Abstract

A detailed theoretical model is provided to analyze the effects of temperature on prism-based surface plasmon resonance (SPR) sensors, including temperature dependence of the metal and prism. A complete sensitivity matrix simultaneously measures variations in refractive index (RI) and temperatures using measurements at two wavelengths for the angular-interrogation mode, or at two angles of incidence for the wavelength-interrogation mode. Correction of matrix coefficients improves accuracy of the two modes. Validation is performed using a self-designed wavelength SPR system with an adjustable incident angle perform. This method provides a new way to detect the RI and may lead to the better design and fabrication of prism-based SPR sensors.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

2016 (1)

2014 (1)

F. Xiao, D. Michel, G. Li, A. Xu, and K. Alameh, “Simultaneous measurement of refractive index and temperature based on surface plasmon resonance sensors,” J. Lightwave Technol. 32(21), 4169–4173 (2014).
[Crossref]

2013 (1)

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

2012 (1)

S. Hearty, P. Leonard, and R. O’Kennedy, “Measuring antibody-antigen binding kinetics using surface plasmon resonance,” Methods Mol. Biol. 907, 411–442 (2012).
[Crossref] [PubMed]

2011 (1)

2009 (3)

M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
[Crossref] [PubMed]

N. Blow, “Proteins and proteomics: life on the surface,” Nat. Methods 6(5), 389–393 (2009).
[Crossref]

K. Lin, Y. Lu, Z. Luo, R. Zheng, P. Wang, and H. Ming, “Numerical and experimental investigation of temperature effects on the surface plasmon resonance sensor,” Chin. Phys. Lett. 7, 428–431 (2009).

2007 (2)

J. B. Fiche, A. Buhot, R. Calemczuk, and T. Livache, “Temperature effects on DNA chip experiments from surface plasmon resonance imaging: isotherms and melting curves,” Biophys. J. 92(3), 935–946 (2007).
[Crossref] [PubMed]

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

2006 (1)

2003 (2)

H.-P. Chiang, Y.-C. Wang, and P. T. Leung, “Effect of temperature on the incident angle-dependence of the sensitivity for surface plasmon resonance spectroscopy,” Thin Solid Films 425(1-2), 135–138 (2003).
[Crossref]

S. K. Ozdemir and G. Turhan-Sayan, “Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor,” J. Lightwave Technol. 21(3), 805–814 (2003).
[Crossref]

2000 (1)

H.-P. Chiang, P. T. Leung, and W. S. Tse, “Remarks on the substrate-temperature dependence of surface-enhanced raman scattering,” J. Phys. Chem. B 104(10), 2348–2350 (2000).
[Crossref]

1998 (1)

1995 (1)

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett. 66(26), 3570–3572 (1995).
[Crossref]

1994 (1)

G. Ghosh, “Temperature dispersion of refractive indexes in some silicate fiber glasses,” IEEE Photonics Technol. Lett. 6(3), 431–433 (1994).
[Crossref]

1992 (1)

1990 (1)

S. Herminghaus and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys., A Mater. Sci. Process. 51(4), 350–353 (1990).
[Crossref]

1977 (1)

R. T. Beach and R. W. Christy, “Electron-electron scattering in the intraband optical conductivity of Cu, Ag, and Au,” Phys. Rev. B Condens. Matter Mater. Phys. 16(12), 5277–5284 (1977).
[Crossref]

1976 (1)

W. E. Lawrence, “Electron-electron scattering in the low-temperature resistivity of the noble metals,” Phys. Rev. B Condens. Matter Mater. Phys. 13(12), 5316–5319 (1976).
[Crossref]

1968 (1)

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Zeitschrift Für Physik A Hadrons and Nuclei 216, 398–410 (1968).

1965 (1)

1954 (1)

T. Holstein, “Optical and infrared volume absorptivity of metals,” Phys. Rev. 96(2), 535–536 (1954).
[Crossref]

Abdulhalim, I.

Agarwal, S.

Alameh, K.

F. Xiao, D. Michel, G. Li, A. Xu, and K. Alameh, “Simultaneous measurement of refractive index and temperature based on surface plasmon resonance sensors,” J. Lightwave Technol. 32(21), 4169–4173 (2014).
[Crossref]

Beach, R. T.

R. T. Beach and R. W. Christy, “Electron-electron scattering in the intraband optical conductivity of Cu, Ag, and Au,” Phys. Rev. B Condens. Matter Mater. Phys. 16(12), 5277–5284 (1977).
[Crossref]

Blow, N.

