Abstract

We have investigated experimentally and numerically the temperature and refractive index (RI) sensitivity characteristics of excessively tilted fiber gratings (Ex-TFGs) in detail. Both results have shown that the temperature and RI sensitivities of Ex-TFGs are mode order dependent. For temperature sensitivity, the higher order cladding mode of Ex-TFG exhibited lower temperature sensitivity, quantitatively, the temperature sensitivities of TM cladding modes at the resonance wavelength around 1550nm are 9pm/°C, 6.8pm/°C, 5.6pm/°C and, 4pm/°C for cladding mode 28th, 31st, 35th, 40th, respectively, indicating the overall temperature sensitivity of Ex-TFGs were lower than that of normal FBGs. The SRI sensing results have shown that the RI sensitivity of Ex-TFG at the special index value could be improved by choosing the cladding mode with effective index close to the refractive index of the detecting medium. The SRI sensitivities at the effective mode index were 2250nm/RIU at 1.408, 864nm/RIU at 1.395, 1536nm/RIU at 1.380 and 1360nm/RIU at 1.355, for the cladding mode of 28th, 31st, 35th, 43rd, respectively. The experimental results have also shown the SRI sensitivity of Ex-TFG was increasing with increasing of the resonance wavelength.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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  5. T. Guo, L. Shao, H.-Y. Tam, P. A. Krug, and J. Albert, “Tilted fiber grating accelerometer incorporating an abrupt biconical taper for cladding to core recoupling,” Opt. Express 17(23), 20651–20660 (2009).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2016 (5)

T. Guo, F. Liu, B.-O. Guan, and J. Albert, “[INVITED] Tilted fiber grating mechanical and biochemical sensors,” Opt. Laser Technol. 78, 19–33 (2016).
[Crossref]

C. Caucheteur, T. Guo, F. Liu, B.-O. Guan, and J. Albert, “Ultrasensitive plasmonic sensing in air using optical fibre spectral combs,” Nat. Commun. 7, 13371 (2016).
[Crossref] [PubMed]

G. Wang, C. Wang, Z. Yan, and L. Zhang, “Highly efficient spectrally encoded imaging using a 45° tilted fiber grating,” Opt. Lett. 41(11), 2398–2401 (2016).
[Crossref] [PubMed]

Z. Yan, H. Wang, C. Wang, Z. Sun, G. Yin, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “Theoretical and experimental analysis of excessively tilted fiber gratings,” Opt. Express 24(11), 12107–12115 (2016).
[Crossref] [PubMed]

Z. Zhang, C. Mou, Z. Yan, Z. Sun, and L. Zhang, “Orthogonally polarized bright–dark pulse pair generation in mode-locked fiber laser with a large-angle tilted fiber grating,” Appl. Phys. B 122(6), 161 (2016).
[Crossref]

2015 (4)

Z. Yan, Z. Sun, K. Zhou, B. Luo, J. Li, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Numerical and experimental analysis of sensitivity enhanced RI sensor based on Ex-TFG in thin cladding fiber,” J. Lightwave Technol. 33(14), 3023–3027 (2015).
[Crossref]

Z. Yan, C. Mou, Z. Sun, K. Zhou, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Hybrid tilted fiber grating based refractive index and liquid level sensing system,” Opt. Commun. 351, 144–148 (2015).
[Crossref]

B. Luo, Z. Yan, Z. Sun, Y. Liu, M. Zhao, and L. Zhang, “Biosensor based on excessively tilted fiber grating in thin-cladding optical fiber for sensitive and selective detection of low glucose concentration,” Opt. Express 23(25), 32429–32440 (2015).
[Crossref] [PubMed]

M. R. Islam, M. Bagherifaez, M. M. Ali, H. K. Chai, K. S. Lim, and H. Ahmad, “Tilted Fiber Bragg Grating Sensors for Reinforcement Corrosion Measurement in Marine Concrete Structure,” IEEE Trans. Instrum. Meas. 64(12), 3510–3516 (2015).
[Crossref]

2014 (2)

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

J. Li, Z. Yan, Z. Sun, H. Luo, Y. He, Z. Li, Y. Liu, and L. Zhang, “Thulium-doped all-fiber mode-locked laser based on NPR and 45°-tilted fiber grating,” Opt. Express 22(25), 31020–31028 (2014).
[Crossref] [PubMed]

2013 (1)

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg gratings sensors,” Laser Photonics Rev. 7(1), 83–108 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (2)

2009 (3)

2006 (3)

2005 (1)

2002 (1)

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

2001 (1)

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37(4), 216–218 (2001).
[Crossref]

2000 (2)

K. S. Chiang, Y. Liu, M. N. Ng, and X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36(11), 966–967 (2000).
[Crossref]

P. S. Westbrook, T. A. Strasser, and T. Erdogan, “In-line polarimeter using blazed fibre gratings,” IEEE Photonics Technol. Lett. 12(10), 1352–1354 (2000).
[Crossref]

1996 (1)

1994 (1)

M. J. Guy, S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Low-loss fibre Bragg grating transmission filter based on a fibre polarisation splitter,” Electron. Lett. 30(18), 1512–1513 (1994).
[Crossref]

1990 (1)

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

1979 (1)

Adebayo, A.

