Abstract

A wide, short unstable cavity laser design is proposed for high-power, single-longitudinal, single-transverse-mode emission from a solid-state laser. Such a laser combines the single-mode master oscillator and the single-mode amplifier in a single piece. Design formulas are suggested; the efficiency and conditions of the single-longitudinal-mode operation are analyzed. Examples with Nd:YAG and Yb:YAG are considered. For a device of a few millimeters wide, the slope efficiency of 50% and the threshold of a few watts are predicted.

© 2005 Optical Society of America

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  1. K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).
  2. D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
    [CrossRef]
  3. H. Liu, S. H. Zhou, and Y. C. Chen. "High-power monolithic unstable-resonator solid-state laser," Opt. Lett. 23, 451-453 (1998).
    [CrossRef]
  4. P. Shi, D. Li, H. Shang, Y. Wang, and K. Du. "An 110 W Nd:YVO4 slab laser with high beam quality output," Opt. Commun. 229, 349-354 (2004).
    [CrossRef]
  5. J. J. Zaihovski, "Microchip lasers," Opt. Mater. 11, 255-257 (1999).
    [CrossRef]
  6. L. W. Casperson, "Laser power calculation. Sources of error," Appl. Opt. 19, 422-434 (1980).
    [CrossRef] [PubMed]
  7. A. C. Nilsson, E. K. Gustafson, and R. Byer, "Eigenpolarization theory of monolithic nonplanar ring oscillators," IEEE J. Quantum Electron. 25, 767-790 (1989).
    [CrossRef]
  8. D. Shen, C. L. Fincher, D. A. Hinkley, R. A. Chodzoko, T. S. Rose, and R. A. Fields, "Semimonolite Nd:YAG ring resonator for generating cw single-frequency output at 1.06 nm," Opt. Lett. 20, 1282-1285 (1995).
    [CrossRef]
  9. K. Nakagawa, Y. Shimizu, and M. Ohtsu, "High power diode-laser-pumped twisted-mode Nd:YAG laser," IEEE Photonics Technol. Lett. 6, 499-501 (1994).
    [CrossRef]
  10. H. G. Danielmeyer and E. H. Turner, "Electro-optic elimination of spatial hole burning in lasers," Appl. Phys. Lett. 17, 519-521 (1970).
    [CrossRef]
  11. T. Dascalu, T. Taira, and N. Pavel, "100-W quasi-continuous-wave diode radially pumped microchip composite Yb:YAG laser," Opt. Lett. 27, 1791-1793 (2002).
    [CrossRef]
  12. D. Kouznetsov and J. V. Moloney, "Highly efficient, high-gain, short-length, and power-scalable incoherent diode slab-pumped fiber amplifier/laser," IEEE J. Quantum Electron. 39, 1452-1461 (2003).
    [CrossRef]
  13. D. Kouznetsov and J. V. Moloney, "Tapered slab delivery of pump to the double-clad fiber amplifier: analytical approach," IEEE J. Quantum Electron. 40, 378-383 (2004).
    [CrossRef]
  14. P. Kano, D. Kouznetsov, J. V. Moloney, and N. Brio, "Slab delivery of incoherent pump light to double-clad fiber amplifiers: numerical simulations," IEEE J. Quantum Electron. 40, 1301-1305 (2004).
    [CrossRef]
  15. A. Siegman, Lasers (University Science, 1986). There is a misprint on p. 875; the ray matrix[1-2L/RL2L/R1]should be corrected to[1-2L/RL2/R1].
  16. R. Oron, N. Davidson, A. Friesem, and E. Hasman, "Continuous-phase elements can improve laser beam quality," Opt. Lett. 25, 939-941 (2000).
    [CrossRef]
  17. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Theory (Academic, 1999).
  18. D. Yu. Kuznetsov, "The transformation of the transverse structure of monochromatic light in the non-linear media," Optics and Lasers, V.A.Shcheglov, ed. (Nova Science, 1995).
  19. T. Y. Fan, "Optimizing the efficiency and stored energy in quasi-three level lasers," IEEE J. Quantum Electron. 28, 2692-2697 (1992).
    [CrossRef]

2004 (4)

