1.

Introduction

The idea of directly converting incoherent and broadband solar radiation into coherent and narrowband laser radiation has emerged shortly after the invention of laser.¹ Since the first report of “A sun-pumped continuous-wave one-watt laser” in 1966,¹ optical and laser material advances have continued to improve solar-laser performance.

By placing a Nd:YAG crystal directly into the focal region of a large primary parabolic concentrator, 18-W laser power was produced.² The introduction of the two-dimensional compound parabolic concentrator (2-D-CPC) and the three-dimensional compound parabolic concentrator (3-D-CPC) further boosted the solar laser output power.^3,4 To enhance the spectral match between the emission spectrum of the pump radiation and the absorption spectrum of the laser medium, the crystals of different active materials were tested,⁵ and others are codoped to improve their laser efficiency due to the enhanced absorption of sunlight spectrum, as the Cr-codoping to Nd:YAG, which will increase the possibility of efficient absorption and optical pumping rate to Nd ion in the solar spectrum.^6,7 Several pumping architectures have been proposed for solar-pumped solid-state lasers.⁸ These lasers can have either side-pumping or end-pumping configurations. Although the most efficient laser systems have end-pumping approaches, the thermal loading effects caused by nonuniform distribution of pump light in these pumping configurations negatively affect their efficiencies. Side pumping is an effective configuration for power scaling and for producing high laser beam quality as it allows uniform absorption distribution along the laser rod axis and spreads the absorbed power within the laser medium, reducing the associated thermal loading problems.⁹

The development of solar lasers mainly concerns space power transmission and propulsion. New potential applications of solar lasers in space are emerging. These include Earth, ocean and atmospheric observation from space; detecting, illuminating and tracking hard targets in space; and deep space communications.

The use of solar pumped lasers on Earth seems constrained by economics. Therefore, prospective applications may be limited to those that require utilization of quantum effects and coherency of the laser to generate extremely high-value products and services when conventional and inexpensive means are ineffective or impossible. The main problem preventing wide spread use of solar-laser today is its low efficiency. Therefore, collection efficiency—defined by the ratio between laser output power and primary concentrator area¹⁰—is generally regarded as a primary figure of merit for solar-laser. The second is thermal problems worsening the efficiency as well as the beam quality. Lasers for many applications generally require high beam quality. This is not easy to achieve when the heat load of the laser crystal is high. The high heat load usually leads to very low efficiency, stability, and output power for fundamental-mode (${\mathrm{TEM}}_{00}$-mode) laser beams from solar-pumped lasers.¹¹

For these purposes, we report here a review of research done on solar-laser field to show the thermal loading effects on Nd:YAG solar-lasers performance in end-pumping and side-pumping configurations. We discuss the thermal loading effects on the stability, the efficiency and the beam quality of solar-laser output-power and compare some of them with the previous experimental results, which give us a better explanation of the theoretical aspects.

2.

Heat Generation in Solid-State Laser Materials

In solid-state lasers, a fraction of the absorbed pump energy converts to heat which acts as the heat source inside the laser material.^12,13 As the heat load of the laser crystal is considered one of the main problems preventing wide spreading of solar-lasers, we address the issue of the heat generation in solid-state laser materials, both theoretically and experimentally.

2.1.

Principle

The difference between the energy of pumping photons and the energy of laser’s photons in optically pumped solid lasers is the main reason for the heat generated in the crystal lattice of the lasing medium in addition to heat resulting from transfer of nonlaser emitting upper levels-and the nonradiative relaxation from the pump band-to ground levels.^14,15 The absorption of pump radiation by the host material in turn causes the heating of the laser medium.¹⁵

Consequently, the heat generated inside the laser material acts as the heat source.^12,13 Spatial and time dependence of the heat source causes important effects on temperature distribution and warming rate of the laser medium, respectively. The spatial form is assumed to be the same shape as pumping light^12,13 and time dependence relates to the pumping procedure. Furthermore, depending on the laser medium configuration and cooling geometry, deposited heat may mostly flow through a preferable direction inside the laser medium and therefore causes thermal gradient. For instance, in traditional rod-shaped laser mediums with water cooling configuration, the main proportion of heat removal occurs through the radial direction which leads to the considerable radial thermal gradient inside the medium.

Figure 1 shows a schematic setup of pumping procedures for the rod-shaped laser medium. The dominant directions of heat removal which are associated with the laser medium configuration and cooling system geometry are illustrated.

Fig. 1

Schematic figure of preferable directions of heat removal in the rod-shaped laser medium in (a) side-pumping configuration and (b) end-pumping configuration.

