Abstract

We have experimentally investigated the multi-parameter sensing characteristics in a novel all-fiber Sagnac loop hybrid interferometer based on a highly birefringent photonic crystal fiber with two asymmetric cores. The sensor device was based on a combination of two types of in-fiber interferences, the intra-core-mode Sagnac interference and the inter-core-mode Mach-Zehnder interference due to the distinct birefringent properties associated with the asymmetric cores. Fast Fourier transform analysis on the transmission spectra of the device exhibited six clear peaks in the spatial frequency domain. By examining the phase shift responses of two distinct Sagnac and one Mach-Zehnder interference peaks, the response matrix that enable simultaneous measurement of torsion, strain, and temperature could be obtained. The proposed all-fiber Sagnac loop hybrid interferometer has the advantages such as simplicity of the device structure, compact device size, and capability for simultaneous sensing of multiple parameters.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]

2013 (2)

2012 (3)

Z. Liu, M.-L. V. Tse, C. Wu, D. Chen, C. Lu, and H.-Y. Tam, “Intermodal coupling of supermodes in a twin-core photonic crystal fiber and its application as a pressure sensor,” Opt. Express 20(19), 21749–21757 (2012).
[Crossref] [PubMed]

B. Kim and Y. Chung, “Polarization dependent inter-core interferences in twin-core photonic crystal fiber and its application to high temperature measurement,” Opt. Commun. 285(21-22), 4376–4380 (2012).
[Crossref]

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (5)

M. K. Szczurowski, T. Martynkien, G. Statkiewicz-Barabach, W. Urbanczyk, and D. J. Webb, “Measurements of polarimetric sensitivity to hydrostatic pressure, strain and temperature in birefringent dual-core microstructured polymer fiber,” Opt. Express 18(12), 12076–12087 (2010).
[Crossref] [PubMed]

O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777–2779 (2010).
[Crossref] [PubMed]

H. M. Kim, T. H. Kim, B. K. Kim, and Y. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

O. Frazão, S. F. O. Silva, J. Viegas, J. M. Baptista, J. L. Santos, J. Kobelke, and K. Schuster, “All Fiber Mach–Zehnder Interferometer Based on Suspended Twin-Core Fiber,” IEEE Photon. Technol. Lett. 22(17), 1300–1302 (2010).
[Crossref]

R. M. André, M. B. Marques, P. Roy, and O. Frazao, “Fiber loop mirror using a small core microstructured fiber for strain and temperature discrimination,” IEEE Photon. Technol. Lett. 22(15), 1120–1122 (2010).
[Crossref]

2009 (2)

2008 (2)

O. Frazão, S. O. Silva, J. M. Baptista, J. L. Santos, G. Statkiewicz-Barabach, W. Urbanczyk, and J. Wojcik, “Simultaneous measurement of multiparameters using a Sagnac interferometer with polarization maintaining side-hole fiber,” Appl. Opt. 47(27), 4841–4848 (2008).
[Crossref] [PubMed]

D.-P. Zhou, L. Wei, W.-K. Liu, and J. W. Y. Lit, “Simultaneous measurement of strain and temperature based on a fiber Bragg grating combined with a high-birefringence fiber loop mirror,” Opt. Commun. 281(18), 4640–4643 (2008).
[Crossref]

2007 (1)

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

2005 (1)

2001 (1)

1995 (1)

1981 (1)

André, R. M.

R. M. André, M. B. Marques, P. Roy, and O. Frazao, “Fiber loop mirror using a small core microstructured fiber for strain and temperature discrimination,” IEEE Photon. Technol. Lett. 22(15), 1120–1122 (2010).
[Crossref]

Bao, X.

Baptista, J. M.

Barlow, A. J.

Chatterjee, S. Kr.

Chaudhuri, P. R.

Chen, D.

Chen, K. S.

Chen, L.

Chen, W.

W. Chen, S. Lou, L. Wang, H. Zou, W. Lu, and J. Shuisheng, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011).
[Crossref]

Chi, H.

Cho, T.

Choi, H. Y.

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

Chung, Y.

B. Kim and Y. Chung, “Polarization dependent inter-core interferences in twin-core photonic crystal fiber and its application to high temperature measurement,” Opt. Commun. 285(21-22), 4376–4380 (2012).
[Crossref]

H. M. Kim, T. H. Kim, B. K. Kim, and Y. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

B. Kim, T. H. Kim, L. Cui, and Y. Chung, “Twin core photonic crystal fiber for in-line Mach-Zehnder interferometric sensing applications,” Opt. Express 17(18), 15502–15507 (2009).
[Crossref] [PubMed]

Claus, R. O.

Cui, L.

Dong, B.

Dong, X.

Dong, X. Y.

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

Eom, J. B.

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

Fang, X.

