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Abstract
An average 9 kilowatt-level direct-D2O-cooled side-pumped Nd:YAG multi-disk laser resonator at QCW mode with a pulse width of 250μs is presented, in which the straight-through geometry is adopted the oscillating laser propagates through 40 Nd:YAG thin disks and multiple cooling D2O flow layers in the Brewster angle. Much attention has been paid on the design of the gain module, including an analysis of the loss of the laser resonator and the design of the Nd:YAG thin disk. Experimentally, laser output with the highest pulse energy of more than 20 J is obtained at a repetition frequency of 10 Hz. At high repetition frequency, the average output power 9.8 kW with ηo-o = 26% and 9.1 kW with ηo-o = 21.8% are achieved in the stable resonator and unstable resonator, respectively, and in the corresponding beam quality factor βstable = 14.7 and βunstable = 9.5 respectively. To the best of our knowledge, this is the first demonstration of a 9 kilowatt-level direct-liquid-cooled Nd:YAG thin disk laser resonator.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Since the first demonstration in 1960, the laser systems with high average power, high efficiency and high beam quality have been an attractive field for a broad range of medical, commercial, scientific, and military applications. Solid state laser (SSL) represents a class of compact and efficient high power laser source, which has been developed rapidly with 100 kW achieved by several institutions [1–3]. Thermal effect is the main suppression factors for obtaining higher output power from the SSL, which may lead to serious thermal optical aberration and the risk of fracturing the gain medium [4–6]. To dissipate the heat efficiently, most solid-state lasers nowadays employ the conduction cooling method [7], in which the heat deposited in the gain medium is conducted to the heat sink. Such a thermal management configuration will lead to increase complexity of the laser system and some other scientific problem. In order to meet the requirements of various practical applications, a compact high power system with efficient thermal management should be developed.
Due to its excellent heat dissipation ability, direct-liquid-cooled configuration lasers (DLCLs) have become extremely attractive in high power laser field [8–12], in which tens of disk pieces are integrated into one gain module and the circulating liquid flows over the largest surface of every disk to take the heat away. Attribution to the efficient thermal management, the DLCL system shows two obvious advantages: firstly, tens even hundreds of disks can be arranged in one gain module resulting that the light transmission path between two disks deceases to millimeter scale, which implies the ratio of power-volume increases a order of magnitude to 0.2kW/kg. On the other hand, the possible surface bending introduced by the disk welding procedure (for conduction cooling method by heat sink) can be circumvented and higher pump intensity is allowed in the DLCL system. In 2010, 100 kW average output power was extracted from six gain modules, reported by Textron Defense Inc [2]. The most impressive case is the “liquid laser” scheme with a 150 kW output power by General Atomics Corp, but its detail has not been disclosed yet [13]. In 2014, M.Gong et al. demonstrated a liquid-cooled multi-slab laser resonator with a multimode laser output with the output power of 3006 W is obtained from the stable cavity [13, 14]. Recently, our group reported several experimental and theoretical results on DLCLs. A direct-liquid-cooled Nd:YLF thin disk laser resonator is presented, in which a linear polarized laser with an average output power of 1120 W is achieved at the pump power of 5202 W, corresponding to an optical-optical efficiency of 21.5%, and a slope efficiency of 30.8% [15]. A direct-liquid-cooled side pumped Nd:YAG multi-disk QCW laser resonator is presented, in which maximum average output power of 7.48 kW is achieved at the repetition rate of 500 Hz with an optical-optical efficiency of 30% [16]. Profited from its more efficient optical mode selection and a bigger fundamental volume, the unstable resonant cavity is a better technical route to achieve high power laser with high beam quality than the stable cavity [17], such as for CO2 high power laser. The advantages of a unstable laser cavity based on direct-liquid-cooled side-pumped Nd:YAG thin disk should be studied intensively.
