Abstract

Generally, the total power attenuation in multimode evanescent-field sensor waveguides is nonproportional to the bulk absorbance because the modal attenuation constants differ. Hence a direct measurement is difficult and is additionally aggravated because the waveguide absorbance is highly sensitive to the specific launching conditions at the waveguide input. A general asymptotic formula for the modal power attenuation in strongly asymmetric inhomogeneous planar waveguides with arbitrarily distributed weak absorption in the low-index superstrate is derived. Explicit expressions for typical refractive-index profiles are given. Except when very close to the cutoff, the predicted asymptotic attenuation behavior agrees well with exact calculations. The ratio of TM versus TE absorption has been derived to be (2 − n 0 2/n f 2) for arbitrary profiles. Waveguides with a linear refractive-index profile show mode-independent attenuation coefficients within each polarization. Further, the asymptotic sensitivity is independent of the wavelength, so that it should be possible to directly measure the spectral variation of the bulk absorption. The mode independence of the attenuation has been verified experimentally for a second-order polynomial profile, which is close to a linear refractive-index distribution. In contrast, the attenuation in the step-profile waveguide has been found to depend strongly on the mode number, as predicted by theory. A strong spread of the modal attenuation coefficients is also predicted for the parabolic-profile waveguide sensor.

© 1995 Optical Society of America

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  1. E. E. Carlyon, C. R. Lowe, D. Reid, I. Bennion, “A single mode fibre-optic evanescent wave biosensor,” Biosensors Bio-electron. 7, 141–146 (1992).
  2. C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
    [Crossref]
  3. M. D. DeGrandpre, L. W. Burgess, “All-fiber spectroscopic probe based on an evanescent wave sensing mechanism,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 170–174 (1988).
  4. M. D. DeGrandpre, L. W. Burgess, “Long path fiber-optic sensor for evanescent field absorbance measurement,” Anal. Chem. 60, 2582–2586 (1988).
    [Crossref]
  5. P. H. Paul, G. Kychakoff, “Fiber-optic evanescent field absorption sensor,” Appl. Phys. Lett. 51, 12–14 (1987).
    [Crossref]
  6. V. Ruddy, B. D. MacCraith, J. A. Murphy, “Evanescent wave absorption spectroscopy using multimode fibers,” J. Appl. Phys. 67, 6070–6074 (1990).
    [Crossref]
  7. R. Klein, E. Voges, Micro System Technologies 91 (Springer-Verlag, Berlin, 1991).
  8. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  9. G. Stewart, J. Norris, D. Clark, M. Tribble, I. Andonovic, B. Culshaw, “Chemical sensing by evanescent field absorption: the sensitivity of optical waveguides,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 188–195 (1988).
  10. H. Gnewuch, R. Ulrich, “Modal characteristics of evanescent-field coupling in fluorescence sensor,” in Proceedings of the First European Conference on Optical Chemical Sensors and Biosensors (Forschungsgesellschaft Johanneum Ges.m.b.H., Graz, Austria, 1992), p. 122.
  11. G. Stewart, J. Norris, D. F. Clark, B. Culshaw, “Evanescent-wave chemical sensors—a theoretical evaluation,” Int. J. Opto-electron. 6, 227–238 (1991).
  12. H. A. Haus, R. V. Schmidt, “Approximate analysis of optical waveguide grating coupling coefficients,” Appl. Opt. 15, 774–781 (1976).
  13. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chaps. 10 and 22.
  14. J. A. Arnaud, W. Mammel, “Application of a property of the Airy function to fiber optics,” IEEE Trans. Microwave Theory Tech. MTT-23, 927–929 (1975).
    [Crossref]
  15. A. Apelblat, Table of Definite and Indefinite Integrals (Elsevier, Amsterdam, 1983), p. 349.
  16. M. J. Adams, An Introduction to Optical Waveguides (Wiley, Chichester, 1981), Chaps. 2, 4, and 5.
  17. E. M. Conwell, “Modes in optical waveguides formed by diffusion,” Appl. Phys. Lett. 23, 328–329 (1973).
    [Crossref]
  18. J. R. Carruthers, I. P. Kaminow, L. W. Stulz, “Diffusion kinetics and optical properties of outdiffused layers in lithium niobate and lithium tantalate,” Appl. Opt. 13, 2333–2342 (1974).
    [Crossref] [PubMed]
  19. R. V. Ramaswamy, H. C. Cheng, R. Srivastava, “Process optimization of buried Ag+–Na+ ion-exchanged waveguides: theory and experiment,” Appl. Opt. 27, 1814–1819 (1988).
    [Crossref] [PubMed]
  20. G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
    [Crossref]
  21. G. Stewart, P. J. R. Laybourn, “Fabrication of ion-exchanged optical waveguides from dilute silver nitrate melts,” IEEE J. Quantum Electron. QE-14, 930–934 (1978).
    [Crossref]
  22. R. D. Standley, V. Ramaswamy, “Nb-diffused LiTaO3 optical waveguides: planar and embedded strip guides,” Appl. Phys. Lett. 25, 711–713 (1974).
    [Crossref]
  23. D. Peters, J. Müller, “Integrated optical devices with silicon oxynitride prepared by PECVD on Si and GaAs substrates,” in Physical Concepts of Materials for Novel Optoelectronic Device Applications II: Device Physics and Applications, M. Razeghi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1362, 338–349 (1990).
  24. O. D. D. Soares, M. J. D. Z. Silva, “Ion-exchanged slab waveguide characterization,” Opt. Acta 33, 1321–1334 (1986).
    [Crossref]
  25. J. M. White, P. F. Heidrich, “Optical waveguide refractive-index profiles determined from measurement of mode indices: a simple analysis,” Appl. Opt. 15, 151–155 (1976).
    [Crossref] [PubMed]
  26. R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
    [Crossref] [PubMed]
  27. A. W. Snyder, J. D. Love, R. A. Sammut, “Green’s function methods for perturbed optical fibers,” J. Opt. Soc. Am. 72, 1131–1135 (1982).
    [Crossref]
  28. H. Renner, “Far-from-core field of bound modes on noncircular weakly guiding optical waveguides,” J. Mod. Opt. 39, 1–7 (1992).
    [Crossref]
  29. H. Renner, “Asymptotic coupling coefficients of well-separated single-mode optical waveguides,” J. Mod. Opt. 39, 907–915 (1992).
    [Crossref]

