1

Distributed Laser Charging:A Wireless Power Transfer Approach

Qingqing Zhang, Student Member, IEEE, Wen Fang, Qingwen Liu∗, Senior Member, IEEE, Jun Wu, SeniorMember, IEEE, Pengfei Xia, Senior Member, IEEE, and Liuqing Yang, Fellow, IEEE

Abstract—Wireless power transfer (WPT) is a promisingsolution to provide convenient and perpetual energy supplies toelectronics. Traditional WPT technologies face the challenge ofproviding Watt-level power over meter-level distance for Internetof Things (IoT) and mobile devices, such as sensors, controllers,smart-phones, laptops, etc.. Distributed laser charging (DLC), anew WPT alternative, has the potential to solve these problemsand enable WPT with the similar experience as WiFi com-munications. In this paper, we present a multi-module DLCsystem model, in order to illustrate its physical fundamentalsand mathematical formula. This analytical modeling enablesthe evaluation of power conversion or transmission for eachindividual module, considering the impacts of laser wavelength,transmission attenuation and photovoltaic-cell (PV-cell) tempera-ture. Based on the linear approximation of electricity-to-laser andlaser-to-electricity power conversion validated by measurementand simulation, we derive the maximum power transmissionefficiency in closed-form. Thus, we demonstrate the variationof the maximum power transmission efficiency depending on thesupply power at the transmitter, laser wavelength, transmissiondistance, and PV-cell temperature. Similar to the maximizationof information transmission capacity in wireless informationtransfer (WIT), the maximization of the power transmissionefficiency is equally important in WPT. Therefore, this work notonly provides the insight of DLC in theory, but also offers theguideline of DLC system design in practice.

Index Terms—Wireless power transfer, distributed lasercharging, power transmission efficiency.

I. INTRODUCTION

Internet of Things (IoT) and mobile devices, such assensors and smart-phones, are typically powered by batteriesthat have limited operation time. Sensors for IoT, especiallysensors that being deployed in special environments such asvolcanoes, are difficult to be charged. Meanwhile, carrying apower cord and looking for a power supplier to charge mobiledevices incur great inconvenience. An alternative is thus totransfer power wirelessly, which virtually provides perpetualenergy supplies. Hence, wireless power transfer (WPT) orwireless charging attracts great attention recently.

Three major wireless charging technologies are surveyedin [1, 2]. Inductive coupling is safe and simple for implementa-tion. However, it is limited by a short charging distance from

Q. Zhang, W. Fang, Q. Liu, J. Wu, and P. Xia, are with theCollege of Electronic and Information Engineering, Tongji University,Shanghai, China, (email: anne@tongji.edu.cn, wen.fang@tongji.edu.cn, qing-wen.liu@gmail.com, wujun@tongji.edu.cn, pengfei.xia@gmail.com).

L. Yang is with the Department of Electrical and Computer En-gineering, Colorado State University, Fort Collins, CO 80523, USA(email:lqyang@engr.colostate.edu).

* Corresponding author.

Inter-Drone Charge

DLC Transmitter-2

DLCTransmitter-1

TV

Laptop

Watch

CameraPhonePad

Drone-1

Drone-2

Phone

Sensor

Fig. 1 Distributed Laser Charging Applications

a few millimeters to centimeters, which is only suitable forcontact-charging devices like toothbrush. Magnetic resonancecoupling has high charging efficiency. However, it is restrictedby short charging distances and big coil sizes, which fitshome appliances like TV. Electromagnetic (EM) radiation haslong effective charging distances. However, it suffers fromlow charging efficiency and is unsafe when the EM powerdensity exposure is high, hence is only favorable for low-powerdevices like sensors. In a nutshell, these traditional WPT tech-nologies provide great wireless charging abilities for differentapplication scenarios, whereas it is still challenging to offersufficient power over long distance for safely charging IoTand mobile devices, e.g., smart-sensor, smart-phone, laptop,drone, etc., which usually need Watt-level power over meter-level distances.

To support the power and distance requirements for IoTand mobile devices, a distributed laser charging (DLC) systemis presented in [3], which could transfer 2-Watt power over a5-meter distance [4]. By using inductive coupling or magneticresonance coupling, IoT and mobile devices, say sensors andsmart-phones, should typically be placed in a special chargingcradle with a particular position. However, the DLC’s self-aligning feature provides a more convenient way of chargingIoT and mobile devices without specific positioning or track-ing, as long as the transmitter and the receiver are in the line ofsight (LOS) of each other. Different from EM radiation, DLC’s

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wireless power transfer can be stopped immediately when thisLOS is blocked by any object, which ensures the safety ofDLC system. The size of the DLC receiver is sufficientlysmall to be embedded in a sensor or a smart-phone. The DLCtransmitter can be installed on the ceiling like a lightbulb. Inaddition, multiple devices can be charged simultaneously by asingle DLC transmitter [5–7]. Therefore, DLC can provide IoTand mobile devices with safe WPT capability, which enablespeople to charge their devices with the similar experience asWiFi communications.

