Abstract

The refractive index changes which can be induced in the Nd:YVO4, Nd:GdVO4 and Nd:KGW high gain laser crystals, when their Nd3+ laser active ions are pumped from their ground- to excited- energy levels, have been carefully measured and characterized. By using two complementary optical techniques based on pump-probe interferometry and transient diffraction grating, the electronic and thermal contributions to the observed refractive index variations have been accurately determined and successfully exploited to derive various parameters such as polarizability changes, thermo-optic coefficients and thermal diffusivities.

© 2010 OSA

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  37. A. H. Krumpel, Ph. Boutinaud, E. vander Kolk, and P. Dorenbos, “Charge transfer transitions in the transition metal oxides ABO4:Ln3+ (A = La, Gd, Y, Lu, Sc; B = V, Nb, Ta; Ln = lanthanides,” J. Lumin. (to appear).
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    [CrossRef]
  39. A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
    [CrossRef]

2008 (4)

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16(17), 12658–12663 (2008).
[PubMed]

R. Moncorgé, O. N. Ereymekin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008).
[CrossRef]

J. Didierjean, E. Herault, F. Balembois, and P. Georges, “Thermal conductivity measurements of laser crystals by infrared thermography. Application to Nd:doped crystals,” Opt. Express 16(12), 8995–9010 (2008).
[CrossRef] [PubMed]

A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
[CrossRef]

2007 (4)

V. V. Filippov, N. V. Kuleshov, and I. T. Bodnar, “Negative thermo-optical coefficients and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Red luminescence induced by intervalence charge transfer in Pr3+ doped compounds,” J. Lumin. 122–123, 430–433 (2007).
[CrossRef]

E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007).
[CrossRef]

S. M. Lima and T. Catunda, “Discrimination of resonant and nonresonant contributions to the nonlinear refraction spectroscopy of ion-doped solids,” Phys. Rev. Lett. 99(24), 243902 (2007).
[CrossRef]

2006 (4)

J. Margerie, R. Moncorgé, and P. Nagtegaele, “Spectroscopic investigation of the variations in refractive index of a Nd:YAG laser crystal: experiments and crystal-field calculations,” Phys. Rev. B 74(23), 235108 (2006).
[CrossRef]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312(5775), 895–897 (2006).
[CrossRef] [PubMed]

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73(2), 218–224 (2006).
[CrossRef]

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[CrossRef] [PubMed]

2005 (2)

A. Minassian, B. A. Thompson, G. Smith, and M. J. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005).
[CrossRef]

S. Biswal, S. P. O’Connor, and S. R. Bowman, “Thermo-optical parameters measured in ytterbium-doped potassium gadolinium tungstate,” Appl. Opt. 44(15), 3093–3097 (2005).
[CrossRef] [PubMed]

2004 (4)

2003 (2)

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorob’ev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
[CrossRef] [PubMed]

2002 (1)

E. Nakazawa, “The lowest 4f-to-5d and charge-transfer transitions of rare earth ions in YPO4 hosts,” J. Lumin. 100(1-4), 89–96 (2002).
[CrossRef]

2001 (1)

M. Laroche, S. Girard, J. Margerie, R. Moncorgé, M. Bettinelli, and E. Cavalli, “Experimental and theoretical investigation of the 4fn – 4fn-15d transitions in YPO4:Pr3+ and YPO4:Pr3+,Ce3+,” J. Phys. Condens. Matter 13(4), 765–776 (2001).
[CrossRef]

2000 (2)

1999 (1)

O. Guillot-Noel, B. Bellamy, B. Viana, and D. Gourier, “Correlation between rare-earth oscillator strengths and rare-earth-valence-band interactions in neodynium doped YMO4 (M=V,P,As), Y3Al5O12 and LiYF4,” Phys. Rev. B 60(3), 1668–1677 (1999).
[CrossRef]

1998 (1)

P. Sillard, A. Brignon, J. P. Huignard, and J. P. Pocholle, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34(3), 465–472 (1998).
[CrossRef]

1997 (1)

