Abstract

In this paper we investigate the electrostriction effect on the whispering gallery modes (WGM) of polymeric microspheres and the feasibility of a WGM-based microsensor for electric field measurement. The electrostriction is the elastic deformation (strain) of a dielectric material under the force exerted by an electrostatic field. The deformation is accompanied by mechanical stress which perturbs the refractive index distribution in the sphere. Both strain and stress induce a shift in the WGM of the microsphere. In the present, we develop analytical expressions for the WGM shift due to electrostriction for solid and thin-walled hollow microspheres. Our analysis indicates that detection of electric fields as small as ~500V/m may be possible using water filled, hollow solid polydimethylsiloxane (PDMS) microspheres. The electric field sensitivities for solid spheres, on the other hand, are significantly smaller. Results of experiments carried out using solid PDMS spheres agree well with the analytical prediction.

© 2009 OSA

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References

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  1. W. von Klitzing, “Tunable whispering modes for spectroscopy and CQED Experiments,” New J. Phys. 3, 14.1–14.14 (2001).
    [CrossRef]
  2. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25(19), 1430–1432 (2000).
    [CrossRef]
  3. H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14(8), 1118–1120 (2002).
    [CrossRef]
  4. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
    [CrossRef]
  5. B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
    [CrossRef]
  6. V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
    [CrossRef]
  7. F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
    [CrossRef]
  8. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
    [CrossRef] [PubMed]
  9. A. T. Rosenberger and J. P. Rezac, “Whispering-gallerymode evanescent-wave microsensor for trace-gas detection,” Proc. SPIE 4265, 102–112 (2001).
    [CrossRef]
  10. N. Das, T. Ioppolo, and V. Ötügen, “Investigation of a micro-optical concentration sensor concept based on whispering gallery mode resonators,” presented at the 45th AIAA Aerospace Sciences Meeting and Exhibition, Reno, Nev., January 8–11 2007.
  11. T. Ioppolo, M. Kozhevnikov, V. Stepaniuk, M. V. Otügen, and V. Sheverev, “Micro-optical force sensor concept based on whispering gallery mode resonators,” Appl. Opt. 47(16), 3009–3014 (2008).
    [CrossRef] [PubMed]
  12. T. Ioppolo, U. K. Ayaz, and M. V. Ötügen, “High-resolution force sensor based on morphology dependent optical resonances of polymeric spheres,” J. Appl. Phys. 105(1), 013535 (2009).
    [CrossRef]
  13. T. Ioppolo and M. V. Ötügen, “Pressure Tuning of Whispering Gallery Mode Resonators,” J. Opt. Soc. Am. B 24(10), 2721–2726 (2007).
    [CrossRef]
  14. G. Guan, S. Arnold, and M. V. Ötügen, “Temperature Measurements Using a Micro-Optical Sensor Based on Whispering Gallery Modes,” AIAA J. 44(10), 2385–2389 (2006).
    [CrossRef]
  15. T. Ioppolo, U. K. Ayaz, M. V. Ötügen, and V. Sheverev, “A Micro-Optical Wall Shear Stress Sensor Concept Based on Whispering Gallery Mode Resonators,” 46th AIAA Aerospace Sciences Meeting and Exhibit, 8–11 January 2008.
  16. V. M. N. Passaro and F. De Leonardis, “Modeling and Design of a Novel High-Sensitivity Electric Field Silicon-on-Insulator Sensor Based on a Whispering-Gallery-Mode Resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
    [CrossRef]
  17. R. W. Soutas-Little, Elasticity, (Dover Publications Inc., Mineola, NY, 1999).
  18. J. A. Stratton, Electromagnetic Theory (Mcgraw-Hill Book Company, Inc., New York and London, 1941).
  19. F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96(12), 341–345 (2004).
    [CrossRef]
  20. J. E. Mark, Polymer Data Handbook (Oxford University Press, 1999).
  21. T. Yamwong, A. M. Voice, and G. R. Davies, “Electrostrictive response of an ideal polar rubber,” J. Appl. Phys. 91(3), 1472–1476 (2002).
    [CrossRef]
  22. A. E. H. Love, The Mathematical Theory of Elasticity (Dover, 1926).
  23. K. C. Kao, Dielectric Phenomena in Solids (Elsevier Academic Press, 2004).

