US 20190173318A1

( 19) United States

(12 ) Patent Application Publication ( 10) Pub . No.: US 2019 /Jun
0173318 A1
Joannopoulos et al. . 6 , 2019(43) Pub . Date :
(54 ) WIRELESS NON -RADIATIVE ENERGY (60 ) Provisional application No. 60/698 ,442, filed on Jul.
TRANSFER 12, 2005.
(71) Applicant: Massachusetts Institute of Publication Classification
Technology , Cambridge, MA (US) (51) Int. CI.
H02J 50 /12 (2006 .01)
(72 ) Inventors: John D . Joannopoulos , Belmont,MA H02J 5 /00 ( 2006 .01)
(US ); Aristeidis Karalis , Boston , MA BOOL 50 /50 ( 2006 .01)
(US ); Marin Soljacic , Belmont, MA H010 9 /04 (2006 .01)
(US) HOIF 38 / 14 (2006 .01)
B60L 53/12 ( 2006 .01)
(21) Appl. No.: 16 /184,354 (52) U .S . CI.
CPC ............. . HO2J 50/ 12 ( 2016 .02); H02J 5 /005
(22 ) Filed : Nov. 8, 2018 ( 2013 .01 ) ; B60L 50 /50 ( 2019 .02 ); H010 9 /04
( 2013.01); HOIF 38/ 14 ( 2013.01); YO2T
Related U .S . Application Data 10 / 7088 ( 2013 .01) ; YO2T 10 / 7072 ( 2013 .01);
YO2T 90 / 122 ( 2013 .01); YO2T 90/ 14 ( 2013.01);
(63 ) Continuation of application No. 15 /793 ,198 , filed on Y1OT 307/ 25 ( 2015 .04 ); YO2T 10 / 7005
Oct. 25 , 2017 , now Pat. No . 10 , 141,790 , which is a (2013 .01) ; B60L 53 / 12 (2019 .02 )
continuation of application No. 15 /083 ,726 , filed on
Mar. 29 , 2016 , now Pat. No. 9 ,831,722 , which is a (57 ) ABSTRACT
continuation of application No. 14 /629, 709, filed on Described herein are embodiments of a source high - Q
Feb . 24 , 2015 , now Pat. No . 9 ,450 ,421, which is a resonator, optionally coupled to an energy source, a second
continuation of application No. 14 / 302,662, filed on high - Q resonator , optionally coupled to an energy drain that
Jun. 12 , 2014 , now Pat. No . 9 , 065 ,286 , which is a may be located a distance from the source resonator. A third
continuation of application No . 12 /639 , 963, filed on high - Q resonator, optionally coupled to an energy drain that
Dec . 16 , 2009 , now Pat. No. 8 ,760, 007, which is a may be located a distance from the source resonator. The
continuation of application No. 12 /553, 957 , filed on source resonator and at least one of the second resonator and
Sep . 3 , 2009, now abandoned , which is a continuation third resonator may be coupled to transfer electromagnetic
of application No . 11 /481 ,077, filed on Jul. 5 , 2006 , energy from said source resonator to said at least one of the
now Pat . No. 7 ,741,734 . second resonator and third resonator.

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US 2019 /0173318 A1 Jun. 6 , 2019

WIRELESS NON -RADIATIVE ENERGY

TRANSFER
SUMMARY OF THE INVENTION
[0006 ] According to one aspect of the invention, there is
CROSS - REFERENCE TO RELATED provided an electromagnetic energy transfer device . The
APPLICATIONS electromagnetic energy transfer device includes a first reso
nator structure receiving energy from an external power
10001] This application is a continuation and claims the supply . The first resonator structure has a first Q - factor. A
benefit of priority under 35 USC § 120 to U .S . application second resonator structure is positioned distal from the first
Ser. No. 15 ,793 , 198 , filed on Oct. 25, 2017 , which is a resonator structure , and supplies useful working power to an
continuation of U . S . application Ser. No . 15 /083 ,726 , filed external load. The second resonator structure has a second
on Mar. 29 , 2016 , now U . S . Pat. No. 9 ,831, 722 , which is a Q - factor. The distance between the two resonators can be
continuation of U . S . application Ser. No . 14 /629 ,709, filed larger than the characteristic size of each resonator. Non
on Feb . 24 , 2015 , now U .S . Pat. No . 9 ,450 ,421, which is a radiative energy transfer between the first resonator structure
continuation of U . S . application Ser. No. 14 /302 ,662, filed and
and the second resonator structure is mediated through
on Jun . 12, 2014 , now U . S . Pat. No . 9 ,065 , 286 , which is a coupling of their resonant- field evanescent tails.
continuation of U . S . application Ser. No. 12 /639 ,963, filed [0007 ] According to another aspect of the invention, there
on Dec . 16 , 2009, now U . S . Pat. No. 8 ,760 ,007, which is a is provided a method of transferring electromagnetic energy.
continuation of U .S . application Ser. No . 12 /553 , 957 , filed The method includes providing a first resonator structure
on Sep . 3 , 2009 , which is a continuation of U .S . application receiving energy from an external power supply . The first
Ser. No . 11 /481 ,077 filed on Jul. 5 , 2006 , now U . S . Pat. No . resonator structure has a first Q - factor . Also , the method
7 ,741,734, which claims priority under 35 USC § 119 (e ) to includes a second resonator structure being positioned distal
U .S . provisional application Ser . No . 60 /698 ,442 filed on from the first resonator structure , and supplying useful
Jul. 12 , 2005 . The contents of the prior applications men working power to an external load . The second resonator
tioned above are incorporated herein by reference in their structure has a second Q - factor. The distance between the
entirety. two resonators can be larger than the characteristic size of
each resonator. Furthermore , the method includes transfer
STATEMENT AS TO FEDERALLY FUNDED ring non -radiative energy between the first resonator struc
RESEARCH ture and the second resonator structure through coupling of
[0002] This invention was made with government support their resonant - field evanescent tails.
awarded by the National Science Foundation under Grant [0008 ] In another aspect , a method of transferring energy
No. DMR -0213282 . The government has certain rights in is disclosed including the steps of providing a first resonator
this invention . structure receiving energy from an external power supply ,
said first resonator structure having a first resonant fre
BACKGROUND OF THE INVENTION quency 01, and a first Q -factor Q?, and characteristic size Lj.
