Abstract

Yb:YAG thin-disk (TD) technology has enabled construction of laser/amplifier systems with unprecedented average/peak power levels, and has become the workhorse of many scientific investigations. On the other hand, for some applications, the narrow emission bandwidth of Yb:YAG limits its potential, and the search for alternative broadband TD gain media with suitable thermo-optomechanical parameters is ongoing. The alexandrite gain medium has a broad emission spectrum centered around 750 nm, possesses thermomechanical strength that even outperforms Yb:YAG, and has unique spectroscopic properties enabling efficient laser operation even at elevated temperatures. In this work, we have numerically investigated the power scaling potential of continuous-wave (cw) alexandrite lasers in TD geometry for the first time. Using a detailed laser model, we have compared the potential cw laser performance of Yb:YAG, Ti:Sapphire, Cr:LiSAF, Cr:LiCAF, and alexandrite thin-disk lasers under similar conditions and show that among the investigated transition metal-doped gain media, alexandrite is the best alternative to Yb:YAG in power scaling studies at room temperature. Our analysis further demonstrates that potentially Ti:Sapphire is also a good alternative TD material, but only at cryogenic temperatures. However, in comparison with Yb:YAG, the achievable laser gain is relatively low for both alexandrite and Ti:Sapphire, which then requires usage of low-loss cavities with small output coupling for efficient cw operation.

© 2020 Optical Society of America

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2019 (8)

H. Cankaya, U. Demirbas, Y. Hua, M. Hemmer, L. E. Zapata, M. Pergament, and F. X. Kärtner, “190-mJ cryogenically-cooled Yb:YLF amplifier system at 1019.7  nm,” OSA Continuum 2, 3547–3553 (2019).

U. Demirbas, H. Cankaya, J. Thesinga, F. X. Kartner, and M. Pergament, “Efficient, diode-pumped, high-power (>300  W) cryogenic Yb:YLF laser with broad-tunability (995-1020.5  nm): investigation of E//a-axis for lasing,” Opt. Express 27, 36562–36579 (2019).
[Crossref]

U. Demirbas, “Cr: colquiriite lasers: current status and challenges for further progress,” Prog. Quantum Electron. 68, 100227 (2019).
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G. Tawy and M. J. Damzen, “Tunable, dual wavelength and self-Q-switched Alexandrite laser using crystal birefringence control,” Opt. Express 27, 17507–17520 (2019).
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M. Fibrich, J. Šulc, and H. Jelínková, “Alexandrite microchip lasers,” Opt. Express 27, 16975–16982 (2019).
[Crossref]

U. Demirbas, A. Sennaroglu, and F. X. Kartner, “Temperature dependence of Alexandrite effective emission cross section and small signal gain over the 25-450°C range,” Opt. Mater. Express 9, 3352–3370 (2019).
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R. S. Nagymihaly, H. B. Cao, P. Jojart, V. Zuba, R. Flender, O. Antipov, I. Seres, A. Borzsonyi, V. Chvykov, K. Osvay, and M. Kalashnikov, “Broadband spectral characterization of the phase shift induced by population inversion in Ti:Sapphire,” Opt. Express 27, 1226–1235 (2019).
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A. Sennaroglu, “Classification of power-degrading mechanisms in an optically pumped four-level laser: an analytical approach,” J. Opt. Soc. Am. B 36, 2202–2209 (2019).
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2018 (14)

J. W. Zhang, F. Schulze, K. F. Mak, V. Pervak, D. Bauer, D. Sutter, and O. Pronin, “High-power, high-efficiency Tm:YAG and Ho:YAG thin-disk lasers,” Laser Photon. Rev. 12, 1700273 (2018).
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M. Wang, G. Z. Zhu, X. Zhu, Y. Q. Chen, J. Dong, H. L. Wang, and Y. F. Qian, “Thickness optimization for an anti-ASE cap in a thin disk laser considering dioptric power and aberration-induced loss,” J. Opt. Soc. Am. B 35, 583–592 (2018).
[Crossref]

J. Hidde, C. Guguschev, S. Ganschow, and D. Klimm, “Thermal conductivity of rare-earth scandates in comparison to other oxidic substrate crystals,” J. Alloys Compd. 738, 415–421 (2018).
[Crossref]