2009 (1)

T. Ioppolo, U. K. Ayaz, and M. V. Ötügen, “High-resolution force sensor based on morphology dependent optical resonances of polymeric spheres,” J. Appl. Phys. 105(1), 013535 (2009).
[CrossRef]

2008 (1)

2007 (1)

2006 (2)

G. Guan, S. Arnold, and M. V. Ötügen, “Temperature Measurements Using a Micro-Optical Sensor Based on Whispering Gallery Modes,” AIAA J. 44(10), 2385–2389 (2006).
[CrossRef]

V. M. N. Passaro and F. De Leonardis, “Modeling and Design of a Novel High-Sensitivity Electric Field Silicon-on-Insulator Sensor Based on a Whispering-Gallery-Mode Resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
[CrossRef]

2004 (1)

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96(12), 341–345 (2004).
[CrossRef]

2003 (1)

2002 (3)

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[CrossRef]

T. Yamwong, A. M. Voice, and G. R. Davies, “Electrostrictive response of an ideal polar rubber,” J. Appl. Phys. 91(3), 1472–1476 (2002).
[CrossRef]

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14(8), 1118–1120 (2002).
[CrossRef]

2001 (2)

W. von Klitzing, “Tunable whispering modes for spectroscopy and CQED Experiments,” New J. Phys. 3, 14.1–14.14 (2001).
[CrossRef]

A. T. Rosenberger and J. P. Rezac, “Whispering-gallerymode evanescent-wave microsensor for trace-gas detection,” Proc. SPIE 4265, 102–112 (2001).
[CrossRef]

2000 (1)

1999 (1)

B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
[CrossRef]

1998 (1)

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Agan, S.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96(12), 341–345 (2004).
[CrossRef]

Arnold, S.

G. Guan, S. Arnold, and M. V. Ötügen, “Temperature Measurements Using a Micro-Optical Sensor Based on Whispering Gallery Modes,” AIAA J. 44(10), 2385–2389 (2006).
[CrossRef]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
[CrossRef] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[CrossRef]

Ay, F.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96(12), 341–345 (2004).
[CrossRef]

Ayaz, U. K.

T. Ioppolo, U. K. Ayaz, and M. V. Ötügen, “High-resolution force sensor based on morphology dependent optical resonances of polymeric spheres,” J. Appl. Phys. 105(1), 013535 (2009).
[CrossRef]

Aydinli, A.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96(12), 341–345 (2004).
[CrossRef]

Beyeler, R.

B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
[CrossRef]

Bona, G. L.

B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
[CrossRef]

Braun, D.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[CrossRef]

Cai, M.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Davies, G. R.

T. Yamwong, A. M. Voice, and G. R. Davies, “Electrostrictive response of an ideal polar rubber,” J. Appl. Phys. 91(3), 1472–1476 (2002).
[CrossRef]

De Leonardis, F.

V. M. N. Passaro and F. De Leonardis, “Modeling and Design of a Novel High-Sensitivity Electric Field Silicon-on-Insulator Sensor Based on a Whispering-Gallery-Mode Resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Germann, R.

B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
[CrossRef]

Guan, G.

G. Guan, S. Arnold, and M. V. Ötügen, “Temperature Measurements Using a Micro-Optical Sensor Based on Whispering Gallery Modes,” AIAA J. 44(10), 2385–2389 (2006).
[CrossRef]

Haroche, S.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Holler, S.

Horst, F.

B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
[CrossRef]

Ilchenko, V. S.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Ioppolo, T.

Khoshsima, M.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
[CrossRef] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[CrossRef]

Kocabas, A.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96(12), 341–345 (2004).
[CrossRef]

Kocabas, C.

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96(12), 341–345 (2004).
[CrossRef]

Kozhevnikov, M.

Laine, J. P.

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14(8), 1118–1120 (2002).
[CrossRef]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Lane, P. A.

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14(8), 1118–1120 (2002).
[CrossRef]

Lefevre-Seguin, V.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Libchaber, A.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[CrossRef]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Offrein, B. J.

B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
[CrossRef]

Otügen, M. V.

Ötügen, M. V.

T. Ioppolo, U. K. Ayaz, and M. V. Ötügen, “High-resolution force sensor based on morphology dependent optical resonances of polymeric spheres,” J. Appl. Phys. 105(1), 013535 (2009).
[CrossRef]

T. Ioppolo and M. V. Ötügen, “Pressure Tuning of Whispering Gallery Mode Resonators,” J. Opt. Soc. Am. B 24(10), 2721–2726 (2007).
[CrossRef]

G. Guan, S. Arnold, and M. V. Ötügen, “Temperature Measurements Using a Micro-Optical Sensor Based on Whispering Gallery Modes,” AIAA J. 44(10), 2385–2389 (2006).
[CrossRef]

Painter, O.

Passaro, V. M. N.

