Abstract

Site-selective time-resolved spectroscopy of Eu3+ in KPb2Cl5 has been investigated by using fluorescence line narrowing technique. A crystal field analysis and simulation of the experimental results has been performed in order to parametrize the crystal field at the Eu3+ sites. Three symmetry independent crystal field sites for the rare-earth ion in this crystal were found. A plausible argument about the crystallographic nature of these sites is given.

©2005 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Optical spectroscopic study of Eu3+ crystal field sites in Na3La9O3(BO3)8 crystal

C. Cascales, R. Balda, V. Jubera, J. P. Chaminade, and J. Fernández
Opt. Express 16(4) 2653-2662 (2008)

Infrared to visible upconversion of Nd3+ ions in KPb2Br5 low phonon crystal

Rolindes Balda, Joaquín Fernändez, Ei Ei Nyein, and Uwe Hömmerich
Opt. Express 14(9) 3993-4004 (2006)

Optical properties of KPb2Cl5 and RbPb2Cl5 single crystals in the far ultraviolet spectral region

Igor N. Ogorodnikov, Natalia S. Bastrikova, Vladimir A. Pustovarov, and Lyudmila I. Isaenko
J. Opt. Soc. Am. B 31(8) 1935-1941 (2014)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. G.L. Vossler, C.L. Brooks, and K.A. Winik, “Planar Er:Yb glass ion exchanged waveguide laser,” Electron. Lett. 31, 1162–1163 (1995).
    [Crossref]
  2. T.H. Whitley, C.A. Millar, R. Wyatt, M.C. Brierley, and D. Szebesta, “Upconversion pumped green lasing in erbium doped fluorozirconate fibre,” Electron. Lett. 27, 1785–1786 (1991).
    [Crossref]
  3. J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
    [Crossref]
  4. A. Pollack and D.B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
    [Crossref]
  5. M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).
  6. M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).
  7. M.C. Nostrand, R.H. Page, S.A. Payne, L.I. Isaenko, and A.P. Yelisseyev, “Optical properties of Dy3+-and Nd3+-doped KPb2Cl5,” J. Opt. Soc. Am. B 18, 264–276 (2001).
    [Crossref]
  8. R. Balda, M. Voda, M. Al-Saleh, and J. Fernández, “Visible luminescence in KPb2Cl5:Pr3+crystal,” J. Lumin. 97, 190–97 (2002).
    [Crossref]
  9. A. Mendioroz, J. Fernández, M. Voda, M. Al-Saleh, R. Balda, and A. J. Garcia-Adeva, “Anti-Stokes laser cooling in Yb3+-doped KPb2Cl5 crystal,” Opt. Lett. 27, 1525–1527 (2002).
    [Crossref]
  10. N.W. Jenkins, S.R. Bowman, S. O′Connor, S.K. Searles, and J. Ganem, “Spectroscopic characterization of Er-doped KPb2Cl5 laser crystal,” Opt. Mat. 22, 311–320 (2003).
    [Crossref]
  11. R. Balda, J. Fernández, A. Mendioroz, M. Voda, and M. Al-Saleh, “Infrared-to-visible upconversion processes in Pr3+/Yb3+-codoped KPb2Cl5,” Phys. Rev. B 68, 1651011–1651017 (2003).
    [Crossref]
  12. R. Balda, A. J. Garcia-Adeva, M. Voda, and J. Fernández, “Upconversion processes in Er3+-doped KPb2Cl5,” Phys. Rev. B 69, 2052031–2052038 (2004).
    [Crossref]
  13. M. Voda, M. Al-Saleh, R. Balda, J. Fernández, and G. Lobera “Crystal Growth of Rare-earth-doped Ternary Potassium Lead Chloride Single Crystals by the Bridgman Method,” Opt. Mat. 26, 359–363 (2004).
    [Crossref]
  14. K. Nitsch, M. Dusek, M. Nikl, K. Polák, and M. Rodová, “Ternary alkali lead chlorides: crystal growth, cristal structure, absorption and emission properties,” Prog. Crystal Growth and Charact. 30, 1–22 (1995).
    [Crossref]
  15. R. Balda, J. Fernández, J.L. Adam, and M.A. Arriandiaga, “Time-resolved fluorescence-line narrowing and energy transfer studies in a Eu3+-doped fluorophosphate glass,” Phys. Rev. B 54, 12076–12086 (1996).
    [Crossref]
  16. G. Blasse, A. Bril, and W.C. Nieuwpoort, “On the Eu3+ fluorescence in mixed metal oxides. Part I-The crystal structure sensitivity of the intensity ratio of electric and magnetic dipole emission,” J. Phys. Chem. Solids 27, 1587–1592 (1966).
    [Crossref]
  17. G. Blasse and A. Bril, “On the Eu3+ fluorescence in mixed metal oxides. II The 5D0-7F0 emission,” Philips Res. Repts. 21, 368–378 (1966).
  18. W.C. Nieuwpoort and G. Blasse, “Linear Crystal-Field Terms and 5D0-7F0 transition of Eu3+ ion,” Sol. State Commun. 4, 227–232 (1966).
    [Crossref]
  19. C. Görller-Walrand and K. Binnemans, “Rationalization of Crystal-Field Parametrization”, in Handbook on the Physics and Chemistry of Rare Earths, K.A. Gschneidner and L. Eyring, eds. (Elsevier Science, Amsterdam, 1996), vol.23 pp. 121–283.
    [Crossref]
  20. B.G. Wybourne, Spectroscopic Properties of Rare Earths, Wiley, New York, 1965.
  21. P. Porcher, Fortran routine GROMINET for simulation of real and complex crystal-field parameters on 4f6 and 4f8 configurations, (unpublished 1995).
  22. S.V. Myagkota, A.S. Voloshinovskii, I.V. Stefanskii, M.S. Mikhalik, and I.P. Pashuk, “Reflection and emission properties of lead-based perovskite-like crystals,” Radiation Measurements 29, 273–277 (1998).
    [Crossref]
  23. L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
    [Crossref]
  24. Cotton and Wilkinson, Advanced Inorganic Chemistry (Wiley1980).
  25. P. Porcher, M. Couto dos Santos, and O. Malta, “Relationship between phenomenological crystal field parameters and the crystal structure: The simple overlap model,” Phys. Chem. Chem. Phys. 1, 397–405 (1999).
    [Crossref]

