Thermal lens study in diode pumped N g - and N p cut Nd:KGd(W04)2 laser crystals

. A comparative study of thermal lensing effect in diode laser pumped Ng- and Ap-cut Nd:KGd(W 04)2 (KGW) laser crystals was performed for laser emission polarized along the principle refractive axis, The thermal lens in the Ag-cnt Nd: KGW was fonnd to be weakly astigmatic with a positive refractive power for both the N„- and Np-directions. For Np -cnt Nd:KGW, strong astigmatism was observed and the refractive powers in the Ng- and A„-directions had opposing signs. The degree of astigmatism was fonnd to be considerably weaker for the A^-cnt Nd:KGW in comparison with the Np-cut one: 0.35 dptr/(W/cm^) and 2.85 dptr/(W/cm^), respectively. The ratio of the thermal lens refractive powers in the planes parallel and perpendicnlar to the laser emission polarisation were measured as + 1.4 and -0.425 for Ng- and Ap-cnt Nd:KGW respectively.


Introduction
Neodymium-doped KGdCWOaji (KGW) is a well known laser material with extensively investigated spectroscopic properties (see [1][2][3][4][5] and references therein). Nd:KGW has good prospects for self-Raman conversion to 1.54 pm [7,8] due to the relatively high emission cross-section at -1.35 pm (7.6 x 10"^° cm^ [6]) also in combination with a high Raman gain coefficient (up to 4.4 cm/GW [1]). This is of specific relevance when the laser is operated in the picosecond time domain [9]. This so-called 'eye-safe ' spectral range is attractive for realization of high frequency range finders at 1.54 pm, and atmospheric CO2 monitoring [10] at 1.57-1.6 pm (via Raman conversion in Ва(ТЮз)2). Power scaling in tungstates is, however, limited compared to Nd:YAG lasers, as the thermal conductivity coefficients are approximately 3 times lower [5]. Commercially available Np-cni Nd:KGW possess strong cylindrical thermal lensing [11], which is difficult to compensate by cavity design alone or by means of adaptive optics [12]. The output power obtainable from tungstate lasers under high power pumping is therefore substantially reduced. Moreover, the poor thermo-optical characteristics typical of tungstates limit its application as effective Raman crystal specifically for high-energy nanosecond pulse operation.
However, there exists a distinctive feature of the KGW crystal which may significantly improve this performance, namely, the negative coefficients of the temperature dependence of the refractive index, dn/dT, for some light polarizations and propagation directions (e.g. -0.8 X 10 ® К ^ for kJ/Np, ki//N") [13][14][15]. In fact, exploitation of this feature has led to higher output powers being obtained at ~1 pm compared with similar Nd:YAG lasers under high power flash-lamp pumping -average output powers of 40 W at 1.4 kW of pumping was obtained from an Ag-cut Nd:KGW crystal laser which compares favourably with 15 W of output from a similarly configured Nd:YAG laser [16]. In the same configuration, the more conventional Np-cut Nd:KGW crystal laser ceased operating at only 0.5 kW of average pump power. In another demonstration, an end-pumped Ng -cut Yb:KGW crystal produced ~5 W of laser output power with a near-diffraction limited beam quality [17] under 18 W pumping.
The key point of these examples was the exploitation of the special, often called athermal. direction of propagation within the KGW crystal, where the temperatnre-and stressdependent refractive indices compensate each other, resnlting in significantly lower thermal lensing [13][14][15]. The direction along the principle refractive axis Ng has been identified as being one of these athermal directions, althongh other orientations are also possible [13,15]. Snch 'smart-cnf tnngstate crystals therefore show great promise for flexible thermal management, giving access to a wider range of applications inclnding self-Raman conversion.
In this paper, we will compare the thermal lensing effect in two diode laser pnmped Nd:KGW lasers having the light propagation direction along the principle refractive axes Ng and Np (hereafter denoted as A^^-cnt and A^^-cnt Nd:KGW crystals, respectively). As a resnlt the thermal lensing sensitivity factors, M, for these crystals can then be determined and the degree of thermal lens' astigmatism for both crystals can be calcnlated and compared. This factor M -the rate at which the thermal lens refractive power varies with pnmp power intensity -then provides a convenient measnre to compare the indnced thermal lensing in different laser crystals and orientations [18]. The degree of astigmatism here is the difference between the valnes of thermal lens refractive power per pnmp intensity (i.e. between the valnes of the factor M) in the plane of polarization (A") and in the perpendicnlar plane -a typical measnre of astigmatism in, for example, ophthalmology [19].