V. M. N. Passaro and F. De Leonardis, “Modeling and Design of a Novel High-Sensitivity Electric Field Silicon-on-Insulator Sensor Based on a Whispering-Gallery-Mode Resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
[CrossRef]

Raimond, J.-M.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Rezac, J. P.

A. T. Rosenberger and J. P. Rezac, “Whispering-gallerymode evanescent-wave microsensor for trace-gas detection,” Proc. SPIE 4265, 102–112 (2001).
[CrossRef]

Rosenberger, A. T.

A. T. Rosenberger and J. P. Rezac, “Whispering-gallerymode evanescent-wave microsensor for trace-gas detection,” Proc. SPIE 4265, 102–112 (2001).
[CrossRef]

Salemink, H. W. M.

B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
[CrossRef]

Sercel, P. C.

Sheverev, V.

Stepaniuk, V.

Tapalian, H. C.

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14(8), 1118–1120 (2002).
[CrossRef]

Teraoka, I.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
[CrossRef] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[CrossRef]

Treussart, F.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Vahala, K. J.

Velichansky, V. L.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Voice, A. M.

T. Yamwong, A. M. Voice, and G. R. Davies, “Electrostrictive response of an ideal polar rubber,” J. Appl. Phys. 91(3), 1472–1476 (2002).
[CrossRef]

Volikov, P. S.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Vollmer, F.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
[CrossRef] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[CrossRef]

von Klitzing, W.

W. von Klitzing, “Tunable whispering modes for spectroscopy and CQED Experiments,” New J. Phys. 3, 14.1–14.14 (2001).
[CrossRef]

Yamwong, T.

T. Yamwong, A. M. Voice, and G. R. Davies, “Electrostrictive response of an ideal polar rubber,” J. Appl. Phys. 91(3), 1472–1476 (2002).
[CrossRef]

AIAA J. (1)

G. Guan, S. Arnold, and M. V. Ötügen, “Temperature Measurements Using a Micro-Optical Sensor Based on Whispering Gallery Modes,” AIAA J. 44(10), 2385–2389 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

B. J. Offrein, R. Germann, F. Horst, H. W. M. Salemink, R. Beyeler, and G. L. Bona,Resonant coupler-based tunable add-after-drop filter in silicon-oxynitride technology for WDM networks,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1400–1406 (1999).
[CrossRef]

V. M. N. Passaro and F. De Leonardis, “Modeling and Design of a Novel High-Sensitivity Electric Field Silicon-on-Insulator Sensor Based on a Whispering-Gallery-Mode Resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photon. Technol. Lett. 14(8), 1118–1120 (2002).
[CrossRef]

J. Appl. Phys. (3)

T. Ioppolo, U. K. Ayaz, and M. V. Ötügen, “High-resolution force sensor based on morphology dependent optical resonances of polymeric spheres,” J. Appl. Phys. 105(1), 013535 (2009).
[CrossRef]

F. Ay, A. Kocabas, C. Kocabas, A. Aydinli, and S. Agan, “Prism coupling technique investigation of elasto-optical properties of thin polymer films,” J. Appl. Phys. 96(12), 341–345 (2004).
[CrossRef]

T. Yamwong, A. M. Voice, and G. R. Davies, “Electrostrictive response of an ideal polar rubber,” J. Appl. Phys. 91(3), 1472–1476 (2002).
[CrossRef]

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

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

New J. Phys. (1)

W. von Klitzing, “Tunable whispering modes for spectroscopy and CQED Experiments,” New J. Phys. 3, 14.1–14.14 (2001).
[CrossRef]

Opt. Commun. (1)

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

A. T. Rosenberger and J. P. Rezac, “Whispering-gallerymode evanescent-wave microsensor for trace-gas detection,” Proc. SPIE 4265, 102–112 (2001).
[CrossRef]

Other (7)

N. Das, T. Ioppolo, and V. Ötügen, “Investigation of a micro-optical concentration sensor concept based on whispering gallery mode resonators,” presented at the 45th AIAA Aerospace Sciences Meeting and Exhibition, Reno, Nev., January 8–11 2007.

R. W. Soutas-Little, Elasticity, (Dover Publications Inc., Mineola, NY, 1999).

J. A. Stratton, Electromagnetic Theory (Mcgraw-Hill Book Company, Inc., New York and London, 1941).

T. Ioppolo, U. K. Ayaz, M. V. Ötügen, and V. Sheverev, “A Micro-Optical Wall Shear Stress Sensor Concept Based on Whispering Gallery Mode Resonators,” 46th AIAA Aerospace Sciences Meeting and Exhibit, 8–11 January 2008.

