Abstract

The optimization of integrated optical evanescent-wave sensors includes two parts. For optimal performance, we require waveguides with both maximal sensitivity to the measurand—the quantity intended to be measured—and minimal sensitivity to perturbations. In this context, fully numerical approaches are extremely powerful but demand huge computer resources. We address this issue by introducing a general and efficient approach, based on the formal derivation of analytical dispersion equations, to express and evaluate all waveguide sensitivities. In particular, we apply this approach to rectangular waveguides and discuss its accuracy and its use within sensitivity optimization procedures.

© 2014 Optical Society of America

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References

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  1. G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003).
  2. H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing, and devices,” Adv. Mater. 14, 1339–1365 (2002).
    [CrossRef]
  3. E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
    [CrossRef]
  4. G. B. Hocker and W. K. Burns, “Mode dispersion in diffused channel waveguides by the effective index method,” Appl. Opt. 16, 113–118 (1977).
    [CrossRef]
  5. A. Kumar, K. Thyagarajan, and A. K. Ghatak, “Analysis of rectangular-core dielectric waveguides: an accurate perturbation approach,” Opt. Lett. 8, 63–65 (1983).
    [CrossRef]
  6. J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).
    [CrossRef]
  7. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
    [CrossRef]
  8. K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).
  9. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
    [CrossRef]
  10. R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B 10, 209–211 (1993).
    [CrossRef]
  11. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
    [CrossRef]
  12. C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
    [CrossRef]
  13. O. Parriaux and G. J. Veldhuis, “Normalized analysis for the sensitivity optimization of integrated optical evanescent-wave sensors,” J. Lightwave Technol. 16, 573–582 (1998).
    [CrossRef]
  14. R. Feng and R. J. Farris, “Influence of processing conditions on the thermal and mechanical properties of SU8 negative photoresist coatings,” J. Micromech. Microeng. 13, 80 (2003).
    [CrossRef]
  15. K. K. Tung, W. H. Wong, and E. Y. B. Pun, “Polymeric optical waveguides using direct ultraviolet photolithography process,” Appl. Phys. A 80, 621–626 (2005).
    [CrossRef]
  16. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [CrossRef]
  17. R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
    [CrossRef]
  18. G. R. Hadley, “High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners,” J. Lightwave Technol. 20, 1219–1231 (2002).
    [CrossRef]
  19. I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16, 1020–1028 (2008).
    [CrossRef]
  20. V. Raghunathan, W. N. Ye, J. Hu, T. Izuhara, J. Michel, and L. Kimerling, “Athermal operation of silicon waveguides: spectral, second order and footprint dependencies,” Opt. Express 18, 17631–17639 (2010).
    [CrossRef]
  21. C. Z. Tan, “Review and analysis of refractive index temperature dependence in amorphous SiO2,” J. Non-Cryst. Solids 238, 30–36 (1998).
    [CrossRef]
  22. X. Zhao, C. Li, and Y. Z. Xu, “Stress-induced birefringence control in optical planar waveguides,” Opt. Lett. 28, 564–566 (2003).
    [CrossRef]

2012 (1)

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

2010 (1)

2008 (4)

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16, 1020–1028 (2008).
[CrossRef]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
[CrossRef]

2005 (1)

K. K. Tung, W. H. Wong, and E. Y. B. Pun, “Polymeric optical waveguides using direct ultraviolet photolithography process,” Appl. Phys. A 80, 621–626 (2005).
[CrossRef]

2003 (2)

R. Feng and R. J. Farris, “Influence of processing conditions on the thermal and mechanical properties of SU8 negative photoresist coatings,” J. Micromech. Microeng. 13, 80 (2003).
[CrossRef]

X. Zhao, C. Li, and Y. Z. Xu, “Stress-induced birefringence control in optical planar waveguides,” Opt. Lett. 28, 564–566 (2003).
[CrossRef]

2002 (2)