On the basis of our previous work, a 9 kilowatt-level direct-D2O-cooled side-pumped Nd:YAG thin disk laser resonator is demonstrated in this paper. The oscillating laser propagates through multiple thin disks and the flowing D2O layers in Brewster angle. For the safe operation of the laser resonator, the maximum thermal stress and the temperature rise has been well-designed. The effect of different kind of cavity loss has been calculated and analyzed. Based on the thermal boundary and the system loss, the size and the number of thin disk are well-designed to achieve the high power laser output. Aberration due to pump and temperature rise of coolant is also analyzed. A variable-focus cylindrical lens group is used to compensate the defocus caused by the negative exponential absorption of the pumping power. Dual gain modules that have opposite flow directions are used to reduce the aberration caused by the temperature rise of coolant. The resonator operates in QCW mode with a pulse width of 250 μs. For comparision, both the stable cavity and the unstable cavity are demonstrated. At the repetition rate of 10 Hz, more than 20 J single pulse energy is obtained both in the stable resonator with the output coupling of 75% and the unstable resonator with the magnification of 2.0. The highest average output power of more than 9 kW is achieved in both the stable resonator and unstable resonator, corresponding to the optical-optical efficiency of 26% in stable resonator and 21.8% in unstable resonator.
2. Design and experimental setup
The schematic diagram of the direct-D2O-cooled side-pumped Nd:YAG thin disk laser resonator is shown in Fig. 1. The laser system consists of two gain modules (GM1 and GM2), each GM contains 20 pieces of Nd:YAG thin disks, 22 cooling channels and 4 fused silica windows (two laser windows and two pumping windows). The Nd:YAG thin disks with a tilt angle of 48.5°, thickness of 2 mm and doping concentration of 0.25 at.% are immersed in the cooling liquid and linearly arranged with a distance of 0.5 mm. Four cubes with the thickness of 0.5 mm are spliced on the corners of the thin disk to provide the cooling channel. All the thin disks are uncoated, while the oscillating laser beam within the cavity passes the windows and the Nd:YAG thin slabs near the incidence of Brewster angle with low reflection losses. Four LDSs radiated at 808 nm are employed to pump the GM at the side surfaces. Each LDS contains 300 LD bars in an array of 5 × 60 at the maximum peak output power of 150 W and a maximum duty cycle of 12.5%. M1 is a polarization beam combiners.
Fig. 1 Experimental setup of the direcct-D2O-cooled side-pumped Nd:YAG thin disk laser resonator. (a) The configuration of the unstable laser resonator. PM, pump module; LDS, laser diode stack; CLG, cylindrical lenses group; M1, polarization beam combiners; GM, gain module; M2, high reflector; SM, scraper mirror, including square loop high reflector and a hole in the middle; M3, convex Mirror. (b) The schematic of the stable laser resonator. M4, high reflector; OC, output coupler.
Dual side-pumped unstable cavity has been adopted (as shown Fig. 1(a)), which consists of a high reflector (M2, R>99.9%@1064 nm, r2 = 6.4 m), a convex mirror (M3, R>40%@1064 nm, r3 = −3.2 m), and a scraper mirror output coupler (SM, middle area is hole with size of 1.7cm × 2.4cm, square loop high reflector, RS>99.9%@1064 nm). Meanwhile, a stable cavity is presented for comparison (as shown Fig. 1(b)),in which a high reflector (M4, R>99.9%@1064 nm, r2 = 15 m) and a plane output coupler (OC, R>25%@1064 nm) form the laser resonator. Both the two cavity lengths are about 1.6 m, in which the length of the GM is 230 mm. The circulating D2O passes through the gain module from the inlet to the outlet, moreover, the flow directions of two GMs are reversely, the role will be discussed detailly in section 2.4. Inside the gain module, the liquid flows over the two largest surfaces of the disks taking away the deposited heat by the way of convection cooling.
2.1 Thermal management
In the system, the Nd:YAG thin disks are cooled directly by the coolant in 500 µm cooling channels between two disks. Benefiting by its high thermal conductivity, high specific heat, low viscosity and low absorption coefficient at the laser wavelength (0.023/cm−1@1064nm), D2O with the purity degree of 99.8% is chosen as the coolant to reduce the influences on oscillating laser. The inset of Fig. 2 shows the convective heat-transfer coefficient h versus flow velocity in 0.5mm micro-channel. The convective heat-transfer coefficient is theoretical calculated by Comsol commercial software. A flow and heat-transfer model for the cooling channels is presented, a total heat flux 200 W/cm3 is loaded on every crystal, and the convective heat-transfer coefficient can be acquired when a steady-state solution is obtained in the theoretical model. In order to avoid the wavefront aberration induced by non-uniform heat transfer, the flow in cooling channels needs to be maintained in laminar. As estimated by the Reynolds number of the flow channel, the flow velocity should not exceed 3 m/s in the 500µm cooling channel to obtain the laminar state, the relevant convective heat-transfer coefficient is 7500 W/m2·k. Based on this convective heat-transfer coefficient, the thickness of the gain medium is limited by the highest heat density of single disk. The stable operation of the direct-D2O-cooled laser resonator is limited by both the fracture stress σmax and the temperature rise of coolant ΔT.
