Cooling Geometry Dependent Operation Properties in a Diode End-Pumped Monolithic Yb:YAG Laser

Abstract

Operation properties, such as output power, beam radius, and crystal temperature rise were investigated in a diode-pumped edge-cooled monolithic Yb:YAG laser with ~ 4 W pumping level. The output power showed saturation behavior because of severe temperature rise and poor spatial overlapping between pump beam and lasing mode. Face cooling geometry by using a sapphire plate was also investigated. No apparent saturation behavior in output power was observed due to the reduced temperature rise, which could be attributed to efficient heat removal through the crystal-sapphire interface.

I. INTRODUCTION

Yb:YAG crystals have been widely studied because they have various advantages for efficient diode-pumped lasers [1-4]. Yb:YAG has a broad pump line at 940 nm that is 10 times broader than the 808 nm pump line in the conventional Nd:YAG, which makes the system less sensitive to thermal drift of the laser diode (LD) wavelength [5]. Due to high quantum efficiency of the 1048 nm transition line, the thermal load can be substantially reduced compared to that of the Nd:YAG lasers. Because the doping concentration of Yb3+ can exceed 50 %, the optimal crystal thickness for diode end pumping can be fairly shortened to below a few 100 μm, which is beneficial for thin disk type or monolithic lasers [6, 7]. Due to relatively broad gain bandwidth, mode locking operations for ultrashort pulse lasers are also reported [8, 9].

Due to the quasi-three level nature of Yb3+ , the operation properties of the Yb:YAG laser depends strongly on the crystal temperature. At room temperature, the low level of 1048 nm laser transitions line has a population of ~ 0.02, which induces non-negligible reabsorption loss [10]. Because the reabsorption loss tends to increase with temperature, the crystal temperature rise due to the thermal load might degrade the laser performance such as the laser efficiency. Therefore, some cooling scheme is essential to prevent severe crystal temperature rise by the absorbed pump beam. A proper measurement scheme for crystal temperature rise is also required to evaluate the cooling capacity.

A few noncontact measurement schemes for crystal temperature have been reported, such as crystal surface temperature mapping by using an infrared camera and the spectral analysis of the upconversion emission from the crystal impurity [11, 12]. Recently, we reported an excellent measurement scheme for crystal temperature by analyzing the spectral shift of the lasing peaks [13]. The temperature and strain profiles induced by the thermal load produce phase change on the cavity modes, resulting in the red shift of each lasing peak. For a small crystal thickness where the plane stress approximation (PSA) is valid, the amount of red shift could be related linearly to the average temperature rise along the beam axis [13].

On the other hand, the previous work was limited to a low pumping level (up to ~ 1 W) with a very small pump spot size (~ 60 μm) [14]. Thus, the reported maximum temperature rise was only ~ 20℃ in an edge cooling configuration. It should be valuable to apply the measurement scheme to a higher pumping level because increased temperature rise might induce unexpected operation behaviors of the laser. Here, we applied the scheme to a higher (~ 4 W) pumping level to measure the temperature rise, and we investigated the laser operation properties. We also investigated the effect of the cooling geometry on the temperature rise and laser operation properties by using two PSA valid face cooling configurations.

 

II. EXPERIMENTS

The experimental setup for the temperature measurement scheme is shown in Fig. 1, which is similar to that in our previous paper [13]. The crystal used was the same as the previous one (20 at.% Yb:YAG with a 0.75 mm thickness). Both faces of the crystal had dichromatic coatings (input face; HR at 1050 nm and HT at 930 nm, output face; 92% reflectivity at 1050 nm and HR at 930 nm). The crystal was sandwiched by two contacting copper plates having a central hole of 3 mm diameter, as depicted in the crystal holder in Fig. 1. The crystal holder was temperature controlled in a crystal oven. A collimated fiber-coupled laser diode (FC-LD) module was used for continuous-wave (cw) pumping. The core size of the fiber (NA of 0.22) in FC-LD was 105 μm, two times larger than that of the previous one [13]. The collimated beam passed through an optical isolator consisting of a Faraday rotator and two prism polarizers (PP1, PP2) in order to block reflected light to FC-LD. Aspheric lenses (L1, L2) with the focal lengths of 18 mm were used for focusing and re-collimation of the pump beam. Finally the pump beam was focused on the crystal by lens L3 (f3 = 18 mm). The maximum pump power at the crystal was ~ 4.5 W with a wavelength of 930 nm.