1992 (4)

E. E. Carlyon, C. R. Lowe, D. Reid, I. Bennion, “A single mode fibre-optic evanescent wave biosensor,” Biosensors Bio-electron. 7, 141–146 (1992).

C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
[Crossref]

H. Renner, “Far-from-core field of bound modes on noncircular weakly guiding optical waveguides,” J. Mod. Opt. 39, 1–7 (1992).
[Crossref]

H. Renner, “Asymptotic coupling coefficients of well-separated single-mode optical waveguides,” J. Mod. Opt. 39, 907–915 (1992).
[Crossref]

1991 (1)

G. Stewart, J. Norris, D. F. Clark, B. Culshaw, “Evanescent-wave chemical sensors—a theoretical evaluation,” Int. J. Opto-electron. 6, 227–238 (1991).

1990 (1)

V. Ruddy, B. D. MacCraith, J. A. Murphy, “Evanescent wave absorption spectroscopy using multimode fibers,” J. Appl. Phys. 67, 6070–6074 (1990).
[Crossref]

1988 (2)

R. V. Ramaswamy, H. C. Cheng, R. Srivastava, “Process optimization of buried Ag+–Na+ ion-exchanged waveguides: theory and experiment,” Appl. Opt. 27, 1814–1819 (1988).
[Crossref] [PubMed]

M. D. DeGrandpre, L. W. Burgess, “Long path fiber-optic sensor for evanescent field absorbance measurement,” Anal. Chem. 60, 2582–2586 (1988).
[Crossref]

1987 (1)

P. H. Paul, G. Kychakoff, “Fiber-optic evanescent field absorption sensor,” Appl. Phys. Lett. 51, 12–14 (1987).
[Crossref]

1986 (1)

O. D. D. Soares, M. J. D. Z. Silva, “Ion-exchanged slab waveguide characterization,” Opt. Acta 33, 1321–1334 (1986).
[Crossref]

1982 (1)

1978 (1)

