Abstract

We describe the analysis of heat flow in a type of tunable optical fiber grating that uses thin-film resistive heaters microfabricated on the surface of the fiber. The high rate of heat loss from these microstructures and the relatively low thermal diffusivity of the glass yield unusual thermal properties. Approximate one-dimensional analytical calculations capture important aspects of the thermal characteristics of these systems. Comparison with experimental results that we obtained from devices with established designs validates certain features of the computations. This modeling also establishes the suitability of integrated thin-film heaters for several new types of tunable fiber grating devices.

© 2000 Optical Society of America

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  1. J. A. Rogers, R. J. Jackman, G. M. Whitesides, “Constructing single and multiple helical microcoils and characterizing their performance as components of microinductors and microelectromagnets,” J. Microelectromech. Syst. 6, 184–192 (1997).
    [Crossref]
  2. J. A. Rogers, R. J. Jackman, J. L. Wagener, A. M. Vengsarkar, G. M. Whitesides, “Using microcontact printing to generate photomasks on the surface of optical fibers: a new method for producing in-fiber gratings,” Appl. Phys. Lett. 70, 7–9 (1997).
    [Crossref]
  3. R. J. Jackman, G. M. Whitesides, “Electrochemistry and soft lithography: a route to 3-D,” Chem. Technol. 29, 18–30 (1999).
  4. J. A. Rogers, R. J. Jackman, G. M. Whitesides, D. L. Olson, J. V. Sweedler, “Using microcontact printing to fabricate microcoils on capillaries for high resolution 1H-NMR on nanoliter volumes,” Appl. Phys. Lett. 70, 2464–2466 (1997).
    [Crossref]
  5. G. R. Fox, C. A. P. Muller, N. Setter, N. H. Ky, H. G. Limberger, “Sputter deposited piezoelectric fiber coatings for acousto-optic modulators,” J. Vac. Sci. Technol. A 14, 800–805 (1996).
    [Crossref]
  6. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
    [Crossref]
  7. G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
    [Crossref]
  8. H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
    [Crossref]
  9. J. A. Rogers, B. J. Eggleton, R. J. Jackman, G. R. Kowach, T. A. Strasser, “Dual on-fiber thin-film heaters for fiber gratings with independently adjustable chirp and wavelength,” Opt. Lett. 24, 1328–1330 (1999).
    [Crossref]
  10. J. A. Rogers, B. J. Eggleton, J. R. Pedrazzani, T. A. Strasser, “Distributed on-fiber thin film heaters for Bragg gratings with adjustable chirp,” Appl. Phys. Lett. 74, 3131–3133 (1999).
    [Crossref]
  11. B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Electrically tunable, power efficient dispersion compensating fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 854–856 (1999).
    [Crossref]
  12. T. Strasser, Lucent Technologies, Murray Hill, N.J. 07974 (personal communication, 1999).
  13. B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
    [Crossref]
  14. T. Nielsen, B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Fiber Bragg grating tunable dispersion compensator for dynamic post dispersion optimization at 40 Gb/s,” IEEE Photon. Technol. Lett. 12, 173–175 (2000).
    [Crossref]
  15. B. Mikkelsen, Lucent Technologies, Holmdel, N.J. 07733 (personal communication, 1999).
  16. S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
    [Crossref]
  17. D. M. Costantini, H. G. Limberger, R. P. Salathe, C. A. P. Muller, S. A. Vasiliov, “Tunable loss filter based on metal coated long period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1460 (1999).
    [Crossref]
  18. M. N. Özisik, Heat Transfer: a Basic Approach (McGraw-Hill, New York, 1985).
  19. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford U. Press, London, 1959).
  20. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).
  21. R. V. Churchill, Operational Mathematics, 3rd ed. (McGraw-Hill, New York, 1972).
  22. A. F. Mills, Heat Transfer (Irwin, Boston, 1992).
  23. D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 78th ed. (CRC Press, Boca Raton, Fla., 1997).
  24. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  25. H. Kogelnik, C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
    [Crossref]
  26. J. T. Kringlebotn, J.-L. Archambault, L. Reekie, D. N. Payne, “Er3 + Yb3+ codoped fiber distributed-feedback laser,” Opt. Lett. 19, 2101–2103 (1994).
    [Crossref] [PubMed]
  27. B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
    [Crossref]
  28. T. Salamon, Lucent Technologies, Murray Hill, N.J. 07974 (personal communication, 2000).
  29. J. A. Rogers, B. J. Eggleton, T. A. Strasser, “Temperature stabilized operation of tunable fiber grating devices that use distributed on-fiber thin film heaters,” Electron. Lett. 35, 2052–2053 (1999).
    [Crossref]

