Abstract

We report optically pumped lasing action at the attractive wavelength of 650 nm in the common organic dye 1-amino-2-methylanthraquinone (Disperse Orange 11). The dye was incorporated into poly(methyl methacrylate) rods, and amplified spontaneous emission was studied under second-harmonic Nd:YAG laser excitation in a transverse pumping configuration. Gain and conversion efficiency were found to be comparable with those for other laser dyes. Dye photodegradation was found to be superior and reversible.

© 2002 Optical Society of America

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  1. A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
    [CrossRef]
  2. F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
    [CrossRef]
  3. M. D. Rahn, T. A. King, A. A. Gorman, and I. Hamblett, “Photostability enhancement of Pyrromethene 567 and Perylene Orange in oxygen-free liquid and solid dye lasers,” Appl. Opt. 36, 5862–5871 (1997).
    [CrossRef] [PubMed]
  4. A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
    [CrossRef]
  5. S. Popov, “Dye photodestruction in a solid-state dye laser with a polymeric gain medium,” Appl. Opt. 37, 6449–6455 (1998).
    [CrossRef]
  6. K. M. Dyumaev, A. A. Manenkov, A. P. Maslyukov, G. A. Matyushin, V. S. Nechitailo, and A. M. Prokhorov, “Dyes in modified polymers: problems of photostability and conversion efficiency at high intensities,” J. Opt. Soc. Am. B 9, 143–151 (1992).
    [CrossRef]
  7. A. V. Deshpande and E. B. Namdas, “Correlation between lasing and photophysical performance of dyes in polymethylmethacrylate,” J. Lumin. 91, 25–31 (2000).
    [CrossRef]
  8. R. Duchowicz, L. B. Scaffardi, A. Costela, I. Garcia-Moreno, R. Sastre, and A. U. Acuña, “Photothermal characterization and stability analysis of polymeric dye lasers,” Appl. Opt. 39, 4959–4963 (2000).
  9. G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye-doped polymer laser,” J. Photochem. Photobiol. A 125, 93–98 (1999).
    [CrossRef]
  10. G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 1 dye-doped polymer laser,” J. Lumin. 90, 1–5 (2000).
    [CrossRef]
  11. G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 490 dye-doped polymer laser,” Chem. Phys. Lett. 324, 25–30 (2000).
    [CrossRef]
  12. K. H. Drexhage, “Structure and properties of laser dyes,” in Topics in Applied Physics, Dye Lasers, F. P. Schäfer, ed. (Springer-Verlag, Berlin, 1990) pp. 171, 176.
  13. K. Yee, T. Tou, and S. Ng, “Hot-press molded poly(methyl methacrylate) matrix for solid-state dye lasers,” Appl. Opt. 37, 6381–6385 (1998).
    [CrossRef]
  14. A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
    [CrossRef]
  15. C. V. Shank, A. Dienes, and W. T. Silfvast, “Single pass gain of Exciplex 4-MU and Rhodamine 6G dye laser amplifiers,” Appl. Phys. Lett. 17, 307–309 (1970).
    [CrossRef]

2000

A. V. Deshpande and E. B. Namdas, “Correlation between lasing and photophysical performance of dyes in polymethylmethacrylate,” J. Lumin. 91, 25–31 (2000).
[CrossRef]

R. Duchowicz, L. B. Scaffardi, A. Costela, I. Garcia-Moreno, R. Sastre, and A. U. Acuña, “Photothermal characterization and stability analysis of polymeric dye lasers,” Appl. Opt. 39, 4959–4963 (2000).

G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 1 dye-doped polymer laser,” J. Lumin. 90, 1–5 (2000).
[CrossRef]

G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 490 dye-doped polymer laser,” Chem. Phys. Lett. 324, 25–30 (2000).
[CrossRef]

1999

G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye-doped polymer laser,” J. Photochem. Photobiol. A 125, 93–98 (1999).
[CrossRef]

1998

1997

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

M. D. Rahn, T. A. King, A. A. Gorman, and I. Hamblett, “Photostability enhancement of Pyrromethene 567 and Perylene Orange in oxygen-free liquid and solid dye lasers,” Appl. Opt. 36, 5862–5871 (1997).
[CrossRef] [PubMed]

1996

A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
[CrossRef]

1995

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
[CrossRef]

1992

1970

C. V. Shank, A. Dienes, and W. T. Silfvast, “Single pass gain of Exciplex 4-MU and Rhodamine 6G dye laser amplifiers,” Appl. Phys. Lett. 17, 307–309 (1970).
[CrossRef]

Acuña, A. U.

