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The dependence of lasing threshold on the output transmission is numerically analyzed to find the condition for the gain-to-loss balance for the orthogonal Np and Nm polarizations with a Ng-cut Yb:KGW laser crystal. With the numerical analysis, an orthogonally polarized dual-comb self-mode-locked operation is experimentally achieved with a coated Yb:KGW crystal to form a monolithic cavity. At a pump power of 5.2 W, the average output power, the pulse repetition rate, and the pulse duration are measured to be 0.24 (0.6) W, 25.8 (25.3) GHz, and 1.06 (1.12) ps for the output along the Np (Nm) polarization.
© 2015 Optical Society of America
1. Introduction
Various Nd-doped gain media have been widely employed to generate dual-wavelength laser sources [1–6] for the applications on laser interferometry, precision measurement, medical instrumentation, holographic microscopy, and differential absorption lidar [7–9]. In recent years, dual-comb mode-locked lasers with slightly different pulse repetition rates have also started to attract much attention due to the applications on laser spectroscopy [10–12] and asynchronous optical sampling for pump-probe measurements without mechanical delay [13].
Comparing with Nd-doped laser crystals, Yb-doped gain media have been confirmed to be superior materials for generating efficient ultrashort mode-locked lasers due to the small quantum defect, broad absorption and fluorescence spectra, and elimination of parasitic effects. Recently, the diode-pumping scheme has been successfully used to achieve efficient self-mode-locked operations in Yb-doped crystal lasers [14–16]. Here, the meaning of the self-mode locking (SML) is that no additional active or passive mode-locking elements (such as saturable absorbers) are used in the laser cavity except for the gain medium. So far, the origin of the SML is conjectured to come from the combined effects of the Kerr-lensing and thermal lensing together with gain aperture [14,15]. More recently, a self-mode-locked laser with a repetition rate up to 22.4 GHz has been successfully demonstrated by using a coated Yb:KGW crystal to form a monolithic cavity [17]. With the large emission band of the Yb:KGW crystal, it is highly desirable to develop an orthogonally polarized dual-wavelength Yb:KGW laser with the SML operation. Even though the Yb:KGW crystal has been utilized to achieve an orthogonally polarized dual-wavelength Q-switched operation [18], the development for the dual-comb SML laser has not been demonstrated thus far.
Here we report on the use of a coated Ng-cut Yb:KGW crystal as a monolithic cavity to achieve the orthogonally polarized dual-comb SML operation. We numerically analyze the dependence of the lasing thresholds on the output transmission T for the orthogonal Np and Nm polarizations to find that the gain-to-loss balance for the orthogonal polarizations can be feasible with a value of T near 1~2%. Based on the numerical analysis, we design a coated Yb:KGW crystal to obtain the orthogonally polarized dual-comb SML operation. At a pump power of 5.2 W, the average output powers along Np and Nm polarizations are 0.6 W and 0.24 W, respectively. The pulse repetition rate is 25.8 GHz and 25.3 GHz for the laser output along the Np and Nm polarization, respectively. The pulse duration is 1.06 ps and 1.12 ps for the Np and Nm polarization
2. Numerical analysis
The Kerr-lens mode locking that employs the Kerr nonlinearity of the gain medium itself and the soft aperture formed by the pumped volume in the gain medium has been identified to be an extremely simple means of ultrafast optical modulation [19]. A simple formulism derived by Krausz et al. to analyze the self-starting threshold of the passive mode locking from mode beating fluctuations in a free-running solid-state laser is given by [19]
where κ is a characteristic of the Kerr nonlinearity used for passive mode locking, Pi is the circulating average intracavity power in the free running laser, Tr is the cavity round-trip time, and Tc is effective correlation time between the longitudinal modes in the free-running laser. Equation (1) reveals that a decrease in Tr can significantly reduce the intensity needed for self-starting at a fixed κ. We experimentally found that combing the high Kerr nonlinearity of the KGW crystal with the high-Q monolithic short cavity can directly achieve the continuous wave SML without the phenomenon of Q-switched mode locking.Next, polarization dependent absorption and emission spectra were measured with an optical spectrum analyzer with a resolution of 0.5 nm. The gain medium was a Yb:KGW crystal with Yb3+ doping concentration of 5 at.% and its length was approximately 3 mm. The Yb:KGW crystal shows anisotropic properties along its three orthogonal refractive index axes which are labeled as Nm, Np, and Ng, resulting in polarization dependent absorption and emission spectra. The present Yb:KGW crystal was cut along the Ng-axis to obtain the higher absorption and emission cross sections along the Nm or Np principal axes. The measured data were calibrated by comparing with the results in ref [20]. Figures 1(a) and 1(b) depict the experimental results for the absorption and emission cross sections, respectively. The absorption and emission cross sections along the Nm axis are obviously larger than those along the Np axis for the wavelength in the range of 970−1030 nm. On the other hand, the absorption and emission spectra reveal that the Yb:KGW crystal has the capacity for simultaneously dual-comb emission with orthogonal polarizations for the wavelength near 1050 nm.
