Optics Communications 282 (2009) 1385–1392
Contents lists available at ScienceDirect
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 Liang CEFITEC, 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 2008 Received in revised form 31 October 2008 Accepted 15 December 2008
Keywords: Lasers Solid-state Pumping Solar-pumped
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-guide assembly is used to transmit 6 kW concentrated solar power from the focal spot of a large parabolic mirror to the entrance aperture of a 2D-CPC pump cavity, where a long and thin Nd:YAG rod is efficiently pumped. Numerical calculations are made for different light-guides, 2D-CPC cavities and laser rods. The laser output power is investigated through finite element analysis. With 4 mm diameter rod, the maximum calculated laser power of 75.8 W is obtained, corresponding to the conversion efficiency of more than 11 W/m2. The tracking error dependent laser power losses are lower than 4%. A small scale prototype was constructed and tested, reaching 8.1 W/m2 conversion efficiency. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The idea of directly converting broad-band solar radiation into coherent and narrow-band laser radiation has gained an increasing importance. If lasers are needed in remote locations where sunlight is abundant and other forms of energy are scarce, a solar laser would seem to be a natural choice. Compared to electrically powered lasers, the solar laser is much simpler and more reliable due to the complete elimination of the electrical power generation and power conditioning equipment. This technology is particularly attractive for space applications where extended run times are required and where compactness, reliability, and efficiency are critical. Since the first reported Nd:YAG solar laser [1], improvement in the laser efficiency has always been a key issue in solar-pumped laser researches [2–4]. Recently, a more efficient solar laser system has been put forward, achieving a conversion efficiency of 18.7 W/m2 by using a Cr3+:YAG laser rod [5]. The Nd:YAG solar laser efficiency and beam quality still need, however, further improvements before it can compete with the diode-pumped solid-state lasers. A typical solar-pumped Nd:YAG laser utilizes a two-stage system that incorporates a first-stage primary parabolic mirror and a second-stage CPC concentrator. The laser head and its associated optics are usually placed near or directly at the focus of the collector. Non-imaging optics plays an important role in solar lasers by providing means for concentrating sunlight to intensities approaching the theoretical limit. The compound parabolic concentrator [6] (CPC) gives the maximum concentration for a two dimensional cavity. Although the non-imaging cavity provides a * Corresponding author. Tel.: +351 212948576; fax: +351 212948549. E-mail addresses:
[email protected] (R. Pereira),
[email protected] (D. Liang). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.12.052
large amount of pump power, it does not give a Gaussian absorption pumping profile [7], affecting hence the laser beam quality. For low-average-power applications, in which thermal lensing is moderate, the overlap of the laser mode with an excitation peaked at the centre of the rod can be advantageous. However, at highaverage-power, even a uniform gain distribution in a water-cooled laser rod has been shown to induce a non-parabolic heat distribution as a result of the temperature dependence of the thermal conductivity [8]. This results in a radially dependent refractive power of the thermal lens, with a maximum on the rod axis. When the absorption profile is centrally peaked, the temperature on the axis increases further, resulting in stronger thermal lensing at the centre, higher-order aberrations at the periphery, and larger stress in the laser rod compared with those of uniform excitation. Consequently, a power deposition that has a slight minimum at the centre of the rod can be useful to scale to high-average-powers. Minimizing a laser rod volume reduces cost, and reducing the diameter makes the rod more resistant to thermal stress. Also, with smaller rod diameter, high-order resonator modes are suppressed by large diffraction losses, and beam quality improves. The resonator stability depends also on how well the Sun is tracked. Tracking displacements move the centre of the absorption distribution inside the laser crystal [9]. If the centre of the thermal lensing moves, it acts as a resonator misalignment and less output laser power is obtained. Tracking error compensation is therefore needed to obtain a stable laser performance [10]. The fused silica and hollow lens ducts have been successfully used for end-pumping solid-state lasers [11,12]. The proposed fused silica light-guide assembly consists of three fused silica light-guides of rectangular cross-section by which the concentrated solar power of circular spot from the primary parabolic concentrator is both efficiently collected and transformed into a
1386
R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392
rectangular light column, facilitating the further light coupling into the small diameter laser medium by a 2D-CPC cavity. The proposed system demonstrates low sensibility to the minor angular tracking errors. The calculated laser conversion efficiency of 11 W/m2 and the optical efficiency of 27% for the 4 mm diameter, 80 mm length Nd:YAG laser rod are reported here. Tracking error dependent laser power losses lower than 4% are numerically obtained. Experimental results of small scale prototype are reported with a maximum laser output power of 14.4 W for an absorbed solar pump power of 71.3 W, corresponding to the conversion efficiency of 8.1 W/m2.
