Abstract

This paper reports for the first time a planarised optical fiber composite formed using Flame Hydrolysis Deposition (FHD). As a way of format demonstration a Micro-Opto-Electro-Mechanical (MOEMS) hot wire anemometer is formed using micro-fabrication processing. The planarised device is rigidly secured to a silicon wafer using optical quality doped silica that has been deposited using flame hydrolysis and consolidated at high temperature. The resulting structure can withstand temperatures exceeding 580K and is sensitive enough to resolve free and forced convection interactions at low fluid velocity.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Integrated-optic Nd:glass laser fabricated by flame hydrolysis deposition using chelates

R. Tumminelli, F. Hakimi, and J. Haavisto
Opt. Lett. 16(14) 1098-1100 (1991)

Long-range distributed optical fiber hot-wire anemometer based on chirped-pulse ΦOTDR

Andres Garcia-Ruiz, Alejandro Dominguez-Lopez, Juan Pastor-Graells, Hugo F. Martins, Sonia Martin-Lopez, and Miguel Gonzalez-Herraez
Opt. Express 26(1) 463-476 (2018)

All-optical fiber anemometer based on laser heated fiber Bragg gratings

Shaorui Gao, A. Ping Zhang, Hwa-Yaw Tam, L. H. Cho, and Chao Lu
Opt. Express 19(11) 10124-10130 (2011)

