Abstract

A hydrostatic pressure sensor based on morphology dependent resonances in a polymeric tube is presented. By internal pressurization, normal tensions will increase the device's size and shrink its wall thickness, inducing a shift in the resonant wavelengths of the resonator. Numerical simulations indicate that there are two modal regimes of sensitivity and a maximum achievable sensitivity, related to the device's geometry, constitutive material and analysed mode order. A sensitivity as high as 0.36 ± 0.01 nm/bar has been experimentally found for a 1.8mm diameter PMMA tube with wall thickness of 80µm.

© 2015 Optical Society of America

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References

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2014 (1)

J. Wang, T. Zhan, G. Huang, P. K. Chu, and Y. Mei, “Optical microcavities with tubular geometry: properties and applications,” Laser Photon. Rev. 8(4), 521–547 (2014).
[Crossref]

2013 (3)

H. Kudo, R. Suzuki, and T. Tanabe, “Whispering gallery modes in hexagonal microcavities,” Phys. Rev. A – At. Mol. Opt. Phys. 88, 023807 (2013).

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113(24), 243101 (2013).
[Crossref]

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

2012 (1)

M. Manzo, T. Ioppolo, U. K. Ayaz, V. Lapenna, and M. V. Ötügen, “A photonic wall pressure sensor for fluid mechanics applications,” Rev. Sci. Instrum. 83(10), 105003 (2012).
[Crossref] [PubMed]

2011 (2)

G. Senthil Murugan, M. N. Petrovich, Y. Jung, J. S. Wilkinson, and M. N. Zervas, “Hollow-bottle optical microresonators,” Opt. Express 19(21), 20773–20784 (2011).
[Crossref] [PubMed]

R. Yang, A. Yun, Y. Zhang, and X. Pu, “Quantum theory of whispering gallery modes in a cylindrical optical microcavity,” Optik (Stuttg.) 122(10), 900–909 (2011).
[Crossref]

2010 (3)

2009 (2)

2007 (1)

2006 (2)

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes - Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[Crossref]

2005 (1)

2004 (1)

2003 (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref] [PubMed]

2002 (1)

D. D. Wright, E. P. Lautenschlager, and J. L. Gilbert, “The effect of processing conditions on the properties of poly(methyl methacrylate) fibers,” J. Biomed. Mater. Res. 63(2), 152–160 (2002).
[Crossref] [PubMed]

2001 (1)

1999 (1)

1997 (1)

1995 (1)

N. C. Frateschi and A. F. J. Levi, “Resonant modes and laser spectrum of microdisk lasers,” Appl. Phys. Lett. 66(22), 2932 (1995).
[Crossref]

1993 (1)

1992 (2)

C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9(9), 1585–1592 (1992).
[Crossref]

W. C. Oliver and G. M. Pharr, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7(06), 1564–1583 (1992).
[Crossref]

1979 (1)

Aouani, H.

Argyros, A.

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref] [PubMed]

Ayaz, U. K.

M. Manzo, T. Ioppolo, U. K. Ayaz, V. Lapenna, and M. V. Ötügen, “A photonic wall pressure sensor for fluid mechanics applications,” Rev. Sci. Instrum. 83(10), 105003 (2012).
[Crossref] [PubMed]

Barton, G. W.

Bassett, I.

Birks, T. A.

Bo, L.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Borri, P.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113(24), 243101 (2013).
[Crossref]

Brambilla, G.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Cheung, G.

Chu, P. K.

J. Wang, T. Zhan, G. Huang, P. K. Chu, and Y. Mei, “Optical microcavities with tubular geometry: properties and applications,” Laser Photon. Rev. 8(4), 521–547 (2014).
[Crossref]

de Sterke, C. M.

Deiss, F.

Ding, M.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Dulashko, Y.

Farrell, G.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Feldman, A.

Ferrand, P.

Fleming, S.

Frateschi, N. C.

N. C. Frateschi and A. F. J. Levi, “Resonant modes and laser spectrum of microdisk lasers,” Appl. Phys. Lett. 66(22), 2932 (1995).
[Crossref]

Gilbert, J. L.

D. D. Wright, E. P. Lautenschlager, and J. L. Gilbert, “The effect of processing conditions on the properties of poly(methyl methacrylate) fibers,” J. Biomed. Mater. Res. 63(2), 152–160 (2002).
[Crossref] [PubMed]

Guo, L. J.

Haus, H. A.

Hewak, D.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Horowitz, D.

Huang, G.

J. Wang, T. Zhan, G. Huang, P. K. Chu, and Y. Mei, “Optical microcavities with tubular geometry: properties and applications,” Laser Photon. Rev. 8(4), 521–547 (2014).
[Crossref]

Ilchenko, V. S.

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35(16), 2822–2824 (2010).
[Crossref] [PubMed]

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes - Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[Crossref]

Ioppolo, T.