Fig. 1 illustrates the DLC potential applications. In Fig. 1,in the room, DLC Transmitter-1 is combined with a light-emitting diode (LED) array and become a DLC-equippedlightbulb. Thus Transmitter-1 can be conveniently installed onthe ceiling, and then provide wireless power to IoT and mobiledevices within its coverage. In the outdoor scenario, Drone-1is equipped with a DLC transmitter, which can charge IoT andmobile devices on demand. At the same time, a DLC receiveris also embedded in Drone-1. Thus, it can be remotely chargedby DLC Transmitter-2, which acts as the power-supply basestation on the ground. In addition, Drone-2 equipped with bothDLC transmitter and receiver can play the role of a relay toreceive power from DLC Transmitter-2 and transmit power toDrone-1 simultaneously.

Similar to the maximization of the information trans-mission capacity of wireless channels in wireless informationtransfer (WIT), an important research topic in WPT is tomaximize the power or energy transmission efficiency [8].The wireless charging efficiency of a DLC system is affectedby many factors, including laser wavelength, electricity-to-laser conversion efficiency, laser transmission attenuation, andlaser-to-electricity conversion efficiency [9–12]. In this pa-per, we focus our study on the modeling of DLC systemand its performance evaluation. In order to understand thefundamental mechanism of DLC system, we separate theDLC system into multiple conceptually independent modules.Thus, the corresponding power conversion or transmissionfor each module can be investigated individually, consideringthe impacts of laser wavelength, transmission attenuation, andphotovoltaic-cell (PV-cell) temperature. Finally, the maximumpower transmission efficiency in closed-form can be obtainedfrom this modular analysis.

In this paper, a multi-module system model is proposedto describe the DLC system. The physical mechanism andmathematical formula are presented to describe the relation-ship between the stimulating electrical power and the outputpower, as well as the efficiency. The relationship between thesupply power and the laser power, the relationship between thereceived laser power and the output power, and thus the rela-tionship between the output power and the supply power areall depicted by both analytical results and illustrative graphs.The relationship between the electricity-to-laser conversionefficiency and the supply power, the relationship between thelaser-to-electricity conversion efficiency and the received laserpower, and thus the relationship between the maximum powertransmission efficiency and the supply power are captured byclosed-form expressions as well as being illustrated by figures.As a result, this work not only provides the insight of DLC

DLC Transmitter DLC Receiver

Intra-cavity

Laser

Power

Supplier

Gain

MediumPV

+

-

Power

Output

External-cavityLaser

Resonant Cavity

R2：95%

Reflectivity

Electricity-

to-Laser

Conversion

Transmitter

Power

Supply

Laser-to-

Electricity

Conversion

Receiver

Power

Output

Laser

Transmis

sion

R1：100%

Reflectivity

Fig. 2 Distributed Laser Charging System Diagram

DLC Transmitter DLC Receiver

Intra-cavity

Laser

Power

Supplier

Gain

MediumPV

+

-

Power

Output

External-cavityLaser

Resonant Cavity

R2：95%

Reflectivity

Electricity-

to-Laser

Conversion

Transmitter

Power

Supply

Laser-to-

Electricity

Conversion

Receiver

Power

Output

Laser

Transmis

sion

R1：100%

Reflectivity

Fig. 3 Distributed Laser Charging System Model

in theory, but also offers the design guideline for DLC systemimplementation in practice.

In the rest of this paper, we will first review the DLCsystem and present the multi-module system model. Then,we will illustrate the analytical modeling of each module toinvestigate the corresponding working principles. After that,we will evaluate the performance of each module and derivethe maximum DLC power transmission efficiency in closed-form. Finally, we will give summarizing remarks and discussopen issues for future research.

II. DLC SYSTEM

DLC is a WPT technology based on the distributed res-onating laser presented in [3]. Traditional laser systems belongto the scope of integrated resonating laser, since all opticalcomponents are integrated in one single device. However, inDLC systems, the optical components are divided into twoseparate parts, the transmitter and the receiver, respectively.Therefore, the laser in DLC systems falls within the scope ofdistributed resonating laser.

Fig. 2 shows the DLC system diagram described in[3]. A retro-reflector mirror R1 with 100% reflectivity anda gain medium are implemented at the transmitter. Whilein the receiver, a retro-reflector mirror R2 with exemplary95% partial reflectivity is contained. R1, R2 and the gainmedium consist the resonant cavity, within which photonsare amplified and form intra-cavity resonating laser. Photonsthat pass through R2 generates the external-cavity laser. Theexternal-cavity laser power can be converted to electricalpower by a photovoltaic-panel (PV-panel) installed behindmirror R2, which is similar to a solar panel. Fig. 2 includesthe power supplier at the transmitter and the power output atthe receiver for the comprehensive DLC system design.

As specified in [3], in the DLC system, photons isamplified without concerning about the incident angle, as longas they travel along LOS of R1 and R2. Hence, the intra-cavity laser generated by the resonator can be self-alignedwithout specific positioning or tracking. This feature enablesusers to charge their devices without placing them in a specificposition cautiously. Besides self-alignment, the DLC systemis intrinsically-safe, since objects blocking the line-of-sight

3

of intra-cavity laser can stop the laser immediately. Thesefeatures offer DLC the capability of safely charging devicesover long distance.

