Abstract

Aerostatic tuning of whispering gallery modes (WGMs) in a microbubble resonator is demonstrated. The optical modes are redshifted over hundreds of gigahertz (GHz) simply by increasing the air pressure (up to 6bars) inside the microbubble. A description of the pressure tuning properties of the WGMs in microbubbles is given in terms of the corresponding elasto-optical equations of spherical shells and the results are compared to experimental data. Microbubbles as small as 74μm are tested and the experimental results show excellent agreement with the theory. An estimation method is developed for calculating the wall thicknesses of the microbubbles from the diameters, which are measured via direct microscopy. A geometrical factor χ is defined and a linear relationship between the shift rate (GHz/bar) of the bubbles modes and χ is observed.

© 2011 Optical Society of America

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2011

J. M. Ward and O. Benson, Laser Photon. Rev. 5, 553 (2011).
[CrossRef]

A. Watkins, J. M. Ward, Y. Wu, and S. N. Chormaic, Opt. Lett. 36, 2113 (2011).
[CrossRef] [PubMed]

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, Appl. Phys. Lett. 99, 091102 (2011).
[CrossRef]

2010

M. Sumetsky, Y. Dulashko, and R. S. Windeler, Opt. Lett. 35, 898 (2010).
[CrossRef] [PubMed]

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, Rev. Sci. Instrum. 96, 231102 (2010).
[CrossRef]

J. M. Ward and S. N. Chormaic, Appl. Phys. B 100, 847(2010).
[CrossRef]

M. Sumetsky, Y. Dulashko, and R. S. Windeler, Opt. Lett. 35, 1866 (2010).
[CrossRef] [PubMed]

2008

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef] [PubMed]

2007

2006

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

2004

D. K. Armani, B. K. Min, A. L. Martin, and K. J. Vahala, Appl. Phys. Lett. 85, 5439 (2004).
[CrossRef]

2003

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

2001

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001).
[CrossRef]

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Armani, D. K.

D. K. Armani, B. K. Min, A. L. Martin, and K. J. Vahala, Appl. Phys. Lett. 85, 5439 (2004).
[CrossRef]

Arnold, S.

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef] [PubMed]

Benson, O.

J. M. Ward and O. Benson, Laser Photon. Rev. 5, 553 (2011).
[CrossRef]

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, Rev. Sci. Instrum. 96, 231102 (2010).
[CrossRef]

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Chormaic, S. N.

Dayan, B.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Dulashko, Y.

Fan, X.

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, Appl. Phys. Lett. 99, 091102 (2011).
[CrossRef]

Goodier, J. N.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 2nd ed. (McGraw-Hill, 1951).

Gregor, M.

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, Rev. Sci. Instrum. 96, 231102 (2010).
[CrossRef]

Hare, J.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001).
[CrossRef]

Henze, R.

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, Rev. Sci. Instrum. 96, 231102 (2010).
[CrossRef]

Ilchenko, V. S.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001).
[CrossRef]

Ioppolo, T.

Kimble, H. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Kippenberg, T. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Lee, W.

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, Appl. Phys. Lett. 99, 091102 (2011).
[CrossRef]

Lefèvre-Seguin, V.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001).
[CrossRef]

Li, H.

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, Appl. Phys. Lett. 99, 091102 (2011).
[CrossRef]

Long, R.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001).
[CrossRef]

Maleki, L.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

Martin, A. L.

D. K. Armani, B. K. Min, A. L. Martin, and K. J. Vahala, Appl. Phys. Lett. 85, 5439 (2004).
[CrossRef]

Matsko, A. B.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

Min, B. K.

D. K. Armani, B. K. Min, A. L. Martin, and K. J. Vahala, Appl. Phys. Lett. 85, 5439 (2004).
[CrossRef]

Ötügen, M. V.

Parkins, A. S.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Peters, A.