2000 (1)

T. Nielsen, B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Fiber Bragg grating tunable dispersion compensator for dynamic post dispersion optimization at 40 Gb/s,” IEEE Photon. Technol. Lett. 12, 173–175 (2000).
[Crossref]

1999 (9)

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

D. M. Costantini, H. G. Limberger, R. P. Salathe, C. A. P. Muller, S. A. Vasiliov, “Tunable loss filter based on metal coated long period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1460 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, T. A. Strasser, “Temperature stabilized operation of tunable fiber grating devices that use distributed on-fiber thin film heaters,” Electron. Lett. 35, 2052–2053 (1999).
[Crossref]

R. J. Jackman, G. M. Whitesides, “Electrochemistry and soft lithography: a route to 3-D,” Chem. Technol. 29, 18–30 (1999).

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, J. R. Pedrazzani, T. A. Strasser, “Distributed on-fiber thin film heaters for Bragg gratings with adjustable chirp,” Appl. Phys. Lett. 74, 3131–3133 (1999).
[Crossref]

B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Electrically tunable, power efficient dispersion compensating fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 854–856 (1999).
[Crossref]

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, R. J. Jackman, G. R. Kowach, T. A. Strasser, “Dual on-fiber thin-film heaters for fiber gratings with independently adjustable chirp and wavelength,” Opt. Lett. 24, 1328–1330 (1999).
[Crossref]

1998 (1)

H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
[Crossref]

1997 (4)

G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, G. M. Whitesides, D. L. Olson, J. V. Sweedler, “Using microcontact printing to fabricate microcoils on capillaries for high resolution 1H-NMR on nanoliter volumes,” Appl. Phys. Lett. 70, 2464–2466 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, G. M. Whitesides, “Constructing single and multiple helical microcoils and characterizing their performance as components of microinductors and microelectromagnets,” J. Microelectromech. Syst. 6, 184–192 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, J. L. Wagener, A. M. Vengsarkar, G. M. Whitesides, “Using microcontact printing to generate photomasks on the surface of optical fibers: a new method for producing in-fiber gratings,” Appl. Phys. Lett. 70, 7–9 (1997).
[Crossref]

1996 (1)

G. R. Fox, C. A. P. Muller, N. Setter, N. H. Ky, H. G. Limberger, “Sputter deposited piezoelectric fiber coatings for acousto-optic modulators,” J. Vac. Sci. Technol. A 14, 800–805 (1996).
[Crossref]

1994 (2)

B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

J. T. Kringlebotn, J.-L. Archambault, L. Reekie, D. N. Payne, “Er3 + Yb3+ codoped fiber distributed-feedback laser,” Opt. Lett. 19, 2101–2103 (1994).
[Crossref] [PubMed]

1972 (1)

H. Kogelnik, C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[Crossref]

Abramov, A.

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

Albert, J.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

Archambault, J.-L.

Bilodeau, F.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford U. Press, London, 1959).

Churchill, R. V.

R. V. Churchill, Operational Mathematics, 3rd ed. (McGraw-Hill, New York, 1972).

Costantini, D. M.

D. M. Costantini, H. G. Limberger, R. P. Salathe, C. A. P. Muller, S. A. Vasiliov, “Tunable loss filter based on metal coated long period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1460 (1999).
[Crossref]

H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
[Crossref]

Dreyer, K. F.

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

Eggleton, B. J.

T. Nielsen, B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Fiber Bragg grating tunable dispersion compensator for dynamic post dispersion optimization at 40 Gb/s,” IEEE Photon. Technol. Lett. 12, 173–175 (2000).
[Crossref]

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, J. R. Pedrazzani, T. A. Strasser, “Distributed on-fiber thin film heaters for Bragg gratings with adjustable chirp,” Appl. Phys. Lett. 74, 3131–3133 (1999).
[Crossref]

B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Electrically tunable, power efficient dispersion compensating fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 854–856 (1999).
[Crossref]

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, T. A. Strasser, “Temperature stabilized operation of tunable fiber grating devices that use distributed on-fiber thin film heaters,” Electron. Lett. 35, 2052–2053 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, R. J. Jackman, G. R. Kowach, T. A. Strasser, “Dual on-fiber thin-film heaters for fiber gratings with independently adjustable chirp and wavelength,” Opt. Lett. 24, 1328–1330 (1999).
[Crossref]

B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Espindola, R. P.