a
Incident concentrated solar light spot
First-stage 3D-CPC
2. Numerical calculations z
2.1. Solar spectra, tabulated model of absorption for Nd:YAG material and overlap between the Nd:YAG absorption spectra and the solar spectra The standard solar spectra [13] for one and a half air mass (AM1.5) are used as the reference data for consulting the spectral irradiance (W/m2/nm) at each wavelength. The irradiance cumulative integral of the whole solar spectra equals the typical terrestrial value of 900 W/m2, which agrees well with the experimental data [4]. For Nd:YAG laser material, 22 absorption peaks ranging between 527 nm and 880 nm are defined in the Monte Carlo ray-tracing software. For a 1.1 at.% Nd:YAG laser medium, the highest absorption coefficient reaches a = 10 cm1, while the lowest is about a = 1.5 cm1. The averaged FWHM absorption bandwidth of each peak is about 1 nm [14]. All the above central wavelengths and their respective absorption coefficients are added to the glass catalogue for Nd:YAG material. On the other hand, the solar irradiance values of the 22 central wavelengths can be consulted from the standard solar spectra for AM1.5 and saved as the source wavelength data.
y x
Second-stage 2D-CPC cavity
b 6mm diameter Nd:YAG laser rod
Cooling water Second-stage 2D-CPC
Flow-tube
Fig. 1. (a) Double-stage 3D-CPC/2D-CPC scheme, and (b) enlarged view of the 2D-CPC cavity with the laser rod of 6mm diameter and 72 mm length.
2.2. Double-stage 3D-CPC/2D-CPC cavity The astigmatic corrected target aligned (ACTA) solar concentrator system [4] provided the effective approach for pumping the solar laser crystal, enabling the convenient placement of the laser system on a horizontal optical table. The double-stage secondary concentrator shown in Fig. 1 is consisted of a 3D-CPC reflector followed by a 2D-CPC reflector. Concentrated solar light at 11.5o half angle cone entered the 3D-CPC, which funneled the light beam out at 55o half angle. The emitted light entered the 33 24 mm2 aperture 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 laser resonator design was commonly plane-parallel. For the segmented primary parabolic mirror with 6.85 m2 collection area, 45 W laser power was measured. 2.2.1. Numerical analysis for the double-stage 3D-CPC/2D-CPC cavity Several factors are important for the correct numerical analysis of the 3D-CPC/2D-CPC solar laser cavity. Eighty-five percent reflectivity for the first-stage ACTA mirror, 90% for the folding mirror and 95% for all the other reflector surfaces are assumed. For the terrestrial insolation of 900 W/m2, 6165 W of solar power reaches the first-stage ACTA mirror. If 14% overlap between the Nd:YAG absorption spectra and the solar spectra is considered [2], the total absorbable solar power lying within the Nd:YAG absorption bands equals to 864 W. Other non-useful solar power is either filtered or simply passes through the rod without significant absorption. The power of 864 W is hence the final value attributed to a circular light source of 3.4 m diameter, representing the absorbable incom-
ing radiation to the ACTA mirror, in the ray-tracing. The solar half angle of 0.27o is also considered. The reported dimensions of the first-stage ACTA solar collector are utilized in the ray-tracing software. The profiles of both the 3D-CPC and the 2D-CPC [4] are essential for designing both the axially symmetric 3D-CPC concentrator and the 2D-CPC pumping cavity. The laser rod, the cooling water and the flow-tube are dimensioned directly in the ray-tracing software. For the efficient cooling of the laser rod, the water gap between its 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 of both the laser rod and the flow-tube are modeled as uncoated. The solar spectra absorption coefficients for both cooling water and quartz flow-tube are defined accordingly. The cylindrical rod is divided into a total of 40,000 zones. During ray-tracing, the path length in each intercepted zone is found. With this value and the absorption coefficients of the 22 absorption wavelengths for the Nd:YAG material, the power absorbed by the laser rod can be calculated by summing up the absorbed pump radiation of all the zones within the rod. The absorption distributions for the laser rod of 72 mm length and 3 mm to 6 mm diameters are analyzed in Section 2.4. 