Abstract

The green noise in intracavity-doubled Nd:YVO4 lasers can be eliminated by single-mode operation of the device, although good long-term stability remains a problem. We have studied the threshold when multimode operation sets in, with both respect to polarization modes and longitudinal modes, as a function of various cavity parameters. It is demonstrated that the device is sensitive to perturbations in the birefringence and the optical path length of the elements in the cavity. The influence of energy migration and intensity-dependent losses that are due to frequency conversion is also discussed. Good control of the cavity temperature and dimensions is a key point for long-term stability.

© 1994 Optical Society of America

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References

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  1. K. Tatsuno, M. Takahashi, J. Nakamura, K. Muraoka, and T. Toda, “Optical disk recording with second-harmonic generation lasers,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CTuN5, p. 128.
  2. T. Baer, “Large-amplitude fluctuations due to longitudinal mode coupling in diode-pumped intracavity-doubled Nd:YAG lasers,” J. Opt. Soc. Am. B 3, 1175–1180 (1986).
    [CrossRef]
  3. D. W. Anthon, D. L. Sipes, T. J. Pier, and M. R. Ressl, “Intracavity doubling of cw diode-pumped Nd:YAG lasers with KTP,” IEEE J. Quantum Electron. 28, 1148–1157 (1992).
    [CrossRef]
  4. H. Nagai, M. Kume, I. Ohta, H. Shimizu, and M. Kazumura, “Low-noise operation of a diode-pumped intracavity-doubled Nd:YAG laser using a Brewster plate,” IEEE J. Quantum Electron. 28, 1164–1168 (1992).
    [CrossRef]
  5. D. Draegert, “Efficient single-longitudinal-mode Nd:YAG laser,” IEEE J. Quantum Electron. QE-8, 235–239 (1972).
    [CrossRef]
  6. T. Kane and R. Byer, “Monolithic, unidirectional single-mode Nd:YAG ring laser,” Opt. Lett. 10, 65–67 (1985).
    [CrossRef] [PubMed]
  7. G. J. Kintz and T. Baer, “Single-frequency operation in solid-state laser materials with short absorption depths,” IEEE J. Quantum Electron. 26, 1457–1459 (1990).
    [CrossRef]
  8. H. G. Danielmeyer and M. Blätte, “Fluorescence quenching in Nd:YAG,” Appl. Phys. 1, 269–274 (1973).
    [CrossRef]
  9. T. Sasaki, T. Kojima, A. Yokotani, O. Oguri, and S. Nakai, “Single-longitudinal-mode operation and second-harmonic generation of Nd:YVO4microchip lasers,” Opt. Lett. 16, 1665–1667 (1991).
    [CrossRef] [PubMed]
  10. J. J. Zayhowski, “The effects of spatial hole burning and energy diffusion on the single-mode operation of standing-wave lasers,” IEEE J. Quantum Electron. 26, 2052–2057 (1990).
    [CrossRef]
  11. Y. Kuwano and S. Saito, “Nd:YVO4single crystal for LD pumped solid state laser,” Laser Res. 18, 616–621 (1990).
    [CrossRef]
  12. J. R. O’Connor, “Unusual crystal field levels and efficient laser properties of YVO4:Nd,” Appl. Phys. Lett. 9, 1412–1423 (1988).
  13. H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
    [CrossRef]
  14. J. D. Bierlein and H. Vanherzeele, “Potassium titanyl phosphate: properties and new applications,” J. Opt. Soc. Am. B 6, 622–633 (1989).
    [CrossRef]
  15. J. J. Zayhowski and A. Mooradian, “Single-frequency microchip Nd lasers,” Opt. Lett. 14, 24–26 (1989).
    [CrossRef] [PubMed]
  16. M. Oka and S. Kubota, “Stable intracavity doubling of orthogonal linearly polarized modes in diode-pumped Nd:YAG lasers,” Opt. Lett. 13, 805–807 (1988).
    [CrossRef] [PubMed]
  17. K. Tatsuno, T. Andou, S. Nakatsuka, T. Miyai, M. Takahashi, and S. Helmfrid, “Highly efficient and stable green micro laser consisting of Nd:YVO4with intracavity KTP for optical storage,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CWQ8.
  18. G. E. James, E. M. Harell, C. Bracikowski, K. Wiesenfeld, and R. Roy, “Elimination of chaos in an intracavity-doubled Nd:YAG laser,” Opt. Lett. 15, 1141–1143 (1990).
    [CrossRef] [PubMed]
  19. J. Q. Yao and T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
    [CrossRef]