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

Ahmad, H.

M. R. Islam, M. Bagherifaez, M. M. Ali, H. K. Chai, K. S. Lim, and H. Ahmad, “Tilted Fiber Bragg Grating Sensors for Reinforcement Corrosion Measurement in Marine Concrete Structure,” IEEE Trans. Instrum. Meas. 64(12), 3510–3516 (2015).
[Crossref]

Albert, J.

T. Guo, F. Liu, B.-O. Guan, and J. Albert, “[INVITED] Tilted fiber grating mechanical and biochemical sensors,” Opt. Laser Technol. 78, 19–33 (2016).
[Crossref]

C. Caucheteur, T. Guo, F. Liu, B.-O. Guan, and J. Albert, “Ultrasensitive plasmonic sensing in air using optical fibre spectral combs,” Nat. Commun. 7, 13371 (2016).
[Crossref] [PubMed]

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg gratings sensors,” Laser Photonics Rev. 7(1), 83–108 (2013).
[Crossref]

Y. Shevchenko, C. Chen, M. A. Dakka, and J. Albert, “Polarization-selective grating excitation of plasmons in cylindrical optical fibers,” Opt. Lett. 35(5), 637–639 (2010).
[Crossref] [PubMed]

T. Guo, L. Shao, H.-Y. Tam, P. A. Krug, and J. Albert, “Tilted fiber grating accelerometer incorporating an abrupt biconical taper for cladding to core recoupling,” Opt. Express 17(23), 20651–20660 (2009).
[Crossref] [PubMed]

T. Guo, H.-Y. Tam, P. A. Krug, and J. Albert, “Reflective tilted fiber Bragg grating refractometer based on strong cladding to core recoupling,” Opt. Express 17(7), 5736–5742 (2009).
[Crossref] [PubMed]

Ali, M. M.

M. R. Islam, M. Bagherifaez, M. M. Ali, H. K. Chai, K. S. Lim, and H. Ahmad, “Tilted Fiber Bragg Grating Sensors for Reinforcement Corrosion Measurement in Marine Concrete Structure,” IEEE Trans. Instrum. Meas. 64(12), 3510–3516 (2015).
[Crossref]

Allsop, T.

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37(4), 216–218 (2001).
[Crossref]

Bagherifaez, M.

M. R. Islam, M. Bagherifaez, M. M. Ali, H. K. Chai, K. S. Lim, and H. Ahmad, “Tilted Fiber Bragg Grating Sensors for Reinforcement Corrosion Measurement in Marine Concrete Structure,” IEEE Trans. Instrum. Meas. 64(12), 3510–3516 (2015).
[Crossref]

Bale, B. G.

Bennion, I.

C. Mou, H. Wang, B. G. Bale, K. Zhou, L. Zhang, and I. Bennion, “All-fiber passively mode-locked femtosecond laser using a 45º-tilted fiber grating polarization element,” Opt. Express 18(18), 18906–18911 (2010).
[Crossref] [PubMed]

R. Suo, X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fibre directional transverse loading sensor based on excessively tilted fibre Bragg gratings,” Meas. Sci. Technol. 20(3), 034015 (2009).
[Crossref]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-Fiber Twist Sensor Based on a Fiber Bragg Grating With 81 Tilted Structure,” IEEE Photonics Technol. Lett. 18, 2596–2598 (2006).
[Crossref]

K. Zhou, L. Z. X. Chen, and I. Bennion, “Low Temperature Sensitivity Grating Devices Based on Ex-45° Tilting Structure Capable of Forward-Propagating Cladding Modes Coupling,” J. Lightwave Technol. 24, 5087–5094 (2006).
[Crossref]

K. Zhou, L. Zhang, X. Chen, and I. Bennion, “Optic sensors of high refractive-index responsivity and low thermal cross sensitivity that use fiber Bragg gratings of >80 ° tilted structures,” Opt. Lett. 31(9), 1193–1195 (2006).
[Crossref] [PubMed]

K. Zhou, G. Simpson, X. Chen, L. Zhang, and I. Bennion, “High extinction ratio in-fiber polarizers based on 45 ° tilted fiber Bragg gratings,” Opt. Lett. 30(11), 1285–1287 (2005).
[Crossref] [PubMed]

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37(4), 216–218 (2001).
[Crossref]

Bilodeau, F.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Bossen, A.

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

Caucheteur, C.

C. Caucheteur, T. Guo, F. Liu, B.-O. Guan, and J. Albert, “Ultrasensitive plasmonic sensing in air using optical fibre spectral combs,” Nat. Commun. 7, 13371 (2016).
[Crossref] [PubMed]

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg gratings sensors,” Laser Photonics Rev. 7(1), 83–108 (2013).
[Crossref]

Chai, H. K.