Fig. 3 presents the system model to elaborate the wirelesspower transfer in the DLC system. This model illustratesa theoretical framework of power transfer by electricity-to-laser conversion, laser transmission, and laser-to-electricityconversion. The physical fundamentals and mathematical for-mulations of this modular model will be specified in thefollowing section.

III. ANALYTICAL MODELING

In this section, we will discuss each module of the DLCmodel in Fig. 3 and describe its wireless power transfermechanism analytically. At the DLC transmitter, the powersupplier provides electrical power to generate the intra-cavitylaser. We will first introduce the electricity-to-laser conversion.Then, the intra-cavity laser will travel through the air andarrive at the DLC receiver. We will discuss the intra-cavitylaser power attenuation along its transmission. At the DLCreceiver, the intra-cavity laser will partially go through themirror R2 and form the external-cavity laser, then the external-cavity laser will be converted into electricity by a PV-panel.We will analyze this laser-to-electricity conversion based onthe PV engineering. Finally, the PV-panel output electricalpower can be used to charge electronics. Based on the aboveanalytical modeling, we will obtain the power conversion andtransmission efficiency of each module and the overall powertransmission efficiency.

A. Electricity-to-Laser Conversion

At the DLC transmitter, the electrical power Ps is pro-vided by the power supplier, which depends on the stimulatingcurrent It and voltage Vt as:

Ps = ItVt. (1)

The supply power Ps can stimulate the gain medium togenerate laser. Thus, the electrical power can be convertedto the laser power. We denote Pl as the external-cavity laserpower when the intra-cavity laser transmission efficiency is100%. It is well-known that laser can be generated, only whenIt provided by the power supplier is over a certain threshold[13]. In the laser diode physics, the laser power Pl relies onIt . Their relationship can be depicted as [13]:

Pl = ζhυ

q(It − Ith), (2)

where ζ is the modified coefficient, h is the Plunk constant, υis the laser frequency, q is the electronic charge constant, andIth is the current threshold.

Thus, the electricity-to-laser conversion efficiency ηel canbe figured out as:

ηel =PlPs. (3)

PV-panel

IoPr

Vo

Fig. 4 PV-panel Power Conversion Circuit Model

B. Laser Transmission

Laser power transmission attenuation means that laserpower decreases along with its transmission through the air,which is similar to EM wave propagation power loss [14].The laser power attenuation level depends on the transmissiondistance and air quality [15, 16]. Relying on the above laser-generation mechanism, the intra-cavity laser can transmit fromthe transmitter to the receiver. During the transmission, lasermay experience power attenuation. For simplicity, we assumethat the laser diameter is a constant. This assumption couldbe validated by controlling aperture diameters of the DLCtransmitter and receiver [15].

The laser transmission efficiency ηlt can be modeled as[15]:

ηlt =PrPl

= e−αd, (4)

where Pr is the external-cavity laser power received at theDLC receiver, α is the laser attenuation coefficient, and d isthe distance. When d is close to zero, the laser transmission ef-ficiency approaches 100%. In this situation, Pr is approximateto Pl.

α can be depicted as:

α =σ

κ

(λχ

)−ρ, (5)

where σ and χ are two constants, κ is the visibility, λ isthe wavelength, and ρ is the size distribution of the scatteringparticles. ρ depends on visibility, which will be discussed later.

C. Laser-to-Electricity Conversion

At the DLC receiver, the external-cavity laser power canbe converted to electrical power. To illustrate the laser-to-electricity conversion mechanism, the single-diode equivalent

TABLE I Transmission or Conversion Efficiency

Parameter SymbolElectricity-to-laser conversion efficiency ηel

Laser transmission efficiency ηltLaser-to-electricity conversion efficiency ηle

The overall DLC power transmission efficiency ηo

4

0 2 4 6 8

Stimulating Current I t (A)

0

10

20

30

40P

ower

(W

)

Ith

= 0.5 A

3.5

4

4.5

5

5.5

Stim

ulat

ing

Vol

tage

V t (

V)

Measured Supply Power Ps

Formula Laser Power Pl

Measured Laser Power Pl

Measured Voltage Vt

Fig. 5 Electricity-to-Laser Conversion Power, Voltage andCurrent (810nm)

circuit model of a PV-panel is depicted in Fig. 4 [17]. The PV-panel output voltage Vo, and current Io can be characterizedas [17]:

Io = Isc − Is(eVo/Vm − 1), (6)

where Isc is the PV-panel short-circuit current, Is is thesaturation current, i.e., the diode leakage current density inthe absence of light, and Vm is the “thermal voltage”, whichcan be defined as:

Vm =nkT

q, (7)

where n is the PV-panel ideality factor, k is the Boltzmannconstant, and T is the absolute PV-cell temperature. Then, thePV-panel output power Po, which relies on Io and Vo, can beobtained as:

Po = IoVo. (8)

Therefore, the laser-to-electricity conversion efficiency,i.e. the PV-panel conversion efficiency, ηle depends on Po andPr, which can be depicted as:

ηle =PoPr

=IoVoPr

. (9)

In summary, the PV-panel converts the received laserpower Pr to the output power Po with the efficiency ηle.

