U.S. Patent Aug. 30, 2022 Sheet 18 of 23 US 11,428,763 B2

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3 ,
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FIG. 18


US 11,428,763 B2

23

zymes. Owing to their ease of coupling with a microwave
feedline and high power-to-field conversion efficiencies,
these devices can be applied in EPR imaging modalities.

Finite element simulations were conducted, and the planar
inverse anapole microresonator was modeled as a perfectly
conducting plane on a dielectric slab. The model included
the microstrip and the microresonator. The microstrip
included a dielectric with a ground plane on one face and a
central conducting strip on the other face. The microreso-
nator was modeled with the dielectric substrate directly in
contact with the central conductor of the microstrip, and the
metallic face pointing upward so that the metal film is
separated from the central conductor of the microstrip by the
dielectric of the microresonator. The dielectric constant of
the microresonator substrate was set to 22 and that of the
microstrip substrate was set to 3.55. A schematic of the
complete model is provided in FIG. 15 while FIG. 16 shows
the dimensions of features of the metallized layer.

The planar inverse anapole microresonators were fabri-

cated on either lanthanum aluminate (LAO) or lanthanum 2

aluminate-strontium aluminum titanate (LSAT) substrates
with a thickness of 500 jum and dielectric constants of
ranging from 22 to 25. The substrates were first cleaned in
piranha solution and then spin-coated with photoresist (LOR

10 pre-baked at 175° C. followed by SPR 220 pre-baked at 2:

115° C.). The resonator layout was pattemed into the pho-
toresist using a UV laser (375 nm at 300 mJ/em?). The resist
was developed using MIF300. The surface of the coated
dielectric was then cleaned by reactive ion etching with
oxygen plasma. Next, a 30 nm thick film of Ti followed by
a 500 nm thick film of gold were deposited over the
patterned photoresist using e-beam evaporation. Excess gold
was removed by manual liftoff (soaked in Remover 1165
overnight). Finally, a 50 nm layer of silicon nitride was
deposited using plasma-enhanced chemical vapor deposi-
tion, to protect the gold from abrasion.

The planar inverse anapole microresonators were coupled
to a RO4003 microstrip feedline. The anapolic substrate was
adhered to the microstrip using a small amount of silicone
grease and was critically coupled to the microstrip by
adjusting its position relative to the central conductor of the
microstrip. The microstrip was terminated with a 50Q load.
Coupling was monitored using a vector network analyzer
(VNA). Internal reflections from the coaxial cable were
calibrated out by 1-port short-open-load (SOL) calibration.

For EPR spectroscopy, the critically coupled planar
inverse anapole microresonator was aflixed in a holder made
of acrylonitrile butadiene styrene (ABS). To provide modu-
lation of the static magnetic field, commercial air-core
inductor coils were mounted on this holder and connected to
the modulation amplifier in either the 10 GHz spectrometer
or 35 GHz spectrometer. The microstrip was connected to
the spectrometer bridge in each instrument using a coaxial
cable. The microresonator-microstrip device was mounted

on the ABS holder and placed in between the magnet poles

of the spectrometer on an ABS post (FIG. 23 of the Sup-
porting Information). In the EPR spectrometer operating at
10 GHz, the reference arm was kept on and the microwave
frequency was locked at a value (around the dip observed on
the VNA) that yielded an absorption lineshape. An auto-
mated procedure was run to match the response of the
external modulation coils to the modulation amplitude set-
tings in the EPR spectrometer. Here the bandwidth of
detection for CW spectra was defined as (0.5*conversion
time). The 35 GHz spectrometer operates without a refer-
ence arm. The resonant frequency of the 35 GHz microre-
sonator-microstrip device was first identified on the VNA

0

&

&

50

0

24

and then confirmed in the spectrometer. In the 35 GHz
system, we were able to apply a maximum modulation
amplitude of only ~0.1 mT due to intemal settings. The
modulation amplitude was determined from the linewidth of
the EPR absorption line of a BDPA-benzene crystal. Here
the bandwidth was defined as Yawt, where t is the time
constant.

Regarding sensitivity analysis, sensitivity of an EPR
resonator can be quantified in terms of the signal-to-noise
ratio (SNR). Here, the noise is the thermal noise of all the
circuit elements including the microresonator and the detec-
tor. The signal is the voltage induced in the resonator loop
by the processing magnetization of the sample placed in the
magnetic field region of the resonator as in the following
equation that shows that the SNR and sensitivity of a
resonator is directly proportional to resonator filling factor
(m) and quality factor (Q-factor). The CW EPR signal
intensity, in terms of voltage (V.), is given by the following
formula.

Vex" ONP Zo

wherein 7 is the resonator filling factor; QL is the loaded
quality factor of the resonator; PA is the microwave power,
in W, incident on the microresonator (i.c., the microwave
power at the end of the microwave transmission line); and
ZO is the characteristic impedance of the microwave trans-
mission line (in Q). x" is the dimensionless imaginary
component of the effective RF susceptibility

‘The filling factor is given by the equation:

f Bidv

Bay

Vacmpte BY sample
Vies Bes

Fron

When B, is homogeneous over the resonator mode volume,
the filling factor can be equated to the ratio of sample
volume divided by the mode volume. This is indicated by the
right side of the above equation. The above formula is
applicable for resonators with homogeneous B, distribu-
tions, such as cavity resonators or dielectric ring resonators.
In structures with large B,-inhomogeneity, volumes with
high B, can make a disproportionately large contribution to
the EPR signal. In such cases, the B, concentration may be
defined in terms of the mode volume, as shown in Table 2.
The quality-factor Q can be defined in terms of resonator
bandwidth as provided in the following equation.

ow
wherein v,,, is the resonant frequency and Av is the reso-
nator bandwidth at 3 dB below the baseline.

The quality-factor Q can be defined in terms of energy
retention in the resonator by the following equation.

average energy stored in resonator volume

‘average power dissipated from resonator surfaces

The thermal noise in a detection setup with a character-
istic impedance of 50@ can be calculated by the following
formula.

NoVakgTRAT


U.S. Patent Aug. 30, 2022 Sheet 12 of 23 US 11,428,763 B2

H-field amplitude E-field amplitude
{A/m)

Anapole

Inverse
Anapole

FIG. 12


U.S. Patent Aug. 30, 2022 Sheet 22 of 23 US 11,428,763 B2

(A)

Coaxial cable
jack

218
(A)

Twinax connector Air core inductors
for modulation coil acting as

modulation coils
FIG. 22


U.S. Patent Aug. 30, 2022 Sheet 3 of 23 US 11,428,763 B2

Rotation of microwave
conductor 212 relative to
inverse anapolic pattern 203
x
217 “

FIG. 3


US 11,428,763 B2

19

field region, the reduction in signal intensity going from 3b
to 3c is attributed solely to the change in amount of sample
occupying the resonator active volume. In 3b, the entire
active volume is occupied by the BDPA-benzene crystal.
Moving the crystal 7 jum+3 jum away from the magnetic field
region causes the signal intensity to decrease by 75%, as
seen from the continuous wave (CW) EPR specira in FIG.
8d. Because they and z dimensions are also much larger than
the simulated dimensions of the active volume, this reduc-
tion in signal intensity can be used to directly estimate the
active range along the x-axis. Assuming an equal range on
both sides of the active surface, the active range along the
x-axis is estimated to be 20 um, which is comparable to the
active range indicated by FIG. 7c. FIG. 8e shows the
power-saturation curves with the BDPA in positions 3b and
3c. FIG. 8fshows that the ratio of double-integrated signals
from 3b and 3c reaches a constant value upon saturation.
These results suggest that even ifa large sample is placed on
the hotspot, most of the signal originates from a small
volume around the central bridge. To estimate the volume
responsible for a majority of the signal from a large sample,
we used finite element simulations to obtain the integral of
B,? overa large sample, and over smaller sub-volumes at the
center of the sample. The field inhomogeneity in planar
microresonators makes it difficult to estimate the active
volume of the resonator. For example, FIG. 8h shows that a
volume of approximately 2 pL around the central bridge
shown in 3a accounts for 20% of the total integrated B, ,?
over a large sample. A volume of approximately 25 pL
accounts for 55% of the integrated B, ,? whereas a volume
of approximately 50 pL accounts for 65% of the total
integrated B, ,? over a large sample. This weighted distri-
bution of B,,? is graphically represented in FIG. 8g. The
mode volumes calculated in Table 2 are much higher than
the active volume of approximately 50 pL to 100 pL
estimated from FIG. 8g. This discrepancy can be explained
by considering the high B, inhomogeneity and diffuse nature
of B, distribution on the resonator surface.

FIG. 8/shows the power saturation curves of the BDPA-
benzene single crystal placed at positions 3b and 3c. The
error bars represent a single standard deviation in double-
integrated area, due to random noise of the EPR spectrum.
Crystalline BDPA saturates at a B, value of 0.03 mT
(assuming a conversion factor of approximately 0.1 mT/WW
for a rectangular cavity with a Q-factor of approximately
3000). The power saturation curves were fit to an asymptotic
growth function and the saturation power was defined as that
at which the saturation curve deviates from linearity (see
FIG. 18(a)). By this analysis, the power-to-field conversion
efliciency for the microresonator-microstrip device
used in FIGS. 7 and 8 was found to be (3+0.5) mT/'VW. The
error represents a single standard deviation due to uncer-
tainty in the power corresponding to saturation. The simu-
lated value of the conversion efficiency based on the highest

value of B, , in the model is (320.4) mT/VW (see Table 2).

These values appear to be low for the active volume in
consideration and are comparable at 10 GHz and 35 GHz,
The apparently low conversion efficiency is calculated based
on the nominal output power of the bridge. In reality, only
a small fraction of this power is ultimately coupled into the
microresonator. Secondly, while the active volume is about
1 pL to 10 pL, it is much smaller than the outer dimensions
of the resonator. Thus, a decrease in overall size of the
resonator is not expected to have a significant effect on the
filling factor or conversion efficiency. While there appears to
be a reasonable correspondence between the experimental
and simulated conversion efficiencies, there are many

FIG. 9) s

20

&

&

20

parameters that affect the coupling between the microreso-
nator and microstrip and hence can be used to tune the
conversion efficiency.

This conversion efficiency does not account for the B, ,-
inhomogeneity in the magnetic field region, which can be
disadvantageous for pulse measurements. An estimate of the
B, homogeneity can be obtained from the power saturation
curve. This analysis of the power saturation data in FIG. 8
resulted in a value of e-0.5+0.1, indicating highly inhomo-
geneous saturation. The fit is presented in FIG. 18(4).