N. Blow, “Proteins and proteomics: life on the surface,” Nat. Methods 6(5), 389–393 (2009).
[Crossref]

Buhot, A.

J. B. Fiche, A. Buhot, R. Calemczuk, and T. Livache, “Temperature effects on DNA chip experiments from surface plasmon resonance imaging: isotherms and melting curves,” Biophys. J. 92(3), 935–946 (2007).
[Crossref] [PubMed]

Calemczuk, R.

J. B. Fiche, A. Buhot, R. Calemczuk, and T. Livache, “Temperature effects on DNA chip experiments from surface plasmon resonance imaging: isotherms and melting curves,” Biophys. J. 92(3), 935–946 (2007).
[Crossref] [PubMed]

Chen, G. C. K.

Chen, L.

Chen, P.

Chen, S.

Chiang, H.-P.

H.-P. Chiang, Y.-C. Wang, and P. T. Leung, “Effect of temperature on the incident angle-dependence of the sensitivity for surface plasmon resonance spectroscopy,” Thin Solid Films 425(1-2), 135–138 (2003).
[Crossref]

H.-P. Chiang, P. T. Leung, and W. S. Tse, “Remarks on the substrate-temperature dependence of surface-enhanced raman scattering,” J. Phys. Chem. B 104(10), 2348–2350 (2000).
[Crossref]

Christy, R. W.

R. T. Beach and R. W. Christy, “Electron-electron scattering in the intraband optical conductivity of Cu, Ag, and Au,” Phys. Rev. B Condens. Matter Mater. Phys. 16(12), 5277–5284 (1977).
[Crossref]

Dou-Gou, Z.

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

Fiche, J. B.

J. B. Fiche, A. Buhot, R. Calemczuk, and T. Livache, “Temperature effects on DNA chip experiments from surface plasmon resonance imaging: isotherms and melting curves,” Biophys. J. 92(3), 935–946 (2007).
[Crossref] [PubMed]

Gao, B. Z.

Gao, H.

Ghosh, G.

G. Ghosh, “Sellmeier coefficients for the birefringence and refractive indices of ZnGeP2 nonlinear crystal at different temperatures,” Appl. Opt. 37(7), 1205–1212 (1998).
[Crossref] [PubMed]

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett. 66(26), 3570–3572 (1995).
[Crossref]

G. Ghosh, “Temperature dispersion of refractive indexes in some silicate fiber glasses,” IEEE Photonics Technol. Lett. 6(3), 431–433 (1994).
[Crossref]

Gu, D.

Gupta, B. D.

Hair, M.

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

He, J.

Hearty, S.

S. Hearty, P. Leonard, and R. O’Kennedy, “Measuring antibody-antigen binding kinetics using surface plasmon resonance,” Methods Mol. Biol. 907, 411–442 (2012).
[Crossref] [PubMed]

Herminghaus, S.

S. Herminghaus and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys., A Mater. Sci. Process. 51(4), 350–353 (1990).
[Crossref]

Ho, H. P.

Holstein, T.

T. Holstein, “Optical and infrared volume absorptivity of metals,” Phys. Rev. 96(2), 535–536 (1954).
[Crossref]

Homola, J.

Hu, Z.

Kai-Qun, L.

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

Kim, M. S.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Lai-Ming, W.

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

Lawrence, W. E.

W. E. Lawrence, “Electron-electron scattering in the low-temperature resistivity of the noble metals,” Phys. Rev. B Condens. Matter Mater. Phys. 13(12), 5316–5319 (1976).
[Crossref]

Lee, J.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Leiderer, P.

S. Herminghaus and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys., A Mater. Sci. Process. 51(4), 350–353 (1990).
[Crossref]

Leonard, P.

S. Hearty, P. Leonard, and R. O’Kennedy, “Measuring antibody-antigen binding kinetics using surface plasmon resonance,” Methods Mol. Biol. 907, 411–442 (2012).
[Crossref] [PubMed]

Leung, P. T.

H.-P. Chiang, Y.-C. Wang, and P. T. Leung, “Effect of temperature on the incident angle-dependence of the sensitivity for surface plasmon resonance spectroscopy,” Thin Solid Films 425(1-2), 135–138 (2003).
[Crossref]

H.-P. Chiang, P. T. Leung, and W. S. Tse, “Remarks on the substrate-temperature dependence of surface-enhanced raman scattering,” J. Phys. Chem. B 104(10), 2348–2350 (2000).
[Crossref]

Li, G.