Providing a second resonator structure being positioned
10003] The invention relates to the field of oscillatory distal from said first resonator structure , at closest distance
resonant electromagnetic modes, and in particular to oscil D , said second resonator structure having a second resonant
latory resonant electromagnetic modes , with localized frequency 02, and a second Q - factor Q , and characteristic
slowly evanescent field patterns, for wireless non -radiative size L2, where the two said frequencies w , and 02 are close
energy transfer. to within the narrower of the two resonance widths 11, and
[0004 ] In the early days of electromagnetism , before the 12, and transferring energy non -radiatively between said
electrical-wire grid was deployed , serious interest and effort first resonator structure and said second resonator structure ,
was devoted towards the development of schemes to trans said energy transfer being mediated through coupling of
port energy over long distances wirelessly , without any their resonant- field evanescent tails, and the rate of energy
carrier medium . These efforts appear to have met with little , transfer between said first resonator and said second reso
if any, success . Radiative modes of omnidirectional anten nator being denoted by K , where non - radiative means D is
nas, which work very well for information transfer, are not smaller than each of the resonant wavelengths à , and 12,
suitable for such energy transfer, because a vast majority of where c is the propagation speed of radiation in the sur
energy is wasted into free space . Directed radiation modes, rounding medium .
using lasers or highly - directional antennas, can be efficiently [0009 ] Embodiments of the method may include any of
used for energy transfer, even for long distances (transfer the following features . In some embodiments , said resona
distance LTRANS< < LDEy , where LDEy is the characteristic tors have Q , < 100 and < 100 , R , < 200 and < 200 ,
size of the device ), but require existence of an uninterrupt Q . < 500 and Qz < 500, or even Q . < 1000 and Qz < 1000 . In
ible line-of-sight and a complicated tracking system in the some such embodiments , K /sqrt( T , * T , ) may be greater than
case of mobile objects . 0 .2 , greater than 0 .5 , greater than 1, greater than 2, or even
[0005 ] Rapid development of autonomous electronics of grater than 5 . In some such embodiments D /L2 may be
recent years ( e. g . laptops , cell - phones , house - hold robots, greater than 1, greater than 2 , greater than 3 , greater than 5 .
that all typically rely on chemical energy storage ) justifies [0010 ] In another aspect, an energy transfer device is
revisiting investigation of this issue. Today, the existing disclosed which includes: a first resonator structure receiv
electrical-wire grid carries energy almost everywhere; even ing energy from an external power supply, said first reso
a medium -range wireless non -radiative energy transfer nator structure having a first resonant frequency 01, and a
would be quite useful. One scheme currently used for some first Q -factor Qu, and characteristic size L1, and a second
important applications relies on induction , but it is restricted resonator structure being positioned distal from said first
to very close-range (L TRANS < < LDEV) energy transfers . resonator structure , at closest distance D , said second reso
US 2019 /0173318 A1 Jun. 6 , 2019

nator structure having a second resonant frequency 02, and BRIEF DESCRIPTION OF THE DRAWINGS
a second Q -factor Q2, and characteristic size L2. [0028 ] FIG . 1 is a schematic diagram illustrating an exem
[0011] The two said frequencies w , and w , are close to plary embodiment of the invention ;
within the narrower of the two resonance widths I , and 2. 0029 ] FIG . 2A is a numerical FDTD result for a high
The non - radiative energy transfer between said first resona
tor structure and said second resonator structure is mediated index disk cavity of radius r along with the electric field ;
through coupling of their resonant- field evanescent tails , and FIG . 2B a numerical FDTD result for a medium -distance
the rate of energy transfer between said first resonator and coupling between two resonant disk cavities: initially , all the
said second resonator is denoted by K . The non - radiative energy is in one cavity (left panel); after some time both
means D is smaller than each of the resonant wavelengths ay cavities are equally excited (right panel).
and 12 , where c is the propagation speed of radiation in the [0030 ] FIG . 3 is schematic diagram demonstrating two
surrounding medium . capacitively -loaded conducting -wire loops;
[ 0012 ] Embodiments of the device may include any of the (0031 ) FIGS. 4A -4B are numerical FDTD results for
following features . In some embodiments , said resonators reduction in radiation - Q of the resonant disk cavity due to
have Q . < 100 and Qz < 100 , Q . < 200 and Q2 < 200 , Q . < 500 scattering from extraneous objects ;
and Q < 500 , or even Q , < 1000 and Q > < 1000 . In some such 10032 ] FIG . 5 is a numerical FDTD result for medium
embodiments , K /sqrt(T * T2) may be greater than 0 .2 , greater distance coupling between two resonant disk cavities in the
than 0 .5 , greater than 1, greater than 2 , or even grater than presence of extraneous objects; and
5 . In some such embodiments D /L2 may be greater than 1, [0033 ] FIGS. 6A -6B are graphs demonstrating efficiencies
greater than 2 , greater than 3 , or even greater than 5 . of converting the supplied power into useful work (m ),
[0013] In some embodiments , the resonant field in the radiation and ohmic loss at the device (n ), and the source
device is electromagnetic . ( n . ) , and dissipation inside a human ( n . ), as a function of the
[0014 ] In some embodiments , the first resonator structure coupling-to -loss ratio K /Td; in panel (a ) Iw is chosen so as
includes a dielectric sphere , where the characteristic size L , to minimize the energy stored in the device, while in panel
is the radius of the sphere . (b ) Tw is chosen so as to maximize the efficiency nw, for each
K /Td
[0015 ] In some embodiments, the first resonator structure [0034 ] FIG . 7 is a schematic diagram of a feedback
includes a metallic sphere , where the characteristic size L , mechanism to correct the resonators exchanging wireless
is the radius of the sphere . energy for detuning because of the effect of an extraneous
[ 0016 . In some embodiments, the first resonator structure object.
