Abstract

A chirped moiré fiber Bragg grating has been demonstrated to be capable of measuring the magnitude, position, and footprint of a transverse load. The device provides an average spatial resolution of 164 μm and has a load accuracy of 0.15 N/mm, or 50 με.

© 2004 Optical Society of America

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References

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  1. S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
    [CrossRef]
  2. L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
    [CrossRef]
  3. L. A. Everall, K. Sugden, J. A. R. Williams, I. Bennion, “Fabrication of multipassband moire resonators in fibres by the dual-phase-mask exposure method,” Opt. Lett. 22, 1473–1475 (1997).
    [CrossRef]
  4. A. Carballar, M. A. Muriel, J. Azaña, “WDM channel selector based on transmissive chirped moiré fibre grating,” Electron. Lett. 35, 386–388 (1999).
    [CrossRef]
  5. K. E. Chisholm, K. Sugden, I. J. Murgatroyd, B. Sundström, B. Lindström, L. Zhang, “Application of chirped moiré fibre Bragg gratings to quasi-distributed monitoring of strains experienced by fibres during processing,” presented at the 14th International Conference on Optical Fiber Sensors (OFS), Venice, Italy, 11–13 October 2000.
  6. K. E. Chisholm, K. Sugden, L. Zhang, I. Bennion, “Novel high spatial resolution and temperature sensor using chirped moiré fibre gratings,” paper presented at the OSA Topical Meeting on Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP), Stuart, Fla., 23–25 September 1999.
  7. P. Torres, L. G. C. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291 (2002).
    [CrossRef]
  8. M. LeBlanc, S. T. Vohra, T. E. Tsai, E. J. Friebele, “Transverse load sensing by use of pi-phase-shifted fiber Bragg gratings,” Opt. Lett. 24, 1091–1093 (1999).
    [CrossRef]
  9. S. C. Tjin, L. Mohanty, N. Q. Ngo, “Pressure sensing with embedded chirped fiber grating,” Opt. Commun. 216, 115–118 (2003).
    [CrossRef]
  10. X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
    [CrossRef]
  11. Y. Liu, L. Zhang, I. Bennion, “Fibre optic load sensors with high transverse strain sensitivity based on long-period gratings in B/Ge co-doped fibre,” Electron. Lett. 35, 661–663 (1999).
    [CrossRef]
  12. L. Zhang, “Design and realisation of long-period grating devices in conventional and high birefringence fibers and their novel applications as fibre optic load sensors,” IEEE J. Sel. Top. Quantum Electron. 5, 1371–1378 (1999).
  13. A. Othonos, K. Kalli, Fiber Bragg Gratings (Artech House, Boston, Mass., 1999).
  14. A. M. Gillooly, K. E. Chisholm, L. Zhang, I. Bennion, “Chirped fibre Bragg grating optical wear sensor,” Meas. Sci. Technol. 15, 885–888 (2004).
    [CrossRef]
  15. R. B. Wagreich, W. A. Atia, H. Singh, J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
    [CrossRef]

2004 (1)

A. M. Gillooly, K. E. Chisholm, L. Zhang, I. Bennion, “Chirped fibre Bragg grating optical wear sensor,” Meas. Sci. Technol. 15, 885–888 (2004).
[CrossRef]

2003 (2)

S. C. Tjin, L. Mohanty, N. Q. Ngo, “Pressure sensing with embedded chirped fiber grating,” Opt. Commun. 216, 115–118 (2003).
[CrossRef]

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

2002 (1)

P. Torres, L. G. C. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291 (2002).
[CrossRef]

1999 (4)

M. LeBlanc, S. T. Vohra, T. E. Tsai, E. J. Friebele, “Transverse load sensing by use of pi-phase-shifted fiber Bragg gratings,” Opt. Lett. 24, 1091–1093 (1999).
[CrossRef]

Y. Liu, L. Zhang, I. Bennion, “Fibre optic load sensors with high transverse strain sensitivity based on long-period gratings in B/Ge co-doped fibre,” Electron. Lett. 35, 661–663 (1999).
[CrossRef]

L. Zhang, “Design and realisation of long-period grating devices in conventional and high birefringence fibers and their novel applications as fibre optic load sensors,” IEEE J. Sel. Top. Quantum Electron. 5, 1371–1378 (1999).