F. Xiao, D. Michel, G. Li, A. Xu, and K. Alameh, “Simultaneous measurement of refractive index and temperature based on surface plasmon resonance sensors,” J. Lightwave Technol. 32(21), 4169–4173 (2014).
[Crossref]

Li, H.

Li, M.

Li, X.

Lin, K.

K. Lin, Y. Lu, Z. Luo, R. Zheng, P. Wang, and H. Ming, “Numerical and experimental investigation of temperature effects on the surface plasmon resonance sensor,” Chin. Phys. Lett. 7, 428–431 (2009).

Lin, Z.

Livache, T.

J. B. Fiche, A. Buhot, R. Calemczuk, and T. Livache, “Temperature effects on DNA chip experiments from surface plasmon resonance imaging: isotherms and melting curves,” Biophys. J. 92(3), 935–946 (2007).
[Crossref] [PubMed]

Lu, Y.

K. Lin, Y. Lu, Z. Luo, R. Zheng, P. Wang, and H. Ming, “Numerical and experimental investigation of temperature effects on the surface plasmon resonance sensor,” Chin. Phys. Lett. 7, 428–431 (2009).

Luo, W.

Luo, Z.

K. Lin, Y. Lu, Z. Luo, R. Zheng, P. Wang, and H. Ming, “Numerical and experimental investigation of temperature effects on the surface plasmon resonance sensor,” Chin. Phys. Lett. 7, 428–431 (2009).

Maier, S. A.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Malitson, I. H.

McEnery, K. R.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Miao, P.

Michel, D.

F. Xiao, D. Michel, G. Li, A. Xu, and K. Alameh, “Simultaneous measurement of refractive index and temperature based on surface plasmon resonance sensors,” J. Lightwave Technol. 32(21), 4169–4173 (2014).
[Crossref]

Ming, H.

K. Lin, Y. Lu, Z. Luo, R. Zheng, P. Wang, and H. Ming, “Numerical and experimental investigation of temperature effects on the surface plasmon resonance sensor,” Chin. Phys. Lett. 7, 428–431 (2009).

Ng, B. K.

O’Kennedy, R.

S. Hearty, P. Leonard, and R. O’Kennedy, “Measuring antibody-antigen binding kinetics using surface plasmon resonance,” Methods Mol. Biol. 907, 411–442 (2012).
[Crossref] [PubMed]

Otto, A.

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Zeitschrift Für Physik A Hadrons and Nuclei 216, 398–410 (1968).

Ozdemir, S. K.

Özdemir, S. K.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Pei, W.

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

Piliarik, M.

Qu, J.

Rong-Sheng, Z.

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

Shao, Y.

Sharma, A. K.

Tame, M. S.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Tse, W. S.

H.-P. Chiang, P. T. Leung, and W. S. Tse, “Remarks on the substrate-temperature dependence of surface-enhanced raman scattering,” J. Phys. Chem. B 104(10), 2348–2350 (2000).
[Crossref]

Turhan-Sayan, G.

Wang, L.

Wang, P.

K. Lin, Y. Lu, Z. Luo, R. Zheng, P. Wang, and H. Ming, “Numerical and experimental investigation of temperature effects on the surface plasmon resonance sensor,” Chin. Phys. Lett. 7, 428–431 (2009).

Wang, Y.-C.

H.-P. Chiang, Y.-C. Wang, and P. T. Leung, “Effect of temperature on the incident angle-dependence of the sensitivity for surface plasmon resonance spectroscopy,” Thin Solid Films 425(1-2), 135–138 (2003).
[Crossref]

Watad, I.

Wong, C. L.

Wu, S. Y.

Xiao, F.

F. Xiao, D. Michel, G. Li, A. Xu, and K. Alameh, “Simultaneous measurement of refractive index and temperature based on surface plasmon resonance sensors,” J. Lightwave Technol. 32(21), 4169–4173 (2014).
[Crossref]

Xu, A.

F. Xiao, D. Michel, G. Li, A. Xu, and K. Alameh, “Simultaneous measurement of refractive index and temperature based on surface plasmon resonance sensors,” J. Lightwave Technol. 32(21), 4169–4173 (2014).
[Crossref]

Yong-Hua, L.

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

Yunus, W. M.

Zeng, Y.

Zheng, R.