With regard to coupling and tuning, an advantage of the
planar inverse anapole resonator is that its overall large size
allows easy coupling to an external microwave feedline.
FIG. 9a shows a microresonator-microstrip device operating
at 9.75 GHz. The microresonator is adhered to a microstrip
using a small amount of silicone grease. The position of the
microresonator relative to the central conductor of the
microstrip is defined in terms of three parameters: x (dis-
tance along the central conductor of the microstrip), y
(vertical offset from the central conductor), and 6 (angle
between the central conductor and capacitive gaps of the
microresonator). The parameters y and 6 can be used to
control the coupling between the microstrip and the microre-
sonator (FIG. 95). The photographs in FIG. Se show the

5 relative positions of the microresonator with respect to the

microstrip in the critically coupled and uncoupled states.
Also shown are the experimental plots of the reflection
coefficient (S11) versus frequency in the critically coupled
and uncoupled states, showing a resonance frequency of
9.75 GHz for the critically coupled device. The linewidth at
3 dB below the baseline is typically used as an estimate of
the Q-factor. Therefore, it is important to establish the
baseline by comparing S11 profiles of the coupled and
uncoupled’ devices. Using these data, the experimental
Q-factor is estimated to be 250+50 at room temperature. The
error is a single standard deviation due to variability in
coupling of the microresonator and microstrip. Since we
have used low-loss dielectric substrates, we attribute this
improvement in Q-factor at room temperature to the dimin-
ished radiation losses provided by the inverse anapole mode.
This improvement is obtained while confining B, to a
volume about 1 pL. Q-factors in the range of 10% to 10° can
be obtained for arrays of coupled resonators in the metama-
terial. However, the planar inverse anapole microresonator
is a unit of the metamaterial array and therefore intrinsically
has a lower Q-factor compared to an array. Secondly, the
thin metal layer deposited on a dielectric substrate results in
additional losses. These factors combine to yield Q-factors
that are much smaller than observed by some others. We
observed that the resonant frequency of the microresonator-
microstrip device can be varied simply by changing the
position of the microresonator on the microstrip (FIG. 19).
This method provides a tunability of approximately 500
MHz at both 10 GHz and 35 GHz. FIGS. 19 and 20 of
Supporting Information provide a detailed phenomenologi-
cal description of the dependence of device frequency and
coupling on x, y, and 6.

Testing microresonator sensitivity at room temperature.
We tested the sensitivity of the planar inverse anapole
microresonator by obtaining EPR spectra of a dilute (0.05
mole %) Mn?*-doped sample of CaTiO, (inset of FIG. 94),
using the critically coupled device with a resonance fre-
quency of 9.75 GHz. A crystal of BDPA was used to
calibrate modulation coil settings. Currently, single-crystal
data for dilute perovskite oxide single crystals are difficult to
obtain because 1) availability of doped single crystals is
limited, 2) there is a high amount of expertise required to



US 11,428,763 B2

Sheet 19 of 23

Aug. 30, 2022

U.S. Patent

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US 11,428,763 B2

3

magnetic field region as the magnetic field region of the
planar inverse anapole microresonator. (b) The left panel
shows a zoomed-in optical micrograph of the magnetic field
region magnetic field region (Design I) of the planar inverse
anapole microresonator. Scale bar=10 jum. The panels to the
right of the optical micrograph show simulated distributions
of perpendicular (B, ,) and tangential (B,)) components of
the microwave magnetic flux density B, in the x-y plane,
showing the central B,, ‘hotspot’. (c, d, e): Normalized
absolute values of simulated B, ,? (solid lines) and By)?
(dashed lines) along the x, y, and z co-ordinates. The dotted
lines in the insets are the cut lines along which the field is
plotted (z is perpendicular to the plane of the planar inverse
anapole microresonator). An input voltage of 1 V and
impedance of 50Q was set in the finite element simulations,
resulting in an input power of 20 mW;

FIG. 8 shows a magnetic field region for 10 GHz planar
inverse anapole microresonator. (a) Optical micrograph of a
10 GHz planar inverse anapole microresonator with the
magnetic field region based on Design I (b), (c): Optical
micrographs of a a,y-Bisdiphenleine-B-phenylallyl (BDPA)-
benzene crystal (approximately 50 umx90 pmx15 jum)
placed over the active surface (b), and 7 um+3 pm away
from the active surface (c). Scale bars in a-c & g represent
10 wm and the width of the central bridge is 5 jum. (d):
Comparison of EPR spectra obtained from (b) and (c) at
approximately 20 uW applied microwave power, and nor-
malized to the maximum signal intensity obtained from (b);
(e) Comparison of microwave power saturation curves ie.
plots of double-integrated (DI) signal intensity vs. square
root of microwave power in positions (b) and (c). The
maximum microwave power output of the EPR bridge is 158
mW. The error bars represent a single standard deviation in
double-integrated area, due to random noise of the EPR
spectrum. (f) Ratio of double-integrated signal intensities in
positions (b) and (c) as a function of attenuation. (g)
Simulation of loss of signal in sample excluding the active
volume (hole) of (60x60x15) jum*, when compared to vol-
ume including active volume. (h) Normalized volume-inte-
grals of B, ,2as a function of selected sample volume. As the
sample radiates outwards from the central bridge, its
weighted contribution to the signal decreases;

FIG. 9 shows microwave coupling between inverse
anapolic pattem and the microwave conductor of the
microstrip in the planar inverse anapole microresonator. (a)
10 GHz planar inverse anapole microresonator that replaces
the resonator in an EPR spectrometer. Scale bar=5 mm. (b)
Representation of the planar inverse anapole microresona-
tor, showing the position parameters that can be used to

control microwave coupling. The double-headed arrow indi- 5

cates the y-oflset of the resonator center from the central
conductor of the microstrip. (©) Photographs show the
microresonator position in the uncoupled and critically
coupled states (dashed blue lines are visual aids to demar-

cate the tops of the microstrip and capacitive gap of the ;

microresonator). Both scale bars represent 0.5 mm. The
plots are shown for reflected microwave power vs. fre-
quency for the uncoupled state and critically coupled states
after background subtraction. (d) Simulated and experimen-
tal continuous wave (CW) EPR spectra of 0.05 mole %
Mn?*-doped CaTiO,. The sharp line at the center is the
signal from the BDPA microcrystal used for modulation coil
calibration. The BDPA signal has been adjusted to make it
visually comparable to the Mn?* signal. The experimental
spectrum was obtained using the coupled planar inverse
anapole microresonator from (c). The inset optical micro-
graph shows the single microparticle placed over the

20

&

&

4

microresonator. The dashed lines show edges of the microre-
sonator below the sample. The signal-to-noise ratio (SNR)
of the component in the dashed box was used for sensitivity
calculations;

FIG. 10 shows a 35 GHz planar inverse anapole microre-
sonator and simulation of active volume of the magnetic
field region. (a) planar inverse anapole microresonator oper-
ating at 35 GHz. The zoomed-in region on the right shows
the microresonator chip (the outline encloses the magnetic
field region). (b) Optical micrograph of the magnetic field
region. The right panel shows the simulated distributions of
the absolute values of perpendicular and tangential compo-
nents of B, in the x-y plane, showing the central B, ‘hotspot”
in a small volume around the central bridge (c, d, e)
Normalized absolute values of B, ,? and B,)? along the x, y,
and z co-ordinates. An input voltage of 1 V and impedance
of 50Q i.e. an input power of 20 mW was set in the finite
element simulations;

FIG. 11 shows performance of the 35 GHz planar inverse
anapole microresonator. Characteristics of planar inverse
anapole microresonator operating at 35 GHz. (a) Frequency
profiles of reflection coefficient in the uncoupled and criti-
cally coupled states. (b) Power saturation curve fora BDPA-

5 benzene single crystal. The error bars represent systematic

uncertainty of a single standard deviation in double-inte-
grated area due to splitting of the EPR signal detected in the
1/Q channels. (c) CW EPR spectrum of a microcrystal of
CuCl,.2H,0. (d) CW EPR spectrum of a microcrystal of
BDPA-benzene complex:

FIG. 12 shows complementary magnetic and electric field
distributions in an anapole structure and an inverse anapole
pattern:

FIG. 13 shows current flow in a coupled microstrip-
microresonator device operating at 10 GHz;

FIG. 14 shows field distributions in the plane of the
microstrip with fringing fields from the microstrip that
extend for much shorter length scales compared to the outer
dimensions of the microresonator;

FIG. 15 shows a model of a planar inverse anapole
microresonator used in finite element simulations. The
bar represents 5 mm. The microstrip, with a characteristic
impedance of 50Q, radiates microwave fields owing to
currents in the central conductor. The coupling of these
fields with the microresonator is dependent on the position
of the microresonator relative to the central conductor of the
microstrip. In the finite element simulations, the length of
the microstrip ranged from 20 mm to 50 mm while the real
microstrip has a length of 50 mm. Smaller lengths were used
in the finite element calculation to reduce computational
time;

FIG. 16 shows a plan view of the microresonator surface,
showing patterns and dimensions for a 10 GHz planar
inverse anapole microresonator with an active volume of the
magnetic field region of approximately 1 pL;

FIG. 17 shows (a) plan view of the microresonator
coupled to microstrip for a planar inv apole microre-
sonator. The scale bar indicates 3 mm. (b) Simulated electric
field distribution, showing that the electric field is concen-
trated at the edges of the central capacitive gaps, as shown
in the left panel. The right panel shows a zoomed-in view of
the magnetic field region. (c) Simulated magnetic field
distribution at the magnetic field region. A comparison of the
right panel of (b) and (c) shows the separation between
regions of magnetic and electric field. Electric field in the
magnetic field region is negligible. The scale bars in (b) and
(c) represent 10 um;



U.S. Patent Aug. 30, 2022 Sheet 21 of 23 US 11,428,763 B2

084
0.6 +
044
0.24

O24

Signal intensity (V)

0.44

0.64

0.84

¥ ba
1.18 1,20 1.22 1.24 1.26 1.28
Field (T)

FIG. 21


US 11,428,763 B2

21

grow single crystal perovskites, 3) high-quality single crys-
tals grown from conventional melt processes exhibit defect
in homogeneities, and 4) non-conventional growth tech-
niques result in crystallite volumes that are typically smaller
than 1 pL and ofien closer to 1 {L.. Therefore, in conventional
EPR spectrometers, novel perovskite chemistries can be
measured in their polycrystalline form, usually as com-
pressed pellets consisting of thousands of microparticles,
with a total volume of several microliters. To test the
sensitivity of the microresonator, we picked out a micropar-
ticle with a total volume of approximately 5 nL. (FIG. 5d).
The finite element simulations detailed in FIG. 8 suggest that
only (50+20) pL of this large volume is probed by the
microresonator. We use this simulated active volume to
estimate the sensitivity, although further corroboration is
required using a smaller crystal of volume <100 pL. To
estimate the sensitivity, we chose the signal enclosed in the
dashed outline in FIG. 9d because it is clearly identifiable,
and its linewidth and peak-to-peak signal intensity can be

determined with reasonable certainty. The data shown in 2

FIG. 9d were obtained with a microwave power output of
158 mW from the 10 GHz EPR spectrometer system. As
noted in the discussion of conversion efficiency above, the
actual power incident on the microresonator is a small
fraction of the nominal input power from an EPR spectrom-
eter microwave source. The total spin density for this sample
is approximately 9x10'*/mL. Therefore, the total number of
Mn** spins in the active volume of (50+20) pL is approxi-
mately 5x10". The number of spins contributing to the
chosen line was calculated from the ratio of its double-
integrated intensity to the double-integrated intensity of the
complete spectrum, excluding the BDPA signal. This ratio
was found to be (10+2)%, leading to a spin count of 5x10°
for the chosen line. The error is a single standard deviation
due to uncertainty in observed linewidth. In previous
reports, the sensitivity is normalized per unit signal-to-noise
ratio (SNR), linewidth and square root of the detection
bandwidth. In the present case, these numbers are 25, 0.8
mI, and 0.7 VHz, respectively. Using these values and the
previous sensitivity calculation approach, our demonstrated
lower limit of detection is:

(34 1)+10%mT Vz

If the sensitivity is calculated based on another method,
the total linewidth for the spectrum would be approximately
40 mT. Therefore, the higher limit of calculated sensitivity,

given by the number of spins in the active volume (1x10!%), °

normalized to the linewidth (40 mT), bandwidth (0.7 Vz),
and SNR (25), is:

S10!"

Teedoegg = (7#2)# 10m Ve

The data were obtained by integrating our devices into
standard operational EPR spectrometers. We anticipate that
further refinements in the detection circuitry will allow us to
increase the power incident on the microresonator and will
result in further improvements in volume-sensitivity.

