Abstract

Temperature sensitivity of optical parameters is an important issue in developing optoelectronic devices. It can dramatically affect the optical performance of interferometric devices, such as arrayed waveguides. Applying thermal stress is a promising method to control temperature effects. In this paper, a general method to study thermal-stress effects on the temperature sensitivity of the effective refractive index is developed. The temperature sensitivities of the effective refractive index of planar waveguides and channel waveguides are obtained theoretically. The thermal-stress effects on the central-wavelength shift are discussed. It is shown that the temperature sensitivity of optical waveguides could be controlled by thermal stresses.

© 2003 Optical Society of America

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  1. Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55 μm wavelength using a silica based athermal waveguide,” Electron. Lett. 34, 367–369 (1998).
    [CrossRef]
  2. N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
    [CrossRef]
  3. A. Kaneko, S. Kamei, Y. Inoue, H. Takahashi, and A. Sugita, “Athermal silica-based arrayed-waveguide grating (AWG) multi/demultiplexers with new low loss groove design,” Electron. Lett. 36, 318–319 (2000).
    [CrossRef]
  4. Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
    [CrossRef]
  5. N. Ooba, Y. Hibino, Y. Inoue, and A. Sugita, “Athermal silica-based arrayed-waveguide grating multiplexer using bimetal plate temperature compensator,” Electron. Lett. 36, 1800–1801 (2000).
    [CrossRef]
  6. D. A. Cohen, M. E. Heimbuch, and L. A. Coldren, “Reduced temperature sensitivity of the wavelength of a diode laser in a stress-engineered hydrostatic package,” Appl. Phys. Lett. 69, 455–457 (1996).
    [CrossRef]
  7. D. A. Cohen, B. Mason, J. Dolan, C. Burns, and L. A. Coldren, “Enhanced wavelength tuning of an InGasP-InP laser with a thermal-strain-magnifying trench,” Appl. Phys. Lett. 77, 2629–2631 (2000).
    [CrossRef]
  8. M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40, 1615–1632 (2003).
    [CrossRef]
  9. W. L. Wolfe, “Properties of optical materials,” in Handbook of Optics, W. G. Driscoll and W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 7.
  10. T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, “Temperature dependence of the refractive index of diamond up to 925 K,” Phys. Rev. B 62, 16578–16581 (2000).
    [CrossRef]
  11. S. S. Ballard, J. S. Browder, and J. F. Ebersole, “Refractive index of special crystals and certain glasses,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), Chap. 6.
  12. F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77, 1614–1616 (2000).
    [CrossRef]
  13. F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
    [CrossRef]
  14. J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, New York, 1992).
  15. J. Sapriel, Acousto-Optics (Wiley, New York, 1976).
  16. P. Hlídek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
    [CrossRef]
  17. U. Tisch, B. Meyler, O. Katz, E. Finlman, and J. Salzman, “Dependence of the refractive index of AlxGa1−xN on temperature and composition at elevated temperatures,” J. Appl. Phys. 89, 2676–2685 (2001).
    [CrossRef]
  18. J. T. Boyd, “Photonic integrated circuits,” in Photonic Devices and Systems, R. G. Hunsperger, eds. (Marcel Dekker, New York, 1994), pp. 313–375.
  19. D. Lee, Electromagnetic Principles of Integrated Optics (Wiley, New York, 1986).
  20. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, New York, 1989).
  21. X. Yan and M. Huang, “A thermal design of arrayed waveguide gratings,” presented at 2002 ASME International Mechanical Engineering Congress, New Orleans, La., November 2002.
  22. X. Yan, “Underfill selection and its impact on the reliability of flip chip assembles,” presented at the Delphi Automotive Systems Analytical Design Forum, Kokomo, Indiana, March 1999.

2003 (1)

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40, 1615–1632 (2003).
[CrossRef]

2001 (3)

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

P. Hlídek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

U. Tisch, B. Meyler, O. Katz, E. Finlman, and J. Salzman, “Dependence of the refractive index of AlxGa1−xN on temperature and composition at elevated temperatures,” J. Appl. Phys. 89, 2676–2685 (2001).
[CrossRef]

2000 (6)

D. A. Cohen, B. Mason, J. Dolan, C. Burns, and L. A. Coldren, “Enhanced wavelength tuning of an InGasP-InP laser with a thermal-strain-magnifying trench,” Appl. Phys. Lett. 77, 2629–2631 (2000).
[CrossRef]

A. Kaneko, S. Kamei, Y. Inoue, H. Takahashi, and A. Sugita, “Athermal silica-based arrayed-waveguide grating (AWG) multi/demultiplexers with new low loss groove design,” Electron. Lett. 36, 318–319 (2000).
[CrossRef]