Amat-Guerri, F.

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
[CrossRef]

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
[CrossRef]

Barroso, J.

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
[CrossRef]

Carrascoso, M.

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

Chen, K.

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

Costela, A.

R. Duchowicz, L. B. Scaffardi, A. Costela, I. Garcia-Moreno, R. Sastre, and A. U. Acuña, “Photothermal characterization and stability analysis of polymeric dye lasers,” Appl. Opt. 39, 4959–4963 (2000).

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
[CrossRef]

F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
[CrossRef]

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

Deshpande, A. V.

A. V. Deshpande and E. B. Namdas, “Correlation between lasing and photophysical performance of dyes in polymethylmethacrylate,” J. Lumin. 91, 25–31 (2000).
[CrossRef]

Dienes, A.

C. V. Shank, A. Dienes, and W. T. Silfvast, “Single pass gain of Exciplex 4-MU and Rhodamine 6G dye laser amplifiers,” Appl. Phys. Lett. 17, 307–309 (1970).
[CrossRef]

Duchowicz, R.

R. Duchowicz, L. B. Scaffardi, A. Costela, I. Garcia-Moreno, R. Sastre, and A. U. Acuña, “Photothermal characterization and stability analysis of polymeric dye lasers,” Appl. Opt. 39, 4959–4963 (2000).

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

Dyumaev, K. M.

Figuera, J. M.

A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
[CrossRef]

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
[CrossRef]

Florido, F.

F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
[CrossRef]

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

Garcia-Moreno, I.

R. Duchowicz, L. B. Scaffardi, A. Costela, I. Garcia-Moreno, R. Sastre, and A. U. Acuña, “Photothermal characterization and stability analysis of polymeric dye lasers,” Appl. Opt. 39, 4959–4963 (2000).

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
[CrossRef]

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
[CrossRef]

Gorman, A. A.

Hamblett, I.

King, T. A.

Manenkov, A. A.

Maslyukov, A. P.

Matyushin, G. A.

Namdas, E. B.

A. V. Deshpande and E. B. Namdas, “Correlation between lasing and photophysical performance of dyes in polymethylmethacrylate,” J. Lumin. 91, 25–31 (2000).
[CrossRef]

Nechitailo, V. S.

Ng, S.

Popov, S.

Prokhorov, A. M.

Rahn, M. D.

Ramalingam, A.

G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 1 dye-doped polymer laser,” J. Lumin. 90, 1–5 (2000).
[CrossRef]

G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 490 dye-doped polymer laser,” Chem. Phys. Lett. 324, 25–30 (2000).
[CrossRef]

G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye-doped polymer laser,” J. Photochem. Photobiol. A 125, 93–98 (1999).
[CrossRef]

Sastre, R.

R. Duchowicz, L. B. Scaffardi, A. Costela, I. Garcia-Moreno, R. Sastre, and A. U. Acuña, “Photothermal characterization and stability analysis of polymeric dye lasers,” Appl. Opt. 39, 4959–4963 (2000).

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
[CrossRef]

F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
[CrossRef]

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

Scaffardi, L. B.

Shank, C. V.

C. V. Shank, A. Dienes, and W. T. Silfvast, “Single pass gain of Exciplex 4-MU and Rhodamine 6G dye laser amplifiers,” Appl. Phys. Lett. 17, 307–309 (1970).
[CrossRef]

Silfvast, W. T.

C. V. Shank, A. Dienes, and W. T. Silfvast, “Single pass gain of Exciplex 4-MU and Rhodamine 6G dye laser amplifiers,” Appl. Phys. Lett. 17, 307–309 (1970).
[CrossRef]

Somasundaram, G.

G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 490 dye-doped polymer laser,” Chem. Phys. Lett. 324, 25–30 (2000).
[CrossRef]

G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 1 dye-doped polymer laser,” J. Lumin. 90, 1–5 (2000).
[CrossRef]

G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye-doped polymer laser,” J. Photochem. Photobiol. A 125, 93–98 (1999).
[CrossRef]

Su, J.

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

Tian, H.

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

Tou, T.

Yee, K.

Appl. Opt.