1992 (2)

D. W. Anthon, D. L. Sipes, T. J. Pier, and M. R. Ressl, “Intracavity doubling of cw diode-pumped Nd:YAG lasers with KTP,” IEEE J. Quantum Electron. 28, 1148–1157 (1992).
[CrossRef]

H. Nagai, M. Kume, I. Ohta, H. Shimizu, and M. Kazumura, “Low-noise operation of a diode-pumped intracavity-doubled Nd:YAG laser using a Brewster plate,” IEEE J. Quantum Electron. 28, 1164–1168 (1992).
[CrossRef]

1991 (1)

1990 (5)

J. J. Zayhowski, “The effects of spatial hole burning and energy diffusion on the single-mode operation of standing-wave lasers,” IEEE J. Quantum Electron. 26, 2052–2057 (1990).
[CrossRef]

Y. Kuwano and S. Saito, “Nd:YVO4single crystal for LD pumped solid state laser,” Laser Res. 18, 616–621 (1990).
[CrossRef]

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

G. J. Kintz and T. Baer, “Single-frequency operation in solid-state laser materials with short absorption depths,” IEEE J. Quantum Electron. 26, 1457–1459 (1990).
[CrossRef]

G. E. James, E. M. Harell, C. Bracikowski, K. Wiesenfeld, and R. Roy, “Elimination of chaos in an intracavity-doubled Nd:YAG laser,” Opt. Lett. 15, 1141–1143 (1990).
[CrossRef] [PubMed]

1989 (2)

1988 (2)

M. Oka and S. Kubota, “Stable intracavity doubling of orthogonal linearly polarized modes in diode-pumped Nd:YAG lasers,” Opt. Lett. 13, 805–807 (1988).
[CrossRef] [PubMed]

J. R. O’Connor, “Unusual crystal field levels and efficient laser properties of YVO4:Nd,” Appl. Phys. Lett. 9, 1412–1423 (1988).

1986 (1)

1985 (1)

1984 (1)

J. Q. Yao and T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

1973 (1)

H. G. Danielmeyer and M. Blätte, “Fluorescence quenching in Nd:YAG,” Appl. Phys. 1, 269–274 (1973).
[CrossRef]

1972 (1)

D. Draegert, “Efficient single-longitudinal-mode Nd:YAG laser,” IEEE J. Quantum Electron. QE-8, 235–239 (1972).
[CrossRef]

Andou, T.

K. Tatsuno, T. Andou, S. Nakatsuka, T. Miyai, M. Takahashi, and S. Helmfrid, “Highly efficient and stable green micro laser consisting of Nd:YVO4with intracavity KTP for optical storage,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CWQ8.

Anthon, D. W.

D. W. Anthon, D. L. Sipes, T. J. Pier, and M. R. Ressl, “Intracavity doubling of cw diode-pumped Nd:YAG lasers with KTP,” IEEE J. Quantum Electron. 28, 1148–1157 (1992).
[CrossRef]

Baer, T.

G. J. Kintz and T. Baer, “Single-frequency operation in solid-state laser materials with short absorption depths,” IEEE J. Quantum Electron. 26, 1457–1459 (1990).
[CrossRef]

T. Baer, “Large-amplitude fluctuations due to longitudinal mode coupling in diode-pumped intracavity-doubled Nd:YAG lasers,” J. Opt. Soc. Am. B 3, 1175–1180 (1986).
[CrossRef]

Bierlein, J. D.

