Optics Communications 282 (2009) 1385–1392

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Optics Communications

journal homepage: www.elsevier .com/locate /optcom

High conversion efficiency solar laser pumping by a light-guide/2D-CPC cavity

Rui Pereira *, Dawei LiangCEFITEC, Departamento de Física, FCT, Universidade Nova de Lisboa, 2825, Campus de Caparica, Portugal

a r t i c l e i n f o

Article history:Received 1 February 2008Received in revised form 31 October 2008Accepted 15 December 2008

Keywords:LasersSolid-statePumpingSolar-pumped

0030-4018/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.optcom.2008.12.052

* Corresponding author. Tel.: +351 212948576; faxE-mail addresses: r.p.pereira@gmail.com (R. Pereir

a b s t r a c t

A simple and efficient light-guide/2D-CPC solar pumping approach is proposed. A fused silica light-guideassembly is used to transmit 6 kW concentrated solar power from the focal spot of a large parabolicmirror to the entrance aperture of a 2D-CPC pump cavity, where a long and thin Nd:YAG rod is efficientlypumped. Numerical calculations are made for different light-guides, 2D-CPC cavities and laser rods. Thelaser output power is investigated through finite element analysis. With 4 mm diameter rod, the maxi-mum calculated laser power of 75.8 W is obtained, corresponding to the conversion efficiency of morethan 11 W/m2. The tracking error dependent laser power losses are lower than 4%. A small scale proto-type was constructed and tested, reaching 8.1 W/m2 conversion efficiency.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

The idea of directly converting broad-band solar radiation intocoherent and narrow-band laser radiation has gained an increasingimportance. If lasers are needed in remote locations where sunlightis abundant and other forms of energy are scarce, a solar laserwould seem to be a natural choice. Compared to electrically pow-ered lasers, the solar laser is much simpler and more reliable due tothe complete elimination of the electrical power generation andpower conditioning equipment. This technology is particularlyattractive for space applications where extended run times are re-quired and where compactness, reliability, and efficiency are criti-cal. Since the first reported Nd:YAG solar laser [1], improvement inthe laser efficiency has always been a key issue in solar-pumped la-ser researches [2–4]. Recently, a more efficient solar laser systemhas been put forward, achieving a conversion efficiency of18.7 W/m2 by using a Cr3+:YAG laser rod [5]. The Nd:YAG solar la-ser efficiency and beam quality still need, however, furtherimprovements before it can compete with the diode-pumped so-lid-state lasers.

A typical solar-pumped Nd:YAG laser utilizes a two-stage sys-tem that incorporates a first-stage primary parabolic mirror anda second-stage CPC concentrator. The laser head and its associatedoptics are usually placed near or directly at the focus of the collec-tor. Non-imaging optics plays an important role in solar lasers byproviding means for concentrating sunlight to intensitiesapproaching the theoretical limit. The compound parabolic con-centrator [6] (CPC) gives the maximum concentration for a twodimensional cavity. Although the non-imaging cavity provides a

ll rights reserved.

: +351 212948549.a), dl@fct.unl.pt (D. Liang).

large amount of pump power, it does not give a Gaussian absorp-tion pumping profile [7], affecting hence the laser beam quality.For low-average-power applications, in which thermal lensing ismoderate, the overlap of the laser mode with an excitation peakedat the centre of the rod can be advantageous. However, at high-average-power, even a uniform gain distribution in a water-cooledlaser rod has been shown to induce a non-parabolic heat distribu-tion as a result of the temperature dependence of the thermal con-ductivity [8]. This results in a radially dependent refractive powerof the thermal lens, with a maximum on the rod axis. When theabsorption profile is centrally peaked, the temperature on the axisincreases further, resulting in stronger thermal lensing at the cen-tre, higher-order aberrations at the periphery, and larger stress inthe laser rod compared with those of uniform excitation. Conse-quently, a power deposition that has a slight minimum at the cen-tre of the rod can be useful to scale to high-average-powers.Minimizing a laser rod volume reduces cost, and reducing thediameter makes the rod more resistant to thermal stress. Also, withsmaller rod diameter, high-order resonator modes are suppressedby large diffraction losses, and beam quality improves.

The resonator stability depends also on how well the Sun istracked. Tracking displacements move the centre of the absorptiondistribution inside the laser crystal [9]. If the centre of the thermallensing moves, it acts as a resonator misalignment and less outputlaser power is obtained. Tracking error compensation is thereforeneeded to obtain a stable laser performance [10].

