Abstract

We present a simple method for simultaneous measurement of thermo-optic and stress-optic coefficients of polymer thin films by measuring the film refractive indices as a function of temperature (dn/dT). Usually, such dn/dT value is considered as the thermo-optic coefficient. However, in the thin film systems, the measured dn/dT values result from both the thermo-optic and stress-optic effects. To demonstrate the stress-induced effects, the dn/dT values have been investigated for two different polymers: benzocyclobutene (high film stress) and epoxy 3505 (negligible film stress), using a prism coupler technique. The finite element method has been used so as to predict the stresses in the polymer film and, by combining them with the experimental dn/dT values, the individual thermo-optic and stress-optic coefficients have been determined. We found that the obtained thermo-optic coefficient is significantly different than the measured dn/dT values. The method is generic in nature and can thus be applied to a wide range of polymer waveguide materials.

© 2010 Optical Society of America

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  5. W. Y. Chan, K. X. Chen, H. P. Chan, B. P. Pal, and R. K. Varshney, “A flattop PLC polymer waveguide interleaver based on folded two-stage-cascaded Y-junction Mach-Zehnder interferometers,” Opt. Commun. 282, 883-886 (2009).
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  6. K. X. Chen, K. S. Chiang, and H. P. Chan, “Broadband multi-port dynamic optical power distributor based on thermo-optic polymer waveguide vertical couplers,” IEEE Photon. Technol. Lett. 20, 273-275 (2008).
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2009

W. Y. Chan, K. X. Chen, H. P. Chan, B. P. Pal, and R. K. Varshney, “A flattop PLC polymer waveguide interleaver based on folded two-stage-cascaded Y-junction Mach-Zehnder interferometers,” Opt. Commun. 282, 883-886 (2009).
[CrossRef]

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, 4678-4685(2009).
[CrossRef]

2008

K. X. Chen, K. S. Chiang, and H. P. Chan, “Broadband multi-port dynamic optical power distributor based on thermo-optic polymer waveguide vertical couplers,” IEEE Photon. Technol. Lett. 20, 273-275 (2008).
[CrossRef]

2007

2006

W. H. Wong, K. K. Liu, K. S. Chan, and E. Y. B. Pun, “Polymer devices for photonic applications,” J. Cryst. Growth 288, 100-104 (2006).
[CrossRef]

K. K. Chung, H. P. Chan, and P. L. Chu, “A 1×4 polarization and wavelength independent optical power splitter based on a novel wide-angle low-loss Y-junction,” Opt. Commun. 267, 367-372 (2006).
[CrossRef]

2004

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, 365-372(2004).
[CrossRef]

S. L. Prins, A. C. Barron, W. C. Herrmann, and J. R. McNeil, “Effect of stress on performance of dense wavelength division multiplexing filters: thermal properties,” Appl. Opt. 43, 633-637 (2004).
[CrossRef] [PubMed]

S. L. Prins, A. C. Barron, W. C. Herrmann, and J. R. McNeil, “Effect of stress on performance of dense wavelength division multiplexing filters: optical properties,” Appl. Opt. 43, 626-632 (2004).
[CrossRef] [PubMed]

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96, 7147-7153 (2004).
[CrossRef]

M.-Y. Tsai, C. H. J. Hsu, and C. T. O. Wang, “Investigation of thermomechanical behaviors of flip chip BGA packages during manufacturing process and thermal cycling,” IEEE Trans. Comp. Packag. Technol. 27, 568-576 (2004).
[CrossRef]

2003

M. Huang and X. Yan, “Thermal-stress effects on the temperature sensitivity of optical waveguides,” J. Opt. Soc. Am. B 20, 1326-1333 (2003).
[CrossRef]

Y. Terui and S. Ando, “Anisotropy in thermo-optic coefficients of polyimide films formed on Si substrate,” Appl. Phys. Lett. 83, 4755-4757 (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, 1210-1212 (2003).
[CrossRef]

