High power tungstate-crystal Raman laser operating in the strong thermal lensing regime

We report an investigation into a double metal tungstate Raman laser when pumped at elevated average powers. Potassium gadolinium tungstate (KGW) was placed in an external cavity configured for secondStokes output and pumped at pulse repetition rate of 38 kHz with up to 46 W of average power. For output powers above 3 W, we observe preferential excitation of Hermite-Gaussian transverse modes whose order in the X1' principal direction of the thermal expansion tensor scales linearly with Raman power. We deduce that strong astigmatic thermal lensing is induced in the Raman crystal with a negative component in the X1' direction. At maximum pump power, 8.3 W of output power was obtained at a conversion efficiency of 18%. ©2014 Optical Society of America OCIS codes: (140.3550) Lasers, Raman; (140.6810) Thermal effects; (160.3380) Laser materials; (190.5650) Raman effect. References and links 1. J. A. Piper and H. M. Pask, “Crystalline Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 692–704 (2007). 2. H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron. 27(1), 3–56 (2003). 3. J.-P. M. Feve, K. E. Shortoff, M. J. Bohn, and J. K. Brasseur, “High average power diamond Raman laser,” Opt. Express 19(2), 913–922 (2011). 4. O. Kitzler, A. McKay, and R. P. Mildren, “Continuous-wave wavelength conversion for high-power applications using an external cavity diamond Raman laser,” Opt. Lett. 37(14), 2790–2792 (2012). 5. A. McKay, H. Liu, O. Kitzler, and R. P. Mildren, “An efficient 14.5 W diamond Raman laser at high pulse repetition rate with first (1240 nm) and second (1485 nm) Stokes output,” Laser Phys. Lett. 10(10), 105801 (2013). 6. R. P. Mildren, A. Sabella, O. Kitzler, D. J. Spence, and A. McKay, “Diamond Raman laser design and performance,” in Optical Engineering of Diamond, R. P. Mildren and J. R. Rabeau, eds. (Wiley-VCH, 2013). 7. P. Dekker, J. M. Dawes, P. A. Burns, H. M. Pask, J. A. Piper, and T. Omatsu, “Power scaling of cw diodepumped Yb:KGW self-Raman laser,” in Proceedings of the Conference on Lasers and Electro-Optics Europe (IEEE, 2003), p. 50. 8. X. H. Chen, X. Y. Zhang, Q. P. Wang, P. Li, S. T. Li, Z. H. Cong, Z. J. Liu, S. Z. Fan, and H. J. Zhang, “Diode side-pumped actively Q-switched Nd:YAG/SrWO4 Raman laser with high average output power of over 10 W at 1180 nm,” Laser Phys. Lett. 6(5), 363–366 (2009). 9. R. Chulkov, V. Lisinetskii, O. Lux, H. Rhee, S. Schrader, H. J. Eichler, and V. Orlovich, “Thermal aberrations and high power frequency conversion in a barium nitrate Raman laser,” Appl. Phys. B 106(4), 867–875 (2012). 10. J. Liu, U. Griebner, V. Petrov, H. Zhang, J. Zhang, and J. Wang, “Efficient continuous-wave and Q-switched operation of a diode-pumped Yb:KLu(WO4)2 laser with self-Raman conversion,” Opt. Lett. 30(18), 2427–2429 (2005). 11. J. E. Hellström, S. Bjurshagen, and V. Pasiskevicius, “Laser performance and thermal lensing in high-power diode-pumped Yb: KGW with athermal orientation,” Appl. Phys. B 83(1), 55–59 (2006). 12. P. A. Loiko, I. A. Denisov, K. V. Yumashev, N. V. Kuleshov, and A. A. Pavlyuk, “Laser performance and thermal lensing in flashlamp pumped Np-cut and Ng-cut Nd:KGW crystals,” Appl. Phys. B 100(3), 477–483 (2010). 