Blätte, M.

H. G. Danielmeyer and M. Blätte, “Fluorescence quenching in Nd:YAG,” Appl. Phys. 1, 269–274 (1973).
[CrossRef]

Bracikowski, C.

Byer, R.

Danielmeyer, H. G.

H. G. Danielmeyer and M. Blätte, “Fluorescence quenching in Nd:YAG,” Appl. Phys. 1, 269–274 (1973).
[CrossRef]

Draegert, D.

D. Draegert, “Efficient single-longitudinal-mode Nd:YAG laser,” IEEE J. Quantum Electron. QE-8, 235–239 (1972).
[CrossRef]

Fahlen, T. S.

J. Q. Yao and T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

Harell, E. M.

Helmfrid, S.

K. Tatsuno, T. Andou, S. Nakatsuka, T. Miyai, M. Takahashi, and S. Helmfrid, “Highly efficient and stable green micro laser consisting of Nd:YVO4with intracavity KTP for optical storage,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CWQ8.

James, G. E.

Kanabe, T.

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Kane, T.

Kazumura, M.

H. Nagai, M. Kume, I. Ohta, H. Shimizu, and M. Kazumura, “Low-noise operation of a diode-pumped intracavity-doubled Nd:YAG laser using a Brewster plate,” IEEE J. Quantum Electron. 28, 1164–1168 (1992).
[CrossRef]

Kintz, G. J.

G. J. Kintz and T. Baer, “Single-frequency operation in solid-state laser materials with short absorption depths,” IEEE J. Quantum Electron. 26, 1457–1459 (1990).
[CrossRef]

Kojima, T.

Kubota, S.

Kume, M.

H. Nagai, M. Kume, I. Ohta, H. Shimizu, and M. Kazumura, “Low-noise operation of a diode-pumped intracavity-doubled Nd:YAG laser using a Brewster plate,” IEEE J. Quantum Electron. 28, 1164–1168 (1992).
[CrossRef]

Kuwano, Y.

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Y. Kuwano and S. Saito, “Nd:YVO4single crystal for LD pumped solid state laser,” Laser Res. 18, 616–621 (1990).
[CrossRef]

Miyai, T.

K. Tatsuno, T. Andou, S. Nakatsuka, T. Miyai, M. Takahashi, and S. Helmfrid, “Highly efficient and stable green micro laser consisting of Nd:YVO4with intracavity KTP for optical storage,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CWQ8.

Mooradian, A.

Muraoka, K.

K. Tatsuno, M. Takahashi, J. Nakamura, K. Muraoka, and T. Toda, “Optical disk recording with second-harmonic generation lasers,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CTuN5, p. 128.

Nagai, H.

H. Nagai, M. Kume, I. Ohta, H. Shimizu, and M. Kazumura, “Low-noise operation of a diode-pumped intracavity-doubled Nd:YAG laser using a Brewster plate,” IEEE J. Quantum Electron. 28, 1164–1168 (1992).
[CrossRef]

Nagamoto, H.

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Naito, K.

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Nakai, S.

Nakamura, J.

K. Tatsuno, M. Takahashi, J. Nakamura, K. Muraoka, and T. Toda, “Optical disk recording with second-harmonic generation lasers,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CTuN5, p. 128.

Nakatsuka, M.

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Nakatsuka, S.

K. Tatsuno, T. Andou, S. Nakatsuka, T. Miyai, M. Takahashi, and S. Helmfrid, “Highly efficient and stable green micro laser consisting of Nd:YVO4with intracavity KTP for optical storage,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CWQ8.

O’Connor, J. R.

J. R. O’Connor, “Unusual crystal field levels and efficient laser properties of YVO4:Nd,” Appl. Phys. Lett. 9, 1412–1423 (1988).