2.3. Double-stage light-guide/2D-CPC cavity A double-stage light-guide/2D-CPC cavity is here proposed. In order to make a correct comparison with the 3D-CPC/2D-CPC cavity, the input-end of the proposed cavity, shown in Fig. 2, is placed at the focal region of a primary parabolic concentrator of 3.4 m
1387
R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392
a
Incident concentrated solar light spot W1=23mm
L 1=23mm
a
Input face
W1=23mm
L 1=23mm
T=9mm z y
T=9mm x
37º
Fused silica light guides assembly
37º
W2=9mm W2=9mm 2D-CPC cavity
L 2=69mm z
b
y
L 2=69mm
x
Light guides output power distribution
b
Output-end of the fused silica lightguide assembly
Curved reflectors
x y
2D-CPC cavity
Nd:YAG laser rod
Cooling water
Fig. 2. (a) Double-stage light-guide/2D-CPC cavity, and (b) enlarged view of the 2D-CPC cavity.
diameter, corresponding to 6.85 m2 collection area. The parabolic mirror has now a comparatively short focal distance of 1.32 m and a large rim-angle of 60o. The incoming solar power is therefore strongly focused into a circular light spot of near Gaussian distribution, as shown in Fig. 2a. The 9 23 mm2 input-end of each of the three fused silica light-guides is mechanically positioned, with the optimized angle of 37° relative to each other, at the focal area of the first parabolic mirror, forming the square input area of 23 23 mm2 of the assembly, as shown in Fig. 3a. The experience of our laboratory in manipulating fused silica light-guides in high temperature environment (hydrogen flames) and pure graphite mould bending process [15] can be utilized to achieve the correct curvature of the light-guides. Based upon both the refractive and the total internal reflection principles, the concentrated power can be efficiently transmitted by high optical quality (99.9999% purity) fused silica light-guides without extra cooling measures. One part of the concentrated solar power from the primary mirror is easily transmit-
Fig. 3. Incident concentrated solar light spot at the input face of the light-guide assembly (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).
ted by the central light-guide 14 cm in height to the entrance of the 2D-CPC cavity, while the other part of large divergent angles is efficiently transmitted through the two inclined light-guides of 7 cm curvature radius. The near Gaussian profile of the concentrated light spot shown in Fig. 2a, incident on the input face of the light-guide assembly is therefore transformed into a rectangular light column at the assembly output end. By both reducing the width of the light-guide assembly from W1 to W2 and increasing the length from L1 to L2, the absorption distribution profile can be improved and smaller diameter rods can be used. In addition, good tracking error compensation is achieved by this simple light-guide assembly. A small dislocation of the solar spot along the x-direction at the input face of the light-guide assembly causes the slight movement of the pump light at the output end along the y-axis, maintaining its profile along the x-axis, as shown in Fig. 3. The dislocations of the focal spot along the y-direction effects are attenuated owing to the pump light homogenization capacity by each rectangular light-guide. To obtain the smooth gain distribution along the laser rod, the rays coming from a pump source should hit each point of the rod’s surface over a wide range of angles. In addition, weak average
1388
R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392
C’
y
C
θi
HT = 6mm
ρ
A θ
Truncation line x
Fig. 4. Cross section of the 2D-CPC pump cavity designed with the edge-ray principle of non-imaging optics.
