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]

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, 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]

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.

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]

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, 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]

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, 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]

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]

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, 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, 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]

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]

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, 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]

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]

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)

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]

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]

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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