The combination of the laser material heating by the absorbed pump-light and surface cooling required for heat extraction leads to a nonuniform temperature distribution in the laser rod resulting in a distortion of the laser beam. The degradation of the laser beam quality is due to thermal lensing.¹⁵

2.2.

Temperature Distribution

The particular temperature profile that exists in the laser material depends, to a large degree on the absorbed pump-light distribution resulting from the pumping methods, which can be either side-pumping or end-pumping techniques.

Using side-pumping configuration, uniform absorbed pump-light distribution can be achieved resulting in uniform heat generation within the laser medium. Although the end-pumping geometry leads to nonuniform absorbed pump-light distribution resulting in nonuniform heat generation into the laser medium.⁹ Another way to decrease the thermal lensing effects than the generation of a uniform heat distribution inside the active medium is to use a lower dopant concentration and to act on the active medium geometry.

2.2.1.

Side-pumping configuration

The pumping process is commonly performed by two methods, which are side-pumping and end-pumping laser techniques.

Figure 2 shows schematically a laser rod pumped by side-pumping technique. In this pumping method, the pump-light is transmitted uniformly to the laser rod by its cylindrical surface resulting in uniform absorbed pump-light distribution within the rod.

Fig. 2

Scheme of side-pumping method of a laser rod.

With the assumption of uniform internal heat generation achieved by the side-pumping configuration and the cooling along the cylindrical surface of a laser rod, the heat flow is strictly radial, and end effects and the small variation of coolant temperature in the axial direction can be neglected. The radial temperature distribution in a cylindrical rod with the thermal conductivity $K_c$, in which heat is uniformly generated at a rate $Q$ per unit volume, is obtained from the 1-D heat conduction equation:¹⁵

Eq. (1)

$$\frac{d^{2}T}{d{r}^2}+\left(\frac{1}{r}\right)\left(\frac{dT}{dr}\right)+\frac{Q}{K_c}=0$$

The solution of this differential equation gives the steady-state temperature at any point along a radius of length $r$. With the boundary condition $T(r_0)$ for $r=r_0$, where $T(r_0)$ is the temperature at the rod surface and $r_0$ is the radius of the rod, it follows that

Eq. (2)

$$T(r)=T(r_0)+\left(\frac{Q}{4K}\right)(r_0^2-r^2).$$

The temperature profile is parabolic, with the highest temperature at the center of the rod. The temperature gradients inside the rod are not a function of the surface temperature $T(r_0)$ of the rod.

The thermal radial gradient as given by Eq. (2) introduces a radial variation of the refractive index. The change of the refractive index can be separated into a temperature and a stress dependent variation. Hence

Eq. (3)

$$n(r)=n_0+\mathrm{\Delta }(n{)}_T+\mathrm{\Delta }{(n)}_{\epsilon },$$

where $n(r)$ is the radial variation of the refractive index, $n_0$ is the refractive index at the center of the rod, $\mathrm{\Delta }{(n)}_T$ and $\mathrm{\Delta }{(n)}_{\epsilon }$ are the temperature and stress dependent changes of the refractive index, respectively.¹⁶

The thermal radial changes generated in the laser rod by using side-pumping method cause radial variations of the refractive index, which consequently lead to distortions of the laser beam. These distortions are due to temperature and stress-dependent variations of the refractive index.¹⁶

2.2.2.

End-pumping configuration

In contrast to side-pumped laser systems, the heat deposition in end-pumped laser systems is very inhomogeneous. Figure 3 shows schematically a laser rod pumped by end-pumping technique. In this pumping method, the pump-light is transmitted to the laser rod through its end resulting in nonuniform absorbed pump-light distribution within the rod.

Fig. 3

Scheme of end-pumping method of a laser rod.

The very localized heat deposition resulting from the end-pumping method leads to highly nonuniform and complex temperature and stress profiles. In addition to the temperature and stress-dependent variations in the refractive index, the contribution of end bulging to the formation of a thermal lens can be substantial in end-pumped laser systems. Inhomogeneous local heating and nonuniform temperature distribution in the laser crystal lead to a degradation of the beam quality due to the highly aberrated nature of the thermal lens.¹⁵

An end-pumped laser rod has a temperature profile across the pumped region that follows the distribution of pump-light. From the edge of the pumped region, the temperature decays to the cooled cylindrical surface of the rod. Along the axis of the rod, the temperature profile will decay following the absorption profile of the pump-light, subject to the absorption law.