The fused silica and hollow lens ducts have been successfullyused for end-pumping solid-state lasers [11,12]. The proposedfused silica light-guide assembly consists of three fused silicalight-guides of rectangular cross-section by which the concen-trated solar power of circular spot from the primary parabolic con-centrator is both efficiently collected and transformed into a

Incident concentrated solar light spot

First-stage 3D-CPC

a

1386 R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392

rectangular light column, facilitating the further light coupling intothe small diameter laser medium by a 2D-CPC cavity. The proposedsystem demonstrates low sensibility to the minor angular trackingerrors. The calculated laser conversion efficiency of 11 W/m2 andthe optical efficiency of 27% for the 4 mm diameter, 80 mm lengthNd:YAG laser rod are reported here. Tracking error dependent laserpower losses lower than 4% are numerically obtained. Experimen-tal results of small scale prototype are reported with a maximumlaser output power of 14.4 W for an absorbed solar pump powerof 71.3 W, corresponding to the conversion efficiency of 8.1 W/m2.

Cooling water

Second-stage 2D-CPC

6mm diameter Nd:YAG laser

rod

Flow-tube

x

yz

Second-stage 2D-CPC cavity

b

Fig. 1. (a) Double-stage 3D-CPC/2D-CPC scheme, and (b) enlarged view of the2D-CPC cavity with the laser rod of 6mm diameter and 72 mm length.

2. Numerical calculations

2.1. Solar spectra, tabulated model of absorption for Nd:YAG materialand overlap between the Nd:YAG absorption spectra and the solarspectra

The standard solar spectra [13] for one and a half air mass(AM1.5) are used as the reference data for consulting the spectralirradiance (W/m2/nm) at each wavelength. The irradiance cumula-tive integral of the whole solar spectra equals the typical terrestrialvalue of 900 W/m2, which agrees well with the experimental data[4].

For Nd:YAG laser material, 22 absorption peaks ranging be-tween 527 nm and 880 nm are defined in the Monte Carlo ray-trac-ing software. For a 1.1 at.% Nd:YAG laser medium, the highestabsorption coefficient reaches a = 10 cm�1, while the lowest isabout a = 1.5 cm�1. The averaged FWHM absorption bandwidthof each peak is about 1 nm [14]. All the above central wavelengthsand their respective absorption coefficients are added to the glasscatalogue for Nd:YAG material. On the other hand, the solar irradi-ance values of the 22 central wavelengths can be consulted fromthe standard solar spectra for AM1.5 and saved as the source wave-length data.

2.2. Double-stage 3D-CPC/2D-CPC cavity

The astigmatic corrected target aligned (ACTA) solar concentra-tor system [4] provided the effective approach for pumping the so-lar laser crystal, enabling the convenient placement of the lasersystem on a horizontal optical table. The double-stage secondaryconcentrator shown in Fig. 1 is consisted of a 3D-CPC reflector fol-lowed by a 2D-CPC reflector. Concentrated solar light at 11.5o halfangle cone entered the 3D-CPC, which funneled the light beam outat 55o half angle. The emitted light entered the 33 � 24 mm2 aper-ture of the 2D-CPC, illuminating an anti-reflection end-coated 1.1%Nd:YAG laser rod, 6 mm in diameter and 72 mm in length,mounted inside a quartz flow-tube along the 2D-CPC axis. The laserresonator design was commonly plane-parallel. For the segmentedprimary parabolic mirror with 6.85 m2 collection area, 45 W laserpower was measured.

2.2.1. Numerical analysis for the double-stage 3D-CPC/2D-CPC cavitySeveral factors are important for the correct numerical analysis

of the 3D-CPC/2D-CPC solar laser cavity. Eighty-five percent reflec-tivity for the first-stage ACTA mirror, 90% for the folding mirror and95% for all the other reflector surfaces are assumed. For the terres-trial insolation of 900 W/m2, 6165 W of solar power reaches thefirst-stage ACTA mirror. If 14% overlap between the Nd:YAGabsorption spectra and the solar spectra is considered [2], the totalabsorbable solar power lying within the Nd:YAG absorption bandsequals to 864 W. Other non-useful solar power is either filtered orsimply passes through the rod without significant absorption. Thepower of 864 W is hence the final value attributed to a circularlight source of 3.4 m diameter, representing the absorbable incom-

ing radiation to the ACTA mirror, in the ray-tracing. The solar halfangle of 0.27o is also considered.