2004 (2)

R. Balda, A. J. Garcia-Adeva, M. Voda, and J. Fernández, “Upconversion processes in Er3+-doped KPb2Cl5,” Phys. Rev. B 69, 2052031–2052038 (2004).
[Crossref]

M. Voda, M. Al-Saleh, R. Balda, J. Fernández, and G. Lobera “Crystal Growth of Rare-earth-doped Ternary Potassium Lead Chloride Single Crystals by the Bridgman Method,” Opt. Mat. 26, 359–363 (2004).
[Crossref]

2003 (2)

N.W. Jenkins, S.R. Bowman, S. O′Connor, S.K. Searles, and J. Ganem, “Spectroscopic characterization of Er-doped KPb2Cl5 laser crystal,” Opt. Mat. 22, 311–320 (2003).
[Crossref]

R. Balda, J. Fernández, A. Mendioroz, M. Voda, and M. Al-Saleh, “Infrared-to-visible upconversion processes in Pr3+/Yb3+-codoped KPb2Cl5,” Phys. Rev. B 68, 1651011–1651017 (2003).
[Crossref]

2002 (2)

2001 (2)

M.C. Nostrand, R.H. Page, S.A. Payne, L.I. Isaenko, and A.P. Yelisseyev, “Optical properties of Dy3+-and Nd3+-doped KPb2Cl5,” J. Opt. Soc. Am. B 18, 264–276 (2001).
[Crossref]

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

1999 (2)

P. Porcher, M. Couto dos Santos, and O. Malta, “Relationship between phenomenological crystal field parameters and the crystal structure: The simple overlap model,” Phys. Chem. Chem. Phys. 1, 397–405 (1999).
[Crossref]

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).

1998 (2)

S.V. Myagkota, A.S. Voloshinovskii, I.V. Stefanskii, M.S. Mikhalik, and I.P. Pashuk, “Reflection and emission properties of lead-based perovskite-like crystals,” Radiation Measurements 29, 273–277 (1998).
[Crossref]

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).

1996 (1)

R. Balda, J. Fernández, J.L. Adam, and M.A. Arriandiaga, “Time-resolved fluorescence-line narrowing and energy transfer studies in a Eu3+-doped fluorophosphate glass,” Phys. Rev. B 54, 12076–12086 (1996).
[Crossref]

1995 (3)

K. Nitsch, M. Dusek, M. Nikl, K. Polák, and M. Rodová, “Ternary alkali lead chlorides: crystal growth, cristal structure, absorption and emission properties,” Prog. Crystal Growth and Charact. 30, 1–22 (1995).
[Crossref]

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

G.L. Vossler, C.L. Brooks, and K.A. Winik, “Planar Er:Yb glass ion exchanged waveguide laser,” Electron. Lett. 31, 1162–1163 (1995).
[Crossref]

1991 (1)

T.H. Whitley, C.A. Millar, R. Wyatt, M.C. Brierley, and D. Szebesta, “Upconversion pumped green lasing in erbium doped fluorozirconate fibre,” Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

1988 (1)

A. Pollack and D.B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
[Crossref]

1966 (3)

G. Blasse, A. Bril, and W.C. Nieuwpoort, “On the Eu3+ fluorescence in mixed metal oxides. Part I-The crystal structure sensitivity of the intensity ratio of electric and magnetic dipole emission,” J. Phys. Chem. Solids 27, 1587–1592 (1966).
[Crossref]

G. Blasse and A. Bril, “On the Eu3+ fluorescence in mixed metal oxides. II The 5D0-7F0 emission,” Philips Res. Repts. 21, 368–378 (1966).