13. I. V. Mochalov, “Laser and nonlinear properties of the potassium gadolinium tungstate laser crystal KGd(WO4)2: Nd-(KGW:Nd),” Opt. Eng. 36, 1660–1669 (1997). 14. P. A. Loiko, K. V. Yumashev, N. V. Kuleshov, G. E. Rachkovskaya, and A. A. Pavlyuk, “Detailed characterization of thermal expansion tensor in monoclinic KRe(WO4)2 (where Re = Gd, Y, Lu, Yb),” Opt. Mater. 34(1), 23–26 (2011). #201384 $15.00 USD Received 14 Nov 2013; revised 18 Dec 2013; accepted 18 Dec 2013; published 6 Jan 2014 (C) 2014 OSA 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000707 | OPTICS EXPRESS 707 15. S. Biswal, S. P. O'Connor, and S. R. Bowman, “Thermo-optical parameters measured in potassium-gadoliniumtungstate,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CThT62. 16. D. Stučinskas, R. Antipenkov, and A. Varanavičius, “Thermal lensing in high-power diode-pumped Yb:KGW laser,” Lith. J. Phys. 50(2), 191–199 (2010). 17. Y. Bai, X. M. Chen, J. X. Guo, H. L. Zhang, J. T. Bai, and Z. Y. Ren, “Kilohertz high power extracavity KGW yellow raman lasers based on pulse LD side-pumped ceramic Nd: YAG,” Laser Phys. 22(3), 535–539 (2012). 18. R. P. Mildren, M. Convery, H. M. Pask, J. A. Piper, and T. McKay, “Efficient, all-solid-state, Raman laser in the yellow, orange and red,” Opt. Express 12(5), 785–790 (2004). 19. H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008). 20. J. Findeisen, H. J. Eichler, and P. Peuser, “Self-stimulating, transversally diode pumped Nd: KGd(WO4)2 Raman laser,” Opt. Commun. 181(1–3), 129–133 (2000). 21. A. Sabella, J. A. Piper, and R. P. Mildren, “Efficient conversion of a 1.064 μm Nd:YAG laser to the eye-safe region using a diamond Raman laser,” Opt. Express 19(23), 23554–23560 (2011). 22. V. A. Lisinetskii, A. S. Grabtchikov, I. A. Khodasevich, H. J. Eichler, and V. A. Orlovich, “Efficient high energy 1st, 2nd or 3rd Stokes Raman generation in IR region,” Opt. Commun. 272(2), 509–513 (2007). 23. L. Macalik, J. Hanuza, and A. A. Kaminskii, “Polarized infrared and Raman spectra of KGd(WO4)2 and their interpretation based on normal coordinate analysis,” J. Raman Spectrosc. 33(2), 92–103 (2002). 24. J. Jakutis-Neto, N. U. Wetter, and H. M. Pask, “Investigation of a blue luminescence power in Raman crystals,” in Latin America Optics and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper LS3A.1. 25. I. A. Khodasevich, A. A. Kornienko, E. B. Dunina, and A. S. Grabtchikov, “On the influence of dopant ions on blue emission in KGW crystal excited by infrared laser radiation,” J. Appl. Spectrosc. 79(1), 38–45 (2012). 26. D. Kasprowicz, M. G. Brik, A. Majchrowski, E. Michalski, and P. Głuchowski, “Up-conversion emission in KGd(WO4)2 single crystals triply-doped with Er/Yb/Tm, Tb/Yb/Tm and Pr/Yb/Tm ions,” Opt. Mater. 33(11), 1595–1601 (2011). 27. S. Saghafi and C. J. R. Sheppard, “The beam propagation factor for higher order Gaussian beams,” Opt. Commun. 153(4-6), 207–210 (1998). 28. C. J. Flood, G. Giuliani, and H. M. van Driel, “Preferential operation of an end-pumped Nd:YAG laser in highorder Laguerre-Gauss modes,” Opt. Lett. 15(4), 215–217 (1990). 29. J. Frauchiger, P. Albers, and H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd lasers,” IEEE J. Quantum Electron. 28(4), 1046–1056 (1992). 30. G. M. Bonner, H. M. Pask, A. J. Lee, A. J. Kemp, J. Wang, H. Zhang, and T. Omatsu, “Measurement of thermal lensing in a CW BaWO4 intracavity Raman laser,” Opt. Express 20(9), 9810–9818 (2012).