The reported dimensions of the first-stage ACTA solar collectorare utilized in the ray-tracing software. The profiles of both the3D-CPC and the 2D-CPC [4] are essential for designing both theaxially symmetric 3D-CPC concentrator and the 2D-CPC pumpingcavity. The laser rod, the cooling water and the flow-tube aredimensioned directly in the ray-tracing software.

For the efficient cooling of the laser rod, the water gap betweenits surface and the inner surface of the flow-tube is set at 1.5 mm.The quartz flow-tube wall thickness is 1 mm. The side surface ofboth the laser rod and the flow-tube are modeled as uncoated.The solar spectra absorption coefficients for both cooling waterand quartz flow-tube are defined accordingly. The cylindrical rodis divided into a total of 40,000 zones. During ray-tracing, the pathlength in each intercepted zone is found. With this value and theabsorption coefficients of the 22 absorption wavelengths for theNd:YAG material, the power absorbed by the laser rod can be cal-culated by summing up the absorbed pump radiation of all thezones within the rod. The absorption distributions for the laserrod of 72 mm length and 3 mm to 6 mm diameters are analyzedin Section 2.4.

2.3. Double-stage light-guide/2D-CPC cavity

A double-stage light-guide/2D-CPC cavity is here proposed. Inorder to make a correct comparison with the 3D-CPC/2D-CPC cav-ity, the input-end of the proposed cavity, shown in Fig. 2, is placedat the focal region of a primary parabolic concentrator of 3.4 m

Nd:YAG laser rod

Curved reflectors

2D-CPC cavity Coolingwater

Output-end of the fused silica light- guide assembly

2D-CPC cavity

x

yz

Incident concentrated solar light spot

Fused silica light guides assembly

W1=23mmL1=23mm

T=9mmInput face

Light guides output power distribution

W2=9mm

L2=69mm

a

b

Fig. 2. (a) Double-stage light-guide/2D-CPC cavity, and (b) enlarged view of the2D-CPC cavity.

x

zy

y

x

L2=69mm

W1=23mm

L1=23mm

37º 37º

T=9mm

W2=9mm

a

b

Fig. 3. Incident concentrated solar light spot at the input face of the light-guideassembly (upper figure) and the correspondent pump distribution (lower figure)from the rectangular output end (a) zero tracking error (b) 2 mrad tracking error(vertical unit in W/cm2).

R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392 1387

diameter, corresponding to 6.85 m2 collection area. The parabolicmirror has now a comparatively short focal distance of 1.32 mand a large rim-angle of 60o. The incoming solar power is thereforestrongly focused into a circular light spot of near Gaussian distribu-tion, as shown in Fig. 2a.

The 9 � 23 mm2 input-end of each of the three fused silicalight-guides is mechanically positioned, with the optimized angleof 37� relative to each other, at the focal area of the first parabolicmirror, forming the square input area of 23 � 23 mm2 of theassembly, as shown in Fig. 3a. The experience of our laboratoryin manipulating fused silica light-guides in high temperature envi-ronment (hydrogen flames) and pure graphite mould bending pro-cess [15] can be utilized to achieve the correct curvature of thelight-guides. Based upon both the refractive and the total internalreflection principles, the concentrated power can be efficientlytransmitted by high optical quality (99.9999% purity) fused silicalight-guides without extra cooling measures. One part of the con-centrated solar power from the primary mirror is easily transmit-

ted by the central light-guide 14 cm in height to the entrance ofthe 2D-CPC cavity, while the other part of large divergent anglesis efficiently transmitted through the two inclined light-guides of7 cm curvature radius. The near Gaussian profile of the concen-trated light spot shown in Fig. 2a, incident on the input face ofthe light-guide assembly is therefore transformed into a rectangu-lar light column at the assembly output end. By both reducing thewidth of the light-guide assembly from W1 to W2 and increasingthe length from L1 to L2, the absorption distribution profile canbe improved and smaller diameter rods can be used. In addition,good tracking error compensation is achieved by this simplelight-guide assembly. A small dislocation of the solar spot alongthe x-direction at the input face of the light-guide assembly causesthe slight movement of the pump light at the output end along they-axis, maintaining its profile along the x-axis, as shown in Fig. 3.The dislocations of the focal spot along the y-direction effects areattenuated owing to the pump light homogenization capacity byeach rectangular light-guide.

