Abstract

It was experimentally found that electronic structures of Russell-Saunders manifolds in Nd:YAG depended on the Nd3+-doping concentration (C Nd) and its fabrication process. Both of the bandwidth and the branching ratio in fluorescent transitions in Nd:YAG varied almost linearly depending on C Nd, and a fabrication process has its own diluted limit of the bandwidth and the branching ratio. Also dependences of Stark splitting in Nd:YAG were also observed. Nd3+-doping causes 1.9% and 4.5% reduction in the stimulated emission cross section of Nd:YAG per 1at.% of C Nd at 1.064 μm and 1.319 μm, respectively.

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References

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  1. A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
    [CrossRef]
  2. R. M. Yamamoto, B. S. Bhachu, K. P. Cutter, S. N. Fochs, S. A. Letts, C. W. Parks, M. D. Rotter, and T. F. Soules, “The use of large transparent ceramics in a high powered, diode pumped solid-state laser,” Proceedings of OSA Topical meeting on Advanced Solid-State Photonics 2008, WC5, Nara, Japan (Jan. 2008).
  3. S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100 kW coherently combined slab MOPAs,” in Proceedings of Conference on Quantum Electronics and Laser Science Conference on Lasers and Electro-Optics, CLEO/QELS, CThA1, Baltimore, MA, USA (2009).
  4. I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
    [CrossRef]
  5. V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
    [CrossRef]
  6. D. L. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21(5), 836–850 (1953).
    [CrossRef]
  7. T. Förster, “Intermolecular energy migration and fluorescence,” Ann. Phys. 2, 55–75 (1948).
  8. Y. Sato, T. Taira, and A. Ikesue, “A study on influences of Nd3+-doping concentration upon spectroscopic properties of Nd:Y3Al5O12 ceramics,” in Proceedings of OSA Topical meeting on Advanced Solid-State Photonics 2009, WB18, Denver, CO, USA (Feb. 2009).
  9. F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
    [CrossRef]
  10. T. Kushida, “Linewidths and thermal shifts of spectral lines in neodymium-doped yttrium aluminum garnet and calcium fluorophosphate,” Phys. Rev. 185(2), 500–508 (1969).
    [CrossRef]
  11. Y. Sato, J. Akiyama, and T. Taira, “Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals,” Opt. Mater. 31(5), 720–724 (2009).
    [CrossRef]
  12. T. Kushida, H. M. Marcos, and J. E. Geusic, “Laser transition cross section and fluorescence branching ratio for Nd3+ in yttrium aluminum garnet,” Phys. Rev. 167(2), 289–291 (1968).
    [CrossRef]
  13. T. Taira, “RE3+-ion-doped YAG ceramic lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 798–809 (2007).
    [CrossRef]
  14. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
    [CrossRef]
  15. G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962).
    [CrossRef]
  16. A. Blumen and J. Manz, “On the concentration and time dependence of the energy transfer to randomly distributed acceptors,” J. Chem. Phys. 71(11), 4694–4702 (1979).
    [CrossRef]

2009 (1)

Y. Sato, J. Akiyama, and T. Taira, “Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals,” Opt. Mater. 31(5), 720–724 (2009).
[CrossRef]

2007 (1)

T. Taira, “RE3+-ion-doped YAG ceramic lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 798–809 (2007).
[CrossRef]

2005 (1)

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

2001 (1)

V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
[CrossRef]

2000 (1)

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
[CrossRef]

1999 (1)

F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
[CrossRef]

1979 (1)

A. Blumen and J. Manz, “On the concentration and time dependence of the energy transfer to randomly distributed acceptors,” J. Chem. Phys. 71(11), 4694–4702 (1979).
[CrossRef]

1969 (1)

T. Kushida, “Linewidths and thermal shifts of spectral lines in neodymium-doped yttrium aluminum garnet and calcium fluorophosphate,” Phys. Rev. 185(2), 500–508 (1969).
[CrossRef]

1968 (1)

T. Kushida, H. M. Marcos, and J. E. Geusic, “Laser transition cross section and fluorescence branching ratio for Nd3+ in yttrium aluminum garnet,” Phys. Rev. 167(2), 289–291 (1968).
[CrossRef]

1962 (2)

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
[CrossRef]

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962).
[CrossRef]

1953 (1)

D. L. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21(5), 836–850 (1953).
[CrossRef]

1948 (1)

T. Förster, “Intermolecular energy migration and fluorescence,” Ann. Phys. 2, 55–75 (1948).

Akchurin, M. S.

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

Akiyama, J.

Y. Sato, J. Akiyama, and T. Taira, “Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals,” Opt. Mater. 31(5), 720–724 (2009).
[CrossRef]

Bettinelli, M.

F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
[CrossRef]

Blumen, A.

A. Blumen and J. Manz, “On the concentration and time dependence of the energy transfer to randomly distributed acceptors,” J. Chem. Phys. 71(11), 4694–4702 (1979).
[CrossRef]

Cavalli, E.

F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
[CrossRef]

Cohen-Adad, M. T.

F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
[CrossRef]

Dexter, D. L.