FIG. 1.Experimental setup. FC-LD: collimated fiber-coupled laser diode, PP1 & PP2: prism polarizers, L1: focusing lens (f1 = 18 mm), L2: collimating lens (f2 = 18 mm), L3: focusing lens (f3 = 18 mm).

The pump beam can be switched from cw mode to pulse mode by inserting an optical chopper between L1 and L2. The chopper blade, locating near the focal region of the pump beam, had a small single slot for one pumping pulse per turn. The lasing spectra in pulse mode (or cw mode) were measured by an optical spectrum analyzer (OSA). The pulse signal of a photo diode, detecting the reflected beam from the crystal through the slot, was used as the triggering input signal of the OSA in pulse mode.

 

III. CW OPERATIONAL PROPERTIES

The pump spot size focused by L3 at the crystal is an important parameter on the operation performance. We measured pump beam size (or diameter) in free space by using previous knife edge method [13]. The pump beam size was defined as the distance between tail points of the pump beam profile, as described in the previous work [13]. The spot size of the pump beam was about 120 μm, which is significantly larger than the previous one of 68 μm due to the larger fiber core size. The measured beam quality factor M2 of the focused pump beam was ~ 25. Because the size variation of the pump beam near the focal spot was very small (~ 10% in the crystal length range), the pump beam size could be approximated as a constant in the crystal. The absorption efficiency during the double pass in the crystal was measured as ~ 80 % and was insensitive to the LD current or input pump power.

Figure 2 shows the dependence of the cw laser output power Pout on the input pump power Pin. The threshold pump power was about 0.4 W. The output power increased linearly up to Pin ~ 2.3 W, as shown as a dotted line. The slope efficiency with respect to the absorbed power was estimated as about 43%, which is slightly smaller than the previous one [13]. When the input power exceeds 2.3 W, Pout was saturated at around 0.7 W and then decreased. If the input power increased more than 3.3 W, Pout was unstable and rapidly decreased to 0. This saturation effect of Pout might be due to severe temperature rise in the crystal or poor spatial overlapping between pump beam and lasing mode.

FIG. 2.Dependency of the cw laser output power Pout on the input pump power Pin.

The intensity profile of the cw output beam was measured by a pinhole-attached photo diode (not shown in Fig. 1), as illustrated in the previous work [13]. Figure 3(a) shows the output beam profiles at various Pin, in which the distance d from crystal to photo diode was 30 cm. The profiles were well fitted with the Gaussian functions depicted as lines, which means that the lasing transverse mode was TEM00 at all ranges of Pin. Figure 3(b) shows the pump power dependent output beam radius w(z = d). It increased slowly up to Pin around 2.0 ~ 2.3 W and then radically. By assuming the lasing mode was TEM00 or Gaussian mode, the waist radius w0 of TEM00 mode in the crystal can be estimated from the relation [14]. In Fig. 3(b), dependency of w0 on the pump power is also shown. Because the waist radius w0 is inversely proportional to the beam radius w(d), it decreased slowly at first and then rapidly above Pin ~ 2.3 W. For small Pin (≤ 2.0 W), the waist size 2 w0 of TEM00 was about 100 μm, which is slightly smaller than the measured pump spot size of ~ 120 μm. Thus, the spatial overlapping between pump beam and lasing mode should be good and resultant lasing efficiency was measured relatively high at low pump power in Fig. 2. However, the spatial overlapping became poor due to rapid decrease of w0 when Pin exceeded 2.3 W, resulting in the saturation behavior of the output power, as shown in Fig. 2. At Pin = 3.0 W, the waist size decreased to ~ 60 μm, which is only half of the pump spot size. Thus, the saturation behavior in Fig. 2 above Pin ~ 2.3 W can be mainly attributed to the poor spatial overlapping between pump beam and lasing mode. The rapid decrease of w0 should be due to the enhanced thermal lensing effect, which is a result of the severe thermal load [15].