Figure 4 shows the calculated temperature distribution in a conductively cooled end-pumped laser rod.¹⁵

Fig. 4

Temperature distribution in an end-pumped laser rod.¹⁵

Assume homogeneous cooling on the surface of the laser rod, which means the temperature at each point along the axis of the rod is fixed and the thermal conductivity coefficient is independent of temperature.¹⁷

Under these assumptions, we can write a differential equation for thermal transfer in a cylindrical rod as follows:^14,17–19

Eq. (4)

$$\frac{1}{r}\frac{\partial }{\partial r}\left[r\frac{\partial T(r,z)}{\partial r}\right]+\frac{{\partial }^{2}T(r,z)}{\partial z^2}=-\frac{Q(r,z)}{K_c},$$

where $T(r,z)$ is the temperature in Kelvin as a function of radial distance $r$ and position along the $z$-axis, $K_c$ is the thermal conductivity $(\mathrm{W}/\mathrm{m}·\mathrm{K})$, and $Q(r,z)$ is the heat in unit volume.

Thermal distribution within a laser crystal is a function of absorbed power density, which in turn takes the form of distributed light pumping at any vertical section on the axis of the laser crystal and parallel to the pumping beam. On the one hand, the intensity of light pumping decreases along the $z$-axis, subject to the law of absorption; ($r,z$) can be given in a number of forms depending on the beam shape.²⁰

Boundary conditions are set based on the assumption that the side surface of the laser crystal is in direct contact with the coolant. The first boundary condition is the continuity of thermal flow through these surfaces¹⁷ and the second boundary condition is $T(r_s)=T_c$, where $T(r_s)$ is the temperature of the side surface of the laser crystal and $T_c$ is the temperature of the coolant.

The change in the refractive index can be separated into two terms: the first part depends on the temperature distribution and the second part depends on the stress.¹⁴ So, we can write

Eq. (5)

$$n(r,z)=n_0+\mathrm{\Delta }n(r,z{)}_T+\mathrm{\Delta }n(r,z{)}_{\epsilon },$$

where $n(r,z)$ is the total index of refraction, $\mathrm{\Delta }n{(r,z)}_T$ is the part of index of refraction related to temperature, $\mathrm{\Delta }n(r,z{)}_{\epsilon }$ is the part of index of refraction related to stress, and $n_0$ is the material index of refraction.

The very inhomogeneous heat deposition in end-pumped laser systems leads to significant thermal changes in the laser rod, resulting in complex refractive index variations. The temperature and stress-dependent variations of the refractive index cause optical distortions that can severely degrade the optical quality of the laser beam and eventually limit the laser output power.¹⁵

Finally, it is very important to notice that the optical distortions due to the end-pumping method are substantial because of the complex refractive index variations, compared with those resulting from the side-pumping method, in which the significant variation of the refractive index is only radially.

3.

Summary of Research Details for Exhibiting the Thermal Loads Effects on Nd:YAG Solar-Lasers Performance

The collection efficiency is generally regarded as a primary figure of merit for solar-lasers. The second is thermal problem worsening the efficiency as well as the beam quality.

The most important research in solar-laser field is summarized and discussed below in order to show, first that the end-pumping solar-laser systems are the most efficient; however, the thermal load effects caused by non-uniform distribution of pump light, typical in these pumping configurations, lead to a poor solar-laser beam quality. Second, that the side-pumping systems are the most effective for power scaling and for producing high solar-laser beam quality and stability as they give uniform absorption within the laser medium, reducing the associated thermal loading problems.

For clearly exhibiting the thermal loads effects on Nd:YAG solar-lasers performance, research details will be given afterward. Some literatures^{1–3,6,7,9,21–29} were made for the solar-laser efficiency improvement, whereas others included laser beam quality enhancements.^{11,26–28,30–35}

Research details will be given for both multimode and monomode (fundamental-mode) solar-laser operations, respectively.

3.1.

Main Research in Multimode Solar-Laser Operation

To clearly expose all the previous multimode solar-laser research studies, details (data and results) are summarized in the following Figs. 5Fig. 6Fig. 7Fig. 8Fig. 9Fig. 10Fig. 11Fig. 12Fig. 13Fig. 14Fig. 15Fig. 16Fig. 17Fig. 18Fig. 19–20.

Fig. 5

Young C. G., (1966).¹

Fig. 6

Arashi H. et al., (1984).²

Fig. 7

Weksler M. and Shwartz J., (1988).³

Fig. 8

Jenkins D. G., (1996).²¹

Fig. 9

Lando M. et al., (2003).⁹

Fig. 10

Yabe Y. et al., (2007).⁶

Fig. 11

Liang D. and Almeida J., (2011).²²

Fig. 12

Dinh T. H. et al., (2012).²³

Fig. 13

Almeida J. et al., (2012).³⁰

Fig. 14

Liang D. et al., (2013).⁷

Fig. 15

Almeida J. et al., (2013).²⁴

Fig. 16

Xu P. et al., (2014).²⁵

Fig. 17

Almeida J. et al., (2015).²⁶

Fig. 18

Liang D. et al., (2016).²⁷

Fig. 19

Liang D. et al., (2017).²⁸

Fig. 20

Guan Z. et al., (2018).²⁹

3.1.1.