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Fox, G. R.

H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, N. H. Ky, H. G. Limberger, “Sputter deposited piezoelectric fiber coatings for acousto-optic modulators,” J. Vac. Sci. Technol. A 14, 800–805 (1996).
[Crossref]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

Hale, A.

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

Hansen, P. B.

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

Hill, K. O.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

Jackman, R. J.

R. J. Jackman, G. M. Whitesides, “Electrochemistry and soft lithography: a route to 3-D,” Chem. Technol. 29, 18–30 (1999).

J. A. Rogers, B. J. Eggleton, R. J. Jackman, G. R. Kowach, T. A. Strasser, “Dual on-fiber thin-film heaters for fiber gratings with independently adjustable chirp and wavelength,” Opt. Lett. 24, 1328–1330 (1999).
[Crossref]

J. A. Rogers, R. J. Jackman, G. M. Whitesides, D. L. Olson, J. V. Sweedler, “Using microcontact printing to fabricate microcoils on capillaries for high resolution 1H-NMR on nanoliter volumes,” Appl. Phys. Lett. 70, 2464–2466 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, G. M. Whitesides, “Constructing single and multiple helical microcoils and characterizing their performance as components of microinductors and microelectromagnets,” J. Microelectromech. Syst. 6, 184–192 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, J. L. Wagener, A. M. Vengsarkar, G. M. Whitesides, “Using microcontact printing to generate photomasks on the surface of optical fibers: a new method for producing in-fiber gratings,” Appl. Phys. Lett. 70, 7–9 (1997).
[Crossref]

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford U. Press, London, 1959).

Johnson, D. C.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

Kogelnik, H.

H. Kogelnik, C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[Crossref]

Kowach, G. R.

Kringlebotn, J. T.

Krug, P. A.

B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Ky, N. H.

H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, N. H. Ky, H. G. Limberger, “Sputter deposited piezoelectric fiber coatings for acousto-optic modulators,” J. Vac. Sci. Technol. A 14, 800–805 (1996).
[Crossref]

Limberger, H. G.

D. M. Costantini, H. G. Limberger, R. P. Salathe, C. A. P. Muller, S. A. Vasiliov, “Tunable loss filter based on metal coated long period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1460 (1999).
[Crossref]

H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, N. H. Ky, H. G. Limberger, “Sputter deposited piezoelectric fiber coatings for acousto-optic modulators,” J. Vac. Sci. Technol. A 14, 800–805 (1996).
[Crossref]

Mihailov, S. J.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

Mikkelsen, B.

B. Mikkelsen, Lucent Technologies, Holmdel, N.J. 07733 (personal communication, 1999).

Mills, A. F.

A. F. Mills, Heat Transfer (Irwin, Boston, 1992).

Muller, C. A. P.

D. M. Costantini, H. G. Limberger, R. P. Salathe, C. A. P. Muller, S. A. Vasiliov, “Tunable loss filter based on metal coated long period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1460 (1999).
[Crossref]

H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, N. H. Ky, H. G. Limberger, “Sputter deposited piezoelectric fiber coatings for acousto-optic modulators,” J. Vac. Sci. Technol. A 14, 800–805 (1996).
[Crossref]

Nielsen, T.

T. Nielsen, B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Fiber Bragg grating tunable dispersion compensator for dynamic post dispersion optimization at 40 Gb/s,” IEEE Photon. Technol. Lett. 12, 173–175 (2000).
[Crossref]

Nielsen, T. N.

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

Olson, D. L.

J. A. Rogers, R. J. Jackman, G. M. Whitesides, D. L. Olson, J. V. Sweedler, “Using microcontact printing to fabricate microcoils on capillaries for high resolution 1H-NMR on nanoliter volumes,” Appl. Phys. Lett. 70, 2464–2466 (1997).
[Crossref]

Ouellette, F.

B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Özisik, M. N.

M. N. Özisik, Heat Transfer: a Basic Approach (McGraw-Hill, New York, 1985).

Payne, D. N.

Pedrazzani, J. R.