To obtain the smooth gain distribution along the laser rod, therays coming from a pump source should hit each point of the rod’ssurface over a wide range of angles. In addition, weak average

θi

ρ

θ

y

x

C’ C

Truncation line

A HT = 6mm

Fig. 4. Cross section of the 2D-CPC pump cavity designed with the edge-rayprinciple of non-imaging optics.

1388 R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392

absorption of the pump power helps to prevent non-uniformity inenergy deposition [8]. Therefore, it is straightforward to use aclosed cavity pumping arrangement formed by the light-guideassembly and a high-reflectivity non-imaging concentrator.

The design of the 2D-CPC cavity is based on the edge-ray prin-ciple [6] to non-planar absorbers. The edge-ray principle for a cir-cular absorber of radius a is a two-region reflector defined by:

q ¼ ah for jhj � ha þ p=2 ð1Þ

q ¼ hþ ha þ p=2� cosðh� haÞ1þ sinðh� haÞ

for ha þ p=2 � jhj � 3p=2� ha

ð2Þ

As shown in Fig. 4, for a ray that enters the CPC with an angle ofhi and strikes the rod tangent to its surface, q ¼ �RA is the distancealong the ray path from the last intersection point of the ray withthe CPC, A, to the tangent point of the rod, R. h is the angle mea-sured from the negative y-axis to the line segment joining the cen-tre of the rod and the point R. The entrance aperture �CC 0 is equal to2ap=sinðhaÞ. The CPC cavity design depends therefore on the accep-tance angle ha and on the rod diameter.

In our CPC design, a is the laser rod radius and the CPC extrusionlength depends directly on the total length of the light-guides. Boththe laser rod and the 2D-CPC internal surface are actively cooled byfilling up the CPC cavity with flowing water, reducing considerablythe acceptance angle ha and eliminating hence the necessity of acooling flow-tube as illustrated in Fig. 2b. The rod is now placedat the optimum position determined by the CPC parameters. TheCPC cavity can be truncated by the truncation height HT =6 mm rel-ative to the rod axis due to the reduction of the acceptance anglecaused by the refractive influence of the water, reaching a nearclose-coupled cavity which also reduces the pump power lossesby absorption in water. The light-guide assembly output end, to-gether with the two curved reflectors, closes the 2D-CPC cavity.

2.3.1. Optical parameters for the double-stage light-guide/2D-CPCcavity

The numerical analysis of the light-guide/2D-CPC cavity is sim-ilar to that of the 3D-CPC/2D-CPC. The power of 864 W is the valueattributed to the circular light source of 3.4 m diameter, 1.32 m fo-cal distance and 60o rim-angle. The solar half angle of 0.27o is con-sidered in the ray-tracing analysis as well. Some practicalconsiderations are important for the ray-tracing analysis. Fused sil-ica material of high optical purity is used to manufacture the light-guides. Both the input and the output faces of the guides are opti-cally polished to allow for the highest transparency for the pumpradiation. The highly concentrated solar flux can easily damageanti-reflection coatings and these polished surfaces are thereforeassumed as uncoated. The 2D-CPC cavity internal surface, thetwo curved reflectors and the two parallel end plates (not shownin Fig. 2) are gold reflectors. The pump wavelengths above

500 nm are therefore efficiently reflected to the laser rod, whilethe wavelengths below 500 nm are poorly reflected and absorptionoccurs at the cavity walls. The efficient cooling of both the laser rodand 2D-CPC pumping cavity is, for this reason, of vital importance.

The cylindrical Nd:YAG rod is divided into a total of 40,000zones. By taking into account the matching between the solar radi-ation spectra with the absorption spectra of the Nd:YAG medium,the cooling water and the fused silica light-guides, the absorbedpower can be calculated. Ninety percent first parabolic mirrorreflectivity, 85% folding mirror reflectivity, 95% 2D-CPC gold cavityreflectivity are also assumed. Five million rays are considered inthe ray-tracing calculations. The cross-sectional absorption distri-butions perpendicular to the rod axis, for laser rods diameters be-tween 3 mm and 6 mm, are also examined in Section 2.4. In orderto make a fare comparison with the 72 mm length rods from the3D-CPC/2D-CPC case, the total length of the laser rods is set at110 mm, of which 70 mm is effectively pumped, leaving 20 mmlength on each edge.