D. L. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21(5), 836–850 (1953).
[CrossRef]

Ermeneux, F. S.

F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
[CrossRef]

Förster, T.

T. Förster, “Intermolecular energy migration and fluorescence,” Ann. Phys. 2, 55–75 (1948).

Gainutdinov, R. V.

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

Georgescu, S.

V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
[CrossRef]

Geusic, J. E.

T. Kushida, H. M. Marcos, and J. E. Geusic, “Laser transition cross section and fluorescence branching ratio for Nd3+ in yttrium aluminum garnet,” Phys. Rev. 167(2), 289–291 (1968).
[CrossRef]

Goutaudier, C.

F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
[CrossRef]

Ikesue, A.

V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
[CrossRef]

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
[CrossRef]

Judd, B. R.

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
[CrossRef]

Kaminskii, A. A.

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

Kurimura, S.

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
[CrossRef]

Kushida, T.

T. Kushida, “Linewidths and thermal shifts of spectral lines in neodymium-doped yttrium aluminum garnet and calcium fluorophosphate,” Phys. Rev. 185(2), 500–508 (1969).
[CrossRef]

T. Kushida, H. M. Marcos, and J. E. Geusic, “Laser transition cross section and fluorescence branching ratio for Nd3+ in yttrium aluminum garnet,” Phys. Rev. 167(2), 289–291 (1968).
[CrossRef]

Lupei, A.

V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
[CrossRef]

Lupei, V.

V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
[CrossRef]

Manz, J.

A. Blumen and J. Manz, “On the concentration and time dependence of the energy transfer to randomly distributed acceptors,” J. Chem. Phys. 71(11), 4694–4702 (1979).
[CrossRef]

Marcos, H. M.

T. Kushida, H. M. Marcos, and J. E. Geusic, “Laser transition cross section and fluorescence branching ratio for Nd3+ in yttrium aluminum garnet,” Phys. Rev. 167(2), 289–291 (1968).
[CrossRef]

Moncorge, R.

F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
[CrossRef]

Ofelt, G. S.

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962).
[CrossRef]

Sato, Y.

Y. Sato, J. Akiyama, and T. Taira, “Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals,” Opt. Mater. 31(5), 720–724 (2009).
[CrossRef]

V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
[CrossRef]

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
[CrossRef]

Shirakava, A.

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

Shoji, I.

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
[CrossRef]

Taira, T.

Y. Sato, J. Akiyama, and T. Taira, “Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals,” Opt. Mater. 31(5), 720–724 (2009).
[CrossRef]

T. Taira, “RE3+-ion-doped YAG ceramic lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 798–809 (2007).
[CrossRef]

V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
[CrossRef]

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
[CrossRef]

Takaichi, K.

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

Ueda, K.

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

Yagi, H.

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

Yanagitani, T.

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

Yoshida, K.

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
[CrossRef]

Ann. Phys. (1)

T. Förster, “Intermolecular energy migration and fluorescence,” Ann. Phys. 2, 55–75 (1948).

Appl. Phys. Lett. (1)

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77(7), 939–941 (2000).
[CrossRef]

Crystallogr. Rep. (1)

A. A. Kaminskii, M. S. Akchurin, R. V. Gainutdinov, K. Takaichi, A. Shirakava, H. Yagi, T. Yanagitani, and K. Ueda, “Microhardness and fracture toughness of Y2O3- and Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 50(5), 869–873 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Taira, “RE3+-ion-doped YAG ceramic lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 798–809 (2007).
[CrossRef]

J. Chem. Phys. (3)

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962).
[CrossRef]

A. Blumen and J. Manz, “On the concentration and time dependence of the energy transfer to randomly distributed acceptors,” J. Chem. Phys. 71(11), 4694–4702 (1979).
[CrossRef]

D. L. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21(5), 836–850 (1953).
[CrossRef]

Opt. Mater. (2)

Y. Sato, J. Akiyama, and T. Taira, “Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals,” Opt. Mater. 31(5), 720–724 (2009).
[CrossRef]

F. S. Ermeneux, C. Goutaudier, R. Moncorge, M. T. Cohen-Adad, M. Bettinelli, and E. Cavalli, “Comparative optical characterization of various Nd3+:YVO4 single crystals,” Opt. Mater. 13(2), 193–204 (1999).
[CrossRef]

Phys. Rev. (3)

T. Kushida, “Linewidths and thermal shifts of spectral lines in neodymium-doped yttrium aluminum garnet and calcium fluorophosphate,” Phys. Rev. 185(2), 500–508 (1969).
[CrossRef]

T. Kushida, H. M. Marcos, and J. E. Geusic, “Laser transition cross section and fluorescence branching ratio for Nd3+ in yttrium aluminum garnet,” Phys. Rev. 167(2), 289–291 (1968).
[CrossRef]

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
[CrossRef]

Phys. Rev. B (1)

V. Lupei, A. Lupei, S. Georgescu, T. Taira, Y. Sato, and A. Ikesue, “The effect of Nd concentration on the spectroscopic and emission decay properties of highly doped Nd:YAG ceramics,” Phys. Rev. B 64(9), 092102 (2001).
[CrossRef]

Other (3)

R. M. Yamamoto, B. S. Bhachu, K. P. Cutter, S. N. Fochs, S. A. Letts, C. W. Parks, M. D. Rotter, and T. F. Soules, “The use of large transparent ceramics in a high powered, diode pumped solid-state laser,” Proceedings of OSA Topical meeting on Advanced Solid-State Photonics 2008, WC5, Nara, Japan (Jan. 2008).

