Abstract

The effects of pressure on the behavior of optical microspherical resonators, prepared from Nd3+ doped, barium titanium silicate glass, have been studied up to 5 GPa inside a diamond anvil cell using silicone oil as the hydrostatic transmission medium and ruby emission lines as the pressure gauge. The optical resonances, known as whispering gallery modes, were observed within the broad emission band of the Nd3+ ions, and the resonances were identified as a function of pressure. By means of simulations, it was found that the average wavelength position of both transverse electric and magnetic modes depended on the radius and refractive index of the sphere, but not on the refractive index of the pressure transmitting medium under the experimental conditions. This was used to define the average sensitivity of the resonant modes with the pressure. Therefore, a value of 6.5×104GPa1 has been obtained for this sensitivity, which is higher than the value for ruby, the most conventional pressure sensor.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. K. Rai, “Temperature sensors and optical sensors,” Appl. Phys. B 88, 297–303 (2007).
  2. G. Adamovsky and M. V. Ötügen, “Morphology-dependent resonances and their applications to sensing in aerospace environments,” J. Aerosp. Comput. Inf. Commun. 5, 409–424 (2008).
  3. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
    [CrossRef]
  4. L. L. Martín, C. Pérez-Rodríguez, P. Haro-González, and I. R. Martín, “Whispering gallery modes in a glass microsphere as a function of temperature,” Opt. Express 19, 25792–25798 (2011).
    [CrossRef]
  5. L. L. Martín, P. Haro-González, I. R. Martín, D. Navarro-Urrios, D. Alonso, C. Pérez-Rodríguez, D. Jaque, and N. E. Capuj, “Whispering-gallery modes in glass microspheres: optimization of pumping in a modified confocal microscope,” Opt. Lett. 36, 615–617 (2011).
    [CrossRef]
  6. L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).
  7. H. Masai, S. Tsuji, T. Fujiwara, Y. Benino, and T. Komatsu, “Structure and non-linear optical properties of BaO–TiO2–SiO2 glass containing Ba2TiSi2O8 crystal,” J. Non-Cryst. Solids 353, 2258–2262 (2007).
    [CrossRef]
  8. L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
    [CrossRef]
  9. G. J. Piermarini, S. Block, J. D. Barnett, and R. A. Forman, “Calibration of pressure-dependence ofR1 ruby fluorescence line to 195  kbar,” J. Appl. Phys. 46, 2774–2780 (1975).
    [CrossRef]
  10. B. E. Little, J.-P. Laine, and H. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17, 704–715 (1999).
    [CrossRef]
  11. S. Schiller, “Asymptotic-expansion of morphological resonance frequencies in Mie scattering,” Appl. Opt. 32, 2181–2185 (1993).
    [CrossRef]
  12. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996).
    [CrossRef]
  13. H. Wang, X. Lan, J. Huang, L. Yuan, C.-W. Kim, and H. Xiao, “Fiber pigtailed thin wall capillary coupler for excitation of microsphere WGM resonator,” Opt. Express 21, 15834–15839 (2013).
    [CrossRef]
  14. G. R. Elliott, D. W. Hewak, G. S. Murugan, and J. S. Wilkinson, “Chalcogenide glass microspheres; their production, characterization and potential,” Opt. Express 15, 17542–17553 (2007).
    [CrossRef]
  15. High Pressure Diamond Optics, Inc., www.HPDO.com .
  16. S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, “Hydrostatic limits of 11 pressure transmitting media,” J. Phys. D 42, 075414 (2009).
  17. K. Shinozaki, T. Honma, and T. Komatsu, “Elastic properties and Vickers hardness of optically transparent glass–ceramics with fresnoite Ba2TiSi2O8 nanocrystals,” Mater. Res. Bull. 46, 922–928 (2011).
    [CrossRef]
  18. R. G. Kuryaeva, “Refractive index and compressibility of the KAlSi3O8 glass at pressures up to 6.0  GPa,” Glass Physics and Chemistry 37, 243–251 (2011).