N. Ooba, Y. Hibino, Y. Inoue, and A. Sugita, “Athermal silica-based arrayed-waveguide grating multiplexer using bimetal plate temperature compensator,” Electron. Lett. 36, 1800–1801 (2000).
[CrossRef]

T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, “Temperature dependence of the refractive index of diamond up to 925 K,” Phys. Rev. B 62, 16578–16581 (2000).
[CrossRef]

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77, 1614–1616 (2000).
[CrossRef]

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[CrossRef]

1998 (1)

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55 μm wavelength using a silica based athermal waveguide,” Electron. Lett. 34, 367–369 (1998).
[CrossRef]

1997 (1)

Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
[CrossRef]

1996 (1)

D. A. Cohen, M. E. Heimbuch, and L. A. Coldren, “Reduced temperature sensitivity of the wavelength of a diode laser in a stress-engineered hydrostatic package,” Appl. Phys. Lett. 69, 455–457 (1996).
[CrossRef]

Bauer, J.

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

Bauer, M.

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

Bok, J.

P. Hlídek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

Burns, C.

D. A. Cohen, B. Mason, J. Dolan, C. Burns, and L. A. Coldren, “Enhanced wavelength tuning of an InGasP-InP laser with a thermal-strain-magnifying trench,” Appl. Phys. Lett. 77, 2629–2631 (2000).
[CrossRef]

Cardona, M.

T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, “Temperature dependence of the refractive index of diamond up to 925 K,” Phys. Rev. B 62, 16578–16581 (2000).
[CrossRef]

Cocorullo, G.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[CrossRef]

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77, 1614–1616 (2000).
[CrossRef]

Cohen, D. A.

D. A. Cohen, B. Mason, J. Dolan, C. Burns, and L. A. Coldren, “Enhanced wavelength tuning of an InGasP-InP laser with a thermal-strain-magnifying trench,” Appl. Phys. Lett. 77, 2629–2631 (2000).
[CrossRef]

D. A. Cohen, M. E. Heimbuch, and L. A. Coldren, “Reduced temperature sensitivity of the wavelength of a diode laser in a stress-engineered hydrostatic package,” Appl. Phys. Lett. 69, 455–457 (1996).
[CrossRef]

Coldren, L. A.

D. A. Cohen, B. Mason, J. Dolan, C. Burns, and L. A. Coldren, “Enhanced wavelength tuning of an InGasP-InP laser with a thermal-strain-magnifying trench,” Appl. Phys. Lett. 77, 2629–2631 (2000).
[CrossRef]

D. A. Cohen, M. E. Heimbuch, and L. A. Coldren, “Reduced temperature sensitivity of the wavelength of a diode laser in a stress-engineered hydrostatic package,” Appl. Phys. Lett. 69, 455–457 (1996).
[CrossRef]

Della Corte, F. G.

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77, 1614–1616 (2000).
[CrossRef]

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[CrossRef]

Dolan, J.

D. A. Cohen, B. Mason, J. Dolan, C. Burns, and L. A. Coldren, “Enhanced wavelength tuning of an InGasP-InP laser with a thermal-strain-magnifying trench,” Appl. Phys. Lett. 77, 2629–2631 (2000).
[CrossRef]

Dreyer, C.

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

Finlman, E.

U. Tisch, B. Meyler, O. Katz, E. Finlman, and J. Salzman, “Dependence of the refractive index of AlxGa1−xN on temperature and composition at elevated temperatures,” J. Appl. Phys. 89, 2676–2685 (2001).
[CrossRef]

Franc, J.

P. Hlídek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

Grill, R.

P. Hlídek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

Hanawa, F.

Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
[CrossRef]

Hattori, K.

Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
[CrossRef]

Heimbuch, M. E.

D. A. Cohen, M. E. Heimbuch, and L. A. Coldren, “Reduced temperature sensitivity of the wavelength of a diode laser in a stress-engineered hydrostatic package,” Appl. Phys. Lett. 69, 455–457 (1996).
[CrossRef]

Hibino, Y.

N. Ooba, Y. Hibino, Y. Inoue, and A. Sugita, “Athermal silica-based arrayed-waveguide grating multiplexer using bimetal plate temperature compensator,” Electron. Lett. 36, 1800–1801 (2000).
[CrossRef]

Hlídek, P.

P. Hlídek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

Huang, M.

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40, 1615–1632 (2003).
[CrossRef]

Inoue, Y.

