Abstract

The processes of energy transfer and diffusion of photons emitted by Nd3+ ions embedded into a glass sample were investigated. The luminescence resolved in space allowed the observation of the photons’ spatial distribution. In this paper, we propose a fuzzy mathematical model that permits carrying out calculations based on the neighborhood luminescence intensity of the excitation spot laser. This proposed model differs from other well-known ones in the literature because it shows clearly the luminescence intensity profile on the sample surface.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  26. N. O. Dantas, Qu Fanyao, A. F. G. Monte, R. S. Silva, and P. C. Morais, “Optical properties of IV–VI quantum dots embedded in glass: size-effects,” J. Non-Cryst. Solids 352, 3525–3529 (2006).
    [CrossRef]
  27. N. O. Dantas, A. F. G. Monte, Qu Fanyao, R. S. Silva, and P. C. Morais, “Energy transfer in PbS quantum dots assemblies measured by means of spatially resolved photoluminescence,” Appl. Surf. Sci. 238, 209–212 (2004).
    [CrossRef]
  28. N. S. Pereira, A. F. G. Monte, A. Reis, P. C. Morais, and M. J. A. Sales, “Luminescence and energy transfer from açai oil in polystyrene matrix,” Opt. Mater. 32, 1134–1138 (2010).
    [CrossRef]

2010 (4)

D. E. Zelmon, J. M. Northridge, J. J. Lee, K. M. Currin, and D. Perlov, “Optical properties of Nd-doped rare-earth vanadates,” Appl. Opt. 49, 4973–4978 (2010).
[CrossRef]

V. M. Martins, D. N. Messias, N. O. Dantas, and A. M. Neto, “Concentration dependent fluorescence quantum efficiency of neodymium doped phosphate glass matrix,” J. Lumin. 130, 2491–2494 (2010).
[CrossRef]

F. A. M. Marques, A. F. G. Monte, E. O. Serqueira, P. C. Morais, and N. O. Dantas, “Enhanced spatial energy transfer in Er-doped silica glasses,” Opt. Mater. 32, 1248–1250 (2010).
[CrossRef]

N. S. Pereira, A. F. G. Monte, A. Reis, P. C. Morais, and M. J. A. Sales, “Luminescence and energy transfer from açai oil in polystyrene matrix,” Opt. Mater. 32, 1134–1138 (2010).
[CrossRef]

2009 (1)

R. Balda, R. I. Merino, J. I. Peña, V. M. Orera, and J. Fernándes, “Laser spectroscopy of Nd3+ ions in glasses with the 0.8CaSiO3−0.2Ca3(PO4)2 eutectic composition,” Opt. Mater. 31, 1319–1322 (2009).
[CrossRef]

2007 (2)

S. S. Badu, P. Badu, C. K. Jayasankar, A. S. Joshi, A. Speghini, and M. Bettinelli, “Laser transition characteristics of Nd3+-doped fluorophosphate laser glasses,” J. Non-Cryst. Solids 353, 1402–1406 (2007).
[CrossRef]

M. Jayasimhadri, L. R. Moorthy, R. V. S. S. N. Ravikumar, and A. S. Joshi, “An investigation of the optical properties of Nd3+ ions in alkali tellurofluorophosphate glasses,” Opt. Mater. 29, 1321–1326 (2007).
[CrossRef]

2006 (3)

E. O. Serqueira, N. O. Dantas, P. C. Morais, and E. O. Serqueira, “Mean free path for excitation energy migration in Nd3+-doped glasses as a function of concentration,” J. Appl. Phys. 99, 036105 (2006).
[CrossRef]

E. O. Serqueira, N. O. Dantas, and P. C. Morais, “Spatial energy transfer in Nd3+-doped glasses as a function of concentration,” J. Non-Cryst. Solids 352, 3642–3646 (2006).
[CrossRef]

N. O. Dantas, Qu Fanyao, A. F. G. Monte, R. S. Silva, and P. C. Morais, “Optical properties of IV–VI quantum dots embedded in glass: size-effects,” J. Non-Cryst. Solids 352, 3525–3529 (2006).
[CrossRef]