References

  • View by:
  • |
  • |
  • |

  1. G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
    [Crossref]
  2. C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
    [Crossref]
  3. J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
    [Crossref]
  4. D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
    [Crossref]
  5. Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
    [Crossref] [PubMed]
  6. C. Pang, H. Bae, A. Gupta, K. Bryden, and M. Yu, “MEMS Fabry-Perot sensor interrogated by optical system-on-a-chip for simultaneous pressure and temperature sensing,” Opt. Express 21(19), 21829–21839 (2013).
    [Crossref] [PubMed]
  7. V. P. Wnuk, A. Méndez, C. Ave, S. Ferguson, and T. Graver, “Process for Mounting and Packaging of Fiber Bragg Grating Strain Sensors for use in Harsh Environment Applications,” Smart Struct. Conf.46, (2005).
    [Crossref]
  8. A. Saran, D. C. Abeysinghe, R. Flenniken, and J. T. Boyd, “Anodic bonding of optical fibers-to-silicon for integrating MEMS devices and optical fibers,” J. Micromech. Microeng. 13(2), 346–351 (2003).
    [Crossref]
  9. R. Knechtel, “Glass frit bonding: an universal technology for wafer level encapsulation and packaging,” Microsyst. Technol. 12(1-2), 63–68 (2005).
    [Crossref]
  10. A. D. Yablon, Optical Fiber Fusion Splicing, Springer Series in Optical Sciences (Springer, 2005).
  11. M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Opt. Quantum Electron. 22(5), 391–416 (1990).
    [Crossref]
  12. H. L. Rogers, S. Ambran, C. Holmes, P. G. R. Smith, and J. C. Gates, “In situ loss measurement of direct UV-written waveguides using integrated Bragg gratings,” Opt. Lett. 35(17), 2849–2851 (2010).
    [Crossref] [PubMed]
  13. A. Kilian, J. Kirchhof, B. Kuhlow, G. Przyrembel, and W. Wischmann, “Birefringence Free Planar Optical Waveguide Made by Flame Hydrolysis Deposition (FHD) Through Tailoring of the Overcladding,” J. Lightwave Technol. 18(2), 193–198 (2000).
    [Crossref]
  14. P. Dumais, “Thermal Stress Birefringence in Buried-Core Waveguides with Over-Etch,” IEEE J. Quantum Electron. 47(7), 989–996 (2011).
    [Crossref]
  15. J. Salort, A. Monfardini, and P.-E. Roche, “Cantilever anemometer based on a superconducting micro-resonator: application to superfluid turbulence,” Rev. Sci. Instrum. 83(12), 125002 (2012).
    [Crossref] [PubMed]
  16. P. Zyłka, P. Modrzynski, and P. Janus, “Vortex Anemometer Using MEMS Cantilever Sensor,” J. Micromechanical Syst. 19(6), 1485–1489 (2010).
    [Crossref]
  17. M. Schwerter, T. Beutel, M. Leester-Schädel, S. Büttgenbach, and A. Dietzel, “Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings,” Microsyst. Technol. 20(4-5), 821–829 (2014).
    [Crossref]
  18. P. Caldas, P. A. S. Jorge, G. Rego, O. Frazão, J. L. Santos, L. A. Ferreira, and F. Araújo, “Fibre Optic Hot-Wire Flowmeter Based on a Metallic Coated Hybrid LPG-FBG Structure,” in Fourth European Workshop on Optical Fibre Sensors (2010), Vol. 7653, p. 76530B.
    [Crossref]
  19. S. Gao, A. P. Zhang, H.-Y. Tam, L. H. Cho, and C. Lu, “All-optical fiber anemometer based on laser heated fiber Bragg gratings,” Opt. Express 19(11), 10124–10130 (2011).
    [Crossref] [PubMed]
  20. X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
    [Crossref]
  21. X. Wang, X. Dong, Y. Zhou, K. Ni, J. Cheng, and Z. Chen, “Hot-Wire Anemometer Based on Silver-Coated Fiber Bragg Grating Assisted by No-Core Fiber,” IEEE Photon. Technol. Lett. 25(24), 2458–2461 (2013).
    [Crossref]
  22. Y.-J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8(4), 355–375 (1997).
    [Crossref]
  23. C. G. Lomas, Fundamentals of Hot Wire Anemometry (Cambridge University, 2011).
  24. B. D. C. Collis and M. J. Williams, “Two-dimensional convection from heated wires at low Reynolds numbers,” J. Fluid Mech. 6(03), 357–384 (1959).
    [Crossref]
  25. C. Holmes, D. O. Kundys, J. C. Gates, C. B. E. Gawith, and P. G. R. Smith, “150 GHz of thermo-optic tuning in direct UV written silica-on-silicon planar Bragg grating,” Electron. Lett. 45(18), 954 (2009).
    [Crossref]
  26. C. Sima, J. C. Gates, H. L. Rogers, P. L. Mennea, C. Holmes, M. N. Zervas, and P. G. R. Smith, “Ultra-wide detuning planar Bragg grating fabrication technique based on direct UV grating writing with electro-optic phase modulation,” Opt. Express 21(13), 15747–15754 (2013).
    [Crossref] [PubMed]
  27. F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).
  28. C. Holmes, L. G. Carpenter, J. C. Gates, and P. G. R. Smith, “Miniaturization of Bragg-multiplexed membrane transducers,” J. Micromech. Microeng. 22(2), 025017 (2012).
    [Crossref]
  29. C. Holmes, L. G. Carpenter, H. L. Rogers, J. C. Gates, and P. G. R. Smith, “Quantifying the optical sensitivity of planar Bragg gratings in glass micro-cantilevers to physical deflection,” J. Micromech. Microeng. 21(3), 035014 (2011).
    [Crossref]
  30. T. H. Laby and G. W. C. Kaye, Tables of Physical and Chemical Constants, 16th ed. (Longman, 2005).

2014 (2)

M. Schwerter, T. Beutel, M. Leester-Schädel, S. Büttgenbach, and A. Dietzel, “Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings,” Microsyst. Technol. 20(4-5), 821–829 (2014).
[Crossref]

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
[Crossref]

2013 (3)

2012 (3)

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

C. Holmes, L. G. Carpenter, J. C. Gates, and P. G. R. Smith, “Miniaturization of Bragg-multiplexed membrane transducers,” J. Micromech. Microeng. 22(2), 025017 (2012).
[Crossref]

J. Salort, A. Monfardini, and P.-E. Roche, “Cantilever anemometer based on a superconducting micro-resonator: application to superfluid turbulence,” Rev. Sci. Instrum. 83(12), 125002 (2012).
[Crossref] [PubMed]

2011 (6)

P. Dumais, “Thermal Stress Birefringence in Buried-Core Waveguides with Over-Etch,” IEEE J. Quantum Electron. 47(7), 989–996 (2011).
[Crossref]

G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
[Crossref]

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
[Crossref] [PubMed]