Discussions

Collection efficiency is generally regarded as a primary figure of merit for solar-laser systems. The second is the beam quality factors ($M_x^2$ and $M_y^2$), which is defined by the ratio between laser beam divergence and divergence of diffraction-limited Gaussian beam.³¹

One of the main problems preventing wide spreading of solar-pumped lasers is the relatively low efficiency, compared with diode-pumped lasers. Since the first report of “A sun-pumped c w one-watt laser” in 1966,¹ optical and laser material advances have continued to improve solar-laser performance. Several pumping architectures have been proposed for solar-pumped solid-state lasers with the intention of achieving the maximum transfer and absorption efficiencies from the pump source to the laser crystal.⁸ These laser systems can have either side-pumping or end-pumping configurations. The most efficient laser systems have end-pumping approaches because of the high absorption efficiency of the pump light by the laser crystal. In turn the thermal loading effects caused by nonuniform distribution of pump-light in these pumping configurations negatively affect the laser beam quality. To prove that, research results will be discussed below.

In multimode regime, by using the end-pumping method, high collection efficiency of $30.0\mathrm{W}/{\mathrm{m}}^2$ was attained by pumping a large Nd:YAG rod through a large Fresnel lens.²³ However, very large $M_x^2=M_y^2=137$ factors have been associated with this approach, resulting in very poor beam quality. Since the report of this result, many research studies have been made to improve both, the collection efficiency and the beam quality factors of the solar-laser systems.

About $31.5\mathrm{W}/{\mathrm{m}}^2$ collection efficiency was achieved by pumping a 4-mm diameter, 35-mm length Nd:YAG rod through $1.18{\mathrm{m}}^2$ area parabolic mirror.²⁸ Although, it was only slightly higher than the previous record value obtained by Ref. 23, this research gave rise to significant improvement of the beam quality factors with $M^2=53.5$. This value is still large to obtain a high-laser beam quality. Record-high collection efficiency of $32.1\mathrm{W}/{\mathrm{m}}^2$ was attained by pumping a large Nd:YAG rod through a large Fresnel lens.²⁹ Despite the high collection efficiency, the $M^2$ factors were large ($M_x^2=M_y^2=61$), being 1.14 times higher than the previous result.

Side-pumping configuration presents high beam quality as it allows uniform absorption distribution along the rod axis and spreads the absorbed power within this laser medium, reducing the associated thermal loading problems. In contrast, this pumping method leads to low collection efficiency because of its low absorption efficiency.

A multi-mode collection efficiency of $9.6\mathrm{W}/{\mathrm{m}}^2$ with the lowest $M^2$ factors ($M_x^2=8.9$ and $M_y^2=9.6$) was obtained by Ref. 30 by pumping a large Nd:YAG rod through a parabolic mirror.

3.2.

Main Research in TEM₀₀-Mode Solar-Laser Operation

To complete the exposition of previous solar-laser research, details (data and results) of the ${\mathrm{TEM}}_{00}$-mode solar-laser research are summarized in the following Figs. 21Fig. 22Fig. 23Fig. 24Fig. 25Fig. 26Fig. 27–28.

Fig. 21

Liang D. and Almeida J., (2013).³⁶

Fig. 22

Liang D. et al., (2015).³²

Fig. 23

Almeida J. et al., (2015).³⁷

Fig. 24

Vistas C. R. et al., (2015).³⁴

Fig. 25

Liang D. et al., (2016).²⁷

Fig. 26

Liang D. et al., (2017).²⁸

Fig. 27

Bouadjemine R. et al., (2017).³⁵

Fig. 28

Mehellou S. et al., (2017).¹¹

3.2.1.

Discussions

The same conclusions remain valid for ${\mathrm{TEM}}_{00}$-mode operation. The end-pumping configuration provides high collection efficiency. However, high $M^2$ factors have been associated with this approach. Record-high collection efficiency of $7.9\mathrm{W}/{\mathrm{m}}^2$ was reported by Ref. 28 with only 1.2 as $M^2$ factors. In contrast, the side-pumping configuration leads to low collection efficiency with very low $M^2$ factors. Record-low $M^2$ factors $<1.05$ have been reported by Refs. 11, 32, and 35. Low collection efficiency was registered for all these literatures.