2005 (1)

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Methodology to determine the evolution of asymptomatic HIV population using fuzzy set theory,” Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13, 39–58 (2005).
[CrossRef]

2004 (3)

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

N. O. Dantas, A. F. G. Monte, Qu Fanyao, R. S. Silva, and P. C. Morais, “Energy transfer in PbS quantum dots assemblies measured by means of spatially resolved photoluminescence,” Appl. Surf. Sci. 238, 209–212 (2004).
[CrossRef]

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Fuzzy modeling in asymptomatic HIV virus infected population,” Bull. Math. Biol. 66, 1597–1620 (2004).
[CrossRef]

2003 (2)

L. C. Barros, R. C. Bassanezi, and M. B. Leite, “The epidemiological models SI with fuzzy parameter of transmission.,” Comput. Math. Appl. 45, 1619–1628 (2003).
[CrossRef]

N. Ortega, L. C. Barros, and E. Massad, “Fuzzy gradual rules in epidemiology,” Kybernetes 32, 460–477 (2003).
[CrossRef]

1998 (1)

V. Krivan and G. Colombo, “A non-stochastic approach for modeling uncertainty in population dynamics,” Bull. Math. Biol. 60 (1998).
[CrossRef]

1997 (2)

A. F. G. Monte, J. M. R. Cruz, and P. C. Morais, “An experimental design for microluminescence,” Rev. Sci. Instrum. 68, 3890–3892 (1997).
[CrossRef]

J. C. Schotland, “Continuous-wave diffusion imaging,” J. Opt. Soc. Am. A 14, 275–279 (1997).
[CrossRef]

1992 (1)

1989 (1)

1986 (1)

B. C. Wilson and M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
[CrossRef]

1965 (1)

L. A. Zadeh, Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Badu, P.

S. S. Badu, P. Badu, C. K. Jayasankar, A. S. Joshi, A. Speghini, and M. Bettinelli, “Laser transition characteristics of Nd3+-doped fluorophosphate laser glasses,” J. Non-Cryst. Solids 353, 1402–1406 (2007).
[CrossRef]

Badu, S. S.

S. S. Badu, P. Badu, C. K. Jayasankar, A. S. Joshi, A. Speghini, and M. Bettinelli, “Laser transition characteristics of Nd3+-doped fluorophosphate laser glasses,” J. Non-Cryst. Solids 353, 1402–1406 (2007).
[CrossRef]

Balda, R.

R. Balda, R. I. Merino, J. I. Peña, V. M. Orera, and J. Fernándes, “Laser spectroscopy of Nd3+ ions in glasses with the 0.8CaSiO3−0.2Ca3(PO4)2 eutectic composition,” Opt. Mater. 31, 1319–1322 (2009).
[CrossRef]

Barros, L. C.

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Methodology to determine the evolution of asymptomatic HIV population using fuzzy set theory,” Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13, 39–58 (2005).
[CrossRef]

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Fuzzy modeling in asymptomatic HIV virus infected population,” Bull. Math. Biol. 66, 1597–1620 (2004).
[CrossRef]

N. Ortega, L. C. Barros, and E. Massad, “Fuzzy gradual rules in epidemiology,” Kybernetes 32, 460–477 (2003).
[CrossRef]

L. C. Barros, R. C. Bassanezi, and M. B. Leite, “The epidemiological models SI with fuzzy parameter of transmission.,” Comput. Math. Appl. 45, 1619–1628 (2003).
[CrossRef]

L. C. Barros and R. C. Bassanezi, Tópicos de Lógica Fuzzy e Biomatemática (State University of Campinas/Institute of Mathematics, Statistics and Computational Sciences, 2006) (in Portuguese).

Bassanezi, R. C.