I. V. Mochalov, “Laser and nonlinear properties of the potassium gadolinium tungstate laser crystal KGd(WO4)2:Nd3+ (KGW:Nd),” Opt. Eng. 36(6), 1660–1669 (1997).
[CrossRef]

1996 (1)

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

1994 (1)

1993 (2)

A. Brignon and J. P. Huignard, “Two-wave mixing in Nd:YAG with gain saturation,” Opt. Lett. 18(19), 1639–1641 (1993).
[CrossRef] [PubMed]

T. Y. Fan, “Heat generation in Nd:YAG and Yb:YAG,” IEEE J. Quantum Electron. 29(6), 1457–1459 (1993).
[CrossRef]

1989 (1)

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index of refraction change in optically pumped solid-state laser materials”, Opt. Lett . 14, 1204–1206 (1989) + “Four-wave mixing of Nd3+ doped crystals and glasses,” Phys. Rev. B 41(13), 8593–8602 (1990).
[CrossRef] [PubMed]

1981 (1)

1967 (1)

E. P. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38(7), 2720–2725 (1967).
[CrossRef]

Abdolvand, A.

Ait-Ameur, K.

Antipov, O. L.

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16(17), 12658–12663 (2008).
[PubMed]

R. Moncorgé, O. N. Ereymekin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008).
[CrossRef]

E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007).
[CrossRef]

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[CrossRef] [PubMed]

O. N. Eremeykin, O. L. Antipov, A. Minassian, and M. J. Damzen, “Efficient continuous-wave generation in a self-organizing diode-pumped Nd:YVO4 laser with a reciprocal dynamic holographic cavity,” Opt. Lett. 29(20), 2390–2392 (2004).
[CrossRef] [PubMed]

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorob’ev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[CrossRef]

Baldwin, G. D.

E. P. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38(7), 2720–2725 (1967).
[CrossRef]

Balembois, F.

Barsi, C.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312(5775), 895–897 (2006).
[CrossRef] [PubMed]

Bellamy, B.

O. Guillot-Noel, B. Bellamy, B. Viana, and D. Gourier, “Correlation between rare-earth oscillator strengths and rare-earth-valence-band interactions in neodynium doped YMO4 (M=V,P,As), Y3Al5O12 and LiYF4,” Phys. Rev. B 60(3), 1668–1677 (1999).
[CrossRef]

Bettinelli, M.

A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Red luminescence induced by intervalence charge transfer in Pr3+ doped compounds,” J. Lumin. 122–123, 430–433 (2007).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Excited-state dynamics of Pr3+ doped YVO4 crystals,” J. Appl. Phys. 96(9), 4923–4929 (2004).
[CrossRef]

M. Laroche, S. Girard, J. Margerie, R. Moncorgé, M. Bettinelli, and E. Cavalli, “Experimental and theoretical investigation of the 4fn – 4fn-15d transitions in YPO4:Pr3+ and YPO4:Pr3+,Ce3+,” J. Phys. Condens. Matter 13(4), 765–776 (2001).
[CrossRef]

Bigelow, M. S.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73(2), 218–224 (2006).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
[CrossRef] [PubMed]

Biswal, S.

Bodnar, I. T.

V. V. Filippov, N. V. Kuleshov, and I. T. Bodnar, “Negative thermo-optical coefficients and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

Boutinaud, Ph.

A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Red luminescence induced by intervalence charge transfer in Pr3+ doped compounds,” J. Lumin. 122–123, 430–433 (2007).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Excited-state dynamics of Pr3+ doped YVO4 crystals,” J. Appl. Phys. 96(9), 4923–4929 (2004).
[CrossRef]

A. H. Krumpel, Ph. Boutinaud, E. vander Kolk, and P. Dorenbos, “Charge transfer transitions in the transition metal oxides ABO4:Ln3+ (A = La, Gd, Y, Lu, Sc; B = V, Nb, Ta; Ln = lanthanides,” J. Lumin. (to appear).

Bowman, S. R.