absorption of the pump power helps to prevent non-uniformity in energy deposition [8]. Therefore, it is straightforward to use a closed cavity pumping arrangement formed by the light-guide assembly and a high-reflectivity non-imaging concentrator. The design of the 2D-CPC cavity is based on the edge-ray principle [6] to non-planar absorbers. The edge-ray principle for a circular absorber of radius a is a two-region reflector defined by:
q ¼ ah for jhj ha þ p=2 ð1Þ h þ ha þ p=2 cosðh ha Þ q¼ for ha þ p=2 jhj 3p=2 ha 1 þ sinðh ha Þ
ð2Þ As shown in Fig. 4, for a ray that enters the CPC with an angle of is the distance hi and strikes the rod tangent to its surface, q ¼ RA along the ray path from the last intersection point of the ray with the CPC, A, to the tangent point of the rod, R. h is the angle measured from the negative y-axis to the line segment joining the cen 0 is equal to tre of the rod and the point R. The entrance aperture CC 2ap=sinðha Þ. The CPC cavity design depends therefore on the acceptance angle ha and on the rod diameter. In our CPC design, a is the laser rod radius and the CPC extrusion length depends directly on the total length of the light-guides. Both the laser rod and the 2D-CPC internal surface are actively cooled by filling up the CPC cavity with flowing water, reducing considerably the acceptance angle ha and eliminating hence the necessity of a cooling flow-tube as illustrated in Fig. 2b. The rod is now placed at the optimum position determined by the CPC parameters. The CPC cavity can be truncated by the truncation height HT =6 mm relative to the rod axis due to the reduction of the acceptance angle caused by the refractive influence of the water, reaching a near close-coupled cavity which also reduces the pump power losses by absorption in water. The light-guide assembly output end, together with the two curved reflectors, closes the 2D-CPC cavity. 2.3.1. Optical parameters for the double-stage light-guide/2D-CPC cavity The numerical analysis of the light-guide/2D-CPC cavity is similar to that of the 3D-CPC/2D-CPC. The power of 864 W is the value attributed to the circular light source of 3.4 m diameter, 1.32 m focal distance and 60o rim-angle. The solar half angle of 0.27o is considered in the ray-tracing analysis as well. Some practical considerations are important for the ray-tracing analysis. Fused silica material of high optical purity is used to manufacture the lightguides. Both the input and the output faces of the guides are optically polished to allow for the highest transparency for the pump radiation. The highly concentrated solar flux can easily damage anti-reflection coatings and these polished surfaces are therefore assumed as uncoated. The 2D-CPC cavity internal surface, the two curved reflectors and the two parallel end plates (not shown in Fig. 2) are gold reflectors. The pump wavelengths above
500 nm are therefore efficiently reflected to the laser rod, while the wavelengths below 500 nm are poorly reflected and absorption occurs at the cavity walls. The efficient cooling of both the laser rod and 2D-CPC pumping cavity is, for this reason, of vital importance. The cylindrical Nd:YAG rod is divided into a total of 40,000 zones. By taking into account the matching between the solar radiation spectra with the absorption spectra of the Nd:YAG medium, the cooling water and the fused silica light-guides, the absorbed power can be calculated. Ninety percent first parabolic mirror reflectivity, 85% folding mirror reflectivity, 95% 2D-CPC gold cavity reflectivity are also assumed. Five million rays are considered in the ray-tracing calculations. The cross-sectional absorption distributions perpendicular to the rod axis, for laser rods diameters between 3 mm and 6 mm, are also examined in Section 2.4. In order to make a fare comparison with the 72 mm length rods from the 3D-CPC/2D-CPC case, the total length of the laser rods is set at 110 mm, of which 70 mm is effectively pumped, leaving 20 mm length on each edge. 2.4. Absorption distribution analysis of the double-stage 3D-CPC/2DCPC cavity and the double-stage light-guide/2D-CPC cavity As a typical illustration, the central cross-sectional absorption distribution perpendicular to the rod axis is chosen. The grey-scale absorption distributions for the rods of 3 mm and 6 mm diameter, pumped by either the 3D-CPC/2D-CPC cavity or the light-guide/2DCPC cavity, are given in Figs. 5 and 6, respectively. Black signifies near maximum absorption, whereas white signifies little or no absorption. The absorption profiles are represented by the absorbed flux/volume distribution along both the central crosssection row and the central cross-section column of the rods. In the 3D-CPC/2D-CPC case, for the 6mm diameter rod, the maximum gain region is located in the lower portion of the laser rod, near the cusp of the 2D-CPC concentrator. This typical location of the maximum gain for CPC schemes is not optimal for laser operation in the TEM00 mode. This gain location is slightly removed by the waterflooded 2D-CPC cavity due to the absorption of the pump power by the cooling water. Although both the 3D-CPC/2D-CPC and the light-guide/2D-CPC cavity do not provide optimal absorption profiles, they give high absorption efficiencies, suitable for high power multimode regime. 