FIG. 3.(a) Pump power dependent output intensity profile measured at a distance d = 30 cm from the crystal. (b) Pump power dependent output beam radius fitted by Gaussian function. Corresponding waist radius of TEM00 mode is also shown

 

IV. TEMPERATURE RISE & SPECTRAL SHIFT

Figure 4(a) shows the pumping and cooling configuration adapted in this study. The cooling geometry is basically the same as the previous edge cooling arrangement [13]. The crystal (thickness of L) is sandwiched by copper plates with a central hole (diameter of 2b). The pump spot size 2a is negligibly smaller than 2b. The copper plate temperature Tc is controlled to a constant value in the crystal oven. When the crystal absorbs radially symmetric pump beam, some portion of the absorbed energy converts to heat. The fractional thermal load η , the ratio of generated heat to absorbed energy, is much smaller than 0.11 in Yb:YAG [16]. The generated heat and its radial flow through the crystal with a limited thermal conductivity enhance the crystal temperature. The local temperature profile T(r, z) at a point P in the crystal is a function of the radial distance r and of the longitudinal distance z. Calculation of T(r, z) at all points in the crystal is theoretically possible by solving the heat equation and by applying boundary conditions on the crystal-copper interface, but is very difficult under real circumstances because there are undetermined parameters such as thermal contact resistance [17]. Averaged temperature with respect to z around the pump beam region is an important parameter because the lasing mode experiences not the local temperature but averaged temperature during round trip in the crystal. Average temperature at a given r is defined as [17]

FIG. 4.(a) Schematic edge cooling geometry. (b) The expected curve of average temperature

Figure 4(b) shows the expected curve in the crystal of Fig. 4(a). The maximal value of is the average temperature along the beam axis. For a given pump power Pin, the difference in the pumping hot region depends on the detailed pump beam profile. Whereas, the difference in the hole region is independent of the pump profile because there occurs only heat transfer from the pump region to the heat sink (copper plate). Temperature gaps at the crystal-copper interface can exist because there might be thermal contact resistance [17]. The overall temperature rise measures the temperature change along the beam axis after pumping. It is notable that in a typical ratio of a/b (< 0.1), is very small compared to the temperature rise , which implies that the temperature rise in the crystal is nearly independent of the detailed profile of the pump beam.

Figure 5 shows measured lasing spectra at various Pin in cw mode and the threshold lasing spectrum in pulse mode with Tc = 20℃. The lasing spectra consisted of periodic peaks with same mode spacing of 0.4 nm at all ranges of Pin. This means that the lasing peaks correspond to different longitudinal modes with the same transverse mode of TEM00. Hence, it was confirmed that the assumption of TEM00 lasing in Fig. 3(b) is reasonable. As Pin increased, each lasing peak shifted to the longer wavelength side. In Fig. 5, the amount of peak shift Δλ is indicated as an arrow starting from a lasing peak in pulse mode, in which the temperature rise could be approximated as 0 because the duty cycle in pulse mode was very low (< 2 %).

FIG. 5.Measured cw lasing spectra with Pin at Tc = 20℃. The threshold lasing spectrum (black line) in pulse mode is also shown. The amount of peak shift Δλ in cw mode is indicated as an arrow starting from a lasing peak in pulse mode

The red shift of the lasing peak was previously attributed to the round-trip optical path length (OPL) change experienced by the cavity modes [13]. With the cw pump on, the non-uniform temperature field T(r, z) induces not only thermally induced refractive index change but also stress field in the crystal, resulting in non-uniform crystal strain field. The strain field produces crystal length change and strain induced birefringence [17]. Hence, the cavity mode experiences thermally induced refractive index change, crystal length change, and strain induced birefringence effect. For a uniform pump profile, the strain induced contribution of OPL change can be derived under the plane stress approximation (PSA), in which the axial stress approaches 0 as the aspect ratio L/2b decreases [18]. The used thin crystal (L/2b = 0.25) is in the valid regime of PSA [18]. For TEM00 mode, small contribution by the phase retardation effect of the Gaussian beam should also be included [14]. Because overall OPL change is positive, the cw lasing wavelength of the cavity mode will show continuous red-shift as Pin increases.

In the previous work, we showed that the amount of red shift Δλ under PSA is proportional to the temperature rise ( as [13]

where SLeff is the effective scale factor or ratio between Δλ and the temperature rise. If the phase retardation effect is neglected, SLeff ranges between SLu and SLnu, where SLu is the scale factor in the case of uniform crystal temperature change and SLnu is the scale factor in the case of non-uniform temperature and strain fields. If the temperature gap at the crystal-copper interface in Fig. 4(b) is negligibly small, SLeff approaches to SLnu. Previously, we derived SLnu with the material parameters and calculated in YAG crystal [13]. The calculated value of SLnu was only 13 % larger than SLu.