I. Tamer, S. Keppler, M. Hornung, J. Korner, J. Hein, and M. C. Kaluza, “Spatio-temporal characterization of pump-induced wavefront aberrations in Yb3+-doped materials,” Laser Photon. Rev. 12, 1700211 (2018).
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P. Loiko, S. Ghanbari, V. Matrosov, K. Yumashev, and A. Major, “Thermo-optical properties of Alexandrite laser crystal,” Proc. SPIE 10511, 105111U (2018).
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P. Loiko, S. Ghanbari, V. Matrosov, K. Yumashev, and A. Major, “Dispersion and anisotropy of thermo-optical properties of Alexandrite laser crystal,” Opt. Mater. Express 8, 3000–3006 (2018).
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A. Munk, B. Jungbluth, M. Strotkamp, H. D. Hoffmann, R. Poprawe, J. Hoffner, and F. J. Lubken, “Diode-pumped alexandrite ring laser in single-longitudinal mode operation for atmospheric lidar measurements,” Opt. Express 26, 14928–14935 (2018).
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U. Demirbas, “Power scaling potential of continuous-wave Cr:LiSAF and Cr:LiCAF lasers in thin-disk geometry,” Appl. Opt. 57, 10207–10217 (2018).
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S. Ghanbari, K. A. Fedorova, A. B. Krysa, E. U. Rafailov, and A. Major, “Femtosecond Alexandrite laser passively mode-locked by an InP/InGaP quantum-dot saturable absorber,” Opt. Lett. 43, 232–234 (2018).
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C. Cihan, A. Muti, I. Baylam, A. Kocabas, U. Demirbas, and A. Sennaroglu, “70 femtosecond Kerr-lens mode-locked multipass-cavity Alexandrite laser,” Opt. Lett. 43, 1315–1318 (2018).
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C. Cihan, C. Kocabas, U. Demirbas, and A. Sennaroglu, “Graphene mode-locked femtosecond Alexandrite laser,” Opt. Lett. 43, 3969–3972 (2018).
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U. Parali, X. Sheng, A. Minassian, G. Tawy, J. Sathian, G. M. Thomas, and M. J. Damzen, “Diode-pumped Alexandrite laser with passive SESAM Q-switching and wavelength tunability,” Opt. Commun. 410, 970–976 (2018).
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C. J. Saraceno, “Mode-locked thin-disk lasers and their potential application for high-power terahertz generation,” J. Opt. 20, 044010 (2018).
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W. R. Kerridge-Johns and M. J. Damzen, “Temperature effects on tunable cw Alexandrite lasers under diode end-pumping,” Opt. Express 26, 7771–7785 (2018).
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2017 (5)

2016 (7)

2015 (3)

C. J. Saraceno, F. Emaury, C. Schriber, A. Diebold, M. Hoffmann, M. Golling, T. Sudmeyer, and U. Keller, “Toward millijoule-level high-power ultrafast thin-disk oscillators,” IEEE J. Sel. Top. Quantum Electron. 21, 106–123 (2015).
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W. R. Kerridge-Johns and M. J. Damzen, “Analysis of pump excited state absorption and its impact on laser efficiency,” Laser Phys. Lett. 12, 125002 (2015).
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U. Demirbas and I. Baali, “Power and efficiency scaling of diode pumped Cr: LiSAF lasers: 770–1110  nm tuning range and frequency doubling to 387–463  nm,” Opt. Lett. 40, 4615–4618 (2015).
[Crossref]

2014 (4)

2013 (2)

2012 (4)

2011 (1)

S. Uemura and K. Torizuka, “Sub-40-fs pulses from a diode-pumped Kerr-lens mode-locked Yb-doped yttrium aluminum garnet laser,” Jpn. J. Appl. Phys. 50, 010201 (2011).
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2010 (2)

2009 (7)

A. K. Jafari and M. Aas, “Continuous-wave theory of Yb:YAG end-pumped thin-disk lasers,” Appl. Opt. 48, 106–113 (2009).
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H. Kiriyama, M. Mori, Y. Nakai, T. Shimomura, M. Tanoue, A. Akutsu, H. Okada, T. Motomura, S. Kondo, S. Kanazawa, A. Sagisaka, J. Ma, I. Daito, H. Kotaki, H. Daido, S. Bulanov, T. Kimura, and T. Tajima, “Generation of high-contrast and high-intensity laser pulses using an OPCPA preamplifier in a double CPA, Ti:sapphire laser system,” Opt. Commun. 282, 625–628 (2009).
[Crossref]