D. DLC Power Transmission Efficiency

Based on the above analysis for each individual moduleof the DLC system model, the DLC power transmissionefficiency from the power supplier at the transmitter to thepower output at the receiver can be depicted as:

ηo = ηelηltηle. (10)

The conversion or transmission efficiency of each module andthe DLC power transmission efficiency are listed in Table I.

The numerical evaluation of the DLC system model willbe presented in the next section.

0 2 4 6 8

Stimulating Current I t (A)

0

20

40

60

Pow

er (

W)

Ith

= 0.6 A

0

5

10

15

Stim

ulat

ing

Vol

tage

V t (

V)

Measured Supply Power Ps

Formula Laser Power Pl

Measured Laser Power Pl

Measured Voltage Vt

Fig. 6 Electricity-to-Laser Conversion Power, Voltage andCurrent (1550nm)

IV. NUMERICAL EVALUATION

Based on the analytical modeling in the previous section,we can find that the DLC system efficiency varies with laserwavelength, transmission attenuation and PV-cell temperature.Their impacts on the performance of each module as wellas the overall DLC system will be discussed in this section.The numerical evaluation is implemented in MATLAB andSimulink.

A. Electricity-to-Laser Conversion

Electrical supply power Ps provided by the power sup-plier at the transmitter depending on the stimulating currentIt and voltage Vt, as in (1). Based on the measurement of It,Vt, and thus Ps, for the laser systems (λ is 800-820nm and1540-1560nm, respectively) in [9, 10], the measured supplypower Ps, the measured laser power Pl, the stimulating currentIt, and the stimulating voltage Vt are shown for 810nm and1550nm in Fig. 5 and Fig. 6, respectively. From the dashed-lines for the measured laser power in Fig. 5 and Fig. 6, themodified coefficient ζ in (2) can be determined and listed inTable II. Thus, from (2), the formulated laser power curvesare given as the solid-lines in Fig. 5 and Fig. 6, respectively.

TABLE II Electricity-to-Laser Conversion Parameters

Parameter Symbol Value810nm 1550nm

Boltzmann constant k 1.38064852× 10−23J/KPlanck constant h 6.62606957× 10−34J · s

Electronic charge constant q 1.6× 10−19CLaser wavelength λ 810nm 1550nmLaser frequency υ 3.7× 1014Hz 1.9× 1014Hz

Stimulation currentthreshold

Ith 0.5A 0.6A

Modified coefficient ζ 1.5 3.52Pl-Ps curve fitting

parametera1 0.445 0.34

Pl-Ps curve fittingparameter

b1 −0.75 −1.1

5

0 10 20 30 40 50

Supply Power Ps (W)

0

5

10

15

20

25La

ser

Pow

er P

l (W

)

Formulated Curve (810nm) Measured Curve (810nm) Formulated Curve (1550nm) Measured Curve (1550nm)

Fig. 7 Laser Power vs. Supply Power

0 10 20 30 40

Supply Power Ps (W)

0

10%

20%

30%

40%

50%

Ele

ctric

ity-t

o-La

ser

Con

vers

ion

Effi

cien

cy

el

810nm 1550nm

Fig. 8 Electricity-to-Laser Conversion Efficiency vs. SupplyPower

In Fig. 5 and Fig. 6, the relationship between Pl andPs is illustrated in Fig. 7. We adopt the linear formula toapproximate this power conversion as:

Pl ≈ a1Ps + b1. (11)

The measured and formulated curves in Fig. 7 depict the linearapproximation between Pl and Ps based on (11), when thewavelength λ is about 810nm and 1550nm, respectively. Wecan find that the fitting curves match the measurement verywell in the given supply power and laser power range in Fig. 7.

From (3) and (11), we can obtain the electricity-to-laserconversion efficiency ηel as:

ηel =PlPs

= a1 +b1Ps. (12)

The solid-line and dashed-line in Fig. 8 illustrate ηel for810nm and 1550nm, respectively. The initial Ps supply powerthreshold in Fig. 8 is corresponding to the current threshold

0 10 20 30 40 50

Distance d (km)

0

20%

40%

60%

80%

100%

Lase

r T

rans

mis

sion

Effi

cien

cy

lt

clear air (1550nm)clear air (810nm) haze (1550nm) haze (810nm) fog (1550nm) fog (810nm)

Fig. 9 Laser Transmission Efficiency vs. Distance

Ith for Pl in Fig. 5 and Fig. 6. In Fig. 8, ηel starts to increasedramatically from the initial supply power Ps threshold andwill reach the plateau as Ps increases. The plateau of ηel for810nm laser is around 43%, which is higher than 31% for1550nm laser.

B. Laser Transmission

From (4) and (5), the laser power attenuation coefficientin transmission can be determined under three typical sce-narios, i.e., clear air, haze, and fog. For the three scenarios,the size distribution of the scattering particles ρ in (5) can bespecified as [16]:

ρ =

1.3 for clear air (6km ≤ κ ≤ 50km),0.16κ+ 0.34 for haze (1km ≤ κ ≤ 6km),0 for fog (κ ≤ 0.5km),

(13)where κ is the visibility.

