Method for predicting junction temperaturedistribution in a high-power laser diode barDAE-SUK KIM, CALEB HOLLOWAY, BONGTAE HAN,* AND AVRAM BAR-COHEN

Mechanical Engineering Department, University of Maryland College Park, Maryland 20742, USA*Corresponding author: bthan@umd.edu

Received 21 June 2016; revised 8 August 2016; accepted 17 August 2016; posted 17 August 2016 (Doc. ID 268935); published 12 September 2016

A hybrid experimental/numerical method is proposed for predicting the junction temperature distribution in ahigh-power laser diode (LD) bar with multiple emitters. A commercial water-cooled LD bar with multiple emit-ters is used to illustrate and validate the proposed method. A unique experimental setup is developed and imple-mented first to measure the average junction temperatures of the LD bar emitters. After measuring the heatdissipation of the LD bar, the effective heat transfer coefficient of the cooling system is determined inverselyfrom the numerical simulation using the measured average junction temperature and the heat dissipation.The characterized heat dissipation and effective heat transfer coefficient are used to predict the junction temper-ature distribution over the LD bar numerically under high operating currents. The results are presented in con-junction with the wall-plug efficiency and the center wavelength shift. © 2016 Optical Society of America

OCIS codes: (140.2020) Diode lasers; (140.3320) Laser cooling; (120.6780) Temperature; (120.6810) Thermal effects.

http://dx.doi.org/10.1364/AO.55.007487

1. INTRODUCTION

High-power laser diodes (LDs) have emerged as the mostpromising pumping sources for solid-state lasers and fiberlasers, and they have been widely used in communication appli-cations, cosmetic and medical applications, material surfacetreatment, joining technologies, cutting technologies, and de-fense applications [1–7]. The junction temperature is one ofthe most important parameters in achieving optimal perfor-mance of a high-power LD bar, determining the centerwavelength, spectrumdistribution, wall-plug efficiency, and reli-ability [8–12]. Thus, experimental and analytical determinationof the junction temperature is critical for the proper operation ofthe diode as well as the development of the packaging design.

As higher optical power is demanded for advanced applica-tions, more closely spaced emitters with higher forward currentare used in LD bars. As a result, the junction temperature fromthe center to the edge emitters may have large variations, whichmakes the center wavelength and wall-plug efficiency of eachemitter different from each other.

Several junction temperature measurement methods forlow-power LDs or light-emitting diodes have been proposed,including techniques based on measurement of the thermal re-sistance [13], wavelength shift [14,15], optical power output[14], and forward voltage [14,16–23]. These methods areapplicable only when the junction temperature is uniform.Micro-Raman spectroscopy [24–26] can be used to measurethe junction temperature distribution by measuring multiple

local temperatures. In practice, it requires a complicated exper-imental setup and has limited accuracy (10°C–20°C) [24–26].

The objective of this study is, thus, to propose a hybridexperimental/numerical method to predict the junction temper-ature distribution of a high-power LD bar. A commercial water-cooled LD bar with multiple emitters is investigated to illustratethe proposed method. After introducing the LD bar system, anexperimental setup that is developed uniquely to measure theaverage junction temperatures of the LD bar is described.Two parameters critical to thermal analysis—heat dissipationand effective heat transfer coefficient–are determined and sub-sequently used to predict numerically the junction temperaturedistribution over the LD bar under high operating currents.

2. LASER DIODE SYSTEM

This section is devoted to the description and the electricalcharacteristics of a commercial water-cooled LD bar testedin the study.

A. LD Bar DescriptionThe commercial LD bar system (E11.4N-940.10-150C-SO13.1: DILAS) is shown in Fig. 1(a). The LD bar consistsof 23 identical GaAs emitters. The fill factor is 50%; each emit-ter is 200 μm wide and has a pitch of 400 μm. The maximumoptical power at 160 A is 160 W with a center wavelengthof 930 nm.

