Abstract

We study the in-plane/out-of-plane anisotropies in refractive indices (n) and in thermo-optic coefficients (dn/dT) of benzocyclobutene (BCB) thin film on a substrate. Both nonoxidized and oxidized films are investigated. Aside from the stress-induced effects, oxidation has significant influence on the refractive index anisotropy. The dependence of the anisotropy on each of the thermal stress and the oxidation is determined quantitatively. The anisotropies in the dn/dT values are mainly caused by the thermal stress and are independent of oxidation. However, the original (stress-free) thermo-optic coefficients are obtained as isotropic and significantly different than the measured dn/dT values. Our findings have the potential to optimize the design of polarization insensitive and/or athermal BCB optical waveguide devices.

© 2010 OSA

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    [CrossRef]
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2010 (2)

2009 (4)

2007 (1)

L.-Y. Chen, W.-S. Tsai, W.-H. Hsu, K.-Y. Chen, and W.-S. Wang, “Fabrication and characterization of benzocyclobutene optical waveguides by UV pulsed-laser illumination,” IEEE J. Quantum Electron. 43(4), 303–310 (2007).
[CrossRef]

2006 (1)

S. Y. Cheng, K. S. Chiang, and H. P. Chan, “Polarization-insensitive polymer waveguide Bragg grating,” Microw. Opt. Technol. Lett. 48(2), 334–338 (2006).
[CrossRef]

2005 (1)

2004 (1)

Z. Elalamy, E. Drouard, T. M. Govern, L. Escoubas, J.-J. Simon, and F. Flory, “Thermo-optical coefficients of sol-gel ZrO2 thin films,” Opt. Commun. 235(4-6), 365–372 (2004).
[CrossRef]

2003 (3)

J.-M. Lee, S. Park, M. H. Lee, J. T. Ahn, J. J. Ju, and K. H. Kim, “Simple method to adjust polarization dependence in polymeric arrayed waveguide gratings,” IEEE Photon. Technol. Lett. 15(7), 927–929 (2003).
[CrossRef]

H. P. Chan, C. K. Chow, and A. K. Das, “A wide-angle X-junction polymeric thermooptic digital switch with low crosstalk,” IEEE Photon. Technol. Lett. 15(9), 1210–1212 (2003).
[CrossRef]

Y. Terui and S. Ando, “Anisotropy in thermo-optic coefficients of polyimide films formed on Si substrate,” Appl. Phys. Lett. 83(23), 4755–4757 (2003).
[CrossRef]

2002 (2)

E.-S. Kang, T.-H. Lee, and B.-S. Bae, “Measurement of the thermo-optic coefficients in sol-gel derived inorganic-organic hybrid material films,” Appl. Phys. Lett. 81(8), 1438–1440 (2002).
[CrossRef]

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[CrossRef]

2001 (2)

Y. Mada, S. Sugitani, K. Arai, and K. Yamasaki, “Optical properties of oxygen-ion-implanted benzocyclobutene films,” J. Vac. Sci. Technol. A 19(3), 883–886 (2001).
[CrossRef]

N. Keil, H. H. Yao, and C. Zawadzki, “Athermal polarisation-independent arrayed-waveguide grating (AWG) multiplexer using an all-polymer approach,” Appl. Phys. B 73, 619–622 (2001).

2000 (1)

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6(1), 54–68 (2000).
[CrossRef]

1999 (1)

T. C. Hodge, S. A. B. Allen, and P. A. Kohl, “In situ measurement of the thermal expansion behavior of benzocyclobutene films,” J. Polym. Sci., B, Polym. Phys. 37(4), 311–321 (1999).
[CrossRef]

1995 (1)

C. F. Kane and R. R. Krchnavek, “Benzocyclobutene optical waveguides,” IEEE Photon. Technol. Lett. 7(5), 535–537 (1995).
[CrossRef]

1981 (1)

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17(10), 2123–2129 (1981).
[CrossRef]

Ahn, J. T.