2.4. Absorption distribution analysis of the double-stage 3D-CPC/2D-CPC cavity and the double-stage light-guide/2D-CPC cavity

As a typical illustration, the central cross-sectional absorptiondistribution perpendicular to the rod axis is chosen. The grey-scaleabsorption distributions for the rods of 3 mm and 6 mm diameter,pumped by either the 3D-CPC/2D-CPC cavity or the light-guide/2D-CPC cavity, are given in Figs. 5 and 6, respectively. Black signifiesnear maximum absorption, whereas white signifies little or noabsorption. The absorption profiles are represented by theabsorbed flux/volume distribution along both the central cross-section row and the central cross-section column of the rods. Inthe 3D-CPC/2D-CPC case, for the 6mm diameter rod, the maximumgain region is located in the lower portion of the laser rod, near thecusp of the 2D-CPC concentrator. This typical location of the max-imum gain for CPC schemes is not optimal for laser operation in theTEM00 mode. This gain location is slightly removed by the water-flooded 2D-CPC cavity due to the absorption of the pump powerby the cooling water. Although both the 3D-CPC/2D-CPC and thelight-guide/2D-CPC cavity do not provide optimal absorption pro-files, they give high absorption efficiencies, suitable for high powermultimode regime.

2.5. Numerical analysis of the laser output power

Numerical ray-tracing code is used to maximize the absorbedpump flux within the laser rod. The absorbed pump flux data fromthe ray-tracing analysis is then processed in a laser cavity finiteelement analysis (FEA) software. Output couplers of differentreflectivities, ranging from 80% to 98%, are tested to maximizethe multimode laser power. The plane-parallel optical resonatorof 450 mm length and the averaged solar pump wavelength of660 nm are considered. The round-trip loss is calculated accord-ingly to the chosen laser rod. For the 1 at.% Nd:YAG laser rod of6 mm diameter, 72 mm length, a round-trip loss of 5.0% is consid-ered [2]. The laser output power of 48.6 W is finally achieved forthe 3D-CPC/2D-CPC scheme by adopting the output coupler of95% reflectivity, matching well with the published experimentaldata [4] of 45 W.

In the laser cavity FEA analysis, the output laser power of48.6 W can be optimized to 57.6 W by using the 6 mm diameter la-ser rod of only 50 mm in length, rather than 72 mm. The laser res-onator round-trip loss can, therefore, be reduced from 5.0% to 3.6%.There is still enough space for both mounting and cooling the laserrod, through the 2D-CPC cavity of only 33 mm in length. In order toevaluate the laser performances of the 3D-CPC/2D-CPC cavity, theNd:YAG laser rods of 3, 4, 5 and 6 mm diameters are tested individ-

Fig. 5. Grey-scale absorption distribution for the 72 mm length Nd:YAG rodspumped by the 3D-CPC/2D-CPC cavity: (a) 3 mm diameter, and (b) 6 mm diameter(vertical unit in W/mm3).

Fig. 6. Grey-scale absorption distribution for the 72 mm length Nd:YAG rodspumped by the light-guide/2D-CPC cavity: (a) 3 mm diameter (b) 6 mm diameter(vertical unit in W/mm3).

R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392 1389

ually. Again, the resonator cavity length of 450 mm and the aver-aged solar pump wavelength of 660 nm are assumed. The outputcoupler of different reflectivities is utilized to optimize the outputlaser power for each laser rod. The multimode and the TEM00 laserpowers for both 50 mm and 72 mm laser rods with different diam-eters are shown in Fig. 8.

For the analysis of the laser performances of the light-guide/2D-CPC cavity, the optimized absorbed pump flux data obtained in theray-tracing analysis is similarly processed by the FEA software. Theplane-parallel laser resonant cavity of 450 mm length is used. A110 mm length laser rod is here considered, leading to 7.14%round-trip loss. The averaged solar pump wavelength of 660 nmis also assumed. Output coupler reflectivity is used for maximizingthe multimode laser power for different rod diameters.

The length of each light-guide and the relative angular arrange-ment are important parameters for achieving the optimal solarpower transmission to the second-stage 2D-CPC cavity. The angu-lar position of each light-guide is carefully optimized by consider-ing the concentrated solar spot angular distribution. Theconcentrated solar power is now fully collected and efficientlytransmitted with small angles through the guides. Smoothlycurved light-guides, shown in Fig. 2a, are crucial to assure the totalinternal reflection. The optimum curvature of each outer light-guide is found by detecting the maximum solar power at the cor-

respondent output end. The length of each light-guide is deter-mined accordingly.