K. Lin, Y. Lu, Z. Luo, R. Zheng, P. Wang, and H. Ming, “Numerical and experimental investigation of temperature effects on the surface plasmon resonance sensor,” Chin. Phys. Lett. 7, 428–431 (2009).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett. 66(26), 3570–3572 (1995).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (1)

S. Herminghaus and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys., A Mater. Sci. Process. 51(4), 350–353 (1990).
[Crossref]

Biophys. J. (1)

J. B. Fiche, A. Buhot, R. Calemczuk, and T. Livache, “Temperature effects on DNA chip experiments from surface plasmon resonance imaging: isotherms and melting curves,” Biophys. J. 92(3), 935–946 (2007).
[Crossref] [PubMed]

Chin. Phys. Lett. (2)

L. Kai-Qun, W. Lai-Ming, Z. Dou-Gou, Z. Rong-Sheng, W. Pei, L. Yong-Hua, and M. Hair, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24(11), 3081–3084 (2007).
[Crossref]

K. Lin, Y. Lu, Z. Luo, R. Zheng, P. Wang, and H. Ming, “Numerical and experimental investigation of temperature effects on the surface plasmon resonance sensor,” Chin. Phys. Lett. 7, 428–431 (2009).

IEEE Photonics Technol. Lett. (1)

G. Ghosh, “Temperature dispersion of refractive indexes in some silicate fiber glasses,” IEEE Photonics Technol. Lett. 6(3), 431–433 (1994).
[Crossref]

J. Lightwave Technol. (2)

F. Xiao, D. Michel, G. Li, A. Xu, and K. Alameh, “Simultaneous measurement of refractive index and temperature based on surface plasmon resonance sensors,” J. Lightwave Technol. 32(21), 4169–4173 (2014).
[Crossref]

S. K. Ozdemir and G. Turhan-Sayan, “Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor,” J. Lightwave Technol. 21(3), 805–814 (2003).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. Chem. B (1)

H.-P. Chiang, P. T. Leung, and W. S. Tse, “Remarks on the substrate-temperature dependence of surface-enhanced raman scattering,” J. Phys. Chem. B 104(10), 2348–2350 (2000).
[Crossref]

Methods Mol. Biol. (1)

S. Hearty, P. Leonard, and R. O’Kennedy, “Measuring antibody-antigen binding kinetics using surface plasmon resonance,” Methods Mol. Biol. 907, 411–442 (2012).
[Crossref] [PubMed]

Nat. Methods (1)

N. Blow, “Proteins and proteomics: life on the surface,” Nat. Methods 6(5), 389–393 (2009).
[Crossref]

Nat. Phys. (1)

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Opt. Express (4)

Phys. Rev. (1)

T. Holstein, “Optical and infrared volume absorptivity of metals,” Phys. Rev. 96(2), 535–536 (1954).
[Crossref]

Phys. Rev. B Condens. Matter Mater. Phys. (2)

W. E. Lawrence, “Electron-electron scattering in the low-temperature resistivity of the noble metals,” Phys. Rev. B Condens. Matter Mater. Phys. 13(12), 5316–5319 (1976).
[Crossref]

R. T. Beach and R. W. Christy, “Electron-electron scattering in the intraband optical conductivity of Cu, Ag, and Au,” Phys. Rev. B Condens. Matter Mater. Phys. 16(12), 5277–5284 (1977).
[Crossref]

Thin Solid Films (1)

H.-P. Chiang, Y.-C. Wang, and P. T. Leung, “Effect of temperature on the incident angle-dependence of the sensitivity for surface plasmon resonance spectroscopy,” Thin Solid Films 425(1-2), 135–138 (2003).
[Crossref]

Zeitschrift Für Physik A Hadrons and Nuclei (1)

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Zeitschrift Für Physik A Hadrons and Nuclei 216, 398–410 (1968).

Other (1)

G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic Press, 1998).