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Methodology to determine the evolution of asymptomatic HIV population using fuzzy set theory,” Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13, 39–58 (2005).
[CrossRef]

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Fuzzy modeling in asymptomatic HIV virus infected population,” Bull. Math. Biol. 66, 1597–1620 (2004).
[CrossRef]

L. C. Barros, R. C. Bassanezi, and M. B. Leite, “The epidemiological models SI with fuzzy parameter of transmission.,” Comput. Math. Appl. 45, 1619–1628 (2003).
[CrossRef]

L. C. Barros and R. C. Bassanezi, Tópicos de Lógica Fuzzy e Biomatemática (State University of Campinas/Institute of Mathematics, Statistics and Computational Sciences, 2006) (in Portuguese).

Bettinelli, M.

S. S. Badu, P. Badu, C. K. Jayasankar, A. S. Joshi, A. Speghini, and M. Bettinelli, “Laser transition characteristics of Nd3+-doped fluorophosphate laser glasses,” J. Non-Cryst. Solids 353, 1402–1406 (2007).
[CrossRef]

Colombo, G.

V. Krivan and G. Colombo, “A non-stochastic approach for modeling uncertainty in population dynamics,” Bull. Math. Biol. 60 (1998).
[CrossRef]

Cruz, J. M. R.

A. F. G. Monte, J. M. R. Cruz, and P. C. Morais, “An experimental design for microluminescence,” Rev. Sci. Instrum. 68, 3890–3892 (1997).
[CrossRef]

Currin, K. M.

Dantas, N. O.

V. M. Martins, D. N. Messias, N. O. Dantas, and A. M. Neto, “Concentration dependent fluorescence quantum efficiency of neodymium doped phosphate glass matrix,” J. Lumin. 130, 2491–2494 (2010).
[CrossRef]

F. A. M. Marques, A. F. G. Monte, E. O. Serqueira, P. C. Morais, and N. O. Dantas, “Enhanced spatial energy transfer in Er-doped silica glasses,” Opt. Mater. 32, 1248–1250 (2010).
[CrossRef]

N. O. Dantas, Qu Fanyao, A. F. G. Monte, R. S. Silva, and P. C. Morais, “Optical properties of IV–VI quantum dots embedded in glass: size-effects,” J. Non-Cryst. Solids 352, 3525–3529 (2006).
[CrossRef]

E. O. Serqueira, N. O. Dantas, and P. C. Morais, “Spatial energy transfer in Nd3+-doped glasses as a function of concentration,” J. Non-Cryst. Solids 352, 3642–3646 (2006).
[CrossRef]

E. O. Serqueira, N. O. Dantas, P. C. Morais, and E. O. Serqueira, “Mean free path for excitation energy migration in Nd3+-doped glasses as a function of concentration,” J. Appl. Phys. 99, 036105 (2006).
[CrossRef]

N. O. Dantas, A. F. G. Monte, Qu Fanyao, R. S. Silva, and P. C. Morais, “Energy transfer in PbS quantum dots assemblies measured by means of spatially resolved photoluminescence,” Appl. Surf. Sci. 238, 209–212 (2004).
[CrossRef]

Ehrt, D.

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

Fanyao, Qu

N. O. Dantas, Qu Fanyao, A. F. G. Monte, R. S. Silva, and P. C. Morais, “Optical properties of IV–VI quantum dots embedded in glass: size-effects,” J. Non-Cryst. Solids 352, 3525–3529 (2006).
[CrossRef]

N. O. Dantas, A. F. G. Monte, Qu Fanyao, R. S. Silva, and P. C. Morais, “Energy transfer in PbS quantum dots assemblies measured by means of spatially resolved photoluminescence,” Appl. Surf. Sci. 238, 209–212 (2004).
[CrossRef]

Fernándes, J.

R. Balda, R. I. Merino, J. I. Peña, V. M. Orera, and J. Fernándes, “Laser spectroscopy of Nd3+ ions in glasses with the 0.8CaSiO3−0.2Ca3(PO4)2 eutectic composition,” Opt. Mater. 31, 1319–1322 (2009).
[CrossRef]

Ferreira, D. P. L.