J.-M. Lee, S. Park, M. H. Lee, J. T. Ahn, J. J. Ju, and K. H. Kim, “Simple method to adjust polarization dependence in polymeric arrayed waveguide gratings,” IEEE Photon. Technol. Lett. 15(7), 927–929 (2003).
[CrossRef]

Allen, S. A. B.

T. C. Hodge, S. A. B. Allen, and P. A. Kohl, “In situ measurement of the thermal expansion behavior of benzocyclobutene films,” J. Polym. Sci., B, Polym. Phys. 37(4), 311–321 (1999).
[CrossRef]

Ando, S.

Y. Terui and S. Ando, “Anisotropy in thermo-optic coefficients of polyimide films formed on Si substrate,” Appl. Phys. Lett. 83(23), 4755–4757 (2003).
[CrossRef]

Arai, K.

Y. Mada, S. Sugitani, K. Arai, and K. Yamasaki, “Optical properties of oxygen-ion-implanted benzocyclobutene films,” J. Vac. Sci. Technol. A 19(3), 883–886 (2001).
[CrossRef]

Bae, B.-S.

E.-S. Kang, T.-H. Lee, and B.-S. Bae, “Measurement of the thermo-optic coefficients in sol-gel derived inorganic-organic hybrid material films,” Appl. Phys. Lett. 81(8), 1438–1440 (2002).
[CrossRef]

Bo, F.

Chan, H. P.

M. F. Hossain, H. P. Chan, and M. A. Uddin, “Simultaneous measurement of thermo-optic and stress-optic coefficients of polymer thin films using prism coupler technique,” Appl. Opt. 49(3), 403–408 (2010).
[CrossRef] [PubMed]

M. F. Hossain, H. P. Chan, M. A. Uddin, and R. K. Y. Li, “Stress-induced birefringence characteristics of polymer optical rib waveguides,” J. Lightwave Technol. 27(21), 4678–4685 (2009).
[CrossRef]

K. P. Lor, K. S. Chiang, Q. Liu, and H. P. Chan, “Ultraviolet writing of buried waveguide devices in epoxy-coated benzocyclobutene,” Opt. Eng. 48(4), 044601–044606 (2009).
[CrossRef]

S. Y. Cheng, K. S. Chiang, and H. P. Chan, “Polarization-insensitive polymer waveguide Bragg grating,” Microw. Opt. Technol. Lett. 48(2), 334–338 (2006).
[CrossRef]

H. P. Chan, C. K. Chow, and A. K. Das, “A wide-angle X-junction polymeric thermooptic digital switch with low crosstalk,” IEEE Photon. Technol. Lett. 15(9), 1210–1212 (2003).
[CrossRef]

Chen, K.-Y.

L.-Y. Chen, W.-S. Tsai, W.-H. Hsu, K.-Y. Chen, and W.-S. Wang, “Fabrication and characterization of benzocyclobutene optical waveguides by UV pulsed-laser illumination,” IEEE J. Quantum Electron. 43(4), 303–310 (2007).
[CrossRef]

Chen, L.-Y.

L.-Y. Chen, W.-S. Tsai, W.-H. Hsu, K.-Y. Chen, and W.-S. Wang, “Fabrication and characterization of benzocyclobutene optical waveguides by UV pulsed-laser illumination,” IEEE J. Quantum Electron. 43(4), 303–310 (2007).
[CrossRef]

Cheng, S. Y.

S. Y. Cheng, K. S. Chiang, and H. P. Chan, “Polarization-insensitive polymer waveguide Bragg grating,” Microw. Opt. Technol. Lett. 48(2), 334–338 (2006).
[CrossRef]

Chiang, K. S.

K. P. Lor, K. S. Chiang, Q. Liu, and H. P. Chan, “Ultraviolet writing of buried waveguide devices in epoxy-coated benzocyclobutene,” Opt. Eng. 48(4), 044601–044606 (2009).
[CrossRef]

L. Xu, G. Zhang, N. Xu, F. Bo, F. Gao, W. Fan, J. Xu, K. P. Lor, and K. S. Chiang, “Active chromatic control on the group velocity of light at arbitrary wavelength in benzocyclobutene polymer,” Opt. Express 17(20), 18292–18303 (2009).
[CrossRef] [PubMed]

S. Y. Cheng, K. S. Chiang, and H. P. Chan, “Polarization-insensitive polymer waveguide Bragg grating,” Microw. Opt. Technol. Lett. 48(2), 334–338 (2006).
[CrossRef]

Q. Liu, K. S. Chiang, and K. P. Lor, “Long-period gratings in polymer ridge waveguides,” Opt. Express 13(4), 1150–1160 (2005).
[CrossRef] [PubMed]

Chow, C. K.