includes a metallodielectric sphere , where the characteristic
size L , is the radius of the sphere. DETAILED DESCRIPTION OF THE
[ 0017 In some embodiments , the first resonator structure INVENTION
includes a plasmonic sphere , where the characteristic size L ,
is the radius of the sphere . [0035 ] In contrast to the currently existing schemes, the
[ 0018 ]. In some embodiments , the first resonator structure invention provides the feasibility of using long - lived oscil
includes a polaritonic sphere , where the characteristic size latory resonant electromagnetic modes, with localized
L , is the radius of the sphere . slowly evanescent field patterns, for wireless non -radiative
[ 00191 In some embodiments, the first resonator structure energy transfer . The basis of this technique is that two
includes a capacitively -loaded conducting-wire loop , where same- frequency resonant objects tend to couple , while inter
the characteristic size L , is the radius of the loop . acting weakly with other off - resonant environmental
[ 0020] In some embodiments, the second resonator struc objects . The purpose of the invention is to quantify this
ture includes a dielectric sphere , where the characteristic mechanism using specific examples , namely quantitatively
size L2 is the radius of the sphere . address the following questions: up to which distances can
such a scheme be efficient and how sensitive is it to external
[0021 ] In some embodiments, the second resonator struc perturbations. Detailed theoretical and numerical analysis
ture includes a metallic sphere where the characteristic size show that a mid -range ( L TRANSæfew * L DEV ) wireless energy
L2 is the radius of the sphere . exchange can actually be achieved , while suffering only
0022]. In some embodiments, the second resonator struc modest transfer and dissipation of energy into other off
ture includes a metallodielectric sphere where the charac resonant objects .
teristic size L2 is the radius of the sphere . [0036 ] The omnidirectional but stationary (non - lossy )
[ 0023] In some embodiments , the second resonator struc nature of the near field makes this mechanism suitable for
ture includes a plasmonic sphere where the characteristic mobile wireless receivers . It could therefore have a variety
size L , is the radius of the sphere . of possible applications including for example , placing a
[0024 ] In some embodiments , the second resonator struc source connected to the wired electricity network on the
ture includes a polaritonic sphere where the characteristic ceiling of a factory room , while devices , such as robots ,
size L2 is the radius of the sphere . vehicles, computers, or similar, are roaming freely within
[0025 ] In some embodiments, the second resonator struc the room . Other possible applications include electric -en
ture includes a capacitively -loaded conducting -wire loop gine buses, RFIDs, and perhaps even nano - robots. Similarly ,
where the characteristic size L2 is the radius of the loop . in some embodiments multiple sources can transfer energy
[0026 ] In some embodiments, the resonant field in the to one or more device objects . For example, as explained at
device is acoustic . in the paragraph bridging pages 4 -5 of U .S . Provisional
10027] It is to be understood that embodiments of the Application No. 60/698 ,442 to which the present application
above described methods and devices may include any of claims benefit and which is incorporated by reference above ,
the above listed features , alone or in combination . for certain applications having uneven power transfer to the
US 2019 /0173318 A1 Jun. 6 , 2019

device object as the distance between the device and the in all directions in air , since in free space : K2 =w²/ c2 .
source changes , multiple sources can be strategically placed Because of this , one can show that they cannot support states
to alleviate the problem , and / or the peak amplitude of the of infinite Q . However, very long - lived (so - called “ high
source can be dynamically adjusted . Q ” ) states can be found , whose tails display the needed
[0037 ] The range and rate of the inventive wireless exponential- like decay away from the resonant object over
energy -transfer scheme are the first subjects of examination , long enough distances before they turn oscillatory (radia
without considering yet energy drainage from the system for tive ). The limiting surface , where this change in the field
use into work . An appropriate analytical framework for behavior happens, is called the “ radiation caustic ” , and, for
modeling the exchange of energy between resonant objects the wireless energy - transfer scheme to be based on the near
is a weak - coupling approach called “ coupled -mode theory ” . field rather than the far /radiation field , the distance between
FIG . 1 is a schematic diagram illustrating a general descrip the coupled objects must be such that one lies within the
tion of the invention . The invention uses a source and device radiation caustic of the other.
to perform energy transferring. Both the source 1 and device [0041] The invention is very general and any type of
2 are resonator structures , and are separated a distance D resonant structure satisfying the above requirements can be
from each other. In this arrangement, the electromagnetic used for its implementation . As examples and for definite
field of the system of source 1 and device 2 is approximated ness ,one can choose to work with twowell -known,but quite
by F (r,t)~ a (t)F (r) + az (t) F2(r), where F1,2 (r)= [E1,2 (r ) H1,2 different electromagnetic resonant systems: dielectric disks
( r ) ] are the eigenmodes of source 1 and device 2 alone, and and capacitively -loaded conducting -wire loops. Even with
then the field amplitudes a (t) and az(t) can be shown to out optimization, and despite their simplicity , both will be
satisfy the “ coupled -mode theory " : shown to exhibit fairly good performance . Their difference
lies mostly in the frequency range of applicability due to
dai = - (wi - ilnai + IK1121 + ?K1202 practical considerations , for example , in the optical regime
dielectrics prevail, since conductive materials are highly
da2
lossy.