2013 (2)

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

H. Wang, X. Lan, J. Huang, L. Yuan, C.-W. Kim, and H. Xiao, “Fiber pigtailed thin wall capillary coupler for excitation of microsphere WGM resonator,” Opt. Express 21, 15834–15839 (2013).
[CrossRef]

2011 (4)

K. Shinozaki, T. Honma, and T. Komatsu, “Elastic properties and Vickers hardness of optically transparent glass–ceramics with fresnoite Ba2TiSi2O8 nanocrystals,” Mater. Res. Bull. 46, 922–928 (2011).
[CrossRef]

R. G. Kuryaeva, “Refractive index and compressibility of the KAlSi3O8 glass at pressures up to 6.0  GPa,” Glass Physics and Chemistry 37, 243–251 (2011).

L. L. Martín, C. Pérez-Rodríguez, P. Haro-González, and I. R. Martín, “Whispering gallery modes in a glass microsphere as a function of temperature,” Opt. Express 19, 25792–25798 (2011).
[CrossRef]

L. L. Martín, P. Haro-González, I. R. Martín, D. Navarro-Urrios, D. Alonso, C. Pérez-Rodríguez, D. Jaque, and N. E. Capuj, “Whispering-gallery modes in glass microspheres: optimization of pumping in a modified confocal microscope,” Opt. Lett. 36, 615–617 (2011).
[CrossRef]

2010 (1)

L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).

2009 (1)

S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, “Hydrostatic limits of 11 pressure transmitting media,” J. Phys. D 42, 075414 (2009).

2008 (1)

G. Adamovsky and M. V. Ötügen, “Morphology-dependent resonances and their applications to sensing in aerospace environments,” J. Aerosp. Comput. Inf. Commun. 5, 409–424 (2008).

2007 (3)

H. Masai, S. Tsuji, T. Fujiwara, Y. Benino, and T. Komatsu, “Structure and non-linear optical properties of BaO–TiO2–SiO2 glass containing Ba2TiSi2O8 crystal,” J. Non-Cryst. Solids 353, 2258–2262 (2007).
[CrossRef]

G. R. Elliott, D. W. Hewak, G. S. Murugan, and J. S. Wilkinson, “Chalcogenide glass microspheres; their production, characterization and potential,” Opt. Express 15, 17542–17553 (2007).
[CrossRef]

V. K. Rai, “Temperature sensors and optical sensors,” Appl. Phys. B 88, 297–303 (2007).

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef]

1999 (1)

1996 (1)

1993 (1)

1975 (1)

G. J. Piermarini, S. Block, J. D. Barnett, and R. A. Forman, “Calibration of pressure-dependence ofR1 ruby fluorescence line to 195  kbar,” J. Appl. Phys. 46, 2774–2780 (1975).
[CrossRef]

Adamovsky, G.

G. Adamovsky and M. V. Ötügen, “Morphology-dependent resonances and their applications to sensing in aerospace environments,” J. Aerosp. Comput. Inf. Commun. 5, 409–424 (2008).

Alonso, D.

Barnett, J. D.

G. J. Piermarini, S. Block, J. D. Barnett, and R. A. Forman, “Calibration of pressure-dependence ofR1 ruby fluorescence line to 195  kbar,” J. Appl. Phys. 46, 2774–2780 (1975).
[CrossRef]

Benino, Y.

H. Masai, S. Tsuji, T. Fujiwara, Y. Benino, and T. Komatsu, “Structure and non-linear optical properties of BaO–TiO2–SiO2 glass containing Ba2TiSi2O8 crystal,” J. Non-Cryst. Solids 353, 2258–2262 (2007).
[CrossRef]

Block, S.

