each of which overlaps with each of the
plurality of retum optical beams and the spatially-expanding
beam within the same volume of space. Such optical appa-
ratus is configured as a part of a magneto-optical trap for an
atom. In one specific implementation, the optical apparatus
is configured to form the spatially-expanding optical beam
such that a cross-section of the spatially expanding optical
beam, measured at the target plane, exceeds a cross-sec-
tional area of the first beam of light at the planar optical
waveguide component by at least a coefficient of 10° and
even 10!” (as discussed in presented herein specific example
of implementation).

Additional Technical Details

[0026] The PIC component 104 is preferably configured to
projects a linearly polarized Gaussian beam 108 in a direc-
tion tilted with respect to the normal to the surface of the PIC
(at about 4°, in implementation shown in FIG. 1F) which—
as a skilled artisan will readily appreciate—allows to maxi-
mize the efficiency of outcoupling of light from the wave-
guide of the PIC 104 when the outcoupler is structured as a
diffraction grating, for example. The QWP 120—when
used—converts polarization of the beam 108 from linear to
circular and transmits the circularly polarized light as beam
146 towards the MS 116. The dielectric (transmissive, in the
case shown) MS 116 is preferably disposed such that the
beam 146 (or, in absence of QWP 120—beam 108) strikes
the MS 116 at a non-zero angle with respect to the respective
normal (ifand when at about 4°, the plane of the MS 116 and
the plane of the PIC 104 are substantially parallel to one
another). The change of the phase profile, imposed on light
by the structure of the MS 116, causes the beam to deflect
preferrably substantially perpendicularly to the MS 116 and

Dec. 8, 2022

to diverge such that an approximately flat-top intensity
profile is realized at a predetermined distance away from the
MS 116 (in one example—after expanding the beam 124
over an approximately 150 mm distance). At this predeter-
mined distance, where the beam 124 was measured to be
about 20 mm in diameter, it was impinged on the three-
segment diffraction grating chip 134. The grating chip 134
(FIG. 1B) was designed to diffract light into a first diffraction
order at about 51° (under condition of normal incidence) at
a predetermined wavelength (780 nm in one experiment).
Three diffracted first order beams one from each of the
grating segments (a, b,c, as shown in FIG. 1E), were made
to overlap with the flat-top mode of the incoming beam 124
within a glass-walled vacuum chamber or cell 140 to form
the laser-cooling volume of the GMOT of FIG. 1A. External
electromagnets (schematically illustrated in FIG. 1A) were
used to generated a quadrupole magnetic field the center of
which resided in the laser beam overlap volume. The
arrangement of the overlapping beams and the quadrupole
magnetic field provided confining forces both along the
z-axis and in the radial (x-y) plane of the GMOT. The glass
cell 140 was attached to an auxiliary chamber containing an
ion pump and a Rb dispenser used to generate adjustable
partial pressures of Rb.

[0027] The SiN,-based PIC 104 (FIG. 1C), which was
used to launch the Gaussian beam 108 into free space,
included a waveguide WG and an EMC 112 (similarly to the
design described in Kim S. et al., in Light: Science &
Applications 7 72, 2017 or in Yulaev A, et al. in Interna-
tional Conference on Optical MEMS and Nanophotonics
(OMN) 2018 International Conference on Optical MEMS
and Nanophotonies pp 1-2, 2018, the disclosure of each of
which is incorporated herein by reference). The PIC 104 in
one case was fabricated from a 250 nm thick layer of
nominally stoichiometric silicon nitride (SiN,) clad from
both sides in 3 um of silicon dioxide (SiO,) with photonic
structures defined using electron-beam lithography followed
by reactive-ion etching. In operation of an embodiment,
light was edge-coupled into the fundamental TE, mode of
the PIC waveguide WG of 250 nmx300 nm cross-section,
aided by an inverse taper at the edge of the chip that
adiabatically expands the optical mode to increase coupling
efficiency of free-space light into the waveguide. Light was
further guided for about 5 mm across the chip of the PIC 104
to the EMC 112 where it was evanescently coupled into a
SiN, slab mode and then scattered into free-space using an
apodized outcoupling grating structure to form a substan-
tially circular in cross-section, collimated Gaussian beam
108 with an 1/e? radius of about 140 yum at an angle of about
4° from the surface normal (along the -y axis of the local
system of coordinates; see FIG, 1F). In the EMC 112, both
the slab-mode coupling and the apodized outcoupling grat-
ing scattering rate were spatially varied to project the desired
collimated, 2D Gaussian intensity profile, thereby increasing,
the mode area by a factor of about 10°. The total power
efficiency of the PIC 104-based structural layer I of the
apparatus (from input of the waveguide WG to the output
beam 108) was approximately 9% with input and output
coupling losses of about 6.5 dB and about 3 dB, respectively.
The free-space linearly polarized beam 108 emanating from
the PIC 104 was converted to that with a circular polariza-
tion using a conventional QWP 120. (In absence of using the
QWP 120, the beam 108 could be propagated directly to the
MS 116.)



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US 2022/0390760 Al

[0046] The GMOT geometry and planar optics demon-
strated here offer a natural pathway toward realizing cali-
bration-free measurement platforms and other quantum
devices utilizing laser-cooled atoms. The demonstrated
architecture is compatible with further integration with
on-chip light sources, solid-state alkali dispensers, MEMS-
based vacuum hardware, and on-chip methods for imaging,
and improvements in near-infrared and visible spectrum
photonic integrated circuits will make these devices more
power eflicient and expand the scope of addressable atoms.
We hope that the small physical size and robustness of
planar optics GMOT designs will enable compact atomic
clock designs, the emerging role of cold atoms in space
interferometry for test of fundamental physics, and compo-
nents required for widespread quantum networking.

[0047] The skilled person will readily appreciate that
different variations of the discussed embodiments are within
the scope of the present disclosure. For example, structural
layer II can be alternatively configured such as to perform
the functions of both the metasurface as a phase plate and the
structural layer III (in which case the presence of the
structural layer III is no longer required), In this case, the
so-configured alternative MS chip (structural layer II) can be
flip-chip bonded to PIC 104 (structural layer I) thereby
resulting in one planar substantially monolithic piece that
configured to emit light towards the location of the MOT
with the desired divergence, directionality and polarization,
resulting is a layered embodiment of the optical diffraction
apparatus in which different layers are in contact with one
another. Furthermore, when the structural layer IV is present
and represented by the diffraction grating chip), the so
stacked and integrated with one another structural layers I
and I] can be further bonded with/to the structural layer TV
with some planar spacer in between, resulting is a related
one-piece optical diffraction apparatus containing layered
planar structures. Understandably, no alignment between or
among the constituent layers is required in this case—the
proposed arrangement of planar optical elements are
designed to function with all components parallel or
mechanically registered without the need for tilt-tip align-
ment, providing the benefit of reduced complexity for manu-
facturing, increased mechanical rigidity, and decreased size.
In one case, the constituent structural layers of an embodi-
ment of the light-delivery system may be necessarily parallel
to one another.

[0048] References throughout this specification to “one
embodiment,” “an embodiment,” “a related embodiment,”
or similar language mean that a particular feature, structure,
or characteristic described in connection with the referred to
“embodiment” is included in at least one embodiment of the
present disclosure. Thus, appearances of the phrases “in one
embodiment,” “in an embodiment,” and similar language
throughout this specification may, but do not necessarily, all
refer to the same embodiment. It is to be understood that no
portion of the present disclosure, taken on its own and in
possible connection with a figure, is intended to provide a
complete description of all possible features of all or pos-
sible embodiments.

[0049] In addition, the following disclosure may describe
features with reference to corresponding drawings, in which
like numbers represent the same or similar elements wher-
ever possible. In the drawings, the depicted structural ele-
ments are generally not to scale, and certain components are
enlarged relative to the other components for purposes of

Dec. 8, 2022
10

emphasis and understanding. It is to be understood that no
single drawing is intended to support a complete description
of all features. In other words, a given drawing is generally
descriptive of only some, and generally not all, features. A
given drawing and an associated portion of the disclosure
containing a description referencing such drawing do not,
generally, contain all elements of a particular view or all
features that can be presented is this view, for purposes of
simplifying the given drawing and discussion, and to direct
the discussion to particular elements that are featured in this
drawing. A skilled artisan will recognize that embodiments
may possibly be utilized without one or more of the specific
features, elements, components, structures, details, or char-
acteristics, or with the use of other methods, components,
materials, and so forth. Therefore, although a particular
detail of an embodiment may not be necessarily shown in
each and every drawing describing such embodiment, the
presence of this detail in the drawing may be implied unless
the context of the description requires otherwise. In other
instances, well known structures, details, materials, or
operations may be not shown in a given drawing or
described in detail to avoid obscuring aspects of an embodi-
ment that are being discussed.