‘The experimental EPR spectrum was validated by simu-
lations using isotropic Landé g-factor=2.001, isotropic
hyperfine splitting parameter A=239.3 MHz, linewidth=0.5
m1, zero field splitting parameters D=434 MHz and E=-41

&

4

s

22
MHz. Random noise to produce a SNR of 25 was added to
the simulated spectrum, to match the SNR measured from
experiment.

Scalability to higher frequencies. We report the first CW
EPR spectra acquired from pL active volumes at 35 GHz.
FIG. 10a shows a microresonator-microstrip device operat-
ing at 35 GHz. FIG. 10b shows an optical micrograph of the
magnetic field region (outlined in red in FIG. 10a) based on
Design II. The area of the active surface is ~1000 m?.
FIGS. 10c, 10d, and 10e show the distribution of B, , along
the x, y, and z directions, respectively.

As is the case at 10 GHz, the coupling of the 35 GHz
microresonators is controlled via the y-position and orien-
tation @ of the microresonator relative to the central con-
ductor of the microstrip. The frequency profiles of reflection
coefficient in the coupled and uncoupled states are shown in
FIG. 1a. The Q-factor of this microresonator-microstrip
device is 25050, The error is a single standard deviation
due to variability in coupling between the microresonator
and microstrip. The power-to-field conversion ratio, deter-
mined from the power saturation curve for the BDPA-
benzene complex, is (7#1) mT/VW (FIG, 116). The error is
a single standard deviation due to uncertainty in measure-
ment of the power at which the EPR signal saturates. The

5 maximum power output of the 35 GHz EPR spectrometer in

CW mode is 200 mW.

1c and 11d show CW EPR spectra obtained from
tals of CuCl;.2H,O and crystalline BDPA-ben-
zene complex, respectively. The signal intensity for
CuCl,.2H,0 is limited by our maximum modulation ampli-
tude of 0.1 mT (limited by spectrometer settings in the
present case), compared to the linewidth of 5.5 mT. For
CuCl,.2H,O, the Landé g-factor, [g, g, g.J=[2.187 2.037
2.252]. We surmise that the two observed signals at 11.1 T
and 12.1 T are caused by crystal twinning. We have also
obtained CW EPR spectra for a dilute (0.01 mole %) doped
single-crystal of Fe**:SrTiO,.

The CW EPR spectra was obtained from picoliter vol-
umes at 35 GHz with improved coupling provided by better
Q-factors and shows scalability of the planar inverse anapole
design to higher frequencies, which has previously been a
significant obstacle in application of conventional microre-
sonators to higher-frequency EPR experiments.

The planar inverse anapole microresonator has a toroidal
metamaterial unit to improve the Q-factors of EPR microre-
sonators by an order of magnitude while confining the
microwave magnetic field to pL volumes. The improvement
in Q-factors enables CW EPR experiments by integration of
microresonator-microstrip devices into standard operation
EPR spectrometers. Experimental demonstration of the
active volume was provided using CW EPR spectra of a
strongly paramagnetic sample. The CW EPR spectrum
obtained for a microparticle of <0.05 mole % Mn2*:CaTiO,
yields a spin detection limit of (7£2x10®)/mTVFz. Mn?*-
doped CaTiO, and Fe**-doped SrTiO, samples were used to
show the applicability of this resonator to dilute doped
samples of oxides, but the results apply equally to any other
dilute microcrystal. We have shown that the planar inverse
anapole microresonator can be incorporated into existing
spectrometers for easy deployment. This resonator design
can easily couple to a microwave feedline and is scalable to
higher frequencies without sacrificing ease of implementa-
tion, overcoming these limitations of previous microresona-
tor designs. Easily applicable microresonator designs are
necessary for routine studies of nanomaterials, for example,
perovskite microcrystals and thin films, and biomacromo-
lecular single crystals such as microcrystals of metalloen-



U.S. Patent Aug. 30, 2022 Sheet 16 of 23 US 11,428,763 B2

FIG. 16

ds 5mm
W,: 250 pm
wy Sum
g; 110 um



U.S. Patent

fa) Britge (design

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Aug. 30, 2022

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US 11,428,763 B2

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US 11,428,763 B2

15

three types of losses: dielectric losses from the substrate,
conductive losses from the metal, and radiative losses from.
the microstrip structure. Dielectric power loss is inversely
proportional to the loss tangent of the substrate, and can be
decreased using a low-loss dielectric substrate. Resistive
power loss can be decreased by operating at lower tempera-
tures, which is a commonly adopted strategy to increase
Q-factors of small-volume planar resonators. Here we mini
mize radiative loss to increase the Q-factor of microresona-
tors at room temperature, while confining the microwave
excitation field within a volume about | pL to 10 pL. It
should be noted that radiation shields can be used to
decrease radiative losses from open resonant structures. This
approach can provide Q-factor improvements of up to 50%.
In comparison, the microresonator design reported here
decreases radiation losses intrinsic to the resonator, improv-
ing the Q-factor by an order of magnitude compared to
microresonators reported previously. Using this approach,
‘we report an upper spin detection limit of (7£2x10°)/mIVHz
in a volume of approximately 100 pL at room temperature.
The sensitivity gains at lower temperatures are expected to
be correspondingly higher.

The reduction in radiation losses, resulting in high Q-fac-
tors of anapole resonators, is due to diminished far-field
radiation because of destructive interference between toroi-
dal and electrical dipole moments. Arrays of such resonators
with toroidal moments can produce Q-factors as high as 10°.
This approach cannot be directly applied to resonators for
EPR spectroscopy because of the following additional con-
siderations: (i) for sensitive measurements of the reflected
power, the resonator must be critically coupled to a micro-
‘wave source, (ii) there must be a sample volume where the
microwave magnetic field B, is perpendicular to the static
magnetic field B, (for perpendicular mode measurements)
and (iii) the microwave electric field must be minimized in
the active volume to avoid dielectric losses from lossy
samples such as aqueous solutions. With these consider-
ations in mind, the planar inverse anapole microresonator
uses a complementary or inverse anapole structure. Previ-
ously investigated anapole resonators typically feature
mostly-bare substrates with regions of patterned metals and
microscale gaps where the electric field is concentrated. In
contrast, we exploited the duality of electric and magnetic
fields to design an inverse, mostly-metallized structure with
‘a central bridging strip that supports a magnetic field “hot-
spot’ at the center of the resonator (FIG. 6a). We have
simulated both anapole and inverse anapole resonators to
verify their complementarity (see FIG. 12 of Supporting
Information.). In the case of a regular anapole design, the

electric dipole is formed in the central gap in the split ring, s

and the resulting circulating magnetic field (in the air gaps)
generates the toroidal moment that is anti-parallel to the
electric dipole. In the complementary or inverse architec-
ture, an in/out of plane magnetic dipole forms around the top

and bottom of the central metal notch (the short). On the

other hand, the electrical field-driven circulating currents
around the etched parts result in a net toroidal moment that
is also in/out of plane—anti-parallel and degenerate with the
magnetic dipole. A simplified picture of the current flow on
the resonator surface is shown in FIG. 6d. The current
distribution in the microstrip-microresonator device is more
complicated (see FIG. 13). In the ideal inverted structure, the
metal plane should be infinite while in the resonator, it is
truncated at the edges. We conducted simulations to test the
effect of this truncation on the inverse anapole mode,
wherein Table 1 lists a dependence of eigenfrequency of
anapole mode on outer length of metal plane. Increasing the

0

20

&

&

16

outer length of the metal rectangle from 12 mm to 15 mm
changes the resonant frequency and loss factor (imaginary
component of eigenmode) by less than 10%. We surmise that
the structure approximates an ideal inverted structure for
two reasons: (i) Fringing fields from the microstrip extend
for a length much smaller than the length of the microreso-
nator (see FIG. 14), and (ii) the outer length of the metal
layer is much larger than the coupling structure (the capaci-
tive gaps) and the central bridge.

TABLE 1

Bdge length Bigenftequency of |B, maximum at
(mm) anapole mode hotspot (A/m)
12 9.86 + 0.181 9x 10"
125 9.77 + 0.181 8x 107
1B 9.69 + 0.181 8x 10"
13.5 9.62 + 0.191 8x 107
14 9.53 + 0.211 8x 10"
145 9.42 + 0.241 7x 10"
15 9.27 + 0.271 6x 10"

This structure was fabricated on a low-loss dielectric
(either lanthanum aluminate, LAO, or lanthanum strontium
titanite, LSAT) to minimize dielectric losses from the reso-
nator. The dielectric permittivities of LAO and LSAT vary in
the ranges of 23.6 to 24.0 and 22.7 to 22.9, respectively, in
the temperature range 2 K to 300 K. In this temperature
range, the loss tangents of LAO and LSAT vary in the ranges
of 1x10-° to 2x10-> and 1x10~ to 6x10~, respectively.
Finite element simulations indicate that the variation in
dielectric permittivity is expected to result in a variation of
<0.5 GHz in the resonance frequency of the device, shifting
it from 9.7 GHz to 9.3 GHz. The observed frequency varies
in the range of 9.2 GHz to 9.8 GHz, depending’ on the
X-position of the microresonator on the microstrip so that the
decrease in frequency caused by low temperature may be
compensated for by changing the position of the microre-
sonator on the microstrip.

Planar inverse anapole microresonators were made with
two types of bridges. In Design I, the bridge is cinched at the
center to obtain a smaller active surface. In Design II, the
bridge is a straight line that results in a large active surface.
Design I results in an active volume of approximately 1 pl
and also decreases the active height to <5 um. Design II
results in an active volume of approximately 100 pL.
Smaller active volumes and active heights are advantageous
for samples such as microcrystals or thin films, in which it
is desirable to restrict the microwave power to the epitaxial
film so that it can be selectively probed without interference
from the substrate. In this paper, we report the use of Design
I for demonstration at 10 GHz and Design I] at 35 GHz. This
choice was arbitrary since either design can be applied at
either frequency.

Lack of scalability to higher frequencies is a limitation of
conventional devices that is overcome by the planar inverse
anapole microresonator. Higher-frequency EPR studies can
provide greater sensitivity and resolution, potentially pro-
viding spectral information not available at lower frequen-
cies. Additionally, multi-frequency EPR can be used to
separate field-dependent and field-independent components
of the EPR spectrum. However, some conventional microre-
sonator designs, such as those based on loop-gap architec-
tures, become impractically small at higher frequencies, In
contrast, the large overall size of the planar inverse anapole
resonator enables scaling to higher frequencies without
sacrificing the active volume or ease of coupling to a



US 11,428,763 B2

9

configured to receive an analyte (also referred to herein as a
sample) that is subjected to performing inductive-detection
electron paramagnetic resonance spectroscopy by the mag-
netic field formed by anapolic conductor 202 and inverse
anapolic pattern 203. The analyte can be an arbitrary analyte
such as a fluid, including condensed and rarefied matter, The
analyte provides an electron paramagnetic resonance signal
in response to the magnetic field of planar inverse anapole
microresonator 200. It is contemplated that the analyte can
be anapolic substrate 201, wherein anapolic conductor 202
and inverse anapolic pattern 203 are disposed on the analyte.
Exemplary analytes include biological tissues, liquids, small
molecules, inorganic compounds, organic compounds, com-
positions, and the like. The volume of the sample disposed
on magnetic field region 208 can be from 500 femtoliters
(fL) to 500 nanoliters (nl), specifically from 1 picoliter (pL)
to 1 nL, and mores specifically from 1 pL, to 100 pL. It is
contemplated that planar inverse anapole microresonator
200 has a spin detection limit from 1x10° (mIVHz)" (ie.,
1x10° (GVHz)"') to 1x10"! (mTVHzy
1x10? (mTVFz)"! to 1x10'° (mTVFz)"!, and more specifi-
cally from 7x10* (mIVHz)"! to 4x10? (mTVHz)"', based on
microwave radiation 215 at 10 GHz with the analyte at room
temperature. For CW microwave operation, anapolic con-
ductor 202 and inverse anapolic pattern 203 can be imped-
ance matched to microwave conductor 212 for critical
coupling to attain a quality factor that can be from 1 to 10°,
specifically from 100 to 10°, and more specifically from 200
to 10

Planar inverse anapole microresonator 200 can be made in
various ways. It should be appreciated that planar inverse
anapole microresonator 200 includes a number of optical,
electrical, or mechanical components, wherein such compo-
nents can be interconnected and placed in communication
(e.g. optical communication, electrical communication,
fluid communication, mechanical communication, and the
like) by physical, chemical, optical, or free-space intercon
nects. The components can be disposed on mounts that can
be disposed on a bulkhead for alignment or physical com-
partmentalization. As a result, planar inverse anapole
microresonator 200 can be disposed in a terrestrial environ-
ment or space environment.