2.5. Numerical analysis of the laser output power Numerical ray-tracing code is used to maximize the absorbed pump flux within the laser rod. The absorbed pump flux data from the ray-tracing analysis is then processed in a laser cavity finite element analysis (FEA) software. Output couplers of different reflectivities, ranging from 80% to 98%, are tested to maximize the multimode laser power. The plane-parallel optical resonator of 450 mm length and the averaged solar pump wavelength of 660 nm are considered. The round-trip loss is calculated accordingly to the chosen laser rod. For the 1 at.% Nd:YAG laser rod of 6 mm diameter, 72 mm length, a round-trip loss of 5.0% is considered [2]. The laser output power of 48.6 W is finally achieved for the 3D-CPC/2D-CPC scheme by adopting the output coupler of 95% reflectivity, matching well with the published experimental data [4] of 45 W. In the laser cavity FEA analysis, the output laser power of 48.6 W can be optimized to 57.6 W by using the 6 mm diameter laser rod of only 50 mm in length, rather than 72 mm. The laser resonator round-trip loss can, therefore, be reduced from 5.0% to 3.6%. There is still enough space for both mounting and cooling the laser rod, through the 2D-CPC cavity of only 33 mm in length. In order to evaluate the laser performances of the 3D-CPC/2D-CPC cavity, the Nd:YAG laser rods of 3, 4, 5 and 6 mm diameters are tested individ-
R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392
1389
Fig. 5. Grey-scale absorption distribution for the 72 mm length Nd:YAG rods pumped 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 rods pumped by the light-guide/2D-CPC cavity: (a) 3 mm diameter (b) 6 mm diameter (vertical unit in W/mm3).
ually. Again, the resonator cavity length of 450 mm and the averaged solar pump wavelength of 660 nm are assumed. The output coupler of different reflectivities is utilized to optimize the output laser power for each laser rod. The multimode and the TEM00 laser powers for both 50 mm and 72 mm laser rods with different diameters are shown in Fig. 8. For the analysis of the laser performances of the light-guide/2DCPC cavity, the optimized absorbed pump flux data obtained in the ray-tracing analysis is similarly processed by the FEA software. The plane-parallel laser resonant cavity of 450 mm length is used. A 110 mm length laser rod is here considered, leading to 7.14% round-trip loss. The averaged solar pump wavelength of 660 nm is also assumed. Output coupler reflectivity is used for maximizing the multimode laser power for different rod diameters. The length of each light-guide and the relative angular arrangement are important parameters for achieving the optimal solar power transmission to the second-stage 2D-CPC cavity. The angular position of each light-guide is carefully optimized by considering the concentrated solar spot angular distribution. The concentrated solar power is now fully collected and efficiently transmitted with small angles through the guides. Smoothly curved light-guides, shown in Fig. 2a, are crucial to assure the total internal reflection. The optimum curvature of each outer lightguide is found by detecting the maximum solar power at the cor-
respondent output end. The length of each light-guide is determined accordingly. The input area of each light-guide assembly is another key issue for the efficient laser production. An oversized input area of the light-guides results in the total capture of the concentrated solar power. The total rectangular output area of the light-guides is consequently large, which adversely affects the further light concentration by the second-stage 2D-CPC. If a small input area is considered, any small tracking error can cause the incident pump spot to partially miss the input area of the light-guide assembly and the light coupling losses are hence largely increased. As a result, it is relevant to evaluate the optimized input area of the light-guide assembly. Fig. 7 shows both the multimode and TEM00 laser output behaviour for different widths, W, of the square input area of the light-guide assembly. A slight decrease of TEM00 laser power is revealed as the width increases. The maximum multimode laser power is obtained through the 23 23 mm2 input areas, corresponding to the 9 mm thickness of each single lightguide. Similar to the analysis of the 3D-CPC/2D-CPC, by using the laser rod of only 80 mm in length, rather than 110mm, the laser resonator round-trip loss can, therefore, be reduced from 7.14% to 5.4%. Again, the space for mounting the laser rod is enough, because the 2D-CPC cavity has only 70 mm length. The multimode and the TEM00 laser powers for both 80 mm and 110 mm rod
1390
R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392
20 60 15
10 40 5
20 20
21
22
23
24
25
TEM00 laser power (W)
Multimode laser power (W)
2.6. Analysis of the tracking error dependent laser output power
25
80
0 26
Width of the light guides input area (mm) PMM Ø3mm
PTEM00 Ø3mm
PMM Ø4mm
PTEM00 Ø4mm
PMM Ø5mm
PTEM00 Ø5mm
PMM Ø6mm
PTEM00 Ø6mm
Fig. 7. Multimode and TEM00 laser output power as a function of the width of the light-guide assembly input area.
