Abstract

A compact in-line modal interferometer based on a long period grating (LPG) inscribed in water-filled photonic crystal fiber (PCF) is proposed and demonstrated. The interferometer works from the interference between fundamental core mode and different vector components of LP11 core mode. The LPG is especially inscribed to realize the energy exchange between the fundamental core mode and different vector components of LP11 core mode in the PCF. We build a complete theoretical model and systematically analyze the multi-component-intermodal-interference mechanism of the interferometer based on coupled-mode theory. Due to the asymmetric index distribution over the cross section of the PCF caused by CO2-laser side illumination, the dispersion curves and temperature sensitivities referring to different vector components of LP11 core mode are quite different. Thus the interferometer is polarization-dependent and the adjacent interference fringes according to different components of LP11 mode show greatly discrimination in sensitivities of temperature and strain, making it a good candidate for multiple physics parameters measurements.

© 2014 Optical Society of America

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  1. S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
    [CrossRef]
  2. Y. Geng, X. Li, X. Tan, Y. Deng, Y. Yu, “In-line flat-top comb filter based on a cascaded all-solid photonic bandgap fiber intermodal interferometer,” Opt. Express 21(14), 17352–17358 (2013).
    [CrossRef] [PubMed]
  3. H. Gong, X. Li, Y. Jin, X. Dong, “Hollow-core photonic crystal fiber based modal interferometer for strain measurement,” Sens. Actuators A Phys. 187, 95–97 (2012).
    [CrossRef]
  4. W. J. Zhou, W. C. Wong, C. C. Chan, L. Y. Shao, X. Y. Dong, “Highly sensitive fiber loop ringdown strain sensor using photonic crystal fiber interferometer,” Appl. Opt. 50(19), 3087–3092 (2011).
    [CrossRef] [PubMed]
  5. G. A. Cárdenas-Sevilla, V. Finazzi, J. Villatoro, V. Pruneri, “Photonic crystal fiber sensor array based on modes overlapping,” Opt. Express 19(8), 7596–7602 (2011).
    [CrossRef] [PubMed]
  6. S. Wang, Y. G. Liu, Z. Wang, T. Han, W. Xu, Y. Wang, S. Wang, “Intermodal interferometer based on a fluid-filled two-mode photonic crystal fiber for sensing applications,” Appl. Opt. 52(14), 3166–3171 (2013).
    [CrossRef] [PubMed]
  7. G. Coviello, V. Finazzi, J. Villatoro, and V. Pruneri, “Encapsulated and coated photonic crystal fibre sensor for temperature measurements up to 1000°C,” in European Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe - EQEC, IEEE (2009).
  8. B. Dong, E. J. Hao, “Temperature-insensitive and intensity-modulated embedded photonic-crystal-fiber modal-interferometer-based micro displacement sensor,” J. Opt. Soc. Am. B 28(10), 2332–2336 (2011).
    [CrossRef]
  9. P. J. Huang, C. H. Hung, P. Y. Tai, and J. M. Hsu, “Sensitivity enhanced photonic crystal fiber interferometers with material dispersion engineering,” in Opto-Electronics and Communications Conference Technical Digest (2012), pp. 403–404.
  10. H. T. Hu, C. H. Chen, Y. C. Chen, J. N. Wang, J. L. Tang, W. T. Wu, “Investigations of refractive index sensing with a photonic crystal fiber interferometer,” in Photonics Global Conference (2010), pp. 1–3.
    [CrossRef]
  11. J. H. Lim, H. S. Jang, K. S. Lee, J. C. Kim, B. H. Lee, “Mach-Zehnder interferometer formed in a photonic crystal fiber based on a pair of long-period fiber gratings,” Opt. Lett. 29(4), 346–348 (2004).
    [CrossRef] [PubMed]
  12. G. A. Cárdenas-Sevilla, D. Monzon-Hernandez, I. Torres-Gomez, A. Martınez-Rıos, “Tapered Mach–Zehnder interferometer based on two mechanically induced long period fiber gratings as refractive index sensor,” Opt. Laser Technol. 44(5), 1516–1520 (2012).
    [CrossRef]
  13. Z. L. Sun, Y. G. Liu, Z. Wang, B. Y. Tai, T. T. Han, B. Liu, W. T. Cui, H. F. Wei, W. J. Tong, “Long period grating assistant photonic crystal fiber modal interferometer,” Opt. Express 19(14), 12913–12918 (2011).
    [CrossRef] [PubMed]
  14. J. Liu, Photonic Devices (Cambridge University, 2005), Chap. 4.
  15. T. Han, Y. G. Liu, Z. Wang, Z. Wu, S. Wang, S. Li, “Simultaneous temperature and force measurement using Fabry-Perot interferometer and bandgap effect of a fluid-filled photonic crystal fiber,” Opt. Express 20(12), 13320–13325 (2012).
    [CrossRef] [PubMed]
  16. Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
    [CrossRef]