H. P. Chan, C. K. Chow, and A. K. Das, “A wide-angle X-junction polymeric thermooptic digital switch with low crosstalk,” IEEE Photon. Technol. Lett. 15(9), 1210–1212 (2003).
[CrossRef]

Dalton, L. R.

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[CrossRef]

Das, A. K.

H. P. Chan, C. K. Chow, and A. K. Das, “A wide-angle X-junction polymeric thermooptic digital switch with low crosstalk,” IEEE Photon. Technol. Lett. 15(9), 1210–1212 (2003).
[CrossRef]

Drouard, E.

Z. Elalamy, E. Drouard, T. M. Govern, L. Escoubas, J.-J. Simon, and F. Flory, “Thermo-optical coefficients of sol-gel ZrO2 thin films,” Opt. Commun. 235(4-6), 365–372 (2004).
[CrossRef]

Edahiro, T.

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17(10), 2123–2129 (1981).
[CrossRef]

Elalamy, Z.

Z. Elalamy, E. Drouard, T. M. Govern, L. Escoubas, J.-J. Simon, and F. Flory, “Thermo-optical coefficients of sol-gel ZrO2 thin films,” Opt. Commun. 235(4-6), 365–372 (2004).
[CrossRef]

Eldada, L.

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6(1), 54–68 (2000).
[CrossRef]

Escoubas, L.

Z. Elalamy, E. Drouard, T. M. Govern, L. Escoubas, J.-J. Simon, and F. Flory, “Thermo-optical coefficients of sol-gel ZrO2 thin films,” Opt. Commun. 235(4-6), 365–372 (2004).
[CrossRef]

Fan, W.

Flory, F.

Z. Elalamy, E. Drouard, T. M. Govern, L. Escoubas, J.-J. Simon, and F. Flory, “Thermo-optical coefficients of sol-gel ZrO2 thin films,” Opt. Commun. 235(4-6), 365–372 (2004).
[CrossRef]

Gao, F.

Govern, T. M.

Z. Elalamy, E. Drouard, T. M. Govern, L. Escoubas, J.-J. Simon, and F. Flory, “Thermo-optical coefficients of sol-gel ZrO2 thin films,” Opt. Commun. 235(4-6), 365–372 (2004).
[CrossRef]

Hodge, T. C.

T. C. Hodge, S. A. B. Allen, and P. A. Kohl, “In situ measurement of the thermal expansion behavior of benzocyclobutene films,” J. Polym. Sci., B, Polym. Phys. 37(4), 311–321 (1999).
[CrossRef]

Hosaka, T.

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17(10), 2123–2129 (1981).
[CrossRef]

Hossain, M. F.

Hsu, W.-H.

L.-Y. Chen, W.-S. Tsai, W.-H. Hsu, K.-Y. Chen, and W.-S. Wang, “Fabrication and characterization of benzocyclobutene optical waveguides by UV pulsed-laser illumination,” IEEE J. Quantum Electron. 43(4), 303–310 (2007).
[CrossRef]

Jen, A. K.-Y.

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[CrossRef]

Ju, J. J.

J.-M. Lee, S. Park, M. H. Lee, J. T. Ahn, J. J. Ju, and K. H. Kim, “Simple method to adjust polarization dependence in polymeric arrayed waveguide gratings,” IEEE Photon. Technol. Lett. 15(7), 927–929 (2003).
[CrossRef]

Kane, C. F.

C. F. Kane and R. R. Krchnavek, “Benzocyclobutene optical waveguides,” IEEE Photon. Technol. Lett. 7(5), 535–537 (1995).
[CrossRef]

Kang, E.-S.