Planar inverse anapole microresonator 200 can be fabri-
cated on anapolic substrate 201 composed of either lantha-
num aluminum oxide (LAO) or lanthanum aluminate-stron-
tium aluminum titanate (LSAT). The anapolic substrate 201
with a thickness of 500 jum and a dielectric constant of 22 to
25 was cleaned in piranha solution and then spin-coated with
a photoresist (LOR 10 prebaked at 175° C. followed by SPR

220 prebaked at 115° C.). Planar inverse anapole microre- 5

sonator 200 layout was patterned into the photoresist using
an ultraviolet laser (375 nm at 300 mJ/em?). The resist was
developed using MIF300. The surface of the coated anapolic
substrate 201 was then cleaned by reactive ion etching with

oxygen plasma, Next, the anapolic conductor 202 was ;

created by deposition of a film of Ti (30 nm) then a film of
Au (500 nm) over the patterned photoresist on anapolic
substrate 201 using e-beam evaporation. Excess gold was
removed by manual liftoff (soaked in a Remover 1165
overnight). A layer of silicon nitride (50 nm) was deposited
on the x-y plane of planar inverse anapolic microresonator
200 using plasma-enhanced chemical vapor deposition.

In an embodiment, planar inverse anapole microresonator
200 was coupled to microwave conductor 212 on dielectric
substrate 211. Planar inverse anapole microresonator 200
was adhered to microstrip 217 using a small amount of
silicone grease. Planar inverse anapole microresonator 200

. specifically from 2

&

&

10

was critically coupled to the microwave radiation 215 propa-
gating through microwave conductor 212 by adjusting the
position of planar inverse anapole microresonator 200 rela-
tive to microwave conductor 212. The coupling angle 6 and
the x-position of planar inverse anapole microresonator 200
on microstrip 217 are adjusted to achieve the operation
frequency and critical-coupling for CW or overcoupling for
pulsed EPR spectroscopy operation. Terminator 214 on
microstrip 217 was a 50-ohm load. Coupling was monitored
using a network analyzer (VNA). Internal reflections from
microwave source 213 were compensated for by one-port
short-open-load calibration. The critically-coupled planar
inverse anapole microresonator 200 adhered to microstrip
217 was disposed on a holder made of acrylonitrile butadi-
ene styrene (ABS) for placement between the magnet poles
of the EPR spectrometer system. A pair of commercial
air-core inductor coils (modulation coils 218) provided static
magnetic field modulation for CW EPR spectroscopy mea-
surements. Modulation coils 218 were mounted on the ABS
holder and connected to a modulation amplifier in either an
EPR spectrometer system operating at 10 GHz or an EPR
spectrometer system operating at 34 GHz. Microstrip 217
was connected to the spectrometer microwave source in
each instrument using a coaxial cable matched to the EPR

5 spectrometer operation frequency. To collect an absorption

spectrum using the EPR spectrometer system operating at 10
GHz, the reference arm was kept on and the incident
microwave frequency was locked at a value close to the
critically-coupled frequency obtained by adjusting the posi-
tion of planar inverse anapole microresonator 200 relative to
microwave conductor 212 and observed on the VNA. The
response of modulation coils 218 was matched to the
modulation amplitude settings used by the EPR spectrom-
eter. For CW operation with the NIST-built EPR spectrom-
eter system, the critically-coupled frequency obtained by
adjusting the position of planar inverse anapole microreso-
nator 200 relative to microwave conductor 212 was provided
by direct frequency adjustment and readout. The modulation
amplitude produced by modulation coils 218 was deter-
mined by measurement of the linewidth of the EPR absorp-
tion line of a BDPA-benzene cry:

Planar inverse anapole microresonator 200 has numerous
advantageous and unexpected benefits and uses. In an
embodiment, with reference to FIG. 5, a process for per-
forming inductive-detection electron paramagnetic reso-
nance spectroscopy includes: communicating microwave
radiation 215 through microwave conductor 212 by use of a
coaxial cable; subjecting inverse anapolic pattern 203 in
anapolic conductor 202 to microwave radiation 215 from
microwave conductor 212 by positioning planar inverse
anapole microresonator 200 relative to microwave conduc-
tor 212 to provide impedance matching (critical coupling for
CW operation) or overcoupling (pulsed operation); and
creating magnetic field region 208 and concentrating a
magnetic field localized between medial tip 207.1 of first
inverse anapolic pattern 203.1 and medial tip 207.2 of
second inver ipolic
pattern 203 in response to subjecting inverse anapolic pat-
tern 203 to microwave radiation 215 from microwave con-
ductor 212 by use of a coaxial cable to perform inductive
detection electron paramagnetic resonance spectroscopy.

In an embodiment, performing CW inductive-detection
electron paramagnetic resonance spectroscopy includes dis-
posing an analyte on anapolic conductor 202 in magnetic
field region 208 by using a microscope to guide positioning
of the sample; and subjecting the analyte to the magnetic
field by placing the critically-coupled planar inverse anapole



U.S. Patent Aug. 30, 2022 Sheet 5 of 23 US 11,428,763 B2

Connect microstrip terminated by 50 Q load to
network analyzer

Adhere microresonator to microstrip using a
small amount of silicone grease.

ijus an orientation 0
microresonator to achieve critical coupling
(largest dip in reflected power).

|

if using external modulation coils, place these on
either side of the critically couple microstrip-
microresonator device.

|

Connect microstrip-microresonator device to
EPR spectrometer and proceed to acquisition of
spectra.

FIG. 5


U.S. Patent Aug. 30, 2022 Sheet 4 of 23 US 11,428,763 B2

Ih
=

212

2u1

FIG. 4


U.S. Patent Aug. 30, 2022 Sheet 17 of 23 US 11,428,763 B2

5000

1EL (V/m)


US 11,428,763 B2

Sheet 7 of 23

Aug. 30, 2022

U.S. Patent

LO

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=
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Aug. 30, 2022

U.S. Patent

|

FIG. 23


United States Patent

US0114287

'63B2

(12) (0) Patent No.: US 11,428,763 B2
Szalai et al. (45) Date of Patent: Aug. 30, 2022
(54) PLANAR INVERSE ANAPOLE (52) US. Cl.
MICRORESONATOR AND PERFORMING cpc GOIR 33/3456 (2013.01); GOIR 33/46
INDUCTIVE-DETECTION ELECTRON (2013.01); GOIR 33/60 (2013.01); HOLP
PARAMAGNETIC RESONANCE 7/082 (2013.01)
SPECTROSCOPY (58) Field of Classification Search
: , CPC ..... GOIR 33/3456; GOIR 33/46; GOIR 33/60
(71) Applicant: Government of the United States of See application file for complete search history.
America, as represented by the
Secretary of Commerce, Gaithersburg, (56) References Cited
MD (US)
U.S. PATENT DOCUMENTS
(72) Inventors: Veronika Ann Szalai, Monrovia, MD 6.278893 BL® 82001. Ardenkjer-Larson
(US); Amit Kumar Agrawal, GoiR 33/5601
Rockville, MD (US); Nandita 324/309
Abhyankar, Rockville, MD (US) 10,677,953 B2* 6/2020 Stetson ... .. GOLR 33/032
(Continued)
(73) Assignee: GOVERNMENT OF THE UNITED
STATES OF AMERICA, AS :
SEPRESENT CD BY THE OTHER PUBLICATIONS
SECRETARY OF COMMERCE, Basharin, A.A., et al., “Extremely high Q-factor metamaterials due
Gaithersburg, MD (US) to anapole excitation”, Physical Review B, 2017, p. 035104, vol. 95
(Continued
(*) Notice: Subject to any disclaimer, the term of this (Continued)
patent is extended or adjusted under 35. Primary Examiner — Dixomara Vargas
U.S. 154(b) by 3 days. (74) Attorney, Agent, or Firm — Office of Chief Counsel
(21) Appl. No.: 17/185,184 for National Institute of Standards and ‘Technology
(22) Filed: Feb. 25, 2021 2) ABSTRACT
A planar inverse anapole microresonator includes: an
(65) Prior Publication Data anapolic substrate; an anapolic conductor that includes a first
US 2021/0270916 1 Sep. 2, 2021 and second inverse anapolic pattem; cach inverse anapolic
pattern including: a semi annular arm that terminates in a
first arm tendril and a second arm tendril; and a medial arm
. terminating at a medial tip, and the medial tip of the first
Related U.S. Application Data inverse anapolic pattern opposes the medial tip of the second
(60) Provisional application No. 63/055,816, filed on Jul. inverse anapolic pattern, such that the medial tip of the first
23, 2020, provisional application No. 62/982,879, inverse anapolic pattern is separated from the medial tip of
filed on Feb. 28, 2020. the second inverse anapolic pattern by a medial gap, and the
planar inverse anapole microresonator produces a magnetic
(51) Int. Cl field region that concentrates a magnetic field localized
GOIR 33/345 (2006.01) between the medial tip of the first inverse anapolic pattern
GOIR 33/46 (2006.01) and the medial tip of the second inverse anapolic pattern in

(Continued)

(Continued)



US 11,428,763 B2

Sheet 10 of 23

Aug. 30, 2022

U.S. Patent

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OT Olt

je'a] pazyeuon



U.S. Patent Aug. 30, 2022

Microwave

anysiet 30 Chtermtnation

{c} Bnompied

“304 mm Coupled

Reflected Power {dB}
&
o

a5 $7 39
Frequency {GHz}

Sheet 9 of 23

EPR Signal {a.u)

FIG. 9

US 11,428,763 B2

Capacitive gap of
sticroraeanater



US 11,428,763 B2

13

confined magnetic-field hotspot and simultaneously high
quality factor (Q-factor). To demonstrate the broad array of
implementations of the planar inverse anapole microreso-
nator and its scalability to higher frequencies, the planar
inverse anapole microresonator is disposed in an electron
paramagnetic resonance (EPR) spectrometer operating at 10
GHz and a an EPR spectrometer operating at 35 GHz. We
report continuous wave (CW) EPR spectra for various
samples, including a dilute Mn?*-doped perovskite oxide,
CaTiO;, and a transition metal complex, CuCl;.2H,0. The
planar inverse anapole microresonator provides multifre
quency EPR characterization of dopants and defects in
perovskite oxide microcrystals and other volume-limited
materials of technological importance.