G. Stewart, P. J. R. Laybourn, “Fabrication of ion-exchanged optical waveguides from dilute silver nitrate melts,” IEEE J. Quantum Electron. QE-14, 930–934 (1978).
[Crossref]

1977 (1)

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[Crossref]

1976 (2)

1975 (1)

J. A. Arnaud, W. Mammel, “Application of a property of the Airy function to fiber optics,” IEEE Trans. Microwave Theory Tech. MTT-23, 927–929 (1975).
[Crossref]

1974 (2)

R. D. Standley, V. Ramaswamy, “Nb-diffused LiTaO3 optical waveguides: planar and embedded strip guides,” Appl. Phys. Lett. 25, 711–713 (1974).
[Crossref]

J. R. Carruthers, I. P. Kaminow, L. W. Stulz, “Diffusion kinetics and optical properties of outdiffused layers in lithium niobate and lithium tantalate,” Appl. Opt. 13, 2333–2342 (1974).
[Crossref] [PubMed]

1973 (2)

R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
[Crossref] [PubMed]

E. M. Conwell, “Modes in optical waveguides formed by diffusion,” Appl. Phys. Lett. 23, 328–329 (1973).
[Crossref]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chaps. 10 and 22.

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, Chichester, 1981), Chaps. 2, 4, and 5.

Andonovic, I.

G. Stewart, J. Norris, D. Clark, M. Tribble, I. Andonovic, B. Culshaw, “Chemical sensing by evanescent field absorption: the sensitivity of optical waveguides,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 188–195 (1988).

Apelblat, A.

A. Apelblat, Table of Definite and Indefinite Integrals (Elsevier, Amsterdam, 1983), p. 349.

Arnaud, J. A.

J. A. Arnaud, W. Mammel, “Application of a property of the Airy function to fiber optics,” IEEE Trans. Microwave Theory Tech. MTT-23, 927–929 (1975).
[Crossref]

Bennion, I.

E. E. Carlyon, C. R. Lowe, D. Reid, I. Bennion, “A single mode fibre-optic evanescent wave biosensor,” Biosensors Bio-electron. 7, 141–146 (1992).

Burgess, L. W.

M. D. DeGrandpre, L. W. Burgess, “Long path fiber-optic sensor for evanescent field absorbance measurement,” Anal. Chem. 60, 2582–2586 (1988).
[Crossref]

M. D. DeGrandpre, L. W. Burgess, “All-fiber spectroscopic probe based on an evanescent wave sensing mechanism,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 170–174 (1988).

Carlyon, E. E.

E. E. Carlyon, C. R. Lowe, D. Reid, I. Bennion, “A single mode fibre-optic evanescent wave biosensor,” Biosensors Bio-electron. 7, 141–146 (1992).

Carruthers, J. R.

Cheng, H. C.

Clark, D.

G. Stewart, J. Norris, D. Clark, M. Tribble, I. Andonovic, B. Culshaw, “Chemical sensing by evanescent field absorption: the sensitivity of optical waveguides,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 188–195 (1988).

Clark, D. F.

G. Stewart, J. Norris, D. F. Clark, B. Culshaw, “Evanescent-wave chemical sensors—a theoretical evaluation,” Int. J. Opto-electron. 6, 227–238 (1991).

Conwell, E. M.

E. M. Conwell, “Modes in optical waveguides formed by diffusion,” Appl. Phys. Lett. 23, 328–329 (1973).
[Crossref]

Culshaw, B.

G. Stewart, J. Norris, D. F. Clark, B. Culshaw, “Evanescent-wave chemical sensors—a theoretical evaluation,” Int. J. Opto-electron. 6, 227–238 (1991).

G. Stewart, J. Norris, D. Clark, M. Tribble, I. Andonovic, B. Culshaw, “Chemical sensing by evanescent field absorption: the sensitivity of optical waveguides,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 188–195 (1988).

DeGrandpre, M. D.

M. D. DeGrandpre, L. W. Burgess, “Long path fiber-optic sensor for evanescent field absorbance measurement,” Anal. Chem. 60, 2582–2586 (1988).
[Crossref]

M. D. DeGrandpre, L. W. Burgess, “All-fiber spectroscopic probe based on an evanescent wave sensing mechanism,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 170–174 (1988).

DeLaRue, R. M.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[Crossref]

Gnewuch, H.