E.-S. Kang, T.-H. Lee, and B.-S. Bae, “Measurement of the thermo-optic coefficients in sol-gel derived inorganic-organic hybrid material films,” Appl. Phys. Lett. 81(8), 1438–1440 (2002).
[CrossRef]

Keil, N.

N. Keil, H. H. Yao, and C. Zawadzki, “Athermal polarisation-independent arrayed-waveguide grating (AWG) multiplexer using an all-polymer approach,” Appl. Phys. B 73, 619–622 (2001).

Kim, K. H.

S. H. Kim, S. H. Lee, J. I. Lim, and K. H. Kim, “Absolute refractive index measurement method over a broad wavelength region based on white-light interferometry,” Appl. Opt. 49(5), 910–914 (2010).
[CrossRef] [PubMed]

J.-M. Lee, S. Park, M. H. Lee, J. T. Ahn, J. J. Ju, and K. H. Kim, “Simple method to adjust polarization dependence in polymeric arrayed waveguide gratings,” IEEE Photon. Technol. Lett. 15(7), 927–929 (2003).
[CrossRef]

Kim, S. H.

Kohl, P. A.

T. C. Hodge, S. A. B. Allen, and P. A. Kohl, “In situ measurement of the thermal expansion behavior of benzocyclobutene films,” J. Polym. Sci., B, Polym. Phys. 37(4), 311–321 (1999).
[CrossRef]

Krchnavek, R. R.

C. F. Kane and R. R. Krchnavek, “Benzocyclobutene optical waveguides,” IEEE Photon. Technol. Lett. 7(5), 535–537 (1995).
[CrossRef]

Lee, J.-M.

J.-M. Lee, S. Park, M. H. Lee, J. T. Ahn, J. J. Ju, and K. H. Kim, “Simple method to adjust polarization dependence in polymeric arrayed waveguide gratings,” IEEE Photon. Technol. Lett. 15(7), 927–929 (2003).
[CrossRef]

Lee, M. H.

J.-M. Lee, S. Park, M. H. Lee, J. T. Ahn, J. J. Ju, and K. H. Kim, “Simple method to adjust polarization dependence in polymeric arrayed waveguide gratings,” IEEE Photon. Technol. Lett. 15(7), 927–929 (2003).
[CrossRef]

Lee, S. H.

Lee, T.-H.

E.-S. Kang, T.-H. Lee, and B.-S. Bae, “Measurement of the thermo-optic coefficients in sol-gel derived inorganic-organic hybrid material films,” Appl. Phys. Lett. 81(8), 1438–1440 (2002).
[CrossRef]

Li, R. K. Y.

Lim, J. I.

Liu, Q.

K. P. Lor, K. S. Chiang, Q. Liu, and H. P. Chan, “Ultraviolet writing of buried waveguide devices in epoxy-coated benzocyclobutene,” Opt. Eng. 48(4), 044601–044606 (2009).
[CrossRef]

Q. Liu, K. S. Chiang, and K. P. Lor, “Long-period gratings in polymer ridge waveguides,” Opt. Express 13(4), 1150–1160 (2005).
[CrossRef] [PubMed]

Liu, W. C.

Lor, K. P.

Ma, H.

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[CrossRef]

Mada, Y.

Y. Mada, S. Sugitani, K. Arai, and K. Yamasaki, “Optical properties of oxygen-ion-implanted benzocyclobutene films,” J. Vac. Sci. Technol. A 19(3), 883–886 (2001).
[CrossRef]

Mak, C. L.

Okamoto, K.

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17(10), 2123–2129 (1981).
[CrossRef]

Park, S.

J.-M. Lee, S. Park, M. H. Lee, J. T. Ahn, J. J. Ju, and K. H. Kim, “Simple method to adjust polarization dependence in polymeric arrayed waveguide gratings,” IEEE Photon. Technol. Lett. 15(7), 927–929 (2003).
[CrossRef]

Shacklette, L. W.

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6(1), 54–68 (2000).
[CrossRef]

Simon, J.-J.