Spin detection in volume-limited samples has applica-
tions in fields ranging from solid-state physics to structural
biology. Magnetic resonance spectroscopies based on induc-
tive detection are powerful and versatile techniques that can
provide atomic-level structural and functional information
for a wide range of samples under broadly variable condi:
tions. However, conventional instrumentation is not sensi
tive enough to detect a large fraction of relevant volume-
limited samples (<10 pL). which are often dilute doped
samples with broad lines and concentrations <1 mole %,
resulting in fewer than 10° spins per picoliter. For example,
electron paramagnetic resonance (EPR) spectroscopy is a
widely used technique to characterize atomic environments
of dopants and defects in technologically relevant materials,
that are often studied in their polycrystalline form because of
the difficulty of growing single crystals. Single crystallites of
perovskite oxides typically have micro- to nano-scale
dimensions and volumes ranging from pico- to nano-liters
The perovskite complex oxide has a crystal structure that,
due its chemical tunability, is suited for a wide variety of
technical and multi-functional applications. Depending on a
number of crystal chemistry considerations that include but
are not limited to stoichiometry, layering, cation ordering,
and defect chemistry, the material can be designed for
piezoelectric, insulating, catalytic, superconducting, and
capacitive uses. Simple perovskite chemistries like SrTiO,
or CaTiO, have limited use in commercial application
however, these compositions serve as important model sys-
tems in which a multitude of fundamental studies are
conducted. The study of point defects in these model sys-
tems helps facilitate metrology of defect chemistry in a
broad range of technical ceramics.

The defect chemistry of a material can have a controlling
effect on its resulting functional properties. The use of single
crystals in EPR spectroscopy can yield orientational depen-

dences of spin Hamiltonian parameters, allowing character- 5

ization of the substitutional properties of dopants. Rigorous
characterization of the site of substitution, valence state, and
nature of defect-complex formation is necessary to explain
the effect of a dopant ion on the resulting physical properties

of a material. Critical information about anisotropies is s

masked by the superposition of EPR spectra from a distri-
bution of orientations in polycrystalline materials. Despite
the clear advantage of studying single crystals, sufliciently
large (several ul. for conventional resonators) single crystals
of dilute doped oxides are dificult to synthesize. Typical
crystallite volumes are smaller than 1 pL, often approaching
only 1 fL. To conduct routine inductive-detection EPR
spectroscopy on single microcrystals of dilute doped oxides
with sub-nanoliter volumes, it is necessary to develop reso-
nators that have active volumes approaching 1 pL. Such
resonators must couple easily to microwave feedlines and
must be scalable to higher frequencies. It is also advanta-

20

&

14

geous if they can be deployed in various spectrometers
without the need for customized hardware. We note that
alternate spin detection techniques can provide ultrahigh
sensitivities; for example, pulsed electrically detected mag-
netic resonance (pEDMR) can provide detection limits of a
few hundred spins, while optically detected magnetic reso-
nance (ODMR) and magnetic resonance force microscopy
(MRFM), can provide sensitivities down to the single-spin
limit. However, these methods cannot provide the same
depth of spectroscopic information provided by inductive-
detection EPR spectroscopy. Sensitivities down to 1000
spins/VHz have been reported for inductive detection using
superconducting microresonators. However, such devices
also require highly restrictive experimental conditions,
including cryogenic temperatures, low magnetic fields, and
exotic detection circuitry such as Josephson parametric
amplifiers. Given that conventional instrumentation in many
laboratories relies on spectrometers built to measure spins
using inductive detection, increasing the sensitivity of
inductive detection for a broad range of experimental con-
ditions extends the power of magnetic resonance spectros-
copies to nanoscale samples. The planar inverse anapole
microresonator for EPR spectroscopy uses a single unit of a
planar inverse anapole metamaterial architecture with a
toroidal moment to increase the quality-factor (Q-factor) and
confine the spatial extent of the electromagnetic field (FIG.
6). We exploit the duality of electric and magnetic fields that
are consistent with Babinet’s principle with an inverse
anapole pattern that efficiently confines microwave mag-
netic fields within a picoliter-scale volume at the center of
the resonator. The active volume of the planar inverse
anapole microresonator provides high Q-factors and a geom-
etry that allows easy coupling to an external microwave
feedline. The planar inverse anapole microresonator was
disposed in an EPR spectrometer operating at 10 GHz and
another EPR spectrometer operating at 35 GHz to obtain
room-temperature continuous wave (CW) EPR spectra of
various materials, including a dilute (<0.05 mole %) Mn2*-
doped sample of CaTiO, and a transition metal complex,
CuCl,.2H,0.

Compared to conventional cavities, the miniaturized
active volumes of the planar inverse anapole microresonator
provide improved detection limits. Non-resonant scanning
probes and microresonators have been designed and dem-
onstrated as planar metallic structures patterned on dielectric
substrates. Such structures can be readily fabricated using
standard photolithographic techniques, yielding nanoliter
active volumes in micromet ‘ale resonators. The effect of
such miniaturization on sensitivity can be explained in terms
of two main resonator characteristics: the filling factor and
the Q-factor. The filling factor can be roughly described as
the fraction of the active volume of the resonator to the
volume occupied by the sample. When the active volume
becomes comparabie to the sample volume, there is a gain
of several orders of magnitude in the filling factor (com-
pared to conventional cavity resonators) and a correspond-
ing gain in absolute sensitivity.

Compared to cavity resonators, power losses are higher in
open resonant structures such as loop-gap resonators and
microstrip-based structures. The lossy nature of microreso-
nators increases the difficulty of coupling with a microwave
source such as a microstrip. Additionally, the size mismatch
between microresonators and microstrips results in further
inefliciency of coupling. Thus, decrease in Q-factor deterio-
rates both absolute sensitivity and concentration sensitivity.
To increase the Q-factor, power losses must be decreased
(FIG. 6c). The Q-factor is dependent on the combination of



US 11,428,763 B2

11

microresonator 200 on microstrip 217 between the magnet
poles of an EPR spectrometer system, applying microwave
radiation 215 and magnetic field modulation through modu-
lation coils 218, and performing data collection via an EPR
spectrometer system.

In an embodiment, performing pulsed inductive-detection
electron paramagnetic resonance spectroscopy includes dis-
posing an analyte on anapolic conductor 202 in magnetic
field region 208 by using a microscope to guide positioning
of the sample; and subjecting the analyte to the magnetic
field by placing the overcoupled planar inverse anapole
microresonator 200 on microstrip 217 between the magnet
poles of an EPR spectrometer system, applying pulses of
microwave radiation 215, and performing data collection via
an EPR spectrometer system.

In an embodiment, performing CW inductive-detection
electron paramagnetic resonance spectroscopy includes
adjusting a position of inverse anapolic pattern 203 relative

to microwave conductor 212 by manual adjustment aided by 2

a magnifying device or microscope; and changing micro-
wave coupling between inverse anapolic pattern 203 and
microwave conductor 212 in response to adjusting the
position of inverse anapolic pattern 203 relative to micro-
wave conductor 212 by sequentially and manually adjusting
coupling angle 0 to produce the maximum absorbed micro-
wave power as monitored on the VNA.

Inan embodiment, performing pulsed inductive-detection
electron paramagnetic resonance spectroscopy includes
adjusting a position of inverse anapolic pattern 203 relative
to microwave conductor 212 by manual adjustment aided by
a magnifying device or microscope; and changing micro-
wave coupling between inverse anapolic pattern 203 and
microwave conductor 212 in response to adjusting the
position of inverse anapolic pattern 203 relative to micro-
wave conductor 212 by sequentially and manually adjusting
coupling angle @ to overcouple planar inverse anapole
microresonator 200 to microwave radiation 215.

In an embodiment, performing CW inductive-detection
electron paramagnetic resonance spectroscopy includes sub-
jecting the analyte to external radiation from modulation
coils 218 by applying a current generated by an EPR
spectrometer system to modulation coils 218.

In an embodiment, performing pulsed inductive-detection
electron paramagnetic resonance spectroscopy includes sub-
jecting the analyte to a sequence of 6 nanosecond (ns) to 1
millisecond (ms) pulses of microwave radiation with powers
ranging from 1 W to 1 kW and a stationary magnetic field,
both supplied by the EPR spectrometer system.

In an embodiment, performing CW inductive-detection 5

electron paramagnetic resonance spectroscopy includes
acquiring an electron paramagnetic resonance spectrum by
detecting microwave radiation 215 that is reflected by ter-
minator 214 connected to microwave conductor 212 after

subjecting the analyte to a modulated magnetic field pro- 5

vided by modulation coils 218 and a swept magnetic field,
both supplied by the EPR spectrometer system.

In an embodiment, performing pulsed inductive-detection
electron paramagnetic resonance spectroscopy includes
acquiring an electron paramagnetic resonance spectrum by
detecting microwave radiation 215 that is reflected by ter-
minator 214 connected to microwave conductor 212 after
subjecting the analyte to a sequence of one or a series of 6
nanosecond (ns) to 1 millisecond (ms) pulses of microwave
radiation with powers ranging from 1 W to 1 kW and a
stationary magnetic field, both supplied by the EPR spec-
trometer system.

&

12

Planar inverse anapole microresonator 200 and processes
disclosed herein have numerous beneficial uses, including,
room temperature measurements of dopants and defects in
technologically-important thin film materials, rapid mea-
surement of structure and dynamics of volume-limited or
concentration-limited biomacromolecular systems, minimal
variation in probed sample volume as a function of operation
frequency, and facile integration with existing EPR spec-
trometer systems. Advantageously, planar inverse anapole
microresonator 200 overcomes limitations of technical defi-
ciencies of conventional compositions such as radiative loss
(low quality factors) and impractical sample volumes at high
operational frequencies.

Planar inverse anapole microresonator 200 provides
inductive-detection of electron spins in picoliter volumes of
a sample with increased sensitivity compared with conven-
tional devices such as microresonators used for spin detec-
tion in volume-limited samples that suffer from poor quality-
factors, which adversely affects sensitivity. Advantageously,
planar inverse anapole microresonator 200 has an inverse
anapole structure that produces toroidal moment and
decreases radiative losses from the planar anapolic condue-
tor 202 and inverse anapolic pattern 203 and simultaneously
confines and centrally concentrates microwave magnetic
fields in an picoliter volumes of magnetic field region 208 at
central bridge 219. It should be appreciated that in view of
the Babinet principle, inverse anapolic pattern 203 produces
a magnetic field hotspot because of the planar inverse
anapole pattern to accomplish inductive-detection electron
magnetic resonance. High quality-factors enable facile cou-
pling with a microwave feedline, allowing continuous wave
EPR experiments not provided by conventional microreso-
nator designs. The size of the hotspot provided by the active
volume of anapolic conductor 202 and inverse anapolic
pattern 203 is smaller than the overall dimensions of planar
inverse anapole microresonator 200. This provides scalabil-
ity to microwave frequencies, e.g., of greater than 100 GHz
so that planar inverse anapole microresonator 200 can be
scaled for use with multiple frequencies without sacrificing
functionality, overcoming a technical limitation of conven-
tional microresonator designs. High quality-factors of planar
inverse anapole microresonator 200 provide easy coupling
to microwave feedlines for deployment of planar inverse
anapole microresonator 200 in spectrometers for measure-
ment of picoliter-volume samples for absolute sensitivity
that can be an order of magnitude higher than conventional
microresonators.

Planar inverse anapole microresonator 200 and processes
herein unexpectedly provide resonance frequency adjust-
ment of inverse anapolic pattern 203 through varying the
y-position of planar inverse anapole microresonator 200
along microwave conductor 212 on microstrip 217.

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

EXAMPLE

Scalable microresonators for room-temperature detection
of electron spin resonance from dilute, sub-nanoliter volume
solids.