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

P. Shi, D. Li, H. Shang, Y. Wang, and K. Du. "An 110 W Nd:YVO4 slab laser with high beam quality output," Opt. Commun. 229, 349-354 (2004).
[CrossRef]

D. Kouznetsov and J. V. Moloney, "Tapered slab delivery of pump to the double-clad fiber amplifier: analytical approach," IEEE J. Quantum Electron. 40, 378-383 (2004).
[CrossRef]

P. Kano, D. Kouznetsov, J. V. Moloney, and N. Brio, "Slab delivery of incoherent pump light to double-clad fiber amplifiers: numerical simulations," IEEE J. Quantum Electron. 40, 1301-1305 (2004).
[CrossRef]

2003 (1)

D. Kouznetsov and J. V. Moloney, "Highly efficient, high-gain, short-length, and power-scalable incoherent diode slab-pumped fiber amplifier/laser," IEEE J. Quantum Electron. 39, 1452-1461 (2003).
[CrossRef]

2002 (1)

2000 (1)

1999 (1)

J. J. Zaihovski, "Microchip lasers," Opt. Mater. 11, 255-257 (1999).
[CrossRef]

1998 (1)

1995 (1)

D. Shen, C. L. Fincher, D. A. Hinkley, R. A. Chodzoko, T. S. Rose, and R. A. Fields, "Semimonolite Nd:YAG ring resonator for generating cw single-frequency output at 1.06 nm," Opt. Lett. 20, 1282-1285 (1995).
[CrossRef]

1994 (1)

K. Nakagawa, Y. Shimizu, and M. Ohtsu, "High power diode-laser-pumped twisted-mode Nd:YAG laser," IEEE Photonics Technol. Lett. 6, 499-501 (1994).
[CrossRef]

1992 (2)

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

T. Y. Fan, "Optimizing the efficiency and stored energy in quasi-three level lasers," IEEE J. Quantum Electron. 28, 2692-2697 (1992).
[CrossRef]

1989 (1)

A. C. Nilsson, E. K. Gustafson, and R. Byer, "Eigenpolarization theory of monolithic nonplanar ring oscillators," IEEE J. Quantum Electron. 25, 767-790 (1989).
[CrossRef]

1980 (1)

1970 (1)

H. G. Danielmeyer and E. H. Turner, "Electro-optic elimination of spatial hole burning in lasers," Appl. Phys. Lett. 17, 519-521 (1970).
[CrossRef]

Alegria, C.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Baek, S.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Becker, P. C.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Theory (Academic, 1999).

Brio, N.

P. Kano, D. Kouznetsov, J. V. Moloney, and N. Brio, "Slab delivery of incoherent pump light to double-clad fiber amplifiers: numerical simulations," IEEE J. Quantum Electron. 40, 1301-1305 (2004).
[CrossRef]

Byer, R.

A. C. Nilsson, E. K. Gustafson, and R. Byer, "Eigenpolarization theory of monolithic nonplanar ring oscillators," IEEE J. Quantum Electron. 25, 767-790 (1989).
[CrossRef]

Casperson, L. W.

Chen, Y. C.

Chodzoko, R. A.

D. Shen, C. L. Fincher, D. A. Hinkley, R. A. Chodzoko, T. S. Rose, and R. A. Fields, "Semimonolite Nd:YAG ring resonator for generating cw single-frequency output at 1.06 nm," Opt. Lett. 20, 1282-1285 (1995).
[CrossRef]

Codemard, C.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Danielmeyer, H. G.

H. G. Danielmeyer and E. H. Turner, "Electro-optic elimination of spatial hole burning in lasers," Appl. Phys. Lett. 17, 519-521 (1970).
[CrossRef]

Dascalu, T.

Davidson, N.

Du, K.

P. Shi, D. Li, H. Shang, Y. Wang, and K. Du. "An 110 W Nd:YVO4 slab laser with high beam quality output," Opt. Commun. 229, 349-354 (2004).
[CrossRef]

Fan, T. Y.

T. Y. Fan, "Optimizing the efficiency and stored energy in quasi-three level lasers," IEEE J. Quantum Electron. 28, 2692-2697 (1992).
[CrossRef]

Fields, R. A.