[0050] For the purposes of this disclosure and the
appended claims, the use of the terms “substantially”,
“approximately”, “about” and similar terms in reference to
a descriptor of a value, element, property or characteristic at
hand is intended to emphasize that the value, element,
property, or characteristic referred to, while not necessarily
being exactly as stated, would nevertheless be considered,
for practical purposes, as stated by a person of skill in the art.
These terms, as applied to a specified characteristic or
quality descriptor means “mostly”, “mainly”, “consider-
ably”, “by and large”, “essentially”, “to great or significant
extent”, “largely but not necessarily wholly the same” such
as to reasonably denote language of approximation and
describe the specified characteristic or descriptor so that its
scope would be understood by a person of ordinary skill in
the art. The use of this term in describing a chosen charac-
teristic or concept neither implies nor provides any basis for
indefiniteness and for adding a numerical limitation to the
specified characteristic or descriptor. As understood by a
skilled artisan, the practical deviation of the exact value or
characteristic of such value, element, or property from that
stated may vary within a range defined by an experimental
measurement error that is typical when using a measurement
method accepted in the art for such purposes. For example,
a reference to a vector or line or plane being substantially
parallel to a reference line or plane is to be construed as such
vector or line extending along a direction or axis that is the
same as or very close to that of the reference line or plane
(with angular deviations from the reference direction or axis
that are considered to be practically typical in the art, for
example between zero and fifteen degrees, more preferably
between zero and ten degrees, even more preferably between.
zero and 5 degrees, and most preferably between zero and 2
degrees). As another example, the use of the term “substan-
tially flat” in reference to the specified feature such as a
spatial profile or a surface implies that such profile or surface
may possess a degree of non-flatness and/or roughness that
is sized and expressed as commonly understood by a skilled
artisan in the specific situation at hand. For example, the
terms “approximately” and about”, when used in reference
to a numerical value, represent a range of plus or minus 20%



US 2022/0390760 Al

ment; and/or (11c) propagating light of the first beam of light
through the first optical system each component of which is
a planar optical component.

[0005] Embodiments further provide an optical apparatus
having an axis. Such optical apparatus is configured as a part
of a magneto-optical trap for an atom and includes a planar
optical waveguide component having an outer surface, and
a first optical system that is configured (a) to accept a first
beam of light, outcoupled from the planar optical waveguide
component transversely to the outer surface, and (b) to
transmit a portion of light of the first beam of light as a
spatially-expanding optical beam, defined by a non-zero
order of diffraction of light at the first optical system, to a
plane in which a distribution of irradiance of said spatially-
expanding optical beam is substantially different from a
Gaussian distribution. The optical apparatus further includes
second optical system disposed at the plane and configured
to transform the spatially-expanding optical beam incident
thereon into a plurality of return optical beams, each of
which overlaps with each of the plurality of return optical
beams and the spatially-expanding beam within the same
volume of space. An embodiment of the optical apparatus
may be configured to form the spatially-expanding optical
beam such that a cross-sectional area of the spatially
expanding optical beam, measured at the plane, exceeds a
cross-section of the first beam of light at the planar optical
waveguide component by at least a coefficient of 10*, and
where the distribution of irradiance is the plane to which the
spatially-expanding optical beam has been transmitted is a
substantially spatially-uniform distribution. Alternatively or
in addition, the first optical system may include (a) a
birefringent substantially planar metasurface that is dimen-
sioned to transform light incident thereon into light having
a circular polarization and a phase profile component cor-
responding to a phase shift that is introduced by a lens with
‘a negative optical power into light propagating through such
lens, and/or (b) an optical retarder, disposed between the
birefringent substantially planar metasurface and the planar
waveguide component, where the birefringent substantially
planar metasurface is configured to change a first state of
polarization of the light incident thereon (which light has
been outcoupled from the planar optical waveguide compo-
nent and that has traversed the optical retarder) to a second
state of polarization that is orthogonal to the first state of
polarization. In the latter case, the birefringent substantially
planar metasurface may be judiciously structure to include
only surface features each of which is a half-wave optical
retarder at a wavelength of the first beam of light, and/or to
satisfy a condition where the planar optical waveguide
component is configured to outcouple light propagating
therein as the first beam of light directed transversely to a
normal drawn to the outer surface, and/or where the first
planar optical system includes a substantially planar meta-
surface configured to transmit light therethrough to form
said spatially-expanding optical beam propagating at a non-
zero angle with respect to the normal to a surface of the first
optical system. Alternatively or in addition—and at least in
one implementation—the first optical system may include a
substantially planar metasurface configured to operate as a
combination of an optical prism and an optical lens with a
negative optical power, thereby deviating a beam of light
propagating therethrough from an original direction of
propagation while spatially expanding such beam of light
Additionally or in the alternative—and in at least one

Dec. 8, 2022

implementation—the second optical system of the optical
apparatus may include either a substantially planar diffrac-
tion grating having multiple surface areas (each of such
multiple surface areas characterized by a corresponding
optical diffractive structure, a first optical diffractive struc-
ture and a second optical diffractive structure being different
from one another and/or being spatially oriented in a dif-
ferent fashion with respect to a chosen reference point) or an
array of s] ly distinct diffraction gratings having corre-
sponding optical diffractive structures (where different dif-
fraction gratings having different optical diffractive struc-
tures and/or being differently oriented with respect to the
chosen reference point). In at t one specific c:
and every optical component of the first optical s
the second optical system is a planar optical component.

[0006] Embodiments further provide a method for propa-
gating light. Such method includes: —outcoupling light
from a waveguide of a planar integrated circuit (PIC)
element in a first direction at a non-zero angle to a surface
of the waveguide; —changing a degree of spatial diver-
gence, a direction of propagation, and a state of polarization
of a first portion of such light by transmitting such portion
through a birefringent planar metasurface while relaying a
second portion of such light in the first direction; —propa-
gating a spatially-expanding first portion of the light from
the birefringent planar metastructure/metasurface at a pre-
defined distance through a substantially optically uniform
medium to define a cross-section (of the first portion) that
has a substantially uniform distribution of irradiance in a
plane transverse to an axis of the first portion of the light;
and—substantially simultaneously diffracting the first por-
tion of the light at multiple different surface areas of a planar
diffractive optical device, disposed in the plane, to form
multiple diffractive optical beams spatially-intersecting each
other and the first portion of the light at the very same spatial
location. In at least one embodiment, the method may
additionally include (a) transmitting light through an optical
retarder along an axis coinciding with the first direction;
and/or (b) impinging light from the waveguide onto the
birefringent planar metasurface at an angle substantially
equal to the non-zero angle. At least in the latter case, the
substantially simultaneously diffracting may include dif-
fracting the first portion of the light at multiple difference
surface areas that have different diffractive characteristics,
and/or the changing a state of polarization may include
delivering light of said first portion with a circular polar-
ization upon transmitting light through the birefringent
planar metasurface. and/or the metasurface may include
only surface structures each of which is configured as a
half-wave optical retarder for said light outcoupled from the
waveguide, and/or the propagating may include defining the
cross-section that is substantially congruent with an area of
the planar diffractive optical element. (The step of defining
a cross-section may be configured to define a substantially
circular cross-section.) Alternatively or in addition—and at
least in one specific embodiment—the step of substantially
simultaneously diffracting may be configured to not produce
light reflected by the planar diffractive optical element along
an axis of an optical beam defined by the first portion of
light; and/or the step of changing a direction of propagation
may include delivering light of the first portion ina direction
substantially perpendicular to the surface of the waveguide
upon transmitting said light through the birefringent planar
metasurface; and/or the method may further contain a step of



Dec. 8, 2022 Sheet 6 of 7 US 2022/0390760 Al

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Patent Application Publication Dec. 8, 2022 Sheet 5 of 7 US 2022/0390760 Al

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US 2022/0390760 Al

with respect to the specified value, more preferably plus or
minus 10%, even more preferably plus or minus 5%, most
preferably plus or minus 2%.

[0051] The claimed subject matter, as recited in claims
appended to this disclosure, is intended to be assessed in
light of the disclosure as a whole.