Boyd, R. W.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312(5775), 895–897 (2006).
[CrossRef] [PubMed]

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73(2), 218–224 (2006).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
[CrossRef] [PubMed]

Bredikhin, D. V.

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[CrossRef] [PubMed]

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorob’ev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[CrossRef]

Brignon, A.

P. Sillard, A. Brignon, J. P. Huignard, and J. P. Pocholle, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34(3), 465–472 (1998).
[CrossRef]

A. Brignon and J. P. Huignard, “Two-wave mixing in Nd:YAG with gain saturation,” Opt. Lett. 18(19), 1639–1641 (1993).
[CrossRef] [PubMed]

Catunda, T.

S. M. Lima and T. Catunda, “Discrimination of resonant and nonresonant contributions to the nonlinear refraction spectroscopy of ion-doped solids,” Phys. Rev. Lett. 99(24), 243902 (2007).
[CrossRef]

Cavalli, E.

A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Red luminescence induced by intervalence charge transfer in Pr3+ doped compounds,” J. Lumin. 122–123, 430–433 (2007).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Excited-state dynamics of Pr3+ doped YVO4 crystals,” J. Appl. Phys. 96(9), 4923–4929 (2004).
[CrossRef]

M. Laroche, S. Girard, J. Margerie, R. Moncorgé, M. Bettinelli, and E. Cavalli, “Experimental and theoretical investigation of the 4fn – 4fn-15d transitions in YPO4:Pr3+ and YPO4:Pr3+,Ce3+,” J. Phys. Condens. Matter 13(4), 765–776 (2001).
[CrossRef]

Chang, S. W.

Chang, T. Y.

Chang-Hasnain, C. J.

Chase, L. L.

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index of refraction change in optically pumped solid-state laser materials”, Opt. Lett . 14, 1204–1206 (1989) + “Four-wave mixing of Nd3+ doped crystals and glasses,” Phys. Rev. B 41(13), 8593–8602 (1990).
[CrossRef] [PubMed]

Chen, J.

Chuang, S. L.

Damzen, M. J.

A. Minassian, B. A. Thompson, G. Smith, and M. J. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005).
[CrossRef]

O. N. Eremeykin, O. L. Antipov, A. Minassian, and M. J. Damzen, “Efficient continuous-wave generation in a self-organizing diode-pumped Nd:YVO4 laser with a reciprocal dynamic holographic cavity,” Opt. Lett. 29(20), 2390–2392 (2004).
[CrossRef] [PubMed]

Danger, T.

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

Didierjean, J.

Dorenbos, P.

A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
[CrossRef]

P. Dorenbos, “The 5d level positions of the trivalent lanthanides in inorganic compounds,” J. Lumin. 91(3-4), 155–176 (2000).
[CrossRef]

A. H. Krumpel, Ph. Boutinaud, E. vander Kolk, and P. Dorenbos, “Charge transfer transitions in the transition metal oxides ABO4:Ln3+ (A = La, Gd, Y, Lu, Sc; B = V, Nb, Ta; Ln = lanthanides,” J. Lumin. (to appear).

Doualan, J. L.

R. Moncorgé, O. N. Ereymekin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008).
[CrossRef]

N. Passilly, M. Fromager, K. Ait-Ameur, R. Moncorgé, J. L. Doualan, A. Hirth, and G. Quarles, “Experimental and theoretical investigation of a rapidly varying nonlinear lensing effect observed in a Cr3+:LiSAF laser,” J. Opt. Soc. Am. B 21, 531–538 (2004).
[CrossRef]

Eremeykin, O. N.

Ereymekin, O. N.

R. Moncorgé, O. N. Ereymekin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008).
[CrossRef]

Fan, T. Y.

T. Y. Fan, “Heat generation in Nd:YAG and Yb:YAG,” IEEE J. Quantum Electron. 29(6), 1457–1459 (1993).
[CrossRef]

Filippov, V. V.

V. V. Filippov, N. V. Kuleshov, and I. T. Bodnar, “Negative thermo-optical coefficients and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

Fotiadi, A. A.

Fromager, M.