H. Gnewuch, R. Ulrich, “Modal characteristics of evanescent-field coupling in fluorescence sensor,” in Proceedings of the First European Conference on Optical Chemical Sensors and Biosensors (Forschungsgesellschaft Johanneum Ges.m.b.H., Graz, Austria, 1992), p. 122.

Haus, H. A.

Heidrich, P. F.

Kaminow, I. P.

Klein, R.

R. Klein, E. Voges, Micro System Technologies 91 (Springer-Verlag, Berlin, 1991).

Kychakoff, G.

P. H. Paul, G. Kychakoff, “Fiber-optic evanescent field absorption sensor,” Appl. Phys. Lett. 51, 12–14 (1987).
[Crossref]

Laybourn, P. J. R.

G. Stewart, P. J. R. Laybourn, “Fabrication of ion-exchanged optical waveguides from dilute silver nitrate melts,” IEEE J. Quantum Electron. QE-14, 930–934 (1978).
[Crossref]

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[Crossref]

Love, J. D.

Lowe, C. R.

E. E. Carlyon, C. R. Lowe, D. Reid, I. Bennion, “A single mode fibre-optic evanescent wave biosensor,” Biosensors Bio-electron. 7, 141–146 (1992).

MacCraith, B. D.

V. Ruddy, B. D. MacCraith, J. A. Murphy, “Evanescent wave absorption spectroscopy using multimode fibers,” J. Appl. Phys. 67, 6070–6074 (1990).
[Crossref]

Mammel, W.

J. A. Arnaud, W. Mammel, “Application of a property of the Airy function to fiber optics,” IEEE Trans. Microwave Theory Tech. MTT-23, 927–929 (1975).
[Crossref]

Millar, C. A.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[Crossref]

Müller, J.

D. Peters, J. Müller, “Integrated optical devices with silicon oxynitride prepared by PECVD on Si and GaAs substrates,” in Physical Concepts of Materials for Novel Optoelectronic Device Applications II: Device Physics and Applications, M. Razeghi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1362, 338–349 (1990).

Murphy, J. A.

V. Ruddy, B. D. MacCraith, J. A. Murphy, “Evanescent wave absorption spectroscopy using multimode fibers,” J. Appl. Phys. 67, 6070–6074 (1990).
[Crossref]

Mwarania, E. K.

C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
[Crossref]

Norris, J.

G. Stewart, J. Norris, D. F. Clark, B. Culshaw, “Evanescent-wave chemical sensors—a theoretical evaluation,” Int. J. Opto-electron. 6, 227–238 (1991).

G. Stewart, J. Norris, D. Clark, M. Tribble, I. Andonovic, B. Culshaw, “Chemical sensing by evanescent field absorption: the sensitivity of optical waveguides,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 188–195 (1988).

O’Dwyer, K.

C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
[Crossref]

Paul, P. H.

P. H. Paul, G. Kychakoff, “Fiber-optic evanescent field absorption sensor,” Appl. Phys. Lett. 51, 12–14 (1987).
[Crossref]

Peters, D.

D. Peters, J. Müller, “Integrated optical devices with silicon oxynitride prepared by PECVD on Si and GaAs substrates,” in Physical Concepts of Materials for Novel Optoelectronic Device Applications II: Device Physics and Applications, M. Razeghi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1362, 338–349 (1990).

Piraud, C.

C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
[Crossref]

Ramaswamy, R. V.

Ramaswamy, V.

R. D. Standley, V. Ramaswamy, “Nb-diffused LiTaO3 optical waveguides: planar and embedded strip guides,” Appl. Phys. Lett. 25, 711–713 (1974).
[Crossref]

Reid, D.

E. E. Carlyon, C. R. Lowe, D. Reid, I. Bennion, “A single mode fibre-optic evanescent wave biosensor,” Biosensors Bio-electron. 7, 141–146 (1992).

Renner, H.

H. Renner, “Far-from-core field of bound modes on noncircular weakly guiding optical waveguides,” J. Mod. Opt. 39, 1–7 (1992).
[Crossref]

H. Renner, “Asymptotic coupling coefficients of well-separated single-mode optical waveguides,” J. Mod. Opt. 39, 907–915 (1992).
[Crossref]

Ruddy, V.