J. A. Rogers, B. J. Eggleton, J. R. Pedrazzani, T. A. Strasser, “Distributed on-fiber thin film heaters for Bragg gratings with adjustable chirp,” Appl. Phys. Lett. 74, 3131–3133 (1999).
[Crossref]

Poladian, L.

B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Reekie, L.

Rogers, J. A.

T. Nielsen, B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Fiber Bragg grating tunable dispersion compensator for dynamic post dispersion optimization at 40 Gb/s,” IEEE Photon. Technol. Lett. 12, 173–175 (2000).
[Crossref]

J. A. Rogers, B. J. Eggleton, J. R. Pedrazzani, T. A. Strasser, “Distributed on-fiber thin film heaters for Bragg gratings with adjustable chirp,” Appl. Phys. Lett. 74, 3131–3133 (1999).
[Crossref]

B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Electrically tunable, power efficient dispersion compensating fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 854–856 (1999).
[Crossref]

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, T. A. Strasser, “Temperature stabilized operation of tunable fiber grating devices that use distributed on-fiber thin film heaters,” Electron. Lett. 35, 2052–2053 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, R. J. Jackman, G. R. Kowach, T. A. Strasser, “Dual on-fiber thin-film heaters for fiber gratings with independently adjustable chirp and wavelength,” Opt. Lett. 24, 1328–1330 (1999).
[Crossref]

J. A. Rogers, R. J. Jackman, G. M. Whitesides, D. L. Olson, J. V. Sweedler, “Using microcontact printing to fabricate microcoils on capillaries for high resolution 1H-NMR on nanoliter volumes,” Appl. Phys. Lett. 70, 2464–2466 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, G. M. Whitesides, “Constructing single and multiple helical microcoils and characterizing their performance as components of microinductors and microelectromagnets,” J. Microelectromech. Syst. 6, 184–192 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, J. L. Wagener, A. M. Vengsarkar, G. M. Whitesides, “Using microcontact printing to generate photomasks on the surface of optical fibers: a new method for producing in-fiber gratings,” Appl. Phys. Lett. 70, 7–9 (1997).
[Crossref]

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

Salamon, T.

T. Salamon, Lucent Technologies, Murray Hill, N.J. 07974 (personal communication, 2000).

Salathe, R. P.

D. M. Costantini, H. G. Limberger, R. P. Salathe, C. A. P. Muller, S. A. Vasiliov, “Tunable loss filter based on metal coated long period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1460 (1999).
[Crossref]

H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
[Crossref]

Setter, N.

G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
[Crossref]

G. R. Fox, C. A. P. Muller, N. Setter, N. H. Ky, H. G. Limberger, “Sputter deposited piezoelectric fiber coatings for acousto-optic modulators,” J. Vac. Sci. Technol. A 14, 800–805 (1996).
[Crossref]

Shank, C. V.

H. Kogelnik, C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[Crossref]

Shu, C.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

Strasser, T.

T. Strasser, Lucent Technologies, Murray Hill, N.J. 07974 (personal communication, 1999).

Strasser, T. A.

T. Nielsen, B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Fiber Bragg grating tunable dispersion compensator for dynamic post dispersion optimization at 40 Gb/s,” IEEE Photon. Technol. Lett. 12, 173–175 (2000).
[Crossref]

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Electrically tunable, power efficient dispersion compensating fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 854–856 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, J. R. Pedrazzani, T. A. Strasser, “Distributed on-fiber thin film heaters for Bragg gratings with adjustable chirp,” Appl. Phys. Lett. 74, 3131–3133 (1999).
[Crossref]

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, T. A. Strasser, “Temperature stabilized operation of tunable fiber grating devices that use distributed on-fiber thin film heaters,” Electron. Lett. 35, 2052–2053 (1999).
[Crossref]

J. A. Rogers, B. J. Eggleton, R. J. Jackman, G. R. Kowach, T. A. Strasser, “Dual on-fiber thin-film heaters for fiber gratings with independently adjustable chirp and wavelength,” Opt. Lett. 24, 1328–1330 (1999).
[Crossref]

Stryckman, D.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

Sweedler, J. V.

J. A. Rogers, R. J. Jackman, G. M. Whitesides, D. L. Olson, J. V. Sweedler, “Using microcontact printing to fabricate microcoils on capillaries for high resolution 1H-NMR on nanoliter volumes,” Appl. Phys. Lett. 70, 2464–2466 (1997).
[Crossref]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Vasiliov, S. A.