The input area of each light-guide assembly is another key issuefor the efficient laser production. An oversized input area of thelight-guides results in the total capture of the concentrated solarpower. The total rectangular output area of the light-guides is con-sequently large, which adversely affects the further light concen-tration by the second-stage 2D-CPC. If a small input area isconsidered, any small tracking error can cause the incident pumpspot to partially miss the input area of the light-guide assemblyand the light coupling losses are hence largely increased. As a re-sult, it is relevant to evaluate the optimized input area of thelight-guide assembly. Fig. 7 shows both the multimode andTEM00 laser output behaviour for different widths, W, of the squareinput area of the light-guide assembly. A slight decrease of TEM00

laser power is revealed as the width increases. The maximum mul-timode laser power is obtained through the 23 � 23 mm2 inputareas, corresponding to the 9 mm thickness of each single light-guide. Similar to the analysis of the 3D-CPC/2D-CPC, by using thelaser rod of only 80 mm in length, rather than 110mm, the laserresonator round-trip loss can, therefore, be reduced from 7.14%to 5.4%. Again, the space for mounting the laser rod is enough, be-cause the 2D-CPC cavity has only 70 mm length. The multimodeand the TEM00 laser powers for both 80 mm and 110 mm rod

PMM Ø3mmPMM Ø4mmPMM Ø5mmPMM Ø6mm

PTEM00 Ø3mmPTEM00 Ø4mmPTEM00 Ø5mmPTEM00 Ø6mm

TEM

00 la

ser p

ower

(W)

20

40

60

80

20 21 22 23 24 25 26

Width of the light guides input area (mm)

Mu

ltim

od

e la

ser

po

wer

(W

)

0

5

10

15

20

25

Fig. 7. Multimode and TEM00 laser output power as a function of the width of thelight-guide assembly input area.

1390 R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392

lengths and for different diameters are also shown in Fig. 8, allow-ing for the good comparison between the two pumpingapproaches.

For the 3D-CPC/2D-CPC approach, with the increase of the roddiameter, there exist gradual increases in the multimode laserpower, reaching its maximum for 6 mm diameter. The productionof TEM00 laser power is, however, adversely affected. For the light-guide/2D-CPC approach, the multimode laser power increases untilthe optimal laser rod diameter of 4 mm is reached. For large roddiameters, the light-guide/2D-CPC approach shows a slight de-crease in multimode laser power, indicating the improved powerconcentration capacity, suitable for pumping the small diameterrod. Small rod diameters are effective in producing TEM00 laserpower. The reduction in the length of the laser rod and the conse-quent decrease in the round-trip losses correspond to an increaseof more than 15% for both multimode and TEM00 laser power.

LG PMM (110mm) LG PMM (80mm)

3D-CPC PMM (72mm) 3D-CPC PMM (50mm)

LG PTEM00 (110mm) LG PTEM00 (80mm)

3D-CPC PTEM00 (72mm) 3D-CPC PTEM00 (50mm)

0

20

40

60

80

100

2Laser rod diameter (mm)

Mul

timod

e la

ser p

ower

(W)

0

5

10

15

3 4 5 6 7

TEM

00 la

ser p

ower

(W)

Fig. 8. Calculated multimode and TEM00 laser output power as a function of laserrod diameter for both the 3D-CPC/2D-CPC approach and the light-guide/2D-CPCapproach. Both optimized and non-optimized rod lengths are considered.

2.6. Analysis of the tracking error dependent laser output power

The tracking error of a primary mirror may reach 2 mrad [16].For the focal distance of 8.5 m, 2 mrad angular tracking error cor-responds to 17 mm transversal shift from the ideal focal positionof the ACTA mirror. If the focal spot moves in the direction parallelto the laser rod axis, then the strong pump absorption distributionwill be shifted correspondingly along the rod in the opposite axialdirection, causing only a minor reduction in output laser power.However, if the focal spot moves in the direction perpendicularto the rod axis (the transversal shift as we named), then the strongabsorption distribution within the rod will be shifted laterally inthe direction perpendicular to the rod axis, causing significantreduction in laser output power. It is therefore understandablefor us to concentrate on the tracking error evaluation for onlythe transversal shift of the focal spot in ray-tracing analysis.Fig. 9a demonstrates the grey-scale absorption distribution forthe 6.0 mm diameter Nd:YAG rod, pumped by the concentratedlight spot with 17 mm transversal shift at the input-plane of the3D-CPC/2D-CPC cavity. By comparing Fig. 5b with Fig. 9a, signifi-cant difference is found between the absorption distributionswithout and with tracking errors, respectively. The transversalshift to the right side causes the dislocation of the absorbed pumppower to the left bottom side of the rod.