C. Holmes, L. G. Carpenter, H. L. Rogers, J. C. Gates, and P. G. R. Smith, “Quantifying the optical sensitivity of planar Bragg gratings in glass micro-cantilevers to physical deflection,” J. Micromech. Microeng. 21(3), 035014 (2011).
[Crossref]

S. Gao, A. P. Zhang, H.-Y. Tam, L. H. Cho, and C. Lu, “All-optical fiber anemometer based on laser heated fiber Bragg gratings,” Opt. Express 19(11), 10124–10130 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (1)

C. Holmes, D. O. Kundys, J. C. Gates, C. B. E. Gawith, and P. G. R. Smith, “150 GHz of thermo-optic tuning in direct UV written silica-on-silicon planar Bragg grating,” Electron. Lett. 45(18), 954 (2009).
[Crossref]

2005 (1)

R. Knechtel, “Glass frit bonding: an universal technology for wafer level encapsulation and packaging,” Microsyst. Technol. 12(1-2), 63–68 (2005).
[Crossref]

2003 (2)

A. Saran, D. C. Abeysinghe, R. Flenniken, and J. T. Boyd, “Anodic bonding of optical fibers-to-silicon for integrating MEMS devices and optical fibers,” J. Micromech. Microeng. 13(2), 346–351 (2003).
[Crossref]

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

2000 (1)

1997 (1)

Y.-J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8(4), 355–375 (1997).
[Crossref]

1995 (1)

D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
[Crossref]

1990 (1)

M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Opt. Quantum Electron. 22(5), 391–416 (1990).
[Crossref]

1959 (1)

B. D. C. Collis and M. J. Williams, “Two-dimensional convection from heated wires at low Reynolds numbers,” J. Fluid Mech. 6(03), 357–384 (1959).
[Crossref]

Abeysinghe, D. C.

A. Saran, D. C. Abeysinghe, R. Flenniken, and J. T. Boyd, “Anodic bonding of optical fibers-to-silicon for integrating MEMS devices and optical fibers,” J. Micromech. Microeng. 13(2), 346–351 (2003).
[Crossref]

Adikan, M.

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

Ambran, S.

Ave, C.

V. P. Wnuk, A. Méndez, C. Ave, S. Ferguson, and T. Graver, “Process for Mounting and Packaging of Fiber Bragg Grating Strain Sensors for use in Harsh Environment Applications,” Smart Struct. Conf.46, (2005).
[Crossref]

Bae, H.

Ben Bakir, B.

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Beutel, T.

M. Schwerter, T. Beutel, M. Leester-Schädel, S. Büttgenbach, and A. Dietzel, “Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings,” Microsyst. Technol. 20(4-5), 821–829 (2014).
[Crossref]

Bogaerts, W.

G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
[Crossref]

Boyd, J. T.

A. Saran, D. C. Abeysinghe, R. Flenniken, and J. T. Boyd, “Anodic bonding of optical fibers-to-silicon for integrating MEMS devices and optical fibers,” J. Micromech. Microeng. 13(2), 346–351 (2003).
[Crossref]

Bryden, K.

Büttgenbach, S.

M. Schwerter, T. Beutel, M. Leester-Schädel, S. Büttgenbach, and A. Dietzel, “Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings,” Microsyst. Technol. 20(4-5), 821–829 (2014).
[Crossref]

Carpenter, L. G.

C. Holmes, L. G. Carpenter, J. C. Gates, and P. G. R. Smith, “Miniaturization of Bragg-multiplexed membrane transducers,” J. Micromech. Microeng. 22(2), 025017 (2012).
[Crossref]

C. Holmes, L. G. Carpenter, H. L. Rogers, J. C. Gates, and P. G. R. Smith, “Quantifying the optical sensitivity of planar Bragg gratings in glass micro-cantilevers to physical deflection,” J. Micromech. Microeng. 21(3), 035014 (2011).
[Crossref]

Chen, Z.

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
[Crossref]

X. Wang, X. Dong, Y. Zhou, K. Ni, J. Cheng, and Z. Chen, “Hot-Wire Anemometer Based on Silver-Coated Fiber Bragg Grating Assisted by No-Core Fiber,” IEEE Photon. Technol. Lett. 25(24), 2458–2461 (2013).
[Crossref]

Cheng, J.