G. R. Hadley, “High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners,” J. Lightwave Technol. 20, 1219–1231 (2002).
[CrossRef]

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing, and devices,” Adv. Mater. 14, 1339–1365 (2002).
[CrossRef]

2000 (1)

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

1998 (2)

O. Parriaux and G. J. Veldhuis, “Normalized analysis for the sensitivity optimization of integrated optical evanescent-wave sensors,” J. Lightwave Technol. 16, 573–582 (1998).
[CrossRef]

C. Z. Tan, “Review and analysis of refractive index temperature dependence in amorphous SiO2,” J. Non-Cryst. Solids 238, 30–36 (1998).
[CrossRef]

1993 (1)

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B 10, 209–211 (1993).
[CrossRef]

1983 (1)

1977 (1)

1969 (2)

J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).
[CrossRef]

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
[CrossRef]

1965 (1)

Abe, I.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

Buckle, M.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Burns, W. K.

Dalton, L. R.

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing, and devices,” Adv. Mater. 14, 1339–1365 (2002).
[CrossRef]

Delezoide, C.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Fabris, J. L.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

Fan, X.

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16, 1020–1028 (2008).
[CrossRef]

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
[CrossRef]

Farris, R. J.

R. Feng and R. J. Farris, “Influence of processing conditions on the thermal and mechanical properties of SU8 negative photoresist coatings,” J. Micromech. Microeng. 13, 80 (2003).
[CrossRef]

Feng, R.

R. Feng and R. J. Farris, “Influence of processing conditions on the thermal and mechanical properties of SU8 negative photoresist coatings,” J. Micromech. Microeng. 13, 80 (2003).
[CrossRef]

Ghatak, A. K.

Goell, J. E.

J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).
[CrossRef]

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Greve, J.

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B 10, 209–211 (1993).
[CrossRef]

Hadley, G. R.

Heideman, R. G.

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B 10, 209–211 (1993).
[CrossRef]

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Hocker, G. B.

Hu, J.

Izuhara, T.

Jen, A. K.-Y.

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing, and devices,” Adv. Mater. 14, 1339–1365 (2002).
[CrossRef]

Kalinowski, H. J.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

Kamikawachi, R. C.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

Kimerling, L.

Kooyman, R. P. H.

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B 10, 209–211 (1993).
[CrossRef]

Kumar, A.

Lautru, J.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Ledoux-Rak, I.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Leh, H.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Li, C.

Lifante, G.

G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003).

Ma, H.

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing, and devices,” Adv. Mater. 14, 1339–1365 (2002).
[CrossRef]

Malitson, I. H.

Marcatili, E. A. J.

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
[CrossRef]

Michel, J.

Muller, M.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

Nguyen, C. T.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Nogues, C.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

Parriaux, O.

Paterno, A. S.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

Pinto, J. L.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Pun, E. Y. B.

K. K. Tung, W. H. Wong, and E. Y. B. Pun, “Polymeric optical waveguides using direct ultraviolet photolithography process,” Appl. Phys. A 80, 621–626 (2005).
[CrossRef]

Raghunathan, V.

Salsac, M.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Shopova, S. I.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
[CrossRef]

Sun, Y.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
[CrossRef]

Suter, J. D.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
[CrossRef]

Tan, C. Z.

C. Z. Tan, “Review and analysis of refractive index temperature dependence in amorphous SiO2,” J. Non-Cryst. Solids 238, 30–36 (1998).
[CrossRef]

Thyagarajan, K.

Tung, K. K.

K. K. Tung, W. H. Wong, and E. Y. B. Pun, “Polymeric optical waveguides using direct ultraviolet photolithography process,” Appl. Phys. A 80, 621–626 (2005).
[CrossRef]

Veldhuis, G. J.

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

White, I. M.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
[CrossRef]

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16, 1020–1028 (2008).
[CrossRef]

Wong, W. H.