Oguri, O.

Ohta, I.

H. Nagai, M. Kume, I. Ohta, H. Shimizu, and M. Kazumura, “Low-noise operation of a diode-pumped intracavity-doubled Nd:YAG laser using a Brewster plate,” IEEE J. Quantum Electron. 28, 1164–1168 (1992).
[CrossRef]

Oka, M.

Pier, T. J.

D. W. Anthon, D. L. Sipes, T. J. Pier, and M. R. Ressl, “Intracavity doubling of cw diode-pumped Nd:YAG lasers with KTP,” IEEE J. Quantum Electron. 28, 1148–1157 (1992).
[CrossRef]

Ressl, M. R.

D. W. Anthon, D. L. Sipes, T. J. Pier, and M. R. Ressl, “Intracavity doubling of cw diode-pumped Nd:YAG lasers with KTP,” IEEE J. Quantum Electron. 28, 1148–1157 (1992).
[CrossRef]

Roy, R.

Saito, S.

Y. Kuwano and S. Saito, “Nd:YVO4single crystal for LD pumped solid state laser,” Laser Res. 18, 616–621 (1990).
[CrossRef]

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Sasaki, T.

T. Sasaki, T. Kojima, A. Yokotani, O. Oguri, and S. Nakai, “Single-longitudinal-mode operation and second-harmonic generation of Nd:YVO4microchip lasers,” Opt. Lett. 16, 1665–1667 (1991).
[CrossRef] [PubMed]

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Shimizu, H.

H. Nagai, M. Kume, I. Ohta, H. Shimizu, and M. Kazumura, “Low-noise operation of a diode-pumped intracavity-doubled Nd:YAG laser using a Brewster plate,” IEEE J. Quantum Electron. 28, 1164–1168 (1992).
[CrossRef]

Sipes, D. L.

D. W. Anthon, D. L. Sipes, T. J. Pier, and M. R. Ressl, “Intracavity doubling of cw diode-pumped Nd:YAG lasers with KTP,” IEEE J. Quantum Electron. 28, 1148–1157 (1992).
[CrossRef]

Takahashi, M.

K. Tatsuno, M. Takahashi, J. Nakamura, K. Muraoka, and T. Toda, “Optical disk recording with second-harmonic generation lasers,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CTuN5, p. 128.

K. Tatsuno, T. Andou, S. Nakatsuka, T. Miyai, M. Takahashi, and S. Helmfrid, “Highly efficient and stable green micro laser consisting of Nd:YVO4with intracavity KTP for optical storage,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CWQ8.

Tatsuno, K.

K. Tatsuno, T. Andou, S. Nakatsuka, T. Miyai, M. Takahashi, and S. Helmfrid, “Highly efficient and stable green micro laser consisting of Nd:YVO4with intracavity KTP for optical storage,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CWQ8.

K. Tatsuno, M. Takahashi, J. Nakamura, K. Muraoka, and T. Toda, “Optical disk recording with second-harmonic generation lasers,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CTuN5, p. 128.

Toda, T.

K. Tatsuno, M. Takahashi, J. Nakamura, K. Muraoka, and T. Toda, “Optical disk recording with second-harmonic generation lasers,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CTuN5, p. 128.

Vanherzeele, H.

Wiesenfeld, K.

Yamanaka, M.

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Yao, J. Q.

J. Q. Yao and T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

Yokotani, A.

Yoshida, K.

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Zayhowski, J. J.

J. J. Zayhowski, “The effects of spatial hole burning and energy diffusion on the single-mode operation of standing-wave lasers,” IEEE J. Quantum Electron. 26, 2052–2057 (1990).
[CrossRef]

J. J. Zayhowski and A. Mooradian, “Single-frequency microchip Nd lasers,” Opt. Lett. 14, 24–26 (1989).
[CrossRef] [PubMed]

Appl. Phys. (1)

H. G. Danielmeyer and M. Blätte, “Fluorescence quenching in Nd:YAG,” Appl. Phys. 1, 269–274 (1973).
[CrossRef]

Appl. Phys. Lett. (1)

J. R. O’Connor, “Unusual crystal field levels and efficient laser properties of YVO4:Nd,” Appl. Phys. Lett. 9, 1412–1423 (1988).