M. Manzo, T. Ioppolo, U. K. Ayaz, V. Lapenna, and M. V. Ötügen, “A photonic wall pressure sensor for fluid mechanics applications,” Rev. Sci. Instrum. 83(10), 105003 (2012).
[Crossref] [PubMed]

T. Ioppolo and M. V. Ötügen, “Pressure tuning of whispering gallery mode resonators,” J. Opt. Soc. Am. B 24(10), 2721–2726 (2007).
[Crossref]

Issa, N.

Jacques, F.

Johnson, B. R.

Jung, Y.

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref] [PubMed]

Knight, J. C.

Kudo, H.

H. Kudo, R. Suzuki, and T. Tanabe, “Whispering gallery modes in hexagonal microcavities,” Phys. Rev. A – At. Mol. Opt. Phys. 88, 023807 (2013).

Laine, J. P.

Lam, C. C.

Langbein, W.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113(24), 243101 (2013).
[Crossref]

Lapenna, V.

M. Manzo, T. Ioppolo, U. K. Ayaz, V. Lapenna, and M. V. Ötügen, “A photonic wall pressure sensor for fluid mechanics applications,” Rev. Sci. Instrum. 83(10), 105003 (2012).
[Crossref] [PubMed]

Large, M.

Large, M. C. J.

Lautenschlager, E. P.

D. D. Wright, E. P. Lautenschlager, and J. L. Gilbert, “The effect of processing conditions on the properties of poly(methyl methacrylate) fibers,” J. Biomed. Mater. Res. 63(2), 152–160 (2002).
[Crossref] [PubMed]

Lee, T.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Leung, P. T.

Levi, A. F. J.

N. C. Frateschi and A. F. J. Levi, “Resonant modes and laser spectrum of microdisk lasers,” Appl. Phys. Lett. 66(22), 2932 (1995).
[Crossref]

Liang, W.

Ling, T.

Little, B. E.

Lutti, J.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113(24), 243101 (2013).
[Crossref]

Lwin, R.

Maleki, L.

Manos, S.

Manzo, M.

M. Manzo, T. Ioppolo, U. K. Ayaz, V. Lapenna, and M. V. Ötügen, “A photonic wall pressure sensor for fluid mechanics applications,” Rev. Sci. Instrum. 83(10), 105003 (2012).
[Crossref] [PubMed]

Matsko, A. B.

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35(16), 2822–2824 (2010).
[Crossref] [PubMed]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes - Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[Crossref]

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

McPhedran, R.

Mei, Y.

J. Wang, T. Zhan, G. Huang, P. K. Chu, and Y. Mei, “Optical microcavities with tubular geometry: properties and applications,” Laser Photon. Rev. 8(4), 521–547 (2014).
[Crossref]

Nicorovici, N. A.

Oliver, W. C.

W. C. Oliver and G. M. Pharr, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7(06), 1564–1583 (1992).
[Crossref]

Ötügen, M. V.

M. Manzo, T. Ioppolo, U. K. Ayaz, V. Lapenna, and M. V. Ötügen, “A photonic wall pressure sensor for fluid mechanics applications,” Rev. Sci. Instrum. 83(10), 105003 (2012).
[Crossref] [PubMed]

T. Ioppolo and M. V. Ötügen, “Pressure tuning of whispering gallery mode resonators,” J. Opt. Soc. Am. B 24(10), 2721–2726 (2007).
[Crossref]

Petrovich, M. N.

Pharr, G. M.

W. C. Oliver and G. M. Pharr, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7(06), 1564–1583 (1992).
[Crossref]

Poladian, L.

Pu, X.

R. Yang, A. Yun, Y. Zhang, and X. Pu, “Quantum theory of whispering gallery modes in a cylindrical optical microcavity,” Optik (Stuttg.) 122(10), 900–909 (2011).
[Crossref]

Rigneault, H.

Roels, J.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
[Crossref]

Savchenkov, A. A.

Schmitzer, H.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113(24), 243101 (2013).
[Crossref]

Seidel, D.

Semenova, Y.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Senthil Murugan, G.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

G. Senthil Murugan, M. N. Petrovich, Y. Jung, J. S. Wilkinson, and M. N. Zervas, “Hollow-bottle optical microresonators,” Opt. Express 19(21), 20773–20784 (2011).
[Crossref] [PubMed]

Sojic, N.

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref] [PubMed]

Sumetsky, M.

Suzuki, R.

H. Kudo, R. Suzuki, and T. Tanabe, “Whispering gallery modes in hexagonal microcavities,” Phys. Rev. A – At. Mol. Opt. Phys. 88, 023807 (2013).

Tanabe, T.

H. Kudo, R. Suzuki, and T. Tanabe, “Whispering gallery modes in hexagonal microcavities,” Phys. Rev. A – At. Mol. Opt. Phys. 88, 023807 (2013).

Tanner, R. I.

Vahala, K. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref] [PubMed]

van Eijkelenborg, M.

Van Thourhout, D.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
[Crossref]

Wagner, H. P.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113(24), 243101 (2013).
[Crossref]

Wang, J.

