Abstract

We successfully used CdSe/ZnS quantum dots (QDs) as a dopant within a polymethylmethacrylate (PMMA) matrix. This doped material was used in the fabrication of a microstructured polymer optical fiber whose photoluminescence was characterized. A detailed analysis of the emission properties of the QDs as a function of temperature is presented, with the temperature dependence of this emission broken into components to show contributions from the thermo-optic effect of the PMMA and the temperature-dependence of the bandgap of the QDs.

© 2010 Optical Society of America

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References

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  1. A. Argryos, “Microstructured polymer optical fibres,” J. Lightwave Technol. 27, 1571–1579 (2009).
    [Crossref]
  2. H. C. Y. Yu, A. Argyros, G. Barton, M. A. van Eijkelenborg, C. Barbe, K. Finnie, L. Kong, F. Ladoucer, and S. McNiven, “Quantum dot and nanoparticle doped microstructured polymer optical fibre,” Opt. Express 15, 9989–9994 (2007).
    [Crossref] [PubMed]
  3. H. C. Y. Yu, A. Argyros, S. G. Leon-Saval, A. Fuerbach, G. W. Barton, and A. Efimov, “Emission properties of quantum dots in PMMA,” Opt. Express 17, 21344–21349 (2009).
    [Crossref] [PubMed]
  4. G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
    [Crossref]
  5. P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
    [Crossref]
  6. M. T. Crisp and N. A. Kotov, “Preparation of nanoparticle coatings on surfaces of complex geometry,” Nano. Lett. 3, 173–177 (2003).
    [Crossref]
  7. G. de Bastida, F. J. Arregui, J. Goicoechea, and I. R. Matias, “Quantum dots-based optical fibre temperature sensors fabricated by layer-by-layer,” IEEE Sensors J. 6, 1378–1379 (2006).
    [Crossref]
  8. N. A. Issa, “High numerical aperture in multimode microstrctured optical fibers,” Appl. Opt. 43, 6191–6197 (2004).
    [Crossref] [PubMed]
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    [Crossref]
  10. N. G. Harbach, “Fiber Bragg gratings in polymer optical fiber,” Doctoral Thesis No 4021 (Ecole Polytechnique Federale de Lausanne, 2008).
  11. N. Tanio, “Structural relaxation and refractive index of low-loss poly(methyl methacrylate) glass,” Polym. J. 34, 466–470(2002).
  12. Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer 47, 4893–4896 (2006).
    [Crossref]
  13. J. M. Cariou, J. Dugas, L. Martin, and P. Michel, “Refractive-index variations with temperature of PMMA and polycarbonate,” Polym. J. 25, 334–336 (1986).
  14. O. Sahlen, “Optical bistability in thin-film CdSe interference filters,” J. Opt. Soc. Am. B 5, 82–85 (1988).
    [Crossref]
  15. U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
    [PubMed]

2009 (2)

2007 (1)

2006 (3)

P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
[Crossref]

G. de Bastida, F. J. Arregui, J. Goicoechea, and I. R. Matias, “Quantum dots-based optical fibre temperature sensors fabricated by layer-by-layer,” IEEE Sensors J. 6, 1378–1379 (2006).
[Crossref]

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer 47, 4893–4896 (2006).
[Crossref]

2005 (1)

D. Valerini, A. Creti, M. Lomascolo, L. Manna, R. Cingolani, and M. Anni, “Temperature dependence of the photoluminescence properties of colloidal CdSe/ZnS core/shell quantum dots embedded in a polystyrene matrix,” Phys. Rev. B 71, 235409 (2005).
[Crossref]

2004 (1)

2003 (2)

M. T. Crisp and N. A. Kotov, “Preparation of nanoparticle coatings on surfaces of complex geometry,” Nano. Lett. 3, 173–177 (2003).
[Crossref]

G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
[Crossref]

2002 (1)

N. Tanio, “Structural relaxation and refractive index of low-loss poly(methyl methacrylate) glass,” Polym. J. 34, 466–470(2002).

1988 (1)

1986 (1)

J. M. Cariou, J. Dugas, L. Martin, and P. Michel, “Refractive-index variations with temperature of PMMA and polycarbonate,” Polym. J. 25, 334–336 (1986).

Anni, M.

D. Valerini, A. Creti, M. Lomascolo, L. Manna, R. Cingolani, and M. Anni, “Temperature dependence of the photoluminescence properties of colloidal CdSe/ZnS core/shell quantum dots embedded in a polystyrene matrix,” Phys. Rev. B 71, 235409 (2005).
[Crossref]

Argryos, A.

Argyros, A.

Arregui, F. J.

G. de Bastida, F. J. Arregui, J. Goicoechea, and I. R. Matias, “Quantum dots-based optical fibre temperature sensors fabricated by layer-by-layer,” IEEE Sensors J. 6, 1378–1379 (2006).
[Crossref]

Barbe, C.