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 corresponds to 17 mm transversal shift from the ideal focal position of the ACTA mirror. If the focal spot moves in the direction parallel to the laser rod axis, then the strong pump absorption distribution will be shifted correspondingly along the rod in the opposite axial direction, causing only a minor reduction in output laser power. However, if the focal spot moves in the direction perpendicular to the rod axis (the transversal shift as we named), then the strong absorption distribution within the rod will be shifted laterally in the direction perpendicular to the rod axis, causing significant reduction in laser output power. It is therefore understandable for us to concentrate on the tracking error evaluation for only the transversal shift of the focal spot in ray-tracing analysis. Fig. 9a demonstrates the grey-scale absorption distribution for the 6.0 mm diameter Nd:YAG rod, pumped by the concentrated light spot with 17 mm transversal shift at the input-plane of the 3D-CPC/2D-CPC cavity. By comparing Fig. 5b with Fig. 9a, significant difference is found between the absorption distributions without and with tracking errors, respectively. The transversal shift to the right side causes the dislocation of the absorbed pump power to the left bottom side of the rod.
lengths and for different diameters are also shown in Fig. 8, allowing for the good comparison between the two pumping approaches. For the 3D-CPC/2D-CPC approach, with the increase of the rod diameter, there exist gradual increases in the multimode laser power, reaching its maximum for 6 mm diameter. The production of TEM00 laser power is, however, adversely affected. For the lightguide/2D-CPC approach, the multimode laser power increases until the optimal laser rod diameter of 4 mm is reached. For large rod diameters, the light-guide/2D-CPC approach shows a slight decrease in multimode laser power, indicating the improved power concentration capacity, suitable for pumping the small diameter rod. Small rod diameters are effective in producing TEM00 laser power. The reduction in the length of the laser rod and the consequent decrease in the round-trip losses correspond to an increase of more than 15% for both multimode and TEM00 laser power.
15 80 10
60 40
5 20
0
TEM00 laser power (W)
Multimode laser power (W)
100
0 2
3
4
5
6
7
Laser rod diameter (mm) 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)
Fig. 8. Calculated multimode and TEM00 laser output power as a function of laser rod diameter for both the 3D-CPC/2D-CPC approach and the light-guide/2D-CPC approach. Both optimized and non-optimized rod lengths are considered.
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 angular tracking error of 2 mrad (vertical unit in W/mm3).
1391
R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392
Laser output power loss
14% 12% 10% 8% 6% 4% 2% 0% 2
3
4
5
6
7
Laser rod diameter (mm) LG ΔPMM (110mm) LG ΔPMM (80mm) 3D-CPC ΔPMM (50mm) 3D-CPC ΔPMM (72mm)
LG ΔPTEM00 (110mm) LG ΔPTEM00 (80mm) 3D-CPC ΔPTEM00 (50mm) 3D-CPC ΔPTEM00 (72mm)
Multi-mode laser output power (W)
Fig. 10. Tracking error dependent laser power losses as a function of the laser rod diameter, both for optimized and non-optimized rod lengths.