M. R. Islam, M. Bagherifaez, M. M. Ali, H. K. Chai, K. S. Lim, and H. Ahmad, “Tilted Fiber Bragg Grating Sensors for Reinforcement Corrosion Measurement in Marine Concrete Structure,” IEEE Trans. Instrum. Meas. 64(12), 3510–3516 (2015).
[Crossref]

Chen, C.

Chen, G.

Chen, L.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

Chen, L. Z. X.

Chen, X.

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

Z. Yan, C. Mou, K. Zhou, X. Chen, and L. Zhang, “UV-Inscription, Polarization-Dependant Loss Characteristics and Applications of 45°Tilted Fiber Gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
[Crossref]

R. Suo, X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fibre directional transverse loading sensor based on excessively tilted fibre Bragg gratings,” Meas. Sci. Technol. 20(3), 034015 (2009).
[Crossref]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-Fiber Twist Sensor Based on a Fiber Bragg Grating With 81 Tilted Structure,” IEEE Photonics Technol. Lett. 18, 2596–2598 (2006).
[Crossref]

K. Zhou, L. Zhang, X. Chen, and I. Bennion, “Optic sensors of high refractive-index responsivity and low thermal cross sensitivity that use fiber Bragg gratings of >80 ° tilted structures,” Opt. Lett. 31(9), 1193–1195 (2006).
[Crossref] [PubMed]

K. Zhou, G. Simpson, X. Chen, L. Zhang, and I. Bennion, “High extinction ratio in-fiber polarizers based on 45 ° tilted fiber Bragg gratings,” Opt. Lett. 30(11), 1285–1287 (2005).
[Crossref] [PubMed]

Chernikov, S. V.

M. J. Guy, S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Low-loss fibre Bragg grating transmission filter based on a fibre polarisation splitter,” Electron. Lett. 30(18), 1512–1513 (1994).
[Crossref]

Chiang, K. S.

K. S. Chiang, Y. Liu, M. N. Ng, and X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36(11), 966–967 (2000).
[Crossref]

Dai, X.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

Dakka, M. A.

Ding, H.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

Dong, X.

K. S. Chiang, Y. Liu, M. N. Ng, and X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36(11), 966–967 (2000).
[Crossref]

Erdogan, T.

P. S. Westbrook, T. A. Strasser, and T. Erdogan, “In-line polarimeter using blazed fibre gratings,” IEEE Photonics Technol. Lett. 12(10), 1352–1354 (2000).
[Crossref]

T. Erdogan and J. E. Sipe, “Tilted fiber phase gratings,” J. Opt. Soc. Am. A 13(2), 296 (1996).
[Crossref]

Guan, B.-O.

T. Guo, F. Liu, B.-O. Guan, and J. Albert, “[INVITED] Tilted fiber grating mechanical and biochemical sensors,” Opt. Laser Technol. 78, 19–33 (2016).
[Crossref]

C. Caucheteur, T. Guo, F. Liu, B.-O. Guan, and J. Albert, “Ultrasensitive plasmonic sensing in air using optical fibre spectral combs,” Nat. Commun. 7, 13371 (2016).
[Crossref] [PubMed]

Guo, T.

C. Caucheteur, T. Guo, F. Liu, B.-O. Guan, and J. Albert, “Ultrasensitive plasmonic sensing in air using optical fibre spectral combs,” Nat. Commun. 7, 13371 (2016).
[Crossref] [PubMed]

T. Guo, F. Liu, B.-O. Guan, and J. Albert, “[INVITED] Tilted fiber grating mechanical and biochemical sensors,” Opt. Laser Technol. 78, 19–33 (2016).
[Crossref]

T. Guo, H.-Y. Tam, P. A. Krug, and J. Albert, “Reflective tilted fiber Bragg grating refractometer based on strong cladding to core recoupling,” Opt. Express 17(7), 5736–5742 (2009).
[Crossref] [PubMed]

T. Guo, L. Shao, H.-Y. Tam, P. A. Krug, and J. Albert, “Tilted fiber grating accelerometer incorporating an abrupt biconical taper for cladding to core recoupling,” Opt. Express 17(23), 20651–20660 (2009).
[Crossref] [PubMed]

Guy, M. J.

M. J. Guy, S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Low-loss fibre Bragg grating transmission filter based on a fibre polarisation splitter,” Electron. Lett. 30(18), 1512–1513 (1994).
[Crossref]

Gwandu, B.

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37(4), 216–218 (2001).
[Crossref]

He, Y.

Hill, K. O.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Hu, X.

Islam, M. R.

M. R. Islam, M. Bagherifaez, M. M. Ali, H. K. Chai, K. S. Lim, and H. Ahmad, “Tilted Fiber Bragg Grating Sensors for Reinforcement Corrosion Measurement in Marine Concrete Structure,” IEEE Trans. Instrum. Meas. 64(12), 3510–3516 (2015).
[Crossref]

Johnson, D.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Kashyap, R.