Barton, G.

Barton, G. W.

Bawendi, M. G.

G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
[Crossref]

Benrashid, R.

P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
[Crossref]

Blachnik, R.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Caldas, P.

P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
[Crossref]

Cariou, J. M.

J. M. Cariou, J. Dugas, L. Martin, and P. Michel, “Refractive-index variations with temperature of PMMA and polycarbonate,” Polym. J. 25, 334–336 (1986).

Chu, J.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Cingolani, R.

D. Valerini, A. Creti, M. Lomascolo, L. Manna, R. Cingolani, and M. Anni, “Temperature dependence of the photoluminescence properties of colloidal CdSe/ZnS core/shell quantum dots embedded in a polystyrene matrix,” Phys. Rev. B 71, 235409 (2005).
[Crossref]

Creti, A.

D. Valerini, A. Creti, M. Lomascolo, L. Manna, R. Cingolani, and M. Anni, “Temperature dependence of the photoluminescence properties of colloidal CdSe/ZnS core/shell quantum dots embedded in a polystyrene matrix,” Phys. Rev. B 71, 235409 (2005).
[Crossref]

Crisp, M. T.

M. T. Crisp and N. A. Kotov, “Preparation of nanoparticle coatings on surfaces of complex geometry,” Nano. Lett. 3, 173–177 (2003).
[Crossref]

de Bastida, G.

G. de Bastida, F. J. Arregui, J. Goicoechea, and I. R. Matias, “Quantum dots-based optical fibre temperature sensors fabricated by layer-by-layer,” IEEE Sensors J. 6, 1378–1379 (2006).
[Crossref]

Dugas, J.

J. M. Cariou, J. Dugas, L. Martin, and P. Michel, “Refractive-index variations with temperature of PMMA and polycarbonate,” Polym. J. 25, 334–336 (1986).

Efimov, A.

Farahi, F.

P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
[Crossref]

Finnie, K.

Fuerbach, A.

Galazka, R. R.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Geurts, J.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Goicoechea, J.

G. de Bastida, F. J. Arregui, J. Goicoechea, and I. R. Matias, “Quantum dots-based optical fibre temperature sensors fabricated by layer-by-layer,” IEEE Sensors J. 6, 1378–1379 (2006).
[Crossref]

Gutowski, J.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Harbach, N. G.

N. G. Harbach, “Fiber Bragg gratings in polymer optical fiber,” Doctoral Thesis No 4021 (Ecole Polytechnique Federale de Lausanne, 2008).

Hofmann, D.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Honerlage, B.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Issa, N. A.

Jorge, P. A. S.

P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
[Crossref]

Kong, L.

Kossut, J.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Kotov, N. A.

M. T. Crisp and N. A. Kotov, “Preparation of nanoparticle coatings on surfaces of complex geometry,” Nano. Lett. 3, 173–177 (2003).
[Crossref]

Ladoucer, F.

Leon-Saval, S. G.

Levy, R.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Lin, P.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer 47, 4893–4896 (2006).
[Crossref]

Lomascolo, M.

D. Valerini, A. Creti, M. Lomascolo, L. Manna, R. Cingolani, and M. Anni, “Temperature dependence of the photoluminescence properties of colloidal CdSe/ZnS core/shell quantum dots embedded in a polystyrene matrix,” Phys. Rev. B 71, 235409 (2005).
[Crossref]

Manna, L.

D. Valerini, A. Creti, M. Lomascolo, L. Manna, R. Cingolani, and M. Anni, “Temperature dependence of the photoluminescence properties of colloidal CdSe/ZnS core/shell quantum dots embedded in a polystyrene matrix,” Phys. Rev. B 71, 235409 (2005).
[Crossref]

Martin, L.

J. M. Cariou, J. Dugas, L. Martin, and P. Michel, “Refractive-index variations with temperature of PMMA and polycarbonate,” Polym. J. 25, 334–336 (1986).

Matias, I. R.

G. de Bastida, F. J. Arregui, J. Goicoechea, and I. R. Matias, “Quantum dots-based optical fibre temperature sensors fabricated by layer-by-layer,” IEEE Sensors J. 6, 1378–1379 (2006).
[Crossref]

Mayeh, M.

P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
[Crossref]

McNiven, S.

Michel, P.

J. M. Cariou, J. Dugas, L. Martin, and P. Michel, “Refractive-index variations with temperature of PMMA and polycarbonate,” Polym. J. 25, 334–336 (1986).

Michler, P.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Neukirch, U.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Nocera, D. G.

G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
[Crossref]

Rossler, U.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Rudzinski, C. M.

G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
[Crossref]

Sahlen, O.

Santos, J. L.