Introduction
Stimulated Raman scattering in crystals is a field currently receiving intense interest as a highly convenient method for laser frequency down-conversion [1,2].Much of the research to date has been performed at average power levels of a few watts in which the heat deposited in the Raman material is insufficient to substantially affect design.Recently, higher average output powers (e.g.>10 W) have been demonstrated using diamond as the Raman gain medium [3][4][5].However, development of high power Raman lasers using other crystals is also valuable for applications that can take of advantage of distinctive crystal characteristics such as their specific Raman shift and in some cases their ability to also act simultaneously as an active laser ion host.
Increasing Raman laser output power in molecular ion crystals such as metal nitrates, tungstates and vanadates is much more challenging due to their relatively low thermal conductivity (typically less than 5 W/(m•K) compared to 2200 W/(m•K) for diamond) and higher coefficients for thermal expansion [6].Thermally-induced beam depolarization and aberration have been observed at output power levels of only 1-2 W [7]. Despite these problems, higher output powers have been recently demonstrated.Up to 8.5 W was obtained for strontium tungstate used in a Q-switched intracavity Raman laser configuration [8].Up to 17 W was generated from barium nitrate, a crystal with notoriously very poor thermal properties, by designing the resonator to accommodate a large induced lens [9].However, the present understanding of the induced thermal effects is relatively immature and restricted to only a few crystal types.
Double metal tungstate crystals such as potassium gadolinium tungstate (KGW) comprise an important class of Raman materials.They have strong Raman transitions with a characteristic spectrum that often allows polarization selection between two high-gain modes.
They have robust mechanical properties, typically high damage threshold, and their ability to accept high dopant concentrations of laser-active ions, such as Nd and Yb enables them to simultaneously act as generator of the fundamental and Stokes beams (as so-called self-Raman lasers, e.g., [7,10]).The crystals belong to the monoclinic crystal class which has biaxial optical and mechanical properties, in contrast to barium nitrate which is isotropic and barium tungstate which is uniaxial.The anisotropic thermo-optical and thermo-mechanical effects interact in complex manner to make design challenging, but also present opportunities for mitigating thermal effects.For instance, athermal crystal cuts of KGW have been investigated [11][12][13][14][15][16] where the phase shifts due to the thermo-optical effect and thermal expansion are balanced with the aim to ameliorate thermal induced phase distortions.However, maximum Raman laser powers investigated for this crystal class thus far have been in a low power regime in which thermal effects are small [17][18][19][20].An improved knowledge in the response of double metal tungstates at higher power is important for enabling the crystal properties to be better understood and to assist high power laser design.
In this paper we investigate the performance characteristics of an external cavity KGW Raman laser in a high average power regime.The crystal was cut so that the optical axis was aligned along the N p crystallo-optic axis (which is parallel to the b crystal axis) which provides access to the high-gain 901 cm −1 or 768 cm −1 Raman shifts depending upon the incident polarization [13,18].We chose to investigate operation in the external cavity configuration to enable the thermal effects in the Raman crystal to be observed separately from any thermal dynamics present in generating the pump beam.The external cavity is also of substantial practical interest as it can be readily adapted to a wide range of pump sources and pump wavelengths.
We report the output behavior as a function of pump power up to the maximum available of 46 W incident on the crystal.We investigate the thermal-induced mechanisms that influence output including efficiency, output spectrum and the spatial properties of the output beam.Analysis of the output beam profile and beam quality has enabled us to deduce some details on the anisotropy and sign of the induced thermal lens.

Experimental setup
The optical arrangement of the external cavity Raman laser, including the pump module laser, single-pass amplifier, subsequent isolators and polarization control is shown schematically in Fig. 1.The 1064-nm pump laser, based on a commercial side-diode-pumped Nd:YVO 4 gain module (Northrop Grumman RBA20-1C2-FR1-1013) and a cavity consisting of a planar 30%T output coupler and 20-cm convex highly reflective end mirror.The laser was Qswitched using an acousto-optic modulator operating at 38.6 kHz, and produced pulses of duration 25 ± 2.5 ns at full width half maximum.A single-pass amplifier, using a second sidediode-pumped Nd:YVO 4 gain module, was also added to the pump path for a total average power of ~60 W which corresponds to a maximum peak power of approximately 62 kW.To compensate for the strong thermal lens of the amplifier module a negative lens was used to telescope the beam with minimal divergence to a 2.0 ± 0.25 mm beam diameter on a 100 mm focusing lens.