Along with ρ, the other attenuation parameters are listedin Table III. Thus, the relationship between ηlt and the trans-mission distance d can be obtained from (4) and (5), which isillustrated in Fig. 9. It is clear that ηlt decays exponentially tozero as d increases. Meanwhile, for the same laser wavelength,laser power attenuation depends on the visibility κ. Laserpower attenuation increases when κ decreases. As can be seenin Fig. 9, for clear air, haze and fog, given the same d, the laserpower attenuation for short-wavelength is more than that oflong-wavelength. For clear air and haze, laser attenuation for810nm is much more than that of 1550nm. However, for fog,since ρ takes 0 for both 810nm and 1550nm, the coefficient

TABLE III Laser Transmission Parameters

Parameter ValueClear Air Haze Fog

σ 3.92χ 550nmκ 10km 3km 0.4kmρ 1.3 0.16κ+ 0.34 0

6

0 10 20 30 40 50 60 70 80 90

PV-panel Output Voltage Vo (V)

0

40

80

120

PV

-pan

el O

utpu

t Cur

rent

I o

(

mA

)

Pr = 1 W

Pr = 5 W

Pr = 10 W

Pr = 15 W

Fig. 10 PV-panel Output Current vs. Voltage (λ = 810nm)

0 10 20 30 40 50

PV-panel Output Voltage Vo (V)

0

50

100

150

200

PV

-pan

el O

utpu

t Cur

rent

I o

(

mA

)

Pr = 1 W

Pr = 5 W

Pr = 10 W

Pr = 15 W

Fig. 11 PV-panel Output Current vs. Voltage (λ = 1550nm)

α has the same value. Therefore, the laser attenuation in fogdoes not dependent on λ.

C. Laser-to-Electricity Conversion

At the DLC receiver, PV-panel takes the role of con-verting laser power to electrical power. PV-panel conversionefficiency relies on laser power, wavelength, and cell temper-ature. With reference to (6)-(7), we can obtain the PV-paneloutput current, voltage, and thus power, given the parameterslisted in Table IV. Fig. 10-17 demonstrate their relationshipsfor different laser wavelength using the standard solar cellSimulink model [18].

Fig. 10 shows the relationship between PV-panel outputcurrent Io and voltage Vo with different input laser power,i.e., the external-cavity laser power Pr at the receiver, forthe GaAs-based PV-panel with 810nm laser at 25◦C [19].Similarly, Fig. 11 is for the GaSb-based PV-panel with 1550nmlaser at 25◦C [20]. The PV-panel output power Po can bederived from the corresponding Io and Vo based on Fig. 10

0 10 20 30 40 50 60 70 80 90

PV-panel Output Voltage Vo (V)

0

2

4

6

8

PV

-pan

el O

utpu

t Pow

er

Po

(W

)

Pr = 1 W

Pr = 5 W

Pr = 10 W

Pr = 15 W

Fig. 12 PV-panel Output Power vs. Voltage (λ = 810nm)

TABLE IV Laser-to-Electricity Conversion Parameters

Parameter Symbol Value810nm 1550nm

Short-circuitcurrent

Isc 0.16732A 0.305A

Open-circuitvoltage

Voc 1.2V 0.464V

Irradianceused for

measurement

Ir0 36.5W/cm2 2.7187W/cm2

Laserfrequency

υ 3.7037× 1014Hz 1.9355× 1014Hz

Qualityfactor

n 1.5 1.1

Number ofseries cells

N 72

PV-panelmaterial

GaAs-based GaSb-based

Measurementtemperature

T 25◦C 120◦C

Simulationtemperature

0◦C / 25◦C / 50◦C

Pm-Pr curvefitting

parameter

a2 0.546/0.541/0.537 0.543/0.498/0.453

Pm-Pr curvefitting

parameter

b2 -0.213/-0.231/-0.249 -0.276/-0.299/-0.321

and Fig. 11. Thus, Fig. 12 and Fig. 13 depict the relationshipbetween Po and Vo for 810nm and 1550nm, respectively.

From Fig. 12 and Fig. 13, given Pr, we can figureout the maximum output power, which is defined as themaximum power point (MPP) and marked by the dots on thecorresponding output power curves. We denote Pm as the MPPof Po. From [21], Pm is proved as the unique output power,i.e., the corresponding current and voltage are unique, giventhe received laser power Pr. For example, given Pr = 10W,the MPP is unique as 4.64W for 1550nm, which is depictedby the dots in Fig. 11 and 13. The corresponding unique Ioand Vo are 121.3mA and 38.3V, respectively.