N. Ooba, Y. Hibino, Y. Inoue, and A. Sugita, “Athermal silica-based arrayed-waveguide grating multiplexer using bimetal plate temperature compensator,” Electron. Lett. 36, 1800–1801 (2000).
[CrossRef]

A. Kaneko, S. Kamei, Y. Inoue, H. Takahashi, and A. Sugita, “Athermal silica-based arrayed-waveguide grating (AWG) multi/demultiplexers with new low loss groove design,” Electron. Lett. 36, 318–319 (2000).
[CrossRef]

Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
[CrossRef]

Iodice, M.

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77, 1614–1616 (2000).
[CrossRef]

Kamei, S.

A. Kaneko, S. Kamei, Y. Inoue, H. Takahashi, and A. Sugita, “Athermal silica-based arrayed-waveguide grating (AWG) multi/demultiplexers with new low loss groove design,” Electron. Lett. 36, 318–319 (2000).
[CrossRef]

Kaneko, A.

A. Kaneko, S. Kamei, Y. Inoue, H. Takahashi, and A. Sugita, “Athermal silica-based arrayed-waveguide grating (AWG) multi/demultiplexers with new low loss groove design,” Electron. Lett. 36, 318–319 (2000).
[CrossRef]

Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
[CrossRef]

Katz, O.

U. Tisch, B. Meyler, O. Katz, E. Finlman, and J. Salzman, “Dependence of the refractive index of AlxGa1−xN on temperature and composition at elevated temperatures,” J. Appl. Phys. 89, 2676–2685 (2001).
[CrossRef]

Keil, N.

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

Kokubun, Y.

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55 μm wavelength using a silica based athermal waveguide,” Electron. Lett. 34, 367–369 (1998).
[CrossRef]

Mason, B.

D. A. Cohen, B. Mason, J. Dolan, C. Burns, and L. A. Coldren, “Enhanced wavelength tuning of an InGasP-InP laser with a thermal-strain-magnifying trench,” Appl. Phys. Lett. 77, 2629–2631 (2000).
[CrossRef]

Matsuura, S.

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55 μm wavelength using a silica based athermal waveguide,” Electron. Lett. 34, 367–369 (1998).
[CrossRef]

Meyler, B.

U. Tisch, B. Meyler, O. Katz, E. Finlman, and J. Salzman, “Dependence of the refractive index of AlxGa1−xN on temperature and composition at elevated temperatures,” J. Appl. Phys. 89, 2676–2685 (2001).
[CrossRef]

Montefusco, M. Esposito

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[CrossRef]

Moretti, L.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[CrossRef]

Ooba, N.

N. Ooba, Y. Hibino, Y. Inoue, and A. Sugita, “Athermal silica-based arrayed-waveguide grating multiplexer using bimetal plate temperature compensator,” Electron. Lett. 36, 1800–1801 (2000).
[CrossRef]

Pickles, C. S. J.

T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, “Temperature dependence of the refractive index of diamond up to 925 K,” Phys. Rev. B 62, 16578–16581 (2000).
[CrossRef]

Rendina, I.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[CrossRef]

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77, 1614–1616 (2000).
[CrossRef]

Ruf, T.

T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, “Temperature dependence of the refractive index of diamond up to 925 K,” Phys. Rev. B 62, 16578–16581 (2000).
[CrossRef]

Salzman, J.

U. Tisch, B. Meyler, O. Katz, E. Finlman, and J. Salzman, “Dependence of the refractive index of AlxGa1−xN on temperature and composition at elevated temperatures,” J. Appl. Phys. 89, 2676–2685 (2001).
[CrossRef]

Schneider, J.

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

Sugita, A.

N. Ooba, Y. Hibino, Y. Inoue, and A. Sugita, “Athermal silica-based arrayed-waveguide grating multiplexer using bimetal plate temperature compensator,” Electron. Lett. 36, 1800–1801 (2000).
[CrossRef]

A. Kaneko, S. Kamei, Y. Inoue, H. Takahashi, and A. Sugita, “Athermal silica-based arrayed-waveguide grating (AWG) multi/demultiplexers with new low loss groove design,” Electron. Lett. 36, 318–319 (2000).
[CrossRef]

Sumida, S.

Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
[CrossRef]

Sussmann, R.

T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, “Temperature dependence of the refractive index of diamond up to 925 K,” Phys. Rev. B 62, 16578–16581 (2000).
[CrossRef]

Takahashi, H.

A. Kaneko, S. Kamei, Y. Inoue, H. Takahashi, and A. Sugita, “Athermal silica-based arrayed-waveguide grating (AWG) multi/demultiplexers with new low loss groove design,” Electron. Lett. 36, 318–319 (2000).
[CrossRef]

Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
[CrossRef]

Tisch, U.