D. P. L. Ferreira, “Sistema p-fuzzy Aplicado á Equações Diferenciais Parciais,” Master’s thesis (Federal University of Uberlândia, 2011) (in Portuguese).

Gomide, F.

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Methodology to determine the evolution of asymptomatic HIV population using fuzzy set theory,” Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13, 39–58 (2005).
[CrossRef]

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Fuzzy modeling in asymptomatic HIV virus infected population,” Bull. Math. Biol. 66, 1597–1620 (2004).
[CrossRef]

W. Pedrycz and F. Gomide, An Introduction to Fuzzy Sets: Analysis and Design, (Massachusetts Institute of Technology, 1998).

Heald, M. A.

M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation (Saunders College, 1995).

Hein, J.

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

Ishimaru, A.

Jafelice, R. M.

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Methodology to determine the evolution of asymptomatic HIV population using fuzzy set theory,” Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13, 39–58 (2005).
[CrossRef]

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Fuzzy modeling in asymptomatic HIV virus infected population,” Bull. Math. Biol. 66, 1597–1620 (2004).
[CrossRef]

Jayasankar, C. K.

S. S. Badu, P. Badu, C. K. Jayasankar, A. S. Joshi, A. Speghini, and M. Bettinelli, “Laser transition characteristics of Nd3+-doped fluorophosphate laser glasses,” J. Non-Cryst. Solids 353, 1402–1406 (2007).
[CrossRef]

Jayasimhadri, M.

M. Jayasimhadri, L. R. Moorthy, R. V. S. S. N. Ravikumar, and A. S. Joshi, “An investigation of the optical properties of Nd3+ ions in alkali tellurofluorophosphate glasses,” Opt. Mater. 29, 1321–1326 (2007).
[CrossRef]

Joshi, A. S.

M. Jayasimhadri, L. R. Moorthy, R. V. S. S. N. Ravikumar, and A. S. Joshi, “An investigation of the optical properties of Nd3+ ions in alkali tellurofluorophosphate glasses,” Opt. Mater. 29, 1321–1326 (2007).
[CrossRef]

S. S. Badu, P. Badu, C. K. Jayasankar, A. S. Joshi, A. Speghini, and M. Bettinelli, “Laser transition characteristics of Nd3+-doped fluorophosphate laser glasses,” J. Non-Cryst. Solids 353, 1402–1406 (2007).
[CrossRef]

Krivan, V.

V. Krivan and G. Colombo, “A non-stochastic approach for modeling uncertainty in population dynamics,” Bull. Math. Biol. 60 (1998).
[CrossRef]

Lallier, E.

Lee, J. J.

Leite, M. B.

L. C. Barros, R. C. Bassanezi, and M. B. Leite, “The epidemiological models SI with fuzzy parameter of transmission.,” Comput. Math. Appl. 45, 1619–1628 (2003).
[CrossRef]

Marion, J. B.

M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation (Saunders College, 1995).

Marques, F. A. M.

F. A. M. Marques, A. F. G. Monte, E. O. Serqueira, P. C. Morais, and N. O. Dantas, “Enhanced spatial energy transfer in Er-doped silica glasses,” Opt. Mater. 32, 1248–1250 (2010).
[CrossRef]

Martins, V. M.

V. M. Martins, D. N. Messias, N. O. Dantas, and A. M. Neto, “Concentration dependent fluorescence quantum efficiency of neodymium doped phosphate glass matrix,” J. Lumin. 130, 2491–2494 (2010).
[CrossRef]

Massad, E.

N. Ortega, L. C. Barros, and E. Massad, “Fuzzy gradual rules in epidemiology,” Kybernetes 32, 460–477 (2003).
[CrossRef]

Merino, R. I.

R. Balda, R. I. Merino, J. I. Peña, V. M. Orera, and J. Fernándes, “Laser spectroscopy of Nd3+ ions in glasses with the 0.8CaSiO3−0.2Ca3(PO4)2 eutectic composition,” Opt. Mater. 31, 1319–1322 (2009).
[CrossRef]

Messias, D. N.