M. J. Guy, S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Low-loss fibre Bragg grating transmission filter based on a fibre polarisation splitter,” Electron. Lett. 30(18), 1512–1513 (1994).
[Crossref]

Krug, P. A.

Li, C.

Li, J.

Li, X.

Li, Z.

Lim, K. S.

M. R. Islam, M. Bagherifaez, M. M. Ali, H. K. Chai, K. S. Lim, and H. Ahmad, “Tilted Fiber Bragg Grating Sensors for Reinforcement Corrosion Measurement in Marine Concrete Structure,” IEEE Trans. Instrum. Meas. 64(12), 3510–3516 (2015).
[Crossref]

Liu, F.

T. Guo, F. Liu, B.-O. Guan, and J. Albert, “[INVITED] Tilted fiber grating mechanical and biochemical sensors,” Opt. Laser Technol. 78, 19–33 (2016).
[Crossref]

C. Caucheteur, T. Guo, F. Liu, B.-O. Guan, and J. Albert, “Ultrasensitive plasmonic sensing in air using optical fibre spectral combs,” Nat. Commun. 7, 13371 (2016).
[Crossref] [PubMed]

Liu, X.

Liu, Y.

Lu, P.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

Luo, B.

Luo, H.

Malo, B.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Meier, C.

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

Mihailov, S. J.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

Miyagi, M.

Mou, C.

Z. Zhang, C. Mou, Z. Yan, Z. Sun, and L. Zhang, “Orthogonally polarized bright–dark pulse pair generation in mode-locked fiber laser with a large-angle tilted fiber grating,” Appl. Phys. B 122(6), 161 (2016).
[Crossref]

Z. Yan, C. Mou, Z. Sun, K. Zhou, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Hybrid tilted fiber grating based refractive index and liquid level sensing system,” Opt. Commun. 351, 144–148 (2015).
[Crossref]

Z. Yan, C. Mou, K. Zhou, X. Chen, and L. Zhang, “UV-Inscription, Polarization-Dependant Loss Characteristics and Applications of 45°Tilted Fiber Gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
[Crossref]

C. Mou, H. Wang, B. G. Bale, K. Zhou, L. Zhang, and I. Bennion, “All-fiber passively mode-locked femtosecond laser using a 45º-tilted fiber grating polarization element,” Opt. Express 18(18), 18906–18911 (2010).
[Crossref] [PubMed]

Ng, M. N.

K. S. Chiang, Y. Liu, M. N. Ng, and X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36(11), 966–967 (2000).
[Crossref]

Nishida, S.

Považay, B.

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

Remund, S.

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

Shao, L.

Shao, L. Y.

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg gratings sensors,” Laser Photonics Rev. 7(1), 83–108 (2013).
[Crossref]

Shen, D.

Shevchenko, Y.

Shu, X.

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37(4), 216–218 (2001).
[Crossref]

Simpson, G.

Sipe, J. E.

Skinner, I.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Smelser, C.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

Strasser, T. A.

P. S. Westbrook, T. A. Strasser, and T. Erdogan, “In-line polarimeter using blazed fibre gratings,” IEEE Photonics Technol. Lett. 12(10), 1352–1354 (2000).
[Crossref]

Sun, Z.

Suo, R.

R. Suo, X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fibre directional transverse loading sensor based on excessively tilted fibre Bragg gratings,” Meas. Sci. Technol. 20(3), 034015 (2009).
[Crossref]

Tam, H.-Y.

Taylor, J. R.

M. J. Guy, S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Low-loss fibre Bragg grating transmission filter based on a fibre polarisation splitter,” Electron. Lett. 30(18), 1512–1513 (1994).
[Crossref]

Vineberg, K. A.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Walker, R. B.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

Wang, C.

Wang, G.

Wang, H.

Wang, L.

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

Wang, Y.

Westbrook, P. S.

P. S. Westbrook, T. A. Strasser, and T. Erdogan, “In-line polarimeter using blazed fibre gratings,” IEEE Photonics Technol. Lett. 12(10), 1352–1354 (2000).
[Crossref]

Yan, Z.