A. Carballar, M. A. Muriel, J. Azaña, “WDM channel selector based on transmissive chirped moiré fibre grating,” Electron. Lett. 35, 386–388 (1999).
[CrossRef]

1997 (1)

1996 (1)

R. B. Wagreich, W. A. Atia, H. Singh, J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

1995 (1)

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

1991 (1)

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Atia, W. A.

R. B. Wagreich, W. A. Atia, H. Singh, J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Azaña, J.

A. Carballar, M. A. Muriel, J. Azaña, “WDM channel selector based on transmissive chirped moiré fibre grating,” Electron. Lett. 35, 386–388 (1999).
[CrossRef]

Bayon, F.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Bennion, I.

A. M. Gillooly, K. E. Chisholm, L. Zhang, I. Bennion, “Chirped fibre Bragg grating optical wear sensor,” Meas. Sci. Technol. 15, 885–888 (2004).
[CrossRef]

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

Y. Liu, L. Zhang, I. Bennion, “Fibre optic load sensors with high transverse strain sensitivity based on long-period gratings in B/Ge co-doped fibre,” Electron. Lett. 35, 661–663 (1999).
[CrossRef]

L. A. Everall, K. Sugden, J. A. R. Williams, I. Bennion, “Fabrication of multipassband moire resonators in fibres by the dual-phase-mask exposure method,” Opt. Lett. 22, 1473–1475 (1997).
[CrossRef]

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

K. E. Chisholm, K. Sugden, L. Zhang, I. Bennion, “Novel high spatial resolution and temperature sensor using chirped moiré fibre gratings,” paper presented at the OSA Topical Meeting on Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP), Stuart, Fla., 23–25 September 1999.

Bernage, P.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Carballar, A.

A. Carballar, M. A. Muriel, J. Azaña, “WDM channel selector based on transmissive chirped moiré fibre grating,” Electron. Lett. 35, 386–388 (1999).
[CrossRef]

Chisholm, K.

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

Chisholm, K. E.

A. M. Gillooly, K. E. Chisholm, L. Zhang, I. Bennion, “Chirped fibre Bragg grating optical wear sensor,” Meas. Sci. Technol. 15, 885–888 (2004).
[CrossRef]

K. E. Chisholm, K. Sugden, L. Zhang, I. Bennion, “Novel high spatial resolution and temperature sensor using chirped moiré fibre gratings,” paper presented at the OSA Topical Meeting on Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP), Stuart, Fla., 23–25 September 1999.

K. E. Chisholm, K. Sugden, I. J. Murgatroyd, B. Sundström, B. Lindström, L. Zhang, “Application of chirped moiré fibre Bragg gratings to quasi-distributed monitoring of strains experienced by fibres during processing,” presented at the 14th International Conference on Optical Fiber Sensors (OFS), Venice, Italy, 11–13 October 2000.

Douay, M.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Everall, L. A.

Felmeri, I.

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

Fertein, E.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Friebele, E. J.

Georges, T.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Gillooly, A.

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

Gillooly, A. M.

A. M. Gillooly, K. E. Chisholm, L. Zhang, I. Bennion, “Chirped fibre Bragg grating optical wear sensor,” Meas. Sci. Technol. 15, 885–888 (2004).
[CrossRef]

Kalli, K.

A. Othonos, K. Kalli, Fiber Bragg Gratings (Artech House, Boston, Mass., 1999).

LeBlanc, M.

Legoubin, S.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Lindström, B.

K. E. Chisholm, K. Sugden, I. J. Murgatroyd, B. Sundström, B. Lindström, L. Zhang, “Application of chirped moiré fibre Bragg gratings to quasi-distributed monitoring of strains experienced by fibres during processing,” presented at the 14th International Conference on Optical Fiber Sensors (OFS), Venice, Italy, 11–13 October 2000.

Liu, Y.

Y. Liu, L. Zhang, I. Bennion, “Fibre optic load sensors with high transverse strain sensitivity based on long-period gratings in B/Ge co-doped fibre,” Electron. Lett. 35, 661–663 (1999).
[CrossRef]

Mohanty, L.