P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
[Crossref]

Story, T.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Strauch, D.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Sun, F.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer 47, 4893–4896 (2006).
[Crossref]

Sundar, V. C.

G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
[Crossref]

Tanio, N.

N. Tanio, “Structural relaxation and refractive index of low-loss poly(methyl methacrylate) glass,” Polym. J. 34, 466–470(2002).

Valerini, D.

D. Valerini, A. Creti, M. Lomascolo, L. Manna, R. Cingolani, and M. Anni, “Temperature dependence of the photoluminescence properties of colloidal CdSe/ZnS core/shell quantum dots embedded in a polystyrene matrix,” Phys. Rev. B 71, 235409 (2005).
[Crossref]

van Eijkelenborg, M. A.

Waag, A.

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

Walker, G. W.

G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
[Crossref]

Wun, A. W.

G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
[Crossref]

Yu, H. C. Y.

Zhang, Z.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer 47, 4893–4896 (2006).
[Crossref]

Zhao, P.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer 47, 4893–4896 (2006).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. W. Walker, V. C. Sundar, C. M. Rudzinski, A. W. Wun, M. G. Bawendi, and D. G. Nocera, “Quantum-dot optical temperature probes,” Appl. Phys. Lett. 83, 3555–3557 (2003).
[Crossref]

IEEE Sensors J. (1)

G. de Bastida, F. J. Arregui, J. Goicoechea, and I. R. Matias, “Quantum dots-based optical fibre temperature sensors fabricated by layer-by-layer,” IEEE Sensors J. 6, 1378–1379 (2006).
[Crossref]

J. Lightwave Technol. (1)

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

Meas. Sci. Technol. (1)

P. A. S. Jorge, M. Mayeh, R. Benrashid, P. Caldas, J. L. Santos, and F. Farahi, “Quantum dots as self-referenced optical fibre temperature probes for luminescent chemical sensors,” Meas. Sci. Technol. 17, 1032–1038 (2006).
[Crossref]

Nano. Lett. (1)

M. T. Crisp and N. A. Kotov, “Preparation of nanoparticle coatings on surfaces of complex geometry,” Nano. Lett. 3, 173–177 (2003).
[Crossref]

Opt. Express (2)

Phys. Rev. B (1)

D. Valerini, A. Creti, M. Lomascolo, L. Manna, R. Cingolani, and M. Anni, “Temperature dependence of the photoluminescence properties of colloidal CdSe/ZnS core/shell quantum dots embedded in a polystyrene matrix,” Phys. Rev. B 71, 235409 (2005).
[Crossref]

Polym. J. (2)

N. Tanio, “Structural relaxation and refractive index of low-loss poly(methyl methacrylate) glass,” Polym. J. 34, 466–470(2002).

J. M. Cariou, J. Dugas, L. Martin, and P. Michel, “Refractive-index variations with temperature of PMMA and polycarbonate,” Polym. J. 25, 334–336 (1986).

Polymer (1)

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer 47, 4893–4896 (2006).
[Crossref]

Other (2)

N. G. Harbach, “Fiber Bragg gratings in polymer optical fiber,” Doctoral Thesis No 4021 (Ecole Polytechnique Federale de Lausanne, 2008).

U. Rossler, R. Blachnik, J. Chu, R. R. Galazka, J. Geurts, J. Gutowski, B. Honerlage, D. Hofmann, J. Kossut, R. Levy, P. Michler, U. Neukirch, T. Story, D. Strauch, and A. Waag, II–VI and I–VII Compounds; Semimagnetic Compounds (Springer-Verlag, 1999).
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

Fabricated rod with a diameter 5 mm and 7 cm in length (left). Fabricated mPOF with 0.2   wt.% . 520 nm QDs embedded in the core. The cracks are due to cleaving and are only present on the end face (right).

Fig. 2
Fig. 2

Experimental setup used to characterize the doped fiber emission.

Fig. 3
Fig. 3

Unannealed doped fiber subjected to a series of heating and cooling cycles. First heating (squares), first cooling (circle), and the “equilibrium” situation reached after two cycles of heating and cooling (crosses).

Fig. 4
Fig. 4

Normalized photoluminescence at 23 ° C and 60 ° C of the first heating cycle and at 31 ° C after “equilibrium” behavior had been established. The peak at 514 nm is residual light from the pump laser.

Equations (5)

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

λ T = 0.08 nm / K .
λ T = λ E g T + λ ϕ QD T + λ n PMMA n PMMA T + λ QDS T ,
E g ( T ) = E g 0 α T 2 ( T + β ) ,
λ E g T = α h c T ( T + 2 β ) [ E g 0 ( T + β ) α T 2 ] 2 = 0.057 ± 0.006 nm / K ,
λ n PMMA n PMMA T = 0.23 ± 0.07 nm / K .

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