In Fig. 10 and Fig. 11, given Pr, Io keeps almost aconstant when Vo is below the MPP. However, Io drops rapidly

7

0 10 20 30 40 50

PV-panel Output Voltage Vo (V)

0

2

4

6

8

PV

-pan

el O

utpu

t Pow

er

Po

(W

)

Pr = 1 W

Pr = 5 W

Pr = 10 W

Pr = 15 W

Fig. 13 PV-panel Output Power vs. Voltage (λ = 1550nm)

0 10 20 30 40 50 60 70 80 90

PV-panel Output Voltage Vo (V)

0

20

40

60

80

PV

-pan

el O

utpu

t Cur

rent

I o

(mA

)

0°C

25°C

50°C73 74 75 76

67

69

71

Fig. 14 PV-panel Output Current vs. Voltage (λ = 810nm)

0 10 20 30 40 50

PV-panel Output Voltage Vo (V)

0

20

40

60

80

100

120

140

PV

-pan

el O

utpu

t Cur

rent

I o

(mA

)

0°C

25°C

50°C

Fig. 15 PV-panel Output Current vs. Voltage (λ = 1550nm)

0 10 20 30 40 50 60 70 80 90

PV-panel Output Voltage Vo (V)

0

1

2

3

4

5

6

PV

-pan

el O

utpu

t Pow

er

Po

(W

)

0°C

25°C

50°C

73 75 775

5.1

5.2

5.3

Fig. 16 PV-panel Output Power vs. Voltage (λ = 810nm)

0 10 20 30 40 50

PV-panel Output Voltage Vo (V)

0

1

2

3

4

5

6

PV

-pan

el O

utpu

t Pow

er

Po

(W

)

0°C

25°C

50°C

Fig. 17 PV-panel Output Power vs. Voltage (λ = 1550nm)

0 5 10 15 20

Received Laser Power Pr (W)

0

2

4

6

8

10

12

Max

imum

Out

put P

ower

Pm

(W

)

0°C

25°C

50°C

17 17.5 189

9.2

9.4

Fig. 18 Maximum Output Power vs. Received Laser Power (λ= 810nm)

8

0 5 10 15

Received Laser Power Pr (W)

0

2

4

6

8M

axim

um O

utpu

t Pow

er P

m (

W)

0°C

25°C

50°C

Fig. 19 Maximum Output Power vs. Received Laser Power (λ= 1550nm)

when Vo is over the MPP. For the same Vo, Io increases whenPr increases. When Io is close to zero, Vo is the open-circuitvoltage, which increases when Pr increases. From Fig. 12 andFig. 13, given Pr, Po increases when Vo increases until itreaches the MPP. However, Po drops dramatically when Vo isabove the corresponding voltage for MPP. For a given voltageVo, the output power Po increases when the input laser powerPr increases.

Besides input laser power, PV-cell temperature also im-pacts the PV-panel output current, voltage, and power. Giventhe three cell temperatures (0◦C, 25◦C, 50◦C), for λ = 810nmand Pr = 10W power, Fig. 14 and Fig. 16 depict the variationof Io and Po on different Vo, respectively. Similarly, for λ =1550nm and Pr = 10W power, Fig. 15 and Fig. 17 show thePV-panel output Io, Vo and Po for these cell temperatures.

From Fig. 14 and Fig. 15, Io keeps almost as a constantwhen Vo is below a certain value. Given different cell tem-peratures, Io curves start dropping at different Vo. The turningvoltage is low when the temperature is high. From Fig. 16 andFig. 17, Po is low when the temperature is high. Additionally,the MPP increases as the cell temperature declines.

Based on the MPP dots in Fig. 10 and Fig. 12 for differentPr and Fig. 14 and Fig. 16 for different cell temperatures, wecan obtain the MPP dots in Fig. 18, which illustrates Pm versusPr for 810nm. Similarly, Fig. 19 demonstrates Pm versus Prfor 1550nm. In order to evaluate the relationship between Pmand Pr, we adopt the approximation formula by using thecurve fitting method as:

Pm ≈ a2Pr + b2, (14)

where a2 and b2 are the linear curve fitting coefficients fordifferent wavelengths and cell temperatures, which are listedin Table IV. From Fig. 18 and Fig. 19, we can find that theapproximate lines based on (14) matches the MPP dots verywell.

We denote ηlem as the maximum PV-panel conversionefficiency when Po is Pm. Based on (9) and (14), ηlem can

0 5 10 15 20

Received Laser Power Pr (W)

0

10%

20%

30%

40%

50%

60%

Max

imum

Las

er-t

o-E

lect

ricity

C

onve

rsio

n E

ffici

ency

le

m

0°C

25°C

50°C

15 20 2552%

53%

54%

Fig. 20 Maximum Laser-to-Electricity Conversion Efficiencyvs. Received Laser Power (λ = 810nm)

0 5 10 15

Received Laser Power Pr (W)

0

10%

20%

30%

40%

50%

60%

Max

imum

Las

er-t

o-E

lect

ricity

C

onve

rsio

n E

ffici

ency

le

m

0°C

25°C

50°C

Fig. 21 Maximum Laser-to-Electricity Conversion Efficiencyvs. Received Laser Power (λ = 1550nm)

be depicted as:

ηlem =PmPr

= a2 +b2Pr. (15)

Fig. 20 and Fig. 21 show how ηlem varies with thereceived laser power Pr for 810nm and 1550nm, respectively.From Fig. 20 and Fig. 21, the changing trend of ηlem is similarwith that of ηel in Fig. 8. ηlem is low when cell temperatureis high. The impact of cell temperature on ηlem is bigger for1550nm than that of 810nm, comparing Fig. 20 and Fig. 21.