Z. Zhang, C. Mou, Z. Yan, Z. Sun, and L. Zhang, “Orthogonally polarized bright–dark pulse pair generation in mode-locked fiber laser with a large-angle tilted fiber grating,” Appl. Phys. B 122(6), 161 (2016).
[Crossref]

Z. Yan, H. Wang, C. Wang, Z. Sun, G. Yin, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “Theoretical and experimental analysis of excessively tilted fiber gratings,” Opt. Express 24(11), 12107–12115 (2016).
[Crossref] [PubMed]

G. Wang, C. Wang, Z. Yan, and L. Zhang, “Highly efficient spectrally encoded imaging using a 45° tilted fiber grating,” Opt. Lett. 41(11), 2398–2401 (2016).
[Crossref] [PubMed]

B. Luo, Z. Yan, Z. Sun, Y. Liu, M. Zhao, and L. Zhang, “Biosensor based on excessively tilted fiber grating in thin-cladding optical fiber for sensitive and selective detection of low glucose concentration,” Opt. Express 23(25), 32429–32440 (2015).
[Crossref] [PubMed]

Z. Yan, C. Mou, Z. Sun, K. Zhou, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Hybrid tilted fiber grating based refractive index and liquid level sensing system,” Opt. Commun. 351, 144–148 (2015).
[Crossref]

Z. Yan, Z. Sun, K. Zhou, B. Luo, J. Li, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Numerical and experimental analysis of sensitivity enhanced RI sensor based on Ex-TFG in thin cladding fiber,” J. Lightwave Technol. 33(14), 3023–3027 (2015).
[Crossref]

J. Li, Z. Yan, Z. Sun, H. Luo, Y. He, Z. Li, Y. Liu, and L. Zhang, “Thulium-doped all-fiber mode-locked laser based on NPR and 45°-tilted fiber grating,” Opt. Express 22(25), 31020–31028 (2014).
[Crossref] [PubMed]

Z. Yan, K. Zhou, and L. Zhang, “In-fiber linear polarizer based on UV-inscribed 45° tilted grating in polarization maintaining fiber,” Opt. Lett. 37(18), 3819–3821 (2012).
[Crossref] [PubMed]

X. Liu, H. Wang, Z. Yan, Y. Wang, W. Zhao, W. Zhang, L. Zhang, Z. Yang, X. Hu, X. Li, D. Shen, C. Li, and G. Chen, “All-fiber normal-dispersion single-polarization passively mode-locked laser based on a 45°-tilted fiber grating,” Opt. Express 20(17), 19000–19005 (2012).
[Crossref] [PubMed]

Z. Yan, C. Mou, K. Zhou, X. Chen, and L. Zhang, “UV-Inscription, Polarization-Dependant Loss Characteristics and Applications of 45°Tilted Fiber Gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
[Crossref]

Yang, Z.

Yin, G.

Zhang, L.

Z. Yan, H. Wang, C. Wang, Z. Sun, G. Yin, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “Theoretical and experimental analysis of excessively tilted fiber gratings,” Opt. Express 24(11), 12107–12115 (2016).
[Crossref] [PubMed]

G. Wang, C. Wang, Z. Yan, and L. Zhang, “Highly efficient spectrally encoded imaging using a 45° tilted fiber grating,” Opt. Lett. 41(11), 2398–2401 (2016).
[Crossref] [PubMed]

Z. Zhang, C. Mou, Z. Yan, Z. Sun, and L. Zhang, “Orthogonally polarized bright–dark pulse pair generation in mode-locked fiber laser with a large-angle tilted fiber grating,” Appl. Phys. B 122(6), 161 (2016).
[Crossref]

Z. Yan, C. Mou, Z. Sun, K. Zhou, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Hybrid tilted fiber grating based refractive index and liquid level sensing system,” Opt. Commun. 351, 144–148 (2015).
[Crossref]

B. Luo, Z. Yan, Z. Sun, Y. Liu, M. Zhao, and L. Zhang, “Biosensor based on excessively tilted fiber grating in thin-cladding optical fiber for sensitive and selective detection of low glucose concentration,” Opt. Express 23(25), 32429–32440 (2015).
[Crossref] [PubMed]

Z. Yan, Z. Sun, K. Zhou, B. Luo, J. Li, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Numerical and experimental analysis of sensitivity enhanced RI sensor based on Ex-TFG in thin cladding fiber,” J. Lightwave Technol. 33(14), 3023–3027 (2015).
[Crossref]

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

J. Li, Z. Yan, Z. Sun, H. Luo, Y. He, Z. Li, Y. Liu, and L. Zhang, “Thulium-doped all-fiber mode-locked laser based on NPR and 45°-tilted fiber grating,” Opt. Express 22(25), 31020–31028 (2014).
[Crossref] [PubMed]

Z. Yan, K. Zhou, and L. Zhang, “In-fiber linear polarizer based on UV-inscribed 45° tilted grating in polarization maintaining fiber,” Opt. Lett. 37(18), 3819–3821 (2012).
[Crossref] [PubMed]

X. Liu, H. Wang, Z. Yan, Y. Wang, W. Zhao, W. Zhang, L. Zhang, Z. Yang, X. Hu, X. Li, D. Shen, C. Li, and G. Chen, “All-fiber normal-dispersion single-polarization passively mode-locked laser based on a 45°-tilted fiber grating,” Opt. Express 20(17), 19000–19005 (2012).
[Crossref] [PubMed]

Z. Yan, C. Mou, K. Zhou, X. Chen, and L. Zhang, “UV-Inscription, Polarization-Dependant Loss Characteristics and Applications of 45°Tilted Fiber Gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
[Crossref]