U. Demirbas, A. Sennaroglu, F. X. Kartner, and J. G. Fujimoto, “Comparative investigation of diode pumping for continuous-wave and mode-locked Cr3+: LiCAF lasers,” J. Opt. Soc. Am. B 26, 64–79 (2009).
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O. L. Antipov, E. A. Anashkina, and K. A. Fedorova, “Electronic and thermal lensing in diode end-pumped Yb:YAG laser rods and discs,” Quantum Electron. 39, 1131–1136 (2009).
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D. A. Vinnik, P. A. Popov, S. A. Archugov, and G. G. Mikhailov, “Heat conductivity of chromium-doped alexandrite single crystals,” Doklady Phys. 54, 449–450 (2009).
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T. Sudmeyer, C. Krankel, C. R. E. Baer, O. H. Heckl, C. J. Saraceno, M. Golling, R. Peters, K. Petermann, G. Huber, and U. Keller, “High-power ultrafast thin disk laser oscillators and their potential for sub-100-femtosecond pulse generation,” Appl. Phys. B 97, 281–295 (2009).
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P. W. Roth, A. J. Maclean, D. Burns, and A. J. Kemp, “Directly diode-laser-pumped Ti:sapphire laser,” Opt. Lett. 34, 3334–3336 (2009).
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2008 (2)

2007 (5)

I. Matsushima, H. Yashiro, and T. Tomie, “10  kHz 54  W Ti:sapphire regenerative amplifier as a pumping laser of a laser-plasma x-ray source,” Proc. SPIE 7022, 70220M (2007).
[Crossref]

A. Dantan, J. Laurat, A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Femtosecond Ti: Sapphire cryogenic amplifier with high gain and MHz repetition rate,” Opt. Express 15, 8864–8870 (2007).
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F. Druon, F. Balembois, and P. Georges, “New laser crystals for the generation of ultrashort pulses,” C. R. Physique 8, 153–164 (2007).
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S. Matsubara, T. Ueda, S. Kawato, and T. Kobayashi, “Highly efficient continuous-wave laser oscillation in microchip Yb:YAG laser at room temperature,” Jpn. J. Appl. Phys. 46, L132–L134 (2007).
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A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
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2006 (2)

2005 (3)

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)(2), and KY(WO4)(2) laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98, 103514 (2005).

M. Okida, M. Itoh, T. Yatagai, H. Ogilvy, J. Piper, and T. Omatsu, “Heat generation in Nd doped vanadate crystals with 1.34  mu m laser action,” Opt. Express 13, 4909–4915 (2005).
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D. C. Brown, R. L. Cone, Y. C. Sun, and R. W. Equall, “Yb:YAG absorption at ambient and cryogenic temperatures,” IEEE J. Sel. Top. Quantum Electron. 11, 604–612 (2005).
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2004 (1)

2002 (3)

A. Sennaroglu, “Broadly tunable Cr$4^+$4+-doped solid-state lasers in the near infrared and visible,” Prog. Quantum Electron. 26, 287–352 (2002).
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H. W. Qiu, P. Z. Yang, J. Dong, P. Z. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
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F. Brunner, T. Sudmeyer, E. Innerhofer, F. Morier-Genoud, R. Paschotta, V. E. Kisel, V. G. Shcherbitsky, N. V. Kuleshov, J. Gao, K. Contag, A. Giesen, and U. Keller, “240-fs pulses with 22-W average power from a mode-locked thin-disk Yb: KY(WO4)(2) laser,” Opt. Lett. 27, 1162–1164 (2002).
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2001 (1)

1999 (2)

C. Honninger, R. Paschotta, M. Graf, F. Morier-Genoud, G. Zhang, M. Moser, S. Biswal, J. Nees, A. Braun, G. A. Mourou, I. Johannsen, A. Giesen, W. Seeber, and U. Keller, “Ultrafast ytterbium-doped bulk lasers and laser amplifiers,” Appl. Phys. B 69, 3–17 (1999).
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K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modelling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29, 697–703 (1999).
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1997 (1)

V. Pilla, P. R. Impinnisi, and T. Catunda, “Measurement of saturation intensities in ion doped solids by transient nonlinear refraction,” Appl. Phys. Lett. 70, 817–819 (1997).
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1996 (1)

X. N. Zhu, J. F. Cormier, and M. Piche, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43, 1701–1721 (1996).
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1994 (1)

A. Giesen, H. Hugel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
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1993 (5)