What is claimed is:

1. A system comprising:

an optical diffractive apparatus having an axis, the appa-

ratus including:

an input structural layer containing an optical wave-
guide disposed substantially in a first plane trans-
verse to the axis; and

an output structural layer that includes a two-dimen-
sional array of spatially-separated from one another
rods of material, the array defining a second plane
transverse to the axis,

wherein the output structural layer is configured to
receive a first beam of light that has a first degree of
divergence and that has been formed from light
channeled by the optical waveguide to propagate
transversely to the axis, and to transform said first
beam of light into a second beam of light having a
second degree of divergence that is different from the
first degree of divergence, and

wherein the system is configured as a magneto-optical
trap for an atom.

2. The system according to claim 1, wherein the optical
diffractive apparatus additionally compris.

an auxiliary structural layer separated from the input

structural layer by the output structural layer, and an
auxiliary structural layer configured transform the sec-
ond beam of light received from the output structural
layer into multiple beams of light propagating in a
direction of the output structural layer.

3. The system according to claim 2, wherein the auxiliary
structural layer is configured to form multiple diffractive
beams of the same order of diffraction, said multiple dif-
fractive beams originating at different respectively-corre-
sponding locations while all overlapping at the same point
between the output and auxiliary structural layers.

4. The system according to claim 3, wherein the auxiliary
structural layer is configured to not reflect or diffract light
incident thereon along the axis.

5. The system according to claim 1, wherein the optical
diffractive apparatus further comprises:

an intermediate structural layer disposed between the

input structural layer and the output structural layer, the
intermediate structural layer configured as a substan-
tially plane-parallel plate of birefringent optical mate-
rial.
. The system according to claim 3, wherein:
the output structural layer is stacked upon and bonded to
the input structural layer such that a light outcoupler
element disposed at the input structural layer in the first
plane faces the output structural layer; and/or

the auxiliary structural layer is integrated with the output

structural layer with a planar spacer therebetween.

7. The system according to claim 1, wherein each and
every one of constituent structural layers of the optical
diffraction apparatus is substantially parallel to each and
every one of remaining constituent layers.

2

Dec. 8, 2022

8. The system according to claim 1, wherein each and
every constituent layer of the optical diffraction apparatus is
a planar optical component

9. The system according to claim 1, wherein:

the output structural layer is configured:

to accept light, outcoupled from the input structural
layer transversely to an outer surface thereof, and

to transmit a portion of said light as a spatially-
expanding optical beam, defined by a non-zero order
of diffraction of light at the output structural layer, to
a plane in which a distribution of irradiance of said
spatially-expanding optical beam is substantially dif-
ferent from a Gaussian distribution.

10. The system according to claim 9, necessarily com-
prising an auxiliary structural layer separated from the input
structural layer by the output structural layer,

wherein the auxiliary structural layer is configured to

transform said spatially-expanding optical beam inci-
dent thereon into a plurality of return optical beams,
each of which overlaps with each of the plurality of
return optical beams and the spatially-expanding dpti-
cal beam within the same volume of space.

11. A method for controlling parameters of a beam of
light, the method comprising:

using the system according to claim 1; and

at the output structural layer, transforming a first beam of

light, that has been outcoupled from the input structural
layer ina first direction at a non-zero angle to a surface
of the input structural layer and received by the output
structural layer,

to change a degree of spatial divergence, a direction of

propagation, and a state of polarization of a first portion
of said first beam of light while relaying a second
portion of said first beam of light in the first direction.
12. The method according to claim 11, wherein the
method comprises one or more of the following:
propagating the first portion of the first beam of light
through a substantially optically uniform medium to
define a cross-section, of said first portion, that has a
substantially non-Gaussian profile of irradiance;

transmitting the first beam of light through an optical
retarder along an axis substantially coinciding with the
first direction; and

impinging light of the first beam of light onto a birefrin-

gent planar metasurface at an angle substantially equal
to the non-zero angle.
13. The method according to claim 11, further compris-
ing
receiving the first portion at an auxiliary structural layer
of the system that is separated from the input structural
layer by the output structural layer such that a cross-
section of the first portion is substantially congruent
with an active area of the auxiliary structural layer; and

transforming light from said first portion to define mul-
tiple beams of light propagating in a direction of the
output structural layer.

14. An optical apparatus having an axis and comprising:

a planar optical waveguide component having an outer

surface;

a first optical system configured:

to accept a first beam of light, outcoupled from the
planar optical waveguide component transversely to
the outer surface, and



US 2022/0390760 Al

PLANAR-OPTICS BASED LIGHT DELIVERY
SYSTEM FOR MAGNETO-OPTICAL TRAPS
AND METHOD FOR USING THE SAME

CROSS-REFERENCE TO RELATED
APPLICATION(S)

[0001] ‘The present application claims priority from and
benefit of the U.S. Provisional Patent Application No.
63/196,559 filed on Jun. 3, 2021, the entire disclosure of
which is hereby incorporated by reference herein.

STATEMENT CONCERNING FEDERALLY
SPONSORED RESEARCH AND.
DEVELOPMENT
[0002] This invention was made with government support
under 70NANB14H209 awarded by the National Institute of
Standards and Technology (NIST). The government has

certain rights in the invention.

[0003] Measurements utilizing gases of laser-cooled
atoms are presently confined to controlled laboratory envi-
ronments due to the large-scale optical assemblies required
to prepare and manipulate cold gases. Methods miniaturiza-
tion, simplification, and integration of laser-cooling tech-
nology impact applications including clocks, inertial sen-
sors, magnetometers, vacuum sensors, quantum simulation,
and quantum networking, to name just a few. Preparing
atoms into a magneto-optical trap (MOT) is a key step in
these applications, and efforts to miniaturize MOT designs
have centered around replacing conventional 6-beam
designs with single-input-beam alternatives such as pyramid
MOTs and grating MOTs (GMOTs). While these methods
provide significant simplification of the optical hardware
required for laser cooling, while lithographically fabricated
grating chips have broadened the scope of GMOT design
(including the realization of integrated Zeeman-slowing,
grating-based two-dimensional (2D) MOTs, and new meth-
ods for trapping alkaline earth atoms), and photonic inte-
grated circuits (PIC) fabricated on SiN, platforms have
‘enabled chip-based interrogation of warm atomic vapors for
clock applications, mass manufacturable solutions that pro-
vide a substantially miniaturized laser-cooling platform in
which constituent components of at least optical systems
configured to deliver light to an MOT are configured as
nanophotonic components that can be lithographically fab-
ricated and integrated to form a portable, manufacturable
package remain desired.

SUMMARY

[0004] Embodiments include a method for controlling
parameters of a beam of light. Such method, performed
during a process of forming a magneto-optical trap (MOT)
for an atom with the use of a first beam of light outcoupled
from a planar photonic integrated circuit (PIC) element,
includes a step of transforming the first beam of light by
having the first beam of light interact with a first optical
system to produce a second beam of light having a substan-
tially non-Gaussian profile at a pre-defined distance from the
PIC element while, at the same time, defining a cross-
sectional area of the second beam at the pre-defined distance
to be at least 10* times larger than that of the first beam of
light at the PIC element, wherein the pre-defined distance is