J. Wang, T. Zhan, G. Huang, P. K. Chu, and Y. Mei, “Optical microcavities with tubular geometry: properties and applications,” Laser Photon. Rev. 8(4), 521–547 (2014).
[Crossref]

Wang, P.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Waxler, R. M.

Wenger, J.

Wilkinson, J. S.

Windeler, R. S.

Wright, D. D.

D. D. Wright, E. P. Lautenschlager, and J. L. Gilbert, “The effect of processing conditions on the properties of poly(methyl methacrylate) fibers,” J. Biomed. Mater. Res. 63(2), 152–160 (2002).
[Crossref] [PubMed]

Wu, Q.

P. Wang, M. Ding, T. Lee, G. Senthil Murugan, L. Bo, Y. Semenova, Q. Wu, D. Hewak, G. Brambilla, and G. Farrell, “Packaged chalcogenide microsphere resonator with high Q-factor,” Appl. Phys. Lett. 102(13), 131110 (2013).
[Crossref]

Xue, S. C.

Yang, R.

R. Yang, A. Yun, Y. Zhang, and X. Pu, “Quantum theory of whispering gallery modes in a cylindrical optical microcavity,” Optik (Stuttg.) 122(10), 900–909 (2011).
[Crossref]

Young, K.

Yun, A.

R. Yang, A. Yun, Y. Zhang, and X. Pu, “Quantum theory of whispering gallery modes in a cylindrical optical microcavity,” Optik (Stuttg.) 122(10), 900–909 (2011).
[Crossref]

Zagari, J.

Zervas, M. N.

Zhan, T.

J. Wang, T. Zhan, G. Huang, P. K. Chu, and Y. Mei, “Optical microcavities with tubular geometry: properties and applications,” Laser Photon. Rev. 8(4), 521–547 (2014).
[Crossref]

Zhang, Y.

R. Yang, A. Yun, Y. Zhang, and X. Pu, “Quantum theory of whispering gallery modes in a cylindrical optical microcavity,” Optik (Stuttg.) 122(10), 900–909 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

N. C. Frateschi and A. F. J. Levi, “Resonant modes and laser spectrum of microdisk lasers,” Appl. Phys. Lett. 66(22), 2932 (1995).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 a) Capillary describing the inner and outer radii - ρint and ρout -, the pressure applied, p - and its morphology response. b) Effective potential and turning points of surface modes SM, and bulk modes BM. The parameter ξ lies as the distance between the first two turning points, ρ1 and ρ2.
Fig. 2
Fig. 2 Sensitivity dependence of resonant modes near 1500 nm of capillaries resonators surrounded by air for surface modes (i) and bulk modes (ii). Numerical data are listed in embedded table.
Fig. 3
Fig. 3 Sensitivity as function of the azimuthal mode number - m - for a capillary resonator with geometrical parameter γ = 10(D = 2mm and a = 0.2mm).
Fig. 4
Fig. 4 a) A 4x optical microscopy of a typical capillary WGR used during the investigation. b) Diagram of the experimental apparatus used to investigate the device.
Fig. 5
Fig. 5 a) Spectral output of a typical pressurized capillary resonator. b) Sensitivity range obtained experimentally.
Fig. 6
Fig. 6 a) Dependence of the sensitivity as function of γ, of all samples listed in Table 1, compared with the analytical sensitivity (Eq. (6)) for two values of Young's modulus (2.2 and 3.1GPa). b) Fitting of the reproducibility (at the inset) of consecutive measurements for the sample 11. Note that no hysteresis has been observed through the try-out, as indicated by each sensitivity value found at each test.

Tables (1)

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Table 1 Experimental sensitivity of samples with different γ.

Equations (6)

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{ d 2 E ˜ z ( ρ, k 0 ) d ρ 2 + V TM m ( ρ, k 0 ) E ˜ z ( ρ, k 0 )=Π E ˜ z (ρ, k 0 ), E z ( ρ, k 0 )= E ˜ z ( ρ, k 0 ) ρ  
u( ρ,p )=ρ.[ ρ int 2 ( ρ out 2 ρ int 2 ) ].[ ( 1υ )+( 1+υ ) ( ρ out ρ ) 2 ]. p E  ,
{ ρ int ( p )= ρ int +u( ρ int ,p) ρ out ( p )= ρ out +u( ρ out ,p) ,
n( ρ,p )= n 1 + n 1 3 2 [ ( c 11 + c 12 )( 1υ ) 2E ] ( ρ out ρ ρ out ρ int ) 2 ( ρ int ρ ) 2 p,
n( ρ,p ) n 1 =[ ( ρ out ρ int ) 2 2( ρ out ρ int )ln( ρ out ρ int )1 ( ρ out ρ int 1 ) 3 ]p( 1.4× 10 6 ),
S Δλ Δp = 2 λ 0 E [ ( γ 2γ ) 2 1 ] 1 ,

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