A. Sennaroglu, C. R. Pollock, and H. Nathel, “Generation of 48-fs pulses and measurement of crystal dispersion by using a regeneratively initiated self-mode-locked chromium-doped forsterite laser,” Opt. Lett. 18, 826–828 (1993).
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R. Scheps, J. F. Myers, T. R. Glesne, and H. B. Serreze, “Monochromatic end-pumped operation of an Alexandrite laser,” Opt. Commun. 97, 363–366 (1993).
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L. K. Smith, S. A. Payne, W. F. Krupke, L. D. DeLoach, R. Morris, E. W. O’Dell, and D. J. Nelson, “Laser emission from the transition-metal compound LiSrCrF6,” Opt. Lett. 18, 200–202 (1993).
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Z. Y. Zhang, K. T. V. Grattan, and A. W. Palmer, “Thermal-characteristics of Alexandrite fluorescence decay at high-temperatures, induced by a visible laser diode emission,” J. Appl. Phys. 73, 3493–3498 (1993).
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L. J. Atherton, S. A. Payne, and C. D. Brandle, “Oxide and fluoride laser crystals,” Annu. Rev. Mater. Sci. 23, 453–502 (1993).
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1992 (1)

1991 (2)

1990 (1)

V. G. Baryshevskii, M. V. Korzhik, A. E. Kimaev, M. G. Livshits, V. B. Pavlenko, M. L. Meil’man, and B. I. Minkov, “Tunable chromium forsterite laser in the near IR region,” J. Appl. Spectrosc. (USSR) 53, 675–676 (1990).
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1989 (1)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index of optical-crystals,” Phys. Rev. B 39, 3337–3350 (1989).
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1988 (1)

R. C. Sam, J. J. Yeh, K. R. Leslie, and W. R. Rapoport, “Design and performance of a 250  Hz alexandrite laser,” IEEE J. Quantum Electron. 24, 1151–1166 (1988).
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1987 (1)

L. G. DeShazer and K. W. Kangas, “Extended infrared operation of titanium sapphire laser,” Conf. Lasers Electro Opt. 14, 296–298 (1987).

1986 (2)

1985 (2)

J. C. Walling, D. F. Heller, H. Samelson, D. J. Harter, J. A. Pete, and R. C. Morris, “Tunable Alexandrite lasers: development and performance,” IEEE J. Quantum Electron. 21, 1568–1581 (1985).
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R. C. Powell, L. Xi, X. Gang, G. J. Quarles, and J. C. Walling, “Spectroscopic properties of alexandrite crystals,” Phys. Rev. B 32, 2788–2797 (1985).
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1983 (2)

M. L. Shand and H. P. Jenssen, “Temperature-dependence of the excited-state absorption of alexandrite,” IEEE J. Quantum Electron. 19, 480–484 (1983).
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M. L. Shand, “Quantum efficiency of Alexandrite,” J. Appl. Phys. 54, 2602–2604 (1983).
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1982 (3)

S. Guch and C. E. Jones, “Alexandrite-laser performance at high-temperature,” Opt. Lett. 7, 608–610 (1982).
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M. L. Shand and J. C. Walling, “Excited-state absorption in the lasing wavelength region of Alexandrite,” IEEE J. Quantum Electron. 18, 1152–1155 (1982).
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M. L. Shand, J. C. Walling, and H. P. Jenssen, “Ground-state absorption in the lasing wavelength region of Alexandrite: theory and experiment,” IEEE J. Quantum Electron. 18, 167–169 (1982).
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1981 (1)

M. L. Shand, J. C. Walling, and R. C. Morris, “Excited-state absorption in the pump region of Alexandrite,” J. Appl. Phys. 52, 953–955 (1981).
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1980 (2)

J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’dell, “Tunable Alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
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J. C. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable alexandrite lasers,” IEEE J. Quantum Electron. 16, 1302–1315 (1980).
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1979 (1)

C. F. Cline, R. C. Morris, M. Dutoit, and P. J. Harget, “Physical-properties of Beal2o4 single-crystals,” J. Mater. Sci. 14, 941–944 (1979).
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1975 (1)

J. A. Caird, L. G. DeShazer, and J. Nella, “Characteristics of room-temperature 2.3-µm laser emission from Tm3+ in YAG and YAlO3,” IEEE J. Quantum Electron. 11, 874–881 (1975).
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1966 (1)

D. Findlay and R. A. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20, 277–278 (1966).
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R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index of optical-crystals,” Phys. Rev. B 39, 3337–3350 (1989).
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Aggarwal, R. L.

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)(2), and KY(WO4)(2) laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98, 103514 (2005).