The close-up view of the side of the LD bar is shown inFig. 1(b). The GaAs chip (the epi-down configuration) is

Research Article Vol. 55, No. 27 / September 20 2016 / Applied Optics 7487

1559-128X/16/277487-10 Journal © 2016 Optical Society of America

mounted on a CuW submount using AuSn die attach. Thesubmount made of CuW [coefficient of thermal expansion(CTE): 6.5 ppm∕°C] is placed between the GaAs chip (CTE:6.4 ppm∕°C) and the water-cooled microchannel made ofCu (CTE: 16.6 ppm∕°C) for the stress-relieving buffer layerto reduce the thermal stress attributed to the mismatch in theCTE between them as well as for the heat spreader [27–29].The specified thermal resistance from the junction to water inlettemperature is approximately 0.3 K∕W [30]. The internalstructures of the commercial microchannel and the interfacialresistance are not available, and thus the effective water heattransfer coefficient for this commercial microcooler cannot bedetermined.

B. Calibration CurveIt has been known that a negative linear relationship exists be-tween the junction temperature and the forward voltage of alaser diode [16–23]. The junction temperature at the operatingcurrent can be measured using this relationship (known as the“calibration curve”), and it is called the forward voltage method[16–23].

The “calibration curve” is obtained using a probe currentmuch lower than the operating current. If the probe current

is too low, the forward voltage loses the negative linear relation-ship at high junction temperatures due to the leakage currenteffect [31]. On the other hand, if it is too high, the loss of lin-earity occurs at low junction temperatures due to the internalseries resistance [32]. In addition, the probe current should beas low as possible to avoid any undesired junction temperatureincrease while obtaining the calibration curve. Every LD hassomewhat different electrical characteristics. Thus, it is impor-tant to determine the lowest probe current that provides thedesired linearity [23].

The LD bar was placed inside a convection oven (EC1A:Sun Electronics Systems) and the forward voltage was measuredat 25°C, 35°C, 45°C, 55°C, and 65°C (with an accuracy of�0.1°C) by a data acquisition module (DAQ: USB-6212:National Instruments) with a 16-bit resolution. The maximumoperating junction temperature was estimated, based on thethermal resistance of 0.3 K∕W, the inlet water temperatureof 20°C, and the measured maximum heat dissipation of84.7 W (this will be explained further in Section 5.A), to be45.4°C. The calibration curve measurement was repeated atvarious probe current values (from 20 to 160 mA with aninterval of 20 mA).

The results are shown in Fig. 2, displaying the expectedlinear relationship between the forward voltage and junctiontemperature. The small deviations from linearity in voltage andtemperature at 65°C are summarized in Table 1. The junctiontemperature error gradually decreased as the probe current

Fig. 1. (a) LD bar with water-cooled microchannel [30] and (b) sideview of the LD bar.

20 30 40 50 60 701.05

1.08

1.11

1.14

1.17

1.20 160 mA 140 mA 120 mA 100 mA 80 mA 60 mA 40 mA 20 mA

For

war

d V

olta

ge (

V)

Junction Temperature (°C)

Fig. 2. Forward voltage as a function of junction temperature.

Table 1. Junction Temperature Error at 65°C underDifferent Probe Currents

I f [mA] Deviation of V f (mV) Error in T j [°C]

20 1.60 1.340 0.80 0.760 0.80 0.780 0.78 0.6100 0.41 0.3120 0.18 0.1140 0.16 0.1160 0.17 0.1

7488 Vol. 55, No. 27 / September 20 2016 / Applied Optics Research Article

increased, and remained virtually the same after 120 mA. Theprobe current of 120 mA generated a heat dissipation of only142 mW at 25°C (6.2 mW per emitter), which was negligiblecompared to the heat dissipation produced by the operatingcurrent. Thus, the calibration curve obtained at 120 mAwas selected for junction temperature measurement. The slopeand the y-intercept of the calibration curve were −1.21 mV∕Kand 1.2104 V, respectively.

C. Electrical Resistance of Single EmitterThe calibration curve is obtained when all the emitters have thesame temperature. The emitters of the LD bar are connected inparallel, and thus the electrical resistance of a single emitter(assuming that all emitters are identical) can be determinedsimply by

R�T � � N ×V f �T �I probe

; (1)

where R is the electrical resistances of the single emitter [Ω]; V fis the forward voltage of the LD bar [V] under the probe cur-rent, I probe [A]; and N is the number of the emitter (N � 23).