K. K. Tung, W. H. Wong, and E. Y. B. Pun, “Polymeric optical waveguides using direct ultraviolet photolithography process,” Appl. Phys. A 80, 621–626 (2005).
[CrossRef]

Xu, Y. Z.

Ye, W. N.

Zhao, X.

Zhu, H.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
[CrossRef]

Zyss, J.

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

Adv. Mater. (1)

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing, and devices,” Adv. Mater. 14, 1339–1365 (2002).
[CrossRef]

Anal. Chim. Acta (1)

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets,” Anal. Chim. Acta 620, 8–26 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

K. K. Tung, W. H. Wong, and E. Y. B. Pun, “Polymeric optical waveguides using direct ultraviolet photolithography process,” Appl. Phys. A 80, 621–626 (2005).
[CrossRef]

Bell Syst. Tech. J. (2)

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).
[CrossRef]

J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. Delezoide, M. Salsac, J. Lautru, H. Leh, C. Nogues, J. Zyss, M. Buckle, I. Ledoux-Rak, and C. T. Nguyen, “Vertically coupled polymer microracetrack resonators for label-free biochemical sensors,” IEEE Photon. Technol. Lett. 24, 270–272 (2012).
[CrossRef]

J. Lightwave Technol. (2)

J. Micromech. Microeng. (1)

R. Feng and R. J. Farris, “Influence of processing conditions on the thermal and mechanical properties of SU8 negative photoresist coatings,” J. Micromech. Microeng. 13, 80 (2003).
[CrossRef]

J. Non-Cryst. Solids (1)

C. Z. Tan, “Review and analysis of refractive index temperature dependence in amorphous SiO2,” J. Non-Cryst. Solids 238, 30–36 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

Opt. Commun. (1)

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Sens. Actuators B (1)

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach–Zehnder interferometer immunosensor,” Sens. Actuators B 10, 209–211 (1993).
[CrossRef]

Other (2)

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of an asymmetrical slab waveguide. Directions of the electric fields corresponding to TE and TM modes are represented.

Fig. 2.
Fig. 2.

Schematic of a rectangular waveguide. Directions of the major electric field components corresponding to quasi-TE and quasi-TM modes are represented. Corner regions appear as shaded zones.

Fig. 3.
Fig. 3.

Comparison of effective indices and sensitivities to the cladding refractive index for fundamental TE and TM modes of a typical polymeric rectangular waveguide with varying height. Reference ADI values, relative differences between ADI and EIM values, and between ADI and MM values are displayed in both instances. MM, disks; EIM, circles; and ADI, solid (nested graphs).

Fig. 4.
Fig. 4.

Sensitivities of the effective indices of fundamental TE and TM modes to the refractive index of the cladding of a rectangular waveguide versus normalized height and width. (a) Asymmetric waveguide with Ncore=1.56, Nsub=1.444, and Nclad=1.323. (b) Symmetric waveguide with Ncore=1.56 and Nclad=Nsub=1.333.

Fig. 5.
Fig. 5.

Full thermal sensitivities ST of the fundamental TE and TM modes to the temperature of a rectangular waveguide versus the normalized height and width.

Equations (26)