D. Shen, C. L. Fincher, D. A. Hinkley, R. A. Chodzoko, T. S. Rose, and R. A. Fields, "Semimonolite Nd:YAG ring resonator for generating cw single-frequency output at 1.06 nm," Opt. Lett. 20, 1282-1285 (1995).
[CrossRef]

Fincher, C. L.

D. Shen, C. L. Fincher, D. A. Hinkley, R. A. Chodzoko, T. S. Rose, and R. A. Fields, "Semimonolite Nd:YAG ring resonator for generating cw single-frequency output at 1.06 nm," Opt. Lett. 20, 1282-1285 (1995).
[CrossRef]

Friesem, A.

Gustafson, E. K.

A. C. Nilsson, E. K. Gustafson, and R. Byer, "Eigenpolarization theory of monolithic nonplanar ring oscillators," IEEE J. Quantum Electron. 25, 767-790 (1989).
[CrossRef]

Hasman, E.

Hinkley, D. A.

D. Shen, C. L. Fincher, D. A. Hinkley, R. A. Chodzoko, T. S. Rose, and R. A. Fields, "Semimonolite Nd:YAG ring resonator for generating cw single-frequency output at 1.06 nm," Opt. Lett. 20, 1282-1285 (1995).
[CrossRef]

Jeong, Y.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Kanabe, T.

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

Kano, P.

P. Kano, D. Kouznetsov, J. V. Moloney, and N. Brio, "Slab delivery of incoherent pump light to double-clad fiber amplifiers: numerical simulations," IEEE J. Quantum Electron. 40, 1301-1305 (2004).
[CrossRef]

Kouznetsov, D.

P. Kano, D. Kouznetsov, J. V. Moloney, and N. Brio, "Slab delivery of incoherent pump light to double-clad fiber amplifiers: numerical simulations," IEEE J. Quantum Electron. 40, 1301-1305 (2004).
[CrossRef]

D. Kouznetsov and J. V. Moloney, "Tapered slab delivery of pump to the double-clad fiber amplifier: analytical approach," IEEE J. Quantum Electron. 40, 378-383 (2004).
[CrossRef]

D. Kouznetsov and J. V. Moloney, "Highly efficient, high-gain, short-length, and power-scalable incoherent diode slab-pumped fiber amplifier/laser," IEEE J. Quantum Electron. 39, 1452-1461 (2003).
[CrossRef]

Kuznetsov, D. Yu.

D. Yu. Kuznetsov, "The transformation of the transverse structure of monochromatic light in the non-linear media," Optics and Lasers, V.A.Shcheglov, ed. (Nova Science, 1995).

Laurell, F.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Li, D.

P. Shi, D. Li, H. Shang, Y. Wang, and K. Du. "An 110 W Nd:YVO4 slab laser with high beam quality output," Opt. Commun. 229, 349-354 (2004).
[CrossRef]

Liu, H.

Mima, K.

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

Moloney, J. V.

D. Kouznetsov and J. V. Moloney, "Tapered slab delivery of pump to the double-clad fiber amplifier: analytical approach," IEEE J. Quantum Electron. 40, 378-383 (2004).
[CrossRef]

P. Kano, D. Kouznetsov, J. V. Moloney, and N. Brio, "Slab delivery of incoherent pump light to double-clad fiber amplifiers: numerical simulations," IEEE J. Quantum Electron. 40, 1301-1305 (2004).
[CrossRef]

D. Kouznetsov and J. V. Moloney, "Highly efficient, high-gain, short-length, and power-scalable incoherent diode slab-pumped fiber amplifier/laser," IEEE J. Quantum Electron. 39, 1452-1461 (2003).
[CrossRef]

Naito, K.

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

Naka, S.

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

Nakagawa, K.

K. Nakagawa, Y. Shimizu, and M. Ohtsu, "High power diode-laser-pumped twisted-mode Nd:YAG laser," IEEE Photonics Technol. Lett. 6, 499-501 (1994).
[CrossRef]

Nakatsuka, M.

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

Nilsson, A. C.