The results obtained for the LD bar at the probe current ofI probe � 120 mA are shown in Fig. 3. The electrical resistancedecreased with the temperature; the change in resistance wasonly 4% (from 226.2 to 216.9 Ω) over the temperature rangefrom 25°C to 65°C.

3. JUNCTION TEMPERATURE MEASUREMENT

The junction temperature at the operating current can be mea-sured by switching the operating current to the probe current[16–23]. As discussed in [33], the forward voltage shows thecombined behavior of RC delay and thermal delay duringthe switching time. The RC delay is attributed to the resistanceof a LD and the capacitance of a current source.

The LD bar is operated at very high forward currents. Apower supply that drives high currents typically has largecapacitance, which can cause the large RC delay, and the tran-sient junction temperature behavior of the CuW submountcannot be documented. Fast switching circuits with two

separate power supplies have been utilized to reduce the delay[19,20]. This scheme is adopted for the current study.

A. Test SetupA test apparatus to minimize the RC delay is illustratedschematically in Fig. 4. The operating current source (LDX-36125-12: ILX Lightwave) applies the operating current witha nominal accuracy of��0.1%� 120 mA�. The probe currentsource (2401: Keithley Instruments) applies the probe currentwith a nominal accuracy of ��0.066%� 20 μA�. The twopower supplies are connected in parallel.

An N-channel metal–oxide–semiconductor field-effecttransistor (MOSFET) (IRL7833PBF: International RectifierCorporation) serves as a switch for the operating current source[19]. The probe current flows from the source (S) to the drain(D) of the N-channel MOSFET, even when the switch is off toblock the operating current. A diode (150EBU02-ND: VishayIntertechnology) is inserted between the operating currentsource and the MOSFET to prevent this undesired flow. TheMOSFET and the diode are mounted on a heat sink to dissi-pate heat at high operating currents.

The chiller (ISOTEMP I 115 V/60 HZ PD-1: FisherScientific) regulates the water inlet temperature with atemperature stability of �0.1°C, and the flow regulator(FLDW3211G: OMEGA Engineering) controls the flow rate.The optical power sensor (USB-PM-150-50: Coherent LaserGroup) measures the optical power with a nominal accuracyof �2.7% in the operating range. The current sources, theDAQs, and the optical power sensor are integrated into aLabVIEW program.

In the actual measurements, the chiller is set to produce theinlet water temperature of 20°C and the flow rate of 16 L∕h.The pressure drop from the water-cooled microchannel cooleris 34 psi. The forward voltage measurement is conducted onlywith the probe current applied to the LD bar. As an example, toapply an operating current of 80 A to the LD bar, the operatingcurrent source and the probe current source applies 79.88 Aand 120 mA, respectively, with the MOSFET switch “on.”When the optical power and the forward voltage of the LDreaches the steady-state condition, the switch is turned offto block the flow of the operating current. The data acquisitionmodule 2 (DAQ2: USB-6212: National Instruments) suppliesthe gate voltage to the MOSFET switch and the data acquis-ition module 1 (DAQ1: USB-6212: National Instruments)measures the forward voltage of the LD with 16-bit resolution

20 30 40 50 60 700

50

100

150

200

250

Res

ista

nce

of s

ingl

e em

itter

(Ω

)

Junction Temperature (°C)

Fig. 3. Electrical resistance of the single emitter as a function ofjunction temperature at I probe � 120 mA.

Fig. 4. Schematic illustration of junction temperature measurementsetup.

Research Article Vol. 55, No. 27 / September 20 2016 / Applied Optics 7489

with the maximum sampling rate of 400 kS∕s continuouslyduring the transient period.

B. Average Junction TemperatureAs mentioned earlier, the junction temperatures of emitters canhave large variations at high operating currents. However, onlya single value for the entire LD bar can be obtained from thissetup. The following investigation is conducted to define thephysical meaning of the measured value.