Gaylord, T. K.

Gehring, G. M.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312(5775), 895–897 (2006).
[CrossRef] [PubMed]

Georges, P.

Girard, S.

M. Laroche, S. Girard, J. Margerie, R. Moncorgé, M. Bettinelli, and E. Cavalli, “Experimental and theoretical investigation of the 4fn – 4fn-15d transitions in YPO4:Pr3+ and YPO4:Pr3+,Ce3+,” J. Phys. Condens. Matter 13(4), 765–776 (2001).
[CrossRef]

Gourier, D.

O. Guillot-Noel, B. Bellamy, B. Viana, and D. Gourier, “Correlation between rare-earth oscillator strengths and rare-earth-valence-band interactions in neodynium doped YMO4 (M=V,P,As), Y3Al5O12 and LiYF4,” Phys. Rev. B 60(3), 1668–1677 (1999).
[CrossRef]

Guillot-Noel, O.

O. Guillot-Noel, B. Bellamy, B. Viana, and D. Gourier, “Correlation between rare-earth oscillator strengths and rare-earth-valence-band interactions in neodynium doped YMO4 (M=V,P,As), Y3Al5O12 and LiYF4,” Phys. Rev. B 60(3), 1668–1677 (1999).
[CrossRef]

Herault, E.

Hirth, A.

Huber, G.

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

Huignard, J. P.

P. Sillard, A. Brignon, J. P. Huignard, and J. P. Pocholle, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34(3), 465–472 (1998).
[CrossRef]

A. Brignon and J. P. Huignard, “Two-wave mixing in Nd:YAG with gain saturation,” Opt. Lett. 18(19), 1639–1641 (1993).
[CrossRef] [PubMed]

Ivakin, E. V.

E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007).
[CrossRef]

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[CrossRef] [PubMed]

Jarabo, S.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73(2), 218–224 (2006).
[CrossRef]

Kostinski, N.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312(5775), 895–897 (2006).
[CrossRef] [PubMed]

Krumpel, A. H.

A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
[CrossRef]

A. H. Krumpel, Ph. Boutinaud, E. vander Kolk, and P. Dorenbos, “Charge transfer transitions in the transition metal oxides ABO4:Ln3+ (A = La, Gd, Y, Lu, Sc; B = V, Nb, Ta; Ln = lanthanides,” J. Lumin. (to appear).

Ku, P. C.

Kuleshov, N. V.

E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007).
[CrossRef]

V. V. Filippov, N. V. Kuleshov, and I. T. Bodnar, “Negative thermo-optical coefficients and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

A. Lagatsky, A. Abdolvand, and N. V. Kuleshov, “Passive Q-switching and self-frequency Raman conversion in a diode-pumped Yb:KGd(WO4)2 laser,” Opt. Lett. 25(9), 616–618 (2000).
[CrossRef]

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

Kuznetsov, M. S.

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorob’ev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[CrossRef]

Lagatsky, A.

Laroche, M.

M. Laroche, S. Girard, J. Margerie, R. Moncorgé, M. Bettinelli, and E. Cavalli, “Experimental and theoretical investigation of the 4fn – 4fn-15d transitions in YPO4:Pr3+ and YPO4:Pr3+,Ce3+,” J. Phys. Condens. Matter 13(4), 765–776 (2001).
[CrossRef]

Lepeshkin, N. N.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73(2), 218–224 (2006).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
[CrossRef] [PubMed]

Li, T.

Lima, S. M.

S. M. Lima and T. Catunda, “Discrimination of resonant and nonresonant contributions to the nonlinear refraction spectroscopy of ion-doped solids,” Phys. Rev. Lett. 99(24), 243902 (2007).
[CrossRef]

Mahiou, R.

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Red luminescence induced by intervalence charge transfer in Pr3+ doped compounds,” J. Lumin. 122–123, 430–433 (2007).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Excited-state dynamics of Pr3+ doped YVO4 crystals,” J. Appl. Phys. 96(9), 4923–4929 (2004).
[CrossRef]

Margerie, J.