= - i(W2 - il 2)a2 + iK2222 + iK2101, [0042 ] Consider a 2D dielectric disk cavity of radius r and
permittivity & surrounded by air that supports high - Q whis
pering - gallery modes , as shown in FIG . 2A . Such a cavity is
where 01.2 are the individual eigen - frequencies, I 1.2 are the studied using both analytical modeling, such as separation of
resonance widths due to the objects ' intrinsic (absorption , variables in cylindrical coordinates and application of
radiation etc.) losses, K12,21 are the coupling coefficients , and boundary conditions , and detailed numerical finite -differ
K11. 22 model the shift in the complex frequency of each ence -time-domain ( FDTD ) simulations with a resolution of
object due to the presence of the other. 30 pts/r. Note that the physics of the 3D case should not be
[0038 ] The approach of Eq . 1 has been shown, on numer significantly different, while the analytical complexity and
ous occasions, to provide an excellent description of reso numerical requirements would be immensely increased. The
nant phenomena for objects of similar complex eigen results of the two methods for the complex eigen - frequen
frequencies (namely 10 , -wz < < |K12 ,211 and 12 - 12), whose cies and the field patterns of the so - called “ leaky ” eigen
resonances are reasonably well defined ( namely 1 , , & modes are in an excellent agreement with each other for a
Im {K11, 22 } < < ]K12,211) and in the weak coupling limit variety of geometries and parameters of interest.
(namely |K12,21 |< < W1,2). Coincidentally, these requirements [0043 ] The radial modal decay length , which determines
also enable optimal operation for energy transfer. Also , Eq. the coupling strength K = 1K211= IK121, is on the order of the
( 1) show that the energy exchange can be nearly perfect at wavelength , therefore , for near -field coupling to take place
exact resonance ( W , = w , and I , = T , ), and that the losses are between cavities whose distance is much larger than their
minimal when the “ coupling -time” is much shorter than all size, one needs subwavelength - sized resonant objects
“ loss - times ” . Therefore, the invention requires resonant ( r < « ). High - radiation - Q and long -tailed subwavelength
modes of high Q = w ( 21 ) for low intrinsic -loss rates 1 , 2 , resonances can be achieved ,when the dielectric permittivity
and with evanescent tails significantly longer than the char ? is as large as practically possible and the azimuthal field
acteristic sizes L , and L , of the two objects for strong variations (of principal number m ) are slow (namely m is
coupling rate |K12,211 over large distances D , where D is the small).
closest distance between the two objects. This is a regime of [0044 ] One such TE -polarized dielectric -cavity mode,
operation that has not been studied extensively , since one
usually prefers short tails , to minimize interference with which has the favorable characteristics Q rad = 1992 and
nearby devices. Nr= 20 using ? = 147.7 and m = 2 , is shown in FIG . 2A , and
will be the “ test” cavity 18 for all subsequent calculations for
[ 0039 ] Objects of nearly infinite extent, such as dielectric this class of resonant objects. Another example of a suitable
waveguides, can support guided modes whose evanescent cavity has Q rad = 9100 and Nr= 10 using 8 =65.61 and m = 3 .
72

tails are decaying exponentially in the direction away from These values of ? might at first seem unrealistically large .
the object, slowly if tuned close to cutoff, and can have However, not only are there in the microwave regime
nearly infinite Q . To implement the inventive energy (appropriate for meter-range coupling applications ) many
transfer scheme, such geometries might be suitable for materials that have both reasonably high enough dielectric
certain applications, but usually finite objects , namely ones constants and low losses , for example , Titania : € – 96 , Im { e }/
that are topologically surrounded everywhere by air, are ? = 103; Barium tetratitanate: ? =37, Im{ ? }/ ? =104; Lithium
more appropriate . tantalite : & ~ 40 , Im {e }/ - 10 - 4; etc.), but also ? could instead
[ 0040] Unfortunately, objects of finite extent cannot sup signify the effective index of other known subwavelength
port electromagnetic states that are exponentially decaying (W /r < < 1) surface-wave systems, such as surface -plasmon
US 2019 /0173318 A1 Jun. 6 , 2019

modes on surfaces of metal- like (negative -? ) materials or vu po /2.Nr/a and Ryad 1 /6 .n .N (wr/c ) , where p is the
metallodielectric photonic crystals . resistivity of the wire material and 7 . - 1200 2 is the
[0045] With regards to material absorption , typical loss impedance of free space . The quality factor of such a
tangents in the microwave ( e . g . those listed for thematerials resonance is then Q = L /(Rohm + Rrad ) and is highest for
above ) suggest that Q abs- ? /Im {e } ~ 10000 . Combining the some frequency determined by the system parameters: at
effects of radiation and absorption , the above analysis lower frequencies it is dominated by ohmic loss and at
implies that for a properly designed resonant device -object higher frequencies by radiation .
d a value of Q - 2000 should be achievable . Note though , [0049] To get a rough estimate in the microwave, one can
that the resonant sources will in practice often be immobile , use one coil (N = 1 ) of copper ( p = 1 .69. 10 - 8 m ) wire and
and the restrictions on its allowed geometry and size will then for r = 1 cm and a = 1 mm , appropriate for example for a
typically be much less stringent than the restrictions on the cell phone , the quality factor peaks to Q = 1225 at f = 380
design of the device ; therefore , it is reasonable to assume MHz, for r = 30 cm and a = 2 mm for a laptop or a household
that the radiative losses can be designed to be negligible robot Q = 1103 at f = 17 MHz, while for r = 1 m and a = 4 mm
allowing for 2 5 ~ 10000 , limited only by absorption . (that could be a source loop on a room ceiling ) Q = 1315 at
[0046 ] To calculate now the achievable rate of energy f = 5 MHz. So in general, expected quality factors are
transfer, one can place two of the cavities 20 , 22 at distance Q - 1000 -1500 at W /r~ 50 -80 , namely suitable for near - field
D between their centers , as shown in FIG . 2B . The normal coupling .
modes of the combined system are then an even and an odd [0050 ] The rate for energy transfer between two loops 10
superposition of the initial modes and their frequencies are and 12 at distance D between their centers, as shown in FIG .