The emitters are connected in parallel, and thus the electri-cal resistance of the LD bar can be expressed as

Rbar�T � � 1PN

i�1 1∕Ri�T i�; (2)

where Rbar is the electrical resistance of the bar [Ω]; Ri and T iare the electrical resistance [Ω] and the temperature of the ithemitter [°C], respectively.

Let us consider a case where the junction temperature of theLD bar increases linearly from the edge to the center (ΔT �T center − T edge). This simple linear variation is analyzed toillustrate the physical meaning of the measured value. Theaverage junction temperature of this case can be expressed asT ave

j � 1N

PNi�1 T i. Then, the true forward voltage and the for-

ward voltage estimated based on the average temperature can beexpressed as

V truef �T � � Rbar�T � · Iprob;V ave

f �T � � 1

NR�T ave

j � · I prob;(3)

where V truef is the true forward voltage of the LD bar [V]; V ave

fand 1

N R�T avej � are the forward voltage [V] and the electrical

resistances [Ω] of the LD bar at the average junction temper-ature, respectively. It is to be noted that the true forward voltageand the forward voltage based on the average temperature aredifferent because the emitters are connected in parallel.

The difference between these two values provides an esti-mate about how the true junction temperature deviates fromthe average junction temperature of the bar by dividing slopeof the calibration curve [V/K]. The deviation can be defined as

δT j �V true

f − V avef

1.21 · 10−3; (4)

where δT j is the deviation of the true junction temperaturefrom the average junction temperature of LD bar [°C]; 1.21 ·10−3 is the slope of the calibration curve [V/K].

Figure 5 shows the deviation as a function of ΔT . Thedeviation is less 1°C even for ΔT of 100°C. The small changein resistance with the temperature (Fig. 3) is attributed to thisbehavior. The results imply that the junction temperaturedetermined from the forward voltage of the LD bar at theoperating current can be considered as the average junctiontemperature of the LD bar in practice. This implication willbe confirmed later with the actual nonlinear temperature dis-tribution of the LD bar.

C. Average Junction Temperature MeasurementFigure 6 shows the transient voltage behavior of the LD barobtained after blocking the operating current of 80 A. An ex-treme voltage peak at the beginning of the transient behavioris clearly visible. It was produced by an inductor voltage

attributed to the large rate of current change (79.88 A to zero)and the nonzero inductance of the LD [34,35]. The peak waslarge but disappeared quickly after 200 μs.

Based on theoretical analysis [36–39], it is known that ajunction temperature changes linearly in the square root ofthe time scale, if heat is dissipated in one direction througha homogenous material. In the case of this epi-down LD barwith the water-cooled microchannel cooler, the heat transferthrough the GaAs substrate, and convection, as well as radia-tion, to the ambient surroundings is practically negligible (lessthan 1% of the total) due to the extremely large heat transfercoefficient in the water-cooled microchannel cooler (this will bediscussed further in Section 4.B). Thus, the linear extrapolationin the square root time scale is applicable for the LD bar. Theenlarged view of the region marked by a dashed box in Fig. 6 is

00.0

0.2

0.4

0.6

0.8

1.0

1.2

δT j (

°C)

20 40 6ΔT

(°C) 0 80 100

Fig. 5. Deviation of the measured junction temperature of the LDbar from the average junction temperature of the LD bar with a lin-early changing temperature of ΔT from the edge to the center.

-2 0 2 4 61.1

1.2

1.3

1.4

1.5

120 mAVol

tage

(V

)

Time (ms)

80 A

Fig. 6. Transient voltage behavior of the LD bar obtained afterblocking the operating current of 80 A.

7490 Vol. 55, No. 27 / September 20 2016 / Applied Optics Research Article

shown in Fig. 7(a). The voltage was converted into the temper-ature using the calibration curve (Fig. 2) and it was plotted inthe square root time scale [Fig. 7(b)].

The transient junction temperature behavior can be dividedinto three zones. Zone 1 is the region dominated by the elec-trical delay. Zone 2 is the region where the linear junction tem-perature variation follows the square root time scale. When thepropagating thermal wave reaches the microcooler interface, thetransient junction temperature behavior of the CuW submountvanishes and we enter Zone 3. It is estimated from Fig. 7(b)that Zone 2 ends at t � 1.57 ms �� 1.25 ms1∕2�. The follow-ing analytical analysis was conducted to confirm Zone 2.