The phase retardation term should be accounted in a real situation where the temperature gap also exists. In the previous work with the same cooling configuration with Fig. 4(a), SLeff was measured by using very complex procedure. Because the phase retardation term has a nature of decreasing the peak shift, SLeff was found to be very close to SLu [13]. Therefore, we will adapt the approximation SLeff ~ SLu in this work. SLu can be derived from the shifting behavior of a threshold lasing peak in pulse mode by varying Tc, in which the crystal temperature profile can be considered to be uniform because the non-uniformity induced by pump pulse is negligibly small. Because the temperature rise in this work is expected to be much larger than the previous case, spectral data with wide range of Tc is required. Figure 6(a) shows the linearly shifting behavior of a threshold peak in pulse mode, measured by varying Tc from 30℃ to 120℃. It shows that the slope, corresponding to SLu, was 0.0119(± 0.0001) nm/℃.

Figure 6(b) shows the dependency of the amount of peak shift Δλ measured from Fig. 5. The temperature scale, calibrated by SLeff = 0.0119 nm/℃ in Eq. (2), is also plotted on the right axis in order to obtain the temperature rise. The temperature rise increased linearly with a slope of 18.9℃/W as Pin increased up to 2.0 W. When Pin exceeded ~ 2.3 W, the temperature rise deviated from this trend and its slope became steeper. The deviation point of Pin ~ 2.3 W is coincident to those in the output power and the waist radius dependency (in Fig. 2 and 3). The temperature rise corresponding to Pin ~ 2.3 W was ~ 45℃ . The maximal temperature rise at Pin = 3.3 W was about 83℃ .

FIG. 6.a) Relative peak shift of a threshold peak in pulse mode with Tc. The slope SLu of the relative peak shift is fitted as 0.0119( ± 0.0001) nm/℃. (b) Dependency of amount of peak shift Δλ and corresponding temperature rise on Pin.

As the crystal temperature increases, the reabsorption loss increases, which affects laser operation performance in succession. First, the increased reabsorption loss shifts the envelope of the lasing spectrum to the longer wavelength side because the threshold condition for lasing occurs at a lower absorption region. Besides the red-shift of each lasing peak, the red-shift of lasing envelope with Pin can also be observable in Fig. 5. The lasing at lower absorption region which corresponds also to the lower gain region, means that the laser efficiency becomes poor, resulting in the deviation of the output power dependency, as observed in Fig. 2. Second, the fractional thermal load η under laser action depends on the laser extraction efficiency as previously reported [19]. As the laser efficiency decreases, η increases. Because the laser efficiency decreases above the deviation point, η increases (or a greater fraction of heat is generated so that steeper temperature rise occurs), which in turn degrades further the laser efficiency, resulting in the saturation of output power. Therefore, the saturation behavior can be partially attributed to increased η in addition to the poor spatial overlapping mentioned before.

In our previous case, the maximal temperature rise at Pin = 1.05 W was ~ 22℃. In this scaled up case, the temperature rise at Pin = 3.0 W, at which maximum output power was obtained, was about 68℃. Therefore, it could be concluded that the temperature rise was roughly proportional to the absorbed pump power regardless of the pump beam size, even though η and contacting condition of copper-crystal interface might be slightly different between both cases.

 

V. FACE COOLING GEOMETRY

The generated heat from the pump region flows radially in the edge cooling geometry of Fig. 4(a). Because the heat sink is located fairly far from the pump region, the temperature rise in the crystal was measured as high. Face cooling configuration is an efficient method of removing generated heat rapidly from the thin crystal because the heat sink can be closely contacted to the pump region [20, 21]. Figure 7 shows the face cooling configurations used in this work, in which a sapphire plate directly contacts to one face of the crystal used in Fig. 4(a). Because the crystal was mechanically contacted to the sapphire plate with no solder, temperature gap might exist at the contact interface. This configuration is similar to the cooling setup of a thin disk laser introduced in Ref. [22, 23], in which indium-based or gold-tin solder was used for more efficient heat removal. Since additional heat flow occurs longitudinally from the pump region to the sapphire, reduced temperature rise is expected compared to the case of Fig. 4(a).

FIG. 7.Schematic face cooling geometry. Case A: Sapphire plate A is contacted to the output face of the crystal. Case B: Sapphire plate B is contacted to the input face of the crystal.