The power from the pump laser and amplifier was controlled using a rotatable half waveplate (HWP) and thin film polarizer (TFP) to ensure constant beam and pulse characteristics.A large area TGG optical rotator, based on a high-power optical isolator (Thorlabs IO-10-1064-VHP), was also used to minimize back reflections into the pump setup.The beam propagation factor of the pump system was measured using a DataRay BeamScope, giving a M 2 of 3.0 and 3.8 for the horizontal and vertical directions.The far field image of the pump beam after the optical rotator is shown in the inset of Fig. 1.A singlet lens (f = 100 mm) was used to focus the collimated pump beam into the 45-mmlong undoped KGW crystal (supplied by EKSMA Optics) so that the confocal parameter of the pump beam was closely matched to the crystal length.The pump waist radius was 105 μm generating peak pump power intensities of 180 MW/cm 2 at maximum power.In these experiments the a-axis of the KGW crystal was aligned vertically.The KGW crystal was conductively cooled in a custom aluminum mount with thermal paste between the crystal sides and mount interfaces.A half waveplate was placed after the isolator to align the polarization axis of the pump radiation to the N m crystallo-optical axis and to preferentially excite KGW's 901 cm −1 Raman mode.The 5 × 5 mm 2 crystal faces were broadband antireflection coated for the pump and first Stokes radiations.
The external cavity Raman laser consisted of a two-mirror resonator with coating designed to maximize second-Stokes output.Mirrors were selected to provide a double pass of the pump beam through the crystal, resonate the first Stokes wavelength and transmit output at the second Stokes wavelength.The input mirror was planar and transmitted 83% of the pump radiation and reflected greater than 99% of the 1177-nm first Stokes and 1316-nm second Stokes.The output mirror transmitted less than 15% at the first Stokes and approximately 68% of the second Stokes radiation.The output mirror had a radius of curvature of 20 cm and the overall resonator length was 5 cm.The calculated TEM 00 mode diameters for the first and second Stokes fields at the cavity waist were 387 μm and 409 μm respectively.
The output power was measured using an optical power meter (Ophir FL250A) and an inline long pass filter to eliminate any residual pump light.Pulse shapes where obtained using 1 ns rise-time silicon (for the pump and residual pump), and a 5 ns rise-time InGaAs photodiodes (for the Raman pulse) at locations shown in Fig. 1, and recorded simultaneously on a 350-MHz bandwidth digital oscilloscope (GW Instek, GDS-3354).The output spectrum was measured using an InGaAs spectrometer with 3.1-nm resolution (StellarNet RED-Wave 512 spectrometer).The M 2 values were obtained using a DataRay BeamScope-P7 beam profiler.Near-beam profiles were obtained using a silicon ccd camera (Spiricon SP620) in combination with a 1100-nm long pass filter to eliminate the residual pump signal.Since the thermal time constant for the KGW crystal was approximately 5 s, measurements were spaced by ~30 s to ensure they were representative of thermal equilibrium conditions.

Output power characteristics
Laser threshold was achieved for an average pump power of 18 W which corresponds to peak power intensity in the waist of approximately 54 MW/cm 2 .The threshold intensity is approximately twice that seen in similar 532 nm-pumped KGW lasers [17,18] the lower gain coefficient expected for the our longer pump wavelength.The output power increases with pump power as shown in Fig. 2. For the maximum incident pump power of 46.2 W, the KGW Raman laser generated 8.3 W at a conversion efficiency of 18%.Pulse shapes are shown for the output pulse along with the input pump and depleted pump pulses for the condition of 5 W of output (see inset of Fig. 2).The Stokes output attains threshold after a 15 ns delay from the pump pulse leading edge and persists for 35 ns producing a pulse of duration ~11.9 ns FWHM.Dashed lines are linear regressions to the experimental data at low output power and at higher output powers delineated by the point at which the transverse mode profile transitioned to higher order operation (refer also Fig. 4).Inset shows the typical pulse shapes for the incident pump (green), reflected residual pump (blue) and Raman output mode (red) at locations indicated in Fig. 1 with corrections for the optical path difference at the different locations.