The transient domain governed by the CuW submount canbe calculated analytically using a time constant, which can beexpressed as [40,41]

τth �ρcpd 2

k; (5)

where τth is the thermal time constant [s]; d is the thicknessalong the heat transfer direction [m]; k is the thermal conduc-tivity �W∕m · K�; cp is the specific heat �J∕kg · K�; and ρ is thedensity �kg∕m3�. Material properties, thickness, and the calcu-lated thermal time constant of CuW are listed in Table 2. Athermal time constant value for the CuW was determined as1.37 ms, which is defined as the heating or cooling time re-quired to produce a temperature change at the heat source(junction) equal to 63.2% of the total temperature differencebetween the initial and the final temperature. This value isreasonably close to the experimental observation, which con-firms the validity of the experimental data.

The average junction temperature at the operating currentwas estimated from the linear extrapolation shown in Fig. 7(b);the estimated average junction temperature at 80 Awas 35.6°C.The discrepancy in the repeatability of the average junctiontemperature measurement was less than 0.1°C, which wasattributed to the probe current source inaccuracy.

The average junction temperatures were measured from 10to 80 A at an interval of 10 A. The results are shown in Fig. 8.The connected lines between the measured data represent thetrend of the results. As expected, the junction temperature in-creased with the current, but the rate started to decrease aroundthe threshold current (26 A), where the stimulated emissionbegan to occur; i.e., the higher wall-plug efficiency led tothe reduction of the heat dissipation as well as the junctiontemperature. The heat dissipation as a function of the forwardcurrent will be discussed further in Section 4.A.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.01.1685

1.1700

1.1715

1.1730V

olta

ge (

V)

Time (ms)

(a)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.030

31

32

33

34

35

36

Zone 3

Ave

rage

Jun

ctio

n T

empe

ratu

re (

°C)

Time1/2 (ms1/2)

Zone 1

Zone 2

(b)

Fig. 7. (a) Enlarged view of the region marked by a dashed box inFig. 6, and (b) average junction temperature in the square root timescale. The linear extrapolation provides the estimated average junctiontemperature at the operating current.

Table 2. Material Properties, Thickness, and CalculatedTime Constant Used in the Analytical Solution [28,29]

MaterialDensity(kg∕m3)

SpecificHeat

(J∕kg ·K)Conductivity(W∕m ·K)

Thickness(μm)

TimeConstant(ms)

CuW 17300 160 200 300 1.37

0 10 20 30 40 50 60 70 80 90Forward Current (A)

Ave

rage

Jun

ctio

n T

empe

ratu

re (

°C)

Threshold current (26 A)

20

24

28

32

36

40

Fig. 8. Average junction temperature at different forward currents.

Research Article Vol. 55, No. 27 / September 20 2016 / Applied Optics 7491

4. HEAT DISSIPATION AND MICROCOOLEREFFECTIVE HEAT TRANSFER COEFFICIENT

The forward voltage and the emitted radiant flux are measuredto quantify the amount of heat dissipation, using the followingrelationship [42]:

Ph�T j� � I f · V f �T j� −Φ�T j�; (6)

where Ph is the heat dissipation [W]; I f is the forward current[A]; V f is the forward voltage [V]; and Φ is the radiant flux[W]. After measuring the heat dissipation in Section 4.A, theeffective heat transfer coefficient of the water-cooled micro-channel is calculated inversely from the numerical simulation,using the measured average junction temperature and the heatdissipation in Section 4.B.

A. Measurement of Heat DissipationThe DAQ1 measured the forward voltage of the LD bar andthe optical power sensor measured the optical power (the radi-ant flux) continuously. When the optical power and the for-ward voltage of the LD reached the steady-state condition,the values of forward voltage and optical power were recorded,from which the heat dissipation was calculated using Eq. (6).