A. E. H. Love, The Mathematical Theory of Elasticity (Dover, 1926).

K. C. Kao, Dielectric Phenomena in Solids (Elsevier Academic Press, 2004).

J. E. Mark, Polymer Data Handbook (Oxford University Press, 1999).

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Figures (9)

Fig. 1
Fig. 1

The sphere in the presence of electric field.

Fig. 2
Fig. 2

The WGM shift of a solid 1 mm diameter PDMS sphere due to applied electric field (base-to-curing-agent ratio of 60:1, a/λ = 381).

Fig. 3
Fig. 3

Notation for a hollow dielectric sphere.

Fig. 4
Fig. 4

Pressure and body force distributions for a spherical PDMS shell (base-to-curing-agent ratio 60:1, a = 300 μm, a/λ = 288) due to applied electric field.

Fig. 5
Fig. 5

The WGM shifts of a hollow PDMS (60:1) sphere with the applied electric field due to strain effects (a/b = 0.95, b/λ = 381).

Fig. 6
Fig. 6

The WGM shifts of a hollow PDMS (60:1) sphere filled with water (a/b = 0.95, b/λ = 381).

Fig. 7
Fig. 7

WGM shifts of a hollow PDMS (60:1) sphere filled with water (a/b = 0.95, b/λ = 381) under constant electric field of 10kV/m. The WGM shifts obtained here are due to the change of refractive index of the surrounding medium.

Fig. 8
Fig. 8

Experimental setup.

Fig. 9
Fig. 9

Experimental and analytical results for a solid PDMS (60: 1) microsphere.

Equations (50)