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
[Crossref]

X. Wang, X. Dong, Y. Zhou, K. Ni, J. Cheng, and Z. Chen, “Hot-Wire Anemometer Based on Silver-Coated Fiber Bragg Grating Assisted by No-Core Fiber,” IEEE Photon. Technol. Lett. 25(24), 2458–2461 (2013).
[Crossref]

Cho, L. H.

Collis, B. D. C.

B. D. C. Collis and M. J. Williams, “Two-dimensional convection from heated wires at low Reynolds numbers,” J. Fluid Mech. 6(03), 357–384 (1959).
[Crossref]

Dietzel, A.

M. Schwerter, T. Beutel, M. Leester-Schädel, S. Büttgenbach, and A. Dietzel, “Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings,” Microsyst. Technol. 20(4-5), 821–829 (2014).
[Crossref]

Dong, X.

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
[Crossref]

X. Wang, X. Dong, Y. Zhou, K. Ni, J. Cheng, and Z. Chen, “Hot-Wire Anemometer Based on Silver-Coated Fiber Bragg Grating Assisted by No-Core Fiber,” IEEE Photon. Technol. Lett. 25(24), 2458–2461 (2013).
[Crossref]

Dumais, P.

P. Dumais, “Thermal Stress Birefringence in Buried-Core Waveguides with Over-Etch,” IEEE J. Quantum Electron. 47(7), 989–996 (2011).
[Crossref]

Fedeli, J.

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Ferguson, S.

V. P. Wnuk, A. Méndez, C. Ave, S. Ferguson, and T. Graver, “Process for Mounting and Packaging of Fiber Bragg Grating Strain Sensors for use in Harsh Environment Applications,” Smart Struct. Conf.46, (2005).
[Crossref]

Flenniken, R.

A. Saran, D. C. Abeysinghe, R. Flenniken, and J. T. Boyd, “Anodic bonding of optical fibers-to-silicon for integrating MEMS devices and optical fibers,” J. Micromech. Microeng. 13(2), 346–351 (2003).
[Crossref]

Gao, S.

Gates, J. C.

C. Sima, J. C. Gates, H. L. Rogers, P. L. Mennea, C. Holmes, M. N. Zervas, and P. G. R. Smith, “Ultra-wide detuning planar Bragg grating fabrication technique based on direct UV grating writing with electro-optic phase modulation,” Opt. Express 21(13), 15747–15754 (2013).
[Crossref] [PubMed]

C. Holmes, L. G. Carpenter, J. C. Gates, and P. G. R. Smith, “Miniaturization of Bragg-multiplexed membrane transducers,” J. Micromech. Microeng. 22(2), 025017 (2012).
[Crossref]

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

C. Holmes, L. G. Carpenter, H. L. Rogers, J. C. Gates, and P. G. R. Smith, “Quantifying the optical sensitivity of planar Bragg gratings in glass micro-cantilevers to physical deflection,” J. Micromech. Microeng. 21(3), 035014 (2011).
[Crossref]

H. L. Rogers, S. Ambran, C. Holmes, P. G. R. Smith, and J. C. Gates, “In situ loss measurement of direct UV-written waveguides using integrated Bragg gratings,” Opt. Lett. 35(17), 2849–2851 (2010).
[Crossref] [PubMed]

C. Holmes, D. O. Kundys, J. C. Gates, C. B. E. Gawith, and P. G. R. Smith, “150 GHz of thermo-optic tuning in direct UV written silica-on-silicon planar Bragg grating,” Electron. Lett. 45(18), 954 (2009).
[Crossref]

Gawith, C. B. E.

C. Holmes, D. O. Kundys, J. C. Gates, C. B. E. Gawith, and P. G. R. Smith, “150 GHz of thermo-optic tuning in direct UV written silica-on-silicon planar Bragg grating,” Electron. Lett. 45(18), 954 (2009).
[Crossref]

Goldberg, L.

D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
[Crossref]

Graver, T.

V. P. Wnuk, A. Méndez, C. Ave, S. Ferguson, and T. Graver, “Process for Mounting and Packaging of Fiber Bragg Grating Strain Sensors for use in Harsh Environment Applications,” Smart Struct. Conf.46, (2005).
[Crossref]

Gupta, A.

Guthy, C.

Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
[Crossref] [PubMed]

Halir, R.

