Time Reversed Electromagnetic Wave Propagation as a Novel Method ofWireless Power Transfer

Frank Cangialosi, Tyler Grover, Patrick Healey, Tim Furman, Andrew Simon and Steven M. AnlageGemstone Team TESLA, Center for Nanophysics and Advanced Materials, Department of Physics,

University of Maryland, College Park, MD 20742-4111 USA

Abstract—We investigate the application of time reversedelectromagnetic wave propagation to transmit energy to a movingtarget in a reverberant environment. “Time reversal” is a signalfocusing method that exploits the time reversal invariance of thelossless wave equation to focus signals on a small region insidea complex scattering environment. In this work, we explore theproperties of time reversed microwave pulses in a low-loss ray-chaotic chamber. We measure the spatial profile of the collapsingwavefront around the target antenna, and demonstrate that timereversal can be used to transfer energy to a receiver in motion.We discuss the results of these experiments, and explore theirimplications for a wireless power transmission system based ontime reversal.

I. INTRODUCTION

Many techniques have been proposed for wireless powertransfer (WPT) ranging from magnetic resonance to mi-crowave beaming. While the ability to transmit power practi-cally and efficiently at short to mid-range is well demonstratedin the literature, there is relatively little prior work that retainsboth high efficiency and practicality at distances beyond a fewmeters [1].

Traditional methods of long-range WPT have relied on mi-crowave beaming [2]. While efficient, this technique requiresprecise alignment of transmitter and receiver, and requires aclear line of sight propagation path. Even in those cases whereline of sight might be achievable, it is highly impractical dueto the danger it introduces to any humans or wildlife thatmight cross its path. Finding a way to transmit microwavepower over long distances in a less concentrated transmissionchannel would be highly desirable.

Magnetic resonance beacons have been used to extendmagnetic resonance coupling to longer distances. While saferthan microwave beaming, these beacons still have a relativelylimited range [1]. There is also interest in MIMO (Multiple In-put Multiple Output) charging devices that allow for combineddata and energy transfer using microwaves [3]. Other methods,such as WattUp, apply phase conjugation to the microwavesignal [4], but suffer from bandwidth limitations in general [5],[6]. The efficiency and reliability of these techniques has yetto be fully explored in the literature.

In this paper, time reversal is proposed as a potentialalternative to the methods described above. The method isespecially well suited for ray chaotic environments, whichare quite commonly found in settings where WPT technologyis desired [7]. The source sends weak signals through manydifferent trajectories in the scattering environment, spread outover an extended time period. All of these signals converge on

the target location where they superimpose coherently at oneinstant to deliver a large burst of power. As a result energy isconcentrated only at the location of the intended target, andthe limitations of microwave beaming are avoided.

While there exists extensive prior work on electromagnetictime reversal [8]–[11], it remains largely unexplored in thecontext of WPT. For the technique to be viable, reconstruc-tions must converge in a small region, without interfering withnearby electronics or biological matter. Here we employ asingle-channel time reversal mirror to accomplish this task.

The primary advantage of time reversal in the contenxt ofWPT is its ability to focus energy on a receiver anywhere inan enclosed space, even at distances well beyond the meterscale [8], [9]. This overcomes the main limitation imposed bytechnologies relying on magnetic near fields.

The rest of this paper is structured as follows. We beginby describing our experimental equipment and proceduresin Section II. In Section III-A, we develop a model forthe spatial distribution of energy around the receiver as afunction of carrier signal wavelength. We then extend thismodel to describe the energy delivered to a moving receiverand experimentally demonstrate the collapse of time reversedenergy on a moving receiver in Section III-B. In Section IVwe describe a practical WPT system based on time reveresaland discuss the limitations of our experiments that should beaddressed in future work. We conclude in Section V.

II. METHODOLOGY

We have investigated the applicability of time reversal towireless power transfer (WPT) within an enclosed, reflectivecavity (Fig. 1a): a 1.06 m3 aluminum box with conductivescattering paddles to make the ray trajectories more ergodic.Ray chaos ensures that a propagating pulse will eventuallyreach every point in the environment. This simultaneouslyexcites many transmission channels and thus improves recon-struction fidelity.

Two monopole antennas inject and extract electromagneticsignals from different points in the enclosure. A transmittingantenna is attached to the cavity wall opposite the receivingantenna. The receiving antenna is attached to a panel that canmove vertically with a total range of 70 mm. Motion of thereceiving antenna is achieved using an externally-mounted PIMikroMove M-415.DG translation stage and the enclosureremains sealed during the translation.

All signals are created and broadcast using a TektronixAWG7052 arbitrary waveform generator feeding into an

978-1-4673-7986-1/16/$31.00 ©2016 IEEE

(a)

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Fig. 1: (a): A ray-chaotic enclosure with two antennas, oneof which is attached to a sliding panel that can move freelyalong the y-axis, as shown in the right inset. A time-reversedsona (b) is broadcast from the transmitting antenna, resultingin a reconstruction at the receiving antenna, shown in (c).