A. C. Nilsson, E. K. Gustafson, and R. Byer, "Eigenpolarization theory of monolithic nonplanar ring oscillators," IEEE J. Quantum Electron. 25, 767-790 (1989).
[CrossRef]

Nilsson, J.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Ohtsu, M.

K. Nakagawa, Y. Shimizu, and M. Ohtsu, "High power diode-laser-pumped twisted-mode Nd:YAG laser," IEEE Photonics Technol. Lett. 6, 499-501 (1994).
[CrossRef]

Olsson, N. A.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Theory (Academic, 1999).

Oron, R.

Pavel, N.

Philippov, V.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Rose, T. S.

D. Shen, C. L. Fincher, D. A. Hinkley, R. A. Chodzoko, T. S. Rose, and R. A. Fields, "Semimonolite Nd:YAG ring resonator for generating cw single-frequency output at 1.06 nm," Opt. Lett. 20, 1282-1285 (1995).
[CrossRef]

Sahu, J. K.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Shang, H.

P. Shi, D. Li, H. Shang, Y. Wang, and K. Du. "An 110 W Nd:YVO4 slab laser with high beam quality output," Opt. Commun. 229, 349-354 (2004).
[CrossRef]

Shen, D.

D. Shen, C. L. Fincher, D. A. Hinkley, R. A. Chodzoko, T. S. Rose, and R. A. Fields, "Semimonolite Nd:YAG ring resonator for generating cw single-frequency output at 1.06 nm," Opt. Lett. 20, 1282-1285 (1995).
[CrossRef]

Shi, P.

P. Shi, D. Li, H. Shang, Y. Wang, and K. Du. "An 110 W Nd:YVO4 slab laser with high beam quality output," Opt. Commun. 229, 349-354 (2004).
[CrossRef]

Shimizu, Y.

K. Nakagawa, Y. Shimizu, and M. Ohtsu, "High power diode-laser-pumped twisted-mode Nd:YAG laser," IEEE Photonics Technol. Lett. 6, 499-501 (1994).
[CrossRef]

Siegman, A.

A. Siegman, Lasers (University Science, 1986). There is a misprint on p. 875; the ray matrix[1-2L/RL2L/R1]should be corrected to[1-2L/RL2/R1].

Simpson, J. R.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Theory (Academic, 1999).

Soh, D. B.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Taira, T.

Turner, E. H.

H. G. Danielmeyer and E. H. Turner, "Electro-optic elimination of spatial hole burning in lasers," Appl. Phys. Lett. 17, 519-521 (1970).
[CrossRef]

Wang, S.

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Wang, Y.

P. Shi, D. Li, H. Shang, Y. Wang, and K. Du. "An 110 W Nd:YVO4 slab laser with high beam quality output," Opt. Commun. 229, 349-354 (2004).
[CrossRef]

Yamanaka, C.

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

Yamanaka, M.

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

Zaihovski, J. J.

J. J. Zaihovski, "Microchip lasers," Opt. Mater. 11, 255-257 (1999).
[CrossRef]

Zhou, S. H.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. G. Danielmeyer and E. H. Turner, "Electro-optic elimination of spatial hole burning in lasers," Appl. Phys. Lett. 17, 519-521 (1970).
[CrossRef]

IEEE J. Quantum Electron. (5)

D. Kouznetsov and J. V. Moloney, "Highly efficient, high-gain, short-length, and power-scalable incoherent diode slab-pumped fiber amplifier/laser," IEEE J. Quantum Electron. 39, 1452-1461 (2003).
[CrossRef]

D. Kouznetsov and J. V. Moloney, "Tapered slab delivery of pump to the double-clad fiber amplifier: analytical approach," IEEE J. Quantum Electron. 40, 378-383 (2004).
[CrossRef]

P. Kano, D. Kouznetsov, J. V. Moloney, and N. Brio, "Slab delivery of incoherent pump light to double-clad fiber amplifiers: numerical simulations," IEEE J. Quantum Electron. 40, 1301-1305 (2004).
[CrossRef]

A. C. Nilsson, E. K. Gustafson, and R. Byer, "Eigenpolarization theory of monolithic nonplanar ring oscillators," IEEE J. Quantum Electron. 25, 767-790 (1989).
[CrossRef]