2013 (2)

2012 (5)

G. A. Cárdenas-Sevilla, D. Monzon-Hernandez, I. Torres-Gomez, A. Martınez-Rıos, “Tapered Mach–Zehnder interferometer based on two mechanically induced long period fiber gratings as refractive index sensor,” Opt. Laser Technol. 44(5), 1516–1520 (2012).
[CrossRef]

H. Gong, X. Li, Y. Jin, X. Dong, “Hollow-core photonic crystal fiber based modal interferometer for strain measurement,” Sens. Actuators A Phys. 187, 95–97 (2012).
[CrossRef]

T. Han, Y. G. Liu, Z. Wang, Z. Wu, S. Wang, S. Li, “Simultaneous temperature and force measurement using Fabry-Perot interferometer and bandgap effect of a fluid-filled photonic crystal fiber,” Opt. Express 20(12), 13320–13325 (2012).
[CrossRef] [PubMed]

Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
[CrossRef]

S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
[CrossRef]

2011 (4)

2004 (1)

Bai, Z. Y.

S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
[CrossRef]

Cárdenas-Sevilla, G. A.

G. A. Cárdenas-Sevilla, D. Monzon-Hernandez, I. Torres-Gomez, A. Martınez-Rıos, “Tapered Mach–Zehnder interferometer based on two mechanically induced long period fiber gratings as refractive index sensor,” Opt. Laser Technol. 44(5), 1516–1520 (2012).
[CrossRef]

G. A. Cárdenas-Sevilla, V. Finazzi, J. Villatoro, V. Pruneri, “Photonic crystal fiber sensor array based on modes overlapping,” Opt. Express 19(8), 7596–7602 (2011).
[CrossRef] [PubMed]

Chan, C. C.

Chen, C. H.

H. T. Hu, C. H. Chen, Y. C. Chen, J. N. Wang, J. L. Tang, W. T. Wu, “Investigations of refractive index sensing with a photonic crystal fiber interferometer,” in Photonics Global Conference (2010), pp. 1–3.
[CrossRef]

Chen, Y. C.

H. T. Hu, C. H. Chen, Y. C. Chen, J. N. Wang, J. L. Tang, W. T. Wu, “Investigations of refractive index sensing with a photonic crystal fiber interferometer,” in Photonics Global Conference (2010), pp. 1–3.
[CrossRef]

Cui, W. T.

Deng, Y.

Dinh, X. Q.

Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
[CrossRef]

Dong, B.

Dong, X.

H. Gong, X. Li, Y. Jin, X. Dong, “Hollow-core photonic crystal fiber based modal interferometer for strain measurement,” Sens. Actuators A Phys. 187, 95–97 (2012).
[CrossRef]

Dong, X. Y.

Finazzi, V.

Gao, S. C.

S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
[CrossRef]

Ge, P. C.

S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
[CrossRef]

Geng, Y.

Gong, H.

H. Gong, X. Li, Y. Jin, X. Dong, “Hollow-core photonic crystal fiber based modal interferometer for strain measurement,” Sens. Actuators A Phys. 187, 95–97 (2012).
[CrossRef]

Han, T.

Han, T. T.

Hao, E. J.

Hu, H. T.

H. T. Hu, C. H. Chen, Y. C. Chen, J. N. Wang, J. L. Tang, W. T. Wu, “Investigations of refractive index sensing with a photonic crystal fiber interferometer,” in Photonics Global Conference (2010), pp. 1–3.
[CrossRef]

Jang, H. S.