V. Ruddy, B. D. MacCraith, J. A. Murphy, “Evanescent wave absorption spectroscopy using multimode fibers,” J. Appl. Phys. 67, 6070–6074 (1990).
[Crossref]

Sammut, R. A.

Schiffrin, D. J.

C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
[Crossref]

Schmidt, R. V.

Silva, M. J. D. Z.

O. D. D. Soares, M. J. D. Z. Silva, “Ion-exchanged slab waveguide characterization,” Opt. Acta 33, 1321–1334 (1986).
[Crossref]

Snyder, A. W.

Soares, O. D. D.

O. D. D. Soares, M. J. D. Z. Silva, “Ion-exchanged slab waveguide characterization,” Opt. Acta 33, 1321–1334 (1986).
[Crossref]

Srivastava, R.

Standley, R. D.

R. D. Standley, V. Ramaswamy, “Nb-diffused LiTaO3 optical waveguides: planar and embedded strip guides,” Appl. Phys. Lett. 25, 711–713 (1974).
[Crossref]

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chaps. 10 and 22.

Stewart, G.

G. Stewart, J. Norris, D. F. Clark, B. Culshaw, “Evanescent-wave chemical sensors—a theoretical evaluation,” Int. J. Opto-electron. 6, 227–238 (1991).

G. Stewart, P. J. R. Laybourn, “Fabrication of ion-exchanged optical waveguides from dilute silver nitrate melts,” IEEE J. Quantum Electron. QE-14, 930–934 (1978).
[Crossref]

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[Crossref]

G. Stewart, J. Norris, D. Clark, M. Tribble, I. Andonovic, B. Culshaw, “Chemical sensing by evanescent field absorption: the sensitivity of optical waveguides,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 188–195 (1988).

Stulz, L. W.

Torge, R.

Tribble, M.

G. Stewart, J. Norris, D. Clark, M. Tribble, I. Andonovic, B. Culshaw, “Chemical sensing by evanescent field absorption: the sensitivity of optical waveguides,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 188–195 (1988).

Ulrich, R.

R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
[Crossref] [PubMed]

H. Gnewuch, R. Ulrich, “Modal characteristics of evanescent-field coupling in fluorescence sensor,” in Proceedings of the First European Conference on Optical Chemical Sensors and Biosensors (Forschungsgesellschaft Johanneum Ges.m.b.H., Graz, Austria, 1992), p. 122.

Voges, E.

R. Klein, E. Voges, Micro System Technologies 91 (Springer-Verlag, Berlin, 1991).

White, J. M.

Wilkinson, C. D. W.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[Crossref]

Wilkinson, J. S.

C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
[Crossref]

Yao, J.

C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
[Crossref]

Anal. Chem. (1)

M. D. DeGrandpre, L. W. Burgess, “Long path fiber-optic sensor for evanescent field absorbance measurement,” Anal. Chem. 60, 2582–2586 (1988).
[Crossref]

Appl. Opt. (5)

Appl. Phys. Lett. (3)

R. D. Standley, V. Ramaswamy, “Nb-diffused LiTaO3 optical waveguides: planar and embedded strip guides,” Appl. Phys. Lett. 25, 711–713 (1974).
[Crossref]

E. M. Conwell, “Modes in optical waveguides formed by diffusion,” Appl. Phys. Lett. 23, 328–329 (1973).
[Crossref]

P. H. Paul, G. Kychakoff, “Fiber-optic evanescent field absorption sensor,” Appl. Phys. Lett. 51, 12–14 (1987).
[Crossref]

Biosensors Bio-electron. (1)

E. E. Carlyon, C. R. Lowe, D. Reid, I. Bennion, “A single mode fibre-optic evanescent wave biosensor,” Biosensors Bio-electron. 7, 141–146 (1992).

IEEE J. Quantum Electron. (2)

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[Crossref]

G. Stewart, P. J. R. Laybourn, “Fabrication of ion-exchanged optical waveguides from dilute silver nitrate melts,” IEEE J. Quantum Electron. QE-14, 930–934 (1978).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. A. Arnaud, W. Mammel, “Application of a property of the Airy function to fiber optics,” IEEE Trans. Microwave Theory Tech. MTT-23, 927–929 (1975).
[Crossref]

Int. J. Opto-electron. (1)

G. Stewart, J. Norris, D. F. Clark, B. Culshaw, “Evanescent-wave chemical sensors—a theoretical evaluation,” Int. J. Opto-electron. 6, 227–238 (1991).