Experimental
The Nd:KGW crystal was grown from the flnx by nsing K2W2O7 as a solvent. The modified Czochralski techniqne was nsed nnder conditions of low thermal gradient [20]. The Ap-cnt Nd:KGW laser gain medinm was grown along the crystallographic axis b which is parallel to the principle refractive axis Np, whereas, the Ag-cnt Nd:KGW material was grown along the crystallographic axis c (the angle between the c-and Ag-axis is 21.5° [21]). Other properties of the Np-and Ag-cnt Nd:KGW crystals were identical.
In all the experiments described here, the Ag-cnt and Ap-cnt Nd:KGW crystals had a doping level of 7 at. % neodyminm and a length оП = 1.9 mm. One polished end-face served as a flat laser cavity mirror -a mnlti-layer dielectric coating was applied to this face to provide both a high-reflectivity at the laser wavelength of 1.35 pm and antireflection at 808 nm (i.e the pnmp wavelength). The coating also provided minimal reflectivity at 1.067 pm to prevent any parasitic laser oscillation at this wavelength. The other crystal end-face was antireflectioncoated for both 1.35 and 1.06 pm. The laser crystal was monnted on a thermo-electric cooled brass plate and the temperatnre was controlled to 15 °C. Finally, the linear laser cavity was terminated by a concave ontpnt conpler having a radins of cnrvatnre of R = 50 mm and a reflectivity of 99% at 1.35 pm.
The experiments reported here were intentionally performed at a laser oscillation wavelength of 1.35 pm dne to the thermal effects in the Nd:KGW laser crystal being higher at this wavelength in comparison to oscillation at 1.067 pm. The diode lasers emitting at a wavelength of 808 nm were nsed as the end-pnmping sonrces for the laser set-np. The Ap-cnt Nd:KGW crystal was qnasi-continnonsly pnmped with the emission being linearly polarized along the A" optical indicatrix axis. Pnmp radiation was focnsed into the crystal to a spot with the diameter of 75 pm. The Ag-cnt Nd:KGW crystal was continnonsly pnmped by the fiberconpled laser diode with nnpolarized emission. The pnmp spot into the Ag-cnt Nd:KGW crystal was symmetric with the diameter of 150 pm.
Length of the crystals (1.9 mm) and doping concentration (7 at. %) provided 98.8% absorption of nnpolarised pnmp emission at 808 nm and -99.2% absorption of the polarized pnmp emission at the same wavelength. We believe the difference in absorption coefficients for polarizations along different crystal axes makes negligible impact on the measnrements. The emission of the Ng-and Ap-cnt Nd:KGW lasers is polarised along the Am-axis, and the lasers were confignred to emit a fnndamental TEMqo spatial mode.
Resonator lengths of 26 mm for the Ag-cnt Nd:KGW and of 49 mm for the A^-cnt Nd:KGW crystals were chosen to provide the highest ontpnt power. The reason for different valnes of the resonator length will be given below. Different techniques can be applied to detennine thermal lens in laser crystals: measurements of the changes of the output beam characteristics for stable resonator operating at TEMoo mode [11,17] and for the resonator close to instability region [16,22]; measurements of the changes in the spatial profile of the probe beam which is passed through a gain medium [22,23]; interferometric measurements [13,24].
Two methods were employed in the present paper to determine the sensitivity factor M. In the first method, the output beam characteristics are measured with respect to the distance from the output coupler at different pump intensities, P^nw /, where Pp and Wp are the pump power and the (1/e^) Gaussian radius of the pump beam, respectively. The measurements are performed by the knife edge method [22] in two directions: parallel to the A^m-and Ng-axes for the Л^р-cut Nd:KGW laser crystal, and parallel to the N^-and Л^р-axes for the A^g-cut Nd:KGW system. Measured output beam size dependencies on the distance from the output coupler are then simulated using the ABCD matrix method [18]. In these calculations, thermo-optical distortions within the gain medium are described by an astigmatic thermal lens of refractive power, D, which is dependent on the pump intensity. The sensitivity factor M is then obtained from the slope of the dependence of thermal lens refractive power versus the pump intensity.
The second method is based on the observation of substantial changes in the spatial and power characteristics of the laser output indicative of the laser resonator becoming unstable due to an action of thermal lensing [22]. Here, the output power of the laser is monitored as a function of the pump intensity at a given cavity length. The pump intensity, {Pplnwp)^, at which the output power begins to reduce is assumed to induce in the gain medium a thermal lens with a critical refractive power, D" corresponding to the edge of the cavity stability on the gi*-g2* diagram [18,22]. The sensitivity factor M is then calculated as the ratio of this critical refractive power to the value of {Pplnw^)^. It should be noted that, in the case of an astigmatic thermal lens, this method provides information on the sensitivity factor in one propagation plane only -i.e. the plane that approaches the stability edge at the least pump power.