split by the coupling coefficient K , which we want to 3 , is given by K12 =0m /2VL , L2, where M is the mutual
calculate. Analytically , coupled -mode theory gives for inductance of the two loops 10 and 12. In the limit r< < D < <
dielectric objects K12 = 02/2•SdPrE , * (r) Ez(r)?j (r) ?dr|E ,(r) l2 one can use the quasi -static result M = 1 /4.u N ,N2(r1r2 )? /D " ,
€ (r), where €1,2(r) denote the dielectric functions of only which means that w /2K ~ (D / Vr182) . For example , by choos
object 1 alone or 2 alone excluding the background dielec ing again D /r = 10 , 8 , 6 one can get for two loops of r = 1 cm ,
tric (free space ) and e (r ) the dielectric function of the entire same as used before, that w /2k = 3033 , 1553, 655 respec
space with both objects present. Numerically, one can find K
using FDTD simulations either by exciting one of the tively, for the r = 30 cm that w / 26 = 7131 , 3651, 1540 , and for
cavities and calculating the energy-transfer timeto the other the r = 1 m that w /2K = 6481, 3318 , 1400 . The corresponding
coupling -to - loss ratios peak at the frequency where peaks
or by determining the split normal -mode frequencies. For the single -loop land are k / T = 0 .4 , 0 .79 , 1 .97 and 0 . 15 , 0 .3 ,
the “ test” disk cavity the radius rc of the radiation caustic is
rc~ 11r, and for non -radiative coupling D < rc, therefore here 0 .72 and 0 .2 , 0 .4 , 0 .94 for the three loop -kinds and distances.
one can choose D /r= 10 , 7 , 5 , 3 . Then , for the mode of FIG . An example of dissimilar loops is that of a r = 1 m ( source on
3 , which is odd with respect to the line that connects the two the ceiling ) loop and a r = 30 cm (household robot on the
cavities, the analytical predictions are w /2k = 1602, 771, 298 , floor ) loop at a distance D = 3 m (room height ) apart, for
48 , while the numerical predictions are w / 2K = 1717 , 770 , which k / TT2 = 0 .88 peaks at f = 6 . 4 MHz, in between the
298 , 47 respectively , so the two methods agree well . The peaks of the individual Q ’s . Again , these values are not in
radiation fields of the two initial cavity modes interfere the optimal regime k /T < < 1, but will be shown to be suffi
constructively or destructively depending on their relative cient.
phases and amplitudes , leading to increased or decreased net [0051 ] It is important to appreciate the difference between
radiation loss respectively , therefore for any cavity distance this inductive scheme and the already used close - range
the even and odd normal modes have Qs that are one larger inductive schemes for energy transfer in that those schemes
and one smaller than the initial single -cavity Q = 1992 (a are non -resonant. Using coupled -mode theory it is easy to
phenomenon not captured by coupled -mode theory ), but in show that,keeping the geometry and the energy stored at the
a way that the average I is always approximately T = 0 /2Q . source fixed , the presently proposed resonant-coupling
Therefore , the corresponding coupling- to - loss ratios are inductive mechanism allows for Q approximately 1000
K / T = 1. 16 , 2 .59, 6 .68 , 42 . 49, and although they do not fall in times more power delivered for work at the device than the
the ideal operating regime k /T < < 1 , the achieved values are traditional non- resonant mechanism , and this is why mid
still large enough to be useful for applications. range energy transfer is now possible. Capacitively -loaded
[0047] Consider a loop 10 or 12 of N coils of radius r of conductive loops are actually being widely used as resonant
conducting wire with circular cross - section of radius a antennas ( for example in cell phones ), but those operate in
surrounded by air , as shown in FIG . 3. This wire has the far- field regime with r ~ 1 , and the radiation Q 's are
inductance L = u Nºr[ ln (8r/a )- 2 ], where yo is the magnetic intentionally designed to be small to make the antenna
permeability of free space , so connecting it to a capacitance efficient, so they are not appropriate for energy transfer.
C will make the loop resonant at frequency w = 1 /VLC . The [0052 ] Clearly , the success of the inventive resonance
nature of the resonance lies in the periodic exchange of based wireless energy - transfer scheme depends strongly on
energy from the electric field inside the capacitor due to the the robustness of the objects ' resonances . Therefore, their
voltage across it to the magnetic field in free space due to the sensitivity to the near presence of random non -resonant
current in the wire . Losses in this resonant system consist of extraneous objects is another aspect of the proposed scheme
ohmic loss inside the wire and radiative loss into free space . that requires analysis . The interaction of an extraneous
[0048 ] For non -radiative coupling one should use the object with a resonant object can be obtained by a modifi
near- field region , whose extent is set roughly by the wave cation of the coupled -mode - theory model in Eq . ( 1 ) , since
length 1 , therefore the preferable operating regime is that the extraneous object either does not have a well- defined
where the loop is small (r < « ). In this limit, the resistances resonance or is far -off - resonance , the energy exchange
associated with the two loss channels are respectively Rohm = between the resonant and extraneous objects is minimal, so
US 2019 /0173318 A1 Jun. 6 , 2019

the term K12 in Eq . ( 1) can be dropped . The appropriate [0057 ] Imagine now a combined system where a resonant
analytical model for the field amplitude in the resonant source - object s is used to wirelessly transfer energy to a
object a (t) becomes : resonant device - object d but there is an off - resonance extra
neous - object e present. One can see that the strength of all
extrinsic loss mechanisms from e is determined by IE , (re) 12 ,
daj
= - i(wi - il 1jai + ik1121
(2 ) by the square of the small amplitude of the tails of the
dt resonant source , evaluated at the position r , of the extrane
ous object. In contrast, the coefficient of resonant coupling
of energy from the source to the device is determined by the
[0053 ] Namely, the effect of the extraneous object is just same-order tail amplitude Es( re) I, evaluated at the position
a perturbation on the resonance of the resonant object and it rg of the device, but this time it is not squared ! Therefore, for
is twofold : First, it shifts its resonant frequency through the equal distances of the source to the device and to the
real part of K11 thus detuning it from other resonant objects . extraneous object , the coupling time for energy exchange
As shown in FIG . 7 , this is a problem that can be fixed rather with the device is much shorter than the time needed for the
easily by applying a feedback mechanism 710 to every losses inside the extraneous object to accumulate , especially
device ( e . g ., device resonators 720 and 730 ) that corrects its if the amplitude of the resonant field has an exponential-like
frequency, such as through small changes in geometry, and decay away from the source . One could actually optimize
matches it to that of the source resonator 740 . Second , it the performance by designing the system so that the desired
forces the resonant object to lose modal energy due to coupling is achieved with smaller tails at the source and
scattering into radiation from the extraneous object through longer at the device , so that interference to the source from
the induced polarization or currents in it, and due to material the other objects is minimal.