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, Rev. Sci. Instrum. 96, 231102 (2010).
[CrossRef]

Pyrlik, C.

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, Rev. Sci. Instrum. 96, 231102 (2010).
[CrossRef]

Reddy, K.

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, Appl. Phys. Lett. 99, 091102 (2011).
[CrossRef]

Savchenkov, A. A.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

Sumetsky, M.

Sun, Y.

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, Appl. Phys. Lett. 99, 091102 (2011).
[CrossRef]

Timoshenko, S. P.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 2nd ed. (McGraw-Hill, 1951).

Vahala, K. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

D. K. Armani, B. K. Min, A. L. Martin, and K. J. Vahala, Appl. Phys. Lett. 85, 5439 (2004).
[CrossRef]

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Vollmer, F.

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef] [PubMed]

von Klitzing, W.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001).
[CrossRef]

Ward, J. M.

J. M. Ward and O. Benson, Laser Photon. Rev. 5, 553 (2011).
[CrossRef]

A. Watkins, J. M. Ward, Y. Wu, and S. N. Chormaic, Opt. Lett. 36, 2113 (2011).
[CrossRef] [PubMed]

J. M. Ward and S. N. Chormaic, Appl. Phys. B 100, 847(2010).
[CrossRef]

Watkins, A.

Wicht, A.

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, Rev. Sci. Instrum. 96, 231102 (2010).
[CrossRef]

Wilcut, E.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Windeler, R. S.

Wu, Y.

Appl. Phys. B

J. M. Ward and S. N. Chormaic, Appl. Phys. B 100, 847(2010).
[CrossRef]

Appl. Phys. Lett.

D. K. Armani, B. K. Min, A. L. Martin, and K. J. Vahala, Appl. Phys. Lett. 85, 5439 (2004).
[CrossRef]

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, Appl. Phys. Lett. 99, 091102 (2011).
[CrossRef]

Electron. Lett.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Laser Photon. Rev.

J. M. Ward and O. Benson, Laser Photon. Rev. 5, 553 (2011).
[CrossRef]

Nat. Methods

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef] [PubMed]

Nature

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

New J. Phys.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, Rev. Sci. Instrum. 96, 231102 (2010).
[CrossRef]

Other

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 2nd ed. (McGraw-Hill, 1951).

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Figures (3)

Fig. 1
Fig. 1

Examples of microbubble resonators. The diameters of the bubbles are (a)  265 μm , (b)  490 μm , (c)  170 μm , (d)  290 μm , (e)  330 μm , (f)  195 μm , (g)  95 μm . (f) is a bubble made by heating the capillary head-on with a single CO 2 laser beam and is shown here filled with water. (g) is a bubble with two openings or ports.

Fig. 2
Fig. 2

Pressure tuning of the WGMs in different microbubbles (dots) and comparison with the theoretical model (lines). The inset is a schematic of the mode shift.

Fig. 3
Fig. 3

Dependence of the WGM pressure tuning slopes of the different resonators in Fig. 1 with geometrical parameter χ = b 3 / ( a 3 b 3 ) . a and b are the outer and inner diameters, respectively.

Equations (5)

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

d ( λ ) λ = d a a + d n n ,
d a ( p i ) a = ( 4 G + 3 K ) p i b 3 4 G p 0 a 3 3 K p 0 b 3 12 G K ( a 3 b 3 ) .
d ( n t ) n t = ( 3 p i b 3 p o b 3 2 p o a 3 ) C 1 + ( 3 p i b 3 + p o b 3 4 p o a 3 ) C 2 2 n o ( a 3 b 3 ) ,
d λ ( p i ) λ = 2 n 0 b 3 + 12 C G b 3 4 G n o ( a 3 b 3 ) p i n 0 ( a 3 + b 3 ) + 12 C G a 3 4 G n 0 ( a 3 b 3 ) p 0 .
w = a a 2 1 4 D 1 2 ( 1 ξ 2 ) ,

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