W.C. Nieuwpoort and G. Blasse, “Linear Crystal-Field Terms and 5D0-7F0 transition of Eu3+ ion,” Sol. State Commun. 4, 227–232 (1966).
[Crossref]

Adam, J.L.

R. Balda, J. Fernández, J.L. Adam, and M.A. Arriandiaga, “Time-resolved fluorescence-line narrowing and energy transfer studies in a Eu3+-doped fluorophosphate glass,” Phys. Rev. B 54, 12076–12086 (1996).
[Crossref]

Al-Saleh, M.

M. Voda, M. Al-Saleh, R. Balda, J. Fernández, and G. Lobera “Crystal Growth of Rare-earth-doped Ternary Potassium Lead Chloride Single Crystals by the Bridgman Method,” Opt. Mat. 26, 359–363 (2004).
[Crossref]

R. Balda, J. Fernández, A. Mendioroz, M. Voda, and M. Al-Saleh, “Infrared-to-visible upconversion processes in Pr3+/Yb3+-codoped KPb2Cl5,” Phys. Rev. B 68, 1651011–1651017 (2003).
[Crossref]

R. Balda, M. Voda, M. Al-Saleh, and J. Fernández, “Visible luminescence in KPb2Cl5:Pr3+crystal,” J. Lumin. 97, 190–97 (2002).
[Crossref]

A. Mendioroz, J. Fernández, M. Voda, M. Al-Saleh, R. Balda, and A. J. Garcia-Adeva, “Anti-Stokes laser cooling in Yb3+-doped KPb2Cl5 crystal,” Opt. Lett. 27, 1525–1527 (2002).
[Crossref]

Arriandiaga, M.A.

R. Balda, J. Fernández, J.L. Adam, and M.A. Arriandiaga, “Time-resolved fluorescence-line narrowing and energy transfer studies in a Eu3+-doped fluorophosphate glass,” Phys. Rev. B 54, 12076–12086 (1996).
[Crossref]

Balda, R.

R. Balda, A. J. Garcia-Adeva, M. Voda, and J. Fernández, “Upconversion processes in Er3+-doped KPb2Cl5,” Phys. Rev. B 69, 2052031–2052038 (2004).
[Crossref]

M. Voda, M. Al-Saleh, R. Balda, J. Fernández, and G. Lobera “Crystal Growth of Rare-earth-doped Ternary Potassium Lead Chloride Single Crystals by the Bridgman Method,” Opt. Mat. 26, 359–363 (2004).
[Crossref]

R. Balda, J. Fernández, A. Mendioroz, M. Voda, and M. Al-Saleh, “Infrared-to-visible upconversion processes in Pr3+/Yb3+-codoped KPb2Cl5,” Phys. Rev. B 68, 1651011–1651017 (2003).
[Crossref]

R. Balda, M. Voda, M. Al-Saleh, and J. Fernández, “Visible luminescence in KPb2Cl5:Pr3+crystal,” J. Lumin. 97, 190–97 (2002).
[Crossref]

A. Mendioroz, J. Fernández, M. Voda, M. Al-Saleh, R. Balda, and A. J. Garcia-Adeva, “Anti-Stokes laser cooling in Yb3+-doped KPb2Cl5 crystal,” Opt. Lett. 27, 1525–1527 (2002).
[Crossref]

R. Balda, J. Fernández, J.L. Adam, and M.A. Arriandiaga, “Time-resolved fluorescence-line narrowing and energy transfer studies in a Eu3+-doped fluorophosphate glass,” Phys. Rev. B 54, 12076–12086 (1996).
[Crossref]

Beguin, A.

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

Binnemans, K.

C. Görller-Walrand and K. Binnemans, “Rationalization of Crystal-Field Parametrization”, in Handbook on the Physics and Chemistry of Rare Earths, K.A. Gschneidner and L. Eyring, eds. (Elsevier Science, Amsterdam, 1996), vol.23 pp. 121–283.
[Crossref]

Blasse, G.