J. Margerie, R. Moncorgé, and P. Nagtegaele, “Spectroscopic investigation of the variations in refractive index of a Nd:YAG laser crystal: experiments and crystal-field calculations,” Phys. Rev. B 74(23), 235108 (2006).
[CrossRef]

M. Laroche, S. Girard, J. Margerie, R. Moncorgé, M. Bettinelli, and E. Cavalli, “Experimental and theoretical investigation of the 4fn – 4fn-15d transitions in YPO4:Pr3+ and YPO4:Pr3+,Ce3+,” J. Phys. Condens. Matter 13(4), 765–776 (2001).
[CrossRef]

McMichael, I.

Mégret, P.

Mikhailov, V. P.

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

Minassian, A.

A. Minassian, B. A. Thompson, G. Smith, and M. J. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005).
[CrossRef]

O. N. Eremeykin, O. L. Antipov, A. Minassian, and M. J. Damzen, “Efficient continuous-wave generation in a self-organizing diode-pumped Nd:YVO4 laser with a reciprocal dynamic holographic cavity,” Opt. Lett. 29(20), 2390–2392 (2004).
[CrossRef] [PubMed]

Mochalov, I. V.

I. V. Mochalov, “Laser and nonlinear properties of the potassium gadolinium tungstate laser crystal KGd(WO4)2:Nd3+ (KGW:Nd),” Opt. Eng. 36(6), 1660–1669 (1997).
[CrossRef]

Moharam, M. G.

Moncorgé, R.

R. Moncorgé, O. N. Ereymekin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008).
[CrossRef]

J. Margerie, R. Moncorgé, and P. Nagtegaele, “Spectroscopic investigation of the variations in refractive index of a Nd:YAG laser crystal: experiments and crystal-field calculations,” Phys. Rev. B 74(23), 235108 (2006).
[CrossRef]

N. Passilly, M. Fromager, K. Ait-Ameur, R. Moncorgé, J. L. Doualan, A. Hirth, and G. Quarles, “Experimental and theoretical investigation of a rapidly varying nonlinear lensing effect observed in a Cr3+:LiSAF laser,” J. Opt. Soc. Am. B 21, 531–538 (2004).
[CrossRef]

M. Laroche, S. Girard, J. Margerie, R. Moncorgé, M. Bettinelli, and E. Cavalli, “Experimental and theoretical investigation of the 4fn – 4fn-15d transitions in YPO4:Pr3+ and YPO4:Pr3+,Ce3+,” J. Phys. Condens. Matter 13(4), 765–776 (2001).
[CrossRef]

Nagtegaele, P.

J. Margerie, R. Moncorgé, and P. Nagtegaele, “Spectroscopic investigation of the variations in refractive index of a Nd:YAG laser crystal: experiments and crystal-field calculations,” Phys. Rev. B 74(23), 235108 (2006).
[CrossRef]

Nakazawa, E.

E. Nakazawa, “The lowest 4f-to-5d and charge-transfer transitions of rare earth ions in YPO4 hosts,” J. Lumin. 100(1-4), 89–96 (2002).
[CrossRef]

O’Connor, S. P.

Palinginis, P.

Passilly, N.

Payne, S. A.

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index of refraction change in optically pumped solid-state laser materials”, Opt. Lett . 14, 1204–1206 (1989) + “Four-wave mixing of Nd3+ doped crystals and glasses,” Phys. Rev. B 41(13), 8593–8602 (1990).
[CrossRef] [PubMed]

Pocholle, J. P.

P. Sillard, A. Brignon, J. P. Huignard, and J. P. Pocholle, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34(3), 465–472 (1998).
[CrossRef]

Powell, R. C.

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index of refraction change in optically pumped solid-state laser materials”, Opt. Lett . 14, 1204–1206 (1989) + “Four-wave mixing of Nd3+ doped crystals and glasses,” Phys. Rev. B 41(13), 8593–8602 (1990).
[CrossRef] [PubMed]

Quarles, G.

Rand, S.

Riedel, E. P.