absorption in the extraneous object through the imaginary [0058 ] The above concepts can be verified in the case of
part of Ky . This reduction in Q can be a detrimental effect dielectric disk cavities by a simulation that combines FIGS.
to the functionality of the energy -transfer scheme, because it 2A - 2B and 4A -4B , namely that of two ( source -device )
cannot be remedied , so its magnitude must be quantified . “ test” cavities 50 placed 10r apart, in the presence of a
[0054 ] In the first example of resonant objects that have same-size extraneous object 52 of e = 49 between them , and
been considered , the class of dielectric disks, small, low at a distance 5r from a large roughened surface 56 of 8 = 2 .5 ,
index , low -material-loss or far - away stray objects will as shown in FIG . 5 . Then , the original values of ( = 1992 ,
induce small scattering and absorption . To examine realistic w /2K = 1717 (and thus k / T = 1. 16 ) deteriorate to Q = 765,
cases that are more dangerous for reduction in Q , one can w /2K = 965 (and thus k /T = 0 .79 ). This change is acceptably
therefore place the “ test ” dielectric disk cavity 40 close to : small, considering the extent of the considered external
a ) another off-resonance object 42, such as a human being , perturbation , and , since the system design has not been
of large Re { E } = 49 and Im {e } = 16 and of same size but optimized , the final value of coupling - to - loss ratio is prom
different shape , as shown in FIG . 4A ; and b ) a roughened ising that this scheme can be useful for energy transfer.
surface 46 , such as a wall, of large extent but of small [0059 ] In the second example of resonant objects being
Re {e } = 2 .5 and Im {E } = 0 .05 , as shown in FIG . 4B . considered , the conducting -wire loops, the influence of
[0055 ] Analytically, for objects that interact with a small extraneous objects on the resonances is nearly absent. The
perturbation the reduced value of radiation due to scat reason for this is that, in the quasi- static regime of operation
tering could be estimated using the polarization ?dºr|Px? (r )l2 (r < < ^ ) that is being considered , the near field in the air
afdr|E , (r ).Re { Ex(r ) } 12 induced by the resonant cavity 1 region surrounding the loop is predominantly magnetic ,
inside the extraneous object X = 42 or roughened surface since the electric field is localized inside the capacitor.
X = 46 . Since in the examined cases either the refractive Therefore , extraneous objects that could interact with this
index or the size of the extraneous objects is large , these field and act as a perturbation to the resonance are those
first- order perturbation - theory results would not be accurate having significantmagnetic properties (magnetic permeabil
enough , thus one can only rely on numerical FDTD simu ity Re { u } < 1 or magnetic loss Im {u } < 0 ). Since almost all
lations. The absorption inside these objects can be esti common materials are non -magnetic , they respond to mag
mated through Im {Ku1 } = 0 /2 ?dr|Ej(r)l2Im {(Ex (r)} /?d²r | E1 netic fields in the same way as free space , and thus will not
(r )l’ e (r ). disturb the resonance of a conducting -wire loop . The only
[0056 ] Using these methods, for distances D /r = 10 , 7, 5 , 3 perturbation that is expected to affect these resonances is a
between the cavity and extraneous -object centers one can close proximity of large metallic structures .
find that Qrad = 1992 is respectively reduced to Qrad = 1988, [0060 ] An extremely important implication of the above
1258 , 702 , 226 , and that the absorption rate inside the object fact relates to safety considerations for human beings .
is labs = 312530 , 86980 , 21864 , 1662, namely the resonance Humans are also non -magnetic and can sustain strong mag
of the cavity is not detrimentally disturbed from high -index netic fields without undergoing any risk . This is clearly an
and/ or high - loss extraneous objects, unless the (possibly advantage of this class of resonant systems for many real
mobile ) object comes very close to the cavity . For distances world applications. On the other hand , dielectric systems of
D /r = 10 , 7 , 5 , 3 , 0 of the cavity to the roughened surface we high ( effective ) index have the advantages that their effi
find respectively Qrad = 2101, 2257 , 1760 , 1110 , 572 , and ciencies seem to be higher, judging from the larger achieved
Rahs < 4000 , namely the influence on the initial resonant values of k /T , and that they are also applicable to much
mode is acceptably low , even in the extreme case when the smaller length -scales, as mentioned before .
cavity is embedded on the surface . Note that a close prox [0061] Consider now again the combined system of reso
imity of metallic objects could also significantly scatter the nant source s and device d in the presence of a human h and
resonant field , but one can assume for simplicity that such a wall, and now let us study the efficiency of this resonance
objects are not present. based energy - transfer scheme, when energy is being drained
US 2019 /0173318 A1 Jun. 6 , 2019

from the device for use into operational work . One can use dynamic geometries of mobile objects , since the energy
the parameters found before : for dielectric disks , absorption transfer time K - 1 - 1 us , which is much shorter than any
dominated loss at the source Q ~ 104 , radiation -dominated timescale associated with motions of macroscopic objects .