G. Blasse, A. Bril, and W.C. Nieuwpoort, “On the Eu3+ fluorescence in mixed metal oxides. Part I-The crystal structure sensitivity of the intensity ratio of electric and magnetic dipole emission,” J. Phys. Chem. Solids 27, 1587–1592 (1966).
[Crossref]

W.C. Nieuwpoort and G. Blasse, “Linear Crystal-Field Terms and 5D0-7F0 transition of Eu3+ ion,” Sol. State Commun. 4, 227–232 (1966).
[Crossref]

G. Blasse and A. Bril, “On the Eu3+ fluorescence in mixed metal oxides. II The 5D0-7F0 emission,” Philips Res. Repts. 21, 368–378 (1966).

Bowman, S.R.

N.W. Jenkins, S.R. Bowman, S. O′Connor, S.K. Searles, and J. Ganem, “Spectroscopic characterization of Er-doped KPb2Cl5 laser crystal,” Opt. Mat. 22, 311–320 (2003).
[Crossref]

Brierley, M.C.

T.H. Whitley, C.A. Millar, R. Wyatt, M.C. Brierley, and D. Szebesta, “Upconversion pumped green lasing in erbium doped fluorozirconate fibre,” Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Bril, A.

G. Blasse and A. Bril, “On the Eu3+ fluorescence in mixed metal oxides. II The 5D0-7F0 emission,” Philips Res. Repts. 21, 368–378 (1966).

G. Blasse, A. Bril, and W.C. Nieuwpoort, “On the Eu3+ fluorescence in mixed metal oxides. Part I-The crystal structure sensitivity of the intensity ratio of electric and magnetic dipole emission,” J. Phys. Chem. Solids 27, 1587–1592 (1966).
[Crossref]

Brocklesby, W.S.

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

Brooks, C.L.

G.L. Vossler, C.L. Brooks, and K.A. Winik, “Planar Er:Yb glass ion exchanged waveguide laser,” Electron. Lett. 31, 1162–1163 (1995).
[Crossref]

Camy, P.

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

Chang, D.B.

A. Pollack and D.B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
[Crossref]

Cotton,

Cotton and Wilkinson, Advanced Inorganic Chemistry (Wiley1980).

Couto dos Santos, M.

P. Porcher, M. Couto dos Santos, and O. Malta, “Relationship between phenomenological crystal field parameters and the crystal structure: The simple overlap model,” Phys. Chem. Chem. Phys. 1, 397–405 (1999).
[Crossref]

Dusek, M.

K. Nitsch, M. Dusek, M. Nikl, K. Polák, and M. Rodová, “Ternary alkali lead chlorides: crystal growth, cristal structure, absorption and emission properties,” Prog. Crystal Growth and Charact. 30, 1–22 (1995).
[Crossref]

Fernández, J.

M. Voda, M. Al-Saleh, R. Balda, J. Fernández, and G. Lobera “Crystal Growth of Rare-earth-doped Ternary Potassium Lead Chloride Single Crystals by the Bridgman Method,” Opt. Mat. 26, 359–363 (2004).
[Crossref]

R. Balda, A. J. Garcia-Adeva, M. Voda, and J. Fernández, “Upconversion processes in Er3+-doped KPb2Cl5,” Phys. Rev. B 69, 2052031–2052038 (2004).
[Crossref]

R. Balda, J. Fernández, A. Mendioroz, M. Voda, and M. Al-Saleh, “Infrared-to-visible upconversion processes in Pr3+/Yb3+-codoped KPb2Cl5,” Phys. Rev. B 68, 1651011–1651017 (2003).
[Crossref]

R. Balda, M. Voda, M. Al-Saleh, and J. Fernández, “Visible luminescence in KPb2Cl5:Pr3+crystal,” J. Lumin. 97, 190–97 (2002).
[Crossref]

A. Mendioroz, J. Fernández, M. Voda, M. Al-Saleh, R. Balda, and A. J. Garcia-Adeva, “Anti-Stokes laser cooling in Yb3+-doped KPb2Cl5 crystal,” Opt. Lett. 27, 1525–1527 (2002).
[Crossref]

R. Balda, J. Fernández, J.L. Adam, and M.A. Arriandiaga, “Time-resolved fluorescence-line narrowing and energy transfer studies in a Eu3+-doped fluorophosphate glass,” Phys. Rev. B 54, 12076–12086 (1996).
[Crossref]

Ganem, J.

N.W. Jenkins, S.R. Bowman, S. O′Connor, S.K. Searles, and J. Ganem, “Spectroscopic characterization of Er-doped KPb2Cl5 laser crystal,” Opt. Mat. 22, 311–320 (2003).
[Crossref]

Garcia-Adeva, A. J.