Dec. 8, 2022

within a range from about 1 mm to about 200 mm. Alter-
natively or in addition, and in at least one implementation,
the step of transforming may include producing the second
beam of light having a substantially flat-top profile at the
pre-defined distance, and/or the method may additionally
include spatially separating, at the first optical system, a
zeroth order of diffraction of the first beam from a non-
zeroth order of diffraction of the first beam, and delivering
light from the non-zeroth order of diffraction as said second
beam of light to a second optical system, disposed at the
pre-defined distance, to form the MOT. When such spatially-
separation takes place, the method may additionally be
configured to satisfy one or more of the following condi-
tions: (a) the delivering includes delivering the second beam
of light having a state of polarization that is substantially
uniform across the second beam; and (b) the transforming
includes controlling the state of polarization of the second
beam of light only with the first optical system. In one
specific implementation of the method, the second optical
system may include a diffraction grating: and/or the first
optical system may include a metasurface that is configured
(i) to modify a state of polarization of light incident thereon
to form the second beam with a state of polarization that is
substantially uniform across the second beam, and (ii) to
cause the second beam have a substantially flat-top profile at
the pre-defined distance by introducing a spatially-depen-
dent phase delay into light of the first beam incident thereon
while, at the same time, effectuating said spatially-separat-
ing by introducing a linear gradient into the light of the first
beam; and/or (iii) the action of spatially separating occurs in
transmission of light of the first beam through a component
of the first optical system. In at least one specific imple-
mentation of the method, the step of transforming may
include producing the second beam having (at the pre-
defined distance) a cross-section that is substantially con-
gruent with an active area of the diffraction grating; and/or
the method may additionally include a step performed
during interaction between the first beam of light and the
first optical system and containing and action of defining a
state of polarization of the second beam of light to be
circular; and/or an action of changing a state of polarization
of light propagating through the first optical system from a
first state of polarization to a second state of polarization that
is orthogonal to the first state of polarization. Alternatively
or in addition, and in at least one implementation, the
method may include outcoupling the first beam of light
having a substantially Gaussian spatial profile from a wave-
guide of the PIC through a diffractive optical element of the
PIC in a direction that is tilted with respect to a normal
drawn to a surface of the PIC; and/or defining a volume of
space in which the second beam and each of beams, formed
by the second optical system in response to being irradiated
with the second beam, overlap simultaneously. In one
ited implementation, the step of transforming may
include producing the second beam having, at the pre-
defined distance, a substantially circular cross-section. In at
least one specific case, the step of transforming may include
(a) transmitting light of the first beam of light through a
quarter-wave plate and interacting such light with a meta-
surface comprising surface structures each of which is
configured as half-wave phase retarder at a wavelength of
the first beam of light; and/or (b) producing the second beam
of light in which the substantially flat-top spatial profile
occurs only at the pre-defined distance from the PIC ele-



as) United States
a2) Patent Application Publication co) Pub. No.: US 2022/0390760 Al

MCGEHEE et al.

0220390760A1

(43) Pub. Date: Dec. 8, 2022

G4)

ay

(72)

(21)

(22)

(60)

PLANAR-OPTICS BASED LIGHT DELIVERY
SYSTEM FOR MA -OPTICAL TRAPS
AND METHOD FOR USING THE SAME

Applicants: University of Maryland, College Park,
College Park, MD (US); Government
of the United States of America, as
represented by the Secretary of
Commerce, Gaithersburg, MD (US)

Inventors: William R. MCGEHEE, Boulder, CO
(US); Jabez MCCLELLAND,
Bethesda, MD (US); Vladimir
AKSYUK, Gaithersburg, MD (US,
Wenqi ZHU, Vienna, VA (US); Amit
Kumar AGRAWAL, Rockville, MD.
(US)

Appl. No.: 17/831,003
Filed: Jun. 2, 2022

Related U.S. Application Data

Provisional application No. 63/196,559, filed on Jun.
3, 2021.

Publication Classi

Int. Cl.
GO2B 2742
GO2B 5/18
(52) US. Cl.
cpc

cation
G6)

(2006.01)
(2006.01)

s» GO2B 27/4272 (2013.01); G02B 5/1833
(2013.01); G02B 27/4233 (2013.01); GO4F
5/145 (2013.01)

(57) ABSTRACT

‘An apparatus for light delivery to magneto-optical trap
(MOT) system utilizes only ‘planar optical diffraction
devices including a planar-integrated-cireuit PIC and a
metasurface MS. When MOT is based on the use of a
diffraction grating, a grating chip is additionally employed to
launch and manipulate light for laser cooling. Bridging the
gap between the sub-micrometer-scale guided mode on the
PIC and the centimeter-scale beam needed for laser cooling,
a magnification of the mode area by about 10'° is demon-
strated using an on-chip extreme-mode-converter to Jaunch
a Gaussian mode into free space from a PIC-waveguide and
a beam-shaping, polarization-dependent MS to form a
diverging laser beam with a flat-top spatial profile, which
efficiently illuminates the grating chip without loss of light.
Comparison to equivalent Gaussian-beam-illuminated
GMOTS evidences advantageous power efficiency of opera-
tion of the proposed light delivery system as compared with
conventional systems employing Gaussian distribution of
illumination at the grating chip.

4384 140

1388


US 2022/0390760 Al

erated with one another according to embodiments of the
present disclosure not only offer a pathway to developing
chip-scale, reduced size and cheaply manufacturable devices
utilizing cold atoms but (according to some estimates pre-
sented below in reference to embodiments) such devices use
at least 2.5 times less optical power to observe the onset of
atom trapping as compared to that required by a conven-
tionally structured GMOT.

[0015] The problem of complexity of the processes of
manufacturing of optical systems for light delivery and
alignment of the constituent components of such systems to
enable magneto-optical trapping of atoms, persisting in
related art, is solved by devising an optical apparatus a
production of which is substantially completely defined by
only lithographic processing, each and every component of
which is a planar—as opposed to bulk—optical component
(although lithographically-defined optical components with
curved surfaces remain within the scope of the proposed
solution), thereby allowing such apparatus to be formatted
as a set of spatially stackable lithographically-defined opti-
cal components substantially free of the need of judicious
alignment. The proposed solution also solves an additional
problem caused by operation of light-delivering sub-systems
of conventional magneto-optical traps (MOTs) for atoms—
specifically, the problem that manifests in wasting (that is,
not utilizing) a substantial part of light delivered to such
traps (due to, for example, not utilizing light necessarily
falling outside of the grating aperture in the case of the
diffraction-grating-based MOT). Here, the combination of
the proposed planar optical components is configured to
define a cross-section of the light beam delivered to the
MOT to be not only substantially spatially congruent with
and having a substantially equal foot-print with the optical
system utilized by the MOT (such as, in the considered
specific example, the diffracting grating) but also possessing
a judiciously engineered, transformed (as compared with
that used in the conventional systems) transverse profile of
irradiance, thereby minimizing or even eliminating the
amount of delivered light not usefully processed by the
MOT.

[0016] As a result of the planar-optics nature of such
opti apparatus, the corollary problem of ever-desired
minimization of the spatial extent of such optical apparatus
is also solved, in that the apparatus lends itself to generally
not exceed a few inches (for example, 6 inches or less) in
linear extent, and in some specific embodiments—no longer
than 3 cm, preferably no longer than 2 cm, even more
preferably no longer than 1 cm. Notably, in the configuration
where the proposed all-planar lithographically-defined light
delivery apparatus is placed in the vacuum chamber of the
MOT system, the typical linear extent of such apparatus can
be practically reduced to be shorter than 1 cm, and prefer-
ably no longer than 5 mm. (This is in advantageous contra-
distinction with the systems of related art, the operation of
which utilizes collimated beams of light used for illumina-
tion of the diffraction grating of the MOT systems.)
[0017] For the purposes of this disclosure and the
appended claims, and unless expressly defined otherwise,
the term “optical metasurface” (interchangeably used below
simply as “metasurface”) is typically used in related art to
refer to a material interface that has structures on it that
impose particular phase shifts on light interacting with this
material interface (that is, which is either transmitted
through or reflected off the interface). In some cases, the

Dec. 8, 2022

optical metasurface may include a planar array of subwave-
length electromagnetic structures that emulate the operation
ofa conventional, bulk refractive, birefringent, or diffractive
optical component (such as, in non-limiting examples, a
lens, a waveplate, or a hologram) through individually
tailored amplitude, phase, or polarization transformations
imposed by the metasurface on incident light with which
such metasurface interacts. The term “spatial profile of a
beam of light” (interchangeably —a transverse profile of a
beam of light) and related terms are used to describe a
transverse distribution of irradiance or intensity of the beam
of light and are generally defined as a profile of irradiance
or intensity of the beam at hand in a plane that is substan-
tially perpendicular to the axis of such beam. A flat-top
profile (or, a uniform profile) of a beam of light is that which
possesses a substantially uniform or substantially constant
irradiance or intensity distribution across the beam (that is,
as would be understood by a skilled person, over most of the
cross-sectional area of the beam, within the limits acceptable
by the system utilizing such beam of light, and regardless of
the phase-distribution across the beam; see, for example, at
rp-photonics.com). A normal to a surface is defined as a
vector that is perpendicular to the surface at a given point.
The terms “planar optics”, or “planar optical component”, or
“planar structural layer” as well as related terms refer to and
are defined as those denoting substantially completely and
fully lithographically-fabricated micro- and nano-sized pho-
tonic components, layers, etc. The term congruent is defined
coinciding at all points when superimposed (and, in refer-
ence to two surfaces—coinciding substantially at at least
90% of the surface area).