Jiang, M.

Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
[CrossRef]

Jin, Y.

H. Gong, X. Li, Y. Jin, X. Dong, “Hollow-core photonic crystal fiber based modal interferometer for strain measurement,” Sens. Actuators A Phys. 187, 95–97 (2012).
[CrossRef]

Kim, J. C.

Lee, B. H.

Lee, K. S.

Li, S.

Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
[CrossRef]

T. Han, Y. G. Liu, Z. Wang, Z. Wu, S. Wang, S. Li, “Simultaneous temperature and force measurement using Fabry-Perot interferometer and bandgap effect of a fluid-filled photonic crystal fiber,” Opt. Express 20(12), 13320–13325 (2012).
[CrossRef] [PubMed]

Li, X.

Y. Geng, X. Li, X. Tan, Y. Deng, Y. Yu, “In-line flat-top comb filter based on a cascaded all-solid photonic bandgap fiber intermodal interferometer,” Opt. Express 21(14), 17352–17358 (2013).
[CrossRef] [PubMed]

H. Gong, X. Li, Y. Jin, X. Dong, “Hollow-core photonic crystal fiber based modal interferometer for strain measurement,” Sens. Actuators A Phys. 187, 95–97 (2012).
[CrossRef]

Lim, J. H.

Liu, B.

Liu, Y.

Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
[CrossRef]

Liu, Y. G.

Martinez-Rios, A.

G. A. Cárdenas-Sevilla, D. Monzon-Hernandez, I. Torres-Gomez, A. Martınez-Rıos, “Tapered Mach–Zehnder interferometer based on two mechanically induced long period fiber gratings as refractive index sensor,” Opt. Laser Technol. 44(5), 1516–1520 (2012).
[CrossRef]

Monzon-Hernandez, D.

G. A. Cárdenas-Sevilla, D. Monzon-Hernandez, I. Torres-Gomez, A. Martınez-Rıos, “Tapered Mach–Zehnder interferometer based on two mechanically induced long period fiber gratings as refractive index sensor,” Opt. Laser Technol. 44(5), 1516–1520 (2012).
[CrossRef]

Pruneri, V.

Shao, L. Y.

Shum, P. P.

Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
[CrossRef]

Sun, Z. L.

Tai, B. Y.

Tan, X.

Tang, J. L.

H. T. Hu, C. H. Chen, Y. C. Chen, J. N. Wang, J. L. Tang, W. T. Wu, “Investigations of refractive index sensing with a photonic crystal fiber interferometer,” in Photonics Global Conference (2010), pp. 1–3.
[CrossRef]

Tong, W. J.

Torres-Gomez, I.

G. A. Cárdenas-Sevilla, D. Monzon-Hernandez, I. Torres-Gomez, A. Martınez-Rıos, “Tapered Mach–Zehnder interferometer based on two mechanically induced long period fiber gratings as refractive index sensor,” Opt. Laser Technol. 44(5), 1516–1520 (2012).
[CrossRef]

Villatoro, J.

Wang, J. N.

H. T. Hu, C. H. Chen, Y. C. Chen, J. N. Wang, J. L. Tang, W. T. Wu, “Investigations of refractive index sensing with a photonic crystal fiber interferometer,” in Photonics Global Conference (2010), pp. 1–3.
[CrossRef]

Wang, S.

Wang, Y.

Wang, Z.

Wei, H. F.

Wong, W. C.

Wu, W. T.

H. T. Hu, C. H. Chen, Y. C. Chen, J. N. Wang, J. L. Tang, W. T. Wu, “Investigations of refractive index sensing with a photonic crystal fiber interferometer,” in Photonics Global Conference (2010), pp. 1–3.
[CrossRef]

Wu, Z.

T. Han, Y. G. Liu, Z. Wang, Z. Wu, S. Wang, S. Li, “Simultaneous temperature and force measurement using Fabry-Perot interferometer and bandgap effect of a fluid-filled photonic crystal fiber,” Opt. Express 20(12), 13320–13325 (2012).
[CrossRef] [PubMed]

Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
[CrossRef]

Xu, W.

Xue, X. L.

S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
[CrossRef]

Yu, Y.

Zhang, H.

S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
[CrossRef]

Zhang, W. G.