Feng, X.

Ferreira, M. S.

Février, S.

Frazao, O.

R. M. André, M. B. Marques, P. Roy, and O. Frazao, “Fiber loop mirror using a small core microstructured fiber for strain and temperature discrimination,” IEEE Photon. Technol. Lett. 22(15), 1120–1122 (2010).
[Crossref]

Frazão, O.

Han, Y.-G.

Hao, J. Z.

Harris, J.

Hwang, K.

Jamier, R.

Kai, G.

Khan, S. N.

Kim, B.

B. Kim and Y. Chung, “Polarization dependent inter-core interferences in twin-core photonic crystal fiber and its application to high temperature measurement,” Opt. Commun. 285(21-22), 4376–4380 (2012).
[Crossref]

B. Kim, T. H. Kim, L. Cui, and Y. Chung, “Twin core photonic crystal fiber for in-line Mach-Zehnder interferometric sensing applications,” Opt. Express 17(18), 15502–15507 (2009).
[Crossref] [PubMed]

Kim, B. K.

H. M. Kim, T. H. Kim, B. K. Kim, and Y. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Kim, G.

Kim, H. M.

H. M. Kim, T. H. Kim, B. K. Kim, and Y. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Kim, M. J.

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

Kim, T. H.

H. M. Kim, T. H. Kim, B. K. Kim, and Y. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

B. Kim, T. H. Kim, L. Cui, and Y. Chung, “Twin core photonic crystal fiber for in-line Mach-Zehnder interferometric sensing applications,” Opt. Express 17(18), 15502–15507 (2009).
[Crossref] [PubMed]

Kim, Y. H.

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

Kobelke, J.

O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777–2779 (2010).
[Crossref] [PubMed]

O. Frazão, S. F. O. Silva, J. Viegas, J. M. Baptista, J. L. Santos, J. Kobelke, and K. Schuster, “All Fiber Mach–Zehnder Interferometer Based on Suspended Twin-Core Fiber,” IEEE Photon. Technol. Lett. 22(17), 1300–1302 (2010).
[Crossref]

Larocque, H.

Lee, B. H.

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

Lee, K.

Lee, K. S.

Lee, S. B.

Liaw, C. Y.

Lit, J. W. Y.

D.-P. Zhou, L. Wei, W.-K. Liu, and J. W. Y. Lit, “Simultaneous measurement of strain and temperature based on a fiber Bragg grating combined with a high-birefringence fiber loop mirror,” Opt. Commun. 281(18), 4640–4643 (2008).
[Crossref]

Liu, B.

Liu, W.-K.

D.-P. Zhou, L. Wei, W.-K. Liu, and J. W. Y. Lit, “Simultaneous measurement of strain and temperature based on a fiber Bragg grating combined with a high-birefringence fiber loop mirror,” Opt. Commun. 281(18), 4640–4643 (2008).
[Crossref]

Liu, Y.

Liu, Z.

Lou, S.

W. Chen, S. Lou, L. Wang, H. Zou, W. Lu, and J. Shuisheng, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011).
[Crossref]

Lu, C.

Lu, P.

Lu, W.

W. Chen, S. Lou, L. Wang, H. Zou, W. Lu, and J. Shuisheng, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011).
[Crossref]

Marques, M. B.

R. M. André, M. B. Marques, P. Roy, and O. Frazao, “Fiber loop mirror using a small core microstructured fiber for strain and temperature discrimination,” IEEE Photon. Technol. Lett. 22(15), 1120–1122 (2010).
[Crossref]

Martynkien, T.

Mondal, K.

Park, K. S.

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

Payne, D. N.

Ramskov-Hansen, J. J.

Rho, B. S.

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

Roy, P.

M. S. Ferreira, J. M. Baptista, P. Roy, R. Jamier, S. Février, and O. Frazão, “Highly birefringent photonic bandgap Bragg fiber loop mirror for simultaneous measurement of strain and temperature,” Opt. Lett. 36(6), 993–995 (2011).
[Crossref] [PubMed]

R. M. André, M. B. Marques, P. Roy, and O. Frazao, “Fiber loop mirror using a small core microstructured fiber for strain and temperature discrimination,” IEEE Photon. Technol. Lett. 22(15), 1120–1122 (2010).
[Crossref]

Santos, J. L.

O. Frazão, S. F. O. Silva, J. Viegas, J. M. Baptista, J. L. Santos, J. Kobelke, and K. Schuster, “All Fiber Mach–Zehnder Interferometer Based on Suspended Twin-Core Fiber,” IEEE Photon. Technol. Lett. 22(17), 1300–1302 (2010).
[Crossref]

O. Frazão, S. O. Silva, J. M. Baptista, J. L. Santos, G. Statkiewicz-Barabach, W. Urbanczyk, and J. Wojcik, “Simultaneous measurement of multiparameters using a Sagnac interferometer with polarization maintaining side-hole fiber,” Appl. Opt. 47(27), 4841–4848 (2008).
[Crossref] [PubMed]

Schuster, K.