Agilent E8267D Vector PSG microwave source. AnAgilent DSO91304A digital storage oscilloscope is usedto record waveforms of interest. MATLAB is used for signalprocessing, instrument control, and coordination.

The basic time reversal process in this environment proceedsas follows: First, a 50 ns Gaussian pulse (with a carrierfrequency of 5 GHz) is injected into the cavity through thetransmitting antenna. A complex time-domain signal (referredto as a “sona”) is measured at the receiving antenna (Fig. 1b).This sona is the sum of the reflections of the initial pulse,scaled in magnitude due to ray-divergence and loss, and shiftedin time due to differing lengths of reflection paths. In thenext step, this sona is time reversed and injected into thetransmitting antenna. The result is a reconstruction of theinitial pulse back at the receiving antenna (Fig. 1c). Thisprocess makes use of another robust symmetry, namely thespatial reciprocity of the wave equation.

III. RESULTS

A. Spatial Profiling

The first experiment conducted measures the spatial profileof a reconstruction with the goal of characterizing recon-struction size as a function of carrier signal wavelength.Initially, a reconstruction is focused on the receiving antennain the middle of its movement range. Without changing thetime reversed sona being broadcast, the receiving antenna issystematically translated through its entire range of movement.Samples are taken every 0.2 mm across the entire 70 mmrange and the maximum peak-to-peak reconstruction voltage isrecorded at each step. We repeated this experiment for carrier

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Fig. 2: Spatial profile of peak-to-peak voltage amplitudes ofreconstructions at carrier frequencies ranging from 4–9 GHzin 1 GHz steps. The inset shows the inverse of the fit bvalue versus carrier frequency, showing the expected linearrelationship. Note that the reconstruction amplitude varies withfrequency as the antenna properties change.

frequencies in the range 4–9 GHz and display these results inFig. 2.

The reconstruction peak-to-peak voltage profile is expectedto take the form of a |sinc(x)| function about the antenna [12].Thus, the following equation is proposed to predict V (x), themaximum peak-to-peak voltage from a given reconstruction,as a function of x, the distance between the reconstructionfocal point and the translated receiver:

V (x) = a ·∣∣∣∣sinc(x+ c

b

)∣∣∣∣ + d , (1)

where a is the maximum peak-to-peak reconstruction ampli-tude, b is the wavelength of the signal divided by 2π, c is thelocation of the antenna along the x-axis, and d is the noise-level offset voltage.

Since b is proportional to the wavelength (and inversely pro-portional to frequency), as the carrier frequency is increased, 1

balso increases, causing the main lobe of the |sinc(x)| functionin Fig. 2 to narrow. This relationship is shown explicitly in theinset of Fig. 2.

Fig. 3 shows Eq. 1 fit to the 5 GHz curve from Fig. 2,including error bars. This fit has a reduced χ2 of 234 duein part to the rather large background noise level. The errorbars are primarily systematic, introduced by the oscilloscope’sinternal voltage multiplier used in scaling.

B. Moving Reconstructions

The time reversal process assumes that the environmentremains fixed between the time-forward and time reversedsteps. It also assumes that the source and target remain fixedbetween these two steps. We performed time reversal on amoving target to better understand how a translating targetaffects reconstruction strength.

For this experiment, the receiving antenna moved at aconstant speed of 0.5 mm

s across the entire 70 mm range

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Fig. 3: Measured peak-to-peak voltage amplitude of recon-structions received in the vicinity of a time reversed wavecollapse location with a 5 GHz carrier frequency, and a fit tothe |sinc(x)| profile from Eq. 1.

provided by the MikroMove. To counteract the degradation ofreconstruction strength as the antenna moved, we periodicallyrepeated the interrogation step, effectively re-centering thereconstruction on the antenna. Since the test equipment doesnot allow broadcast of one sona while collecting another, itwas not possible to transmit power during the collection time,leading to a finite “dead time”, denoted td in Fig. 4. Duringthe broadcast period, the time reversed sona was continuallybroadcast into the cavity (once every 15 µs) and the peak-to-peak voltage across the receiver was measured once every2.05 seconds, meaning that the reconstructions are highlyunder-sampled in this plot. After 15 samples were collected,we initiated the collection of a new sona, processed andrebroadcast it, and began again. We refer to this full processof collecting a new sona and then broadcasting it for a givenperiod time as a full “cycle” of length tc. The results inFig. 4 were obtained using a carrier frequency of 5 GHz, tdof 7 seconds, and tc of 39.8 seconds.

Based on the results from Section III-A, the peak-to-peak reconstruction voltage measured by the receiver is ex-pected to decay according to the |sinc(x)| function as thereceiver moves away from the reconstruction focal point. This|sinc(x)| function will be centered on the position where thesona was last collected, making the reconstruction focus con-tinually lag behind the antenna. Consequently, the maximumreconstruction strength is limited by the time needed to collect,time reverse and re-broadcast an updated sona.