S. C. Tjin, L. Mohanty, N. Q. Ngo, “Pressure sensing with embedded chirped fiber grating,” Opt. Commun. 216, 115–118 (2003).
[CrossRef]

Molony, A.

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

Murgatroyd, I. J.

K. E. Chisholm, K. Sugden, I. J. Murgatroyd, B. Sundström, B. Lindström, L. Zhang, “Application of chirped moiré fibre Bragg gratings to quasi-distributed monitoring of strains experienced by fibres during processing,” presented at the 14th International Conference on Optical Fiber Sensors (OFS), Venice, Italy, 11–13 October 2000.

Muriel, M. A.

A. Carballar, M. A. Muriel, J. Azaña, “WDM channel selector based on transmissive chirped moiré fibre grating,” Electron. Lett. 35, 386–388 (1999).
[CrossRef]

Ngo, N. Q.

S. C. Tjin, L. Mohanty, N. Q. Ngo, “Pressure sensing with embedded chirped fiber grating,” Opt. Commun. 216, 115–118 (2003).
[CrossRef]

Niay, P.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Othonos, A.

A. Othonos, K. Kalli, Fiber Bragg Gratings (Artech House, Boston, Mass., 1999).

Shu, X. W.

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

Singh, H.

R. B. Wagreich, W. A. Atia, H. Singh, J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Sirkis, J. S.

R. B. Wagreich, W. A. Atia, H. Singh, J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Sugden, K.

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

L. A. Everall, K. Sugden, J. A. R. Williams, I. Bennion, “Fabrication of multipassband moire resonators in fibres by the dual-phase-mask exposure method,” Opt. Lett. 22, 1473–1475 (1997).
[CrossRef]

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

K. E. Chisholm, K. Sugden, I. J. Murgatroyd, B. Sundström, B. Lindström, L. Zhang, “Application of chirped moiré fibre Bragg gratings to quasi-distributed monitoring of strains experienced by fibres during processing,” presented at the 14th International Conference on Optical Fiber Sensors (OFS), Venice, Italy, 11–13 October 2000.

K. E. Chisholm, K. Sugden, L. Zhang, I. Bennion, “Novel high spatial resolution and temperature sensor using chirped moiré fibre gratings,” paper presented at the OSA Topical Meeting on Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP), Stuart, Fla., 23–25 September 1999.

Sundström, B.

K. E. Chisholm, K. Sugden, I. J. Murgatroyd, B. Sundström, B. Lindström, L. Zhang, “Application of chirped moiré fibre Bragg gratings to quasi-distributed monitoring of strains experienced by fibres during processing,” presented at the 14th International Conference on Optical Fiber Sensors (OFS), Venice, Italy, 11–13 October 2000.

Tjin, S. C.

S. C. Tjin, L. Mohanty, N. Q. Ngo, “Pressure sensing with embedded chirped fiber grating,” Opt. Commun. 216, 115–118 (2003).
[CrossRef]

Torres, P.

P. Torres, L. G. C. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291 (2002).
[CrossRef]

Tsai, T. E.

Valente, L. G. C.

P. Torres, L. G. C. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291 (2002).
[CrossRef]

Vohra, S. T.

Wagreich, R. B.

R. B. Wagreich, W. A. Atia, H. Singh, J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Williams, J. A. R.

Zhang, L.

A. M. Gillooly, K. E. Chisholm, L. Zhang, I. Bennion, “Chirped fibre Bragg grating optical wear sensor,” Meas. Sci. Technol. 15, 885–888 (2004).
[CrossRef]

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

Y. Liu, L. Zhang, I. Bennion, “Fibre optic load sensors with high transverse strain sensitivity based on long-period gratings in B/Ge co-doped fibre,” Electron. Lett. 35, 661–663 (1999).
[CrossRef]

L. Zhang, “Design and realisation of long-period grating devices in conventional and high birefringence fibers and their novel applications as fibre optic load sensors,” IEEE J. Sel. Top. Quantum Electron. 5, 1371–1378 (1999).

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

K. E. Chisholm, K. Sugden, L. Zhang, I. Bennion, “Novel high spatial resolution and temperature sensor using chirped moiré fibre gratings,” paper presented at the OSA Topical Meeting on Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP), Stuart, Fla., 23–25 September 1999.