[0018] The discussed examples of embodiments relate to
and address the laser cooling methodology using a light
delivery system or apparatus that includes planar optical
elements operating at 780 nm, with the specific implemen-
tations demonstrating a GMOT of *’Rb. A skilled person,
however, will readily appreciate that these are but specific
examples and generally the scope of the disclosure covers a
method for controlling parameters of a beam of light during
a process of forming a magneto-optical trap for an atom with
the use ofa beam of light outcoupled from a planar photonic
integrated circuit (PIC) element and processed by (interact-
ing with) a collection of planar optical devices, a corre-
sponding diffractive optical light delivery system in which
each of the constituent components is a planar optical
component, and related method of propagating of light
through the planar optical system configured to deliver light
to the MOT.

[0019] In particular, this disclosure addresses a system
(generally, a magneto-optical trap for atoms) that includes an
optical diffractive apparatus configured as a system of light
delivery to such MOT. The optical diffraction apparatus has
an axis and, according to embodiments includes a first
structural planar-optics (or, interchangeably, planar optical)
layer and a second structural planar-optics layer generally
disposed substantially in parallel to and/or stacked upon the
first structural layer. The first structural layer is a layer of a
planar integrated circuit containing an optical waveguide
disposed substantially in a first plane transverse to the axis,
while a second structural layer includes a two-dimensional
array of spatially-separated from one another rods or col-
umns or pillars of material. Such an array defines a second
plane transverse to the axis. The second structural layer is
configured to receive a first beam of light (that has a first



US 2022/0390760 Al

passing light from the second portion outside of boundaries
of the planar diffractive optical device and substantially
without illuminating the planar diffractive optical device
with the light from the second portion. In at least one specific
implementation, the step of propagating a spatially-expand-
ing first portion of the light from the birefringent planar
metastructure at the pre-defined distance may be judiciously
defined as propagating the first portion at a distance within
the range not exceeding 200 mm.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Aspects of the present disclosure will be more fully
understood by referring to the following Detailed Descrip-
tion of Specific Embodiments in conjunction with the Draw-
ings, of which:

[0008] FIGS. 1A, 1B, 1C, 1D, 1E, and IF illustrate a
specific embodiment of a planar-optics-based GMOT appa-
ratus. FIG. 1A: A linearly polarized Gaussian beam,
launched from the PIC, is circularly polarized during tra-
versal through an optical quarter-wave plate (QWP). The
planar optical component including a judiciously devised
metasurface (MS) generates a spatially-expanding mode of
light with an orthogonal (opposite) polarization while form-
ing a flat-top intensity profile of such mode at the segmented
grating chip. Each of the three first-order diflracted beams
(respectively generated by diffraction at a corresponding one
from each of the spatially-distinct and non-overlapping with
‘one another grating segments) overlap with the incident light
at the same point of space to form the four-beam GMOT.
Positive and negative first orders of diffraction from one
grating segment are shown. In this specific example, the
GMOT is realized inside a glass vacuum chamber with a
magnetic quadrupole field created by external electromag-
nets. FIG. 1B provides an illustration of a first order dif-
fraction beam emanating from the grating chip and the status
of polarization of such a beam. FIG. 1C presents an optical
image of a first planar layer component (of the GMOT
apparatus of FIG. 1A) that includes a PIC carrying wave-
guide and EMC structures therein/thereon. Inset to FIG. 1C
illustrates components of the EMC. FIG. 1D is a scanning
electron micrograph showing a two-dimensional array of
metasurface pillars/columns dimensioned and spatially-ori-
ented to generate a desired polarization-dependent phase
profile of light upon interaction of such light with the MS.
FIG. 1E is an optical image of a three-segment grating chip
(of the GMOT of FIG. 1A); ruled region has an approxi-
mately 22 mm diameter. FIG. 1F is a cross-section of the
system of FIG. 1A providing detailed geometry of the
apparatus. Dotted lines indicate Gaussian and flat-top inten-
sity profiles. Beams’ polarizations in this example are left-
hand circular (LHC) and right-hand circular (RHC). Star
point indicates GMOT position. Inset to FIG. 1F illustrates
atomic fluorescence at 780 nm empirically generated with
the use of the apparatus of FIG. 1A and the laser-cooling
beams at Rb partial pressure of about 1x10~* Pa

[0009] FIGS. 2A, 2B, 2C, 2D illustrate the process of
characterization of the flat-top beam of laser light formed by
a planar-optics based portion of the diffractive optical sys-
tem of light delivery of the apparatus of FIG. 1A formed at
the grating chip of the apparatus. FIG. 2A: Intensity of the
flat-top and 0” diffractive order beams at about 150 mm
from the location of the MS (which is substantially equal to
the distance between the MS and the grating chip). FIG. 2B:
a slice/cross-section of the intensity profile along the x-axis

Dec. 8, 2022

(formed along an arrow indicated in FIG. 2A) evidences
substantial spatial uniformity of the flat-top distribution of
irradiance of light formed in a given diffraction order by the
MS at a predetermined distance from the MS. FIG. 2C: a
computed phase profile of the MS planar optical structural
layer, of the apparatus of FIG. 1A, including both the
beam-shaping and prism phase contributions. MS area is
300 jumx300 jum. FIG. 2D schematically illustrates an MS
unit cell (a pillar or column) configured to introduce a
predetermined phase delay to light propagating therethrough
(in a discussed example—a quarter-wave phase pillar).
Rotation of the pillar in the plane of the MS structural layer
defines the local geometrical phase shift of the light.
[0010] FIG. 3 illustrates the results of a time-of-flight
temperature measurement. Temperature of the GMOT is
~200 [KK at I,,,)/1,0.5. Insets show absorption images at
tror=@) 1.8 ms and (ii) 3.5 ms.

[0011] FIG. 4 illustrates the steady-state GMOT popula-
tion vs. cooling light intensity. Data are shown for a 20 mm
diameter, flat-top illumination of the grating chip (curve 1)
as well as apodized Gaussian beam illumination with w~24
mm (curve 2) and w~16 mm (curve 3). Dashed lines are
linear fits to the data below 2 mW cm”. Inset shows the
same data over a larger intensity range. Extrapolated popu-
lation using GMOT performance and volume scaling (bor-
rowed from Nshii C et al., Nature Nanotechnology 8, 321-4,
213) is plotted for V,,.,0.34 cm® (black star 410).

[0012] Generally, the sizes and relative scales of elements
in Drawings may be set to be different from actual ones to
appropriately facilitate simplicity, clarity, and understanding
of the Drawings. For the same reason, not all elements
present in one Drawing may necessarily be shown in
another.

DETAILED DESCRIPTION,

[0013] Laser-cooled atoms are a key technology for many
calibration-free measurement platforms— including clocks,
gyroscopes, and gravimeters—and are a promising system
for quantum networking and quantum computing. The
optics and vacuum hardware required to prepare these gases
are often bulky and not amenable to large-volume manu-
facturing, limiting practical realization of devices that ben-
efit from the properties of cold atoms. Furthermore, one
striking disadvantageous characteristic of the existing
implementations of diffraction-gratings based MOTs is a
waste of the MOT illuminating light—which understand-
ably translates to unnecessarily lowered efficiency of the
overall MOT system. (As is well known in related art, this
is typically caused by the fact that the spatial profile of the
grating-chip irradiating light of the GMOT is a substantially
Gaussian profile. In a Gaussian-beam illuminated GMOT,
illumination of the grating chup is typically accomplished
using beam waist of similar or larger dimension than the
clear aperture of the grating, which is a current standard in
related art. See, for example, Eckel S, et al., Challenges to
miniaturizing cold atom technology for deployable vacuum
metrology Metrologia 55 $182-S193, 2018; or McGilligan J
P. et al., Grating chips for quantum technologies Scientific
Reports 7, 2017; to name just a few). Light falling outside
of the grating aperture is expressly lost or wasted as it is not
used in formation of the trap for atoms.