Fig. 2 The limits of heat generation rate as a fuction of the thickness of disk, the inset shows the the relevant convective heat-transfer coefficient with different velocity of flow which is simulated by Comsol.
As for the side-pumped Nd:YAG thin disk laser resonator, the strongest heat density and temperature gradient appear on the end surface along the pumping direction. The highest heat density loading on a single disk is limited by:
where f = 8.2 × 10−6 K−1 is the coefficient of thermal expansion, E = 300 GPa is the Young's modulus, ν = 0.33 is the Poisson's ratio, k = 10 W/mK is the thermal conductivity. σmax = 43 MPa is selected as the maximum thermal stress (far lower than the typical stress fracture limit of 130 MPa for Nd:YAG). As can be seen from Eq. (1), the maximum thermal density is inversely proportional to the square of the thickness d.As for the temperature rise of coolant ΔT, under the no-slip assumption, the boundary of low viscosity liquid has a temperature boundary layer close to the velocity boundary layer, meaning that: for the liquid boundary layer, the flow velocity decreases and the temperature rises. the maximum temperature ΔT is calculated as:
in which hc = 7500 W/m2⋅k is the convective heat transfer coefficient. Temperature of inlet is 15°C. To avoid the maximum temperature of the liquid near the boiling point, ΔT can be close to 85 K. To avoid the bubble generation, ΔT will be controlled within 45 K.Based on the analysis of the limitation of σmax and ΔT mentioned above, the limits of heat generation Qmax in two kinds of boundary conditions as a function of the thickness of a disk are shown in Fig. 2. The heat generation is limited by thermal stress with the disk thickness of more than 2 mm, and limited by temperature rise with the disk thickness of less than 2 mm. Therefore, the thickness of disk is designed to be 2 mm, and the corresponding maximum heat generation rate of 330 W/cm3. Considering the uniformity of pump beam, the chamfer at the end of the disk, the maximum heat generation rate at the pump inlet will be designed below 200 W/cm3.
2.2 Loss analysis
For the direct-D2O-cooled laser resonator, as the gain module contains dozens of solid-liquid interfaces and thin disks, the superposition of tiny losses at each interface may result in serious cavity losses. Typically, the cavity loss mainly consists of the following parts: The absorption and scattering loss of the Nd:YAG disk lsa, about 0.2 ‰ for a disk. The intrinsic absorption loss of the coolant lla, the theoretical value of a single flow channel is about 0.5 ‰. The depolarized loss ldp is attributed to the 0.5mm shims in the four corners of the disk in order to separate disks and form the cooling channels. As a result, the disturbed flow will be formed leading to non-uniform heat transfer in the shims area. Based on the CFD model, the flow condition of the disturbed flow in the four shims area can be obtained, and then the heat distribution and the thermal stress of every crystal can be calculated by the finite element method. Therefore, the depolarization distribution of the polarization light can be acquired by introduced the elasto-optical coefficient to the computation model, and the polarization light transmittance loss can be estimated. As shown in the inset (c) of Fig. 3, the main depolarization distribution of s polarization light appears at the four corners of the disks. The depolarized loss caused by thermal for a single disk is less than 0.2 ‰, taking into account the fixing stress and the uneven pressure caused by the pressure drop of the coolant, the loss will not exceed 0.3‰. The interface loss la caused by angle offset due to the Fresnel Reflection is related to the assembling accuracy of GM and the debug accuracy of the resonator. The loss of single disk versus the angle deviation is shown in the inset (b) in Fig. 3. The loss lt caused by the Brewster angle variation in different temperature is described in the inset (a) in Fig. 3, the loss lt of single disk exponentially increases with the temperature at the interface. The loss lo is caused by the bubbles caused by liquid cavitation effect. From the analysis above, with the number of disks N. the cavity loss L can be calculated as:
Fig. 3 The round-trip loss of the laser resonator varies with the number of disks. The inset (a) shows the loss lt caused by the Brewster angle variation in different temperature, the inset (b) shows the loss of single disk versus the angle deviation, and the inset (c) shows the main depolarization distribution of s polarization light.