‘A planar inverse anapole microresonator provides room-
temperature detection of electron spins in picoliter volumes
that can include low levels of analytes, e.g., dopants in
perovskite oxides. The planar inverse anapole microresona-
tor exploits a toroidal moment in an inverse planar anapole
from a monolithic inverse anapole metamaterial architecture
to produce a microwave resonance exhibiting a spatially



US 11,428,763 B2

Sheet 6 of 23

Aug. 30, 2022

U.S. Patent

9 Dla

PAGHY * is re ee gt Ta
— roe
saoyy IDR SY PYF
be}
nt
o



U.S. Patent Aug. 30, 2022 Sheet 20 of 23 US 11,428,763 B2

y
&
fa)
| nent ‘Wetter
(b} ‘ne 4 cecaci
Increasing y increasing y
ceca enna
ete
“10
& -20
oe
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2 84 a2

Frequency (GHz) Frequency (GHz)
(d} {e)
x-position 1 iAf/m) x-position 2 By (A/mm)

180

35)
90° ~«92”~«*
Frequency (GHz)

FIG. 20


US 11,428,763 B2

27

microwave conductor and that receives the microwave
radiation from the microwave conductor.

9. The planar inverse anapole microresonator of claim 2,
further comprising a microwave source in communication
with the microwave conductor and that produces the micro-
wave radiation and communicates the microwave radiation
to the microwave conductor.

10. The planar inverse anapole microresonator of claim 1,
wherein a frequency of the microwave radiation is from 9
GHz to 34 GHz.

AL. The planar inverse anapole microresonator of claim 1,
wherein the anapolic conductor is planar.

12. A process for performing inductive-detection electron
paramagnetic resonance spectroscopy, the process compris-
ing:

‘communicating microwave radiation through a micro-

wave conductor;

subjecting an inverse anapolic pattern in an anapolic

conductor to the microwave radiation from the micro-
wave conductor; and

creating a magnetic field region and concentrating a

magnetic field localized between a medial tip of a first
inverse anapolic pattern and a medial tip of a second
inverse anapolic pattern of the inverse anapolic pattern
in response to subjecting the inverse anapolic pattern to

1s

28

the microwave radiation from the microwave conduc-
tor to perform inductive detection electron paramag-
netic resonance spectroscopy.
13. The process of claim 12, farther comprising:
disposing an analyte on the anapolic conductor in the
magnetic field region; and
subjecting the analyte to the magnetic field.
14. The process of claim 13, further comprising:
adjusting a position of the inverse anapolic pattern rela-
tive to the microwave conductor; and
changing microwave coupling between the inverse
anapolic pattern and the microwave conductor in
response to adjusting the position of the inverse
anapolic pattern relative to the microwave conductor.
15. The process of claim 14, further comprising subject-
ing the analyte to external radiation from a modulation coil.
16. The process of claim 13, further comprising acquiring
an electron paramagnetic resonance spectrum by detecting
the microwave radiation that is reflected by a terminator
connected to the microwave conductor after subjecting the
analyte to the magnetic field.
17. The process of claim 13, wherein a frequency of the
microwave radiation is from 9 GHz to 35 GHz.

+e Ree


US 11,428,763 B2

5

FIG. 18 shows (a) fits of the power saturation curve of
BDPA on 10 GHz planar inverse anapole microresonator to
linear and asymptotic growth functions. The power at which
the curve deviates from the linearity is taken as the satura-
tion power. (b) Fit of peak-to-peak amplitude ‘A’ vs. power
*P’ to the following egn.: A=IP,,o[1+(2!*-1)P/P,91*. The
fit yielded ©=0.5+0.1, indicating highly inhomogeneous
saturation;

FIG. 19 shows (a) a plan view of a coupled microreso-
nator-microstrip in a planar inverse anapole microresonator.
(b) A plan view of the planar inverse anapole microresonator
showing the parameters x, y, and @, which affect resonant
frequency and coupling. (c) Dependence of resonant fre-
quency of the 9.75 GHz planar inverse anapole microreso-
nator on the x-position of the microresonator relative to the
microstrip. (d) Dependence of resonant frequency of the 35
GHz planar inverse anapole microresonator on the x-posi-
tion of the microresonator on the microstrip;

FIG. 20 shows (a) a plan view of the planar inverse
anapole microresonator showing the parameters x, y, and 0,
which affect resonant frequency and coupling. (b) Simula-
tion of shift in resonant frequency upon changing y-position
at constant x-position and 6, evident from the change in S11
profiles. (c) Changes in voltage standing wave ratio corre-
sponding to the scans in (b). (d) and (e) Comparison of
coupling at incremental positions, when x is changed by
approximately 4 mm from (d) to (e). These data show that
they-position has a dominant effect in determining resonant
frequency and coupling. However, when x is changed, the
y-position of critical coupling also changes, which in turn
shifts the resonant frequency of the device at critical cou-
pling. The field distributions in (d) and (e) show that the
conversion efficiency is also dependent on they-position at
which critical coupling occurs;

FIG. 21 shows the CW EPR spectrum of 0.01 mole %
Fe*:SrTiO3, obtained from a planar inverse anapole
microresonator operating at 35 GHz;

FIG. 22 shows (a) a plan view and (b) side view of a 10
GHz planar inverse anapole microresonator that substituted
for the resonator and modulation coils in an EPR spectrom-
eter. Scale bars represent 5 mm; and

FIG. 23 shows a planar inverse anapole microresonator
interposed between magnet poles of an electromagnet in an
EPR spectrometer system.

DETAILED DESCRIPTION

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

It has been discovered that a planar inverse anapole
microresonator provides inductive-detection of electron
spins in picoliter volumes. The planar inverse anapole
microresonator has a spin detection limit that is an order of

magnitude more sensitive than conventional microresonator

devices. Conventional microresonators for spin detection in
volume-limited samples can suffer from poor quality-fac-
tors, which adversely affects sensitivity. The planar inverse
anapole microresonator includes an inverse anapole that
produces a toroidal moment that decreases radiative loss in
a planar format that confines microwave magnetic fields to
picoliter volumes. The planar inverse anapole microresona-
tor produces a magnetic field hotspot for inductive-detection
electron magnetic resonance. The planar inverse anapole
microresonator has a quality-factor that mediates facile
coupling with a microwave feedline for continuous wave
(CW) and pulsed electron paramagnetic resonance (EPR).

20

&

4

5

6

The size of the magnetic field hotspot provides an active
volume of the resonator for a sample that is smaller than
overall dimensions of the planar inverse anapole microre-
sonator and provides scalability to microwave frequencies
that are greater than 100 GHz. The planar inverse anapole
microresonator can be scaled for multiple frequencies and
overcomes operational limitations of conventional microre-
sonator devices.

Planar inverse anapole microresonator 200 produces a
magnetic field region 208. In an embodiment, with reference
to FIG. 1, FIG. 2, FIG. 3, and FIG. 4, planar inverse anapole
microresonator 200 includes: anapolic substrate 201;
anapolic conductor 202 disposed on anapolic substrate 201
and including first inverse anapolic pattern 203.1 and second
inverse anapolic pattern 203.2 arranged such that second
inverse anapolic pattern 203.2 is disposed in a plane with
first inverse anapolic pattern 203.1 and opposes first inverse
anapolic pattern 203.1; each inverse anapolic pattern 203
including: semi annular arm 204 that terminates in first arm
tendril 210.1 and second arm tendril 210.2 distal to first arm.
tendril 210.1; and medial arm 205 extending from concave
portion 216 of semi annular arm 204 and terminating at
medial tip 207 distal to concave portion 216 of semi annular
arm 204 so that medial tip 207 is separated from first arm

5 tendril 210.1 and second arm tendril 210.2 and medially

disposed between first arm tendril 210.1 and second arm
tendril 210.2, such that: first arm tendril 210.1 of first inverse
anapolic pattern 203.1 opposes first arm tendril 210.1 of
second inverse anapolic pattern 203.2; second arm tendril
210.2 of first inverse anapolic pattern 203.1 opposes second
arm tendril 210.2 of second inverse anapolic pattern 203.2;
and medial tip 207.1 of first inverse anapolic pattern 203.1
opposes medial tip 207.2 of second inverse anapolic pattern
203.2, such that medial tip 207.1 of first inverse anapolic
pattern 203.1 is separated from medial tip 207.2 of second
inverse anapolic pattern 203.2 by medial gap 206, and planar
inverse anapole microresonator 200 produces magnetic field
region 208 that concentrates a magnetic field localized
between medial tip 207.1 of first inverse anapolic pattern
203.1 and medial tip 207.2 of second inverse anapolic
pattern 203.2 in response to planar inver
sonator 200 being subjected to microwave radiation 215. As
shown in panel A of FIG. 1, concave portion 216 of inverse
anapolic pattern 203 surrounds interior plenum 221 of
anapolic conductor 202, and convex portion 223 of inverse
anapolic pattern 203 borders exterior plenum 222 of
anapolic conductor 202

In an embodiment, with reference to FIG. 2, FIG. 3, and
FIG. 4, planar inverse anapole microresonator 200 includes
microstrip 217 on which anapolic substrate 201 is disposed,
wherein anapolic substrate 201 is interposed between
microstrip 217 and anapolic conductor 202.

In an embodiment, microstrip 217 includes dielectric
substrate 211; and microwave conductor 212 that is disposed
on dielectric substrate 211 and that receives microwave
radiation 215 and communicates microwave radiation 215 to
subject inverse anapolic pattern 203 to microwave radiation
215 and produce magnetic field region 208. In an embodi-
ment, anapolic substrate 201 is adjustably disposed on
microstrip 217 such that medial arm 205 of first inverse
anapolic pattern 203.1 and medial arm 205 of second inverse
anapolic pattern 203.1 are rotationally adjustable with
respect to microwave conductor 212, as shown in FIG. 3
with coupling angle @ between medial arm 205 of first
inverse anapolic pattern 203.1 and medial arm 205 of second
inverse anapolic pattern 203.1 and microwave conductor
212. It is contemplated that coupling angle 6 can be from 0°



U.S. Patent Aug. 30, 2022 Sheet 2 of 23 US 11,428,763 B2

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U.S. Patent Aug. 30, 2022 Sheet 13 of 23 US 11,428,763 B2

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US 11,428,763 B2

Sheet 15 of 23

Aug. 30, 2022

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US 11,428,763 B2

25

wherein k, is Boltzmann’s constant; T is temperature; R is
the resistance of the microresonator coil, and Af is the
bandwidth of the detection electronics.

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 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). Option, 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, collection of elements, and the
like.

As used herein, a combination thereof refers to a combi-
nation comprising at least one of the named constituents,
components, compounds, or elements, optionally together
with one or more of the same class of constituents, compo-
nents, compounds, or elements.

All references are incorporated herein by reference.

The use of the terms “a,” “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. It can 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 distin-
guish one element from another. It will also be understood
that, although the terms first, second, etc. are, in some
instances, used herein to describe various elements, these
elements should not be limited by these terms. For example,
a first current could be termed a second current, and,
similarly, a second current could be termed a first current,
without departing from the scope of the various described
embodiments. The first current and the second current are
both currents, but they are not the same condition unless
explicitly stated as such.