The following equation is proposed as a model for the peak-to-peak voltage of the reconstruction on a moving target as afunction of time, assuming a constant velocity v̄:

V (t) =

{0 : t (mod tc) ≤ tda ·

∣∣sinc ( v̄tb

)∣∣ + d : t (mod tc) > td. (2)

In Fig. 4, the green curve represents a fit of Eq. 2 to onefull cycle. As in Fig. 3, this function fits the data well usingthe same parameters.

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Fig. 4: Peak-to-peak reconstruction voltage measured overtime as the target moves along one wall of the enclosure at0.5 mm

s . A new sona signal is acquired every tc seconds.

IV. DISCUSSION

A. A Time Reveresal WPT System

This research represents a first step in the exploration ofbuilding a time reversal WPT system. We demonstrate onepossible realization of this idea in Fig. 5. However, we leaveoptimization of performance and efficiency to future work.

The proposed system consists of two basic components. Thefirst is a rectenna that serves as the receiver. Although thesystem as described in Section II would require an out-of-band feedback channel between the receiver and transmitter,prior work has shown how a transmitter can target receiversentirely in-band [9], [13]. Our system in Fig. 5 builds on thesefindings. The second is a transmitter that performs the timereversal process. This component is responsible for recordingcharacteristic signals from the receiver(s), time reversing thesignals, and re-broadcasting them into the environment.

In a practical system, the rectenna could be integrated intothe hardware of a mobile device, or into an external componentthat plugs into the battery. The transmitter would need to beconnected to an external power source, but could otherwise belocated anywhere in the room.

Although not a component of the system, another importantconsideration in this scenario is the environment; a low-lossscattering environment is necessary for time reversal to beeffective.

B. Limitations and Future Work

Our experiments were limited primarily by the environmentand equipment used in testing. A consumer electronics envi-ronment is likely to be much larger than the chamber usedin this study, and filled with clutter. Both of these propertieswould improve the modal density of the environment, creatingmore transmission channels between source and target, ulti-mately improving reconstruction quality. On the other hand,such environments would likely create more loss.

In our experiments, we found that approximately 0.44%of energy transmitted through our test cavity was received.Although this initial result is too low to act as the sole sourceof energy for a device, it may be sufficient to perform long-term trickle charging or to act as a secondary source of energy

Fig. 5: A notional time reversal WPT system. In the acquistionphase, a new receiver joins the system by broadcasting oremitting a characteristic signal (0). Here, the receiver activelyemits a signal, but it is also possible for the transmitter to finda passive target, as shown in [9]. In either case, the next sonathat the transmitter collects will contain spatial informationunique to the receiver’s location (1). In the power transfercycle, the sona is time reversed (2), amplified, and broadcastback into the environment. The amplified signal reconstructson the receiver (3) and is converted to usable DC power bythe rectifier (4). A small fraction of the signal is used to re-broadcast a new characteristic signal (5) into the environment,which will be collected in the next sona (6). The cycle repeatsfrom (2).

for extending battery life. In order to improve efficiency, themost important area of future work would be developing abetter understanding of sources of environmental loss and howto mitigate them. In addition, our experiments used a singlechannel, but other WPT systems, such as Cota, rely on a largenumber of channels [14]. Modifying the time reversal systemto exploit multiple channels could improve power transmissionto levels sufficient for fully powering a device.

In Section III-B, we showed that the ability of a time rever-sal system to transmit energy to a moving target is dependenton the spatial profile and transmission dead time, td. In thiswork, our equipment limited us to a td of 7 seconds, whichwould be too slow to handle most typical movement, such aswalking across a room. The primary bottlenecks here werethe communication between the oscilloscope and computer,and the fast Fourier transform (FFT) operations performedin MATLAB on the computer. A practical system couldovercome these limitations by combining the two componentsinto a single device, which would remove the communicationoverhead, and optimizing for the FFT computation in hard-ware. Once a sona has been recorded (shown in Fig. 1b tobe on the order of 10 µs), the theoretical lower bound onprocessing time would be limited only by the amount of timerequired to compute an FFT.

V. CONCLUSION

This paper proposes time reversed electromagnetic wavepropagation as a new approach for WPT. Our experimentsdemonstrate that the spatial profile of reconstruction voltageis very tightly confined to the area surrounding the intendedreceiving antenna, and roughly follows a |sinc(x)| profile.Further, we successfully demonstrate the ability to focustime reversed signals onto a moving target in a ray-chaoticscattering environment. We believe that, with improvementsto the transmitter and receiver, time reversal could provide aviable approach for WPT in certain environments.

ACKNOWLEDGMENTS

This work was supported by ONR through grant#N000141512134, the UMD Gemstone program, and CNAM.We would like to acknowledge all members of Gemstone TeamTESLA for their feedback on results and data used in thispaper.

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