U. Tisch, B. Meyler, O. Katz, E. Finlman, and J. Salzman, “Dependence of the refractive index of AlxGa1−xN on temperature and composition at elevated temperatures,” J. Appl. Phys. 89, 2676–2685 (2001).
[CrossRef]

Yao, H. H.

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

Yoneda, S.

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55 μm wavelength using a silica based athermal waveguide,” Electron. Lett. 34, 367–369 (1998).
[CrossRef]

Zawadzki, C.

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

Appl. Phys. Lett. (3)

D. A. Cohen, M. E. Heimbuch, and L. A. Coldren, “Reduced temperature sensitivity of the wavelength of a diode laser in a stress-engineered hydrostatic package,” Appl. Phys. Lett. 69, 455–457 (1996).
[CrossRef]

D. A. Cohen, B. Mason, J. Dolan, C. Burns, and L. A. Coldren, “Enhanced wavelength tuning of an InGasP-InP laser with a thermal-strain-magnifying trench,” Appl. Phys. Lett. 77, 2629–2631 (2000).
[CrossRef]

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, “Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 μm,” Appl. Phys. Lett. 77, 1614–1616 (2000).
[CrossRef]

Electron. Lett. (5)

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55 μm wavelength using a silica based athermal waveguide,” Electron. Lett. 34, 367–369 (1998).
[CrossRef]

N. Keil, H. H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, and J. Schneider, “Athermal all-polymer arrayed-waveguide grating multiplexer,” Electron. Lett. 37, 579–580 (2001).
[CrossRef]

A. Kaneko, S. Kamei, Y. Inoue, H. Takahashi, and A. Sugita, “Athermal silica-based arrayed-waveguide grating (AWG) multi/demultiplexers with new low loss groove design,” Electron. Lett. 36, 318–319 (2000).
[CrossRef]

Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, and S. Sumida, “Athermal silica-based arrayed-waveguide grating multiplexer,” Electron. Lett. 33, 1945–1947 (1997).
[CrossRef]

N. Ooba, Y. Hibino, Y. Inoue, and A. Sugita, “Athermal silica-based arrayed-waveguide grating multiplexer using bimetal plate temperature compensator,” Electron. Lett. 36, 1800–1801 (2000).
[CrossRef]

Int. J. Solids Struct. (1)

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40, 1615–1632 (2003).
[CrossRef]

J. Appl. Phys. (3)

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[CrossRef]

P. Hlídek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

U. Tisch, B. Meyler, O. Katz, E. Finlman, and J. Salzman, “Dependence of the refractive index of AlxGa1−xN on temperature and composition at elevated temperatures,” J. Appl. Phys. 89, 2676–2685 (2001).
[CrossRef]

Phys. Rev. B (1)

T. Ruf, M. Cardona, C. S. J. Pickles, and R. Sussmann, “Temperature dependence of the refractive index of diamond up to 925 K,” Phys. Rev. B 62, 16578–16581 (2000).
[CrossRef]

Other (9)

S. S. Ballard, J. S. Browder, and J. F. Ebersole, “Refractive index of special crystals and certain glasses,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), Chap. 6.

J. T. Boyd, “Photonic integrated circuits,” in Photonic Devices and Systems, R. G. Hunsperger, eds. (Marcel Dekker, New York, 1994), pp. 313–375.

D. Lee, Electromagnetic Principles of Integrated Optics (Wiley, New York, 1986).

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, New York, 1989).

X. Yan and M. Huang, “A thermal design of arrayed waveguide gratings,” presented at 2002 ASME International Mechanical Engineering Congress, New Orleans, La., November 2002.

X. Yan, “Underfill selection and its impact on the reliability of flip chip assembles,” presented at the Delphi Automotive Systems Analytical Design Forum, Kokomo, Indiana, March 1999.

J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, New York, 1992).

J. Sapriel, Acousto-Optics (Wiley, New York, 1976).

W. L. Wolfe, “Properties of optical materials,” in Handbook of Optics, W. G. Driscoll and W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 7.

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Figures (7)

Fig. 1
Fig. 1

Schematic of different loading methods. (a) Thermal stress is induced only by thermal mismatch between core and cladding. (b) Additional thermal stress is induced by attaching two metal plates on both sides of the waveguide.

Fig. 2
Fig. 2

Schematic of a symmetric three-layer planar waveguide.

Fig. 3
Fig. 3

Temperature sensitivity of the effective refractive index as a function of core thickness for a planar waveguide. (a) TE mode; (b) TM mode.

