Abstract

The strain-optic coefficients of PMMA are measured in a broad wavelength range from 800 to 2000 nm. The sensitivity of the azimuthal whispering gallery mode resonances to the strain is exploited to measure the strain-optic coefficients of PMMA micro-rods. The technique is based on measuring the wavelength shift of the resonances of both polarizations states, the TE and TM, when an axial strain is applied to the polymer rods. This method enables the determination of the strain-optic coefficients of the material in a broad wavelength range. In particular, in the near-infrared range, the PMMA exhibits negligible dispersion and anisotropy, and the strain-optic coefficients show constant values within the experimental error: p11 = 0.298 ± 0.010 and p12 = 0.294 ± 0.010.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (1)

2015 (2)

2014 (1)

2011 (2)

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

K. Peters, “Polymer optical fiber sensors—a review,” Smart Mater. Struct. 20(1), 013002 (2011).
[Crossref]

2010 (1)

X. Chen, C. Zhang, D. J. Webb, G.-D. Peng, and K. Kalli, “Bragg grating in a polymer optical fibre for strain, bend and temperature sensing,” Meas. Sci. Technol. 21(9), 094005 (2010).
[Crossref]

2007 (1)

2006 (1)

H. Liu, H. Liu, G. Peng, and P. Chu, “Polymer optical fibre bragg gratings based fibre laser,” Opt. Commun. 266(1), 132–135 (2006).
[Crossref]

2005 (1)

2004 (1)

D. York, N. M. Evensen, M. López-Martínez, and J. D. Basabe-Delgado, “Unified equations for the slope, intercept, and standard errors of the best straight line,” Am. J. Phys. 72(3), 367–375 (2004).
[Crossref]

1997 (2)

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microwave Theory Tech. 45(11), 2025–2034 (1997).
[Crossref]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22(15), 1129–1131 (1997).
[Crossref]

1979 (1)

Andrés, M.

X. Roselló-Mechó, M. Delgado-Pinar, A. Díez, and M. Andrés, “Anisotropic elasto-optic effect in optical fibers under axial strain: a perturbative approach, in Latin America Optics and Photonics Conference (Optical Society of America, 2016), p. LTu4A.37.

Andrés, M. V.

Andresen, S.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Annino, G.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microwave Theory Tech. 45(11), 2025–2034 (1997).
[Crossref]

Avila, P. D.

Bache, M.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Bang, O.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Barton, J.

Basabe-Delgado, J. D.

D. York, N. M. Evensen, M. López-Martínez, and J. D. Basabe-Delgado, “Unified equations for the slope, intercept, and standard errors of the best straight line,” Am. J. Phys. 72(3), 367–375 (2004).
[Crossref]

Beadie, G.

Bennion, I.

Birks, T. A.

Brindza, M.

Brøsted-Sørensen, O.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Cassettari, M.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microwave Theory Tech. 45(11), 2025–2034 (1997).
[Crossref]

Chen, X.

X. Chen, C. Zhang, D. J. Webb, G.-D. Peng, and K. Kalli, “Bragg grating in a polymer optical fibre for strain, bend and temperature sensing,” Meas. Sci. Technol. 21(9), 094005 (2010).
[Crossref]

Cheung, G.

Chu, P.

H. Liu, H. Liu, G. Peng, and P. Chu, “Polymer optical fibre bragg gratings based fibre laser,” Opt. Commun. 266(1), 132–135 (2006).
[Crossref]

Cordeiro, C. M. B.

Cruz, J. L.

Delgado-Pinar, M.

Díez, A.

Dobb, H.

Evensen, N. M.

D. York, N. M. Evensen, M. López-Martínez, and J. D. Basabe-Delgado, “Unified equations for the slope, intercept, and standard errors of the best straight line,” Am. J. Phys. 72(3), 367–375 (2004).
[Crossref]

Feldman, A.

Fender, A.

Flynn, R. A.

Gouveia, M. A.

Herholdt-Rasmussen, N.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Horowitz, D.

Ioppolo, T.

Jacobsen, T.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Jacques, F.

Jones, J.

Kalli, K.

X. Chen, C. Zhang, D. J. Webb, G.-D. Peng, and K. Kalli, “Bragg grating in a polymer optical fibre for strain, bend and temperature sensing,” Meas. Sci. Technol. 21(9), 094005 (2010).
[Crossref]

Knight, J. C.

Kryger-Nielsen, F.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Liu, H.

H. Liu, H. Liu, G. Peng, and P. Chu, “Polymer optical fibre bragg gratings based fibre laser,” Opt. Commun. 266(1), 132–135 (2006).
[Crossref]

H. Liu, H. Liu, G. Peng, and P. Chu, “Polymer optical fibre bragg gratings based fibre laser,” Opt. Commun. 266(1), 132–135 (2006).
[Crossref]

Longo, I.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microwave Theory Tech. 45(11), 2025–2034 (1997).
[Crossref]

López-Martínez, M.

D. York, N. M. Evensen, M. López-Martínez, and J. D. Basabe-Delgado, “Unified equations for the slope, intercept, and standard errors of the best straight line,” Am. J. Phys. 72(3), 367–375 (2004).
[Crossref]

Macpherson, W.

Marques, T. H. R.

Martinelli, M.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microwave Theory Tech. 45(11), 2025–2034 (1997).
[Crossref]

Ötügen, M. V.

Peng, G.

H. Liu, H. Liu, G. Peng, and P. Chu, “Polymer optical fibre bragg gratings based fibre laser,” Opt. Commun. 266(1), 132–135 (2006).
[Crossref]

Peng, G.-D.