Appl. Phys. B

A. Costela, F. Florido, I. Garcia-Moreno, R. Duchowicz, F. Amat-Guerri, J. M. Figuera, and R. Sastre, “Solid-state dye lasers based on copolymers of 2-hydroxyethyl methacrylate and methyl methacrylate doped with Rhodamine 6G,” Appl. Phys. B 60, 383–389 (1995).
[CrossRef]

Appl. Phys. Lett.

C. V. Shank, A. Dienes, and W. T. Silfvast, “Single pass gain of Exciplex 4-MU and Rhodamine 6G dye laser amplifiers,” Appl. Phys. Lett. 17, 307–309 (1970).
[CrossRef]

Chem. Phys. Lett.

A. Costela, I. Garcia-Moreno, H. Tian, J. Su, K. Chen, F. Amat-Guerri, M. Carrascoso, J. Barroso, and R. Sastre, “Internal photostabilization of polymeric solid-state dye lasers based on trichromophoric Rhodamine 6G molecules,” Chem. Phys. Lett. 277, 392–398 (1997).
[CrossRef]

G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 490 dye-doped polymer laser,” Chem. Phys. Lett. 324, 25–30 (2000).
[CrossRef]

J. Lumin.

A. V. Deshpande and E. B. Namdas, “Correlation between lasing and photophysical performance of dyes in polymethylmethacrylate,” J. Lumin. 91, 25–31 (2000).
[CrossRef]

G. Somasundaram and A. Ramalingam, “Gain studies of Courmarin 1 dye-doped polymer laser,” J. Lumin. 90, 1–5 (2000).
[CrossRef]

J. Opt. Soc. Am. B

J. Photochem. Photobiol. A

G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye-doped polymer laser,” J. Photochem. Photobiol. A 125, 93–98 (1999).
[CrossRef]

Opt. Commun.

F. Amat-Guerri, A. Costela, J. M. Figuera, F. Florido, I. Garcia-Moreno, and R. Sastre, “Laser action from a Rhodamine 640-doped copolymer of 2-hydroxyethyl methacrylate and methyl methacrylate,” Opt. Commun. 114, 442–446 (1995).
[CrossRef]

A. Costela, I. Garcia-Moreno, J. M. Figuera, F. Amat-Guerri, J. Barroso, and R. Sastre, “Solid-state dye laser based on Coumarin 540A-doped polymeric matrices,” Opt. Commun. 130, 44–50 (1996).
[CrossRef]

Other

K. H. Drexhage, “Structure and properties of laser dyes,” in Topics in Applied Physics, Dye Lasers, F. P. Schäfer, ed. (Springer-Verlag, Berlin, 1990) pp. 171, 176.

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Figures (6)

Fig. 1
Fig. 1

(a) Absorption spectrum of DO11-doped PMMA, (b) Fluorescence spectrum of DO11-doped PMMA when pumped with 532 nm. Inset, molecular diagram of DO11.

Fig. 2
Fig. 2

Transition of DO11 fluorescence to complete ASE dominance centered at 649 nm with increasing 532-nm pump power. Inset, corresponding fluorescence and ASE intensity versus 532-nm pump power through ASE threshold.

Fig. 3
Fig. 3

DO11-doped PMMA conversion efficiencies for 3, 6, 9-g/l dye concentrations displayed as ASE power versus 532-nm pump power.

Fig. 4
Fig. 4

Calculated gain versus 532-nm pump peak power for DO11-doped PMMA.

Fig. 5
Fig. 5

Photodegradation of DO11-doped PMMA ASE intensity as a function of time. (a) First degradation run, sample area not previously degraded; (b) third degradation run, twice previously degraded and recovered sample area. Excitation source is continuously on 10-Hz, 0.2-mJ/pulse, 35-ps, 532-nm pump radiation.

Fig. 6
Fig. 6

Two successive photodegradation and recovery cycles of a single DO11-doped PMMA sample area. (a) First degradation, (b) corresponding first recovery, (c) second degradation, (d) second recovery. Excitation source is 10-Hz, 0.2-mJ/pulse, 35-ps, 532-nm pump radiation continuously on for degradation runs and intermittent for recovery runs.

Equations (2)

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

G=(2/L)ln(IL/IL/2-1),
I=P1exp(-t/τ1)+P2[1-exp(-t/τ2)]+I0,

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