Fig. 1 Experimental results for the (a) absorption and (b) emission cross sections of the Ng-cut Yb:KGW crystal along the Nm and Np principal axes. The inset is the energy levels.
Without polarization controlling elements, the emission wavelength of material is mainly determined by the gain-to-loss ratio which is governed by the pump condition, re-absorption loss, and useful output coupling [21]. Considering the absorption effect, the laser threshold power can be estimated from the equation [22]:
where ωp and ωc are the pump and cavity mode radii, hvp is the pump photon energy, τ is the emission life time, σa and σe are the absorption and emission cross sections at the laser wavelength, respectively, f1 and f2 are the fractional population in the upper and lower energy levels, T is the output coupling of the output coupler, L stands for the double-pass passive loss, N1 is the population of the lower laser level at threshold, and lc represents the length of the laser crystal. With the absorption and emission cross sections shown in Fig. 1(a) and (b) and using the parameter values of ωp = 0.2 mm and ωc = 0.2 mm, τ = 250 μs [23], f1 = 0.75 and f2 = 0.04, N1 = 1.7 × 1020 cm−3 for the lower level at 385 cm−1, N1 = 0.8 × 1020 cm−3 for the lower level at 535 cm−1, L = 0.5%, the threshold pump power given by Eq. (1) was calculated as a function of the wavelength. Note that the value of L was estimated from the experimental data. Figures 2(a) and 2(b) show the calculated results for the output couplers of T = 5% and T = 1.5%, respectively. For the case of T = 5% shown in Fig. 2(a), the minimum lasing threshold can be seen to be near the wavelength of 1035 nm with the polarization along the Nm axis. For the case of T = 1.5% shown in Fig. 2(b), it can be seen that the Nm and Np polarized states almost possess the same minimum lasing threshold near the wavelength of 1048 nm. In other words, the dual-comb laser emission with two orthogonal polarizations is possible to be obtained with an output coupler of T around 1.5%. In the following, we demonstrated an orthogonally polarized dual-comb monolithic Yb:KGW laser to confirm this analysis.Fig. 2 Calculated results for the dependence of the threshold pump power on the laser wavelength of the Yb:KGW crystal for output coupling of (a) T = 5% and (b) T = 1.5%.
3. Experimental results and discussion
Figure 3(a) depicts the scheme of exploiting a coated Yb:KGW crystal as a monolithic cavity. One of the end facet of the laser crystal was coated for high reflection (HR, R > 99.8%) centered at 1065 nm with total spectral bandwidth of 70 nm (1030-1100 nm) and high transmission (HT, T > 95%) at 980 nm to serve as a front mirror. The rear facet was coated for high reflection (HR, R > 99%) at 980 nm to increase the absorption efficiency of the pump power and was coated for partial reflection (PR, R ≈98.5%) centered at 1050 nm with total spectral bandwidth of 40 nm (1030-1070 nm) to serve as an output coupler. Note that the output coupling T of the cavity was designed to be 1.5% as discussed above to achieve dual-comb operation. The Yb:KGW crystal was wrapped with indium foil and mounted within a water-cooled copper heat sink maintained at 8°C to ensure stable laser output. The pumping source was a 980 nm fiber-coupled laser diode with a core diameter of 200 μm and a numerical aperture of 0.2. A lens with a focal length of 25 mm was used to focus the pump beam into the laser crystal. The overall coupling efficiency was nearly 90%.