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Figures (10)

Fig. 1
Fig. 1 Schematic of angular-interrogation mode surface plasmon resonance (SPR) sensor.
Fig. 2
Fig. 2 Schematic of wavelength-interrogation mode surface plasmon resonance (SPR) sensor.
Fig. 3
Fig. 3 Angular-interrogation mode with an incident wavelength of 632.8 nm and a gold film thickness of 50 nm at a reference temperature of 300 K: (a) surface plasmon resonance (SPR) reflectance curves at different temperatures from 100 to 800 K with a refractive index (RI) of 1.330. (b) Fitting lines for resonance angle versus RI at different temperatures. (c) Variation of SPR resonance sensitivity with RI at different temperatures. The RI ranges from 1.330 to 1.346. (d) Variation of SPR resonance sensitivity with temperature at different RIs. The temperature variation ranges from 270 to 380 K, and R2 is the coefficient of determination for the fitting lines.
Fig. 4
Fig. 4 Surface plasmon resonance (SPR) resonance shift versus the simultaneous changes of refractive index (RI) and temperature for the angular-interrogation mode.
Fig. 5
Fig. 5 Angular-interrogation mode: (a) Variation in mn with wavelength. The refractive index (RI) ranges from 1.330 to 1.346 with a temperature of 300 K. (b) Variation in mT with incident wavelength. The temperature changes from 270 to 380 K with an RI of 1.330.
Fig. 6
Fig. 6 Wavelength-interrogation mode with a fixed angle of incidence of 70°: (a) surface plasmon resonance (SPR) reflectance curves at different temperatures ranging from 100 to 800 K with a refractive index (RI) of 1.330. (b) Fitting lines for resonance wavelength versus RI at different temperatures. (c) Variation of SPR resonance sensitivity with RI at different temperatures. The RI ranges from 1.330 to 1.340. (d) Variation of SPR resonance sensitivity with temperature at different RIs. The temperature variation ranges from 270 to 380 K.
Fig. 7
Fig. 7 Wavelength-interrogation mode: (a) Variation in mn with fixed angle of incidence. The refractive index (RI) ranges from 1.330 to 1.340 at a temperature of 300 K. (b) Variation in mT with angle of incidence. The temperature changes from 270 to 380 K with an RI of 1.330.
Fig. 8
Fig. 8 Experimental setup.
Fig. 9
Fig. 9 Resonance wavelength shift versus refractive index (RI) and the corresponding linear fitting lines.
Fig. 10
Fig. 10 Resonance wavelength shift versus temperature and the corresponding linear fitting lines.

Tables (2)

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Table 1 Parameter values used in the calculation of temperature effects on gold sensor film

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Table 2 Prism parameters used for the numerical simulation

Equations (20)

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ε ( ω ) = ( n r + j n i ) 2 = 1 ω p 2 ω ( ω + i ω c ) ,
ω p = 4 π N e 2 m ,
ω p = ω p 0 [ 1 + γ e ( T T ) 0 ] 1 2 ,
ω c = ω c p ( T ) + ω c e ( T )
ω c p ( T ) = ω 0 [ 2 5 + 4 ( T T D ) 5 0 T D / T z 4 d z e z 1 ] ,
ω c e ( T ) = 1 6 π 4 Γ Δ E F [ ( k B T ) 2 + ( ω 4 π 2 ) 2 ] ,
d ( T ) = d 0 [ 1 + ( T T 0 ) γ 1 + μ 1 μ ] ,
n ( T ) = n ( T 0 ) + ( T T 0 ) d n d T
R = λ 2 ( λ 2 λ i g 2 ) ,
2 n ( λ ) d n d T ( λ ) = G R + H R 2 ,
n ( λ ) = ( 1 + A 1 λ 2 λ 2 B 1 2 + A 2 λ 2 λ 2 B 2 2 + A 3 λ 2 λ 2 B 3 2 ) 1 / 2 ,
r = | r 01 + r 12 exp ( 2 i d 1 k z 1 ) 1 + r 01 r 12 exp ( 2 i d 1 k z 1 ) | 2 .
r i j = k z i / ε i k z j / ε j k z i / ε i + k z j / ε j ,
k z i = 2 π λ ε i ε 0 ( sin θ ) 2 ,
Δ A = m n Δ n + m T Δ T ,
( Δ A i Δ A j ) = ( m n i m T i m n j m T j ) ( Δ n Δ T ) = M ( Δ n Δ T ) ,
( Δ n Δ T ) = M 1 ( Δ A i Δ A j )
( Δ A i Δ A j ) = ( f n i ( T ) f T i ( R I ) f n j ( T ) f T j ( R I ) ) ( Δ n Δ T ) = M ( Δ n Δ T ) .
( Δ A i Δ A j ) = ( f n i ( T ) m T i f n j ( T ) m T j ) ( Δ n Δ T ) = M ( Δ n Δ T ) .
( Δ n Δ T ) = ( 8.7861 1.1318 6.9026 0.7905 ) 1 ( Δ A 1 Δ A 2 ) .

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