‘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 associated
with measurement of the particular quantity). The conjunc-

tion or is used to link 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. A planar inverse anapole microresonator comprising:

an anapolic substrate:

‘an anapolic conductor disposed on the anapolic substrate
and comprising a first inverse anapolic pattern and a
second inverse anapolic pattern arranged such that the
second inverse anapolic pattern is disposed in a plane
with the first inverse anapolic pattem and opposes the
first inverse anapolic pattern;

each inverse anapolic pattern comprising:

20

0

&

0

&

26

a semi annular arm that terminates in a first arm tendril
and a second arm tendril distal to the first arm tendril;
and

a medial arm extending from a concave portion of the
semi annular arm and terminating at a medial tip
distal to the concave portion of the semi annular arm
so that the medial tip is separated from the first arm
tendril and the second arm tendril and medially
disposed between the first arm tendril and the second
arm tendril, such that:

the first arm tendril of the first inverse anapolic pattern
opposes the first arm tendril of the second inverse
anapolic pattern;

the second arm tendril of the first inverse anapolic
pattern opposes the second arm tendril of the second
inverse anapolic pattern; and

the medial tip of the first inverse anapolic pattern
‘opposes the medial tip of the second inverse anapolic
pattern,

such that the medial tip of the first inverse anapolic pattern

is separated from the medial tip of the second inverse
anapolic pattern by a medial gap, and the planar inverse
anapole microresonator produces a magnetic field
region that concentrates a magnetic field localized
between the medial tip of the first inverse anapolic
pattern and the medial tip of the second inverse
anapolic pattern in response to the planar inverse
anapole microresonator being subjected to microwave
radiation.

2. The planar inverse anapole microresonator of claim 1,
further comprising a microstrip on which the anapolic
substrate is disposed,

wherein the anapolic substrate is interposed between the

microstrip and the anapolic conductor.

3. The planar inverse anapole microresonator of claim 1,
wherein the microstrip comprises:

a dielectric substrate; and

a microwave conductor disposed on the dielectric sub-

strate and that receives microwave radiation and com-

municates the microwave radiation to subject the
inverse anapolic pattem to the microwave radiation and
produce the magnetic field region.

4. The planar inverse anapole microresonator of claim 1,
wherein the anapolic substrate is adjustably disposed on the
microstrip such that the medial arm of the first inverse
anapolic pattern and the medial arm of the second inverse
anapolic pattern are rotationally adjustable with respect to
the microwave conductor.

5. The planar inverse anapole microresonator of claim 4,
wherein a coupling angle between the medial arm of the first
inverse anapolic pattern and the medial arm of the second
inverse anapolic pattern and the microwave conductor is
from 0° to 90°.

6. The planar inverse anapole microresonator of claim 5,
wherein the coupling angle is variable to obtain critically
coupling of the inverse anapolic pattern to the microwave
conductor for CW operation of the planar inverse anapole
microresonator, and over-coupling of the inverse anapolic
pattern to the microwave conductor for pulsed operation of
the planar inverse anapole microresonator.

7. The planar inverse anapole microresonator of claim 2,
further comprising a first modulation coil and a second
modulation coil between which is disposed the inverse
anapolic pattern.

8. The planar inverse anapole microresonator of claim 2,
further comprising a terminator in communication with the


US 11,428,763 B2

1
PLANAR INVERSE ANAPOLE
MICRORESONATOR AND PERFORMING

SPECTROSCOPY

CROSS REFERENCE TO RELATED
APPLICATIONS

‘The application claims priority to U.S. Provisional Patent
Application Ser. No. 63/055,816 filed Jul. 23, 2020, and U.S.
Provisional Patent Application Ser. No. 62/982,879 filed
Feb. 28, 2020, the disclosures of which are incorporated
herein by reference in their 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. 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 20-031US1.

BRIEF DESCRIPTION

Disclosed is a planar inverse anapole microresonator
comprising: an anapolic substrate; an anapolic conductor
disposed on the anapolic substrate and comprising a first
inverse anapolic pattern and a second inverse anapolic
pattern arranged such that the second inverse anapolic
pattern is disposed in a plane with the first inverse anapolic
pattern and opposes the first inverse anapolic pattern; each
inverse anapolic pattern comprising: a semi annular arm that
terminates in a first arm tendril and a second arm tendril
distal to the first arm tendril; and a medial arm extending
from a concave portion of the semi annular arm and termi-
nating at a medial tip distal to the concave portion of the
semi annular arm so that the medial tip is separated from the
first arm tendril and the second arm tendril and medially
disposed between the first arm tendril and the second arm
tendril, such that: the first arm tendril of the first inverse
anapolic pattern opposes the first arm tendril of the second
inverse anapolic pattern; the second arm tendril of the first
inverse anapolic pattern opposes the second arm tendril of

the second inverse anapolic pattern; and the medial tip of the s

first inverse anapolic pattern opposes the medial tip of the
second inverse anapolic pattern, such that the medial tip of
the first inverse anapolie pattern is separated from the medial
tip of the second inverse anapolic pattern by a medial gap,

and the planar inverse anapole microresonator produces a;

magnetic field region that concentrates a magnetic field
localized between the medial tip of the first inver apolic
pattern and the medial tip of the second inverse anapolic
pattern in response to the planar inverse anapole microre-
sonator being subjected to microwave radiation.

Disclosed is a process for performing inductive-detection
electron paramagnetic resonance spectroscopy, the process
comprising: communicating microwave radiation through a
microwave conductor; subjecting an inverse anapolic pat-
tern in an anapolic conductor to the microwave radiation
from the microwave conductor; and creating a magnetic
field region and concentrating a magnetic field localized

3

at

2

between a medial tip of a first inverse anapolic pattern and
a medial tip of a second inverse anapolic pattem of the
inverse anapolic pattern in response to subjecting the inverse
anapolic pattern to the microwave radiation from the micro-
wave conductor to perform inductive detection electron
paramagnetic resonance spectroscopy.

BRIEF DESCRIPTION OF THE DRAWINGS

The following description cannot be considered limiting
in any way. With reference to the accompanying drawings,
like elements are numbered alike,

FIG. 1 shows a planar inverse anapole microresonator in
panel A, a cross-section along line A-A thereof in panel B,
and a cross-section along line B-B in panel C;

FIG. 2 shows a planar inverse anapole microresonator in
panel A, a cross-section along line A-A thereof in panel B,
and a cross-section along line B-B in panel C;

FIG. 3 shows mutual rotary motion of an anapolic con-
ductor 202 and an inverse anapolic pattern relative to a
microstrip of a planar inverse anapole microresonator;

FIG. 4 shows a microstrip for microwave coupling to an
anapolic conductor and an inverse anapolic pattern in a
planar inverse anapole microresonator:

FIG. 5 shows a flow chart for performing inductive-
detection electron paramagnetic resonance spectroscopy;

FIG. 6 shows various views of a planar inverse anapole
microresonator. (a) Perspective view of the planar inverse
anapole resonator including a dielectric substrate whose top
surface is coated with a gold film. The central portion,
indicated by the enlarged view in panel b, is where the
microwave magnetic field is concentrated around the central
bridge between the medial arms of the inverse anapolic
patterns. (b) Two designs of the central bridge, providing
active volumes of 1 picoliter (pL) (Design I) and 100 pL
(Design II). (c) Types of power losses occurring from a
planar inverse anapole microresonator, (d) Schematic of
currents (arrows in plane with inverse anapolic patterns) and
dipoles in the planar inverse anapole microresonator. The
zoomed region shows the central bridge, where the magnetic
flux density B, is concentrated. The in-plane arrows indicate
the directions of currents flowing through and adjacent to the
central bridge. Current through the central bridge results in
a magnetic dipole in and out of the plane of the planar
inverse anapole microresonator. The currents flowing
through the inverse anapolic pattern adjacent to the central
bridge provide a degenerate toroidal moment that is directed
into and out of the plane. (e) Planar inverse anapole microre-
sonator coupled to electromagnetic fields radiating from the
central microwave conductor of the microstrip. (f) Plan view
of exposed surface of the planar inverse anapole microre-
sonator. In the left panel, the solid arrows indicate the
electric dipole moment, and the dashed arrow indicates the
toroidal moment. The right panel shows a simulation of the
microwave magnetic flux density B, concentrated in a small
volume in the magnetic field region at the central bridge and
directed perpendicular to the current flowing through the
central bridge, wherein the curved arrow shows the domi-
nant direction of B,;

FIG. 7 shows a planar inverse anapole microresonator
configured for operation at 10 GHz with a finite element
simulation of the magnetic field region as an active volume
of the planar inverse anapole microresonator. (a) Top view
of a planar inverse anapole microresonator with a resonant
frequency of 9.7 GHz. Scale bar=5 mm. A zoomed region in
the panel on the right shows the microresonator chip. The
outline portion at the center of the right panel encloses the



US 11,428,763 B2
Page 2

response to the planar inverse anapole microresonator being
subjected to microwave radiation.

17 Claims, 23 Drawing Sheets

(51) Int. CL.

HOIP 7/08 (2006.01)
GOIR 33/60 (2006.01)
(56) References Cited

U.S. PATENT DOCUMENTS.

2010/0213941 AL* 8/2010 Driesel GOIR 33/5659
324/322

2013/0093424 AL* 4/2013 Blank GOIR 33/60
324/318

20140163664 A1* 6/2014 Goldsmith AG1B 17/0057
604/93.01

2014/0285198 A1* 9/2014 Halpern GOLV 3/104

324/322
2019/0247050 AL* 8/2019 Goldsmith . AGLF 2/82
2020/0303534 AL" 9/2020 Ram . HOAL 31/112
2020/0309602 AL* 10/2020 El Fatimy GOLI 5/20
2021/0225531 AL* 7/2021 Brown .... G21B 3/00

OTHER PUBLICATIONS,

Abhyankar, N., et al., “Highly Sensitive Microresonators for EPR
Spectroscopy of Submicromolar Biomacromolecular Samples”, GRC
Conference 2019, Jan. 2019.

Abhyankar, N., et al., “Planar Anapole Microresonators for Induc-
tive Detection EPR Spectroscopy”, Rocky Mountain Conference on
Magnetic Resonance, Snowbird Resort & Conference Center, Jul

2018.

Szalai, V.A., et al., “Electron Paramagnetic Resonance (EPR) Spec-
troscopy for Bionanomaterial Measurements”, Air Force Office of
Science Research Biophysics Program Review, Apr. 2018.

* cited by examiner


US 11,428,763 B2

17

microwave source. Thus, this design overcomes the chal-
lenges of ring or loop-gap microresonators, which become
difficult to fabricate and couple to microwave sources owing
to progressively small radii with increasing frequency. The

18
The patterned gold film converges on the small central
bridge of Design I, with an area of approximately (5x5) jum?.
FIGS. 7c-7e show plots of the simulated B, ,? and B,,? in the
x, y and z directions, respectively, normalized to the highest