Results and discussion
The typical measured dependence of the output beam mode diameter with distance from the output coupler for both the Ng-and Np-cni Nd:KGW lasers are shown in Fig. 1. From these data, it is clear that for the Ag-cut Nd:KGW laser, the output beam suffered compression in both A"-and Ap-directions with increasing pump intensity ( Fig. l(a, b)). The compression along the A"-direction was notably greater than that observed along the Ap-axis. However, in the case of the Ap-cut Nd:KGW laser (Fig. l(c, d)) as the pump intensity increases, the size of the output beam decreases along the direction but increases along Np. It follows from a calculation of the laser mode behaviour outside the laser cavity that a decrease in the mode size corresponds to an inducted positive thermal lens within the gain crystal, whereas a defocusing lens induces an increase in the mode size. From this ABCD matrix analysis the data of Fig. 1  The dependences of the thermal lensing as a function of pump intensity for the Л/^-and Npcut Nd:KGW crystals were measured and are shown in Fig. 2. As expected from theory [22], these dependences are linear with pump intensity, and from the respective gradients of the data the thermal lensing sensitivity factors M can be calculated -these were found to be, in units of dioptric power per (W/cm^):  Resonator with the length of 49 mm for the A^-cut Nd:KGW provided the widest stability region against the negative thermal lensing (which was found to be stronger in this crystal than the positive one), while the A^-cut Nd:KGW laser with the cavity length of 26 mm was about two times more stable against positive thermal lensing in eomparison with the eavity length of 49 mm (see the ealeulated eritieal values of the thermal lens refraetive power below). The differenee in the resonator length for two Nd:KGW erystals does not influenee the measurements of the thermal lens, as the ealeulations of the beam profile outside the eavity are performed separately for the given eavity length.
The measured output power dependenee on pump intensity ( P /ttw/ ) for the Np-cut and Ng-cut Nd:KGW lasers is presented in Fig. 3(a). Here, the output power inereases with inereasing pump intensity up to a eertain eritieal value, (P/7TWp^)c, above whieh the output power abruptly drops. This value of (P/7rWp^)c is equal to ^2.4 kW/em^ and ^4.3 kW/em^ for the Np-cut and Ng-cut Nd:KGW lasers, respeetively. Aeeording to [22], sueh a feature in the output power behaviour is observed when the laser resonator, due to the thermal lens indueed in the aetive element, approaehes the edge of stability region. Caleulations in [22] show that, for the resonator eonfiguration used in the experiment, there are two eritieal values of the thermal lens refraetive power (T>c)i = 1/(T-/ + ІлГ^) and (Dc)2 = -l/(R-(L-l + (where L is the eavity length, / is the gain medium length, and n is the index of refraetion of the gain medium) at whieh the laser resonator interseets the stability limits ( Fig. 3(b)). For the Np-cut Nd:KGW laser, (T>c)i = 20.8 dptr and Фс)2 = -511.6 dptr (the refraetive index of Nd:KGW for the light polarization along the Ащaxis is n = 2.01 [25]). Comparing (Т>с)і with (T>c)2 yields the relation І(Т)с)іІ«К^с)2І, and the abrupt drop in the output power for the Np-cut Nd:KGW laser ean be related to the foeusing thermal lens as the eritieal value (Т>с)і will be reaehed at lower pump intensity eompared with the eritieal value (T>c)2 of the defoeusing thermal lens. Therefore, the sensitivity faetor ean be found to be (М^р.сш)мт = (f^c)i/(^/Avp/)c = 0.87 x 10~^ dptr/(W/em^). For the Ng-cut Nd:KGW laser, (T>c)i = 59.9 dptr and (T>c)2 = -40.1 dptr. Beeause the Ng-cut Nd:KGW erystals possesses a foeusing thermal lens, the sensitivity faetor ean be found to be (M^g.^ut) = Ф с)іКР/^р^)с = 0.92 X 10~^ dptr/(W/em^). However, it is not possible to assign this value of M to a eertain (Nm or Ng) direetion.
It should be noted that the differenee in the slope effieieneies of the two lasers does not influenee the measurements of the thermal lens sinee the eritieal pump intensity depends only on the resonator parameters.