G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
[Crossref]

Holmes, C.

C. Sima, J. C. Gates, H. L. Rogers, P. L. Mennea, C. Holmes, M. N. Zervas, and P. G. R. Smith, “Ultra-wide detuning planar Bragg grating fabrication technique based on direct UV grating writing with electro-optic phase modulation,” Opt. Express 21(13), 15747–15754 (2013).
[Crossref] [PubMed]

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

C. Holmes, L. G. Carpenter, J. C. Gates, and P. G. R. Smith, “Miniaturization of Bragg-multiplexed membrane transducers,” J. Micromech. Microeng. 22(2), 025017 (2012).
[Crossref]

C. Holmes, L. G. Carpenter, H. L. Rogers, J. C. Gates, and P. G. R. Smith, “Quantifying the optical sensitivity of planar Bragg gratings in glass micro-cantilevers to physical deflection,” J. Micromech. Microeng. 21(3), 035014 (2011).
[Crossref]

H. L. Rogers, S. Ambran, C. Holmes, P. G. R. Smith, and J. C. Gates, “In situ loss measurement of direct UV-written waveguides using integrated Bragg gratings,” Opt. Lett. 35(17), 2849–2851 (2010).
[Crossref] [PubMed]

C. Holmes, D. O. Kundys, J. C. Gates, C. B. E. Gawith, and P. G. R. Smith, “150 GHz of thermo-optic tuning in direct UV written silica-on-silicon planar Bragg grating,” Electron. Lett. 45(18), 954 (2009).
[Crossref]

Janus, P.

P. Zyłka, P. Modrzynski, and P. Janus, “Vortex Anemometer Using MEMS Cantilever Sensor,” J. Micromechanical Syst. 19(6), 1485–1489 (2010).
[Crossref]

Kawachi, M.

M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Opt. Quantum Electron. 22(5), 391–416 (1990).
[Crossref]

Kilian, A.

Kirchhof, J.

Kliner, D. A. V.

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

Knechtel, R.

R. Knechtel, “Glass frit bonding: an universal technology for wafer level encapsulation and packaging,” Microsyst. Technol. 12(1-2), 63–68 (2005).
[Crossref]

Koplow, J. P.

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

Kopp, C.

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Kuhlow, B.

Kundys, D. O.

C. Holmes, D. O. Kundys, J. C. Gates, C. B. E. Gawith, and P. G. R. Smith, “150 GHz of thermo-optic tuning in direct UV written silica-on-silicon planar Bragg grating,” Electron. Lett. 45(18), 954 (2009).
[Crossref]

Leester-Schädel, M.

M. Schwerter, T. Beutel, M. Leester-Schädel, S. Büttgenbach, and A. Dietzel, “Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings,” Microsyst. Technol. 20(4-5), 821–829 (2014).
[Crossref]

Li, Y.

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
[Crossref]

Lu, C.

Mahdi, M. A.

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

Méndez, A.

V. P. Wnuk, A. Méndez, C. Ave, S. Ferguson, and T. Graver, “Process for Mounting and Packaging of Fiber Bragg Grating Strain Sensors for use in Harsh Environment Applications,” Smart Struct. Conf.46, (2005).
[Crossref]

Mennea, P. L.

Modrzynski, P.

P. Zyłka, P. Modrzynski, and P. Janus, “Vortex Anemometer Using MEMS Cantilever Sensor,” J. Micromechanical Syst. 19(6), 1485–1489 (2010).
[Crossref]

Monfardini, A.

J. Salort, A. Monfardini, and P.-E. Roche, “Cantilever anemometer based on a superconducting micro-resonator: application to superfluid turbulence,” Rev. Sci. Instrum. 83(12), 125002 (2012).
[Crossref] [PubMed]

Moore, S. W.

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

Ni, K.

X. Wang, X. Dong, Y. Zhou, K. Ni, J. Cheng, and Z. Chen, “Hot-Wire Anemometer Based on Silver-Coated Fiber Bragg Grating Assisted by No-Core Fiber,” IEEE Photon. Technol. Lett. 25(24), 2458–2461 (2013).
[Crossref]

Orobtchouk, R.

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Pang, C.

Porte, H.

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Przyrembel, G.

Rafiq, F.