Two cases of one-face cooling were tried in this study. In case A, the sapphire A was contacted to the output face of the crystal. The non-contact side of the sapphire A was AR coated on the lasing wavelength, while the contacting side was uncoated. In case B, the sapphire B was contacted to the input face of the crystal. The contacted face of the sapphire B was uncoated, while the other side was AR coated on the pump wavelength. The sapphire plate intermediates heat flow between crystal and copper. Because thermal conductivity of sapphire is relatively high as ~ 42W/m/K, which is 3 times larger than that of Yb:YAG, the temperature of the sapphire contacting to the copper can be assumed to be nearly equal to Tc. That is, the sapphire can be considered as a heat sink.

Figure 8(a) shows the dependency of the output power Pout on the input pump power Pin in the two cases. The output power increases nearly linearly in both cases and no apparent saturation phenomenon, below Pin ~ 4.0 W, was observable. The slope efficiencies in both cases were higher than for the case of Fig. 4(a). The improved output power performance must be due to the considerably reduced temperature rise in the face cooling cases. It is notable that case B showed slightly higher output power than case A. Because the intensity of the pump beam decreases rapidly by absorption during propagation through the crystal, the input face of the crystal should be hotter than the output face in Fig. 4(a). The sapphire contacting hotter face will remove more efficiently the generated heat than the other case, resulting in the better output performance of case B in Fig. 8(a). In case B, the maximum Pout was measured 1.3 W, which is about 2 times larger than that in Fig. 2.

FIG. 8.(a) Dependency of the cw laser output power Pout on Pin in the face cooling geometry. (b) Dependency of amount of peak shift Δλ and corresponding temperature rise in the face cooling geometry.

In case of Fig. 4(a), the thin crystal is free to expand along both directions so that the axial stress was assumed to be 0. In the face cooling case of Fig. 7, the crystal is also free to expand along one direction so that the axial stress can be also approximated to be 0. As proved by Cousins, PSA is valid in the one-face cooling configuration in the limit of small aspect ratio [18]. Therefore, the relation of Eq. (2) can be also applicable in the face cooling cases in order to obtain the temperature rise.

In order to derive the temperature rise, the amount of peak shift Δλ was measured by using the spectral analysis procedure used in Fig. 5. Figure 8(b) shows the dependency of Δλ in both face cooling cases. The temperature rise calibrated by the same SLeff = 0.0119 nm/℃ was also shown in Fig. 8(b). The temperature rise in case A was slightly higher than the case B in whole range of Pin. This must be because input face cooling is slightly more efficient than the output face cooling, as mentioned. Nevertheless, it can be concluded that the face cooling configuration has similar cooling capacity regardless of the location of the sapphire plate. The input power corresponding to the temperature rise ~ 45℃, which was the deviation point of the output power in Fig. 2, was around 4.0 W in the face cooling case. Therefore, beginning part of the output saturation curve can be seen in Fig. 8(a) around Pin ~ 4.0 W.

The maximum temperature rise in Fig. 8(b) was about 55℃ at Pin = 4.3 W, which is smaller than the maximum one of 83℃ at Pin = 3.3 W in Fig. 6(b). Comparison of temperature rises with same Pin is meaningful to evaluate the cooling capacity between edge-cooling and face cooled cases. For instance, the temperature rise in case B of Fig. 8(b) was only 37℃ at Pin = 3.0 W, which is nearly half of 68℃ at Pin = 3.0 W in Fig. 6(b). The considerable reduction of the temperature rise in Fig. 8(b) should be due to the effective heat removal of the face cooling configuration.

 

VI. CONCLUSION

We measured temperature rise of an end-pumped monolithic Yb:YAG crystal by using a previous temperature measurement scheme, in which the pumping power level was scaled up to ~ 4 W. Preferential cooling geometry investigated here was the previous PSA valid one where the crystal was sandwiched by copper plates with a central hole. The temperature rise was derived from the lasing spectrum by analyzing the red shift of each lasing peak. Operation properties, such as output power and output beam radius were also investigated. The output power, beam radius, and peak shift showed deviating behaviors around the common input power of ~ 2.3 W, which corresponded to the temperature rise of ~ 45℃. Above this deviation point, the output power showed saturation behavior, the beam size increased rapidly, and the change of the peak shift became steeper due to poor spatial overlapping and increased fractional thermal load. Through the comparison with the previous work, we could conclude that the temperature rise was roughly proportional to the absorbed pump power regardless of the pumping level and pump beam size. PSA valid face cooling geometry was also investigated, in which input or output face of the crystal was contacted with a sapphire plate having high thermal conductivity. The temperature rise was considerably reduced and the laser efficiency was fairly improved in both cases due to the efficient heat removal through the crystal-sapphire interface.