In Table 1 a summary of the results obtained for the thermal lensing sensitivity faetors M and for the degree of astigmatism for the Np-cut and Ng-cut Nd:KGW erystals are given. As ean be seen from Table 1, the M-values for the Np-and A^-eut Nd:KGW obtained by the two methods are in close agreement. Also it is clear that the Ap-cnt Nd:KGW possesses a thermal lens having strong astigmatism with the degree of 2.85 dptr/(W/cm^). The ratio of the Mfactors for and Ag-directions, (Mffp.cut)Nn/(MNp-cut)Ng, eqnals -0.425. The refractive powers of thermal lens for the Ng-and A"-directions have different sign, minns and pins, respectively. In contrast, the thermal lens in the Ag-cnt Nd:KGW displays weak astigmatism with the degree of 0.35 dptr/(W/cm^), and the valne of (Mfpg-cut)Nn/(MNg-cut)Np here is fonnd to be 1.4. This implies that the Ag-cnt Nd:KGW laser, as compared to the Ap-cnt Nd:KGW one, can operate at significantly higher pnmp intensities.  In snpport of this statement it was observed in onr experiments that the 7at.%-doped Npcnt Nd:KGW laser conld not operate in the cw regime, and laser oscillation was only obtained nnder qnasi-cw pnmping. In contrast, the 7at.%-doped Ag-cnt Nd:KGW laser easily demonstrated cw oscillation with the same cavity confignration. It shonld be noted that the characteristics of the thermal lens in the Ng-and Np-cut diode-pnmped Nd:KGW crystals obtained here are in good agreement with the resnlts of thermal lens stndies in Ng-and Np-cut Nd:KGW crystals nnder flashlamp-pnmping at a wavelength of 1.067 pm [16]. Moreover, resnlts of onr measnrements of the thermal lens in Ag-cnt Nd:KGW are also consistent with the observations of the thermal lens in Yb:KGW crystal cnt along the same direction [17]. Positive valnes of the thermal lens in vertical and horizontal directions (nnfortnnately, these directions were not assigned with the direction of polarization of the laser emission) were reported for this crystal [17]. Resnlts in [11] on the thermal lens measnrements in the Np-cut Nd:KGW demonstrated strong negative thermal lens in the plane of polarization and the positive one in the perpendicnlar plane. These observations (regarding the sign of the thermal lens) are in contrast to the one made in [16] and in the present paper. Cnrrently we cannot explain snch discrepancy in the signs of the thermal lens.
Several factors contribnte thermal lensing effect in the solid-state lasers: temperatnre-and stress-dependent variations of refractive index, bowling of the crystal faces nnder thermal expansion [18], specific diode beam profiles and collimation optics [17]. Thermo-optic coefficient dn/dT is the more significant among them especially in diode-pnmped lasers [18]. Therefore, one can compare thermal lens sign with the one of dn/dT coefficient for the laser polarization (in onr experiment it is parallel to the A"-axis for both crystals). Onr resnlts on thermal lens signs are in correlation with [13], where dependence of dn/dT coefficient on the beam propagation direction was observed, with the negative valne for light propagation along the Ap-axis and positive valne for light propagation along the Ag-axis for light polarization along A"-axis at 1.06 pm; and [14], where dnIdT coefficient (at 435.8 and 632.8 nm) for light polarization along Ag-axis was fonnd to be negative while the two other valnes for light polarizations along Np and N" axes were positive [14].
We snppose that the laser performance of Nd:KGW crystal nnder diode pnmping can be improved by ending the crystal along some directions in the Np-Ng plane for which thermal lens wonld be positive or close to zero with a weak astigmatism resnlting in near-symmetric ontpnt beam.

Conclusion
A comparative study of the thermal lensing in diode laser pumped Ng-and Np-cut Nd:KGW laser crystals was performed for laser emission polarized along the principle refractive axis Ащ. The thermal lens in A^-cnt Nd:KG was fonnd to have a weak astigmatism with positive refractive power for both the N"-and Ap-directions. In contrast, the thermal lens in Ap-cnt Nd:KGW possesses strong astigmatism with refractive powers of different signs for the Ngand A"-directions. The degree of astigmatism was fonnd to be considerably weaker for the N"cnt Nd:KGW in comparison with the Ap-cnt one: 0.35 dptr/(W/cm^) and 2.85 dptr/(W/cm5, respectively. The factor M, the thermal lens sensitivity, for both confignrations has also been stndied and characterised. The ratios of the M-factors in the plane of polarisation and in the perpendicnlar plane were evalnated to be = 1.4 and (M"p.",)"J(M"p.,J"g = -0.425 for the Ng-and Ap-cnt Nd:KGW, respectively. Thns the 'athermaT Ag-cnt crystal configuration shows significant promise specifically for diode-pnmped 1.3 pm Nd:KGW lasers operating at high pnmp intensities.