Z. Elalamy, E. Drouard, T. M. Govern, L. Escoubas, J.-J. Simon, and F. Flory, “Thermo-optical coefficients of sol-gel ZrO2 thin films,” Opt. Commun. 235(4-6), 365–372 (2004).
[CrossRef]

Sugitani, S.

Y. Mada, S. Sugitani, K. Arai, and K. Yamasaki, “Optical properties of oxygen-ion-implanted benzocyclobutene films,” J. Vac. Sci. Technol. A 19(3), 883–886 (2001).
[CrossRef]

Terui, Y.

Y. Terui and S. Ando, “Anisotropy in thermo-optic coefficients of polyimide films formed on Si substrate,” Appl. Phys. Lett. 83(23), 4755–4757 (2003).
[CrossRef]

Tsai, W.-S.

L.-Y. Chen, W.-S. Tsai, W.-H. Hsu, K.-Y. Chen, and W.-S. Wang, “Fabrication and characterization of benzocyclobutene optical waveguides by UV pulsed-laser illumination,” IEEE J. Quantum Electron. 43(4), 303–310 (2007).
[CrossRef]

Uddin, M. A.

Wang, W.-S.

L.-Y. Chen, W.-S. Tsai, W.-H. Hsu, K.-Y. Chen, and W.-S. Wang, “Fabrication and characterization of benzocyclobutene optical waveguides by UV pulsed-laser illumination,” IEEE J. Quantum Electron. 43(4), 303–310 (2007).
[CrossRef]

Wong, K. H.

Xu, J.

Xu, L.

Xu, N.

Yamasaki, K.

Y. Mada, S. Sugitani, K. Arai, and K. Yamasaki, “Optical properties of oxygen-ion-implanted benzocyclobutene films,” J. Vac. Sci. Technol. A 19(3), 883–886 (2001).
[CrossRef]

Yao, H. H.

N. Keil, H. H. Yao, and C. Zawadzki, “Athermal polarisation-independent arrayed-waveguide grating (AWG) multiplexer using an all-polymer approach,” Appl. Phys. B 73, 619–622 (2001).

Zawadzki, C.

N. Keil, H. H. Yao, and C. Zawadzki, “Athermal polarisation-independent arrayed-waveguide grating (AWG) multiplexer using an all-polymer approach,” Appl. Phys. B 73, 619–622 (2001).

Zhang, G.

Adv. Mater. (1)

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

N. Keil, H. H. Yao, and C. Zawadzki, “Athermal polarisation-independent arrayed-waveguide grating (AWG) multiplexer using an all-polymer approach,” Appl. Phys. B 73, 619–622 (2001).

Appl. Phys. Lett. (2)

Y. Terui and S. Ando, “Anisotropy in thermo-optic coefficients of polyimide films formed on Si substrate,” Appl. Phys. Lett. 83(23), 4755–4757 (2003).
[CrossRef]

E.-S. Kang, T.-H. Lee, and B.-S. Bae, “Measurement of the thermo-optic coefficients in sol-gel derived inorganic-organic hybrid material films,” Appl. Phys. Lett. 81(8), 1438–1440 (2002).
[CrossRef]

IEEE J. Quantum Electron. (2)

L.-Y. Chen, W.-S. Tsai, W.-H. Hsu, K.-Y. Chen, and W.-S. Wang, “Fabrication and characterization of benzocyclobutene optical waveguides by UV pulsed-laser illumination,” IEEE J. Quantum Electron. 43(4), 303–310 (2007).
[CrossRef]

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17(10), 2123–2129 (1981).
[CrossRef]

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

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6(1), 54–68 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

C. F. Kane and R. R. Krchnavek, “Benzocyclobutene optical waveguides,” IEEE Photon. Technol. Lett. 7(5), 535–537 (1995).
[CrossRef]

J.-M. Lee, S. Park, M. H. Lee, J. T. Ahn, J. J. Ju, and K. H. Kim, “Simple method to adjust polarization dependence in polymeric arrayed waveguide gratings,” IEEE Photon. Technol. Lett. 15(7), 927–929 (2003).
[CrossRef]