V. M. Martins, D. N. Messias, N. O. Dantas, and A. M. Neto, “Concentration dependent fluorescence quantum efficiency of neodymium doped phosphate glass matrix,” J. Lumin. 130, 2491–2494 (2010).
[CrossRef]

Monte, A. F. G.

F. A. M. Marques, A. F. G. Monte, E. O. Serqueira, P. C. Morais, and N. O. Dantas, “Enhanced spatial energy transfer in Er-doped silica glasses,” Opt. Mater. 32, 1248–1250 (2010).
[CrossRef]

N. S. Pereira, A. F. G. Monte, A. Reis, P. C. Morais, and M. J. A. Sales, “Luminescence and energy transfer from açai oil in polystyrene matrix,” Opt. Mater. 32, 1134–1138 (2010).
[CrossRef]

N. O. Dantas, Qu Fanyao, A. F. G. Monte, R. S. Silva, and P. C. Morais, “Optical properties of IV–VI quantum dots embedded in glass: size-effects,” J. Non-Cryst. Solids 352, 3525–3529 (2006).
[CrossRef]

N. O. Dantas, A. F. G. Monte, Qu Fanyao, R. S. Silva, and P. C. Morais, “Energy transfer in PbS quantum dots assemblies measured by means of spatially resolved photoluminescence,” Appl. Surf. Sci. 238, 209–212 (2004).
[CrossRef]

A. F. G. Monte, J. M. R. Cruz, and P. C. Morais, “An experimental design for microluminescence,” Rev. Sci. Instrum. 68, 3890–3892 (1997).
[CrossRef]

Moorthy, L. R.

M. Jayasimhadri, L. R. Moorthy, R. V. S. S. N. Ravikumar, and A. S. Joshi, “An investigation of the optical properties of Nd3+ ions in alkali tellurofluorophosphate glasses,” Opt. Mater. 29, 1321–1326 (2007).
[CrossRef]

Morais, P. C.

F. A. M. Marques, A. F. G. Monte, E. O. Serqueira, P. C. Morais, and N. O. Dantas, “Enhanced spatial energy transfer in Er-doped silica glasses,” Opt. Mater. 32, 1248–1250 (2010).
[CrossRef]

N. S. Pereira, A. F. G. Monte, A. Reis, P. C. Morais, and M. J. A. Sales, “Luminescence and energy transfer from açai oil in polystyrene matrix,” Opt. Mater. 32, 1134–1138 (2010).
[CrossRef]

N. O. Dantas, Qu Fanyao, A. F. G. Monte, R. S. Silva, and P. C. Morais, “Optical properties of IV–VI quantum dots embedded in glass: size-effects,” J. Non-Cryst. Solids 352, 3525–3529 (2006).
[CrossRef]

E. O. Serqueira, N. O. Dantas, P. C. Morais, and E. O. Serqueira, “Mean free path for excitation energy migration in Nd3+-doped glasses as a function of concentration,” J. Appl. Phys. 99, 036105 (2006).
[CrossRef]

E. O. Serqueira, N. O. Dantas, and P. C. Morais, “Spatial energy transfer in Nd3+-doped glasses as a function of concentration,” J. Non-Cryst. Solids 352, 3642–3646 (2006).
[CrossRef]

N. O. Dantas, A. F. G. Monte, Qu Fanyao, R. S. Silva, and P. C. Morais, “Energy transfer in PbS quantum dots assemblies measured by means of spatially resolved photoluminescence,” Appl. Surf. Sci. 238, 209–212 (2004).
[CrossRef]

A. F. G. Monte, J. M. R. Cruz, and P. C. Morais, “An experimental design for microluminescence,” Rev. Sci. Instrum. 68, 3890–3892 (1997).
[CrossRef]

Neto, A. M.

V. M. Martins, D. N. Messias, N. O. Dantas, and A. M. Neto, “Concentration dependent fluorescence quantum efficiency of neodymium doped phosphate glass matrix,” J. Lumin. 130, 2491–2494 (2010).
[CrossRef]

Northridge, J. M.