J. Appl. Phys. (1)

V. Ruddy, B. D. MacCraith, J. A. Murphy, “Evanescent wave absorption spectroscopy using multimode fibers,” J. Appl. Phys. 67, 6070–6074 (1990).
[Crossref]

J. Lightwave Technol. (1)

C. Piraud, E. K. Mwarania, J. Yao, K. O’Dwyer, D. J. Schiffrin, J. S. Wilkinson, “Optoelectrochemical transduction on planar optical waveguides,” J. Lightwave Technol. 10, 693–699 (1992).
[Crossref]

J. Mod. Opt. (2)

H. Renner, “Far-from-core field of bound modes on noncircular weakly guiding optical waveguides,” J. Mod. Opt. 39, 1–7 (1992).
[Crossref]

H. Renner, “Asymptotic coupling coefficients of well-separated single-mode optical waveguides,” J. Mod. Opt. 39, 907–915 (1992).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

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[Crossref]

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M. D. DeGrandpre, L. W. Burgess, “All-fiber spectroscopic probe based on an evanescent wave sensing mechanism,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 170–174 (1988).

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R. Klein, E. Voges, Micro System Technologies 91 (Springer-Verlag, Berlin, 1991).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

G. Stewart, J. Norris, D. Clark, M. Tribble, I. Andonovic, B. Culshaw, “Chemical sensing by evanescent field absorption: the sensitivity of optical waveguides,” in Imaging Applications in the Work Place, R. J. Clouthier, G. K. Starkweather, A. G. Tescher, T. L. Vogelsong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.990, 188–195 (1988).

H. Gnewuch, R. Ulrich, “Modal characteristics of evanescent-field coupling in fluorescence sensor,” in Proceedings of the First European Conference on Optical Chemical Sensors and Biosensors (Forschungsgesellschaft Johanneum Ges.m.b.H., Graz, Austria, 1992), p. 122.

A. Apelblat, Table of Definite and Indefinite Integrals (Elsevier, Amsterdam, 1983), p. 349.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for remote evanescent-field absorption spectroscopy.

Fig. 2
Fig. 2

Refractive-index profiles: (a) step profile, (b) linear profile, (c) parabolic profile, (d) second-order polynomial profile.

Fig. 3
Fig. 3

Normalized attenuation coefficients of TM m (dashed curves) and TE m (dotted-dashed curves) modes for linear-profile waveguides: n f = 1.51, n s = 1.50, and n 0 = 1.33.

Fig. 4
Fig. 4

Normalized attenuation coefficients of TM m (dashed curves) and TE m (dotted-dashed curves) modes for step-index waveguides: n f = 1.505, n s = 1.50, and n 0 = 1.33. The upper and the lower dotted curves represent the ultimate upper loss limit from relation (40) for all TM and TE modes, respectively.

Fig. 5
Fig. 5

Attenuation coefficients of TE modes for planar waveguides: step-index profile [calculated (open circles) and measured (pluses)] and second-order polynomial refractive-index profile [calculated (open squares) and measured (crosses)].

Equations (56)