G. J. Piermarini, S. Block, J. D. Barnett, and R. A. Forman, “Calibration of pressure-dependence ofR1 ruby fluorescence line to 195  kbar,” J. Appl. Phys. 46, 2774–2780 (1975).
[CrossRef]

Cáceres, J. M.

L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).

Capuj, N.

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

Capuj, N. E.

L. L. Martín, P. Haro-González, I. R. Martín, D. Navarro-Urrios, D. Alonso, C. Pérez-Rodríguez, D. Jaque, and N. E. Capuj, “Whispering-gallery modes in glass microspheres: optimization of pumping in a modified confocal microscope,” Opt. Lett. 36, 615–617 (2011).
[CrossRef]

L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).

Chervin, J.-C.

S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, “Hydrostatic limits of 11 pressure transmitting media,” J. Phys. D 42, 075414 (2009).

Dominguez, C.

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

Elliott, G. R.

Ferrarese-Lupi, F.

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

Forman, R. A.

G. J. Piermarini, S. Block, J. D. Barnett, and R. A. Forman, “Calibration of pressure-dependence ofR1 ruby fluorescence line to 195  kbar,” J. Appl. Phys. 46, 2774–2780 (1975).
[CrossRef]

Fujiwara, T.

H. Masai, S. Tsuji, T. Fujiwara, Y. Benino, and T. Komatsu, “Structure and non-linear optical properties of BaO–TiO2–SiO2 glass containing Ba2TiSi2O8 crystal,” J. Non-Cryst. Solids 353, 2258–2262 (2007).
[CrossRef]

Garrido, B.

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

Gorodetsky, M. L.

Haro-González, P.

Haus, H.

Hewak, D. W.

Honma, T.

K. Shinozaki, T. Honma, and T. Komatsu, “Elastic properties and Vickers hardness of optically transparent glass–ceramics with fresnoite Ba2TiSi2O8 nanocrystals,” Mater. Res. Bull. 46, 922–928 (2011).
[CrossRef]

Huang, J.

Ilchenko, V. S.

Jaque, D.

Kim, C.-W.

Klotz, S.

S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, “Hydrostatic limits of 11 pressure transmitting media,” J. Phys. D 42, 075414 (2009).

Komatsu, T.

K. Shinozaki, T. Honma, and T. Komatsu, “Elastic properties and Vickers hardness of optically transparent glass–ceramics with fresnoite Ba2TiSi2O8 nanocrystals,” Mater. Res. Bull. 46, 922–928 (2011).
[CrossRef]

H. Masai, S. Tsuji, T. Fujiwara, Y. Benino, and T. Komatsu, “Structure and non-linear optical properties of BaO–TiO2–SiO2 glass containing Ba2TiSi2O8 crystal,” J. Non-Cryst. Solids 353, 2258–2262 (2007).
[CrossRef]

Kuryaeva, R. G.

R. G. Kuryaeva, “Refractive index and compressibility of the KAlSi3O8 glass at pressures up to 6.0  GPa,” Glass Physics and Chemistry 37, 243–251 (2011).

Laine, J.-P.

Lan, X.

Le Marchand, G.

S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, “Hydrostatic limits of 11 pressure transmitting media,” J. Phys. D 42, 075414 (2009).

Little, B. E.

Martin, L. L.

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).

Martín, I. R.

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

L. L. Martín, P. Haro-González, I. R. Martín, D. Navarro-Urrios, D. Alonso, C. Pérez-Rodríguez, D. Jaque, and N. E. Capuj, “Whispering-gallery modes in glass microspheres: optimization of pumping in a modified confocal microscope,” Opt. Lett. 36, 615–617 (2011).
[CrossRef]

L. L. Martín, C. Pérez-Rodríguez, P. Haro-González, and I. R. Martín, “Whispering gallery modes in a glass microsphere as a function of temperature,” Opt. Express 19, 25792–25798 (2011).
[CrossRef]

L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).

Martín, L. L.

Masai, H.