[0014] In advantageous contradistinction, planar, litho-
graphically produced optics including photonic integrated
circuits, optical metasurfaces, and gratings judiciously coop-



Dec. 8, 2022 Sheet 7 of 7 US 2022/0390760 Al

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Patent Application Publication Dec. 8, 2022 Sheet 3 of 7 US 2022/0390760 Al

140
FIG, 1F

Vacuum chamber

108


US 2022/0390760 Al

[0028] The MS 116 was that of a Pancharatnam-Berry
(PB) type MS (see, for example, Bomzon Z. et al. Opt. Lett.
26 1424-6, 2001) composed of dielectric Si pillars (see FIG.
1D), was used to convert the PIC-launched Gaussian beam
into a diverging beam 124 with half angle of 3.8°, such that
a substantially flat-top intensity profile was realized at a
distance d= 150 mm, and to redirect the beam 124 formed by
light diffracted at the MS 116 in a non-zero diffraction order
substantially perpendicularly to the MS optic with a deflec-
tion angle of 4° with respect to the original direction of
propagation, as shown in FIG. 1F. Referring now to FIGS.
2A, 2B, the induced by the MS 116 divergence of the beam
124 enables the beam 124 to fill a substantially circular
region of radius R~10 mm such as to match the ruled region
of the grating chip 134 disposed at distance d from the MS
116. The flat-top intensity of the cross-section of the beam
124, realized at the surface of the grating 134, provides
substantially uniform illumination of the grating chip such
that the generated optical forces from the incident and
diffracted beams are approximately balanced across the
intended laser-cooling volume. The 4° deflection allows
spatial separation from the 0” order transmission (beam
124A) and ensures a uniform polarization state of the
expanding beam 124.

[0029] Referring now to FIGS. 2C and 2D, the MS 116
contained a two-dimensional array 210 of substantially
rectangular, polycrystalline Si nanopillars supported by a
fused: substrate and extending across the beam 108 and
the axis of the optical light-delivery system. Individual
pillars 214 (interchangeably referred to herein as columns or
rods) resided on a square grid with about 280 nm spacing
covering an area of about 300 mx300 pm. These pillars or
rodshad nominal in-plane dimensions of 92 nmx176 nm and
a substantially constant (across the array 160 of the columns
160A) height of 660 nm. The geometry of Si pillars 160A
have shape-birefringence such that each pillar 160A acted as
a half-wave retarding element for 780 nm light (the wave-
length of the Rb cooling transitions). (Understandably, in a
related embodiment that is devoid of the QWP 120, the MS
116 can be configured to act as a quarter-wave tearding
element.) Circularly polarized light 146 incident on these
rod-like structures from the QWP 120 has its polarization
handedness reversed and receives a local geometrical phase
shift set by the in-plane rotational orientation of the pillars/
rods 160A. The pillar-orientation-dependent phase shift is
used to generate the desired phase profile and, understand-
ably, varied to achieve a desired result in a related imple-
mentation. The metasurface 116 was substantially centered
on the PIC-launched beam 108.

[0030] In the embodiment considered in reference to
FIGS. 2A-2D, the phase profile encoded on the MS 116 was
that of the planar equivalent of a prism complemented with
a non-spherical, negative focal length lens. The phase profile
was determined using a ray optics approach assuming that
the local phase gradients 6’ in the planar optic deflect
normally incident light at an angle @, from normal as

where A is the vacuum wavelength of light and n is the
effective index of the propagating medium. The radially
symmetric phase gradient, judiciously devised to map the

Dec. 8, 2022

power of an ideal Gaussian beam of 1/e* radius w substan-
tially uniformly into a circle of radius R at a distance d from
the MS 116, can be expressed as:

co)

[0031] Since this phase profile is not stationary upon
propagation of the beam 124 as it depends on the distance d,
the approximately flat-top distributions of intensity (FIG.
2B) was realized in a region around the design distance d
away from the MS 116 which includes the capture volume
of the overall MOT system. The 4° deflection was achieved
using an additional linear phase ramp along the y-axis of the
metasurface and spatially separated the flat-top mode from
the undesired 0" order transmission at the location of the
grating 134. The composite phase profile of the beam 124 in
the plane at the exit of light from the MS 116 is plotted in
FIG. 2C.

[0032] The intensity profile of the flat-top beam was
measured at the location of the diffraction grating 134 and
caused high uniformity of light distribution over the mode
area (FIG. 2C). Root-mean-squared (RMS) intensity varia-
tions were observed at 7% in the central 20% of the mode
area and <20% over the central 80% of the mode area. It can
be seen that two lobes with peak intensities=2.5x the central
mode intensity were formed on the periphery of the flat-top
mode (as seen in a cross-section of the beam 124) and
explained by the ~4° incidence angle of the PIC-launched
beam at the MS 116. While in practice these lobes likely
altered the total GMOT capture rate, it is believed that the
balance of forces at the location of the trapped atoms was
minimally impacted by these lobes as they did not signifi-
cantly overlap within trap volume. Ripples in the mode
profile, observed in FIG. 2C, are explained both by diffrac-
tive effects during beam 124 propagation and spatially
varying diffraction efficiency and optical absorption across
the MS 116, primarily at the location of phase discontinui-
ties. Notably, as the person of skill will readily appreciate,
the spatial separation between the flat-top light 124 and the
0” order beam 124A is required in practice as the peak
intensity of the unshaped, 0” order beam 124 is tens of time
(in one case=up to a hundred time) higher than that of the
flat-top mode 124 at the location of the planar structural
layer IV of the optical apparatus. If not separated from the
beam 124 and delivered to and overlap with the planar
structural layer IV when such layer is represented by the
grating 134, the intense, 0” order beam 124 could distort or
destroy the GMOT. High-order diffraction is seen in the 0”
order beam due to clipping of the Gaussian profile in the
EMC.

[0033] The MS 116 had an experimentally verified con-
version efficiency of light power incident upon it into the
flat-top beam at the location of the structural layer IV of
about 71%. The efficiency was limited by several factors
including Fresnel reflection, optical absorption in Si due to
above-bandgap operation, fabrication imperfections, and
lithographic limits on the number of sub-wavelength ele-
ments 160A that can be placed within an optical wavelength.



US 2022/0390760 Al

reached a population of =2.8x10° at I,,.,1.8 mW cm”?
(FIG. 4). The GMOT population below I,,.,,-0.5 mW cmTM?
was minimal due to a combination of decreased scattering
forces and increased trap loss at low I,,,,[41,42]. Linear
growth of atom number with I,,.,. Was typical at low satu-
ration of the atomic transition, and maximum steady-state
GMOT populations were typically observed at Iyu,>>Lyar
For comparison, Nayor in Nature Nanotechnology 8, 321-4,
2013 was observed to peak at 6x10" using 1,50 mW
cm”? (#14 I,,,) in V,,.,1 cm®, The same work demonstrated
a volume scaling Nyjo7~Vpap'?s predicting an equivalent
maximum Nyopof 18x10” atoms in our system (V,.,-0.34
cm, star point in inset of FIG. 4). The volume-scaled
population was consistent with GMOT population trend
observed in current experiments.

‘Comparison of Operation of Proposed Embodiment(s) with
that of a Conventionally-Used System.

[0041] The skilled artisan will now readily appreciate
various practical advantages of use of the light delivery
system configured as a combination of planar optical com-
ponent based on a simple comparison between the perfor-
mance of the planar-optics, flat-top illuminated GMOT
discussed above with that of a traditional, conventionally-
used in related art Gaussian-beam illuminated GMOT. To
perform such a comparison, a bulk-optics assembly was
employed to prepare collimated, circularly polarized Gauss-
ian beams normally incident to the grating chip. Two beam
waists (intensity 1/e? radii) of w~16 mm and ~24 mm were
tested. Each Gaussian beam was delivered at normal inci-
dence on the segmented grating chip 134 and apodized
within a 20 mm diameter circle to match the boundary size
of the 20 mm diameter flat-top beam 124. The concomitant
beam overlap volume approximated that of the flat-top beam
GMOT and enabled a fair comparison of their relative
performance. GMOTs were prepared using the same nomi-
nal laser frequencies, quadrupole field gradient, and Rb
partial pressure used in the flat-top illuminated GMOT
experiments discussed above. The intensity of the trapping
light was varied (quoted using the Gaussian beam’s central
intensity), and atom number and temperature measurements
were made using TOF imaging. Measured temperatures and
in-trap sizes were consistent with the flat-top illuminated
GMOT values.