Orera, V. M.

R. Balda, R. I. Merino, J. I. Peña, V. M. Orera, and J. Fernándes, “Laser spectroscopy of Nd3+ ions in glasses with the 0.8CaSiO3−0.2Ca3(PO4)2 eutectic composition,” Opt. Mater. 31, 1319–1322 (2009).
[CrossRef]

Ortega, N.

N. Ortega, L. C. Barros, and E. Massad, “Fuzzy gradual rules in epidemiology,” Kybernetes 32, 460–477 (2003).
[CrossRef]

Paoloni, S.

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

Patterson, M. S.

B. C. Wilson and M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
[CrossRef]

Pedrycz, W.

W. Pedrycz and F. Gomide, An Introduction to Fuzzy Sets: Analysis and Design, (Massachusetts Institute of Technology, 1998).

Peña, J. I.

R. Balda, R. I. Merino, J. I. Peña, V. M. Orera, and J. Fernándes, “Laser spectroscopy of Nd3+ ions in glasses with the 0.8CaSiO3−0.2Ca3(PO4)2 eutectic composition,” Opt. Mater. 31, 1319–1322 (2009).
[CrossRef]

Pereira, N. S.

N. S. Pereira, A. F. G. Monte, A. Reis, P. C. Morais, and M. J. A. Sales, “Luminescence and energy transfer from açai oil in polystyrene matrix,” Opt. Mater. 32, 1134–1138 (2010).
[CrossRef]

Perlov, D.

Ravikumar, R. V. S. S. N.

M. Jayasimhadri, L. R. Moorthy, R. V. S. S. N. Ravikumar, and A. S. Joshi, “An investigation of the optical properties of Nd3+ ions in alkali tellurofluorophosphate glasses,” Opt. Mater. 29, 1321–1326 (2007).
[CrossRef]

Reis, A.

N. S. Pereira, A. F. G. Monte, A. Reis, P. C. Morais, and M. J. A. Sales, “Luminescence and energy transfer from açai oil in polystyrene matrix,” Opt. Mater. 32, 1134–1138 (2010).
[CrossRef]

Sales, M. J. A.

N. S. Pereira, A. F. G. Monte, A. Reis, P. C. Morais, and M. J. A. Sales, “Luminescence and energy transfer from açai oil in polystyrene matrix,” Opt. Mater. 32, 1134–1138 (2010).
[CrossRef]

Sauerbrey, R.

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

Schotland, J. C.

Serqueira, E. O.

F. A. M. Marques, A. F. G. Monte, E. O. Serqueira, P. C. Morais, and N. O. Dantas, “Enhanced spatial energy transfer in Er-doped silica glasses,” Opt. Mater. 32, 1248–1250 (2010).
[CrossRef]

E. O. Serqueira, N. O. Dantas, P. C. Morais, and E. O. Serqueira, “Mean free path for excitation energy migration in Nd3+-doped glasses as a function of concentration,” J. Appl. Phys. 99, 036105 (2006).
[CrossRef]

E. O. Serqueira, N. O. Dantas, P. C. Morais, and E. O. Serqueira, “Mean free path for excitation energy migration in Nd3+-doped glasses as a function of concentration,” J. Appl. Phys. 99, 036105 (2006).
[CrossRef]

E. O. Serqueira, N. O. Dantas, and P. C. Morais, “Spatial energy transfer in Nd3+-doped glasses as a function of concentration,” J. Non-Cryst. Solids 352, 3642–3646 (2006).
[CrossRef]

Silva, R. S.

N. O. Dantas, Qu Fanyao, A. F. G. Monte, R. S. Silva, and P. C. Morais, “Optical properties of IV–VI quantum dots embedded in glass: size-effects,” J. Non-Cryst. Solids 352, 3525–3529 (2006).
[CrossRef]

N. O. Dantas, A. F. G. Monte, Qu Fanyao, R. S. Silva, and P. C. Morais, “Energy transfer in PbS quantum dots assemblies measured by means of spatially resolved photoluminescence,” Appl. Surf. Sci. 238, 209–212 (2004).
[CrossRef]

Speghini, A.