Fig. 3 (a) Schematic of the experimental cavity setup for the dual-comb self-mode-locked monolithic Yb:KGW laser. (b) Dependence of the average output power on the incident pump power with different polarizations.
Figure 3(b) shows experimental results for the average output power of the dual-comb Yb:KGW laser with orthogonal polarizations versus the incident pump power. The total output power is found to reach 0.82 W under the pump power of 5.2 W, corresponding to a slope efficiency of 28.3% and an optical-to-optical efficiency of 16.0%. Experimental results revealed that both transverse modes of two orthogonally polarized states are the near TEM00 mode with the beam quality better than 1.3 for the pump power less than 5.2 W. It can be seen that the lasing with polarization along the Np axis is prior to the lasing along the Nm axis. The threshold pump power is found to be 2.2 W for polarization parallel to the Np axis and 2.5 W for Nm direction, rather consistent with the calculated result shown in Fig. 2(b). The output power with polarization along the Np axis initially increases linearly with the pump power, and tends to get saturated at 0.24 W with the pump power higher than 3.9 W. On the other hand, the output power with polarization parallel to the Nm axis rises as the pump power increases with higher slope efficiency in comparison with the lasing along the Np axis, up to 0.58 W at a pump power of 5.2 W. The outputs for two orthogonal polarizations have an equal power of 0.24 W at a pump power of 4.3 W. It is worthwhile to mention that the Nm polarized state turns out to be the high order mode for the pump power greater than 5.2 W. Nevertheless, it is confirmed that the dual-comb laser operation displays good temporal stability without power competition between the two polarization states for the pump power less than 5.2 W.
The optical spectrum of the laser output was measured with a Michelson optical interferometer (Advantest, Q8347) with a resolution of 0.003 nm that is able to perform first-order autocorrelations by Fourier transforming the optical spectrum. Figure 4 depicts the experimental result for the lasing spectrum at the pump power of 4.3 W where the two polarization states have the same output power. It can be seen that there are dual lasing bands with central wavelengths at 1047.32 nm (Np axis) and 1048.48 nm (Nm axis). The values of the full width at half maximum (FWHM) of the spectral bands at 1047.32 nm (Np axis) and 1048.48 nm (Nm axis) are 1.6 nm and 1.5 nm, respectively. The longitudinal mode spacings within each spectral band are found to be 25.8 GHz (1047.32 nm, Np axis) and 25.3 GHz (1048.48 nm, Nm axis). This mode spacing exactly corresponds to the free spectral range of the Yb:KGW crystal.
The temporal behavior of the laser output was analyzed by exploiting the schemes of first- and second-order autocorrelations. The second-order autocorrelation trace was performed with a commercial autocorrelator (APE GmbH, PulseCheck). Figure 5 shows experimental results for the first-order autocorrelation trace at the pump power of 4.3 W. The pulse repetition rates are consistent with the mode spacings shown in Fig. 4. With the group indexes of 1.986 for the Np axis and 2.023 for the Nm axis, the precise length of the Yb:KGW crystal was deduced to be 2.93 mm. Figures 6(a) and 6(b) show the FWHM widths of the single pulses in the second-order autocorrelation traces for two orthogonal polarizations. Assuming the Gaussian-shaped temporal profile, the pulse durations were estimated to be 1.06 ps for the Np axis and 1.12 ps for the Nm axis. As a result, the time-bandwidth products of the SML pulses were evaluated to be 0.463 and 0.458 for the Np and Nm axes, respectively; both values are slightly greater than the Fourier-limited value of 0.441. The chirped pulses for two orthogonal polarizations mainly come from the group velocity dispersion induced by the gain medium. In comparison with other dual-band mode-locked laser with orthogonal polarization by utilizing the Nd:GdVO4 crystal [24] which the output pulse duration is 7 ps, the significant reduction of the pulse duration shows the advantage of the Yb-doped materials with wider emission bandwidths.