C. Mou, H. Wang, B. G. Bale, K. Zhou, L. Zhang, and I. Bennion, “All-fiber passively mode-locked femtosecond laser using a 45º-tilted fiber grating polarization element,” Opt. Express 18(18), 18906–18911 (2010).
[Crossref] [PubMed]

R. Suo, X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fibre directional transverse loading sensor based on excessively tilted fibre Bragg gratings,” Meas. Sci. Technol. 20(3), 034015 (2009).
[Crossref]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-Fiber Twist Sensor Based on a Fiber Bragg Grating With 81 Tilted Structure,” IEEE Photonics Technol. Lett. 18, 2596–2598 (2006).
[Crossref]

K. Zhou, L. Zhang, X. Chen, and I. Bennion, “Optic sensors of high refractive-index responsivity and low thermal cross sensitivity that use fiber Bragg gratings of >80 ° tilted structures,” Opt. Lett. 31(9), 1193–1195 (2006).
[Crossref] [PubMed]

K. Zhou, G. Simpson, X. Chen, L. Zhang, and I. Bennion, “High extinction ratio in-fiber polarizers based on 45 ° tilted fiber Bragg gratings,” Opt. Lett. 30(11), 1285–1287 (2005).
[Crossref] [PubMed]

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37(4), 216–218 (2001).
[Crossref]

Zhang, W.

Zhang, Z.

Z. Zhang, C. Mou, Z. Yan, Z. Sun, and L. Zhang, “Orthogonally polarized bright–dark pulse pair generation in mode-locked fiber laser with a large-angle tilted fiber grating,” Appl. Phys. B 122(6), 161 (2016).
[Crossref]

Zhao, M.

Zhao, W.

Zhou, K.

Z. Yan, H. Wang, C. Wang, Z. Sun, G. Yin, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “Theoretical and experimental analysis of excessively tilted fiber gratings,” Opt. Express 24(11), 12107–12115 (2016).
[Crossref] [PubMed]

Z. Yan, Z. Sun, K. Zhou, B. Luo, J. Li, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Numerical and experimental analysis of sensitivity enhanced RI sensor based on Ex-TFG in thin cladding fiber,” J. Lightwave Technol. 33(14), 3023–3027 (2015).
[Crossref]

Z. Yan, C. Mou, Z. Sun, K. Zhou, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Hybrid tilted fiber grating based refractive index and liquid level sensing system,” Opt. Commun. 351, 144–148 (2015).
[Crossref]

Z. Yan, K. Zhou, and L. Zhang, “In-fiber linear polarizer based on UV-inscribed 45° tilted grating in polarization maintaining fiber,” Opt. Lett. 37(18), 3819–3821 (2012).
[Crossref] [PubMed]

Z. Yan, C. Mou, K. Zhou, X. Chen, and L. Zhang, “UV-Inscription, Polarization-Dependant Loss Characteristics and Applications of 45°Tilted Fiber Gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
[Crossref]

C. Mou, H. Wang, B. G. Bale, K. Zhou, L. Zhang, and I. Bennion, “All-fiber passively mode-locked femtosecond laser using a 45º-tilted fiber grating polarization element,” Opt. Express 18(18), 18906–18911 (2010).
[Crossref] [PubMed]

R. Suo, X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fibre directional transverse loading sensor based on excessively tilted fibre Bragg gratings,” Meas. Sci. Technol. 20(3), 034015 (2009).
[Crossref]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-Fiber Twist Sensor Based on a Fiber Bragg Grating With 81 Tilted Structure,” IEEE Photonics Technol. Lett. 18, 2596–2598 (2006).
[Crossref]

K. Zhou, L. Zhang, X. Chen, and I. Bennion, “Optic sensors of high refractive-index responsivity and low thermal cross sensitivity that use fiber Bragg gratings of >80 ° tilted structures,” Opt. Lett. 31(9), 1193–1195 (2006).
[Crossref] [PubMed]

K. Zhou, L. Z. X. Chen, and I. Bennion, “Low Temperature Sensitivity Grating Devices Based on Ex-45° Tilting Structure Capable of Forward-Propagating Cladding Modes Coupling,” J. Lightwave Technol. 24, 5087–5094 (2006).
[Crossref]

K. Zhou, G. Simpson, X. Chen, L. Zhang, and I. Bennion, “High extinction ratio in-fiber polarizers based on 45 ° tilted fiber Bragg gratings,” Opt. Lett. 30(11), 1285–1287 (2005).
[Crossref] [PubMed]

Appl. Phys. B (1)

Z. Zhang, C. Mou, Z. Yan, Z. Sun, and L. Zhang, “Orthogonally polarized bright–dark pulse pair generation in mode-locked fiber laser with a large-angle tilted fiber grating,” Appl. Phys. B 122(6), 161 (2016).
[Crossref]