O. Frazão, S. F. O. Silva, J. Viegas, J. M. Baptista, J. L. Santos, J. Kobelke, and K. Schuster, “All Fiber Mach–Zehnder Interferometer Based on Suspended Twin-Core Fiber,” IEEE Photon. Technol. Lett. 22(17), 1300–1302 (2010).
[Crossref]

O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777–2779 (2010).
[Crossref] [PubMed]

Shuisheng, J.

W. Chen, S. Lou, L. Wang, H. Zou, W. Lu, and J. Shuisheng, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011).
[Crossref]

Shum, P.

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

Silva, R. M.

Silva, S. F. O.

O. Frazão, S. F. O. Silva, J. Viegas, J. M. Baptista, J. L. Santos, J. Kobelke, and K. Schuster, “All Fiber Mach–Zehnder Interferometer Based on Suspended Twin-Core Fiber,” IEEE Photon. Technol. Lett. 22(17), 1300–1302 (2010).
[Crossref]

Silva, S. O.

Statkiewicz-Barabach, G.

Szczurowski, M. K.

Tam, H. Y.

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

Tam, H.-Y.

Tao, X.-M.

Tse, M.-L. V.

Urbanczyk, W.

Viegas, J.

O. Frazão, S. F. O. Silva, J. Viegas, J. M. Baptista, J. L. Santos, J. Kobelke, and K. Schuster, “All Fiber Mach–Zehnder Interferometer Based on Suspended Twin-Core Fiber,” IEEE Photon. Technol. Lett. 22(17), 1300–1302 (2010).
[Crossref]

Wang, L.

W. Chen, S. Lou, L. Wang, H. Zou, W. Lu, and J. Shuisheng, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011).
[Crossref]

Webb, D. J.

Wei, L.

D.-P. Zhou, L. Wei, W.-K. Liu, and J. W. Y. Lit, “Simultaneous measurement of strain and temperature based on a fiber Bragg grating combined with a high-birefringence fiber loop mirror,” Opt. Commun. 281(18), 4640–4643 (2008).
[Crossref]

Wojcik, J.

Wu, C.

Xu, Y.

Xu, Z. W.

Yang, D.-X.

Yuan, S.

Zhang, W.

Zhou, D.-P.

D.-P. Zhou, L. Wei, W.-K. Liu, and J. W. Y. Lit, “Simultaneous measurement of strain and temperature based on a fiber Bragg grating combined with a high-birefringence fiber loop mirror,” Opt. Commun. 281(18), 4640–4643 (2008).
[Crossref]

Zhou, G.

Zou, H.

W. Chen, S. Lou, L. Wang, H. Zou, W. Lu, and J. Shuisheng, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

IEEE Photon. Technol. Lett. (4)

W. Chen, S. Lou, L. Wang, H. Zou, W. Lu, and J. Shuisheng, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011).
[Crossref]

H. M. Kim, T. H. Kim, B. K. Kim, and Y. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

O. Frazão, S. F. O. Silva, J. Viegas, J. M. Baptista, J. L. Santos, J. Kobelke, and K. Schuster, “All Fiber Mach–Zehnder Interferometer Based on Suspended Twin-Core Fiber,” IEEE Photon. Technol. Lett. 22(17), 1300–1302 (2010).
[Crossref]

R. M. André, M. B. Marques, P. Roy, and O. Frazao, “Fiber loop mirror using a small core microstructured fiber for strain and temperature discrimination,” IEEE Photon. Technol. Lett. 22(15), 1120–1122 (2010).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

D.-P. Zhou, L. Wei, W.-K. Liu, and J. W. Y. Lit, “Simultaneous measurement of strain and temperature based on a fiber Bragg grating combined with a high-birefringence fiber loop mirror,” Opt. Commun. 281(18), 4640–4643 (2008).
[Crossref]

B. Kim and Y. Chung, “Polarization dependent inter-core interferences in twin-core photonic crystal fiber and its application to high temperature measurement,” Opt. Commun. 285(21-22), 4376–4380 (2012).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Sensors (Basel) (1)

B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric fiber optic sensors,” Sensors (Basel) 12(3), 2467–2486 (2012).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

(a) SEM image of the highly birefringent PCF with asymmetric two cores, and (b) the core region in a magnified view. Two cores are highly elliptical and the slow axes of the cores were aligned to approximately 65° with each other.