IEEE J. Quantum Electron. (5)

J. J. Zayhowski, “The effects of spatial hole burning and energy diffusion on the single-mode operation of standing-wave lasers,” IEEE J. Quantum Electron. 26, 2052–2057 (1990).
[CrossRef]

D. W. Anthon, D. L. Sipes, T. J. Pier, and M. R. Ressl, “Intracavity doubling of cw diode-pumped Nd:YAG lasers with KTP,” IEEE J. Quantum Electron. 28, 1148–1157 (1992).
[CrossRef]

H. Nagai, M. Kume, I. Ohta, H. Shimizu, and M. Kazumura, “Low-noise operation of a diode-pumped intracavity-doubled Nd:YAG laser using a Brewster plate,” IEEE J. Quantum Electron. 28, 1164–1168 (1992).
[CrossRef]

D. Draegert, “Efficient single-longitudinal-mode Nd:YAG laser,” IEEE J. Quantum Electron. QE-8, 235–239 (1972).
[CrossRef]

G. J. Kintz and T. Baer, “Single-frequency operation in solid-state laser materials with short absorption depths,” IEEE J. Quantum Electron. 26, 1457–1459 (1990).
[CrossRef]

J. Appl. Phys. (1)

J. Q. Yao and T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

J. Opt. Soc. Am. B (2)

Laser Res. (2)

Y. Kuwano and S. Saito, “Nd:YVO4single crystal for LD pumped solid state laser,” Laser Res. 18, 616–621 (1990).
[CrossRef]

H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, and Y. Kuwano, “Laser diode pumped Nd:YVO4laser,” Laser Res. 18, 639–645 (1990).
[CrossRef]

Opt. Lett. (5)

Other (2)

K. Tatsuno, M. Takahashi, J. Nakamura, K. Muraoka, and T. Toda, “Optical disk recording with second-harmonic generation lasers,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CTuN5, p. 128.

K. Tatsuno, T. Andou, S. Nakatsuka, T. Miyai, M. Takahashi, and S. Helmfrid, “Highly efficient and stable green micro laser consisting of Nd:YVO4with intracavity KTP for optical storage,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CWQ8.

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Figures (11)

Fig. 1
Fig. 1

Plot of the function f(r0).

Fig. 2
Fig. 2

Open squares, enhancement factor; i.e., the d/l-depending factor in inequality (16) as a function of length of the gain medium in units of the absorption depth. Filled squares, second-harmonic output power, normalized to be 1 when the gain medium is infinitely thick.

Fig. 3
Fig. 3

Multimode threshold as function of the diffusion constant times the fluorescence lifetime. We have used the same gain-medium thickness and absorption depths as measured in Ref. 9. Other numerical data are identical with those of the example in Subsection 2.B.

Fig. 4
Fig. 4

Emission cross section for the first two oscillating modes. Left, ideal situation, with the largest possible difference in emission cross section. Right, situation when the cavity length is shifted by 1/4 wavelength. In this case multimode oscillation will set in as soon as the lasing threshold is reached.

Fig. 5
Fig. 5

Multimode threshold as function of shift in the cavity length. The shift is given in units of the lasing wavelength, i.e., 1064 nm for Nd:YVO4. Different curves in the graph correspond to different values of the threshold at the origin and at 5, 10, 20, and 30 units.

Fig. 6
Fig. 6

Multimode threshold as function of shift in the cavity length, with and without energy migration (diffusion). The shift is given in units of the lasing wavelength. When energy migration is present, the threshold at the origin of the x axis is 1.68 if the diffusion constant is set to zero.