Examination of the output power characteristic curve reveals two distinct regimes of operation characterized by different linear slopes.Below 3 W of output power, the slope efficiency was 26% which increased in a step-wise fashion to 44% at higher power.This two regime behavior was found to be highly reproducible and was also exhibited in the spatial beam properties as discussed below.Despite many attempts to improve mode-matching and cavity alignment, we were unable to reproduce the slope efficiencies typically seen in other external cavity systems [19,21] that approach the quantum limit (ω s /ω p ~75% in our case).However, the slope efficiency is similar to other reported external cavity Raman lasers with similar pump beam quality [22].Our output power of 8.3 W represents a major increase (by approximately three times) in the maximum output power generated from KGW Raman lasers so far to our knowledge.
The spectral output of the Raman laser contains minor peaks at 1177 nm and 1206 nm as well as the 1316-nm second Stokes (see Fig. 3 for spectrum at 5.5 W of output power).The 1177 nm is the residual output of the strongly resonated first Stokes shift.We attribute the 1206 nm peak to a cascade at a Stokes shift of KGW at ~204 ± 3 cm −1 from the 1177 nm process.It is possible that this Stokes shift corresponds to a translation Raman mode involving Gd ions and oxygen bridges as reported in [23].At 1 W of output power, the 1177nm and 1206 nm peaks comprised 20% of the output.At maximum power, the second Stokes output increases to more than 90% of the total spectral content.The inset of Fig. 3 shows the spectrum of visible fluorescence emitted transversely from the KGW crystal.An intense peak at 475 nm is seen as in many other studies [24,25] as well as smaller peaks at 645 nm and 795 nm.This emission is attributed to multi-photon upconversion in impurities such as thulium in the KGW crystal [26].

Beam profiles and quality factor
The near-field beam profiles and M 2 beam quality factor values are found to vary markedly with laser power as shown in Fig. 4.These images provide the intensity pattern of the minor output lines near 1200 nm as our ccd camera sensitivity decreased steeply for longer wavelengths.We found by using scanning knife edge technique that the second Stokes beam profiles had similar dimensions at all measured power levels, thus the images are assumed to closely correspond to the spatial properties of the full beam.For output powers below 3 W, the output beam profiles are near Gaussian.As the power is increased, the output mode becomes elongated along an axis offset from the crystal a-axis.By measuring the angle to the N m axis (which can be readily determined by finding the pump polarization angle that provides the lowest laser threshold), we deduced that axis of elongation was in the direction of the thermal expansion axis X 1 ' which is offset from the a-axis by approximately 8° as illustrated in Fig. 5.The beam in the horizontal orientation retains its Gaussian-like profile with a small reduction of the waist size in the X 3 ' thermal expansion axis.
Figure 4 also shows the beam quality factor of the KGW Raman laser in the two principal directions of anisotropy as a function of Stokes power.At modest powers (up to ~3 W) the M 2 values in X 3 ' direction is in the range 1.1 to 1.5, and increases steadily to 2.7 at maximum power.Similar behavior is seen in the elongated direction for output powers up to 3 W, but diverges markedly thereafter, increasing to M 2 = 16 at near full power.In Fig. 5(b) we show the line profiles at approximately 7 W of Raman output power.In the X 3 ' direction the beam is compared with a Gaussian fit.In the X 1 ' direction, we overlay the profile of a TEM 07 Hermite-Gaussian (H-G) mode, where the distribution is proportional to H m (x) is the Hermite polynomial of order m = 7, and w 0 is the waist size.This higher order mode shows a good agreement with the recorded beam profile, except for the central region which shows closer agreement to the fundamental mode (with same parameters used for the orthogonal direction).The lobe spacing and the increase in the intensity of the outer lobes are reproduced well in the experiment.The large intensity on axis is attributed to a secondary axial component superimposed onto the TEM 07 mode.The location and width of this secondary component closely matches the pump mode which suggests that its development is a consequence of strong Raman gain-guiding.By integrating across the profile, we find that approximately 82% of the beam power is in the TEM 07 mode.The relationship between the near-field images and the M 2 shown in Fig. 4 is close to M 2 ~2m + 1 where m is the number of nodes in the beam profiles as expected for standard higher-order H-G modes [27].