S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
[CrossRef]

Zhou, W. J.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Z. Wu, Y. Liu, Z. Wang, T. Han, S. Li, M. Jiang, P. P. Shum, X. Q. Dinh, “In-line Mach–Zehnder interferometer composed of microtaper and long-period grating in all-solid photonic bandgap fiber,” Appl. Phys. Lett. 101(14), 141106 (2012).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

S. C. Gao, W. G. Zhang, P. C. Ge, X. L. Xue, H. Zhang, Z. Y. Bai, “Highly sensitive in-fiber refractive index sensor based on down-bitaper seeded up-bitaper pair,” IEEE Photonics Technol. Lett. 24(20), 1878–1881 (2012).
[CrossRef]

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

Opt. Express (4)

Opt. Laser Technol. (1)

G. A. Cárdenas-Sevilla, D. Monzon-Hernandez, I. Torres-Gomez, A. Martınez-Rıos, “Tapered Mach–Zehnder interferometer based on two mechanically induced long period fiber gratings as refractive index sensor,” Opt. Laser Technol. 44(5), 1516–1520 (2012).
[CrossRef]

Opt. Lett. (1)

Sens. Actuators A Phys. (1)

H. Gong, X. Li, Y. Jin, X. Dong, “Hollow-core photonic crystal fiber based modal interferometer for strain measurement,” Sens. Actuators A Phys. 187, 95–97 (2012).
[CrossRef]

Other (4)

P. J. Huang, C. H. Hung, P. Y. Tai, and J. M. Hsu, “Sensitivity enhanced photonic crystal fiber interferometers with material dispersion engineering,” in Opto-Electronics and Communications Conference Technical Digest (2012), pp. 403–404.

H. T. Hu, C. H. Chen, Y. C. Chen, J. N. Wang, J. L. Tang, W. T. Wu, “Investigations of refractive index sensing with a photonic crystal fiber interferometer,” in Photonics Global Conference (2010), pp. 1–3.
[CrossRef]

G. Coviello, V. Finazzi, J. Villatoro, and V. Pruneri, “Encapsulated and coated photonic crystal fibre sensor for temperature measurements up to 1000°C,” in European Conference on Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe - EQEC, IEEE (2009).

J. Liu, Photonic Devices (Cambridge University, 2005), Chap. 4.

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Figures (8)

Fig. 1
Fig. 1

Schematic configuration of the proposed interferometer. The inset (a) is the cross section of the PCF.

Fig. 2
Fig. 2

(a) Phase-matching curves (the curves of HE 21 (1) mode and HE 21 (2) mode almost coincide) and theoretical intensity distributions of different vector components of LP11 core mode in PCF, and the inset is equivalent model for the cross-section of the LPG; (b) Calculated transmission spectra of the interferometers with (red line) and without (blue line) the LPG.

Fig. 3
Fig. 3

Calculated temperature sensitivity of the interferometer for different theoretical models, the inset images are the theoretical equivalent models for the cross-section of the LPG.

Fig. 4
Fig. 4

(a) Calculated transmission spectrum when TM01 mode and HE21 mode exist simultaneously, the inset images is the spectra when only TM01 or HE21 mode exists; (b) Theoretical temperature responses of peak ① and peak ②.

Fig. 5
Fig. 5

Measured transmission spectra of the interferometers for the LPGs with a period of (a) 180 μm and (b) 190 μm; (c) Microscopic image of the LPG area.

Fig. 6
Fig. 6

Spectra characteristics of the proposed interferometer with regard to the state of polarization of incident light.

Fig. 7
Fig. 7

Wavelength responses of the interferometer at different polarization states.

Fig. 8
Fig. 8

Wavelength responses of the interferometer for variations of applied strain.