D. DLC Power Transmission Efficiency

The relationship between the laser power Pl and the sup-ply power Ps is demonstrated by (11), when the transmissiondistance d is close to zero in the electricity-to-laser conversion.The relationship between Pl and the received laser power Prdue to laser transmission is illustrated in (4). The relationshipbetween Pr and the maximum PV-panel output power Pm in

9

0 10 20 30 40

Supply Power Ps (W)

0

2

4

6

8

10

Max

imum

Out

put P

ower

Pm

(W

)

0°C, lt=100%

25°C, lt=100%

50°C, lt=100%

0°C, lt=50%

25°C, lt=50%

50°C, lt=50%

39.5 40 40.5 418.8

9

9.2

39 40 414.3

4.4

4.5

Fig. 22 Maximum Output Power vs. Supply Power (λ =810nm)

0 10 20 30 40

Supply Power Ps (W)

0

2

4

6

8

Max

imum

Out

put P

ower

Pm

(W

)

0°C, lt=100%

25°C, lt=100%

50°C, lt=100%

0°C, lt=50%

25°C, lt=50%

50°C, lt=50%

Fig. 23 Maximum Output Power vs. Supply Power (λ =1550nm)

0 10 20 30 40

Supply Power Ps (W)

0

5%

10%

15%

20%

25%

Max

imum

Pow

er T

rans

mis

sion

Effi

cien

cy

om

0°C, lt=100%

25°C, lt=100%

50°C, lt=100%

0°C, lt=50%

25°C, lt=50%

50°C, lt=50%

29 30 3121.5%

22%

22.5%

29 30 3110.4%

10.6%

10.8%

Fig. 24 Maximum Power Transmission Efficiency vs. SupplyPower (λ = 810nm)

0 10 20 30 40

Supply Power Ps (W)

0

5%

10%

15%

20%

Max

imum

Pow

er T

rans

mis

sion

Effi

cien

cy

om

0°C, lt=100%

25°C, lt=100%

50°C, lt=100%

0°C, lt=50%

25°C, lt=50%

50°C, lt=50%

Fig. 25 Maximum Power Transmission Efficiency vs. SupplyPower (λ = 1550nm)

0 5 10 15 20 25 30 35

Distance d (km)

0

5%

10%

15%

20%

25%

Max

imum

Pow

er T

rans

mis

sion

Effi

cien

cy

om 0°C, 810nm

25°C, 810nm

50°C, 810nm

0°C, 1550nm

25°C, 1550nm

50°C, 1550nm1.8 2 2.2

14%

14.5%

15%

Fig. 26 Maximum Power Transmission Efficiency vs. Distance(Clear Air)

0 1 2 3 4 5 6

Distance d (km)

0

5%

10%

15%

20%

25%

Max

imum

Pow

er T

rans

mis

sion

Effi

cien

cy

om 0°C, 810nm

25°C, 810nm

50°C, 810nm

0°C, 1550nm

25°C, 1550nm

50°C, 1550nm

0.7 0.75 0.811%

11.5%

12%

Fig. 27 Maximum Power Transmission Efficiency vs. Distance(Haze)

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Distance d (km)

0

5%

10%

15%

20%

25%

Max

imum

Pow

er T

rans

mis

sion

Effi

cien

cy

om 0°C, 810nm

25°C, 810nm

50°C, 810nm

0°C, 1550nm

25°C, 1550nm

50°C, 1550nm

0.095 0.1 0.1058%

8.25%

8.5%

Fig. 28 Maximum Power Transmission Efficiency vs. Distance(Fog)

the laser-to-electricity conversion is shown in (14). Thus, from(11), (4) and (14), we can obtain the relationship between Psat the transmitter and Pm at the receiver as:

Pm = a2ηltPl + b2

= a1a2ηltPs + (a2b1ηlt + b2).(16)

Fig. 22 depicts the linear relationship between Pm andPs for ηlt = 100% and ηlt = 50%, respectively, when PV-celltemperature is 0◦C, 25◦C, 50◦C, and λ = 810nm. Meanwhile,Fig. 23 illustrates the similar circumstances for λ = 1550nm.

From (10), we denote ηom as the maximum powertransmission efficiency, when Po is Pm, i.e. ηle approachesηlem. From (3), (4), (9), (10), (12) and (15), the maximumpower transmission efficiency ηlem can be obtained as:

ηom = ηelηltηlem

= ηelηlt(a2 +b2

ηelηltPs)

= a1a2ηlt +a2b1ηlt + b2

Ps

= a1a2e−αd +

a2b1e−αd + b2Ps

.

(17)

Fig. 24 shows the relationship between ηom and Ps whenηlt are 100% and 50% and cell temperatures are 0◦C, 25◦C,and 50◦C for 810nm. Fig. 25 shows the same circumstancesfor 1550nm. ηom raises up with Ps increasing at first, thenit reaches the plateau. The growth pattern of ηom in Fig. 24and Fig. 25 is similar as ηel in Fig. 8 and ηlem in Fig. 20 andFig. 21.