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P tot ( z ) = j = 0 M - 1 P m ( 0 ) exp ( - γ m z ) ,
A W = - log 10 P tot ( z ) P tot ( 0 ) ,
A B = γ B z ,
n ( x ) = { n 0 x < 0 n ( x ) 0 < x n s x .
γ = 2 k ( 0 μ 0 ) 1 / 2 Q P ,
Q = n 0 - 0 n 0 i ( x ) e · e * d x ,
P = Re [ - + ( e × h * ) · z ^ d x ] ,
[ d 2 d x 2 - ζ n 2 ( x ) d n 2 ( x ) d x d d x + k 2 n 2 ( x ) - β 2 ] ψ ( x ) = 0 ,
ψ ( x ) = a 1 exp ( η x ) ,             - < x 0 ,
η = ( β 2 - k 2 n 0 2 ) 1 / 2
ψ ( - 0 ) = ψ ( + 0 ) = a 1 = ξ η d ψ d x | x = + 0 ξ η ψ ( + 0 ) ,
κ = ( k 2 n f 2 - β 2 ) 1 / 2 ,
β k n f ,             η k ( n f 2 - n 0 2 ) 1 / 2 .
P = ( 0 μ 0 ) 1 / 2 β k N ,
P = ( μ 0 0 ) 1 / 2 β k n f 2 N ,
N = 0 ψ 2 ( x ) d x ,
e ( x ) = y ^ ψ ( x ) ,
e ( x ) = ( μ 0 0 ) 1 / 2 1 k n 2 ( x ) [ x ^ β ψ ( x ) + i z ^ d ψ ( x ) d x ] ,
Q = a 1 2 n 0 - 0 n 0 i ( x ) exp [ 2 k ( n f 2 - n 0 2 ) 1 / 2 x ] d x { 1 ( μ 0 / 0 ) n 0 - 4 ( 2 n f 2 - n 0 2 ) ,             for TE modes for TM modes .
γ = 2 n 0 [ ψ ( + 0 ) ] 2 - 0 n 0 i ( x ) exp [ 2 k ( n f 2 - n 0 2 ) 1 / 2 x ] d x k n f ( n f 2 - n 0 2 ) N { 1 ( 2 - n 0 2 / n f 2 ) ,             for TE modes for TM modes .
γ = n 0 n 0 c i [ ψ ( + 0 ) ] 2 k 2 n f ( n f 2 - n 0 2 ) 3 / 2 N { 1 ( 2 - n 0 2 / n f 2 ) ,             for TE modes for TM modes .
R = [ ψ ( + 0 ) ] 2 / N ,
n 2 ( x ) = { n 0 2 n f 2 - ( n f 2 - n s 2 ) x / d n s 2 ,             x < 0 0 < x d d x ,
ψ ( x ) = { a 1 exp ( η x ) A i [ χ ( x ) ] + a 2 B i [ χ ( x ) ] a 3 exp ( - σ x ) ,             x 0 0 x d d x .
V = d k ( n f 2 - n s 2 ) 1 / 2 ,
σ = ( β 2 - k 2 n s 2 ) 1 / 2 ,
ψ ( x ) { 0 x 0 A i [ χ ( x ) ] 0 x .
N = 0 A i 2 [ χ ( x ) ] d x = d V 2 / 3 χ m + 1 A i 2 ( χ ) d χ ,
A i ( χ m + 1 ) = 0 ,             m = 0 , 1 , 2 , .
β m = ( k 2 n f 2 + V 4 / 3 χ m + 1 / d 2 ) 1 / 2 .
N = d V - 2 / 3 { [ A i ( χ m + 1 ) ] 2 - χ m + 1 [ A i ( χ m + 1 ) 2 ] } = d V - 2 / 3 [ A i ( χ m + 1 ) ] 2 ,
d ψ d x | x = + 0 = V 2 / 3 d A i ( χ m + 1 ) .
γ = k n 0 c i n 0 V n f ( n f 2 - n s 2 n f 2 - n 0 2 ) 3 / 2 { 1 ( 2 - n 0 2 / n f 2 ) ,             for TE modes for TM modes .
γ N = γ / 2 k n 0 c i .
n 2 ( x ) = { n 0 2 n f 2 n s 2 ,             x < 0 0 < x < d d < x , }
ψ ( x ) = { 0 sin ( U x / d ) sin U exp [ W ( 1 - x / d ) ] ,             x 0 0 x d d x ,
γ = 2 k n 0 n 0 c i U 2 W n f V 3 ( 1 + W ) ( n f 2 - n s 2 n f 2 - n 0 2 ) 3 / 2 { 1 ( 2 - n 0 2 / n f 2 ) ,             for TE modes for TM modes .