H. P. Chan, C. K. Chow, and A. K. Das, “A wide-angle X-junction polymeric thermooptic digital switch with low crosstalk,” IEEE Photon. Technol. Lett. 15(9), 1210–1212 (2003).
[CrossRef]

J. Lightwave Technol. (1)

J. Polym. Sci., B, Polym. Phys. (1)

T. C. Hodge, S. A. B. Allen, and P. A. Kohl, “In situ measurement of the thermal expansion behavior of benzocyclobutene films,” J. Polym. Sci., B, Polym. Phys. 37(4), 311–321 (1999).
[CrossRef]

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

Y. Mada, S. Sugitani, K. Arai, and K. Yamasaki, “Optical properties of oxygen-ion-implanted benzocyclobutene films,” J. Vac. Sci. Technol. A 19(3), 883–886 (2001).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

S. Y. Cheng, K. S. Chiang, and H. P. Chan, “Polarization-insensitive polymer waveguide Bragg grating,” Microw. Opt. Technol. Lett. 48(2), 334–338 (2006).
[CrossRef]

Opt. Commun. (1)

Z. Elalamy, E. Drouard, T. M. Govern, L. Escoubas, J.-J. Simon, and F. Flory, “Thermo-optical coefficients of sol-gel ZrO2 thin films,” Opt. Commun. 235(4-6), 365–372 (2004).
[CrossRef]

Opt. Eng. (1)

K. P. Lor, K. S. Chiang, Q. Liu, and H. P. Chan, “Ultraviolet writing of buried waveguide devices in epoxy-coated benzocyclobutene,” Opt. Eng. 48(4), 044601–044606 (2009).
[CrossRef]

Opt. Express (3)

Other (3)

D. W. V. Krevelen, Properties of Polymers: their correlation with chemical structure, their numerical estimation and prediction from additive group contributions (Elsevier, 1997) Chap. 10.

“Data and Properties,” Quartz glass for optics, http://optics.heraeus-qarzglas.com/en/productsapplications/
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Processing procedures for CYCLOTENE 3000 series resin, Dow Chemical Company, http://www.dow.
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Figures (4)

Fig. 1
Fig. 1

(a) Refractive indices (n) for the TE and TM polarizations and (b) their birefringence ( Δ n ) versus flow rate of nitrogen measured at room temperature.

Fig. 2
Fig. 2

(a) Measured refractive indices (n) for the TE and TM polarizations and (b) their birefringence ( Δ n ) as a function of temperature for a typical sample corresponding to the nitrogen flow of 1 LPM.

Fig. 3
Fig. 3

Measured refractive index anisotropy Δ n versus the oxidation induced change of average refractive index n a v . The numbers in the figure correspond to those of sample sets.

Fig. 4
Fig. 4

Relationship between the thermo-optic coefficient d n / d T and the oxidation-induced change of average refractive index n a v . The numbers in the figure correspond to those of the samples.

Tables (3)

Tables Icon

Table 1 Measured film refractive indices (n) at room temperature, and in- plane/out-of-plane anisotropy ( Δ n ) at a wavelength of 1536 nm*.

Tables Icon

Table 2 Measured temperature dependence of the film refractive indices for TE ( d n T E / d T ) and TM ( d n T M / d T ) polarizations, and their corresponding anisotropy ( d ( Δ n ) / d T ) at a wavelength of 1536 nm*.

Tables Icon

Table 3 Calculated values of thermal expansion coefficients of BCB films ( α f ), temperature dependence of the film stress ( d σ / d T ) and birefrigence ( d ( Δ n ) / d T ), and stress-free thermo-optic coefficient ( d n s f / d T ) at a wavelength of 1536 nm*.

Equations (6)

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Δ n = ( C 1 C 2 ) σ ,
d n d T = ( n 2 1 ) ( n 2 + 2 ) 6 n β ,
d n T E d T = d n s f d T + ( C 1 + C 2 ) d σ d T ,
d n T M d T = d n s f d T + 2 C 2 d σ d T ,
d ( Δ n ) d T = d n T E d T d n T M d T = ( C 1 C 2 ) d σ d T .
d σ / d T = ( α s α f ) E f / ( 1 ν f ) ,

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