ηom depends not only on the supply power Ps but also onthe distance d. Fig. 26 depicts the relationship between ηomand d for different laser wavelength and PV-cell temperature,when Ps = 40W and air quality is clear. Fig. 27 and Fig. 28illustrate ηom for the similar situation when air condition ishaze and fog, respectively. Fig. 29 describes how ηom changesover ηlt under clear air when Ps is 40W.

0 20% 40% 60% 80% 100%

Laser Transmission Efficiency lt

0

5%

10%

15%

20%

25%

Max

imum

Pow

er T

rans

mis

sion

Effi

cien

cy

om

°C°C°C

°C°C°C

63% 64% 65%14%

15%

Fig. 29 Maximum Power Transmission Efficiency vs. LaserTransmission Efficiency

From Fig. 26 and Fig. 27, ηom decreases when d in-creases. ηom of 810nm laser is higher than that of 1550nmlaser when d is short. However, ηom for 810nm is lower thanthat of 1550nm when d is long. From Fig. 28, ηom of 810nmlaser always keep higher than that of 1550nm laser until ηomdecrease to 0. At the same time, as described above, the celltemperature has bigger impact on ηom for 1550nm than thatof 810nm.

From Fig. 29, ηom increases linearly as ηlt enhancesbased on (17). Fig. 29 provides a guideline of designing theDLC systems. For example, if 20% of DLC maximum trans-mission efficiency is expected, the 1550nm DLC system cannot meet the requirement, however, the 810nm DLC systemis preferred. Meanwhile, when deploying the DLC system,the transmission efficiency at a certain distance provides thetheoretical reference to determine the radius, i.e., the coverage,which is similar to the base station coverage analysis in mobilecommunications [22, 23]. Therefore, the maximum economicbenefits can be obtained by minimizing the number of DLCtransmitters to cover a given area [24]. This analysis providesa guideline for the efficient deployment of the DLC systems.

In summary, the numerical evaluation in this sectionvalidates the analytical model presented in Section III. At first,for the three modules: electricity-to-laser conversion, lasertransmission, laser-to-electricity conversion, the conversionor transmission efficiency of each module is quantitativelyanalyzed. Secondly, through numerical analysis, we obtain theapproximate linear relationship between the supply power Psat the transmitter and the maximum PV-panel output power Pmat the receiver. Next, the maximum DLC power transmissionefficiency ηom in closed-form is derived. Finally, based on themaximum power transmission efficiency, DLC system designand development guidelines are provided, for example, howto select the laser wavelength and determine the coverage ofthe DLC systems.

11

V. CONCLUSIONS

This paper presents the distributed laser charging technol-ogy for wireless power transfer. The multi-module analyticalmodeling of distributed laser charging provides the in-depthview of its physical mechanism and mathematical formulation.The numerical evaluation illustrates the power conversion ortransmission in each module under the impacts of laser wave-length, transmission attenuation, and PV-cell temperature. Thelinear approximation is adopted and validated by measurementand simulation for electricity-to-laser and laser-to-electricitypower conversion. Thus the maximum power transmissionefficiency in closed-form is derived and its performance de-pending on the supply power, laser wavelength, transmissiondistance, and PV-cell temperature is illustrated by figures.Therefore, this paper not only provides the theoretical insight,but also offers the practical guideline in system design anddeployment of distributed laser charging.

Due to the space limitation, there are serval importantissues unaddressed in this paper and left for our future work,some of which are briefly discussed here:

• The PV-panel efficiency used in the DLC system is about50%, which is not much efficient. More studies on thePV-panel types, the efficiency analyzation, and the totalefficiency of the DLC system could be improved in thefuture.

• Only 810nm and 1550nm laser wavelengths are consid-ered in this paper. Wider range of wavelengths can bestudied to make the DLC system more universal in thefuture work.

• To convert the PV-panel output current and voltage todifferent preferred charging current and voltage for dif-ferent applications, the circuit or device that can convert asource of direct current from one voltage level to anotheris worth to be discussed in the future.

• The point-to-point charging procedure is well illustratedin this paper. On this basis, the accessing protocols, thescheduling algorithms, the influencing factors of powerconversion and transmission, and the system optimiza-tion for charging batteries adaptively in the the point-to-multiple-point wireless charging scenario should beanother interesting topic to discuss.

• Since point-to-multiple-point wireless power transfer isnaturally supported by distributed laser charging systems,the network architecture of WPT becomes an interestingresearch topic worthy of further investigation. The relatedprotocols and algorithms to effectively operate WPTnetworks could be developed, e.g., WPT network accessprotocols, WPT scheduling algorithms and so on [1].

• It is interesting to investigate the potential simultaneouswireless information and power transfer (SWIPT) in dis-tributed laser charing systems. Due to the huge availablebandwidth conveyed by laser, such high-power and high-rate SWIPT systems have the potential to support thedemanding applications, e.g., IoT, mobile virtual real-ity/augmented reality, ultra-high-definition video stream-ing and so on [8].

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