4.

TEM₀₀-Mode Solar Laser Power Stability

In this last part of this paper, we give a description of the output power measurement process of a solar-laser system using side-pumping and end-pumping methods, respectively, to show that in addition to the high solar-laser beam quality, the side-pumping configuration presents the advantage to be able to produce a stable ${\mathrm{TEM}}_{00}$-mode solar-laser power.

Using the side-pumping method, low ${\mathrm{TEM}}_{00}$-mode solar-laser power was measured during 240 s, with the maximum output power variation being $<1.7\%$. The Gaussian fundamental-mode profile was also found stable during the measurement.¹¹ In the same experimental conditions as the previous pumping-method, the end-pumped laser,²⁸ provided high ${\mathrm{TEM}}_{00}$-mode laser output power. Strong oscillations of 12% were observed during the measurement process of 240 s. These oscillations are due to high thermal lensing effect and consequently short thermal focal lens, which make the ${\mathrm{TEM}}_{00}$-mode laser output power very sensible to both pumping flux and temperature variation of the laser rod.

The end-pumped laser offered the maximum ${\mathrm{TEM}}_{00}$-mode solar-laser collection efficiency, but also suffered from a very strong thermal load effect, much more than the 1.7% of the side-pumped laser. Figure 29 shows a favorable result in fundamental mode laser beam stability of $<12\%$ for the end-pumped laser.

Fig. 29

Time dependent ${\mathrm{TEM}}_{00}$-mode solar-laser power variations of both end-pumped laser²⁸ and side-pumped laser.¹¹

During the measurement process, however, it was found not easy to maintain a perfect Gaussian mode profile due to the strong thermal load effect of this type of laser. Solar irradiance variation of $<0.5\%$, cooling water temperature oscillation of $<2\mathrm{deg}$ during the measurement were found sufficient to change a solar laser beam with Gaussian profile into a low-order mode beam with a two-mode, sometimes a four-mode or even a doughnut-shaped profiles were observed.¹¹

5.

Conclusion

The growing importance of solar-pumped lasers has attracted considerable attention. Many studies have already been carried out to improve solar-laser efficiencies. As the sunlight does not provide enough flux to initiate laser emission, additional focusing optics are needed to both collect and concentrate the solar radiation to excite laser medium. Parabolic mirrors have long been explored to achieve tight focusing of incoming solar radiation. Significant progresses in solar laser efficiency have been made with the adoption of Fresnel lenses as primary solar concentrators.

To maximize the solar radiation that impinges on the laser crystal, the 2-D-CPC, the 3-D-CPC and the V-shaped pump cavity are usually used as secondary and tertiary concentrators in solar-lasers because they can either compress or wrap the concentrated solar radiations from their input aperture to the laser rod and give an additional concentration.

Moreover, to improve solar laser performance, several pumping architectures have been proposed. These pumping architectures can be either side-pumping or end-pumping configurations.

The most efficient laser systems have end-pumping configurations, the thermal loading effects caused by nonuniform distribution of absorbed pump light typical in these pumping configurations affect negatively their laser beams quality, high collection efficiency can be achieved with these pumping approaches. Record-high multimode collection efficiency of 32.1 and $7.9\mathrm{W}/{\mathrm{m}}^2$ for ${\mathrm{TEM}}_{00}$-mode regime were attained.

In the side-pumping configuration there are a lot of heat around the solar laser rod (quite different from that of LD-pumped) so the uniform distribution of pumping flux along the rod is important for solar-lasers due to the heat removal issue. Therefore, the side-pumping is an effective configuration for producing high laser beam quality as it allows a uniform absorption distribution along the rod axis, reducing the associated thermal loading problems.

It gives the lowest $M^2$ beam quality factors, $<10$ for multimode and $<1.05$ for ${\mathrm{TEM}}_{00}$-mode operating regimes. This pumping method also makes it possible to obtain a stable ${\mathrm{TEM}}_{00}$-mode solar-pumped laser output power.

Finally, it was worth noting that by pumping smaller diameter rods it can lead to meliorate the solar-laser beam quality of high efficiency solar-pumping schemes. Furthermore the thermal management of end-pumped lasers can be greatly improved by the use of composite rods. Laser crystals have become available with sections of undoped host material on one or both ends. These end caps are diffusion bonded to the doped laser crystal. Composite rods are proven to provide a very effective way to reduce temperature and stresses at the face of end-pumped lasers. Regarding the collection efficiency of side-pumped lasers, it can be significantly enhanced by the use of the power scaling method.