Discussion and conclusions
The slope efficiency (approximately 45% for operating conditions well above threshold) is notably below the maximum observed achieved in crystal Raman lasers which can have slope efficiencies above 60% and approaching the quantum limit (see for example [6,19]).We found that efficient conversion with high beam quality output was challenging to achieve in KGW under the present pumping conditions.We attribute this to a combination of factors.A common cause for low Raman laser efficiency is due to poor overlap of the pump with the first-Stokes mode.Compared to previous external cavity of high conversion efficiency [19,21], our pump beam has a relatively poor beam quality (M 2 ~3.5 cf., others is typically M 2 < 2) which makes it more challenging to confine the pump within the Stokes mode along the full length of the crystal.We also clearly observe a major impact on the performance that can be attributed to thermal loading of the Raman crystal.Above 3 W of output power, the stepwise increase in slope efficiency and the transition to higher-order spatial modes provide clear evidence for significant power dependent effects.We noted that, in addition to the Raman process, significant crystal heating occurred due to linear absorption at the pump wavelength (e.g., due to impurity absorption).This was observed as an increase in the KGW temperature even when pumping below laser threshold.As a result, heating of the crystal in the pumped region will have contributions due to Raman heating and linear absorption of the pump and Stokes fields, each of which will have a slightly different spatial dependence.
The high-order H-G modes in one direction observed at high power indicate formation of a thermal-induced lens in the KGW crystal that is astigmatic and with strength in one direction at least of the order of the inverse of the resonator length.We deduce that this lens contains a negative cylindrical component in the X 1 ' direction of the thermal expansion tensor that is chiefly responsible for the observed beam dynamics.Our argument is based upon the key observation that the spatial output mode is a relatively pure high-order mode which is uncommon in solid-state lasers with thermal lensing.Many solid-state lasers have thermooptic parameters that lead to positive lenses in the cavity, so that mode sizes in the gain material decrease with pump power leading ultimately leading to an increase in the number of spatial modes simultaneously excited.In the converse situation, in which the cavity mode sizes become significantly greater than the pumped region, preferential excitation of higherorder spatial modes has been shown experimentally and theoretically [28,29].For cw endpumped Nd:YAG lasers for example, increasing the cold-cavity TEM 00 waist size above the pump waist size, achieved in [28,29] by translating a cavity mirror, led to preferential excitation of a single higher-order cylindrically-symmetric Laguerre-Gaussian mode.Under such conditions, the gain profile was found to closely overlap the central lobe of the mode so that the mode experiences amplification and index gradients that are strong only in the central portion of the beam.As the usual assumptions of quadratic index guiding and a large Gaussian gain profile used to calculate cavity eigen-solutions do not apply, the gain medium cannot be modeled by a single ABCD matrix and more complex analysis is required.
In our case, the preferential excitation of higher order modes is thus deduced to be indicative of an increase in the effective waist size, which will occur in our Raman cavity only for a negative thermally induced lens.As there is little change in the beam profile in the orthogonal direction, we deduce that the lens in X 3 ' direction is much weaker or of opposite sign.In addition to this asymmetry, our case is more complicated than in Nd:YAG due to the roles of Raman beam cleanup, rapid cascading of Stokes during the Q-switched pulse duration, and the long length of the induced KGW lens duct.Despite these complexities, however, the approximately linear increase in mode order (and thus M 2 ) with Stokes power above 3 W [Fig. 4] indicates a relatively simple relationship with the induced lens strength.
In addition to the spatial beam properties, there are other laser characteristics that are contrasting to that normally expected in end-pumped lasers operating in a regime with a large induced lens.The discontinuity in slope efficiency at the transition from single to preferential high-order modes is different to what might be expected in cases for which the output transitions from a single mode to multiple modes.The slope efficiency is also observed to increase despite reduced overlap between the higher order mode with the pumped region.We attribute this relatively unusual behavior to the characteristic cavity eigen-solutions for a resonator containing a gain guide and negative lens of radial extent of the order of the coldcavity TEM 00 waist size.It may also be important to consider the lensing effect on the incident and reflected pump beam profiles in the Raman crystal.It is also interesting to note that the beam quality in the X 1 ' direction exceeds that of the pump for power levels above approximately 4 W.This highlights a dominant role of index and gain guiding on the spatial output characteristics that, at high power, overshadows any positive effects arising from Raman beam cleanup effect.