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100 kW coherently combined slab MOPAs,” in Proceedings of Conference on Quantum Electronics and Laser Science Conference on Lasers and Electro-Optics, CLEO/QELS, CThA1, Baltimore, MA, USA (2009).

Y. Sato, T. Taira, and A. Ikesue, “A study on influences of Nd3+-doping concentration upon spectroscopic properties of Nd:Y3Al5O12 ceramics,” in Proceedings of OSA Topical meeting on Advanced Solid-State Photonics 2009, WB18, Denver, CO, USA (Feb. 2009).

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Figures (7)

Fig. 1
Fig. 1

Normalized fluorescent intensities of 0.8at.% Nd:YAG ceramics (WS) and 5.4at.% ceramics (SS) at 1.06-μm (a), and 0.4at.% Nd:YAG ceramics (WS) and 5.4at.% ceramics (SS) at 1.32-μm (b).

Fig. 2
Fig. 2

The dependence of the bandwidth of several fluorescence lines of Nd:YAG on C Nd (a), and the label of each Stark level in manifolds 4 F 3/2, 4 I 13/2, and 4 I 11/2 of Nd3+(b). Circle, triangle, and square indicate the evaluated value of the fluorescent bandwidth of CZ, SS, and WS, respectively. Labels R i, X i and Y i indicates the i-th lower Stark level of 4 F 3/2, 4 I 13/2, and 4 I 11/2 manifolds, respectively.

Fig. 3
Fig. 3

Stark splitting in Nd:YAG. The splitting of 4 F 3/2 is estimated from the transition from R i to Y 1 (a), and similarly the splitting of X 1 and X 2 are calculated from the transition from R i to X 1 and X 2 (b). The right axes indicate the ratio of the splitting variation, where ν min is the minimum value of the measured splitting in each graph. Circle, triangle, and square indicate the evaluated value of the Stark splitting in CZ, SS, and WS, respectively.

Fig. 4
Fig. 4

Ratios of fluorescent bandwidths under the final states Y i to Y 1 in Nd:YAG, which coincide with ratios of | ψ f | V 1 | ψ i | 2 . Initial states are R 1 (a) and R 2 (b). Circle, triangle, and square indicate the evaluated ratios of | ψ f | V 1 | ψ i | 2 in CZ, SS, and WS, respectively.

Fig. 5
Fig. 5

Ratios of | ψ f | μ | ψ i | 2 (Bi - f ) from the initial states R 2 to R 1 in Nd:YAG. Final states are Y 1 (a) and Y 3 (b). Circle, triangle, and square indicate the evaluated ratios of | ψ f | μ | ψ i | 2 in CZ, SS, and WS, respectively.

Fig. 6
Fig. 6

C Nd-dependence of branching ratio of Nd:YAG. The main peak of 1.1-μm emission (R 2 to Y 3) and of 1.3-μm emission (R 2 to X 1) have alternate dependences on C Nd. Circle, triangle, and square indicate the evaluated branching ratios of CZ, SS, and WS, respectively.

Fig. 7
Fig. 7

The estimated variation of σif m of Nd:YAG at 1.064-μm (a) and 1.319-μm (b). Circle, triangle, and square indicate σ em / σ em 0 of CZ, SS, and WS, respectively.

Tables (1)

Tables Icon

Table 1 The Accuracy of Evaluations in This Work

Equations (11)

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

σ ( ν ) = h ν c B g ( ν ) ,
B i f = 8 π 3 3 h 2 λ | ψ f | μ λ | ψ i | 2 ,
V C = V 0 + V 1 ε + V 2 ε 2 + ,
V i f = | ψ i | V 0 | ψ i ψ f | V 0 | ψ f | ,
Δ ν i f = 9 2 π 3 c ν 2 h 2 ρ 2 v 10 | ψ f | V 1 | ψ i | 2 ( 2 π k Θ h ) 7 0 Θ T x 6 e x ( e x 1 ) 2 d x ,
g i f ( ν ) = Δ ν i f 2 π 1 ( Δ ν i f / 2 ) 2 + ( ν ν i f ) 2 ,
I i f ( ν ) = η n 2 ( ν ) ν 4 Δ ν i f B i f ( Δ ν i f / 2 ) 2 + ( ν ν i f ) 2 ,
I j k ( ν ) = i j f k η f i n 2 ( ν ) ν 4 Δ ν i f B i f ( Δ ν i f / 2 ) 2 + ( ν ν i f ) 2 ,
b i f = f i B i f / i j , f k f i B i f .
σ i f m = 2 π Δ ν i f h ν i f c B i f .
σ em ( λ , C Nd ) = [ 1 A ( λ ) C Nd ] σ em 0 ( λ ) ,

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