Fig. 7
Fig. 7

Multimode threshold as function of optical length of the cavity. The different curves correspond to different values of the threshold in a long cavity: 1.5, 2, 5, 10, 20, and 30. We assume a 0.8-nm FWHM of the laser transition.

Fig. 8
Fig. 8

Fraction of the light intensity of the mode with the highest gain that is polarized parallel to the optical axis as function of KTP retardation and Nd:YVO4 retardation. The angle between the axes of KTP and Nd:YVO4 is ϕ = 45°.

Fig. 9
Fig. 9

Fraction of the light intensity of the mode with the highest gain that is polarized parallel to the optical axis as function of KTP retardation and Nd:YVO4 retardation. The angle between the axes of KTP and Nd:YVO4 is ϕ = 45°.

Fig. 10
Fig. 10

g factor as function of KTP phase retardation for Nd:YVO4 retardations of 10, 30 and 90. The angle between the axes of KTP and Nd:YVO4 is (a) ϕ = 45° and (b) ϕ = 15°,

Fig. 11
Fig. 11

Gain as function of frequency deviation from the center of the Lorentzian-shaped laser transition for some different phase shifts in the Nd:YVO4 crystal at the center frequency. The gain is given in units of the gain for a wave polarized parallel to the optical axis in the gain medium. Length of the KTP crystal, 4 mm; length of the Nd:YVO4 crystal, 1 mm; KTP phase shift at the center frequency, 90°; KTP rotation angle, 45°. The typical longitudinal-mode spacing in a 10-mm-long intracavity-doubled device is 10 GHz.

Equations (40)

Equations on this page are rendered with MathJax. Learn more.