E. P. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38(7), 2720–2725 (1967).
[CrossRef]

Sandrock, T.

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

Savikin, A. P.

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[CrossRef] [PubMed]

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorob’ev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[CrossRef]

Saxena, R.

Schweinsberg, A.

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73(2), 218–224 (2006).
[CrossRef]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312(5775), 895–897 (2006).
[CrossRef] [PubMed]

Sedgwick, F.

Shcherbitsky, V. G.

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

Shinkevitch, A. S.

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

Shu, Q.

Sillard, P.

P. Sillard, A. Brignon, J. P. Huignard, and J. P. Pocholle, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34(3), 465–472 (1998).
[CrossRef]

Smith, G.

A. Minassian, B. A. Thompson, G. Smith, and M. J. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005).
[CrossRef]

Sukhadolau, A. V.

E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007).
[CrossRef]

O. L. Antipov, D. V. Bredikhin, O. N. Eremeykin, A. P. Savikin, E. V. Ivakin, and A. V. Sukhadolau, “Electronic mechanism for refractive-index changes in intensively pumped Yb:YAG laser crystals,” Opt. Lett. 31(6), 763–765 (2006).
[CrossRef] [PubMed]

Thompson, B. A.

A. Minassian, B. A. Thompson, G. Smith, and M. J. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005).
[CrossRef]

Tuller, H.

vander Kolk, E.

A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
[CrossRef]

A. H. Krumpel, Ph. Boutinaud, E. vander Kolk, and P. Dorenbos, “Charge transfer transitions in the transition metal oxides ABO4:Ln3+ (A = La, Gd, Y, Lu, Sc; B = V, Nb, Ta; Ln = lanthanides,” J. Lumin. (to appear).

Viana, B.

O. Guillot-Noel, B. Bellamy, B. Viana, and D. Gourier, “Correlation between rare-earth oscillator strengths and rare-earth-valence-band interactions in neodynium doped YMO4 (M=V,P,As), Y3Al5O12 and LiYF4,” Phys. Rev. B 60(3), 1668–1677 (1999).
[CrossRef]

Vorob’ev, V. A.

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorob’ev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[CrossRef]

Wang, H.

Wilke, G. D.

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index of refraction change in optically pumped solid-state laser materials”, Opt. Lett . 14, 1204–1206 (1989) + “Four-wave mixing of Nd3+ doped crystals and glasses,” Phys. Rev. B 41(13), 8593–8602 (1990).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (2)

E. V. Ivakin, A. V. Sukhadolau, O. L. Antipov, and N. V. Kuleshov, “Transient grating measurements of refractive-index changes in intensively pumped Yb-doped laser crystals,” Appl. Phys. B 86(2), 315–318 (2007).
[CrossRef]

V. V. Filippov, N. V. Kuleshov, and I. T. Bodnar, “Negative thermo-optical coefficients and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

Europhys. Lett. (1)

A. Schweinsberg, N. N. Lepeshkin, M. S. Bigelow, R. W. Boyd, and S. Jarabo, “Observation of superluminal and slow light propagation in erbium-doped optical fiber,” Europhys. Lett. 73(2), 218–224 (2006).
[CrossRef]

IEEE J. Quantum Electron. (3)

O. L. Antipov, O. N. Eremeykin, A. P. Savikin, V. A. Vorob’ev, D. V. Bredikhin, and M. S. Kuznetsov, “Electronic changes of refractive index in intensively pumped Nd:YAG laser crystals,” IEEE J. Quantum Electron. 39(7), 910–918 (2003).
[CrossRef]

P. Sillard, A. Brignon, J. P. Huignard, and J. P. Pocholle, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34(3), 465–472 (1998).
[CrossRef]

T. Y. Fan, “Heat generation in Nd:YAG and Yb:YAG,” IEEE J. Quantum Electron. 29(6), 1457–1459 (1993).
[CrossRef]

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

A. Minassian, B. A. Thompson, G. Smith, and M. J. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005).
[CrossRef]

J. Appl. Phys. (2)

E. P. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38(7), 2720–2725 (1967).
[CrossRef]

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Excited-state dynamics of Pr3+ doped YVO4 crystals,” J. Appl. Phys. 96(9), 4923–4929 (2004).
[CrossRef]