Astigmatic lensing in KGW is expected as a result of the tensorial thermo-mechanical and thermo-optical properties of the monoclinic crystal.Some of the parameter asymmetries in the plane transverse to the laser axis for N p -cut KGW are illustrated in Fig. 5(a).Astigmatism has also been observed previously in other N p -cut Nd-and Yb-doped KGW inversion lasers [11,12].These two studies also observe elongation in the X 1 ' direction, however, higher-order mode excitation was not observed and the elongation was attributed to an induced positive induced lens.Large astigmatism has also been observed in a Raman laser using barium tungstate, which, although shares a similar composition to KGW, has a lattice structure in the tetragonal crystal class [30].The barium tungstate lens was found to contain a strong negative component in the c-direction and one approximately eight times weaker in the a-direction.Our results suggest here, suggest we may be observing a similar magnitude of astigmatism in KGW.The induced lens will include contributions from thermo-optic (dn/dT), photo-elastic and crystal shape distortion effects, and thus involves details of the crystal geometry and the spatial dependence of the induced temperature profile.A complete analysis will require a good knowledge of thermo-optic, thermal expansion, compliance and photo-elastic tensors.Our further work will be aimed to better understand the lensing contributions and determine methods for compensation by, for example, including cylindrical lens elements in the resonator.
In conclusion, we have investigated the performance of an external-cavity KGW Raman laser operated in regime of strong astigmatic thermal lensing.From 46 W of pump power, Raman output powers of 8.3 W were demonstrated, which is more than a two times increase on previously reported KGW Raman lasers.We have shown that the thermal effects in the Raman medium affect efficiency and induce strong astigmatic thermal lensing in the KGW crystal.The Raman laser provides a simple alternative system for generating one-dimensional H-G transverse modes of high order and with high average power.

Fig. 1 .
Fig. 1.Experiment schematic showing pump and amplifier arrangement.Inset graphs depict a typical far field image of the amplified pump beam.

Fig. 2 .
Fig.2.Output power of the KGW Raman laser as a function of incident pump power.Dashed lines are linear regressions to the experimental data at low output power and at higher output powers delineated by the point at which the transverse mode profile transitioned to higher order operation (refer also Fig.4).Inset shows the typical pulse shapes for the incident pump (green), reflected residual pump (blue) and Raman output mode (red) at locations indicated in Fig.1with corrections for the optical path difference at the different locations.

Fig. 3 .
Fig. 3. Spectral features of the external cavity KGW Raman laser with 5.5 W total Raman output.A, C and D show the locations of the first, second and third Stokes wavelengths, and B feature we attribute to a Stokes line shifted from the first Stokes by ~200 cm −1 .The inset shows visible upconversion spectrum for off-axis propagating light collected adjacent the Raman crystal.

Fig. 4 .
Fig. 4. Experimentally determined beam propagation factor, M 2 of the KGW Raman laser as a function of average Raman output power.Error bars, where indicated, show the range of the measured values.Inset show typical quasi-near-field profiles of the Raman output beam at selected power levels.

Fig. 5 .
Fig. 5. (a) Near field profile of 1200 nm output at maximum pump power with principal axes of the crystal a and c (dotted), thermal expansion tensor X 1 ' and X 3 ' (dashed), and thermooptical tensor N m and N g (solid lines) overlaid.Ellipsoids indicate proportional strengths of thermal expansion α T and thermo-optic dn/dT coefficients.(b) Intensity line profiles of the beam along the X 1 ′ and X 3 ′ directions.The red line is a Gaussian function (TEM 00 ) fit to the beam profile along the X 3 ′ direction and overlaid on the orthogonal profile.The blue line shows the profile for a seventh-order standard Hermite-Gaussian mode (TEM 07 ).