2002

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

Y.-J. Kim, U.-C. Paek, and B. H. Lee, “Measurement of refractive-index variation with temperature by use of long-period fiber gratings,” Opt. Lett. 27, 1297-1299 (2002).
[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, 1438-1440(2002).
[CrossRef]

2001

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).
[CrossRef]

2000

C. -L. Tien, C. -C. Jaing, C. -C. Lee, and K. -P. Chuang, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681-1691 (2000).
[CrossRef]

1999

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, 311-321(1999).
[CrossRef]

1996

1994

K. Fischer, J. Muller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12, 163-169 (1994).
[CrossRef]

1988

Agan, S.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96, 7147-7153 (2004).
[CrossRef]

Aggarwal, I. D.

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, 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, 4755-4757 (2003).
[CrossRef]

Ay, F.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96, 7147-7153 (2004).
[CrossRef]

Aydinli, A.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96, 7147-7153 (2004).
[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, 1438-1440(2002).
[CrossRef]

Barron, A. C.

Bayya, S. S.

Chan, H. P.

W. Y. Chan, K. X. Chen, H. P. Chan, B. P. Pal, and R. K. Varshney, “A flattop PLC polymer waveguide interleaver based on folded two-stage-cascaded Y-junction Mach-Zehnder interferometers,” Opt. Commun. 282, 883-886 (2009).
[CrossRef]

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, 4678-4685(2009).
[CrossRef]

K. X. Chen, K. S. Chiang, and H. P. Chan, “Broadband multi-port dynamic optical power distributor based on thermo-optic polymer waveguide vertical couplers,” IEEE Photon. Technol. Lett. 20, 273-275 (2008).
[CrossRef]

K. X. Chen, P. L. Chu, H. P. Chan, and K. S. Chiang, “Three-dimensional broadband polymer optical waveguide switch matrix,” Appl. Opt. 46, 8188-8192 (2007).
[CrossRef] [PubMed]

K. K. Chung, H. P. Chan, and P. L. Chu, “A 1×4 polarization and wavelength independent optical power splitter based on a novel wide-angle low-loss Y-junction,” Opt. Commun. 267, 367-372 (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, 1210-1212 (2003).
[CrossRef]

Chan, K. S.

W. H. Wong, K. K. Liu, K. S. Chan, and E. Y. B. Pun, “Polymer devices for photonic applications,” J. Cryst. Growth 288, 100-104 (2006).
[CrossRef]

Chan, W. Y.

W. Y. Chan, K. X. Chen, H. P. Chan, B. P. Pal, and R. K. Varshney, “A flattop PLC polymer waveguide interleaver based on folded two-stage-cascaded Y-junction Mach-Zehnder interferometers,” Opt. Commun. 282, 883-886 (2009).
[CrossRef]

Chen, K. X.

W. Y. Chan, K. X. Chen, H. P. Chan, B. P. Pal, and R. K. Varshney, “A flattop PLC polymer waveguide interleaver based on folded two-stage-cascaded Y-junction Mach-Zehnder interferometers,” Opt. Commun. 282, 883-886 (2009).
[CrossRef]

K. X. Chen, K. S. Chiang, and H. P. Chan, “Broadband multi-port dynamic optical power distributor based on thermo-optic polymer waveguide vertical couplers,” IEEE Photon. Technol. Lett. 20, 273-275 (2008).
[CrossRef]

K. X. Chen, P. L. Chu, H. P. Chan, and K. S. Chiang, “Three-dimensional broadband polymer optical waveguide switch matrix,” Appl. Opt. 46, 8188-8192 (2007).
[CrossRef] [PubMed]

Chiang, K. S.