X. Chen, C. Zhang, D. J. Webb, G.-D. Peng, and K. Kalli, “Bragg grating in a polymer optical fibre for strain, bend and temperature sensing,” Meas. Sci. Technol. 21(9), 094005 (2010).
[Crossref]

Peters, K.

K. Peters, “Polymer optical fiber sensors—a review,” Smart Mater. Struct. 20(1), 013002 (2011).
[Crossref]

Rose, B.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Roselló-Mechó, X.

X. Roselló-Mechó, M. Delgado-Pinar, A. Díez, and M. V. Andrés, “Measurement of pockels’ coefficients and demonstration of the anisotropy of the elasto-optic effect in optical fibers under axial strain,” Opt. Lett. 41(13), 2934–2937 (2016).
[Crossref]

X. Roselló-Mechó, M. Delgado-Pinar, A. Díez, and M. Andrés, “Anisotropic elasto-optic effect in optical fibers under axial strain: a perturbative approach, in Latin America Optics and Photonics Conference (Optical Society of America, 2016), p. LTu4A.37.

Rosenberg, A.

Shirk, J. S.

Silva-López, M.

Stefani, A.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Styhr-Hansen, K.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Torres, M. C.

Villegas, I. L.

Waxler, R. M.

Webb, D.

Webb, D. J.

X. Chen, C. Zhang, D. J. Webb, G.-D. Peng, and K. Kalli, “Bragg grating in a polymer optical fibre for strain, bend and temperature sensing,” Meas. Sci. Technol. 21(9), 094005 (2010).
[Crossref]

York, D.

D. York, N. M. Evensen, M. López-Martínez, and J. D. Basabe-Delgado, “Unified equations for the slope, intercept, and standard errors of the best straight line,” Am. J. Phys. 72(3), 367–375 (2004).
[Crossref]

Yuan, W.

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

Zhang, C.

X. Chen, C. Zhang, D. J. Webb, G.-D. Peng, and K. Kalli, “Bragg grating in a polymer optical fibre for strain, bend and temperature sensing,” Meas. Sci. Technol. 21(9), 094005 (2010).
[Crossref]

Zhang, L.

Zhao, D.

Am. J. Phys. (1)

D. York, N. M. Evensen, M. López-Martínez, and J. D. Basabe-Delgado, “Unified equations for the slope, intercept, and standard errors of the best straight line,” Am. J. Phys. 72(3), 367–375 (2004).
[Crossref]

Appl. Opt. (2)

IEEE Trans. Microwave Theory Tech. (1)

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering gallery modes in a dielectric resonator: characterization at millimeter wavelength,” IEEE Trans. Microwave Theory Tech. 45(11), 2025–2034 (1997).
[Crossref]

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

Meas. Sci. Technol. (1)

X. Chen, C. Zhang, D. J. Webb, G.-D. Peng, and K. Kalli, “Bragg grating in a polymer optical fibre for strain, bend and temperature sensing,” Meas. Sci. Technol. 21(9), 094005 (2010).
[Crossref]

Opt. Commun. (2)

W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. Kryger-Nielsen, S. Andresen, O. Brøsted-Sørensen, K. Styhr-Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber bragg gratings,” Opt. Commun. 284(1), 176–182 (2011).
[Crossref]

H. Liu, H. Liu, G. Peng, and P. Chu, “Polymer optical fibre bragg gratings based fibre laser,” Opt. Commun. 266(1), 132–135 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Smart Mater. Struct. (1)

K. Peters, “Polymer optical fiber sensors—a review,” Smart Mater. Struct. 20(1), 013002 (2011).
[Crossref]

Other (1)

X. Roselló-Mechó, M. Delgado-Pinar, A. Díez, and M. Andrés, “Anisotropic elasto-optic effect in optical fibers under axial strain: a perturbative approach, in Latin America Optics and Photonics Conference (Optical Society of America, 2016), p. LTu4A.37.

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Figures (4)

Fig. 1.
Fig. 1. (a) Scheme of the experimental setup employed to characterize the PMMA resonators. (b) Detail of the tapered fiber and the microresonator under axial strain.
Fig. 2.
Fig. 2. (a) Illustrative example of the wavelength shift suffered by the resonances for an axial strain of $\epsilon _z=400 \, \mu \epsilon$. (b) Spectral separation between resonances of different polarization.
Fig. 3.
Fig. 3. Relative wavelength shift of WGM resonances as a function of the axial strain for a resonance centered at 1550 nm. Inset: Values of the $C_{\textrm {TE,TM}}$ coefficients as a function of the wavelength for a PMMA rod of $130\,\upmu$m of diameter.
Fig. 4.
Fig. 4. Strain-optic coefficients of PMMA at different wavelengths. The solid lines indicate the mean values of the measurements in the whole spectral range. The shaded area corresponds to the standard deviation.

Equations (6)

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

TE: 1 n t J m ( k 0 n t a ) J m ( k 0 n t a ) = 1 n 2 H m ( 2 ) ( k 0 n 2 a ) H m ( 2 ) ( k 0 n 2 a ) ,
TM: n z J m ( k 0 n z a ) J m ( k 0 n z a ) = n 2 H m ( 2 ) ( k 0 n 2 a ) H m ( 2 ) ( k 0 n 2 a ) ,
Δ n t n 0 = p e t ϵ z ; p e t n 0 2 2 [ ν p 11 + ( 1 ν ) p 12 ] ,
Δ n z n 0 = p e z ϵ z ; p e z n 0 2 2 [ p 11 2 ν p 12 ] ,
Δ a a = ν ϵ z .
[ Δ λ R λ R ] TE,TM = [ ν ( 1 C TE,TM ) p e t , z ] ϵ z ,

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