T. Y. Fan, "Optimizing the efficiency and stored energy in quasi-three level lasers," IEEE J. Quantum Electron. 28, 2692-2697 (1992).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

K. Nakagawa, Y. Shimizu, and M. Ohtsu, "High power diode-laser-pumped twisted-mode Nd:YAG laser," IEEE Photonics Technol. Lett. 6, 499-501 (1994).
[CrossRef]

D. B. S. Soh, C. Codemard, S. Wang, J. Nilsson, J. K. Sahu, F. Laurell, V. Philippov, Y. Jeong, C. Alegria, and S. Baek, "A 980-nm Yb-doped fiber MOPA source and its frequency doubling," IEEE Photonics Technol. Lett. 16, 1032-1034 (2004).
[CrossRef]

Jpn. J. Appl. Phys. Part 1 (1)

K. Naito, M. Yamanaka, M. Nakatsuka, T. Kanabe, K. Mima, C. Yamanaka, and S. Naka, "Conceptual design of a laser diode pumped solid state laser system for laser fusion reactor driver," Jpn. J. Appl. Phys. Part 1 31, 250-271 (1992).

Opt. Commun. (1)

P. Shi, D. Li, H. Shang, Y. Wang, and K. Du. "An 110 W Nd:YVO4 slab laser with high beam quality output," Opt. Commun. 229, 349-354 (2004).
[CrossRef]

Opt. Lett. (4)

Opt. Mater. (1)

J. J. Zaihovski, "Microchip lasers," Opt. Mater. 11, 255-257 (1999).
[CrossRef]

Other (3)

A. Siegman, Lasers (University Science, 1986). There is a misprint on p. 875; the ray matrix[1-2L/RL2L/R1]should be corrected to[1-2L/RL2/R1].

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Theory (Academic, 1999).

D. Yu. Kuznetsov, "The transformation of the transverse structure of monochromatic light in the non-linear media," Optics and Lasers, V.A.Shcheglov, ed. (Nova Science, 1995).

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Figures (10)

Fig. 1
Fig. 1

Pie-shaped solid-state laser with an unstable cavity.

Fig. 2
Fig. 2

(a) Rays of the signal in a laser with an unstable cavity pumped laterally; (b) the pie-shaped pumped region can be merged into a disk of an active medium.

Fig. 3
Fig. 3

Ray tracing in the unstable cavity and the resulting geometry of the device.

Fig. 4
Fig. 4

Magnification M = r 2 r 1 = M ( r 1 r 0 ) as a function of the relative size r 1 r 0 of a spherical mirror for h r 0 = 0.039 [ M ( 0 ) = 1.196 , thin curve] and h r 0 = 0.002 [ M ( 0 ) = 1.314 , thick curve] as a result of ray tracing. The parameters suggested in the text for lasers with Nd and those with Yb are shown with a large and small circle, respectively.

Fig. 5
Fig. 5

Example of distribution of intensity in the vicinity of the pump beam, calculated by approximation (16). (a) Contour lines of pump intensity focused from radius r 2 = 2 mm with a NA of 0.091 into the seed region (shown by the circle) or radius w = 0.04 mm ; levels exp ( 1 ) , 0.6, 0.8 are marked. (b) Distribution of intensity along the direction of propagation of the pump. The solid curve is the profile of intensity u ( r ) for r 2 = 2 mm , A = 0.769 mm . The dashed curve is the exponential profile exp [ A ( r 2 r ) ] .

Fig. 6
Fig. 6

Affective absorption and emission cross sections for Nd : YAG and Yb : YAG (solid curves); fits of approximations (33, 34) for Nd and approximations (36, 37) for Yb (dashed curves).

Fig. 7
Fig. 7

Upper graphics: Pump threshold power P pt by Eq. (41) for the case with Nd and Yb. Lower graphics: Estimates of the slope efficiency without hole burning. The two dashed curves show the optimistic and pessimistic estimates η ± = I so I po [ ( G 0 G ) 1 ] ( r 2 r 1 2 h ) u ± . The thin solid curves show independent estimate η 3 = ( λ s λ p ) η p η s . The thick curves show the mean geometric values of three estimates above; the corresponding error bars are cut at η = λ p λ s .