Fig. 9. Grey-scale absorption distribution for the 6mm diameter rod pumped by:(a) the 3D-CPC/2D-CPC, and (b) the light-guide/2D-CPC schemes, for the angulartracking error of 2 mrad (vertical unit in W/mm3).

LG ΔPMM (110mm) LG ΔPTEM00 (110mm)LG ΔPMM (80mm) LG ΔPTEM00 (80mm)3D-CPC ΔPMM (50mm) 3D-CPC ΔPTEM00 (50mm)3D-CPC ΔPMM (72mm) 3D-CPC ΔPTEM00 (72mm)

0%

2%

4%

6%

8%

10%

12%

14%

2 3 4 5 6 7Laser rod diameter (mm)

Las

er o

utp

ut

po

wer

loss

Fig. 10. Tracking error dependent laser power losses as a function of the laser roddiameter, both for optimized and non-optimized rod lengths.

0

2

4

6

8

10

12

14

0 10 20 30 40 50 60 70 80Absorbed solar power (W)

Mu

lti-

mo

de

la

se

r o

utp

ut

p

ow

er

(W)

Fig. 11. Laser output power as a function of the absorbed solar pump power.

R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392 1391

For the light-guide/2D-CPC approach, the same calculation iscarried out as for the ACTA solar laser system analysis. The trackingerror of 2 mrad is also assumed for the primary parabolic concen-trator of 3.4 m diameter and 1.32 m focal distance, causing in thiscase 2.7 mm transversal shift from the ideal focal position. Simi-larly, we concentrate here only on the tracking error analysis forthe transversal shift of the focal spot in ray-tracing analysis.Fig. 9b shows the corresponding grey-scale cross-sectional absorp-tion distribution for the 6.0 mm diameter Nd:YAG. Contrary to theACTA case, the absorption profiles do not reveal significant differ-ences when compared with Fig. 6b for zero tracking deviation. Atransversal shift of the solar spot at the input face causes only aslight change of the pump profile along the direction parallel tothe rod axis at the output end of the light-guide assembly. As a re-sult, the absorbed pump power distribution is preserved at thetransversal axis direction. The pumped region of the laser rod isonly slightly dislocated from its original central location. An excel-lent tracking error compensation capacity is therefore achieved.

Table 1Multimode and TEM00 laser output power improvements for different laser rod diameters

Laser output power improvements (%)

Laser rod diameter 3 mm

Multimode Non-optimized rod length 72.4Optimized rod length 70.6

TEM00 Non-optimized rod length 63.8Optimized rod length 60.6

The tracking error dependent laser power losses is calculated bydividing the difference between the power values without andwith tracking errors by the original power value without trackingerror. The power losses evaluation as a function of the laser roddiameter, both for multimode and TEM00 laser powers, is shownin Fig. 10. Both the 3D-CPC/2D-CPC and the light-guide/2D-CPC ap-proaches are analysed.

Large tracking errors losses for both multimode and TEM00

operation are dominant phenomena in the 3D-CPC/2D-CPC ap-proach. For 2 mrad tracking error, the laser power loss reaches12.3% when the rod of 6 mm diameter and 72 mm length is used.As the rod diameter increases, there exists a slow increase in mul-timode output laser power losses. For TEM00 laser power, a mini-mum power loss of 9.3% occurs for the laser rod of 5 mmdiameter. There exists a general reduction in laser power lossesby the light-guide/2D-CPC scheme. Compared with the 3D-CPC/2D-CPC scheme, lower and more stable laser power losses, bothin multimode and in TEM00, are observed. The maximum laserpower losses of 4% for multimode and 3% for TEM00 are observed.The tracking error dependent laser power losses remain stable forany rod diameter.

3. Experimental results

A small scale of the numerically tested light-guide/2D-CPC set-up was constructed in order to prove the proposed pumping con-cept. A parabolic mirror, 1.5 m diameter, 0.66 m focal length and85% reflectivity was used to collect 1258 W of solar power.