D. M. Costantini, H. G. Limberger, R. P. Salathe, C. A. P. Muller, S. A. Vasiliov, “Tunable loss filter based on metal coated long period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1460 (1999).
[Crossref]

Vengsarkar, A. M.

J. A. Rogers, R. J. Jackman, J. L. Wagener, A. M. Vengsarkar, G. M. Whitesides, “Using microcontact printing to generate photomasks on the surface of optical fibers: a new method for producing in-fiber gratings,” Appl. Phys. Lett. 70, 7–9 (1997).
[Crossref]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Wagener, J. L.

J. A. Rogers, R. J. Jackman, J. L. Wagener, A. M. Vengsarkar, G. M. Whitesides, “Using microcontact printing to generate photomasks on the surface of optical fibers: a new method for producing in-fiber gratings,” Appl. Phys. Lett. 70, 7–9 (1997).
[Crossref]

Westbrook, P. S.

T. Nielsen, B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Fiber Bragg grating tunable dispersion compensator for dynamic post dispersion optimization at 40 Gb/s,” IEEE Photon. Technol. Lett. 12, 173–175 (2000).
[Crossref]

B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Electrically tunable, power efficient dispersion compensating fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 854–856 (1999).
[Crossref]

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

Whitesides, G. M.

R. J. Jackman, G. M. Whitesides, “Electrochemistry and soft lithography: a route to 3-D,” Chem. Technol. 29, 18–30 (1999).

J. A. Rogers, R. J. Jackman, G. M. Whitesides, D. L. Olson, J. V. Sweedler, “Using microcontact printing to fabricate microcoils on capillaries for high resolution 1H-NMR on nanoliter volumes,” Appl. Phys. Lett. 70, 2464–2466 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, J. L. Wagener, A. M. Vengsarkar, G. M. Whitesides, “Using microcontact printing to generate photomasks on the surface of optical fibers: a new method for producing in-fiber gratings,” Appl. Phys. Lett. 70, 7–9 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, G. M. Whitesides, “Constructing single and multiple helical microcoils and characterizing their performance as components of microinductors and microelectromagnets,” J. Microelectromech. Syst. 6, 184–192 (1997).
[Crossref]

Windeler, R. S.

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

Appl. Phys. Lett. (3)

J. A. Rogers, R. J. Jackman, J. L. Wagener, A. M. Vengsarkar, G. M. Whitesides, “Using microcontact printing to generate photomasks on the surface of optical fibers: a new method for producing in-fiber gratings,” Appl. Phys. Lett. 70, 7–9 (1997).
[Crossref]

J. A. Rogers, R. J. Jackman, G. M. Whitesides, D. L. Olson, J. V. Sweedler, “Using microcontact printing to fabricate microcoils on capillaries for high resolution 1H-NMR on nanoliter volumes,” Appl. Phys. Lett. 70, 2464–2466 (1997).
[Crossref]

J. A. Rogers, B. J. Eggleton, J. R. Pedrazzani, T. A. Strasser, “Distributed on-fiber thin film heaters for Bragg gratings with adjustable chirp,” Appl. Phys. Lett. 74, 3131–3133 (1999).
[Crossref]

Chem. Technol. (1)

R. J. Jackman, G. M. Whitesides, “Electrochemistry and soft lithography: a route to 3-D,” Chem. Technol. 29, 18–30 (1999).

Electron. Lett. (3)

B. J. Eggleton, T. N. Nielsen, J. A. Rogers, P. S. Westbrook, T. A. Strasser, P. B. Hansen, K. F. Dreyer, “Dispersion compensation in a dynamic 20 Gbit/s nonlinear lightwave system using electrically tunable chirped fiber grating,” Electron. Lett. 35, 832–833 (1999).
[Crossref]

B. J. Eggleton, P. A. Krug, L. Poladian, F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

J. A. Rogers, B. J. Eggleton, T. A. Strasser, “Temperature stabilized operation of tunable fiber grating devices that use distributed on-fiber thin film heaters,” Electron. Lett. 35, 2052–2053 (1999).
[Crossref]

IEEE Photon. Technol. Lett. (6)

T. Nielsen, B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Fiber Bragg grating tunable dispersion compensator for dynamic post dispersion optimization at 40 Gb/s,” IEEE Photon. Technol. Lett. 12, 173–175 (2000).
[Crossref]