The forward voltages, electrical input power (product of theforward voltage and the forward current), optical powers, andheat dissipations were measured as a function of current with aninterval of 10 A. The results are shown in Fig. 9. The forwardvoltage and the electrical input power increased with thecurrent. The optical power was virtually negligible before thethreshold current (26 A) and increased linearly with the oper-ating current after the threshold current. Similar to the junctiontemperature, the heat dissipation increased with the currentand the rate started to decrease around the threshold current.

B. Effective Heat Transfer CoefficientThe numerical model (ANSYS 16.1) used in the current analy-sis is shown in Fig. 10. The model has the same geometry as theLD bar (23 emitters; emitter width of 200 μm and the fill factorof 50%, i.e., the pitch of 400 μm). A metallization layer (Ti/Pt/Au) between the emitter and the AuSn solder was not consid-ered in the model due to the negligible thermal resistance. Thevalues of thermal conductivity of GaAs, CuW submount, andAuSn solder used in the analysis are 54 W∕m · K [43],200 W∕m · K [28,29], and 58 W∕m · K [44], respectively.

The ambient temperature was set at 20°C (the same as theinlet water temperature). The effective heat transfer coefficientof the water-cooled microchannel cooler was assumed to beuniform on the bottom of the CuW submount. The effectiveheat transfer coefficients for natural convection (5 W∕m2 · K)and radiation (GaAs emissivity of 0.62 [45]) were set on the topand the sides of the model, albeit with the expectation of neg-ligible effects on the junction temperature.

It is important to note that Eq. (6) is applicable only whenthe junction temperature is uniform. In addition, the uniformheat dissipation would be desired to determine the effectiveheat transfer coefficient most accurately. Thus, the lowest op-erating current (10 A) was used to calculate the effective heattransfer coefficient.

The heat dissipation obtained in Section 4.A was applieduniformly on the emitters, and then, the effective heat transfer

coefficient was adjusted until the difference between the mea-sured average junction temperature and the numerically calcu-lated average junction temperature reached its minimum value.The average junction temperature difference, after typically fiveiterations, was less than 0.1°C, and the resulting effective heattransfer coefficient was found to equal 98 kW∕m2 K.

The junction temperature distribution at 20 A was also cal-culated to validate the effective heat dissipation. The difference

0 10 20 30 40 50 60 70 80 900.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Forward Current (A)

For

war

d V

olta

ge (

V)

(a)

0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

70

80

90

100

110

120

Pow

er (

W)

Forward Current (A)

Threshold current (26 A)

Electrical input power Radiant flux Heat dissipation

(b)

Fig. 9. (a) Forward voltage and (b) electrical input power, radiantflux, and heat dissipation as a function of forward current.

Fig. 10. 3D model.

7492 Vol. 55, No. 27 / September 20 2016 / Applied Optics Research Article

between the average junction temperatures (experimental andnumerical) was less than 0.1°C, which confirmed the validity ofthe effective heat dissipation.

5. NUMERICAL PREDICTION OF JUNCTIONTEMPERATURE DISTRIBUTION

It is important to understand the effect of the junction temper-ature on the heat dissipation before performing numericalanalyses at high operating currents because Eq. (6) is applicableonly when the junction temperature is uniform. The heatdissipation at 80 A was measured with three inlet water temper-atures (10°C, 15°C, and 20°C). The junction temperature ateach inlet temperature was also measured, and the resultsare summarized in Table 3.

As the average junction temperature increased from 25.6°Cto 35.6°C, the forward voltage as well as the radiant flux de-creased. The forward voltage reduction reduced the total elec-trical power consumption, while the radiant flux reductionincreased the fraction of the input power converted to heat.It is worth noting that the net heat dissipation increased onlyby 2.2 W (or 4%) corresponding to the junction temperatureincrease of only 0.6°C, as the two parameters compensatedtheir effects on heat dissipation [46]. The results indicate thatthe junction temperature dependency on the heat generation,over a range of 10°C, is not significant, which provides a tech-nical rationale for the following numerical study.

A. Temperature Distribution in LD BarThe heat dissipation and effective heat transfer coefficient ob-tained in the previous section were used to predict the junctiontemperature distribution over the LD bar numerically underhigh operating currents. The junction temperature distributionof the LD bar at 80 A is shown in Fig. 11(a). The GaAs sub-strate was not shown in order to clearly show the temperaturedistribution of the emitters.