The round-trip loss versus the number of disks under different tolerance of incident angle is shown in Fig. 3. It is obvious that the loss almost linearly increases with the number of the disk. In the direct- D2O-cooled side-pumped thin disk laser resonator, 40 Nd:YAG thin disks are selected implying that about 20% total loss will be introduced in one round-trip with the tolerance of offset angle 2°,worsely, the loss will be more serious due to the pollution of D2O which is caused by the oxidation reaction between D2O and the metal pipeline. As discussed in the reference [16], the total loss is a pivotal factor to impact the output power and efficiency in a laser resonator, and consequently various control measures should be adopted to reduce the loss of the laser resonator, such as the solid-liquid interface tratement.
2.3 Laser dynamics analysis of the laser resonator
In the direcct-D2O-cooled side-pumped Nd:YAG thin disk laser resonator, pieces of Nd:YAG thin disks with the thickness d and transverse area S = a × b are arranged in the resonant cavity in which a is the length of the disk perpendicular to the pumping direction and b is the length of disk along the pumping direction. The total pump injection power is Pin. Based on the maximum heat generation rate of the material, the relationship between the number and size of disks and the power of pump light can be calculated. In order to obtain a absorption efficiency close to 95%, the pump absorption length b is determined by the absorption coefficient α which is related to the doping concentration, b≈3/α. Perpendicular to the pumping direction, the size of disks a is limited by the pump power and the number of disks. Based on the relationship of pump power and the thermal boundary Eq. (2), the size a can be calculated as follows:
where ηh is the comprehensive heat generation rate of the material which concludes the heat generated by Stokes effect, cross relaxation, excited state absorption, phonon effect and concentration quenching [18]. For 0.25at%-doped Nd: YAG material, the ηh is 38%. Qmax is the heat density limited by the temperature rise of coolant. Based on a stable thermal management condition, the number and size of the disks are correlatively. More disks used means the size of disk can be smaller, leading to a longer gain length and higher round-trip gain, but the cavity loss will increase. On the contrary, fewer thin disks mean lower cavity loss, but the gain length will reduce. By using the rate equation, the output power with different disk number and size can be calculated as follows [19]: in which g0 is the gain coefficient, νP is the frequency of the pump light. R is the equivalent feedback rate of the resonator. τ is the effective lifetime, the effective of ASE should be taken into account with low reflectivity output coupler [20]. Following reference [20], we assume that the average photon of the spontaneous emission travels an average distance Z. The averaged photon of spontaneous emission becomes eGZ photons as it leaves the active medium. This changes the effective decay rate of the medium by a factor eGZ. If τ0 is the lifetime of the upper manifold, the effective life time can be estimated as τ = τ0* exp(-GZ). For the Nd:YAG with 0.25at%, the τ0 is 250 μs, as a result the τ is about 190 μs. It is noteworthy that the Eq. (7) is a theoretical calculation model based on the rate equation, which is appropriate for both stable cavity and unstable cavity. The main difference is that the equivalent feedback rate R of the unstable cavity could be described as R = 1/M2, M is the resonator magnification. In addition, the Eq. (7) is applied to optimize the number and the size of the Nd:YAG disk rather than achieve a particularly accurate power result, hence, some approximation are introduced in Eq. (7) reasonably, such as the overlap efficiency of unstable cavity.Under the QCW mode with the duty cycle of 12.5%, the average pump power is 42 kW (pump efficiency of 90%, due to the loss caused by the pump coupled system), the output power versus the number of disks at different lsd (comprehensive loss of single disk) is shown in Fig. 4(a). For the sake of obtaining 10 kW scale laser output, and the loss of a disk in a single path lsd can be controlled to 2~3‰ in the system, so that the number of the disk could be set as 40 and the area size is about 17 cm2. In addition, the the absorption coefficient α of the 0.25 at% Nd:YAG disk is about 0.62 cm−1, the pump absorption length b should be set as 4.8 cm, as a result the scale of the disk is designed as 4.8 cm × 3.5 cm × 0.2 cm.