loss at the device Qr- 10 (which includes scattering from [0065 ] The invention provides a resonance-based scheme
the human and the wall ), absorption of the source - and for mid -range wireless non - radiative energy transfer. Analy
device -energy at the human scho Q d-h ~ 104- 10 % depending ses of very simple implementation geometries provide
on his/her not-very -close distance from the objects , and encouraging performance characteristics for the potential
negligible absorption loss in the wall ; for conducting -wire applicability of the proposed mechanism . For example, in
loops, Q - Qr~ 10°, and perturbations from the human and the macroscopic world , this scheme could be used to deliver
the wall are negligible . With corresponding loss -rates T = 0 / 2 power to robots and/ or computers in a factory room , or
Q , distance -dependent coupling K , and the rate at which electric buses on a highway (source - cavity would in this
working power is extracted Iw , the coupled -mode- theory case be a " pipe ” running above the highway ) . In the micro
equation for the device field -amplitude is scopic world , where much smaller wavelengths would be
used and smaller powers are needed , one could use it to
implement optical inter - connects for CMOS electronics or
dad* -= - 11ilw - ildad + ikas - Id -had - Twad . (3 )
else to transfer energy to autonomous nano- objects, without
worrying much about the relative alignment between the
sources and the devices ; energy -transfer distance could be
[0062] Different temporal schemes can be used to extract even longer compared to the objects' size , since Im {({ ( w )}
power from the device and their efficiencies exhibit different of dielectric materials can be much lower at the required
dependence on the combined system parameters. Here , one optical frequencies than it is at microwave frequencies.
can assume steady state, such that the field amplitude inside [0066 ] As a venue of future scientific research , different
the source is maintained constant, namely a (t) = A .e -107, so material systems should be investigated for enhanced per
then the field amplitude inside the device is aj(t) = Age - 206 formance or different range of applicability . For example , it
with Afik (Tc + Id-n + Iw)Ag. Therefore , the power lost at the might be possible to significantly improve performance by
source is P = 2T | A3/?, at the device it is P 21 / A >, the exploring plasmonic systems. These systemscan often have
power absorbed at the human is P , = 2C - A12 + 210- | A ,I?, spatial variations of fields on their surface that are much
and the useful extracted power is Pw = 2TWIAdl2 . From energy shorter than the free -space wavelength , and it is precisely
conservation , the total power entering the system is this feature that enables the required decoupling of the
Ptotal = P + Pc+ P + P w . Denote the total loss-rates 1 tot - T ,+ scales : the resonant object can be significantly smaller than
Ish and I dot = 1c +Id-h . Depending on the targeted applica the exponential- like tails of its field . Furthermore , one
tion , the work -drainage rate should be chosen either Iwatot should also investigate using acoustic resonances for appli
to minimize the required energy stored in the resonant cations in which source and device are connected via a
objects or I . =rtot= V 1 + K2/T tot tot > I tot such that the common condensed -matter object.
ratio of useful - to -lost powers , namely the efficiency nw = Pw ! [0067 ] Although the present invention has been shown and
Pota1, is maximized for some value of K . The efficiencies n
tota
described with respect to several preferred embodiments
for the two different choices are shown in FIGS. 6A and 6B thereof , various changes , omissions and additions to the
respectively , as a function of the k / T figure -of-merit which form and detail thereof, may be made therein , without
in turn depends on the source - device distance . departing from the spirit and scope of the invention .
[0063] FIGS. 6A -6B show that for the system of dielectric 1 . A wireless power system for providing power to a
disks and the choice of optimized efficiency, the efficiency vehicle , the system comprising:
can be large , e . g ., at least 40 % . The dissipation of energy
inside the human is small enough , less than 5 % , for values a source resonator and a power supply coupled to the
K /T < 1 and < 10 % , namely for medium - range source source resonator to provide power to the source reso
device distances (Dyr < 10 ) and most human -source / device nator, the source resonator having a resonant frequency
distances (D /r < 8 ). For example , for Ddr = 10 and D /r = 8, if W1, an intrinsic loss rate 11, and capable of storing
10 W must be delivered to the load , then , from FIG . 6B , - 0 .4 electromagnetic energy with an intrinsic quality factor
W will be dissipated inside the human , m4 W will be Qi = w , /(2T ), the source resonator comprising at least
absorbed inside the source , and - 2 .6 W will be radiated to one loop of conductive material and further comprising
free space . For the system of conducting -wire loops, the a capacitance ; and
achieved efficiency is smaller, ~ 20 % for k T/ 1 , but the a device resonator and a load coupled to the device
significant advantage is that there is no dissipation of energy resonator to receive power from the device resonator
inside the human , as explained earlier. and for powering the vehicle, the device resonator
[0064 ] Even better performance should be achievable having a resonant frequency Wz, an intrinsic loss rate
through optimization of the resonant object designs. Also , by T2, and capable of storing electromagnetic energy with
exploiting the earlier mentioned interference effects between an intrinsic quality factor Q = w2/ (212) , the device
the radiation fields of the coupled objects, such as continu resonator comprising at least one loop of conductive
ous -wave operation at the frequency of the normalmode that material and further comprising a capacitance ,
has the larger radiation - Q , one could further improve the wherein the source resonator and the device resonator are
overall system functionality . Thus the inventive wireless configured to resonantly and wirelessly couple electro
energy -transfer scheme is promising for many modern appli magnetic power from the source resonator to the device
cations. Although all considerations have been for a static resonator using non -radiative electromagnetic induc
geometry , all the results can be applied directly for the tion having an energy transfer rate K , and wherein the
 US 2019 /0173318 A1 Jun . 6 , 2019

intrinsic loss rates satisfy K /VT 12 > 5 over a range of Q2 =02/(212 ), the device resonator comprising at least one
distances D between the source resonator and the loop of conductive material and further comprising a capaci
device resonator , tance,
wherein Q . < 100 and Qz < 100 , and the source module comprising:
wherein the power supply is configured to dynamically a source resonator and a power supply coupled to the
adjust a peak amplitude of the electromagnetic power source resonator to provide power to the source reso
in the source resonator over the range of distances D . nator, the source resonator having a resonant frequency
2 . The wireless power system of claim 1 , wherein Q . > 200 W , , an intrinsic loss rate I , and capable of storing
and Q > 200 . electromagnetic energy with an intrinsic quality factor
3 . The wireless power system ofclaim 1 , wherein Q . > 500 Q = 0 / (2T ) , the source resonator comprising at least
and Q2 > 500 . one loop of conductivematerial and further comprising
4 . The wireless power system of claim 1 , wherein the a capacitance,
power provided to the load from the device resonator defines wherein the source resonator and the device resonator are
a work drainage rate Ty , and wherein the work drainage rate configured to resonantly and wirelessly couple electro
Tw is configured to be dynamically set as a function of the magnetic power from the source resonator to the device
energy transfer rate k between the first and second resona resonator using non - radiative electromagnetic induc
tors as the device resonator is moveable relative to the tion having an energy transfer rate K , and wherein the
source resonator over the range of distances D . intrinsic loss rates satisfy K /VT, 1 , > 5 over a range of
5 . The wireless power system of claim 4 , wherein the distances D between the source resonator and the
work drainage rate Iw is configured to be dynamically set device resonator, and
such that the ratio of useful -to - lost power is maximized as a wherein Q . > 100 and Q2 > 100, and
function of the energy transfer rate k over the range of wherein the power supply is configured to dynamically
distances D . adjust a peak amplitude of the electromagnetic power
6 . The wireless power system of claim 4 , wherein the in the source resonator over the range of distances D .