J. Lumin. (4)

E. Nakazawa, “The lowest 4f-to-5d and charge-transfer transitions of rare earth ions in YPO4 hosts,” J. Lumin. 100(1-4), 89–96 (2002).
[CrossRef]

P. Dorenbos, “The 5d level positions of the trivalent lanthanides in inorganic compounds,” J. Lumin. 91(3-4), 155–176 (2000).
[CrossRef]

A. H. Krumpel, Ph. Boutinaud, E. vander Kolk, and P. Dorenbos, “Charge transfer transitions in the transition metal oxides ABO4:Ln3+ (A = La, Gd, Y, Lu, Sc; B = V, Nb, Ta; Ln = lanthanides,” J. Lumin. (to appear).

Ph. Boutinaud, R. Mahiou, E. Cavalli, and M. Bettinelli, “Red luminescence induced by intervalence charge transfer in Pr3+ doped compounds,” J. Lumin. 122–123, 430–433 (2007).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Condens. Matter (1)

M. Laroche, S. Girard, J. Margerie, R. Moncorgé, M. Bettinelli, and E. Cavalli, “Experimental and theoretical investigation of the 4fn – 4fn-15d transitions in YPO4:Pr3+ and YPO4:Pr3+,Ce3+,” J. Phys. Condens. Matter 13(4), 765–776 (2001).
[CrossRef]

Mat. Sc. Eng, B (1)

A. H. Krumpel, E. vander Kolk, P. Dorenbos, Ph. Boutinaud, E. Cavalli, and M. Bettinelli, “Energy level diagram for lanthanide-doped lanthanum orthovanadate,” Mat. Sc. Eng, B 146, 114–120 (2008).
[CrossRef]

Opt. Commun. (1)

R. Moncorgé, O. N. Ereymekin, J. L. Doualan, and O. L. Antipov, “Origin of athermal refractive index changes observed in Yb3+ doped YAG and KGW,” Opt. Commun. 281(9), 2526–2530 (2008).
[CrossRef]

Opt. Eng. (1)

I. V. Mochalov, “Laser and nonlinear properties of the potassium gadolinium tungstate laser crystal KGd(WO4)2:Nd3+ (KGW:Nd),” Opt. Eng. 36(6), 1660–1669 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett (1)

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index of refraction change in optically pumped solid-state laser materials”, Opt. Lett . 14, 1204–1206 (1989) + “Four-wave mixing of Nd3+ doped crystals and glasses,” Phys. Rev. B 41(13), 8593–8602 (1990).
[CrossRef] [PubMed]

Opt. Lett. (6)

Opt. Mater. (1)

N. V. Kuleshov, A. S. Shinkevitch, V. G. Shcherbitsky, V. P. Mikhailov, T. Danger, T. Sandrock, and G. Huber, “Luminescence and time-resolved excited-state absorption measurements in Pr3+ doped La2Be2O5 and KGd(WO4)2,” Opt. Mater. 5(1-2), 111–118 (1996).
[CrossRef]

Phys. Rev. B (2)

J. Margerie, R. Moncorgé, and P. Nagtegaele, “Spectroscopic investigation of the variations in refractive index of a Nd:YAG laser crystal: experiments and crystal-field calculations,” Phys. Rev. B 74(23), 235108 (2006).
[CrossRef]

O. Guillot-Noel, B. Bellamy, B. Viana, and D. Gourier, “Correlation between rare-earth oscillator strengths and rare-earth-valence-band interactions in neodynium doped YMO4 (M=V,P,As), Y3Al5O12 and LiYF4,” Phys. Rev. B 60(3), 1668–1677 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

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[CrossRef]

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Other (4)

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Figures (4)