Fig. 2
Fig. 2

(a) Experimental setup of the Sagnac loop hybrid interferometer based on a HB-ATCPCF (L ~12.3 cm), (b) Simulated electric-field patterns for the fundamental core modes of the cores with two polarization directions, (c) the schematic diagram showing the birefringence axis orientations β1 (core 1) and β2 (core 2) with respect to the input light polarization, and (d) the schematic diagram of the effective indices of the cores along with the slow and fast axes. In the figures, s and f indicate the slow and fast axes of the birefringent cores, respectively.

Fig. 3
Fig. 3

Transmission spectra of the in-line Mach-Zehnder interferometer made by 12.3cm-long HB-ATCPCF with the different input polarization states; (a) for x- polarization and (b) for y-polarization.

Fig. 4
Fig. 4

(a) Transmission spectrum of the SLHI made by the 12.3cm-long HB-ATCPCF in the wavelength domain, and (b) its corresponding FFT spectrum in the spatial frequency domain. The FFT spectra obtained from the transmission spectra of the MZI shown in Fig. 3 were also plotted as references.

Fig. 5
Fig. 5

(a) Transmission spectra of the SLHI with the torsion in the range of 150-210° applied in the counter clockwise direction, and (b) their corresponding phase spectra showing the phase shifts for the selected spatial peaks of P1, P2, and P6.

Fig. 6
Fig. 6

(a) Phase shifts of the three spatial peaks of P1, P2, and P6 for the torsion with the angle ranging from −150 to 320° (t < 0 for clockwise and t > 0 for counter clockwise rotation). (b) The absolute phase-shifts in the angle ranges of –40° to 40° and 140 to 220°, respectivly.

Fig. 7
Fig. 7

(a) Transmission spectra of the SLHI under different applied strains, and (b) phase shifts for the spatial peaks of P1, P2, and P6 with the strain in the range of 0 to 3000 με.

Fig. 8
Fig. 8

(a) Transmission spectra of the SLHI under different applied temperatures, and (b) phase shifts of the spatial peaks, P1, P2, and P6, with the temperature in the range of 25 to 145 °C.

Fig. 9
Fig. 9

Sensing performance of the SLHI for simultaneous measurement of two parameters of torsion and strain using the Sagnac interference peaks of P1 and P2.

Equations (14)

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E 3 = k E 1 , E 4 = 1k H E 1 ;H=( e iπ/2 0 0 e iπ/2 ),
E 3in = R 1 E 3 , E 4in = R 2 1 E 4 ;R(θ)=( cosθ sinθ sinθ cosθ ),
E 3in = s 1 E 3in + s 2 E 3in , E 4in = s 1 E 4in + s 2 E 4in .
E 3out = s 1 M 1 E 3in + s 2 M 2 E 3in , E 4out = s 1 M 1 E 4in + s 2 M 2 E 4in .
M m =R( β m )J( Φ m )R( β m );J( Φ m )=( e i k 0 n m f L 0 0 e i k 0 n m s L )
M m =( e i k 0 n m f L cos 2 β m + e i k 0 n m s L sin 2 β m 1 2 ( e i k 0 n m f L e i k 0 n m s L )sin2 β m 1 2 ( e i k 0 n m f L e i k 0 n m s L )sin2 β m e i k 0 n m f L sin 2 β m + e i k 0 n m s L cos 2 β m ).
M t = s 2 e i k 0 n 2 f L ( 1+ s 1 s 2 e i k 0 αL 0 0 e i k 0 B 2 L + s 1 s 2 e i k 0 B 1 L+i k 0 αL ).
E 2out =[ k R 2 M t R 1 +(1k)H R 1 1 M t R 2 1 H ] E 1 ,
I= ( E 2out *) T E 2out ( E 1 *) T E 1 = 1 2 sin 2 θ[ s 1 2 + s 2 2 + s 1 2 cos k 0 B 1 L+ s 2 2 cos k 0 B 2 L+ s 1 s 2 cos k 0 αL+ s 1 s 2 cos k 0 (α+ B 1 )L+ s 1 s 2 cos k 0 (α+ B 2 )L+ s 1 s 2 cos k 0 (α+ B 1 + B 2 )L ].
δ Φ ij =2πLδ( Δ n ij (λ) λ )=2π( Δ n gij L λ 0 2 )δλ.
ξ ij = Δ n gij L λ 0 2 .
δ Φ ij =2π ξ ij δλ.
Δ Φ q = Φ q τ Δτ+ Φ q ε Δε+ Φ q T ΔT;q=1,2,and6.
( Δ Φ 1 Δ Φ 2 Δ Φ 6 )=[ 5.87× 10 3 5.47× 10 5 5.58× 10 4 1.73× 10 3 1.91× 10 4 9.26× 10 4 1.77× 10 2 2.15× 10 3 2.67× 10 2 ]( Δτ Δε ΔT )(zone-I).

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