B. J. Eggleton, J. A. Rogers, P. S. Westbrook, T. A. Strasser, “Electrically tunable, power efficient dispersion compensating fiber Bragg grating,” IEEE Photon. Technol. Lett. 11, 854–856 (1999).
[Crossref]

A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broadband long-period fiber grating filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[Crossref]

H. G. Limberger, N. H. Ky, D. M. Costantini, R. P. Salathe, C. A. P. Muller, G. R. Fox, “Efficient miniature fiber-optic tunable filter based on intracore Bragg grating and electrically resistive coating,” IEEE Photon. Technol. Lett. 10, 361–363 (1998).
[Crossref]

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, D. Stryckman, C. Shu, “Comparison of fiber Bragg grating dispersion-compensators made with holographic and E-beam written phase masks,” IEEE Photon. Technol. Lett. 11, 572–574 (1999).
[Crossref]

D. M. Costantini, H. G. Limberger, R. P. Salathe, C. A. P. Muller, S. A. Vasiliov, “Tunable loss filter based on metal coated long period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1460 (1999).
[Crossref]

J. Appl. Phys. (1)

H. Kogelnik, C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972).
[Crossref]

J. Microelectromech. Syst. (1)

J. A. Rogers, R. J. Jackman, G. M. Whitesides, “Constructing single and multiple helical microcoils and characterizing their performance as components of microinductors and microelectromagnets,” J. Microelectromech. Syst. 6, 184–192 (1997).
[Crossref]

J. Vac. Sci. Technol. (1)

G. R. Fox, C. A. P. Muller, N. Setter, D. M. Costantini, N. H. Ky, H. G. Limberger, “Wavelength tunable fiber Bragg grating devices based on sputter deposited resistive and piezoelectric coatings,” J. Vac. Sci. Technol. 15, 1791–1795 (1997).
[Crossref]

J. Vac. Sci. Technol. A (1)

G. R. Fox, C. A. P. Muller, N. Setter, N. H. Ky, H. G. Limberger, “Sputter deposited piezoelectric fiber coatings for acousto-optic modulators,” J. Vac. Sci. Technol. A 14, 800–805 (1996).
[Crossref]

Opt. Lett. (2)

Other (10)

T. Salamon, Lucent Technologies, Murray Hill, N.J. 07974 (personal communication, 2000).

T. Strasser, Lucent Technologies, Murray Hill, N.J. 07974 (personal communication, 1999).

B. Mikkelsen, Lucent Technologies, Holmdel, N.J. 07733 (personal communication, 1999).

M. N. Özisik, Heat Transfer: a Basic Approach (McGraw-Hill, New York, 1985).

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford U. Press, London, 1959).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

R. V. Churchill, Operational Mathematics, 3rd ed. (McGraw-Hill, New York, 1972).

A. F. Mills, Heat Transfer (Irwin, Boston, 1992).

D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 78th ed. (CRC Press, Boca Raton, Fla., 1997).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

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Figures (10)

Fig. 1
Fig. 1

Schematic illustrations of three thermally actuated fiber devices that use integrated thin-film heaters. Devices in (a), (b), and (c) rely on uniform, tapered, and multilayer geometries to adjust the temperature and gradients in temperature in the fiber. The temperature changes affect the optical characteristics of gratings in the cores of the fibers.

Fig. 2
Fig. 2

(a) Reflectivity spectra of a thermally tuned, ∼4-cm-long unchirped fiber Bragg grating that uses a thin-film on-fiber heater. The spectra shift uniformly by an amount proportional to the change in temperature induced in the core of the fiber by joule heating in the thin film. (b) The shift as a function of applied electrical power. The data indicate a tuning power efficiency of ∼0.03 Å/mW.

Fig. 3
Fig. 3

(a) and (b) Spectral reflectivity and group delays, respectively, for a thermally tunable, ∼4-cm-long fiber Bragg grating. Data were recorded at various voltages applied to thin-film heaters formed on the bare surface of the fiber. When we overlap spectra by linearly translating them along the x axis, it illustrates that the reflectivity and group-delay characteristics shift uniformly during tuning.

Fig. 4
Fig. 4

Rise time of a thermally tuned fiber Bragg grating that uses a thin-film on-fiber resistive heater. Data were collected with four different heating powers applied suddenly at t = 0 s: 47 mW (squares), 92 mW (circles), 142 mW (up triangles), and 210 mW (down triangles). The curves correspond to fits that use single exponential forms. The time constants determined from these fits show no systematic dependence on applied power.