γ = 2 k n 0 n 0 c i π 2 ( m + 1 ) 2 n f V 2 ( V + 3 ) ( n f 2 - n s 2 n f 2 - n 0 2 ) 3 / 2 { 1 ( 2 - n 0 2 / n f 2 ) ,             for TE modes for TM modes .
γ 2 k n 0 n 0 c i π 2 ( m + 1 ) 2 n f V 3 ( n f 2 - n s 2 n f 2 - n 0 2 ) 3 / 2 { 1 ( 2 - n 0 2 / n f 2 ) ,             for TE modes for TM modes .
γ k n 0 n 0 c i ( 2 V + π ) 2 2 n f V 3 ( n f 2 - n s 2 n f 2 - n 0 2 ) 3 / 2 { 1 ( 2 - n 0 2 / n f 2 ) ,             for TE modes for TM modes .
n 2 ( x ) = { n 0 2 n f 2 - ( n f 2 - n s 2 ) x 2 / d 2 n s 2 ,             x < 0 0 < x d d x ,
ψ ( x ) { 0 H 2 m + 1 ( x 2 w 0 ) exp ( - x 2 w 0 2 ) ,             x 0 x x ,             m = 0 , 1 , 2 , ,
γ = 4 ( 2 m + 1 ) ( 2 m ) ! k n 0 c i n 0 2 2 m ( m ! ) 2 π n f V 3 / 2 ( n f 2 - n s 2 n f 2 - n 0 2 ) 3 / 2 { 1 ( 2 - n 0 2 / n f 2 ) ,             for TE modes for TM modes .
( n 0 c i ) - 1 2 k ( n f 2 - n 0 2 ) 1 / 2 - 0 n 0 i ( x ) exp { 2 k ( n f 2 - n 0 2 ) 1 / 2 x } d x .
n ( x ) = { n 0 n f - Δ n f s [ ( x / d ) + b ( x / d ) 2 ] n s ,             x < 0 0 < x d d x ,
( d 2 d x 2 - η 2 ) ψ ( x ) = - k 2 Δ n 2 ( x ) ψ ( x ) + ζ n 2 ( x ) d ψ ( x ) d x d n 2 ( x ) d x ,
G ( x , x 0 ) = ( 2 π / η ) exp ( - η x - x 0 )
( d 2 d x 2 - η 2 ) G ( x , x 0 ) = - 4 π δ ( x - x 0 ) .
ψ ( x 0 ) = 1 η - + [ k 2 Δ n 2 ( x ) ψ ( x ) - ζ n 2 ( x ) d ψ d x d n 2 ( x ) d x ] × exp ( - η x - x 0 ) d x .
ψ ( x 0 < - ) = exp ( η x 0 ) η - + [ k 2 Δ n 2 ( x ) ψ ( x ) - ζ n 2 ( x ) d ψ ( x ) d x d n 2 ( x ) d x ] exp ( - η x ) d x .
n 2 ( x ) = n 0 2 + ( n f 2 - n 0 2 ) - x δ ( x ) d x + ( n f 2 - n s 2 ) g ( x ) ,
ψ ( x 0 < - ) = exp ( η x 0 ) η { 0 + [ k 2 Δ n 2 ( x ) ψ ( x ) - ζ ( n f 2 - n s 2 ) n 2 ( x ) d ψ ( x ) d x d g ( x ) d x ] × exp ( - η x ) d x - ζ n f 2 - n 0 2 n f 2 ψ ( + 0 ) }
k 2 Δ n 2 ( x ) ψ ¯ ( x ) - ζ ( n f 2 - n s 2 ) n 2 ( x ) d ψ ¯ ( x ) d x d g ( x ) d x = d 2 ψ ¯ ( x ) d x 2 - η ¯ 2 ψ ¯ ( x ) ,             x > 0 ,             ψ ¯ ( x = 0 ) = 0
ψ ( x 0 < - ) exp ( η x 0 ) η { 0 + [ η ¯ 2 ψ ¯ ( x ) - d 2 ψ ¯ ( x ) d x 2 ] × exp ( - η x ) d x - ζ n f 2 - n 0 2 n f 2 ψ ¯ ( 0 ) } .
ψ ( x 0 < - ) exp ( η x 0 ) η [ ψ ¯ ( 0 ) + η ¯ 2 - η 2 η 0 + d ψ ¯ d x × exp ( - η x ) d x - ζ n f 2 - n 0 2 n f 2 ψ ¯ ( 0 ) ] .
ψ ( x < 0 ) exp ( η x ) η ψ ( 0 ) { 1 n 0 2 / n f 2 ,             for TE modes for TM modes .

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