K. X. Chen, K. S. Chiang, and H. P. Chan, “Broadband multi-port dynamic optical power distributor based on thermo-optic polymer waveguide vertical couplers,” IEEE Photon. Technol. Lett. 20, 273-275 (2008).
[CrossRef]

K. X. Chen, P. L. Chu, H. P. Chan, and K. S. Chiang, “Three-dimensional broadband polymer optical waveguide switch matrix,” Appl. Opt. 46, 8188-8192 (2007).
[CrossRef] [PubMed]

Chin, G. D.

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, 1210-1212 (2003).
[CrossRef]

Chu, P. L.

K. X. Chen, P. L. Chu, H. P. Chan, and K. S. Chiang, “Three-dimensional broadband polymer optical waveguide switch matrix,” Appl. Opt. 46, 8188-8192 (2007).
[CrossRef] [PubMed]

K. K. Chung, H. P. Chan, and P. L. Chu, “A 1×4 polarization and wavelength independent optical power splitter based on a novel wide-angle low-loss Y-junction,” Opt. Commun. 267, 367-372 (2006).
[CrossRef]

Chuang, K.-P.

C. -L. Tien, C. -C. Jaing, C. -C. Lee, and K. -P. Chuang, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681-1691 (2000).
[CrossRef]

Chung, K. K.

K. K. Chung, H. P. Chan, and P. L. Chu, “A 1×4 polarization and wavelength independent optical power splitter based on a novel wide-angle low-loss Y-junction,” Opt. Commun. 267, 367-372 (2006).
[CrossRef]

Conrad, D. C.

Dalton, L. R.

H. Ma, A. K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing and devices,” Adv. Mater. 14, 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, 1210-1212 (2003).
[CrossRef]

Day, G. W.

Detrio, J. A.

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, 365-372(2004).
[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, 365-372(2004).
[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, 365-372(2004).
[CrossRef]

Fischer, K.

K. Fischer, J. Muller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12, 163-169 (1994).
[CrossRef]

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, 365-372(2004).
[CrossRef]

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, 365-372(2004).
[CrossRef]

Hale, P. D.

Herrmann, W. C.

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, 311-321(1999).
[CrossRef]

Hoffmann, R.

K. Fischer, J. Muller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12, 163-169 (1994).
[CrossRef]

Hossain, M. F.

Hsu, C. H. J.

M.-Y. Tsai, C. H. J. Hsu, and C. T. O. Wang, “Investigation of thermomechanical behaviors of flip chip BGA packages during manufacturing process and thermal cycling,” IEEE Trans. Comp. Packag. Technol. 27, 568-576 (2004).
[CrossRef]

Huang, M.

Jaing, C.-C.

C. -L. Tien, C. -C. Jaing, C. -C. Lee, and K. -P. Chuang, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681-1691 (2000).
[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, 1339-1365 (2002).
[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, 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).
[CrossRef]

Kim, Y.-J.

Kocabas, A.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96, 7147-7153 (2004).
[CrossRef]

Kocabas, C.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96, 7147-7153 (2004).
[CrossRef]

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, 311-321(1999).
[CrossRef]

Lee, B. H.

Lee, C.-C.

C. -L. Tien, C. -C. Jaing, C. -C. Lee, and K. -P. Chuang, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681-1691 (2000).
[CrossRef]

Lee, K. S.

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, 1438-1440(2002).
[CrossRef]

Li, R. K. Y.

Liu, K. K.

W. H. Wong, K. K. Liu, K. S. Chan, and E. Y. B. Pun, “Polymer devices for photonic applications,” J. Cryst. Growth 288, 100-104 (2006).
[CrossRef]

Ma, H.

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

McNeil, J. R.

Muller, J.

K. Fischer, J. Muller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12, 163-169 (1994).
[CrossRef]

Paek, U.-C.

Pal, B. P.

W. Y. Chan, K. X. Chen, H. P. Chan, B. P. Pal, and R. K. Varshney, “A flattop PLC polymer waveguide interleaver based on folded two-stage-cascaded Y-junction Mach-Zehnder interferometers,” Opt. Commun. 282, 883-886 (2009).
[CrossRef]

Prins, S. L.