R. Balda, A. J. Garcia-Adeva, M. Voda, and J. Fernández, “Upconversion processes in Er3+-doped KPb2Cl5,” Phys. Rev. B 69, 2052031–2052038 (2004).
[Crossref]

A. Mendioroz, J. Fernández, M. Voda, M. Al-Saleh, R. Balda, and A. J. Garcia-Adeva, “Anti-Stokes laser cooling in Yb3+-doped KPb2Cl5 crystal,” Opt. Lett. 27, 1525–1527 (2002).
[Crossref]

Görller-Walrand, C.

C. Görller-Walrand and K. Binnemans, “Rationalization of Crystal-Field Parametrization”, in Handbook on the Physics and Chemistry of Rare Earths, K.A. Gschneidner and L. Eyring, eds. (Elsevier Science, Amsterdam, 1996), vol.23 pp. 121–283.
[Crossref]

Hempstead, M.

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

Isaenko, L.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Isaenko, L.I.

M.C. Nostrand, R.H. Page, S.A. Payne, L.I. Isaenko, and A.P. Yelisseyev, “Optical properties of Dy3+-and Nd3+-doped KPb2Cl5,” J. Opt. Soc. Am. B 18, 264–276 (2001).
[Crossref]

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).

Ivanova, S.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Jenkins, N.W.

N.W. Jenkins, S.R. Bowman, S. O′Connor, S.K. Searles, and J. Ganem, “Spectroscopic characterization of Er-doped KPb2Cl5 laser crystal,” Opt. Mat. 22, 311–320 (2003).
[Crossref]

Krupke, W.F.

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).

Lerminiaux, C.

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

Lobera, G.

M. Voda, M. Al-Saleh, R. Balda, J. Fernández, and G. Lobera “Crystal Growth of Rare-earth-doped Ternary Potassium Lead Chloride Single Crystals by the Bridgman Method,” Opt. Mat. 26, 359–363 (2004).
[Crossref]

Malta, O.

P. Porcher, M. Couto dos Santos, and O. Malta, “Relationship between phenomenological crystal field parameters and the crystal structure: The simple overlap model,” Phys. Chem. Chem. Phys. 1, 397–405 (1999).
[Crossref]

Mendioroz, A.

R. Balda, J. Fernández, A. Mendioroz, M. Voda, and M. Al-Saleh, “Infrared-to-visible upconversion processes in Pr3+/Yb3+-codoped KPb2Cl5,” Phys. Rev. B 68, 1651011–1651017 (2003).
[Crossref]

A. Mendioroz, J. Fernández, M. Voda, M. Al-Saleh, R. Balda, and A. J. Garcia-Adeva, “Anti-Stokes laser cooling in Yb3+-doped KPb2Cl5 crystal,” Opt. Lett. 27, 1525–1527 (2002).
[Crossref]

Merkulov, A.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Mikhalik, M.S.

S.V. Myagkota, A.S. Voloshinovskii, I.V. Stefanskii, M.S. Mikhalik, and I.P. Pashuk, “Reflection and emission properties of lead-based perovskite-like crystals,” Radiation Measurements 29, 273–277 (1998).
[Crossref]

Millar, C.A.

T.H. Whitley, C.A. Millar, R. Wyatt, M.C. Brierley, and D. Szebesta, “Upconversion pumped green lasing in erbium doped fluorozirconate fibre,” Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Myagkota, S.V.

S.V. Myagkota, A.S. Voloshinovskii, I.V. Stefanskii, M.S. Mikhalik, and I.P. Pashuk, “Reflection and emission properties of lead-based perovskite-like crystals,” Radiation Measurements 29, 273–277 (1998).
[Crossref]

Nieuwpoort, W.C.

G. Blasse, A. Bril, and W.C. Nieuwpoort, “On the Eu3+ fluorescence in mixed metal oxides. Part I-The crystal structure sensitivity of the intensity ratio of electric and magnetic dipole emission,” J. Phys. Chem. Solids 27, 1587–1592 (1966).
[Crossref]

W.C. Nieuwpoort and G. Blasse, “Linear Crystal-Field Terms and 5D0-7F0 transition of Eu3+ ion,” Sol. State Commun. 4, 227–232 (1966).
[Crossref]

Nikl, M.

K. Nitsch, M. Dusek, M. Nikl, K. Polák, and M. Rodová, “Ternary alkali lead chlorides: crystal growth, cristal structure, absorption and emission properties,” Prog. Crystal Growth and Charact. 30, 1–22 (1995).
[Crossref]

Nitsch, K.