Fig. 5 Experimental traces of the temporal behavior of first-order autocorrelation for polarization direction along (a) Np axis and (b) Nm axis.
Fig. 6 FWHM width of a single pulse of the second-order autocorrelations for polarization direction along (a) Np axis and (b) Nm axis.
4. Conclusion
In conclusion, we have analyzed the condition of gain-to-loss balance via tuning the output coupling in a Yb:KGW laser to achieve the orthogonally polarized dual-wavelength operation. Based on the numerical analysis, we have designed a monolithic Yb:KGW crystal laser to generate an orthogonally polarized dual-comb SML laser. At a pump power of 5.2 W, the average output powers along Np and Nm polarizations are 0.6 W and 0.24 W, respectively. The pulse repetition rate and the pulse duration are found to be 25.8 (25.3) GHz and 1.06 (1.12) ps for the laser output along the Np (Nm) polarization. We believe that the orthogonally polarized dual-comb monolithic SML laser is a promising light source for many applications.
Acknowledgments
The authors thank the National Science Council for the financial support of this research under Contract No. MOST 103-2112-M-009-0016-MY3.
References and links
1. B. Wu, P. Jiang, D. Yang, T. Chen, J. Kong, and Y. Shen, “Compact dual-wavelength Nd:GdVO4 laser working at 1063 and 1065 nm,” Opt. Express 17(8), 6004–6009 (2009). [CrossRef] [PubMed]
2. A. A. Sirotkin, S. V. Garnov, V. I. Vlasov, A. I. Zagumennyi, Y. D. Zavartsev, S. A. Kutovoi, and I. A. Shcherbakov, “Two-frequency vanadate lasers with mutually parallel and orthogonal polarizations of radiation,” Quantum Electron. 42(5), 420–426 (2012). [CrossRef]
3. A. Brenier, Y. Wu, P. Fu, J. Zhang, and Y. Zu, “Diode-pumped laser properties of Nd3+-doped La2CaB10O19 crystal including two-frequency generation with 4.6 THz separation,” Opt. Express 17(21), 18730–18737 (2009). [PubMed]
4. Y. P. Huang, C. Y. Cho, Y. J. Huang, and Y. F. Chen, “Orthogonally polarized dual-wavelength Nd:LuVO4 laser at 1086 nm and 1089 nm,” Opt. Express 20(5), 5644–5651 (2012). [CrossRef] [PubMed]
5. Y. J. Chen, X. H. Gong, Y. F. Lin, J. H. Huang, Z. D. Luo, and Y. D. Huang, “Diode-pumped orthogonally polarized dual-wavelength Nd3+:LaBO2MoO4 laser,” Appl. Phys. B 112(1), 55–60 (2013). [CrossRef]
6. Y. Zhao, S. Zhuang, X. Xu, J. Xu, H. Yu, Z. Wang, and X. Xu, “Anisotropy of laser emission in monoclinic, disordered crystal Nd:LYSO,” Opt. Express 22(3), 2228–2235 (2014). [CrossRef] [PubMed]
7. J. Min, B. Yao, P. Gao, R. Guo, B. Ma, J. Zheng, M. Lei, S. Yan, D. Dan, T. Duan, Y. Yang, and T. Ye, “Dual-wavelength slightly off-axis digital holographic microscopy,” Appl. Opt. 51(2), 191–196 (2012). [CrossRef] [PubMed]
8. S. N. Son, J. J. Song, J. U. Kang, and C. S. Kim, “Simultaneous second harmonic generation of multiple wavelength laser outputs for medical sensing,” Sensors (Basel) 11(12), 6125–6130 (2011). [CrossRef] [PubMed]