Fused silica is an ideal optical material for a Nd:YAG laserpumping since it is transparent over the Nd:YAG absorption spec-trum. Fused silica materials are also effective in absorbing undesir-able radiations to the laser crystal. Furthermore, it has a lowcoefficient of thermal expansion, and is resistant to scratchingand thermal shock.

Fused silica light-guides optically polished both in the input andoutput ends were used. The light-guides were curved under hightemperature environment (hydrogen flames). A pure graphitemould was also used to help the correct bending of the light-guides. The 7 � 18 mm2 input-end of each of the three fused silicalight-guides was mechanically positioned, with the optimized an-gle of 37� relative to each other, at the focal area of the first para-bolic mirror, forming the square input area of 7 � 7 mm2. Thecentral light-guide was 11 cm in height. Slight misalignments wereobserved due geometrical imperfections of the light-guides.

The gold plated 2D-CPC cavity composed of the internal surface,the two curved reflectors and the two parallel end plates were ma-chined. A cylindrical 1.1% Nd:YAG rod, AR coated on both ends,3 mm in diameter and 76 mm in length was tested. The resonantcavity of 204 mm in length was formed by the PR output mirrorof 92% reflectivity and the HR mirror of 99.97% reflectivity, bothwith 1m radius of curvature.

The cw laser output power (Fig. 11) was measured as a functionof the absorbed solar pump power by partially blocking the para-bolic mirror with different opaque covers.

and lengths pumped by the light-guide/2D-CPC cavity.

4 mm 5 mm 6 mm

58.1 43.5 27.854.0 38.9 27.4

33.5 31.6 21.730.2 25.1 19.9

Table 2Laser tracking error improvements for different laser rod diameters and lengths pumped by the light-guide/2D-CPC cavity.

Tracking error improvements (%)

Laser rod diameter 3 mm 4 mm 5 mm 6 mm

Multimode Non-optimized rod length 69.9 68.5 68.1 69.3Optimized rod length 65.9 64.3 64.0 64.9

TEM00 Non-optimized rod length 78.1 76.6 74.5 73.6Optimized rod length 72.6 70.3 68.1 69.1

1392 R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392

For the absorbed solar pump power of 71.3 W, the measured cwmultimode laser output power was 14.4 W at 1064 nm. An overallefficiency of 1.15% was obtained, corresponding to the conversionefficiency of 8.1 W/m2. The measured M2

x and the M2y were 21.2

and 22.7, respectively. The beam profile was near rotationally sym-metric and no significant variations in the multi-mode laser beamprofile were found with pump power variations.

4. Conclusions

A simple and efficient light-guide pumping scheme for solar-pumped solid-state lasers is proposed. Non-sequential ray-tracingcode and finite element analysis are used to firstly evaluate the la-ser output performance of the 3D-CPC/2D-CPC scheme, providingthe reference values for the numerical analysis of the proposedlight-guide/2D-CPC pumping approach.

Table 1 reveals the significant improvements both in the multi-mode and in the TEM00 laser output power, for both the non-opti-mized and optimized laser rod lengths. For both multimode andTEM00 laser powers, the improvements increase with the reductionin the laser rod diameters. For the laser rod diameter of 3 mm,72.4% enhancement is achieved for non-optimized laser rod lengthpumped by the light-guide/2D-CPC cavity. With the reduction ofthe laser rod diameter, the improvements in the TEM00 laser out-put power also reach more than 60%. For the 4 mm diameter rod,the maximum laser power of 75.8 W is obtained for 6165 W col-lected solar power, which corresponds to the conversion efficiencyof more than 11 W/m2.

The tracking error compensation capacity revealed by the pro-posed approach is also significantly enhanced when compared tothe 3D-CPC/2D-CPC scheme. The tracking error improvement bythe light-guide/2D-CPC pumping scheme is more than 64% forany case, as illustrated in Table 2.

To support the proposed pumping scheme, a small scale proto-type was constructed and tested. The Nd:YAG laser crystal of3 mm diameter and 76 mm length was used within the water-flooded light-guide/2D-CPC cavity. The laser output power of14.4 W was measured, corresponding to the conversion efficiencyof 8.1 W/m2. This result confirms the validity of the proposedpumping scheme calculations in large scale regime.

In summary, the proposed light-guide/2D-CPC pumping ap-proach can provide significant enhancement in laser efficiency.The tracking error dependent laser power losses are also largelyreduced.

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