K. Nitsch, M. Dusek, M. Nikl, K. Polák, and M. Rodová, “Ternary alkali lead chlorides: crystal growth, cristal structure, absorption and emission properties,” Prog. Crystal Growth and Charact. 30, 1–22 (1995).
[Crossref]

Nostrand, M.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Nostrand, M.C.

M.C. Nostrand, R.H. Page, S.A. Payne, L.I. Isaenko, and A.P. Yelisseyev, “Optical properties of Dy3+-and Nd3+-doped KPb2Cl5,” J. Opt. Soc. Am. B 18, 264–276 (2001).
[Crossref]

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).

Nouth, S.

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

O'Connor, S.

N.W. Jenkins, S.R. Bowman, S. O′Connor, S.K. Searles, and J. Ganem, “Spectroscopic characterization of Er-doped KPb2Cl5 laser crystal,” Opt. Mat. 22, 311–320 (2003).
[Crossref]

Page, R.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Page, R.H.

M.C. Nostrand, R.H. Page, S.A. Payne, L.I. Isaenko, and A.P. Yelisseyev, “Optical properties of Dy3+-and Nd3+-doped KPb2Cl5,” J. Opt. Soc. Am. B 18, 264–276 (2001).
[Crossref]

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).

Pashuk, I.P.

S.V. Myagkota, A.S. Voloshinovskii, I.V. Stefanskii, M.S. Mikhalik, and I.P. Pashuk, “Reflection and emission properties of lead-based perovskite-like crystals,” Radiation Measurements 29, 273–277 (1998).
[Crossref]

Payne, S.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Payne, S.A.

M.C. Nostrand, R.H. Page, S.A. Payne, L.I. Isaenko, and A.P. Yelisseyev, “Optical properties of Dy3+-and Nd3+-doped KPb2Cl5,” J. Opt. Soc. Am. B 18, 264–276 (2001).
[Crossref]

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).

Polák, K.

K. Nitsch, M. Dusek, M. Nikl, K. Polák, and M. Rodová, “Ternary alkali lead chlorides: crystal growth, cristal structure, absorption and emission properties,” Prog. Crystal Growth and Charact. 30, 1–22 (1995).
[Crossref]

Pollack, A.

A. Pollack and D.B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
[Crossref]

Porcher, P.

P. Porcher, M. Couto dos Santos, and O. Malta, “Relationship between phenomenological crystal field parameters and the crystal structure: The simple overlap model,” Phys. Chem. Chem. Phys. 1, 397–405 (1999).
[Crossref]

P. Porcher, Fortran routine GROMINET for simulation of real and complex crystal-field parameters on 4f6 and 4f8 configurations, (unpublished 1995).

Rodová, M.

K. Nitsch, M. Dusek, M. Nikl, K. Polák, and M. Rodová, “Ternary alkali lead chlorides: crystal growth, cristal structure, absorption and emission properties,” Prog. Crystal Growth and Charact. 30, 1–22 (1995).
[Crossref]

Roman, J.E.

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

Schunemann, P. G.

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).

Searles, S.K.

N.W. Jenkins, S.R. Bowman, S. O′Connor, S.K. Searles, and J. Ganem, “Spectroscopic characterization of Er-doped KPb2Cl5 laser crystal,” Opt. Mat. 22, 311–320 (2003).
[Crossref]

Stefanskii, I.V.

S.V. Myagkota, A.S. Voloshinovskii, I.V. Stefanskii, M.S. Mikhalik, and I.P. Pashuk, “Reflection and emission properties of lead-based perovskite-like crystals,” Radiation Measurements 29, 273–277 (1998).
[Crossref]

Szebesta, D.

T.H. Whitley, C.A. Millar, R. Wyatt, M.C. Brierley, and D. Szebesta, “Upconversion pumped green lasing in erbium doped fluorozirconate fibre,” Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Tkachuk, A.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Vatnik, S.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Voda, M.

R. Balda, A. J. Garcia-Adeva, M. Voda, and J. Fernández, “Upconversion processes in Er3+-doped KPb2Cl5,” Phys. Rev. B 69, 2052031–2052038 (2004).
[Crossref]

M. Voda, M. Al-Saleh, R. Balda, J. Fernández, and G. Lobera “Crystal Growth of Rare-earth-doped Ternary Potassium Lead Chloride Single Crystals by the Bridgman Method,” Opt. Mat. 26, 359–363 (2004).
[Crossref]

R. Balda, J. Fernández, A. Mendioroz, M. Voda, and M. Al-Saleh, “Infrared-to-visible upconversion processes in Pr3+/Yb3+-codoped KPb2Cl5,” Phys. Rev. B 68, 1651011–1651017 (2003).
[Crossref]

R. Balda, M. Voda, M. Al-Saleh, and J. Fernández, “Visible luminescence in KPb2Cl5:Pr3+crystal,” J. Lumin. 97, 190–97 (2002).
[Crossref]

A. Mendioroz, J. Fernández, M. Voda, M. Al-Saleh, R. Balda, and A. J. Garcia-Adeva, “Anti-Stokes laser cooling in Yb3+-doped KPb2Cl5 crystal,” Opt. Lett. 27, 1525–1527 (2002).
[Crossref]

Voloshinovskii, A.S.