A. Sanchez, R. E. Fahey, A. J. Strauss, and R. L. Aggarwal, “Room-temperature continuous-wave operation of a Ti:Al2O3 laser,” Opt. Lett. 11, 363–364 (1986).
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O. L. Antipov, E. A. Anashkina, and K. A. Fedorova, “Electronic and thermal lensing in diode end-pumped Yb:YAG laser rods and discs,” Quantum Electron. 39, 1131–1136 (2009).
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C. J. Saraceno, F. Emaury, O. H. Heckl, C. R. E. Baer, M. Hoffmann, C. Schriber, M. Golling, T. Sudmeyer, and U. Keller, “275  W average output power from a femtosecond thin disk oscillator operated in a vacuum environment,” Opt. Express 20, 23535–23541 (2012).
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T. Sudmeyer, C. Krankel, C. R. E. Baer, O. H. Heckl, C. J. Saraceno, M. Golling, R. Peters, K. Petermann, G. Huber, and U. Keller, “High-power ultrafast thin disk laser oscillators and their potential for sub-100-femtosecond pulse generation,” Appl. Phys. B 97, 281–295 (2009).
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F. Druon, F. Balembois, and P. Georges, “New laser crystals for the generation of ultrashort pulses,” C. R. Physique 8, 153–164 (2007).
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A. Giesen, H. Hugel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
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Figures (8)

Fig. 1.
Fig. 1. (a) Schematic of the alexandrite TDL resonator where the TD acts as an end mirror (${\rm m} = {1}$, single bounce on TD in a round trip). (b) TD is used as an intracavity mirror (${\rm m} = {2}$). HR, high reflector; OC, output coupler.
Fig. 2.
Fig. 2. (a) Calculated cw laser efficiency curves for the Yb:YAG TDL for OCs with transmission values in the 0.01%–10% range. The calculations have been performed for a TD cavity with two bounces on the TD every round trip (${m} = {2}$), employing a 10% Yb-doped TD with a thickness of 100 µm, a pump spot diameter of 3 mm, a MMF of 0.75, and an intracavity loss level of 0.115%. Pump and laser wavelengths are assumed to be 968 and 1030 nm, respectively. (b) Calculated variation of cw laser output power, laser crystal fluorescence lifetime and temperature as a function of absorbed pump power for the Yb:YAG TDL employing the 1% OC. Temperature dependence of thermal conductivity is modeled via $ {\kappa _{\rm Yb:YAG}}( T {\hskip 1pt}) = 880*{( {T + 273} )^{ - 0.83}} $ [81,100].
Fig. 3.
Fig. 3. (a) Calculated cw laser efficiency curves for the RT Ti:Sapphire TDL for OCs with transmission values in the 0.01%–1% range. The calculations have been performed for a TD cavity with two bounces on the TD every round trip (${ m} = {2}$), employing a 0.25% Ti-doped TD with a thickness of 100 µm, a pump spot diameter of 3 mm, a MMF of 0.75, and an intracavity loss level of 0.115%. Pump and laser wavelengths are assumed to be 532 and 800 nm, respectively. (b) Calculated variation of cw laser output power, laser crystal fluorescence lifetime, and temperature as a function of absorbed pump power for the Ti:Sapphire TDL employing the 0.1% OC. Note that lifetime x100 is shown for better visibility in the graph. Temperature dependence of thermal conductivity is modeled assuming $ {\kappa _{\rm Ti:Sapphire}}( T{\hskip 1pt}) = 1.26 + 4070{( {T + 273} )^{ - 1}} + 1.1 \times {10^{ - 6}}{( {T + 273} )^{ - 2}} $.
Fig. 4.
Fig. 4. Calculated cw performance of Ti:Sapphire TDL when the back side of the heat sink material is cooled to cryogenic temperatures (cooling to 100 K is assumed here via liquid nitrogen cooling). All the other parameters are the same as in Fig. 3.
Fig. 5.
Fig. 5. (a) Calculated cw laser efficiency curves for the Cr:LiSAF TDL for OCs with transmission values in the 0.001% to 0.075% range. The calculations have been performed for an a cut, 1% Cr-doped TD with a thickness of 100 µm, a pump spot diameter of 3 mm, a MMF of 0.75, and an intracavity loss level of 0.115%. Lasing could not be achieved with the 0.075% OC. Pump and laser wavelengths are assumed to be 640 and 850 nm, respectively. (b) Calculated variation of cw laser output power, laser crystal fluorescence lifetime, and temperature as a function of pump power for the Cr:LiSAF TDL for the 0.05% transmitting OC. Temperature dependence of thermal conductivity is modeled assuming $ {\kappa _{\rm Cr:LiSAF}}( T{\hskip 1pt}) = 207*{( {T + 273} )^{ - 0.836}} $ [111].
Fig. 6.
Fig. 6. (a) Calculated cw laser efficiency curves for the Cr:LiCAF TDL for OCs with transmission values in the 0.01% to 1% range. The calculations have been performed for a $c$-cut, 2% Cr-doped TD with a thickness of 100 µm, a pump spot diameter of 3 mm, a MMF of 0.75, and an intracavity loss level of 0.115%. Lasing could not be achieved with the 1% OC. Pump and laser wavelengths are assumed to be 640 and 800 nm, respectively. (b) Calculated variation of cw laser output power, laser crystal fluorescence lifetime, and temperature as a function of pump power for the Cr:LiCAF TDL for the 0.25% transmitting OC. Lifetime and temperature has been shown with and without lasing, which shows a significant difference due to the presence of Auger upconversion. Temperature dependence of thermal conductivity is modeled via $ {\kappa _{\rm Cr:LiCAF}}( T{\hskip 1pt}) = 592*{( {T + 273} )^{ - 0.836}} $.
Fig. 7.
Fig. 7. (a) Calculated cw laser efficiency curves for the alexandrite TDL for OCs with transmission values in the 0.01% to 1% range. The calculations have been performed for a $c$-cut, 0.2% Cr-doped TD with a thickness of 100 µm, a pump spot diameter of 3 mm, a MMF of 0.75, and an intracavity loss level of 0.115%. Pump and laser wavelengths are assumed to be 681 and 760 nm, respectively. (b) Calculated variation of cw laser output power, laser crystal fluorescence lifetime, and temperature as a function of pump power for the alexandrite TDL for the 0.5% transmitting OC.
Fig. 8.
Fig. 8. (a) Calculated cw laser efficiency curves for the Yb:YAG, alexandrite, Cr:LiCAF, Ti:Sapphire, and Cr:LiSAF TDLs are shown together. The calculations have been performed for a TD thickness of 100 µm, a pump spot diameter of 3 mm, a MMF of 0.75, and an intracavity loss level of 0.115%. For each material, the data are shown with the optimum output coupling ratio, which is determined from Figs. 27. Calculated variation of laser crystal temperature (b) and fluorescence lifetime (c) as a function of absorbed pump power are also shown for the different TDL materials investigated in this study.