Fig. 4 (a) The variation of simulation output power and size of a Nd:YAG disk with the number of disks. (b) The output power and the optical-optical efficiency with different pump power and reflectivity of output coupler.
The variation of the output characteristic for different reflectivity of output coupler versus pump power is depicted in Fig. 4(b). Both the output power and optical efficiency are optimum in the 40% reflectivity of output coupler, which indicated a high gain in the resonator. However, for the direcct-D2O-cooled side-pumped Nd:YAG thin disk laser unstable resonator, the resonator length and resonator magnification should be taken in consideration comprehensively, the resonator magnification of 2.0 is elected in the system and the equivalent reflectivity of output coupler is 25%. Therefore, as for theoretical calculation the output power and optical efficiency are 12 kW and 30%,respectively.
2.4 Wavefront aberration compensation
Based on dual side-pumped configuration, the intrinsic aberration caused by the negative exponential absorption of the pump light can be approximated as:
For the Taylor expansion of Eq. (8), the main portion intrinsic aberration is quadratic term which predicates defocus aberration, as shown in Fig. 5(a). The focal length of the defocus aberration obtained by the finite element method approximately is on the order magnitude of 10 m with the increasing of the number of thin disks. For the unstable cavity with a cavity length of 1.6 m, this defocus aberration will significantly change the output coupling ratio, overlap efficiency and loss, which ultimately reduces the optical-optical efficiency and beam quality. In the direcct-D2O-cooled side-pumped Nd:YAG thin disk laser resonator, the pivotal method to compensate defocus is to insert variable-focus lens group which are composed of two cylindrical lens. The simulation result of cylindrical defocus compensation in unstable resonator is drawn in Fig. 5(b). It is demonstrated that the variation of the beam size caused by defocus aberration is small after compensated by variable- focus lens group.
Fig. 5 (a) The thermal aberration caused by side-pumping. (b) The influence and compensation of cylindrical defocus in unstable resonator.
In the 22 cooling channels, laminar flow is utilized to cool the Nd:YAG thin disks. It is obviously that the temperature of coolant will increase linearly along the flow direction, meaning that the temperature is lower at the flow entrance than the exit. Such a temperature difference of the flow ΔT leads to a difference of refractive index (n = n0 + ΔT × dn/dT, dn/dT is thermo-optical coeffecient of coolant), and then resulting in a thermal-gradient-induced tilt aberration along the flow direction. Two same gain modules with opposite flow directions placed within the cavity will compensate the non-uniform distribution of the refractive index.
The k- ε model is chosen to discuss the flow field in cooling channel. Based on the assumption of the ideal pump absorption and the uniform flow velocity, the temperature distribution of the gain medium and the coolant can be calculated under the solid-liquid coupling condition. The CFD numerical simulation results are shown in Fig. 6(a) and Fig. 6(b). The tilt aberration in the flow direction induced by thermal distribution which is one of the main factors reducing the output power and the stability of the laser resonator. To solve this problem, two same gain modules with opposite flow directions are placed in the cavity to self-compensate the tilt aberration [14]. The schematic diagram of the tilt self-compensation is shown in Fig. 6(c).The OPD decreases from 54 μm (the same flow direction) to 14 μm (the opposite flow direction), demonstrating that the self-compensation of tilt aberration is effective.
Fig. 6 The thermal aberration caused by cooling flow field and the self-compensation of tilt aberration. (a) The OPD with same flow direction; (b) The OPD with opposite flow direction; (c) The schematic diagram of the tilt self-compensation.
3. Experimental results
The detailed configuration of the direct-D2O-cooled side-pumped Nd:YAG thin disk laser resonator is expressed in Section 2, as shown in Fig. 1(a). The coolant D2O is kept circulating in the opposite direction with Vflow = 3 m/s. During the experimental procedure, the QCW mode is used to obtain higher laser gain with a highest repetition frequency of 500 Hz (1~500 Hz) and a constant pulse width of 250 μs.