S. S. Badu, P. Badu, C. K. Jayasankar, A. S. Joshi, A. Speghini, and M. Bettinelli, “Laser transition characteristics of Nd3+-doped fluorophosphate laser glasses,” J. Non-Cryst. Solids 353, 1402–1406 (2007).
[CrossRef]

Topfer, T.

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

Walther, H. G.

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

Wilson, B. C.

B. C. Wilson and M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
[CrossRef]

Wintzer, W.

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

Zadeh, L. A.

L. A. Zadeh, Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Zelmon, D. E.

Appl. Opt. (3)

Appl. Phys. B (1)

S. Paoloni, J. Hein, T. Topfer, H. G. Walther, R. Sauerbrey, D. Ehrt, and W. Wintzer, “Laser beam induced optical aberrations in phosphate and fluoride phosphate glasses,” Appl. Phys. B 78, 415–419 (2004).
[CrossRef]

Appl. Surf. Sci. (1)

N. O. Dantas, A. F. G. Monte, Qu Fanyao, R. S. Silva, and P. C. Morais, “Energy transfer in PbS quantum dots assemblies measured by means of spatially resolved photoluminescence,” Appl. Surf. Sci. 238, 209–212 (2004).
[CrossRef]

Bull. Math. Biol. (2)

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Fuzzy modeling in asymptomatic HIV virus infected population,” Bull. Math. Biol. 66, 1597–1620 (2004).
[CrossRef]

V. Krivan and G. Colombo, “A non-stochastic approach for modeling uncertainty in population dynamics,” Bull. Math. Biol. 60 (1998).
[CrossRef]

Comput. Math. Appl. (1)

L. C. Barros, R. C. Bassanezi, and M. B. Leite, “The epidemiological models SI with fuzzy parameter of transmission.,” Comput. Math. Appl. 45, 1619–1628 (2003).
[CrossRef]

Inf. Control (1)

L. A. Zadeh, Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Int. J. Uncertain. Fuzziness Knowl.-Based Syst. (1)

R. M. Jafelice, L. C. Barros, R. C. Bassanezi, and F. Gomide, “Methodology to determine the evolution of asymptomatic HIV population using fuzzy set theory,” Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13, 39–58 (2005).
[CrossRef]

J. Appl. Phys. (1)

E. O. Serqueira, N. O. Dantas, P. C. Morais, and E. O. Serqueira, “Mean free path for excitation energy migration in Nd3+-doped glasses as a function of concentration,” J. Appl. Phys. 99, 036105 (2006).
[CrossRef]

J. Lumin. (1)

V. M. Martins, D. N. Messias, N. O. Dantas, and A. M. Neto, “Concentration dependent fluorescence quantum efficiency of neodymium doped phosphate glass matrix,” J. Lumin. 130, 2491–2494 (2010).
[CrossRef]

J. Non-Cryst. Solids (3)

E. O. Serqueira, N. O. Dantas, and P. C. Morais, “Spatial energy transfer in Nd3+-doped glasses as a function of concentration,” J. Non-Cryst. Solids 352, 3642–3646 (2006).
[CrossRef]

S. S. Badu, P. Badu, C. K. Jayasankar, A. S. Joshi, A. Speghini, and M. Bettinelli, “Laser transition characteristics of Nd3+-doped fluorophosphate laser glasses,” J. Non-Cryst. Solids 353, 1402–1406 (2007).
[CrossRef]

N. O. Dantas, Qu Fanyao, A. F. G. Monte, R. S. Silva, and P. C. Morais, “Optical properties of IV–VI quantum dots embedded in glass: size-effects,” J. Non-Cryst. Solids 352, 3525–3529 (2006).
[CrossRef]

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

Kybernetes (1)