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

df=0=fλdλ+fNeffdNeff+fNcoredNcore+fNsubdNsub+fNcladdNclad+fwdw.
dNeff=ScoredNcore+SsubdNsub+ScladdNclad+Swdw+Sλdλ.
{Score=NeffNcore=(fNeff)1fNcore,Ssub=NeffNsub=(fNeff)1fNsub,Sclad=NeffNclad=(fNeff)1fNclad,Sw=Neffw=(fNeff)1fw,Sλ=Neffλ=(fNeff)1fλ.
SX=dNeffdX=Score·dNcoredX+Ssub·dNsubdX+Sclad·dNcladdX+Sw·dwdX.
ScladADI=NeffADI(Nclad+δ)NeffADI(Nclad)δ.
ST=ΓcoredNcoredT+ΓcladdNcladdT+ΓsubdNsubdT,
ST=dNeffdT=Score·dNcoredT+Ssub·dNsubdT+Sclad·dNcladdT+Sw·dwdT+Sh·dhdT.
1hdhdT=1wdwdT=βcore,
ST=Score·αcore+Sclad·αclad+Ssub·αsub+(w·Sw+h·Sh)βcore,
dNeff=i=1NNeffaidai=i=1NSidai.
{b=Neff2Nsub2Ncore2Nsub2,γ=Nsub2Nclad2Ncore2Nsub2,v=kw(Ncore2Nsub2)1/2,
{fTE(m)=0=v(1b)1/2mπtan1(b1b)1/2tan1(b+γ1b)1/2,fTM(m)=0=v(1b)1/2mπtan1(Ncore2Nsub2(b1b)1/2)tan1(Ncore2Nclad2(b+γ1b)1/2).
{bV=Neff,I2Nsub2Ncore2Nsub2,vV=kh(Ncore2Nsub2)1/2,bL=Neff2Nclad2Neff,I2Nclad2,vL=kw(Neff,I2Nclad2)1/2.
{fL(p)=0=vL(1bL)1/2pπ2tan1(bL1bL)1/2,fV(q)=0=vV(1bV)1/2qπtan1(Ncore2Nsub2(bV1bV)1/2)tan1(Ncore2Nclad2(bV+γ1bV)1/2).
{fL(p)=0=vL(1bL)1/2pπ2tan1Neff,I2Nclad2(bL1bL)1/2,fV(q)=0=vV(1bV)1/2qπtan1(bV1bV)1/2tan1(bV+γ1bV)1/2.
dNeff=ScoredNcore+SsubdNsub+ScladdNclad+Swdw+Shdh+Sλdλ.
{Score=(fLNeff)1·fLNeff,I×(fVNeff,I)1·fVNcore,Ssub=(fLNeff)1·fLNeff,I×(fVNeff,I)1·fVNsub,Sclad=(fLNeff)1·fLNeff,I×(fVNeff,I)1·fVNclad(fLNeff)1·fLNclad.
{Sh=(fLNeff)1·fLNeff,I×(fVNeff,I)1·fVh,Sw=(fLNeff)1·fLw.
{Sλ=(fLNeff)1fLNeff,I×(fVNeff,I)1fVλ(fLNeff)1fLλ.
Neff2=Neff,L2+Neff,V2Ncore2.
{bL=Neff,L2Nclad2Ncore2Nclad2,vL=kw(Ncore2Nclad2)1/2,bV=Neff,V2Nsub2Ncore2Nsub2,vV=kh(Ncore2Nsub2)1/2.
{fL(p)=0=vL(1bL)1/2pπ2tan1(bL1bL)1/2,fV(q)=0=vV(1bV)1/2qπtan1(Ncore2Nsub2(bV1bV)1/2)tan1(Ncore2Nclad2(bV+γ1bV)1/2).
{fL(p)=vL(1bL)1/2pπ2tan1Ncore2Nclad2(bL1bL)1/2,fV(q)=vV(1bV)1/2qπtan1(bV1bV)1/2tan1(bV+γ1bV)1/2.
{SNcore=Neff,LNeff(fLNeff,L)1fLNcoreNeff,VNeff(fVNeff,V)1fVNcoreNcoreNeff,SNclad=Neff,LNeff(fLNeff,L)1fLNcladNeff,VNeff(fVNeff,V)1fVNclad,SNsub=Neff,VNeff(fVNeff,V)1fVNsub.
{Sw=Neff,LNeff(fLNeff,L)1fLw,Sh=Neff,VNeff(fVNeff,V)1fVh.
{Sλ=Neff,LNeff(fLNeff,L)1fLλNeff,VNeff(fVNeff,V)1fVλ.

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