work drainage rate I is configured to be dynamically set 22 . The source module of claim 21 , wherein Q . > 200 and
such that I w = 12V 1 +(K /T , 12) as a function of the energy Rz > 200 .
transfer rate k over the range of distances D . 23 - 27 . ( canceled )
7 . The wireless power system of claim 1 , wherein the 28 . A method for providing power wirelessly to a vehicle
power provided to the load from the device resonator defines portable electronic device , wherein the vehicle is configured
a work drainage rate I w , and wherein the work drainage rate for use with a source resonator and a power supply coupled
to the source resonator to provide power to the source
T „ is configured to be set such that I w = 12V 1 +(K ? /T , 12) for resonator, the source resonator having a resonant frequency
some value of the energy transfer rate k in the range of 01, an intrinsic loss rate 1 1, and capable of storing electro
distances D as the device resonator is moveable relative to magnetic energy with an intrinsic quality factor Q = w ,
the source resonator over the range of distances D . (211), the method comprising :
8 . The wireless power system of claim 1 , wherein the providing the vehicle with a device resonator and a load
power provided to the load from the device resonator defines coupled to the device resonator to receive power from
a work drainage rate Iw , and wherein the work drainage rate the device resonator and provide power to the vehicle ,
T is configured to be set such that the ratio of useful- to -lost the device resonator having a resonant frequency 02, an
power is maximized for some value of the energy transfer intrinsic loss rate 12, and capable of storing electro
rate K in the range of distances D as the device resonator is magnetic energy with an intrinsic quality factor Q2 = w2
moveable relative to the source resonator over the range of ( 21 ,), the device resonator comprising at least one loop
distances D . of conductive material and further comprising a capaci
9 . The wireless power system of claim 8 , wherein the tance , wherein the device resonator is spaced from the
work drainage rate Iw is configured to be set such that source resonator and configured to move freely relative
Tw = 12V 1+ (K²/T , 12) for said value of the energy transfer to the source resonator over a range of distances D
between the source resonator and the device resonator ;
rate k in the range of distances D as the device resonator is
moveable relative to the source resonator over the range of and
distances D . resonantly and wirelessly receiving electromagnetic
10 . The wireless power system of claim 1 , wherein the power at the device resonator from the source resonator
range of distances D includes D = 6 cm . using non -radiative electromagnetic induction having
11 . The wireless power system of claim 1, wherein the an energy transfer rate K , wherein the intrinsic loss rates
range of distances D includes D = 8 cm . satisfy K /VT , 1 > 5 over the range of distances D , and
12 . The wireless power system of claim 1 , wherein the wherein each intrinsic loss rate comprises a resistive
range of distances D includes D = 10 cm . component and a radiative component,
13 -20 . (canceled ) wherein Q . > 100 and Q2 > 100 , and
21. A source module for a wireless power system for wherein the method further comprises dynamically
providing power to a vehicle , the wireless power system adjusting a peak amplitude of the electromagnetic
including a device module housed in the vehicle and com power in the source resonator over the range of dis
prising a device resonator and a load coupled to the device tances D .
resonator to receive power from the device resonator and for 29. The method of claim 28 , further comprising:
powering the vehicle , the device resonator having a resonant providing power to the load in the vehicle from the device
frequency 02, an intrinsic loss rate I 2, and capable of storing resonator, wherein the power provided to the load from
electromagnetic energy with an intrinsic quality factor the device resonator defines a work drainage rate Iw ,
US 2019 /0173318 A1 Jun. 6 , 2019

and wherein the work drainage rate Iwis dynamically the device resonator defines a work drainage rate Iws
set as a function of the energy transfer rate k between and wherein the work drainage rate Tw is set such that
the first and second resonators as the device resonator Tw = 12V 1 + (K ?/T , 12) for some value of the energy
moves relative to the source resonator over the range of transfer rate k in the range of distances D as the device
distances D . resonator is moveable relative to the source resonator
30 . The method of claim 29 , wherein the work drainage over the range of distances D .
rate Iwis dynamically set such that the ratio of useful- to -lost 33 . The method of claim 28 , further comprising :
power is maximized as a function of the energy transfer rate providing power to the load in the vehicle from the device
K over the range of distances D . resonator, wherein the power provided to the load from
31. The method of claim 29 , wherein the work drainage the device resonator defines a work drainage rate T . ,
w

rate T w is dynamically set such that I w = 12V1 + (K /T ,: 12 ) as and wherein the work drainage rate Twis set such that
a function of the energy transfer rate k over the range of the ratio of useful- to -lost power is maximized for some
distances D . value of the energy transfer rate k in the range of
32 . The method of claim 28 , further comprising : distances D as the device resonator is moveable relative
providing power to the load in the vehicle from the device to the source resonator over the range of distances D .
resonator, wherein the power provided to the load from