Pun, E. Y. B.

W. H. Wong, K. K. Liu, K. S. Chan, and E. Y. B. Pun, “Polymer devices for photonic applications,” J. Cryst. Growth 288, 100-104 (2006).
[CrossRef]

Rose, A. H.

Salle, D.

K. Fischer, J. Muller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12, 163-169 (1994).
[CrossRef]

Sanghera, J. S.

Sasaki, K.

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, 365-372(2004).
[CrossRef]

Terui, Y.

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

Tien, C.-L.

C. -L. Tien, C. -C. Jaing, C. -C. Lee, and K. -P. Chuang, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681-1691 (2000).
[CrossRef]

Tsai, M.-Y.

M.-Y. Tsai, C. H. J. Hsu, and C. T. O. Wang, “Investigation of thermomechanical behaviors of flip chip BGA packages during manufacturing process and thermal cycling,” IEEE Trans. Comp. Packag. Technol. 27, 568-576 (2004).
[CrossRef]

Uddin, M. A.

Varshney, R. K.

W. Y. Chan, K. X. Chen, H. P. Chan, B. P. Pal, and R. K. Varshney, “A flattop PLC polymer waveguide interleaver based on folded two-stage-cascaded Y-junction Mach-Zehnder interferometers,” Opt. Commun. 282, 883-886 (2009).
[CrossRef]

Wang, C. T. O.

M.-Y. Tsai, C. H. J. Hsu, and C. T. O. Wang, “Investigation of thermomechanical behaviors of flip chip BGA packages during manufacturing process and thermal cycling,” IEEE Trans. Comp. Packag. Technol. 27, 568-576 (2004).
[CrossRef]

Wasse, F.

K. Fischer, J. Muller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12, 163-169 (1994).
[CrossRef]

Williams, P. A.

Wong, W. H.

W. H. Wong, K. K. Liu, K. S. Chan, and E. Y. B. Pun, “Polymer devices for photonic applications,” J. Cryst. Growth 288, 100-104 (2006).
[CrossRef]

Yan, X.

Yao, H. H.

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Fused Quartz Properties & Usage Guide, http://www.quartz.com/gedata.html.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a prism coupler system and the heating apparatus.

Fig. 2
Fig. 2

(a) Measured refractive indices for the TE and TM polarizations and (b) their birefringence at different temperatures for a typical sample of BCB film on quartz substrate.

Fig. 3
Fig. 3

Measured refractive indices as a function of temperature for a typical sample of epoxy film on quartz substrate.

Tables (4)

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Table 1 Material Properties of the Film Layer and the Substrates

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Table 2 Film Refractive Indices (n) Measured at Room Temperature, In-Plane/Out-of-Plane Anisotropy ( Δ n ) and Their Temperature Dependence ( d n / d T ) at a Wavelength of 1536 nm

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Table 3 Calculated In-Plane Stresses ( σ x ) at Room Temperature and its Temperature Dependence ( σ x / T ) for BCB Films on Quartz and BK7 Substrates

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Table 4 Determined Thermo-Optic (B) and Stress-Optic ( C 1 and C 2 ) Coefficients at 1536 nm for BCB and Epoxy Films

Equations (7)

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

n T = B ,
n x = n 0 + C 1 σ x + C 2 ( σ y + σ z ) ,
n y = n 0 + C 1 σ y + C 2 ( σ x + σ z ) ,
n x = n 0 + B ( T T 0 ) + C 1 σ x + C 2 ( σ y + σ z ) ,
n y = n 0 + B ( T T 0 ) + C 1 σ y + C 2 ( σ x + σ z ) ,
d n x d T = B + C 1 σ x T + C 2 ( σ y + σ z ) T ,
d n y d T = B + C 1 σ y T + C 2 ( σ x + σ z ) T .

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