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2πn0a=lλ
dλλ=dn0n0+daa
2u+112νu+fG=0
f=12E2ε114(a1+a2)E2
E=3ε2ε1+2ε2E0
2u+112νu=0
ur=[An(n+1)(n2+4ν)rn+1+Bnnrn1]Pn(cosϑ)uϑ=[An(n+1)(n+54ν)rn+1+Bnnrn1]dPn(cosϑ)dϑ}
σrr=2G[An(n+1)(n2n22ν)rn+Bnn(n1)rn2]Pn(cosϑ)
σϑϑ=2G{[An(n2+4n+2+2ν)(n+1)rn+Bnn2rn2]Pn(cosϑ)+[An(n+54ν)rn+Bnrn2]cot(ϑ)dPn(cosϑ)dϑ}
σϕϕ=2G{[An(n+1)(n22ν4nν)rn+Bnnrn2]Pn(cosϑ)+[An(n+54ν)rn+Bnrn2]cotϑdPn(cosϑ)dϑ}
σrϑ=2G[An(n2+2n1+2ν)rn+Bn(n1)rn2]Pn(cosϑ)ϑ
P=[αE(En)]2+[αE(En)]1[βE2n]2[βE2n]1
α=ε+a2a12   ,       β=ε+a22
α=ε       ,       β=ε06(k22k2)
P=(A'B')Cos(ϑ)2+B'
A'=(3ε2ε1+2ε2E0)2[(ε1ε2)2(α2β2)α1+β1]
B'=(3ε2ε1+2ε2E0)2(β1β2)
P=ε06E2(k21)(k2+2)
σrr(a)=Pσrϑ(a)=0
P=ZnPn(cosϑ)
Zo=13(A'+2B')   ,   Z2=23(A'B')
A0=(A'+2B')12G(1+ν),A2=(A'B')6Ga2(5ν+7),B2=(A'B')(2ν+7)6G(5ν+7)
ur=2A0(2ν1)r+(12A2νr3+2B2r)12(3cos(ϑ)21)
daa=(3ε2ε1+2ε2E0)2{(12ν)6G(1+ν)[((ε1ε2)2(α2β2)α1+3β12β2)]+(4ν7)3G(5ν+7)[(ε1ε2)2(α2β2)+α1β2]}
nr=nor+Cσ1rr+C2(σϑϑ+σφφ)nϑ=noϑ+Cσ1ϑϑ+C2(σrr+σφφ)nφ=noφ+Cσ1φφ+C2(σϑϑ+σrr)
dnono=nrnornor=nϑnoϑnoϑ=nrnoφnoφ=C(σrr+σϑϑ+σφφ)n
Φ(r,ϑ,ϕ)=i=0(Airi+Biri1)Pi(cosϑ)
Φ1=Bab(ra)cosϑ+C(ba)(ar)2cosϑΦ2=E0b(rb)cosϑ+D(br)2cosϑΦ3=A(ra)cosϑ
Φ3(a)=Φ1(a)     Φ1(b)=Φ2(b)ε3Φ3r|a=ε1Φ1r|aε1Φ1r|b=ε2Φ2r|b
(α12α12α13α14α21α22α23α24α31α32α33α34α41α42α43α44)(ABCD)=(γ1γ2γ3γ4)
E=Φ
E1,r=[B1ab+2C(abr3)]cosϑ       E1,ϑ=[B1ab+Cabr3]sinϑE2,r=[2Db2r3+E0]cosϑ           E2,ϑ=[Db2r3E0]sinϑE3,r=Aacosϑ                     E3,ϑ=Aasinϑ
P=[αE(En)]a+[αE(En)]b[βE2]a[βE2]b
P1,3=(ZY)cos(ϑ)2+YP1,2=(KW)cosϑ2+W
Z=(Aa)2[(ε3ε1)2(α1β1)α3+β3]   ,Y=(Aa)2(β3β1)
K=(B1ab2Cab2)2[(ε1ε2)2(α2β2)α1+β1],W=(Bab1a+Cab2)2(β1β2)
P3=ε06A2a2(k31)(k3+2)
f=14(a1+a2){[(18C2a2b2r7+18BCabr4)Cos2(ϑ)6C2a2b2r76BCabr4]r+Sin(2ϑ)(3C2a2b2r76BCabr4)ϑ}
ur=[An(n+1)(n2+4ν)Rn+1+BnnRn1]Pn(cosϑ)+[CnRn(n2+3n2ν)+Dn(n+1)(n+2)Rn+2]Pn(cosϑ)
σrr=2G[An(n+1)(n2n22ν)Rn+Bnn(n1)Rn2]Pn(cosϑ)+[CnnRn+1(n2+3n2ν)+Dn(n+1)(n+2)Rn+3]Pn(cosϑ)
σϑϑ=2G[An(n2+4n+2+2ν)(n+1)rn+Bnn2rn2+Cnnrn+1(n22n1+2ν)Dn(n+1)2rn+3]Pn(cosϑ)[An(n+54ν)rn+Bnrn2Cnrn+1(n+44ν)+Dnrn+3]cotϑdPn(cosϑ)dϑ
σφφ=2G[An(n+1)(n22ν4nν)rn+Bnnrn2+Cnnrn+1(n+34nν2ν)Dn(n+1)rn+3]Pn(cosϑ)+[An(n+54ν)rn+Bnrn2+Cnrn+1(n+44ν)+Dnrn+3]cotϑdPn(cosϑ)dϑ
σrϑ=2G[An(n2+2n1+2ν)Rn+Bn(n1)Rn2]Pn(cosϑ)ϑ+[CnRn+1(n22+2ν)Dn(n+2)Rn+3]Pn(cosϑ)ϑ
σrr(a)=P3P1,3       σrr(b)=P1,2σrϑ(a)=0           σrϑ(b)=0
P1,3=EnPn(cosϑ)=(ZY)cos(ϑ)2+YP1,2=FnPn(cosϑ)=(KW)cos(ϑ)2+W
E0=13(Z+2Y)   F0=13(K+2W)E2=23(ZY)     F2=23(KW)
(β11β12β13β14β21β22β23β24β31β32β33β34β41β42β43β44)(A0B0C0D0)=(ϕ1ϕ2ϕ3ϕ4)   (δ11δ12δ13δ14δ21δ22δ23δ24δ31δ32δ33δ34δ41δ42δ43δ44)(A2B2C2D2)=(ρ1ρ2ρ3ρ4)
α11=α24=1,α12=ab,α13=ba,α14=α21=α34=0,α22=ba,α23=ab,α31=ε1aε2,α32=1ab,α33=2ba2,α43=2ab,α42=1ab,α44=ε3ε22b,γ1=γ3=0,γ2=E0b,γ4=ε3ε2E0
δ11=6νa2,δ12=δ22=2,δ13=2a3(102ν),δ14=12a5,δ21=6νb2,δ23=2b3(102ν),δ24=12b5,δ31=(2ν+7)a2,   δ32=δ42=1,δ33=2a3(1+ν),   δ34=4a5,   δ41=(2ν+7)b2,   δ43=2b3(1+ν),   δ44=4b5,ρ1=13G(ZY),ρ2=13G(KW),ρ3=ρ4=0
β11=β21=2(1+ν),β14=2a3,β24=2b3,β32=1a2,β12=β13=β22=β23=0β31=β41=2v1,β33=2a(ν1),β34=2a3,β42=1b2,β43=2b(ν1),   β44=2b3ϕ1=(Z+2Y)6Gε06A2a(k1)(k+2),ϕ2=(K+2W)6G,ϕ3=ϕ4=0

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