N. Ortega, L. C. Barros, and E. Massad, “Fuzzy gradual rules in epidemiology,” Kybernetes 32, 460–477 (2003).
[CrossRef]

Opt. Mater. (4)

M. Jayasimhadri, L. R. Moorthy, R. V. S. S. N. Ravikumar, and A. S. Joshi, “An investigation of the optical properties of Nd3+ ions in alkali tellurofluorophosphate glasses,” Opt. Mater. 29, 1321–1326 (2007).
[CrossRef]

R. Balda, R. I. Merino, J. I. Peña, V. M. Orera, and J. Fernándes, “Laser spectroscopy of Nd3+ ions in glasses with the 0.8CaSiO3−0.2Ca3(PO4)2 eutectic composition,” Opt. Mater. 31, 1319–1322 (2009).
[CrossRef]

F. A. M. Marques, A. F. G. Monte, E. O. Serqueira, P. C. Morais, and N. O. Dantas, “Enhanced spatial energy transfer in Er-doped silica glasses,” Opt. Mater. 32, 1248–1250 (2010).
[CrossRef]

N. S. Pereira, A. F. G. Monte, A. Reis, P. C. Morais, and M. J. A. Sales, “Luminescence and energy transfer from açai oil in polystyrene matrix,” Opt. Mater. 32, 1134–1138 (2010).
[CrossRef]

Phys. Med. Biol. (1)

B. C. Wilson and M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
[CrossRef]

Rev. Sci. Instrum. (1)

A. F. G. Monte, J. M. R. Cruz, and P. C. Morais, “An experimental design for microluminescence,” Rev. Sci. Instrum. 68, 3890–3892 (1997).
[CrossRef]

Other (5)

M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation (Saunders College, 1995).

D. P. L. Ferreira, “Sistema p-fuzzy Aplicado á Equações Diferenciais Parciais,” Master’s thesis (Federal University of Uberlândia, 2011) (in Portuguese).

L. C. Barros and R. C. Bassanezi, Tópicos de Lógica Fuzzy e Biomatemática (State University of Campinas/Institute of Mathematics, Statistics and Computational Sciences, 2006) (in Portuguese).

W. Pedrycz and F. Gomide, An Introduction to Fuzzy Sets: Analysis and Design, (Massachusetts Institute of Technology, 1998).

MATLAB reference, “Fuzzy Logic Toolbox,” http://www.mathworks.com/access/helpdesk/help/toolbox/fuzzy/index.htm .

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Figures (11)

Fig. 1.
Fig. 1.

Structure of FRBSs [16].

Fig. 2.
Fig. 2.

Schematic diagram of luminescence [21].

Fig. 3.
Fig. 3.

Luminescence curve of the transitions F 3 / 2 4 I 9 / 2 4 (emission: 880 nm; 11 , 364 cm 1 ) of Nd 3 + ions inserted in the glass matrix SNPZ.

Fig. 4.
Fig. 4.

Scheme to obtain luminescence through FBRS.

Fig. 5.
Fig. 5.

Membership functions for input variable x .

Fig. 6.
Fig. 6.

L ( x , y ) for the emission 880 nm.

Fig. 7.
Fig. 7.

Comparason of L ( x , y ) for the emission 880 nm.

Fig. 8.
Fig. 8.

Projection of L ( x , y ) for the emission 880 nm.

Fig. 9.
Fig. 9.

Projection of L ( x , y ) for the emission 1060 nm.

Fig. 10.
Fig. 10.

Projection of L ( x , y ) for the emission 1330 nm.

Fig. 11.
Fig. 11.

Luminescence as a function of potency for emissions of 880, 1060, and 1330 nm.

Tables (1)

Tables Icon

Table 1. Experimental and Fuzzy Values

Equations (4)

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

L 2 1 r r ( r n ( r ) r ) + n ( r ) = G 0 δ ( r ) ,
n ( r ) = n 0 1 r L eff exp ( r L eff ) ,
2 P x y ( x , y ) L ( x , y ) = 0 ,
y = 50 ± r 2 ( x 50 ) 2 .

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