Tables (1)

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Table 1. Comparison of Selected Laser-Related Parameters of Alexandrite, Ti:Sapphire, and Yb:YAG at RTa

Equations (18)

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P t h = π ( w p 2 + w c 2 ) h υ p 4 m ( M M F ) ( σ e σ , e s a + σ a ) τ f ( O C + m L + 2 m A g ) ,
η e f f = [ ( h v l h v p ) ( σ e σ , e s a σ e ) ( M M F ) × ( 1 σ p , e s a σ e m ( O C + m L ) 4 m ) ] O C O C + m L ,
P o u t = ( P a b s P t h ) η e f f .
L ( 0.0005 + 0.05 w p ) .
A g σ a N C r h ,
σ a ( E , T ) = σ e m ( E , T ) E x p ( E E ( T ) k ( T + 273 ) ) ,
E ( T ) = 14720.1 0.7 T .
σ e m ( T ) = 0.415 + 6.28 × 10 3 T + 2.58 × 10 5 T 2 + 1.16 × 10 8 T 3 6.90 × 10 11 T 4 .
f l ( T ) = 0.07 + 0.001 T .
T T 0 + 1 2 I h e a t ( R d i s k + R h s ) ,
κ ( T ) = 300000 ( T + 273 ) 1.63 ,
I h e a t = P a b s π w p 2 η h e a t ,
η h e a t = 1 λ p λ l ( ( σ e σ , e s a σ e ) ( 1 σ p , e s a σ e m ( O C + m L ) 4 m ) ( M M F ) τ f τ R + I c I s a t 1 + I c I s a t ) .
I c = 2 P o u t π w c 2 1 O C ,
I s a t = h ν p ( σ e m + σ a ) τ f .
τ F = τ R η R E ,
τ R = τ E 1 + E x p ( Δ E k ( T + 273 ) ) 1 + τ E τ T E x p ( Δ E k ( T + 273 ) ) ,
η R E = ( 1 + τ E τ N R E x p ( Δ E N R k ( T + 273 ) ) ) 1 ,

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