Electron. Lett. (4)

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “Room-temperature operation of widely tunable loss filter,” Electron. Lett. 37(4), 216–218 (2001).
[Crossref]

K. S. Chiang, Y. Liu, M. N. Ng, and X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36(11), 966–967 (2000).
[Crossref]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

M. J. Guy, S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Low-loss fibre Bragg grating transmission filter based on a fibre polarisation splitter,” Electron. Lett. 30(18), 1512–1513 (1994).
[Crossref]

IEE Proc., Optoelectron. (1)

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, “UV-Induced polarization-dependent loss(PDL) in tilted fiber Bragg grating: Application of a PDL equalizer,” IEE Proc., Optoelectron. 149(5), 211–216 (2002).
[Crossref]

IEEE Photonics Technol. Lett. (2)

P. S. Westbrook, T. A. Strasser, and T. Erdogan, “In-line polarimeter using blazed fibre gratings,” IEEE Photonics Technol. Lett. 12(10), 1352–1354 (2000).
[Crossref]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-Fiber Twist Sensor Based on a Fiber Bragg Grating With 81 Tilted Structure,” IEEE Photonics Technol. Lett. 18, 2596–2598 (2006).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

M. R. Islam, M. Bagherifaez, M. M. Ali, H. K. Chai, K. S. Lim, and H. Ahmad, “Tilted Fiber Bragg Grating Sensors for Reinforcement Corrosion Measurement in Marine Concrete Structure,” IEEE Trans. Instrum. Meas. 64(12), 3510–3516 (2015).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (1)

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

Laser Photonics Rev. (1)

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg gratings sensors,” Laser Photonics Rev. 7(1), 83–108 (2013).
[Crossref]

Meas. Sci. Technol. (1)

R. Suo, X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fibre directional transverse loading sensor based on excessively tilted fibre Bragg gratings,” Meas. Sci. Technol. 20(3), 034015 (2009).
[Crossref]

Nat. Commun. (1)

C. Caucheteur, T. Guo, F. Liu, B.-O. Guan, and J. Albert, “Ultrasensitive plasmonic sensing in air using optical fibre spectral combs,” Nat. Commun. 7, 13371 (2016).
[Crossref] [PubMed]

Opt. Commun. (1)

Z. Yan, C. Mou, Z. Sun, K. Zhou, H. Wang, Y. Wang, W. Zhao, and L. Zhang, “Hybrid tilted fiber grating based refractive index and liquid level sensing system,” Opt. Commun. 351, 144–148 (2015).
[Crossref]

Opt. Express (7)

B. Luo, Z. Yan, Z. Sun, Y. Liu, M. Zhao, and L. Zhang, “Biosensor based on excessively tilted fiber grating in thin-cladding optical fiber for sensitive and selective detection of low glucose concentration,” Opt. Express 23(25), 32429–32440 (2015).
[Crossref] [PubMed]

T. Guo, H.-Y. Tam, P. A. Krug, and J. Albert, “Reflective tilted fiber Bragg grating refractometer based on strong cladding to core recoupling,” Opt. Express 17(7), 5736–5742 (2009).
[Crossref] [PubMed]

T. Guo, L. Shao, H.-Y. Tam, P. A. Krug, and J. Albert, “Tilted fiber grating accelerometer incorporating an abrupt biconical taper for cladding to core recoupling,” Opt. Express 17(23), 20651–20660 (2009).
[Crossref] [PubMed]

Z. Yan, H. Wang, C. Wang, Z. Sun, G. Yin, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “Theoretical and experimental analysis of excessively tilted fiber gratings,” Opt. Express 24(11), 12107–12115 (2016).
[Crossref] [PubMed]

C. Mou, H. Wang, B. G. Bale, K. Zhou, L. Zhang, and I. Bennion, “All-fiber passively mode-locked femtosecond laser using a 45º-tilted fiber grating polarization element,” Opt. Express 18(18), 18906–18911 (2010).
[Crossref] [PubMed]

J. Li, Z. Yan, Z. Sun, H. Luo, Y. He, Z. Li, Y. Liu, and L. Zhang, “Thulium-doped all-fiber mode-locked laser based on NPR and 45°-tilted fiber grating,” Opt. Express 22(25), 31020–31028 (2014).
[Crossref] [PubMed]

X. Liu, H. Wang, Z. Yan, Y. Wang, W. Zhao, W. Zhang, L. Zhang, Z. Yang, X. Hu, X. Li, D. Shen, C. Li, and G. Chen, “All-fiber normal-dispersion single-polarization passively mode-locked laser based on a 45°-tilted fiber grating,” Opt. Express 20(17), 19000–19005 (2012).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

T. Guo, F. Liu, B.-O. Guan, and J. Albert, “[INVITED] Tilted fiber grating mechanical and biochemical sensors,” Opt. Laser Technol. 78, 19–33 (2016).
[Crossref]

Opt. Lett. (5)

Proc. SPIE (1)

S. Remund, A. Bossen, X. Chen, L. Wang, A. Adebayo, L. Zhang, B. Považay, and C. Meier, “Cost-effective optical coherence tomography spectrometer based on a tilted fiber Bragg grating,” Proc. SPIE 8938, 2039409 (2014).