[0042] The Gaussian-illuminated GMOT population was
measure to be lower than that observed with the flat-top
illumination as shown in FIG. 4. For Gaussian illumination,
the onset of appreciable capture was also observed at
non-zero laser intensity and Nyor also increases approxi-
mately linearly in the jow-saturation regime. Reduced cap-
ture rate for Gaussian illumination was expected due to
decreased optical forces at the periphery of the capture
volume and to imperfect balancing of laser-cooling forces
arising from the Gaussian intensity profile. Accordingly, the
oO intensity of the linear population trends also shifted to
higher intensity for smaller w. Zero Nyor intercept values of
Tjnqp@0-48 mW cm, I,,.,~0.61 mW cm, and 1,,.,=0.88
mW cm”? were observed for the flat-top beam 124, w~24
mm and w~16 mm Gaussian beams, respectively. The shift
to capture beginning at higher central beam intensity corre
sponded roughly to equal intensities averaged over the
trapping volume. Mean intensities over the trapping volume
were calculated to be =110%, ~84.7%, and =77% of 1, for
the flat-top beam 124, and w=24 mm, and w=16 mm
Gaussian beams, respectively. The population reduction

Dec. 8, 2022

with Gaussian illumination was most pronounced in the low
saturation regime in which optical forces were linearly
related to intensity. At high values of Ij,.,. the observed
Nyor trends for flat-top and Gaussian illumination began to
converge due to saturation of the atomic transition, as shown
in inset of FIG. 4.

[0043] The use of the light beam possessing a substantially
non-Gaussian (and, in particular, a substantially flat-top,
uniform) profile of irradiance/intensity, generated at the MS
of the embodiment of the optical diffraction apparatus
discussed above, allowed for efficient use of the available
optical power in illuminating the structural layer IV (the
grating chip 134, as discussed). Uniform illumination in a
GMOT ensured that diffracted light from the grating seg-
ments (a, b, c) could balance the forces created from the
incident beam 12. In Gaussian-beam illuminated GMOTs,
similar effect is typically achieved using beam waists of
similar or larger dimension than the clear aperture of the
grating (see, for example, “Grating chips for quantum tech-
nologies”, Scientific Reports 7, 2017). As a result, grating-
illuminating light falling outside of the grating aperture is
wasted—for the w~24 mm beam used here, ~30% of the
light strikes the ruled grating area and ~2.5 times the optical
power was required to observe the onset of trapping (ac-
counting for the ~71% efficiency of the MS 116). Similarly,
~2.5 times more optical power is required for the w=24 mm
beam to trap 10° atoms relative to the flat-top beam.
[0044] The absolute power efficiency of the planar optics
in generating the divergent flat-top beam from a fiber-
launched Gaussian beam was about 6.4% (=12 dB loss).
Coupling light into and projecting light from the PIC was the
largest source of loss at approximate 10.5 dB due to a
combination of insertion loss into the PIC, waveguide loss,
and scattering into the PIC substrate in the EMC. Similar
devices demonstrated losses as low as 7.5 dB+0.5 dB using
fiber edge coupling, and significant improvement in the
mode coupler efficiencies are possible with more complex
designs. The MS efficiency corresponded to 1.5 dB loss and
was competitive with other high-performance designs. The
specific design of the diffractive grating (in the structural
layer IV) was also a source of lost optical power as, by
design, only ¥4 of the incident light was diffracted toward the
capture volume. Schemes using large area metasurfaces or
PIC-based beam launching for all required beams provide
paths to potentially higher power efficiency at the expense of
greater experimental complexity.

[0045] Overall, a GMOT of Rb was demonstrated with the
use of planar constituent optical devices including a PIC,
MS, and grating chip to launch and manipulate light for laser
cooling. Bridging the gap between the sub-micrometer-scale
guided mode on the PIC and the centimeter-scale beam
needed for laser cooling, a magnification of the mode area
by ~10"°, is accomplished using an on-chip EMC to launch
a Gaussian mode into free well as a beam-shaping,
polarization-dependent MS to generate an expandin
top mode laser beam. The flat-top beam efficiently
nates a grating chip to realize a four-beam GMOT with
capture rates demonstrated as high as ~10’ s“! and gas
temperatures below 200 jiK. Steady-state GMOT popula-
tions were demonstrated at ~2.8x10°, consistent with pub-
lished volume and intensity scaling for GMOT performance.
Comparisons to equivalent Gaussian-beam-illuminated
GMOTs demonstrate the power efficiency of the flat-top
beam profile relative to conventional Gaussian-illumination,



Dec. 8, 2022 Sheet 2 of 7 US 2022/0390760 Al

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degree of divergence and that is formed from light channeled
by the optical waveguide to propagate transversely to the
axis) and to transform such first beam of light into a second
beam of light having a second degree of divergence that is
different from the first degree of divergence.

[0020] Optionally—but in a specific implementation dis-
cussed below in reference to FIGS. LA through 1F, prefer-
ably—the optical diffractive apparatus may additionally
contain a third structural planar optics layer disposed
between the first and second structural layers and structured
as a substantially plane-parallel plate of bireftingent optical
material. Substantially in any implementation, the optical
diffractive apparatus may additionally include an optional
fourth structural planar optics layer that is separated from
the first structural layer by the second structural layer, and
that is configured to transform the second beam of light
received from the second structural layer into multiple
beams of light propagating in a direction of the second
structural layer. (In at least one specific embodiment, the
fourth structural layer may be configured to not reflect or
diffract light incident thereon along the axis.) Alternatively
or in addition, such a fourth structural layer may be config-
ured to form multiple diffractive beams of the same order of
diffraction (these multiple diffractive beams originate at
different respectively-corresponding locations but all over-
lap at the same point between the second and fourth struc-
tural layers). The skilled person will readily appreciate that
at least one (and preferably two) structural layers of the
discussed optical diffraction apparatus are configured as
diffractive planar optic components that in operation form
diffracted beams in various orders of diffraction from light
incident on such components. Notably, the apparatus is
dimensioned to provide for extreme increase of a cross-
sectional area of the light beam (generally, in excess of 10*
and up to 10°) between the moment when light exits the
first structural layer to the moment it is delivered to the
vicinity of the location of the MOT (and, specifically, to the
location of the optional fourth structural layer that is
between 1 mm and 200 mm away from the second structural
layer). In one case, the linear dimension of the cross-section
of the beam is increased from a few hundreds of nanometers
to about 140 microns upon the outcoupling of light from the
first structural layer, and from about 140 microns to about 1
cm or so upon free-space propagation of light from the
second structural layer to the location of the fourth structural
layer.

Examples of Specific Non-Limiting Embodiments of an
Apparatus

[0021] One of the practical challenges remaining unsolved
by related art is eflicient conversion of the dimensions of the
input light beam—that is, a cross-sectional size of spatial
light distribution at the entry of the system of delivery of
light to MOT—to a free-space mode of centimeter scale,
required for formation of the operationally viable laser-
cooling volume at the location of the MOT. Beam expansion
is necessary as magneto-optical trapping is inefficient with
millimeter-scale or smaller laser beams due to the finite
optical scattering forces present in laser cooling. It is also
necessary to increase the capture rate into the MOT, which
scales strongly with the size of the laser cooling beams.

[0022] According to embodiments—and in reference to
the schematic of FIG. 1A illustrating in part an example of
system 100 of a light-delivery apparatus—a multi-stage or

Dec. 8, 2022

multi-step approach is used to expand a light beam repre-
sented by a waveguide mode emanating from the first
structural layer (shown as a PIC 104). At the first stage, the
size of the waveguide mode propagating through PIC 104
(which defines a first structural layer I of a system 100) is
expanded via outcoupling of such light in the form of beam
108 through the extreme mode converter, EMC, shown as an
element 112 of the PIC 104. As shown, the beam 108 may
preferably have a linear polarization. At the second stage,
with the use of the second structural layer II (which includes
a dielectric metasurface MS 116, configured to operate as an
aspheric beam-shaper while changing the state of polariza-
tion of light 108 upon interaction of light 108 with the MS
116), a re-shaped free-space propagating beam 124 is
formed. In the example of system 100, the MS 116 is shown
to operate in transmission, but a skilled person can under-
stand that in a related embodiment the interaction between
light of the beam 108 and the MS 116 can alternatively or in
addition be arranged in reflection. Optionally, in a specific
embodiment (which is actually illustrated in FIG. 1A), the
light-delivery apparatus may be complemented by yet
another structural layer (labelled here as III and illustrated
with a dashed bracket) that, as shown includes a substan-
tially plane-parallel optical plate 120 in this case configured
as a quarter-wave plate QWP at the wavelength of light 108.
[0023] The shaped free-space beam of light 124 is further
delivered to an additional structural layer of the system 100
while expanding the cross-sectional area of the beam by a
factor of at least 10 (and at least 10°, or even about 10!° in
‘one case) as compared to that of the modal distribution of
light in the waveguide of the PIC 104. Here, layer/V is
shown to be represented by a spatially segmented (with three
segments, in implementation illustrated in FIG. 1B), reflec-
tive grating chip or element 134 (grating, for short). This
specific implementation of the structural layer/V is config-
ured to return incident light of beam 124 in the form of
multiple (three, as illustrated) return beams (as shown—
138A, 138B, 138C) to aggregately form a multiple-beam (in
this example—four-beam) MOT within a conventional glass
vacuum chamber 140 disposed in the vicinity of the struc-
tural layer IV. The spatial coordination of the structural
layers II and IV is such that the free-space propagating beam
124 and all of the return beams (here, 138A, 138B, 138C)
simultaneously overlap in the same spatial point/location/
volume 142.