S.V. Myagkota, A.S. Voloshinovskii, I.V. Stefanskii, M.S. Mikhalik, and I.P. Pashuk, “Reflection and emission properties of lead-based perovskite-like crystals,” Radiation Measurements 29, 273–277 (1998).
[Crossref]

Vossler, G.L.

G.L. Vossler, C.L. Brooks, and K.A. Winik, “Planar Er:Yb glass ion exchanged waveguide laser,” Electron. Lett. 31, 1162–1163 (1995).
[Crossref]

Whitley, T.H.

T.H. Whitley, C.A. Millar, R. Wyatt, M.C. Brierley, and D. Szebesta, “Upconversion pumped green lasing in erbium doped fluorozirconate fibre,” Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Wilkinson,

Cotton and Wilkinson, Advanced Inorganic Chemistry (Wiley1980).

Wilkinson, J. S.

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

Winik, K.A.

G.L. Vossler, C.L. Brooks, and K.A. Winik, “Planar Er:Yb glass ion exchanged waveguide laser,” Electron. Lett. 31, 1162–1163 (1995).
[Crossref]

Wyatt, R.

T.H. Whitley, C.A. Millar, R. Wyatt, M.C. Brierley, and D. Szebesta, “Upconversion pumped green lasing in erbium doped fluorozirconate fibre,” Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Wybourne, B.G.

B.G. Wybourne, Spectroscopic Properties of Rare Earths, Wiley, New York, 1965.

Yelisseyev, A.

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Yelisseyev, A.P.

Electron. Lett. (3)

G.L. Vossler, C.L. Brooks, and K.A. Winik, “Planar Er:Yb glass ion exchanged waveguide laser,” Electron. Lett. 31, 1162–1163 (1995).
[Crossref]

T.H. Whitley, C.A. Millar, R. Wyatt, M.C. Brierley, and D. Szebesta, “Upconversion pumped green lasing in erbium doped fluorozirconate fibre,” Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

J.E. Roman, P. Camy, M. Hempstead, W.S. Brocklesby, S. Nouth, A. Beguin, C. Lerminiaux, and J. S. Wilkinson, “Ion-exchanged Er/Yb waveguide laser at 1.5 µm pumped by laser diode,” Electron. Lett. 31, 1345–1346 (1995).
[Crossref]

J. Appl. Phys. (1)

A. Pollack and D.B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
[Crossref]

J. Lumin. (1)

R. Balda, M. Voda, M. Al-Saleh, and J. Fernández, “Visible luminescence in KPb2Cl5:Pr3+crystal,” J. Lumin. 97, 190–97 (2002).
[Crossref]

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

J. Phys. Chem. Solids (1)

G. Blasse, A. Bril, and W.C. Nieuwpoort, “On the Eu3+ fluorescence in mixed metal oxides. Part I-The crystal structure sensitivity of the intensity ratio of electric and magnetic dipole emission,” J. Phys. Chem. Solids 27, 1587–1592 (1966).
[Crossref]

Mater. Science and Engineering (1)

L. Isaenko, A. Yelisseyev, A. Tkachuk, S. Ivanova, S. Vatnik, A. Merkulov, S. Payne, R. Page, and M. Nostrand, “New laser crystal based on KPb2Cl5 for IR region,” Mater. Science and Engineering B81188–190 (2001).
[Crossref]

Opt. Lett. (1)

Opt. Mat. (2)

N.W. Jenkins, S.R. Bowman, S. O′Connor, S.K. Searles, and J. Ganem, “Spectroscopic characterization of Er-doped KPb2Cl5 laser crystal,” Opt. Mat. 22, 311–320 (2003).
[Crossref]

M. Voda, M. Al-Saleh, R. Balda, J. Fernández, and G. Lobera “Crystal Growth of Rare-earth-doped Ternary Potassium Lead Chloride Single Crystals by the Bridgman Method,” Opt. Mat. 26, 359–363 (2004).
[Crossref]

OSA TOPS (2)

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Spectroscopic data for infrared transitions in CaGa2S4:Dy3+ and KPb2Cl5: Dy3+,” OSA TOPS 19, 524–528 (1998).

