Abstract

We investigate the possibility of using magnetorheological polydimethylsiloxane (MR-PDMS) spheres as micro- optical resonators. In particular, the effect of a magnetic field on the whispering gallery modes (WGM) of these resonators is studied. The applied field induces mechanical deformation, causing shifts in the WGM. The microspheres are made of PDMS with embedded magnetically polarizable particles. An analysis is carried out to estimate the WGM shifts induced by an external magnetic field. An experiment is also carried out to demonstrate the magnetic field-induced WGM shifts in an MR-PDMS microsphere. The results indicate that MR-PDMS microspheres can be used as high-Q-factor tunable optical cavities with potential applications in sensing.

© 2010 Optical Society of America

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References

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  1. M. R. Jolly, J. D. Carlos, and B. C. Munoz, Smart Mater. Struct. 5, 607 (1996).
    [CrossRef]
  2. M. Lokander and B. Stenberg, Polym. Test. 22, 253 (2003).
    [CrossRef]
  3. M. Lokander and B. Stenberg, Polym. Test. 22, 245 (2003).
    [CrossRef]
  4. J. M. Ginder, M. E. Nichols, L. D. Elie, and J. L. Tardiff, Proc. SPIE 3675, 131 (1999).
    [CrossRef]
  5. H. Bose, in Proceedings of the 10th International Conference on Electrorheological Fluids and Magnetorheological Suspensions (2006), pp. 51–55.
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    [CrossRef]
  8. T. Ioppolo, M. Kozhevnikov, V. Stepaniuk, M. V. Ötügen, and V. Sheverev, Appl. Opt. 47, 3009 (2008).
    [CrossRef] [PubMed]
  9. T. Ioppolo, Y. K. Ayaz, and M. V. Ötügen, J. Appl. Phys. 105, 013535 (2009).
    [CrossRef]
  10. T. Ioppolo, U. K. Ayaz, and M. V. Ötügen, Opt. Express 17, 16465 (2009).
    [CrossRef] [PubMed]
  11. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
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    [CrossRef]
  13. T. J. Fiske, H. Gokturk, and D. M. Kalyon, J. Appl. Polym. Sci. 65, 1371 (1997).
    [CrossRef]

2009 (2)

T. Ioppolo, Y. K. Ayaz, and M. V. Ötügen, J. Appl. Phys. 105, 013535 (2009).
[CrossRef]

T. Ioppolo, U. K. Ayaz, and M. V. Ötügen, Opt. Express 17, 16465 (2009).
[CrossRef] [PubMed]

2008 (1)

2006 (1)

J. Guan, S. Arnold, and M. V. Otugen, AIAA J. 44, 2385 (2006).
[CrossRef]

2003 (2)

M. Lokander and B. Stenberg, Polym. Test. 22, 253 (2003).
[CrossRef]

M. Lokander and B. Stenberg, Polym. Test. 22, 245 (2003).
[CrossRef]

1999 (2)

J. M. Ginder, M. E. Nichols, L. D. Elie, and J. L. Tardiff, Proc. SPIE 3675, 131 (1999).
[CrossRef]

L. C. Davis, J. Appl. Phys. 85, 3348 (1999).
[CrossRef]

1997 (1)

T. J. Fiske, H. Gokturk, and D. M. Kalyon, J. Appl. Polym. Sci. 65, 1371 (1997).
[CrossRef]

1996 (1)

M. R. Jolly, J. D. Carlos, and B. C. Munoz, Smart Mater. Struct. 5, 607 (1996).
[CrossRef]

Abbo, C.

G. Bossis, C. Abbo, S. Cutillas, S. Lacis, and C. Metayer, in Proceedings of the 7th International Conference on Electro-Rheological Fluids and Magneto-Rheological Suspensions (2000), pp. 18–27.

Arnold, S.

J. Guan, S. Arnold, and M. V. Otugen, AIAA J. 44, 2385 (2006).
[CrossRef]

Ayaz, U. K.