The tracking error dependent laser power losses is calculated by dividing the difference between the power values without and with tracking errors by the original power value without tracking error. The power losses evaluation as a function of the laser rod diameter, both for multimode and TEM00 laser powers, is shown in Fig. 10. Both the 3D-CPC/2D-CPC and the light-guide/2D-CPC approaches are analysed. Large tracking errors losses for both multimode and TEM00 operation are dominant phenomena in the 3D-CPC/2D-CPC approach. For 2 mrad tracking error, the laser power loss reaches 12.3% when the rod of 6 mm diameter and 72 mm length is used. As the rod diameter increases, there exists a slow increase in multimode output laser power losses. For TEM00 laser power, a minimum power loss of 9.3% occurs for the laser rod of 5 mm diameter. There exists a general reduction in laser power losses by the light-guide/2D-CPC scheme. Compared with the 3D-CPC/ 2D-CPC scheme, lower and more stable laser power losses, both in multimode and in TEM00, are observed. The maximum laser power losses of 4% for multimode and 3% for TEM00 are observed. The tracking error dependent laser power losses remain stable for any rod diameter.
3. Experimental results
14 12 10 8 6 4 2 0 0
10
20
30
40
50
60
70
80
Absorbed solar power (W) Fig. 11. Laser output power as a function of the absorbed solar pump power.
For the light-guide/2D-CPC approach, the same calculation is carried out as for the ACTA solar laser system analysis. The tracking error of 2 mrad is also assumed for the primary parabolic concentrator of 3.4 m diameter and 1.32 m focal distance, causing in this case 2.7 mm transversal shift from the ideal focal position. Similarly, we concentrate here only on the tracking error analysis for the transversal shift of the focal spot in ray-tracing analysis. Fig. 9b shows the corresponding grey-scale cross-sectional absorption distribution for the 6.0 mm diameter Nd:YAG. Contrary to the ACTA case, the absorption profiles do not reveal significant differences when compared with Fig. 6b for zero tracking deviation. A transversal shift of the solar spot at the input face causes only a slight change of the pump profile along the direction parallel to the rod axis at the output end of the light-guide assembly. As a result, the absorbed pump power distribution is preserved at the transversal axis direction. The pumped region of the laser rod is only slightly dislocated from its original central location. An excellent tracking error compensation capacity is therefore achieved.
A small scale of the numerically tested light-guide/2D-CPC setup was constructed in order to prove the proposed pumping concept. A parabolic mirror, 1.5 m diameter, 0.66 m focal length and 85% reflectivity was used to collect 1258 W of solar power. Fused silica is an ideal optical material for a Nd:YAG laser pumping since it is transparent over the Nd:YAG absorption spectrum. Fused silica materials are also effective in absorbing undesirable radiations to the laser crystal. Furthermore, it has a low coefficient of thermal expansion, and is resistant to scratching and thermal shock. Fused silica light-guides optically polished both in the input and output ends were used. The light-guides were curved under high temperature environment (hydrogen flames). A pure graphite mould was also used to help the correct bending of the lightguides. The 7 18 mm2 input-end of each of the three fused silica light-guides was mechanically positioned, with the optimized angle of 37° relative to each other, at the focal area of the first parabolic mirror, forming the square input area of 7 7 mm2. The central light-guide was 11 cm in height. Slight misalignments were observed 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 machined. A cylindrical 1.1% Nd:YAG rod, AR coated on both ends, 3 mm in diameter and 76 mm in length was tested. The resonant cavity of 204 mm in length was formed by the PR output mirror of 92% reflectivity and the HR mirror of 99.97% reflectivity, both with 1m radius of curvature. The cw laser output power (Fig. 11) was measured as a function of the absorbed solar pump power by partially blocking the parabolic mirror with different opaque covers.