M.C. Nostrand, R.H. Page, S.A. Payne, W.F. Krupke, P. G. Schunemann, and L.I. Isaenko, “Room temperature CaGa2S4:Dy3+ laser action at 2.43 and 4.31 µm and KPb2Cl5: Dy3+ laser action at 2.43 µm,” OSA TOPS 26, 441–449 (1999).

Philips Res. Repts. (1)

G. Blasse and A. Bril, “On the Eu3+ fluorescence in mixed metal oxides. II The 5D0-7F0 emission,” Philips Res. Repts. 21, 368–378 (1966).

Phys. Chem. Chem. Phys. (1)

P. Porcher, M. Couto dos Santos, and O. Malta, “Relationship between phenomenological crystal field parameters and the crystal structure: The simple overlap model,” Phys. Chem. Chem. Phys. 1, 397–405 (1999).
[Crossref]

Phys. Rev. B (3)

R. Balda, J. Fernández, A. Mendioroz, M. Voda, and M. Al-Saleh, “Infrared-to-visible upconversion processes in Pr3+/Yb3+-codoped KPb2Cl5,” Phys. Rev. B 68, 1651011–1651017 (2003).
[Crossref]

R. Balda, A. J. Garcia-Adeva, M. Voda, and J. Fernández, “Upconversion processes in Er3+-doped KPb2Cl5,” Phys. Rev. B 69, 2052031–2052038 (2004).
[Crossref]

R. Balda, J. Fernández, J.L. Adam, and M.A. Arriandiaga, “Time-resolved fluorescence-line narrowing and energy transfer studies in a Eu3+-doped fluorophosphate glass,” Phys. Rev. B 54, 12076–12086 (1996).
[Crossref]

Prog. Crystal Growth and Charact. (1)

K. Nitsch, M. Dusek, M. Nikl, K. Polák, and M. Rodová, “Ternary alkali lead chlorides: crystal growth, cristal structure, absorption and emission properties,” Prog. Crystal Growth and Charact. 30, 1–22 (1995).
[Crossref]

Radiation Measurements (1)

S.V. Myagkota, A.S. Voloshinovskii, I.V. Stefanskii, M.S. Mikhalik, and I.P. Pashuk, “Reflection and emission properties of lead-based perovskite-like crystals,” Radiation Measurements 29, 273–277 (1998).
[Crossref]

Sol. State Commun. (1)

W.C. Nieuwpoort and G. Blasse, “Linear Crystal-Field Terms and 5D0-7F0 transition of Eu3+ ion,” Sol. State Commun. 4, 227–232 (1966).
[Crossref]

Other (4)

C. Görller-Walrand and K. Binnemans, “Rationalization of Crystal-Field Parametrization”, in Handbook on the Physics and Chemistry of Rare Earths, K.A. Gschneidner and L. Eyring, eds. (Elsevier Science, Amsterdam, 1996), vol.23 pp. 121–283.
[Crossref]

B.G. Wybourne, Spectroscopic Properties of Rare Earths, Wiley, New York, 1965.

P. Porcher, Fortran routine GROMINET for simulation of real and complex crystal-field parameters on 4f6 and 4f8 configurations, (unpublished 1995).

Cotton and Wilkinson, Advanced Inorganic Chemistry (Wiley1980).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. 5D0→F0, 1, 2 emissions of Eu3+ in KPb2Cl5

Download Full Size | PPT Slide | PDF

Fig. 2.
Fig. 2. 5D0→F0→6 emissions of Eu3+ in KPb2Cl5

Download Full Size | PPT Slide | PDF

Fig. 3.
Fig. 3. Observed (o) and calculated (c) energy levels for the three Eu3+ sites

Download Full Size | PPT Slide | PDF

Fig. 4.
Fig. 4. Coordination polyhedra of Pb and K in KPb2Cl5. Their site symmetries are Pb(1)=C2/Cs, K=D3/C3v, and Pb(2)~C2v. Grey, red, yellow, and blue balls represent Pb(1), K, Pb(2), and Cl atoms, respectively. Crystal data were derived from Ref. 14.

Download Full Size | PPT Slide | PDF

Tables (3)

Tables Icon

Table 1. Observed and calculated energy levels (cm-1) of observed Eu3+ optical centers in KPb2Cl5

View Table | View all tables in this article
Tables Icon

Table 2. Phenomenological crystal-field parameters (cm-1) for observed Eu3+ optical centers in KPb2Cl5

View Table | View all tables in this article
Tables Icon

Table 3. Summary of spectroscopic results and crystal field calculation and simulation

View Table | View all tables in this article

Equations (1)

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

H CF = ∑ k=2 4,6 ∑ q=0 k [ B q k ( C q k + (−1) q C −q k )+i S q k ( C q k − (−1) q C −q k )]

Metrics