Fig. 5
Fig. 5

(a) and (b) Spectral reflectivity and group delay, respectively, of a tunable dispersion compensator formed with a linearly chirped fiber Bragg grating and a tapered distributed thin-film heater. In this device, thermal gradients established when current passes through the tapered film increase the chirp rate of the grating, which leads to an increase in the width of the reflection band and a decrease in the slope of the group delay. The coating is designed to produce a linear variation in temperature along the length of the fiber that contains the grating: Its thickness varies inversely with position. The linearity of the group delays at all voltages provides evidence for a linear temperature distribution. The straight dashed lines in (b) represent linear fits to the data. The ratio of the shift of the short to the long wavelength sides of the reflection spectra is ∼1:9, a value that is roughly consistent with the 1:10 variation in the thickness of the coating.

Fig. 6
Fig. 6

(a) Time dependence of distributions of temperature in a segment of optical fiber heated with an input power that varies linearly between x = 0.0 and 10.0 cm. The dotted line shows the geometry of the heating. The inset shows the calculated temporal evolution of the spatial slope in temperature (symbols) and a single exponential rise computed with a time constant of 2.5 s-1 (curve). (b) Time dependence of distributions of temperature near x = 10.0 cm. Thermal diffusion along the length of the fiber causes the spatial profile of the rise in temperature to deviate from the geometry of the heating (dotted line). The inset shows the temporal evolution of the change in temperature evaluated at x = 9.75 and 10.0 cm. The solid curves correspond to single exponential rises in temperature with time constants of 2.5 s-1.

Fig. 7
Fig. 7

Computed distributions of temperature in optical fiber heated with an input power that varies linearly with position between x = 0.0 and x = 10.0 cm. The results shown here are for three different values of the ratio of the heat loss parameter a to the thermal diffusivity κ, where a/κ = 2.5 mm-2 corresponds, approximately, to a glass fiber heated with a thin metal coating; and a/κ = 0.025 mm-2 represents the case of a solid metal fiber with a value of a that is similar to the one measured for the glass fiber (i.e., a ∼ 2.5 s-1). The curves demonstrate that thermal diffusion can be important for large κ or small a. The dashed curve shows the geometry of the heating.

Fig. 8
Fig. 8

(a) and (b) Computed temperature profiles for heating powers that vary linearly and inversely with position along the fiber, respectively. For these short gratings, it is clear that thermal diffusion along the fiber can be important. For a given value of a, the significance of this diffusion increases with κ. These results motivate, in part, modeling that explicitly accounts for the thermal effects of the thin metal coatings in fiber-optic devices that use integrated resistive heaters.

Fig. 9
Fig. 9

Computed temperature profiles for optical fiber heated by thin films centered at x = 0.0 cm and with various widths. The dotted line shows the geometry of a heater with a width of 0.8 cm. The solid curves show the temperature distributions. As the widths of the heaters decrease, the amplitudes and widths (full width at half-maximum, FWHM) of the temperature changes also decrease. The width of the change in temperature does not decrease, however, significantly below ∼0.1 cm. The thermal diffusivity of the glass and the rate of heat loss from the fiber establish this length scale.

Fig. 10
Fig. 10

Computed temperature profiles for optical fiber heated by thin films that generate heating at rates that vary by a factor of 100 in periodic (wavelength λ) fashion along the length of the fiber. In these cases, the widths of the strongly heated regions (<0.1 cm) are much narrower than the distances between them. Heaters with geometries such as these maximize the depth of modulation (D.O.M.) of the temperature.

Equations (12)

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

Tx, tt=κ 2Tx, tx2+Pinx, t-Poutx, tρcpπRfiber2,
Poutx, t=2πRfiberhTx, t,
Poutx, tρcpπRfiber2=aTx, t.
a=2hρcpRfiber.
t¯α, s=12π-0 Tx, texp-iαxexp-stdtdx,
t¯α, s=pinαs1s+κα2+a.
tx, s=12π- Pinzdz -1s1s+κα2+aexpiαx-zdα.
tx, s=12κ- Pinzdz 1s1s + a×exp-|x-z|κs + a.
Tx, t=12πκ- Pinzdz 0t1τexp-aτ-x-z24κτdτ.
Tt=Pina1-exp-at.
Tx, t=12aκ- Pinzexp-a/κ |x-z|dz.
Tx, t  exp-a/κ |x|.

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