Fig. 8
Fig. 8

Pump threshold power P pt for a laser with Nd and a laser with Yb and various estimates of the slope efficiency η slope for the case with SHB: pessimistic and optimistic estimates η ± = η d u ± are shown with two dashed curves; η 3 = ( λ s λ p ) η p η s is shown with thin solid curves; and the thick curves show the mean geometric values of three estimates. We also plot the corresponding error bars.

Fig. 9
Fig. 9

Output signal power versus input pump power. Lines with a larger tangent correspond to the case without SHB. Lines with a lower tangent correspond to the case with SHB. Here, r 2 = 2 mm , h = 0.75 mm for Nd, and r 2 = 1.6 mm , h = 0.16 mm for Yb.

Fig. 10
Fig. 10

Relative gain G ̃ G of closest modes by Eqs. (40, 43) for Nd : YAG and Yb : YAG lasers versus pump power for various values of h. The dashed curves correspond to the highest mode, the solid curves correspond to the lower mode. Case of Nd: h = 1 mm (upper curves), h = 0.75 mm (intermediate curves), h = 0.5 mm (lowest curves). Case of Yb: h = 0.2 mm (upper curves), h = 0.16 mm (intermediate curves), h = 0.1 mm (lowest curves).

Tables (5)

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Table 1 Parameters of the Fits of Eqs. (33, 34, 35)

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Table 2 Parameters of the Fit of Eq. (38)

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Table 3 General Properties of Media and Examples of Resonators

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Table 4 Parameters of a Laser without SHB and Examples of Values

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Table 5 Parameters of a Laser with SHB and Examples of Values

Equations (61)