H. Masai, S. Tsuji, T. Fujiwara, Y. Benino, and T. Komatsu, “Structure and non-linear optical properties of BaO–TiO2–SiO2 glass containing Ba2TiSi2O8 crystal,” J. Non-Cryst. Solids 353, 2258–2262 (2007).
[CrossRef]

Montserrat, J.

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

Munsch, P.

S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, “Hydrostatic limits of 11 pressure transmitting media,” J. Phys. D 42, 075414 (2009).

Murugan, G. S.

Navarro-Urrios, D.

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

L. L. Martín, P. Haro-González, I. R. Martín, D. Navarro-Urrios, D. Alonso, C. Pérez-Rodríguez, D. Jaque, and N. E. Capuj, “Whispering-gallery modes in glass microspheres: optimization of pumping in a modified confocal microscope,” Opt. Lett. 36, 615–617 (2011).
[CrossRef]

Ötügen, M. V.

G. Adamovsky and M. V. Ötügen, “Morphology-dependent resonances and their applications to sensing in aerospace environments,” J. Aerosp. Comput. Inf. Commun. 5, 409–424 (2008).

Pérez-Rodríguez, C.

Piermarini, G. J.

G. J. Piermarini, S. Block, J. D. Barnett, and R. A. Forman, “Calibration of pressure-dependence ofR1 ruby fluorescence line to 195  kbar,” J. Appl. Phys. 46, 2774–2780 (1975).
[CrossRef]

Puerto, D.

L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).

Rai, V. K.

V. K. Rai, “Temperature sensors and optical sensors,” Appl. Phys. B 88, 297–303 (2007).

Savchenkov, A. A.

Schiller, S.

Shinozaki, K.

K. Shinozaki, T. Honma, and T. Komatsu, “Elastic properties and Vickers hardness of optically transparent glass–ceramics with fresnoite Ba2TiSi2O8 nanocrystals,” Mater. Res. Bull. 46, 922–928 (2011).
[CrossRef]

Solís, J.

L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).

Tsuji, S.

H. Masai, S. Tsuji, T. Fujiwara, Y. Benino, and T. Komatsu, “Structure and non-linear optical properties of BaO–TiO2–SiO2 glass containing Ba2TiSi2O8 crystal,” J. Non-Cryst. Solids 353, 2258–2262 (2007).
[CrossRef]

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef]

Wang, H.

Wilkinson, J. S.

Xiao, H.

Yuan, L.

Appl. Opt. (1)

Appl. Phys. B (1)

V. K. Rai, “Temperature sensors and optical sensors,” Appl. Phys. B 88, 297–303 (2007).

Glass Physics and Chemistry (1)

R. G. Kuryaeva, “Refractive index and compressibility of the KAlSi3O8 glass at pressures up to 6.0  GPa,” Glass Physics and Chemistry 37, 243–251 (2011).

J. Aerosp. Comput. Inf. Commun. (1)

G. Adamovsky and M. V. Ötügen, “Morphology-dependent resonances and their applications to sensing in aerospace environments,” J. Aerosp. Comput. Inf. Commun. 5, 409–424 (2008).

J. Appl. Phys. (1)

G. J. Piermarini, S. Block, J. D. Barnett, and R. A. Forman, “Calibration of pressure-dependence ofR1 ruby fluorescence line to 195  kbar,” J. Appl. Phys. 46, 2774–2780 (1975).
[CrossRef]

J. Lightwave Technol. (1)

J. Non-Cryst. Solids (1)

H. Masai, S. Tsuji, T. Fujiwara, Y. Benino, and T. Komatsu, “Structure and non-linear optical properties of BaO–TiO2–SiO2 glass containing Ba2TiSi2O8 crystal,” J. Non-Cryst. Solids 353, 2258–2262 (2007).
[CrossRef]

J. Phys. D (1)

S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, “Hydrostatic limits of 11 pressure transmitting media,” J. Phys. D 42, 075414 (2009).