Ayaz, Y. K.

T. Ioppolo, Y. K. Ayaz, and M. V. Ötügen, J. Appl. Phys. 105, 013535 (2009).
[CrossRef]

Bose, H.

H. Bose, in Proceedings of the 10th International Conference on Electrorheological Fluids and Magnetorheological Suspensions (2006), pp. 51–55.

Bossis, G.

G. Bossis, C. Abbo, S. Cutillas, S. Lacis, and C. Metayer, in Proceedings of the 7th International Conference on Electro-Rheological Fluids and Magneto-Rheological Suspensions (2000), pp. 18–27.

Carlos, J. D.

M. R. Jolly, J. D. Carlos, and B. C. Munoz, Smart Mater. Struct. 5, 607 (1996).
[CrossRef]

Cutillas, S.

G. Bossis, C. Abbo, S. Cutillas, S. Lacis, and C. Metayer, in Proceedings of the 7th International Conference on Electro-Rheological Fluids and Magneto-Rheological Suspensions (2000), pp. 18–27.

Davis, L. C.

L. C. Davis, J. Appl. Phys. 85, 3348 (1999).
[CrossRef]

Elie, L. D.

J. M. Ginder, M. E. Nichols, L. D. Elie, and J. L. Tardiff, Proc. SPIE 3675, 131 (1999).
[CrossRef]

Fiske, T. J.

T. J. Fiske, H. Gokturk, and D. M. Kalyon, J. Appl. Polym. Sci. 65, 1371 (1997).
[CrossRef]

Ginder, J. M.

J. M. Ginder, M. E. Nichols, L. D. Elie, and J. L. Tardiff, Proc. SPIE 3675, 131 (1999).
[CrossRef]

Gokturk, H.

T. J. Fiske, H. Gokturk, and D. M. Kalyon, J. Appl. Polym. Sci. 65, 1371 (1997).
[CrossRef]

Guan, J.

J. Guan, S. Arnold, and M. V. Otugen, AIAA J. 44, 2385 (2006).
[CrossRef]

Ioppolo, T.

Jolly, M. R.

M. R. Jolly, J. D. Carlos, and B. C. Munoz, Smart Mater. Struct. 5, 607 (1996).
[CrossRef]

Kalyon, D. M.

T. J. Fiske, H. Gokturk, and D. M. Kalyon, J. Appl. Polym. Sci. 65, 1371 (1997).
[CrossRef]

Kozhevnikov, M.

Lacis, S.

G. Bossis, C. Abbo, S. Cutillas, S. Lacis, and C. Metayer, in Proceedings of the 7th International Conference on Electro-Rheological Fluids and Magneto-Rheological Suspensions (2000), pp. 18–27.

Lokander, M.

M. Lokander and B. Stenberg, Polym. Test. 22, 253 (2003).
[CrossRef]

M. Lokander and B. Stenberg, Polym. Test. 22, 245 (2003).
[CrossRef]

Metayer, C.

G. Bossis, C. Abbo, S. Cutillas, S. Lacis, and C. Metayer, in Proceedings of the 7th International Conference on Electro-Rheological Fluids and Magneto-Rheological Suspensions (2000), pp. 18–27.

Munoz, B. C.

M. R. Jolly, J. D. Carlos, and B. C. Munoz, Smart Mater. Struct. 5, 607 (1996).
[CrossRef]

Nichols, M. E.

J. M. Ginder, M. E. Nichols, L. D. Elie, and J. L. Tardiff, Proc. SPIE 3675, 131 (1999).
[CrossRef]

Otugen, M. V.

J. Guan, S. Arnold, and M. V. Otugen, AIAA J. 44, 2385 (2006).
[CrossRef]

Ötügen, M. V.

Sheverev, V.

Stenberg, B.