Fig. 4
Fig. 4

Temperature sensitivity of the effective refractive index of the fundamental mode (m=0) for a planar waveguide with t=1 μm. (a) TE mode; (b) TM mode. The solid lines represent different core thickness, and the dashed line is dne/dT=dnyy/dT for the TE mode, and dnh/dT=dnxx/dT for the TM mode.

Fig. 5
Fig. 5

(a) Schematic of a channel waveguide. (b) Effective-index model equivalent planar waveguide.

Fig. 6
Fig. 6

Temperature sensitivity of the effective refractive index of lowest-order Ex mode for a channel waveguide. The dash line is dnEx/dT=dnxx/dT.

Fig. 7
Fig. 7

Temperature sensitivity of the central wavelength for a silica waveguide bent by a bimetal plate.

Tables (1)

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Table 1 Thermo-Optic and Mechanical Properties of Some Materials9-13

Equations (45)

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ε=nxx2nxy2nxz2nxy2nyy2nyz2nxz2nyz2nzz2,
nT=Bn,
Δnxxnyynzznyznxznxy=BΔTnxxnyynzznyznxznxy-C1C2C2000C2C1C2000C2C2C1000000C3000000C3000000C3ΔσxxΔσyyΔσzzΔσyzΔσxzΔσxy,
σxxσxyσxzσxyσyyσyzσxzσyzσzz,
nxxnyynzznyznxznxy=[1+B(T-T0)]n0n0n0000-C1C2C2000C2C1C2000C2C2C1000000C3000000C3000000C3σxxσyyσzzσyzσxzσxy,
σxx=gxEΔα(T-T0)+σrx,
σyy=gyEΔα(T-T0)+σry,
σzz=gzEΔα(T-T0)+σrz,
σyz=σxz=σxy=0,
gx=0,
gy=gz=1/(1-ν),
gx=0,
gy=gz=11-ν1+αmetal-αcladdingαcladding-αcore×11+1-νmetal1-νcladdingEcladdingEmetalhcladdinghmetal  ,
nxx=n0+[Bn0-C1gxEΔα-C2(gy+gz)EΔα]×(T-T0)-C1σrx-C2(σry+σrz),
nyy=n0+[Bn0-C1gyEΔα-C2(gx+gz)EΔα]×(T-T0)-C1σry-C2(σrx+σrz),
nzz=n0+[Bn0-C1gzEΔα-C2(gx+gy)EΔα]×(T-T0)-C1σrz-C2(σrx+σry).
dnxx/dT=Bn0-C1gxEΔα-C2(gy+gz)EΔα,
dnyy/dT=Bn0-C1gyEΔα-C2(gx+gz)EΔα,
dnzz/dT=Bn0-C1gzEΔα-C2(gx+gy)EΔα.
(TE)d2eydx2+k2(nyy2-ne2)ey=0,
(TM)d2hydx2+k2(nzz2-nzz2nh2/nxx2)hy=0,
(even)p tan(ktp/2)=q,
(odd)q tan(ktp/2)=-p.
(even)n12p tan(ktp/2)=nzz2q,
(odd)nzz2q tan(ktp/2)=-n12p,
p=nyy2-ne2forTEnzz2-nzz2nh2/nxx2forTM,
q=ne2-n12forTEnzz2nh2/nxx2-n12forTM,
(TE)[q+(p2+q2)kt/2] dpdT=p dqdT,
(TM)[q+(p2n12/nzz2+q2nzz2/n12)kt/2] dpdT
=p dqdT+2pq dln(nzz/n1)dT.
n12nzz2-nzz2nh2(t)/nxx2tan(ktnzz2-nzz2nh2(t)/nxx2/2)
=nzz2nzz2nh2(t)/nxx2-n12.
nh2(t2)-nEx2tan(kwnh2(t2)-nEx2/2)
=nEx2-nh2(t1).
nExdnExdT
=nh(t2) dnh(t2)dT
-[nh2(t2)-nEx2]nh(t2) dnh(t2)dT-nh(t1) dnh(t1)dT[nh2(t2)-nh2(t1)][1+kwnEx2-nh2(t1)/2].
λ=neff ΔLm,
dλdT=λ1neffneffσi+1ΔLΔLσidσidT+λ1ΔLΔLT+1neffneffT.
1ΔLΔLσi=γzzσi,
γij=1+νE σij-νE σkkδij+αΔTδij.
dλdT=λneffneffσidσidT-λEd[ν(σxx+σyy)-σzz]dT+λαsub+1neffneffT.
dneffdT=neffσidσidT+neffT,
dλdT=λ1neffdneffdT+αsub-1Ed[ν(σxx+σyy)-σzz]dT.
dneffdT=neffEd ν(σxx+σyy)-σzzdT-neff αsub.

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