Table 1 Multimode and TEM00 laser output power improvements for different laser rod diameters and lengths pumped by the light-guide/2D-CPC cavity. Laser output power improvements (%) 3 mm
4 mm
5 mm
6 mm
Multimode
Laser rod diameter Non-optimized rod length Optimized rod length
72.4 70.6
58.1 54.0
43.5 38.9
27.8 27.4
TEM00
Non-optimized rod length Optimized rod length
63.8 60.6
33.5 30.2
31.6 25.1
21.7 19.9
1392
R. Pereira, D. Liang / Optics Communications 282 (2009) 1385–1392
Table 2 Laser 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 Optimized rod length
69.9 65.9
68.5 64.3
68.1 64.0
69.3 64.9
TEM00
Non-optimized rod length Optimized rod length
78.1 72.6
76.6 70.3
74.5 68.1
73.6 69.1
For the absorbed solar pump power of 71.3 W, the measured cw multimode laser output power was 14.4 W at 1064 nm. An overall efficiency of 1.15% was obtained, corresponding to the conversion efficiency of 8.1 W/m2. The measured M 2x and the M2y were 21.2 and 22.7, respectively. The beam profile was near rotationally symmetric and no significant variations in the multi-mode laser beam profile were found with pump power variations. 4. Conclusions A simple and efficient light-guide pumping scheme for solarpumped solid-state lasers is proposed. Non-sequential ray-tracing code and finite element analysis are used to firstly evaluate the laser output performance of the 3D-CPC/2D-CPC scheme, providing the reference values for the numerical analysis of the proposed light-guide/2D-CPC pumping approach. Table 1 reveals the significant improvements both in the multimode and in the TEM00 laser output power, for both the non-optimized and optimized laser rod lengths. For both multimode and TEM00 laser powers, the improvements increase with the reduction in the laser rod diameters. For the laser rod diameter of 3 mm, 72.4% enhancement is achieved for non-optimized laser rod length pumped by the light-guide/2D-CPC cavity. With the reduction of the laser rod diameter, the improvements in the TEM00 laser output 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 collected solar power, which corresponds to the conversion efficiency of more than 11 W/m2. The tracking error compensation capacity revealed by the proposed approach is also significantly enhanced when compared to the 3D-CPC/2D-CPC scheme. The tracking error improvement by the light-guide/2D-CPC pumping scheme is more than 64% for any case, as illustrated in Table 2.
To support the proposed pumping scheme, a small scale prototype was constructed and tested. The Nd:YAG laser crystal of 3 mm diameter and 76 mm length was used within the waterflooded light-guide/2D-CPC cavity. The laser output power of 14.4 W was measured, corresponding to the conversion efficiency of 8.1 W/m2. This result confirms the validity of the proposed pumping scheme calculations in large scale regime. In summary, the proposed light-guide/2D-CPC pumping approach can provide significant enhancement in laser efficiency. The tracking error dependent laser power losses are also largely reduced.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
C.G. Young, Appl. Opt. 5 (6) (1966) 993. M. Weksler, J. Shwartz, IEEE J. Quant. Electron 24 (6) (1988) 1222. D. Cooke, Appl. Opt. 31 (36) (1992) 7541. M. Lando, J. Kagan, B. Linyekin, V. Dorbrusin, Opt. Commun. 222 (2003) 371. T. Yabe, T. Ohkubo, S. Uchida, K. Yoshida, M. Nakatsuka, et al., Appl. Phys. Lett. 90 (26) (2007) 261120. W.T. Welford, R. Winston, High Collection Non-imaging Optics, Academic Press, New York, 1989. R.J. Koshel, I.A. Walmsley, Opt. Eng. 43 (7) (2004) 1511. T. Brand, Opt. Lett. 20 (17) (1995) 1776. D. Jenkins, Thesis (Ph.D.), The University of Chicago, 57-02 (Section B), 1996. D. Liang, P. Bernardes, R. Pereira, in: Conf. Lasers and Electro-Optics, Tech. Dig. Ser., CA7-5-TUE, vol. 29B, 2005. R.J. Beach, Appl. Opt. 35 (12) (1996) 2000. Eric C. Honea, Raymond J. Beach, Scott C. Mitchell, Petras V. Avizonis, Opt. Lett. 24 (3) (1999) 154. See for example: ASTM Standard G159, 1998. A. Brignon, G. Feugnet, J.P. Huignard, J.P. Pocholle, IEEE J. Quant. Electron 34 (3) (1998) 577. P.H. Bernardes, D. Liang, Appl. Opt. 45 (16) (2006) 3811. A. Kribus, I. Vishnevetsky, M. Meri, A. Yogev, A. Sytnik, J. Sol. Energy Eng. 126 (3) (2004) 842.