The highest temperature occurred at the emitting side of thecenter emitter and the lowest temperature was observed at theopposite side of the edge emitter. The junction temperaturedecrease toward the edge emitter and the back end was attrib-uted to the effect of the heat spreader. Because the edge emitterand the back end had cooling area enhancement from the CuWsubmount, more heat could be dissipated due to the extra heatspreading. The maximum temperature difference was 10.1°C.This result confirms that the application of uniform heatdissipation across all the emitters in a multiemitter LD barcan be expected to provide acceptable numerical results forinput current of up to 80 A.

The junction temperature distribution was also calculated atthe operating current of 160 A. Since the test apparatus was

only capable of providing 125 A, an additional power supply(N5744A: Keysight Technologies) was connected to the oper-ating current source in parallel to provide the additional currentof 35 A. The forward voltage and the optical power at 160 Awere 1.544 V and 162.4 W, respectively, and the heat dissipa-tion was 84.7 W (65.7% wall-plug efficiency). It is to be notedthat the average junction temperature could not be measured at160 A because the threshold current of the MOSFET switchwas around 90 A.

The junction temperature distribution of the LD bar at160 A is shown in Fig. 11(b). The highest and lowest temper-atures are 47.9°C and 31.7°C; the junction temperature differ-ence is 16.2°C.

The average junction temperature of each emitter is com-pared in Fig. 12, where the only left half is shown due to thesymmetry. The average junction temperatures remain virtuallyunchanged over the center half of the emitters (from #12 to #7)and then rapidly drop toward the edge emitter. The maximumaverage junction temperature differences among the 12 emit-ters are 4.9°C and 7.8°C at 80 A and 160 A, respectively.

The front-to-back junction temperature variations withinthe center (#12) and the edge (#1) emitter are plotted inFig. 13. The junction temperature decreases exponentially fromthe emitting side to the back end. The junction temperaturevariations within the emitter are largest at the center emitter,and the magnitude increases as the operating current increases.The junction temperature variations of the center emitter are5.4°C and 8.7°C for 80 A and 160 A, respectively.

The deviations of the true junction temperature fromthe average junction temperature of the bar were calculated withthe actual nonlinear temperature distribution of the LD bar.Equation (3) was first used to determine the true forward voltageand the forward voltage from the average junction temperature:V true

f �80� � 1.168239 V and V avef �80� � 1.168242 V, and

V truef �160� � 1.157465 V and V ave

f �160� � 1.157472 V.

Fig. 11. Temperature distribution of the LD bar at (a) 80 A and(b) 160 A.

Table 3. Heat Dissipation at 80 A under Different InletWater Temperatures

T inlet [°C] 10 15 20T ave

j [°C] 25.6 29.2 35.6V f [V] 1.458 1.457 1.456I f · V f [W] 116.66 116.58 116.46Φ [W] 67.80 66.85 65.34Ph [W] 48.9 49.7 51.1

Research Article Vol. 55, No. 27 / September 20 2016 / Applied Optics 7493

The deviations were then calculated from Eq. (4); they were0.002°C and 0.006°C for 80 A and 160 A, respectively. As ex-pected from the small change in resistance with the temperature,the deviations were negligible. The results confirmed the validityof the proposed method.

B. Wall-Plug Efficiency and Spectral PowerDistributionThe junction temperature change affects the wall-plug effi-ciency, which is defined as the optical output power dividedby the electrical input power. Each emitter of the LD bar testedin the study produced an optical power of ≈7.06 W at the op-erating current of 6.95 A (the LD bar with 23 emitters at theoperating current of 160 A).

It was reported in [47] that for a single emitter (a centerwavelength of 975 nm) producing 6 W at 6 A, the wall-plugefficiency increased by 3% from 275 K (71%) to 260 K (74%).Thus, it is reasonable to assume that each emitter of the LD bar

tested in the study has similar behavior to that of the singleemitter reported in [47].