Laser Phys. (1)

L. L. Martin, D. Navarro-Urrios, F. Ferrarese-Lupi, C. Pérez-Rodríguez, I. R. Martín, J. Montserrat, C. Dominguez, B. Garrido, and N. Capuj, “Laser emission in Nd3+ doped barium–titanium–silicate microspheres under continuous and chopped wave pumping in a non-coupled pumping scheme,” Laser Phys. 23, 075801 (2013).
[CrossRef]

Mater. Res. Bull. (1)

K. Shinozaki, T. Honma, and T. Komatsu, “Elastic properties and Vickers hardness of optically transparent glass–ceramics with fresnoite Ba2TiSi2O8 nanocrystals,” Mater. Res. Bull. 46, 922–928 (2011).
[CrossRef]

Nature (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Opt. Materials (1)

L. L. Martin, P. Haro-González, I. R. Martín, D. Puerto, J. Solís, J. M. Cáceres, and N. E. Capuj, “Local devitrification of Dy3+ doped Ba2TiSi2O8 glass by laser irradiation,” Opt. Materials 33, 186–190 (2010).

Other (1)

High Pressure Diamond Optics, Inc., www.HPDO.com .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Spectrum of a microsphere obtained at the center of the microsphere (in black), which shows the broad F43/2I49/2 band emission of Nd3+ ions in the BTS glass, and spectrum obtained at the air–microsphere boundary (in red), which shows the characteristic WGM pattern.

Fig. 2.
Fig. 2.

Picture of the pressure chamber inside the diamond anvil cell at visible light (Left), in which the microsphere and the ruby chips (labeled R1–R5) employed as pressure gauges are clearly observed. Fluorescent image (false color) of a microsphere with a radius about 20 μm in air (Right), illuminated by a 532 nm laser and showing the Nd3+ luminescent emission between 880 and 900 nm.

Fig. 3.
Fig. 3.

Simulated positions of the resonances using Eq. (4) where the parameters are ns=1.71, Rs=20μm, and no=1.25. The parameter of the x axis varies by 2% from the nominal value. (Top) Variation of the spheres radius. (Central) Variation of the refractive index of the sphere. (Bottom) Variation of the refractive index of the outer medium. Red line is the TE230, black line is the TM231, and blue line is the λAVG given by Eq. (7).

Fig. 4.
Fig. 4.

Positions of the resonances at rising pressures. Black data correspond to the TM modes and red data to the TE modes.

Fig. 5.
Fig. 5.

Average positions of the TE and TM resonant peaks obtained using Eq. (7). Black dots show the positions of rising pressures and red dots show the decreasing pressure positions. Red dashed line is the linear fit of the rising data.

Fig. 6.
Fig. 6.

Full width at half-maximum of the resonances at various pressures for the TM modes with error bars; in black the rising pressures, in red the decreasing pressures (Left). Spectral image of one resonance (Right, Top) centered about 876 nm at the lowest pressure (0.1 GPa) and (Right, Bottom) centered about 872 nm at the highest pressure (5.2 GPa).

Equations (11)

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

P=AB{[1+(Δλλ0)]B1},
λ=2πneffRSl,
(p·αS+lRS)·jl(knSRS)=k·nS·jl+1(knSRS),
αS=βl2+k2no2,βl=l(l+1)RS,k=2πλ,
p={1TEmodesnr2TEmodes;nr=ns/no.
k=1noRs[l+1/2nr+ζ1nr(l+1/22)1/3pnr21+3ζ1220nr(l+1/22)1/3+],
S=λλP=nSnSP+RSRSP.
1Q=1QR+1QC+1QS+1QM=λFWHM(λ),
λAVG=λTE(l)+λTM(l+1)2.
1RS·RSP=13K=57×104GPa1.
nSnSP=0.0047GPa1,

Metrics