K. E. Chisholm, K. Sugden, I. J. Murgatroyd, B. Sundström, B. Lindström, L. Zhang, “Application of chirped moiré fibre Bragg gratings to quasi-distributed monitoring of strains experienced by fibres during processing,” presented at the 14th International Conference on Optical Fiber Sensors (OFS), Venice, Italy, 11–13 October 2000.

Appl. Phys. Lett. (1)

X. W. Shu, K. Chisholm, I. Felmeri, K. Sugden, A. Gillooly, L. Zhang, I. Bennion, “Highly sensitive transverse load sensing with reversible sampled fiber Bragg gratings,” Appl. Phys. Lett. 83, 3003–3005 (2003).
[CrossRef]

Electron. Lett. (5)

Y. Liu, L. Zhang, I. Bennion, “Fibre optic load sensors with high transverse strain sensitivity based on long-period gratings in B/Ge co-doped fibre,” Electron. Lett. 35, 661–663 (1999).
[CrossRef]

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, T. Georges, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

L. Zhang, K. Sugden, I. Bennion, A. Molony, “Wide-stopband chirped fibre moiré grating transmission filters,” Electron. Lett. 31, 477–479 (1995).
[CrossRef]

A. Carballar, M. A. Muriel, J. Azaña, “WDM channel selector based on transmissive chirped moiré fibre grating,” Electron. Lett. 35, 386–388 (1999).
[CrossRef]

R. B. Wagreich, W. A. Atia, H. Singh, J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

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

L. Zhang, “Design and realisation of long-period grating devices in conventional and high birefringence fibers and their novel applications as fibre optic load sensors,” IEEE J. Sel. Top. Quantum Electron. 5, 1371–1378 (1999).

Meas. Sci. Technol. (1)

A. M. Gillooly, K. E. Chisholm, L. Zhang, I. Bennion, “Chirped fibre Bragg grating optical wear sensor,” Meas. Sci. Technol. 15, 885–888 (2004).
[CrossRef]

Opt. Commun. (2)

S. C. Tjin, L. Mohanty, N. Q. Ngo, “Pressure sensing with embedded chirped fiber grating,” Opt. Commun. 216, 115–118 (2003).
[CrossRef]

P. Torres, L. G. C. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291 (2002).
[CrossRef]

Opt. Lett. (2)

Other (3)

K. E. Chisholm, K. Sugden, I. J. Murgatroyd, B. Sundström, B. Lindström, L. Zhang, “Application of chirped moiré fibre Bragg gratings to quasi-distributed monitoring of strains experienced by fibres during processing,” presented at the 14th International Conference on Optical Fiber Sensors (OFS), Venice, Italy, 11–13 October 2000.

K. E. Chisholm, K. Sugden, L. Zhang, I. Bennion, “Novel high spatial resolution and temperature sensor using chirped moiré fibre gratings,” paper presented at the OSA Topical Meeting on Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP), Stuart, Fla., 23–25 September 1999.

A. Othonos, K. Kalli, Fiber Bragg Gratings (Artech House, Boston, Mass., 1999).

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Figures (7)

Fig. 1
Fig. 1

Transmission spectrum of a CMFBG fabricated by the double-scan technique.

Fig. 2
Fig. 2

CMFBG loading and interrogation setup.

Fig. 3
Fig. 3

(a) Transmission spectrum of a CMFBG with a loading element placed in the middle of the grating. (b) Magnification of the central region of the sensor.

Fig. 4
Fig. 4

Magnitude of the redshift that is due to the loading element, showing the footprint and the position of the load.

Fig. 5
Fig. 5

Comparison of phase shifts before and after a load is applied, showing the peak splitting that is due to the induced birefringence.

Fig. 6
Fig. 6

Linear dependence of birefringence on the applied load.

Fig. 7
Fig. 7

Distributed load of a 7-mm-wide loading element.

Equations (10)

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

Δnz=2δn1+cos2πzΛacos2πzΛb,
Λa=2Λ1Λ2Λ1+Λ2,
Λb=2Λ1Λ2Λ1-Λ2,
Δz=Λb/2.
N=L/Δz.
x=λ0-λxneffC,
B=Δnn¯=Δλλ¯,
Δn=n1-n2
λ¯=λ1+λ22
εxΔ-εyΔ=81+νfEfFπdf,

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