The power spectrum of the LD bar was obtained by a spec-trometer (AvaSpec-ULS3648-USB2: Avantes) combined with acosine corrector (CC-UV/VIS/NIR-5.0: Avantes). The diam-eter of the corrector was larger than the LD bar to ensure thatthe spectrometer received light from all 23 emitters equally.The output obtained from the measurement system was theirradiance (W∕m2) of the LD bar as a function of wavelength.The power spectrum was obtained by normalizing the irradi-ance distribution by the peak irradiance. The results obtained at30, 60, and 120 A are shown in Fig. 14.

LDs are known to show the spectral redshift (i.e., higherpeak wavelength) at higher junction temperatures due to thereduced bandgap energy [48]. The spectral redshift caused bythe junction temperature has been reported to be 0.28 nm∕K[49] and 0.32 nm∕K [50] for 808 nm and 980 nm LDs,respectively. The results in Fig. 14 show the redshift of≈0.3 nm∕K, which is consistent with the reported values.

The results also show that the spectrum is broadened as thecurrent increases; i.e., the larger full width at half-maximum atthe higher forward current. The asymmetry of the spectrum(i.e., more broadening toward the lower wavelength) becomesmore severe as the current increases. Both broadening andasymmetry are attributed to the larger junction temperaturegradient at the high currents.

The analysis was based on a very large heat transfer coeffi-cient. In practice, various thermal solutions can be employedfor cooling the LD bar. In terms of the coefficient of perfor-mance (COP), the lower heat transfer coefficients (i.e., the de-creased flow rate) can reduce the operating costs. However, thejunction temperature will rise and the temperature variationwithin the LD bar will also increase with lower heat transfercoefficients. This will increase the asymmetry of the spectralpower distribution (SPD) and the peak wavelength shift, whichcan reduce the pumping efficiency [6].

A high heat transfer coefficient is desired to increase thepumping efficiency, which can be achieved with an extremeflow rate of a coolant. However, the higher flow rate reduces

1 2 3 4 5 6 7 8 9 10 11 1220

22

24

26

28

30

32

34

36

38

40

42

44

46

48

160 A

Ave

rage

Jun

ctio

n T

empe

ratu

re (

°C)

Emitter Number

80 A

Fig. 12. Average junction temperature of each emitter in the lefthalf (symmetry).

0 1 2 3 40

1

2

3

4

5

6

7

8

9

Center Emitter

Edge Emitter

Center Emitter

Edge Emitter

Junc

tion

Tem

pera

ture

Var

iatio

ns (

°C)

Distance along the emitter (mm)

160 A 80 A

Fig. 13. Junction temperature variations along the emitter.

924 926 928 930 932 9340.00

0.25

0.50

0.75

1.00

1.4 nm0.7 nm

120A60A

Rel

ativ

e P

ower

Wavelength (nm)

30A

2.0 nm

Fig. 14. Normalized power spectrum at 30, 60, and 160 A.

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the COP, which increases the operating cost. In addition, it canaccelerate the erosion process of the surface structures insidemicrochannels, which will increase the junction temperatureand will eventually reduce the lifetime of the LD bar [51,52].Consequently, optimization of thermal solutions for high-power LD bars should be sought while considering theoperating cost as well as various thermal, mechanical, andoptical aspects of the system.

6. CONCLUSIONS

A hybrid experimental and numerical method was proposedand implemented for predicting the junction temperature dis-tribution of a high-power LD bar. A commercial water-cooledLD bar was utilized to illustrate and validate the proposedmethod. The average junction temperature and the heat dissi-pation were measured, and the effective heat transfer coefficientof the cooling system was determined inversely using numericalsimulation. The characterized properties were used to predictthe junction temperature distributions of the LD bar at the ex-treme operating currents. The results showed significant junc-tion temperature variations not only among emitters (7.8°C)but also along each emitter (8.7°C) at 160 A, which increasedthe asymmetry of the power spectrum. In addition, the ex-pected redshift and the spectral broadening were observed.The proposed method can be used to determine the properoperation condition of the LD bar as well as to evaluate designsduring packaging platform development. The future work willaddress a methodology to define the optimum design of LDbars considering the COP, performance, and reliability.

Funding. Defense Advanced Research Projects Agency(DARPA) (FA8650-15-1-7526).

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