M. Lokander and B. Stenberg, Polym. Test. 22, 245 (2003).
[CrossRef]

M. Lokander and B. Stenberg, Polym. Test. 22, 253 (2003).
[CrossRef]

Stepaniuk, V.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Tardiff, J. L.

J. M. Ginder, M. E. Nichols, L. D. Elie, and J. L. Tardiff, Proc. SPIE 3675, 131 (1999).
[CrossRef]

AIAA J. (1)

J. Guan, S. Arnold, and M. V. Otugen, AIAA J. 44, 2385 (2006).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (2)

T. Ioppolo, Y. K. Ayaz, and M. V. Ötügen, J. Appl. Phys. 105, 013535 (2009).
[CrossRef]

L. C. Davis, J. Appl. Phys. 85, 3348 (1999).
[CrossRef]

J. Appl. Polym. Sci. (1)

T. J. Fiske, H. Gokturk, and D. M. Kalyon, J. Appl. Polym. Sci. 65, 1371 (1997).
[CrossRef]

Opt. Express (1)

Polym. Test. (2)

M. Lokander and B. Stenberg, Polym. Test. 22, 253 (2003).
[CrossRef]

M. Lokander and B. Stenberg, Polym. Test. 22, 245 (2003).
[CrossRef]

Proc. SPIE (1)

J. M. Ginder, M. E. Nichols, L. D. Elie, and J. L. Tardiff, Proc. SPIE 3675, 131 (1999).
[CrossRef]

Smart Mater. Struct. (1)

M. R. Jolly, J. D. Carlos, and B. C. Munoz, Smart Mater. Struct. 5, 607 (1996).
[CrossRef]

Other (3)

H. Bose, in Proceedings of the 10th International Conference on Electrorheological Fluids and Magnetorheological Suspensions (2006), pp. 51–55.

G. Bossis, C. Abbo, S. Cutillas, S. Lacis, and C. Metayer, in Proceedings of the 7th International Conference on Electro-Rheological Fluids and Magneto-Rheological Suspensions (2000), pp. 18–27.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

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Figures (5)

Fig. 1
Fig. 1

Schematic of sphere in the presence of magnetic field H 0 . (Magnetic field is normal to the plane of light circulation in the sphere.)

Fig. 2
Fig. 2

Photograph of an MR-PDMS microsphere and detail showing embedded polarizable particles.

Fig. 3
Fig. 3

Schematic of experimental setup.

Fig. 4
Fig. 4

Transmission spectrum of WGM. Q = 2 × 10 6 .

Fig. 5
Fig. 5

Experimental and analytical results with an 400 μm radius MR-PDMS sphere.

Equations (9)

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Δ λ / λ = Δ R / R ,
2 u + 1 1 2 ν ( · u ) + f G = 0
σ r r = p and σ r ϑ = 0 at r = R ,
f = 1 4 ( b 1 + b 2 ) H 2 .
u r = [ A n ( n + 1 ) ( n 2 + 4 ν ) r n + 1 + B n n r n 1 ] P n ( cos ϑ ) ,
p = μ 0 ( μ r 1 ) 2 [ H 2 + ( μ r 1 ) H 2 cos 2 ϑ ] + b 1 b 2 2 H 2 cos 2 ϑ + b 2 2 H 2 .
p = [ μ 0 ( μ r 1 ) + b 2 2 ] H 2 + [ μ 0 ( μ r 1 ) 2 + ( b 1 b 2 ) μ 0 μ 0 ] 1 3 P 2 H 2 + [ μ 0 ( μ r 1 ) 2 + b 1 b 2 ] 1 4 H 2 ,
p = [ ( μ r 1 ) 2 + b 1 b 2 μ 0 ] 3 B 0 2 μ 0 ( μ r + 2 ) 2 P 2 .
Δ λ λ = Δ R R = 7 4 ν 4 G ( 7 + 5 ν ) [ ( μ r 1 ) 2 + b 1 b 2 μ 0 ] 3 B 0 2 μ 0 ( μ r + 2 ) 2 .

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