The single pulse output energy and optical-optical efficiency ηo-o as a function of the pumping energy at 10Hz is shown in Fig. 7(a). More than 20 J single pulse energy is obtained both in the stable resonator with R = 75% and the unstable resonator with M = 2.0. The ηo-o of the stable resonator and unstable resonator are 27% and 23% respectively. The ηo-o in experiment is lower than the theoretical simulation results (as shown Fig. 4). The increasing loss introduced by the D2O coolant pollution is the main reason attributing this phenomenon. The low overlap efficiency of unstable resonator with high magnification is another reason. Moreover, the poor efficiency of the pumping coupled system (only 90%) limits the laser efficiency, the ηo-o has the potential to increase 2 ~3 percentage point with majorization of the pumping system.
Fig. 7 (a) Output pulse energy and optical-optical efficiency as a function of the pumping energy at 10 Hz, the inset is the picture of the laser system. (b) Average output power with different pumping power, the insets (c) and (d) show the near-field intensity distributions of the laser beam with the maximum output power in stable resonator and stable resonator respectively.
The average output power as a function of the pumping power is shown in Fig. 7(b). At high repetition frequency, the average output power 9.8 kW with ηo-o = 26% and 9.1 kW with ηo-o = 21.8% are achieved in the stable resonator and unstable resonator respectively. In the resonator, due to the Brewster angle transmission, the output is linearly polarized beam. The heat generation and thermal aberration will be more serious with the increasing of repetition frequency. The output power shows a linear increase with pumping power, and the efficiency is about 26% (the black line in Fig. 7(b)). However, for the unstable resonator without defocusing compensation (the red line in Fig. 7(b)), the ηo-o decreases rapidly which can be ascribed to the increasing cavity loss and the decreasing overlap efficiency caused by the thermal-induced-defocus. With defocusing compensation by a cylindrical lens in the unstable resonator (the blue line in Fig. 7(b)), the ηo-o increases conspicuously to 21.8%, nevertheless the ηo-o is still lower than that of low heat loading condition (about 24%).
The insets (c) and (d) of Fig. 7(b) show the near-field intensity distribution of the laser beam with the maximum output power in stable and unstable resonator respectively. The size of the laser beam is close to that of the clear aperture both in the vertical and horizontal directions.
The far-field spot patterns of the unstable cavity and stable cavity are displayed in Fig. 8(a) and Fig. 8(b) respectively. Obviously, the laser power of unstable resonator cavity is more concentrated than that of stable laser. This result can be interpreted as that there are more high-order modes with larger divergence angles in the laser output from stable cavity, which leads to more divergent laser beam. Owing to the special structure of unstable cavity, the loss of high-order modes is larger than low-order modes, therefore, it is easier to obtain fundamental mode laser from unstable cavity, which results in a more convergent far-field spot pattern.
The beam quality β factor is employed to measure the beam quality of direct-D2O-cooled side-pumped Nd:YAG thin disk QCW laser. The β is defined as the ratio of the divergence angle of the actual spot (θ1) and that of the ideal spot with same spot size (θ0) [21]: β = θ1 / θ0. The β is a value greater than 1, and the closer to 1 the better beam quality is. The beam quality of the unstable cavity laser βunstable = 9.5, while the stable laser βstable = 14.7, implying a better beam quality for unstable cavity. Nevertheless, owing to the lack of the high-order aberration compensation, the output beam quality of the unstable resonator is still imperfect. It is inferred that a good beam quality will be obtained once the uniform of pump and coolant is improved and the deformation mirror is used.
4. Conclusion
In summary, a direct-D2O-cooled side-pumped Nd:YAG thin disk QCW laser resonator has been presented. The system is quite compact with a volume of less than 0.4 m3. More than 20 J single pulse energy is obtained both in the stable and the unstable resonators under low heat loading. At high repetition frequency, the average output power 9.8 kW with ηo-o = 26% and 9.1 kW with ηo-o = 21.8% are achieved in the stable resonator and unstable resonator respectively, and the corresponding beam quality factor βstable = 14.7 and βunstable = 9.5 respectively. The experiment results exhibit the validity and feasibility of the novel configuration in high power operation, in terms of distributed gain and distributed cooling. To our knowledge, the output power demonstrated in this paper is the reported highest output power based on YAG direct-liquid-cooled multi-disk laser. Higher power scaling with this configuration is realizable in the future with the reduction of loss of single disk and the increase of the number of the thin disk.
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