9. S. L. Zhang, Y. D. Tan, and Y. Li, “Orthogonally polarized dual frequency lasers and applications in self-sensing metrology,” Meas. Sci. Technol. 21(5), 054016 (2010). [CrossRef]
10. A. Schliesser, M. Brehm, F. Keilmann, and D. van der Weide, “Frequency-comb infrared spectrometer for rapid, remote chemical sensing,” Opt. Express 13(22), 9029–9038 (2005). [CrossRef] [PubMed]
11. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008). [CrossRef] [PubMed]
12. B. Bernhardt, A. Ozawa, P. Jaquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. Hänsch, and N. Piqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010). [CrossRef]
13. A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78(3), 035107 (2007). [CrossRef] [PubMed]
14. Y. F. Chen, W. Z. Zhuang, H. C. Liang, G. W. Huang, and K. W. Su, “High-power subpicosecond harmonically mode-locked Yb:YAG laser with pulse repetition rate up to 240 GHz,” Laser Phys. Lett. 10(1), 1–4 (2012).
15. G. Q. Xie, D. Y. Tang, L. M. Zhao, L. J. Qian, and K. Ueda, “High-power self-mode-locked Yb:Y2O3 ceramic laser,” Opt. Lett. 32(18), 2741–2743 (2007). [CrossRef] [PubMed]
16. A. Lagatsky, C. Brown, and W. Sibbett, “Highly efficient and low threshold diode-pumped Kerr-lens mode-locked Yb:KYW laser,” Opt. Express 12(17), 3928–3933 (2004). [CrossRef] [PubMed]
17. W. Z. Zhuang, M. T. Chang, H. C. Liang, and Y. F. Chen, “High-power high-repetition-rate subpicosecond monolithic Yb:KGW laser with self-mode locking,” Opt. Lett. 38(14), 2596–2599 (2013). [CrossRef] [PubMed]
18. A. Brenier, “Active Q-switching of the diode-pumped two-frequency Yb3+:KGd(WO4)2 laser,” IEEE J. Quantum Electron. 47(3), 279–284 (2011). [CrossRef]
19. F. Krausz, T. Brabec, and C. Spielmann, “Self-starting passive mode locking,” Opt. Lett. 16(4), 235–237 (1991). [CrossRef] [PubMed]
20. M. Zhou, D. X. Cao, M. Z. Wang, X. F. Wang, and Y. M. Luo, “Polarized fluorescence spectra analysis of Yb3+:KGd(WO4)2,” Opt. Commun. 282(20), 4109–4113 (2009). [CrossRef]
21. J. Dong, A. Shirakawa, K. I. Ueda, and A. A. Kaminskii, “Effect of ytterbium concentration on cw Yb:YAG microchip laser performance at ambient temperature - Part II: Theoretical modeling,” Appl. Phys. B 89(2–3), 367–376 (2007). [CrossRef]
22. T. Taira, W. M. Tulloch, and R. L. Byer, “Modeling of quasi-three-level lasers and operation of cw Yb:YAG lasers,” Appl. Opt. 36(9), 1867–1874 (1997). [CrossRef] [PubMed]
23. V. E. Kisel, A. E. Troshin, V. G. Shcherbitsky, and N. V. Kuleshov, “Luminescence lifetime measurements in Yb3+-doped KY(WO4)2 and KGd (WO4)2,” in Advanced Solid-State Photonics, OSA Technical Digest (Optical Society of America, 2004), paper WB7. [CrossRef]
24. W. D. Tan, D. Y. Tang, C. W. Xu, J. Zhang, H. H. Yu, and H. J. Zhang, “Dual-wavelength passively mode-locked Nd:GdVO4 laser with orthogonal polarizations,” Appl. Phys. B 102(4), 775–779 (2011). [CrossRef]