Fig. 1
Fig. 1

Origin of thermal loads in 4-level laser systems

Fig. 2
Fig. 2

Kinetics of the phase shift changes (a, b) and of the square root of the diffraction efficiencies (c, d) measured with the interferometric and transient grating techniques, respectively, for E / / c (a, c) and E / / a (b, d) probe beam polarisations in a 1% Nd3+ doped YVO4 crystal

Fig. 3
Fig. 3

Comparison of the total refractive index changes Δ n max ( 0 ) ¯ z normalized by the number of excited ions per cm3 obtained with each technique (left) and comparison of the ratios η e and Δ ϕ 10 Δ ϕ 10 + Δ ϕ 20 + Δ ϕ 0 between the components with the decay time equal to the emission lifetime and the amplitudes measured at time t=0 with the transient grating and the interferometric techniques, respectively (right). Vertical lines stand for error bars.

Fig. 4
Fig. 4

Up and down thermal and purely electronic contributions to the refractive index changes normalized by the number of excited ions per cm3 (left) and extracted polarizability changes at 633 nm (right) calculated with Exp. (1) in the text. Error bars are indicated by vertical lines

Tables (3)

Tables Icon

Table 1 Data and parameters used in the fitting of the interferometric transient signals with Exp. (3) in the text.

Tables Icon

Table 2 Data and parameters used in the fitting of the transient grating signals with Exp. (6) in the text.

Tables Icon

Table 3 Thermal parameters for GdVO4, YVO4 and KGW calculated with Exp. (4), Exp. (8) and Exp. (12) in the text (references to literature data appear within parentheses)

Equations (16)

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Δ n e ( t = 0 ) ¯ z = 2 π f l 2 Δ α p Δ N ( t = 0 ) ¯ z / n 0
Δ I ( t ) / 2 I 0 ¯ x , y Δ ϕ ( t ) ¯ x , y = 2 π Δ n ( t ) ¯ x , y , z ( 2 l ) / λ 0
Δ φ ( t ) ¯ x , y , z = Δ φ 10 × exp ( t / τ e ) + Δ φ 20 / ( 1 + t / τ t h i n t ) + Δ φ 0
τ t h int = ω p u m p 2 / 8 χ
Q ν 1
D ( t ) = P 1 P 0 = ( π 0 l Δ n ( t , z ) d z λ 0 ) 2 ¯ x , y = ( π Δ n ( 0 ) ¯ z l λ 0 ) 2 ¯ x , y [ η e exp ( t / τ e ) + η t h exp ( t / τ t h d i f ) ] 2
( π Δ n ( 0 ) ¯ z l λ 0 ) 2 ¯ x , y = ( π Δ n max ( 0 ) ¯ z l 2 λ 0 ) 2 ω p u m p 2 ω p u m p 2 + ( 2 ω p r o b e ) 2
τ t h d i f = Λ 2 / 4 π 2 χ
η e = Δ n e ¯ Δ n e ¯ + Δ n t h u p ¯ and Δ ϕ 10 Δ ϕ 10 + Δ ϕ 20 + Δ ϕ 0 = Δ n e ¯ Δ n t h d o w n ¯ Δ n e ¯ + Δ n t h u p ¯
Δ T ( r , z ) = E a b s ( r , z ) ρ C p d 3 r
Δ n t h u p + Δ n t h d o w n ¯ z = n T Δ T ¯ z = η h h ν p Δ N ¯ z ρ C p n T
χ t h e o = κ ρ C p
E 5d (Nd 3 + ,YPO 4 ) E 5d (Ce 3 + ,YPO 4 ) + E 5d (Nd 3 + )-E 5d (Ce 3 + ) ¯
Δ α p ( ν ¯ ) = 7.1 x10 -15 [ f e x ( ν ¯ e x Δ ν ¯ ) 2 ν ¯ 2 f g ν ¯ e x 2 ν ¯ 2 ]
Δ α p Y V O 4 Δ α p Y A G 0.43 x f Y V O 4 f Y A G
E 5d (Nd 3 + ,KGW) E 5d (Pr 3 + ,KGW) + E 5d (Nd 3 + )-E 5d (Pr 3 + ) ¯

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