Equations (19)

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E ( x , y , z ) = E 1 ( x , y , z ) + E 2 ( x , y , z ) = a 1 I e i β 01 L 1 + b 1 I e i β 11 L 1
E 1 ( x , y , z ) = A ( z ) a 1 I e i β 01 L 1 + B ( z ) a 1 I e i β 01 L 1
d A ( z ) d z = i κ * B ( z ) e i 2 Δ z , d B ( z ) d z = i κ A ( z ) e i 2 Δ z
κ μ ν ( z ) exp ( i 2 π z Λ ) ω 4 E μ * ( x , y ) Δ ε ( x , y ) E ν ( x , y ) d x d y
A ( z ) = e i Δ z [ cos γ z + i Δ γ sin γ z ] , B ( z ) = e i Δ z i κ γ sin γ z
E ( x , y , z ) = e i Δ L c [ cos γ L c + i Δ γ sin γ L c ] a 1 I e i β 01 L 1 + e i Δ L c i κ γ sin γ L c a 1 I e i β 01 L 1 + e i Δ L c [ cos γ L c + i Δ γ sin γ L c ] b 1 I e i β 11 L 1 + e i Δ L c i κ γ sin γ L c b 1 I e i β 11 L 1
E ( x , y , z ) = e i Δ L c [ cos γ L c + i Δ γ sin γ L c ] a 1 a 2 I e i β 01 ( L 1 + L 2 ) + e i Δ L c i κ γ sin γ L c a 1 b 2 I e i ( β 01 L 1 + β 11 L 2 ) + e i Δ L c [ cos γ L c + i Δ γ sin γ L c ] b 1 b 2 I e i β 11 ( L 1 + L 2 ) + e i Δ L c i κ γ sin γ L c b 1 a 2 I e i ( β 11 L 1 + β 01 L 2 )
I o u t = E ( x , y ) E * ( x , y )
I o u t = ( a 2 + b 2 ) I A 1 + a b I B 1 + a a b I C 1 + b a b I D 1
A 1 = cos 2 γ L c + Δ 2 γ 2 sin 2 γ L c
B 1 = 2 [ cos 2 γ L c + Δ 2 γ 2 sin 2 γ L c ] cos [ ( β 11 β 01 ) ( L 1 + L c ) ] + π 2 2 γ 2 L c 2 sin 2 γ L c [ 1 + cos [ ( β 11 β 01 ) ( L 1 L 2 ) ] ]
C 1 = 2 π cos γ L c sin γ L c γ L c [ sin [ G L c 2 Δ L c ( β 01 β 11 ) L 1 + L 2 2 ] cos [ ( β 01 β 11 ) L 1 L 2 2 ] ] 2 Δ π sin 2 γ L c γ 2 L c [ cos [ G L c 2 Δ L c ( β 01 β 11 ) L 1 + L 2 2 ] cos [ ( β 01 β 11 ) L 1 L 2 2 ] ]
D 1 = 2 π cos γ L c sin γ L c γ L c [ sin [ G L c 2 Δ L c ( β 11 β 01 ) L 1 + L 2 2 ] cos [ ( β 11 β 01 ) L 1 L 2 2 ] ] 2 Δ π sin 2 γ L c γ 2 L c [ cos [ G L c 2 Δ L c ( β 11 β 01 ) L 1 + L 2 2 ] cos [ ( β 11 β 01 ) L 1 L 2 2 ] ]
I o u t = ( a 2 + b 2 ) I ( cos 2 γ L c + Δ 2 γ 2 sin 2 γ L c ) + a b I π 2 2 L c 2 γ 2 sin 2 γ L c [ 1 + cos [ ( β 11 β 01 ) ( L 1 L 2 ) ] ] + 2 a b I ( cos 2 γ L c + Δ 2 γ 2 sin 2 γ L c ) cos [ ( β 11 β 01 ) ( L 1 + L 2 ) ]
I o u t ' = ( a 2 + b 2 ) I + 2 a b I cos [ ( β 11 β 01 ) ( L 1 + L c + L 2 ) ]
O P D = [ n 1 ( λ , T ) × L 1 + n 2 ( λ , T ) × L 2 ] [ n 2 ( λ , T ) × L 1 + n 1 ( λ , T ) × L 2 ] = Δ n ( λ , T ) × Δ L
Δ n ( λ , T ) × Δ L λ ( T ) = m + 1 2
S = d λ d T = Δ n ( λ , T ) T × λ ( T ) Δ n Δ n ( λ , T ) λ × λ ( T ) = Δ n ( λ , T ) T × λ ( T ) N g
N g = Δ n Δ n ( λ , T ) λ × λ ( T )

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