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β i + 1 = β i + 2 arcsin ( X i r 0 ) .
X i + 1 X i = t i ( Y i Y i + 1 ) ,
X i + 1 2 + ( Y i + 1 h r 0 ) 2 = r 0 2 ,
t i = tan ( β i + 1 ) .
Y i + 1 = h + r ξ i [ ( r ξ i ) 2 ( 1 + t i 2 ) ξ i 2 ] 1 2 1 + t i 2 ,
X i + 1 = X i + ( Y i + Y i + 1 ) t i ,
ξ i = ( X i + Y i t i + h t i ) t i .
H = r 0 ( r 0 2 r 1 2 ) 1 2 + h h + r 1 2 ( 2 r 0 ) .
M = X i + 1 X i = 1 + 2 [ h r 0 ( 1 + h r 0 ) ] 1 2 + 2 h r 0 .
N eq = n w 2 2 h λ s ( M 1 M ) ,
w = ( 2 h λ s n M 1 M ) 1 2 .
NA = λ p n q w
w ( z ) = w 0 [ 1 + ( λ z π q w 0 2 ) 2 ] 1 2 ,
exp ( A r 2 ) = w NA r 2 ,
q = λ p 2 n w NA
I p ( x 1 , x 2 ) I p ( 0 , r 2 ) u ( x 1 ) exp [ ( x 2 w ( x 1 ) ) 2 ] ,
u ( r ) = r 2 exp ( A r ) { r 2 2 + [ exp ( 2 A r 2 ) 1 ] r 2 } 1 2 .
Ψ ( x ) R exp ( G h ) M Ψ ( x M ) ,
Ψ 1 ( x ) = x ̃ ψ f ( x ) ,
x ̃ ψ f ( x ) R exp ( G h ) M x ̃ M ψ f ( x M ) .
Z 0 = [ ( r 0 + h ) h ] 1 2
NA 1 = ( r 2 r 1 ) ( 2 Z ) , NA 2 = NA p ( Z )
R 2 M 2 exp ( 2 G h ) = 1 ,
n 2 t = W u n 1 + W d n 2 ,
n 1 t = W u n 1 W d n 2 ,
W u = I p σ ap ω p + I s σ as ω s , W d = I p σ ep ω p + I s σ es ω s + 1 τ
n 1 = W d W u + W d , n 2 = W u W u + W d .
I po = ω p ( σ ap + σ ep ) τ , I so = ω s ( σ as + σ es ) τ .
A 0 = N D σ as + σ es , G 0 = N D σ ep + σ ap ,
D = σ ap σ es σ ep σ as .
A = A 0 U + s 1 + p + s , G = G 0 p V 1 + p + s ,
η q = 1 V p 1 + U s , η m = I s G I p A = λ p λ s η q ,
A A 0 + G G 0 = 1 ,
σ a ( λ ) f 0 ( λ nm ) × 10 20 cm 2 ,
σ e ( λ ) f 1 ( λ nm ) × 10 20 cm 2 ,
f j ( x ) = m = 1 K j a j , m 1 + ( x b j , m c j , m ) 2 , j { 0 , 1 } .
σ a ( λ ) f 3 ( λ nm ) exp ( Λ λ Λ λ 0 ) × 10 20 cm 2 ,
σ e ( λ ) f 3 ( λ nm ) exp ( Λ λ 0 Λ λ ) × 10 20 cm 2 ,
f 3 ( x ) = m = 1 5 a m 1 + ( 1 x 1 b m c m b m 2 ) 2 ,
A = A 0 1 π 0 π U + s 1 + s 2 + 2 s 1 s 2 cos ( θ ) 1 + p + s 1 + s 2 + 2 s 1 s 2 cos ( θ ) d θ = A 0 { 1 1 + p U [ ( 1 + p + s 1 + s 2 ) 2 4 s 1 s 2 ] 1 2 } ,
G 1 = G 0 1 π 0 π 1 + s 2 s 1 cos ( θ ) 1 + p + s 1 + s 2 + 2 s 1 s 2 cos ( θ ) d θ = G 0 p V 2 s 1 { 1 1 + p + s 2 s 1 [ ( 1 + p + s 1 + s 2 ) 2 4 s 1 s 2 ] 1 2 } ,
η q = 1 V p 1 + U [ ( 1 + p ) 2 + 2 ( 1 + p ) ( s 1 + s 2 ) + ( s 1 s 2 ) 2 ] 1 2 1 p .
G ̃ = G ̃ ( λ ) = N π 0 π [ n 2 σ e ( λ ) n 1 σ a ( λ ) ] d θ ,
G ̃ ( λ ) = 1 b [ d + b c a d ( a 2 b 2 ) 1 2 ] ,
where { a = 1 + p + s 1 + s 2 b = 2 σ 1 s 1 s 2 c = σ 2 p σ a + σ 1 ( s 1 + s 1 ) d = σ 1 ( s 1 + s 2 ) σ 1 = σ as σ e σ es σ a σ as + σ es σ 2 = σ ap σ e σ ep σ a σ ap + σ ep σ a = σ a ( λ ) ; σ e = σ e ( λ ) } .
A = A 0 { 1 1 + p U [ ( 1 + p ) 2 + 2 ( 1 + p ) s ] 1 2 } ,
G 1 = G 0 p V s { 1 1 + p [ ( 1 + p ) 2 + 2 ( 1 + p ) s ] 1 2 } ,
η q = 1 V p 1 + U [ ( 1 + p ) 2 + 2 ( 1 + p ) s ] 1 2 1 p .
G 1 = G 0 2 ( p V ) 1 + p + 2 s + [ ( 1 + p ) ( 1 + p + 2 s ) ] 1 2 .
G = ln ( M R ) h .
A = A 0 [ 1 ln ( M R ) G 0 h ] .
η p = 1 exp ( A r 2 ) .
s = ( G 0 G 1 ) p G 0 G V 1 = δ i ( p p t ) ,
P p = 2 L ( r 2 r 1 ) I s o p ,
P s = L ( r 2 r 1 ) I s o s .
P s = η slope ( P p P th ) ,
P th = 2 L h I p o p t
η slope = ( G 0 G 1 ) I s o I p o r 2 r 1 2 h
η s = ( r 2 2 r 1 2 ) ( r 2 2 r 1 2 ) + r 1 2 ( 1 R ) + ( r 2 + r 1 2 ) 2 ( 1 R ) = M 1 M R + O ,
s = G 0 G 1 ( p V ) 1 + p 4 { 1 + [ 1 + 8 G 0 ( p V ) G 1 ( 1 + p ) ] 1 2 } .
λ ± = λ s 1 ± λ s ( 2 n h ) .

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