I p ( z ) = I p ( 0 ) exp ( - z / l ) ,
R ( z ) = ( σ a N 0 / h ν p ) I p ( z ) ,             0 z d ,
R ( z ) = 2 ( σ 1 e / h ν 1 ) [ 1 - cos ( 2 k 1 z ) ] I 1 N ( z ) + N ( z ) / τ f ,
2 0 d σ 1 e [ 1 - cos ( 2 k 1 z ) ] N ( z ) d z = T ,
R th = T 2 σ 1 e τ f l [ 1 - exp ( - d / l ) ] , N th = T 2 σ 1 e l [ 1 - exp ( - d / l ) ] , I sat = h ν 1 σ 1 e τ f ,
n ( z ) = r 0 exp ( - z / l ) 2 [ 1 - cos ( 2 k 1 z ) ] i 1 + 1 ,
1 l [ 1 - exp ( - d / l ) ] 0 d [ 1 - cos ( 2 k 1 z ) ] n ( z ) d z = 1 ,
r 0 2 i 1 [ 1 - 1 ( 1 + 4 i 1 ) 1 / 2 ] = 1 ,
i 1 = [ 4 r 0 - 1 - ( 1 + 8 r 0 ) 1 / 2 ] / 8.
σ m e σ 1 e 1 l [ 1 - exp ( - d / l ) ] 0 d [ 1 - cos ( 2 k m z ) ] n ( z ) d z < 1.
k m z = k 1 z + ( 2 n gm π Δ λ z / λ 2 ) ,
1 l [ 1 - exp ( - d / l ) ] 0 d [ 1 - cos ( 2 τ δ z l ) ] × f ( r 0 ) exp ( - z l ) d z < σ 1 e / σ m e - 1 ,
f ( r 0 ) = 2 r 0 ( 4 i 1 + 1 ) 1 / 2 - 1 4 i 1 - 1 ,
f ( r 0 ) = - 3 2 + ( 1 4 + 2 r 0 ) 1 / 2 ,
r 0 ( f ) = ½ ( f + 1 ) ( f + 2 ) .
f ( r 0 ) < 1 - exp ( - d / l ) 2 - ( d 2 / l 2 + 2 d / l + 2 ) exp ( - d / l ) 1 τ 2 .
r 0 exp ( - z l ) = 2 [ 1 - cos ( 2 k 1 z ) ] i 1 n ( z ) + n ( z ) - D τ f d 2 n ( z ) d z 2 ,
n ( z ) = q = 0 N c q cos ( q Ω z ) ,
( 2 i 1 + 1 ) c 0 - i 1 c 1 = r 0 ,
- 2 i 1 c 0 + ( D τ f Ω 2 + 2 i 1 + 1 ) c 1 - i 1 c 2 = 0 ,
- i 1 c q - 1 + ( q 2 D τ f Ω 2 + 2 i 1 + 1 ) c q - i 1 c q + 1 = 0 ,             2 q N ,
c N + 1 = 0.
c q ( z ) = c q exp ( - z / l ) .
c 0 = 0.5 c 1 = 1 ,
c 0 - c 1 2 [ 1 - exp ( - d / l ) ] [ 1 - cos ( 2 τ δ d / l ) exp ( - d / l ) 1 + ( 2 τ δ ) 2 + 2 τ δ 1 + ( 2 τ δ ) 2 sin ( 2 τ δ d l ) exp ( - d l ) ] < σ 1 e σ m e .
f ( r 0 ) < 1 - exp ( - d / l ) 2 - ( d 2 / l 2 + 2 d / l + 2 ) exp ( - d / l ) τ 2 × 1 τ 2 σ 1 e / σ m e - 1 δ 2 ,
f ( r 0 ) < 1 2 τ 2 + 2 δ 2 ,
δ = λ 2 L Δ λ 0 .
R ( ϕ ) = [ cos ϕ - sin ϕ sin ϕ cos ϕ ] , C ( ξ ) = [ exp ( i ξ / 2 ) 0 0 exp ( - i ξ / 2 ) ] , C ( δ ) = [ exp ( i δ / 2 ) 0 0 exp ( - i δ / 2 ) ] ,
M = R ( - ϕ ) C ( δ ) R ( ϕ ) C ( ξ ) C ( ξ ) R ( - ϕ ) C ( δ ) R ( ϕ ) .
M = [ α i β i β α * ] ,
M = C ( ξ ) R ( - ϕ ) C ( δ ) C ( δ ) R ( ϕ ) C ( ξ ) .
ν 1 = ( sin ( 2 ϕ ) sin δ Im ( α ) ± { [ Im ( α ) ] 2 + [ sin ( 2 ϕ ) sin δ ] 2 } 1 / 2 ) , ν 2 = ( Im ( α ) ± { [ Im ( α ) ] 2 + [ sin ( 2 ϕ ) sin δ ] 2 } 1 / 2 - sin ( 2 ϕ ) sin δ ) ,
α = exp ( i ξ ) [ cos 2 ϕ exp ( i δ ) + sin 2 ϕ exp ( - i δ ) ] .
g = 4 ν par 2 ν ort 2 / ( ν par 2 + ν ort 2 ) 2 ,
ν 1 = ( - sin ( 2 ϕ ) sin ξ Im ( α ) ± { [ Im ( α ) ] 2 + [ sin ( 2 ϕ ) sin ξ ] 2 } 1 / 2 ) , ν 2 = ( Im ( α ) ± { [ Im ( α ) ] 2 + [ sin ( 2 ϕ ) sin ξ ] 2 } 1 / 2 sin ( 2 ϕ ) sin ξ ) ,
α = exp ( i δ ) [ cos 2 ϕ exp ( i ξ ) + sin 2 ϕ exp ( - i ξ ) ] .
σ e = ( σ par ν par 2 + σ ort ν ort 2 ) / ( ν par 2 + ν ort 2 ) ,
lim l 1 2 l 0 l [ 1 - cos ( 2 τ δ z / l ) ] f ( r 0 ) d z < σ 1 e / σ 2 e - 1 ,
f ( r 0 ) < 2 ( σ 1 e / σ 2 e - 1 ) .

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