[0024] Specifically, in the example of FIG. 1A, a linearly
polarized beam 108 is launched from the PIC 104 and, upon
the transmission through the QWP 120 becomes circularly
polarized (LHC, as shown) beam 146, from which the MS
116 generates an expanding light mode of orthogonal polar-
ization (RHC, as shown) as a non-zero order diffraction
beam 124, which realizes a substantially flat-top intensity
profile at the location of the structural layer IV. (The unused
zeroth order diffraction beam—or a portion of transmitted
through the MS 116 beam 146—is shown as 124A. The
GMOT is realized inside a glass vacuum chamber with a
magnetic quadrupole field created by external electromag-
nets. FIG. 1B illustrates first order diffraction and beam
polarizations (arrows) of the beams diffracted at the grating
chip 134 of the structural layer IV as a result of irradiation
of the grating chip 134 with the incident beam 124. FIG. 1C
provides an optical image of the planar structural layer I
(PIC 104) showing an optical waveguide WG and a corre-
sponding EMC structure 112. Inset illustrates components of


US 2022/0390760 Al

Other MS types, including designs based on propagation
phase (as discussed, for example, in Yulaev A, et al., ACS
Photonics 6, 2902-9, 2019, the disclosure of which is
incorporated by reference herein), could be used to generate
the desired circular polarization and phase profile simulta-
neously and without the use of QWP 120 as was already
alluded to above),

[0034] Understandably, variations in absorption and dif-
fraction, including the effect of phase discontinuities, exist
in MS ofall types and lead to spatial structure in the intensity
distribution of the output beam. In the case of the spatially
divergent beam 124 of the present embodiment, undesired
spatial structure in the beam’s intensity formed at the MS
may likely persist as the beam propagates due to the beam’s
significant divergence. While such non-ideal intensity varia-
tions may undesirably detrimentally affect the performance
of the overall GMOT system considered in reference to
FIGS. 1A, 1F the PB-type MS utilized in current implemen-
tations offered acceptable variation in absorption and dif-
fraction across the surface of the device. Notably, while it
was chosen to use separate elements for the EMC and MS.
(respectively, elements 112 and 116), direct integration of
metasurfaces with the EMC is possible and may be imple-
mented in a related embodiment.

[0035] Addressing now a specific implementation of the
optional planar structural layer IV of one embodiment of the
light-delivery apparatus—the one in which such structural
layer IV was represented by the grating-chip 134—the
grating 134 included, in one case, three one-dimensional
diffraction grating sector segments a, b, and c (FIG. 1E)
adjoined to one another such that axes of symmetry of each
of these segments lying in the plane of the grating 134 were
angularly separated from one another by 120 degrees in such
plane. First order diffraction beams generated by each of the
grating segments a, b, and c were directed substantially
against the incoming beam 124 such as —together with the
beam 124—to provide both axial and radial confining forces
for the atoms in a spatial volume defined by simultaneous
overlap each of the beams with each of the rest of the beams,
thereby realizing a four-beam geometry GMOT. The grating
chip was fabricated from Al-coated Si with periodic square
grooves arranged with a nominal pitch of 1 1m and trench
width of 500 nm. The ruled grating pattern filled a circular
region with diameter of 22 mm. A triangular opening with an
inscribed circular diameter of 3 mm (see in the center of the
structure in FIG. 1E) was etched through the center of the
grating chip 134 to eliminate reflected light along the beam
axis. First order diffraction (beams 138A, 138B, 138C) for
normally incident light 124 at 780 nm occurred at about
51.3° with a diffraction efficiency of approximately 33%.
Such diffraction angle was chosen to provide a balance
between axial and radial confining forces, thereby defining
GMOT as shown in FIG. 3. The optimal
ion efliciency of ’4 was approximated by controlling
the etch depth and duty cycle of the grating 134, as known
in related art. The grating was mounted ex vacuo parallel to
the wall of the vacuum cell 140 substantially perpendicu-
larly to the diverging beam 124 at the location of the flat-top
cross section of this beam. The GMOT was formed at about
5 mm, along the -z-axis from the inside surface of the glass
chamber wall, as can be seen in FIG. 1F. In one case, the
overlap of the incident and diffracted beams 124, 138A,
138B, 138C created a GMOT trapping volume V,,.,,~0.34

wrap"

Dec. 8, 2022

cm®, which was partially restricted by the 4 mm wall
thickness of the vacuum chamber 140.

Example of an Overall GMOT System Utilizing an
Embodiment of the Light-Delivery Apparatus.

[0036] In one practical implementation demonstrating the
operation of the MOT system utilizing the planar structural
layers discussed above, the D, transitions in *7Rb were used
Laser cooling light was prepared using standard methods to
address the 58,,.>5P,,, F=2-F=3 (trapping) and
F=1—>F'=2 (repumping) transitions near 780.24 nm (see, for
example, Phillips W D 1998 Nobel Lecture: Laser cooling
and trapping of neutral atoms Rev. Mod. Phys. 70, 721-41,
1998).

[0037] The laser-cooling beams were combined and
coupled into the waveguide of the PIC 104 using fiber and
free-space optics to match the 0.93 pm 1/e? mode radius at
the waveguide facet. The transitions (separated by 6.6 GHz)
had natural linewidths P of 2xx6.1 MHz and the trapping
light had a saturation intensity 1,,,~3.6 mW cm”. Imaging
of the GMOT was performed along an optical path substan-
tially orthogonal to the axis of the beam 124 (x-direction in
FIG. 1A, 1F). The loading rate of the GMOT was measured
using fluorescence imaging while atom number and tem-
perature are measured using absorption imaging in time-of-
flight (TOF). (As known in related art, absorption imaging
measures the optical depth (OD) of the gas, proportional to
the atomic column density, as the natural logarithm of the
ratio of incident to transmitted optical intensity.) During
TOF expansion and imaging, the GMOT electromagnets and
MOT optical fields was switched off. A permanent magnet
created an ~50 uT field along the x-direction to serve as a
spin quantization axis for imaging.

[0038] Capture into the GMOT was maximized when the
trapping light detuning was about -1.5 T° and the axial
gradient of the magnetic quadrupole field was about 0.11 T
m”', consistent with values reported in related art. Repump-
ing light, copropagating with the trapping light, was reso-
nant to the repumping transition and had a central intensity
of 25 W cm for all measurements. In the low intensity
limit, the trapped gas had an approximately Gaussian shape
with Ie? radii (Wayor) of 270 jum axially and 390 jm
radially. The dimensions of the gas increased with I, as the
total GMOT population grows. and the radial-to-axial aspect
ratio saturated to 2 at high trapping light intensity.

[0039] At the maximum trapping light intensity 1,,.,~1.8
mW cm (~0.5 I,,,). the GMOT loading rate measured
using fluorescence imaging was ~10’ s! with a trapping
lifetime of =0.25 s, consistent with a background Rb partial
pressure of 8x10-7 Pa. The gas temperature measured using
time-of-flight absorption imaging was (176+5) WK in the
axial direction and (219+7) j1K in the radial direction (FIG.
3). Here, uncertainties and tolerance as indicated were the
standard uncertainty of the mean. The measured temperature
was close to the *”7Rb D, Doppler cooling limit of 146 uK,
and the axis-dependent temperature was a consequence of
the force balance set by the diffraction angle of the grating
chip 134, Lower temperatures would be achievable using
additional cooling stages including polarization-gradient
cooling or A-enhanced grey molasses, for example.

[0040] The steady-state population of the GMOT (Nyon)
was characterized at varying trapping laser intensities. It was
observed that Nyyoy grew in an approximately linear fashion
starting from near 0 population at I,,.,,~0.45 mW cm? and

rap"