scalability of the anapole architecture can enable high- 5 value of B, ,?. The dotted lines in the insets are the cut lines
frequency EPR studies for volume-limited samples. along which B, ,7 and B,,? are plotted. They were chosen to
In both bridge designs, the microwave magnetic field B, cut through the region of strongest B, in the plane of the
s concentrated ma smi vonme aod the central bridge resonator. These distributions indicate that approximately
oanel nG oevelow we ‘ the that th current (eight 80% of B, ,? is localized within a volume of (15 jumx20
pe ). Below we show that the experimental 10 15.5 um) around the central bridge—i.e. approximately
Q-factors for these structures are in the approximate range of ° ne Be " ;
1500 jum* or 1.5 pL. The dimension in the z direction is
250 to 350 at both 10 GHz and 35 GHz. Important advan- 1d because only the volume above th tor our
tages of this design include the picoliter active volume, ease Halve 7 le for on yr nr olume a Th e me cotta OF Surlace
of coupling to a microwave feedline and scalability to higher _'8 available for sample placement. The tangential component
frequencies. Finally, we demonstrate that these devices can 15 0f B.* te. B,\" is also plotted in FIGS. 7e-7e and comprises
be integrated into existing EPR spectrometers for wide less than 5% of the total B, ,. Table 2 shows the calculated
implementation. mode volumes for the 2 different bridge designs at two
The planar inverse anapole microresonators were fabri- __ different frequencies. In FIG. 8, we show that mode volumes
cated by patterning gold films of thickness 500 nm on either are not an accurate representation of the volume responsible
lanthanum aluminate (LAO) or lanthanum aluminate-stron- 20. for most of the signal in an open resonant structure such as
tium titanate (LSAT) substrates (dielectric constants ranging a microstrip resonator. The calculated mode volumes are
from 22 to 25) with thicknesses of 500 um. Simulations of much higher than the estimated active volume, and we show
field distributions of the devices were conducted using the __ in FIG. 8 that most of the signal does indeed originate from
commercial finite element analysis software COMSOL. The a much smaller active volume at the center of the microre-
complete finite element model of the planar inverse anapole _sonator.
TABLE 2
Design 1, Design Il, Design 1 Design 11,
10 GHz 10 GHz 35 GHz 35 GHz
Noes 931098 GHz 9.3t098 GHz 3471035 GHz 34.7 10 35 Giz
Q (simulation) 220 + 20 200 + 20 580 + 30 760 * 50
Q (experiment) 250 + 50 250 + 50
Conversion 3204 mTWW 9=1 mIVW lL +2 mTVW 3.£03 mIWW
efficiency
(simulation)
Conversion 3 £03 mINW 621 mINW
efficiency
(experiment)
Pip 0.025 + 0.05 mW _— _— Lower than lowest
(experiment) available power
Mode volume 30 ab 3 nb 400 pL. 4aL
(simulation)*
resonator with dimensions is shown in FIG. 15. FIG. 16 In Table 2, mode volume was calculated based on the
provides dimensions of features of the metallized layer. _,, filling factor of a small volume in the magnetic field region
With regard to simulation and experimental verification of ~” of the microresonator by the following formula.
the active volume, FIG. 7a the planar inverse anapole
microresonator coupled to a microstrip that is connected to .
the microwave source of an EPR spectrometer system via a { BRav
coaxial cable. The resonator was designed to exhibit a Mode volume = Small yolumex stor
high-Q anapole mode at 10 GHz. The left panel of FIG. 7b ~ Jeni vine BRAY
shows a micrograph of the magnetic field region of the
aarti based on Design r while ne Tight Panel ‘The estimated active volume and trends in simulations of
shows dieu  (B_) and tangential (B 5 omponents of the _, elt distributions were verified by simulating and observing
perpendicular (B, 1) orth By, components Of MME ss_the loss in signal when a sample is moved away from the
microwave magnetic field in the magnetic field region. Bi, magnetic field region (FIG. 8). A single crystal of the
is the sum of components of B, that are perpendicular to the adi :
‘ that ar c.y-bisdiphenylene-B-phenylallyl (BDPA)-benzene com-
static magnetic field By. Here B, is designated as the absolute 1 oe mle ct a cane
VB, caB,.>). wit : - plex was placed on the B, hotspot and then moved away by
value of V(B,.°+B,2"). with By applied along the y axis. 4 small increment along the x-axis. The crystal had a volume
Thus, VB,,” is the absolute value of the tangential compo- 60 of about 70 pL and covered an area much larger than the
nent of the microwave magnetic field. The EPR signal is active area of the resonator. FIG. 8a shows the magnetic
directly proportional to B, ,. FIG. 17 shows that the electric field region of the microresonator surface with no sample on
field is concentrated at the edges of the capacitive gaps and it. FIGS. 8b and 8c show the sample at two different
is well-separated from the magnetic field region at the center _ positions separated in x by 7 umz3 jm. The BDPA-benzene
of the resonator. This separation of electric and magnetic 65. crystal was chosen because it has a strong and narrow signal

fields is particularly advantageous for samples with high
dielectric losses.

that is easy to quantify. Based on the large extent of the
BDPA microcrystal compared to the size of the magnetic


US 11,428,763 B2

7

to 90°. In an embodiment, coupling angle 6 is variable to
obtain critical coupling of inverse anapolic pattern 203 to
microwave conductor 212 for CW operation of planar
inverse anapole microresonator 200, and over-coupling of
inverse anapolic pattern 203 to microwave conductor 212
for pulsed operation of planar inverse anapole microreso-
nator 200.

In an embodiment, anapolic substrate 201 is adjustably
disposed on microstrip 217 in the y-direction as shown in
FIG. 2 to adjust the resonant frequency of inverse anapolic
pattern 203 for operation of planar inverse anapole microre-
sonator 200. It is contemplated that the y-distance on
microstrip 217 is variable and can be from 10 mm to 7 mm.

In an embodiment, with reference to FIG. 22 and FIG. 23
planar inverse anapole microresonator 200 includes first
modulation coil 218 and second modulation coil 218
between which is disposed inverse anapolic pattern 203.
Terminator 214 can be disposed in communication with
microwave conductor 212 to receive microwave radiation

215 from microwave conductor 212 for termination of the 2

microwave line and reflection of microwave radiation 215,
as shown in FIG. 4 and FIG, 22. Microwave source 213 can
be in communication with microwave conductor 212 to
produce microwave radiation 215 and communicate micro-
wave radiation 215 to microwave conductor 212.

Planar inverse anapole microresonator 200 can be made
from various elements and components. Anapolic substrate
201 can include a dielectric material that is transparent to
microwave radiation for communication of microwave
radiation 215 from microwave conductor 212 to anapolic
conductor 202 so that magnetic field region 208 is formed by
inverse anapolic pattern 203 in anapolic conductor 202.
Exemplary materials for anapolic substrate 201 include
ceramic, plastic, oxides of various metals, and the like.

‘Anapolic conductor 202 is diposed on anapolic substrate
201 for formation of inverse anapolic pattern 203 in inverse
anapolic pattern 203 to provide an inverse anopolic structure
that centurally concentrates magnetic field strength at mag-
netic field region 208 coincideent at central bridge 219.
Anapolic conductor 202 can include electrically conductive
materials such as conductively-doped polycrystalline sili-
con, a metal (e.g., copper, gold, and the like), tin-doped
indium oxide, and the like. The conductive material can be
selected to provide inverse anapolic pattern 203 by pattern-
ing such as performing etching or photolithography or
machining such as cutting or oblation to form inverse
anapolic pattern 203 from anapolic conductor 202. Inverse
anapolic pattern 203 concentrates the magnetic field cen-
trally within central bridge 219 as shown in FIG. 6f, FIG. 7.

FIG. 10, and FIG. 12, Further, as shown in FIG. 12, it should s

be appreciated that an inverse anapole that concentrates the
magnetic field centrally in a hotspot of magnetic field
strength, and an anapole distributes magnetic field at other
parts of a conductor instead of a central portion. That is, a

maximum magnetic field strength for the inverse anapolic

pattern is an inverse of that for an anapole structure.

Inverse anapolic pattern 203 includes semi annular arms
(204.1, 204.2) that oppose each other. Medial arm 205
extends radially from concave border 216 of semi annular
arm 204 to medial tip 207 abutting central bridge 219 in
interior plenum 221 of anapolic conductor 202 having
medial gap 206. Opposing semi annular arms (204.1, 204.2)
terminate at arm tendrils 210 spaced apart by arm gap 209.
An interior of semi annular arm 204 has concave border 216
with a concave shape that borders interior plenum 221 of
anapolic conductor 202. An exterior of semi annular arm 204
has convex border 223 with a convex shape that borders

&

&

8

exterior plenum 222 of anapolic conductor 202. It should be
appreciated that to produce the inverse anapole for concen-
trated, centralized magnetic field strength, anapolic conduc-
tor 202 is co-planar with inverse anapolic pattern 203.
Medial gap 206 located at central bridge 219 of interior
plenum 221 has a distance w, from a proximate portion of
first medial tip 207.1 to second medial tip 207.2 that can be
from 50 nanometers (nm) to 800 millimeters (mm), specifi-
cally from 100 nm to 100 mm, and more specifically from
10 micrometers (um) to 1 mm. Medial tip 207 can have
various shapes to provide localization of magnetic field
region 208 as exemplified, but not limited by, FIG. 6b FIG.
7b, and FIG. 10. Various other size parameters of inverse
anapolic pattern 203 are shown in FIG. 16. Outer distance d,
from convex border 223 of first inverse anapolic pattern
203.1 to convex border 223 of second inverse anapolic
pattern 204.1 can be from 50 nanometers (nm) to 800
millimeters (mm), specifically from 100 nm to 100 mm, and
more specifically from 10 micrometers (jim) to 1 mm. Inner
distance d, from concave border 216 of first inverse anapolic
pattern 203.1 to concave border 216 of second inverse
anapolic pattern 203.2 can be from 50 nanometers (nm) to
800 millimeters (mm), specifically from 100 nm to 100 mm,
and more specifically from 10 micrometers (jum) to 1 mm.

5 Distance w, of arm gap 209 between opposing arm tendrils

210 of first inverse anapolic pattern 203.1 and second
inverse anapolic pattern 203.2 can be from 50 nanometers
(nm) to 800 millimeters ( from 100 nm to
100 mm, and more specifically from 10 micrometers (jum) to
1 mm. Further, medial arm 205 can have a transverse width
gi that can be from 50 nanometers (nm) to 800 millimeters
(mm), specifically from 100 nm to 100 mm, and more
specifically from 10 micrometers (um) to 1 mm. Thickness
T of anapolic conductor 202 and inverse anapolic pattern
203 can be from 50 nanometers (nm) to 800 millimeters
(mm), specifically from 100 nm to 100 mm, and more
specifically from 200 nm to 2 um.

To achieve concentration of the magnetic field in the
magnetic field region 208 at central bridge 219, microwave
conductor 212 receives microwave radiation 215 and sub-
ject: olic conductor 202 and inverse anapolic pattern
203 to microwave radiation 215. Microwave conductor 212
is an efficient conductor of microwave frequencies and is
disposed on dielectric substrate 211. Dielectric substrate 211
electrically isolates microwave conductor 212 without inter-
fering with communication of microwave radiation 215 in
microwave conductor 212. Exemplary dielectric substrates
include glass, ceramic, and the like. Exemplary microwave
s include copper, silver, and the like. A frequency
of the microwave radiation 215 can be from 1 gigahertz
(GHz) to 100 GHz, specifically from 5 GHz to 50 GHz, and
more specifically from 9 GHz to 34 GHz. A power of the
microwave conductor 212 can be from 100 microwatts (1W)
to 100 watts (W), specifically from 1 milliwatt (mW) to 50
W, and more specifically from 9 mW to 25 W.

Microwave source 213 produces microwave radiation 215
and communicates microwave radiation 215 to microwave
conductor 212. Exemplary microwave sources 213 include
a magnetron, klystron, traveling-wave tube, gyrotron, field-
effect transistor, tunnel diode, Gunn diode, voltage-con-
trolled oscillator, frequency synthesizer, and the like. In an
embodiment, microwave source 213 is an EPR spectrometer
microwave source.

An exposed surface, e.g., the top-most surface (with
respect to the Z-axis shown in FIG. 1) of planar inverse
anapole microresonator 200 that includes inverse anapolic
pattern 203 and central bridge 219 as shown in FIG. 1 is



U.S. Patent Aug. 30, 2022 Sheet 11 of 23 US 11,428,763 B2

{a) (b)
_~ | 3
S ae
rad : 2
g H S
= i ec
5 | &
S40 | E
3 | =
g 3
o ~~ Uncoupled / 2
Se 20 o
@ ~~ Coupled H
i nee ee
34.6 35.0 34 2060 8.001 0.003.008
Frequency (GHz) Power (VW)

BOB Leeper el

sae ena Poy
LOB Laz RIS 120 4.2820 1.2536 £2840

Field (T) Field (T)

FIG. 11


U.S. Patent Aug. 30, 2022 Sheet 14 of 23 US 11,428,763 B2

[E,| (V/m)

fix10°

1B,| (A/m)
375

FIG. 14