Other (2)

J. L. Wagener, T. A. Strasser, J. R. Pedrazzani, J. DeMarco, and D. DiGiovanni, “Fiber grating optical spectrum analyzer tap,” in Proceeding of Integrated Optics and Optical Fibre Communications, Edinburgh 65–68 (1997)

G. Meltz, W. W. Morey, and W. H. Glenn, “In-fiber Bragg grating tap,”in Proc. OFC’90, TuG1 (1990).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 The simulation results of (a) temperature dependence of waveguide dispersion and (b) the temperature sensitivity of first 50 TM resonant cladding modes for three different ξco values: 7.97 × 10-6 (square), 7.3 × 10-6 (circle), and 7.07 × 10-6 (triangle) at 1550nm (inset: enlarged scale of Fig. (b) for the mode orders from 20 to 50).
Fig. 2
Fig. 2 The simulation results of (a) surrounding refractive index dependence of waveguide dispersion; (b) wavelength shift of Ex-TFGs with different axial period (35.1µm, 28.8 µm 22.6 µm, 17.4 µm and 15µm) at around 1550nm peak in air; (c) wavelength shift of different cladding mode order of Ex-TFGs under 23.2 µm axial period.
Fig. 3
Fig. 3 The wavelength shift of Ex-TFG versus temperature: (a) for TM (red circle) and TE (black square) cladding modes of 81°-TFG; (b) for TM cladding modes of Ex-TFGs tilted at 83°, 81°, 79°, 75°.
Fig. 4
Fig. 4 The experiment setup for refractive index sensing.
Fig. 5
Fig. 5 The SRI response of 79° Ex-TFG: (a) 35th TE mode at 1556nm (circle) and TM at 1550nm (square); (b) TM peaks at 1710nm (cross), 1550nm (star) and 1320nm (bar).
Fig. 6
Fig. 6 (a) The SRI responses of the TM modes (at around 1550nm) of Ex-TFGs with structure tilted at 72°, 75°, 79° and 83° for SRI range from 1.305 to 1.408; (b) the transmission spectral of TM modes (at around 1550nm) of 72° Ex-TFGs at around 1550nm with skimmed milk with 0% fat, semi-skimmed milk with 2% fat and whole milk with 4% fat (inset shown the wavelength shift versus different fat concentration).

Tables (4)

Tables Icon

Table 1 List of mask and grating parameters

Tables Icon

Table 2 List of TM mode resonance wavelength, mode index and mode order of the Ex-TFGs with different tilt angles

Tables Icon

Table 3 Effective TM mode index and measured SRI sensitivity for 79°-TFG

Tables Icon

Table 4 Effective TM mode index and measured SRI sensitivity for Ex-TFG with different tilt angle

Equations (14)

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

λ=(nef f co (λ)nef f cl,m i (λ)) Λ G cosθ i=TE or TM
λ'=(nef f co (λ')nef f cl,m (λ')) Λ G cosθ +(δnef f co δnef f cl,m ) Λ G cosθ .. + nef f co (λ')nef f cl,m (λ') cosθ )δ Λ G
nef f co (λ')nef f co (λ)+ dnef f co f dλ (λ'λ)
nef f cl,m (λ')nef f cl,m (λ)+ dnef f cl,m dλ (λ'λ).
Δλ=λ'λ = 1 1( dnef f co dλ dnef f cl,m dλ ) Λ G cosθ ( (δnef f co δnef f cl,m ) nef f co (λ)nef f cl,m f (λ) + d Λ G Λ G )λ
Δλ=γ(Γ +α)λ
Γ Tem = ( dnef f co nef f co dT dT×nef f co dnef f cl,m nef f cl,m dT dT×nef f cl,m ) nef f co (λ)nef f cl,m (λ) = ( ξ co nef f co ξ cl nef f cl,m ) nef f co (λ)nef f cl,m (λ)
Γ SRI = (δnef f cl,m ) nef f co (λ)nef f cl,m (λ)
nef f cl,m = ( n cl 2 u m λ 2πr (1 λ 2πr n cl 2 n sur 2 )) 1/2
dnef f cl,m d n sur = u m 2 λ 3 n sur 8 π 3 r 3 nef f cl,m ( n cl 2 n sur 2 ) 3/2 .
Γ SRI = u m 2 λ 2 Λ G n sur 8 π 3 r 3 nef f cl,m ( n cl 2 n sur 2 ) 3/2 cosθ .
Δλ=γ Γ SRI λ
θ int = π 2 tan 1 [ 1 n UV tan( θ ext ) ]
Λ axial = Λ G cos θ int = Λ AM cos θ ext

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