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

Rao, Y.-J.

Y.-J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8(4), 355–375 (1997).
[Crossref]

Ripin, D. J.

D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
[Crossref]

Roche, P.-E.

J. Salort, A. Monfardini, and P.-E. Roche, “Cantilever anemometer based on a superconducting micro-resonator: application to superfluid turbulence,” Rev. Sci. Instrum. 83(12), 125002 (2012).
[Crossref] [PubMed]

Roelkens, G.

G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
[Crossref]

Rogers, H. L.

Salort, J.

J. Salort, A. Monfardini, and P.-E. Roche, “Cantilever anemometer based on a superconducting micro-resonator: application to superfluid turbulence,” Rev. Sci. Instrum. 83(12), 125002 (2012).
[Crossref] [PubMed]

Sandoghchi, S. R.

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

Saran, A.

A. Saran, D. C. Abeysinghe, R. Flenniken, and J. T. Boyd, “Anodic bonding of optical fibers-to-silicon for integrating MEMS devices and optical fibers,” J. Micromech. Microeng. 13(2), 346–351 (2003).
[Crossref]

Schrank, F.

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Schwerter, M.

M. Schwerter, T. Beutel, M. Leester-Schädel, S. Büttgenbach, and A. Dietzel, “Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings,” Microsyst. Technol. 20(4-5), 821–829 (2014).
[Crossref]

Selvaraja, S.

G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
[Crossref]

Sima, C.

Simpson, R. E.

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

Smith, P. G. R.

C. Sima, J. C. Gates, H. L. Rogers, P. L. Mennea, C. Holmes, M. N. Zervas, and P. G. R. Smith, “Ultra-wide detuning planar Bragg grating fabrication technique based on direct UV grating writing with electro-optic phase modulation,” Opt. Express 21(13), 15747–15754 (2013).
[Crossref] [PubMed]

C. Holmes, L. G. Carpenter, J. C. Gates, and P. G. R. Smith, “Miniaturization of Bragg-multiplexed membrane transducers,” J. Micromech. Microeng. 22(2), 025017 (2012).
[Crossref]

C. Holmes, L. G. Carpenter, H. L. Rogers, J. C. Gates, and P. G. R. Smith, “Quantifying the optical sensitivity of planar Bragg gratings in glass micro-cantilevers to physical deflection,” J. Micromech. Microeng. 21(3), 035014 (2011).
[Crossref]

H. L. Rogers, S. Ambran, C. Holmes, P. G. R. Smith, and J. C. Gates, “In situ loss measurement of direct UV-written waveguides using integrated Bragg gratings,” Opt. Lett. 35(17), 2849–2851 (2010).
[Crossref] [PubMed]

C. Holmes, D. O. Kundys, J. C. Gates, C. B. E. Gawith, and P. G. R. Smith, “150 GHz of thermo-optic tuning in direct UV written silica-on-silicon planar Bragg grating,” Electron. Lett. 45(18), 954 (2009).
[Crossref]

Tam, H.-Y.

Tekin, T.

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Tian, Y.

Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
[Crossref] [PubMed]

Van Thourhout, D.

G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
[Crossref]

Vermeulen, D.

G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
[Crossref]

Wang, W.

Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
[Crossref] [PubMed]

Wang, X.

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
[Crossref]

X. Wang, X. Dong, Y. Zhou, K. Ni, J. Cheng, and Z. Chen, “Hot-Wire Anemometer Based on Silver-Coated Fiber Bragg Grating Assisted by No-Core Fiber,” IEEE Photon. Technol. Lett. 25(24), 2458–2461 (2013).
[Crossref]

Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
[Crossref] [PubMed]

Webb, A. S.

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

Williams, M. J.

B. D. C. Collis and M. J. Williams, “Two-dimensional convection from heated wires at low Reynolds numbers,” J. Fluid Mech. 6(03), 357–384 (1959).
[Crossref]

Wischmann, W.

Wnuk, V. P.

V. P. Wnuk, A. Méndez, C. Ave, S. Ferguson, and T. Graver, “Process for Mounting and Packaging of Fiber Bragg Grating Strain Sensors for use in Harsh Environment Applications,” Smart Struct. Conf.46, (2005).
[Crossref]

Wu, N.

Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
[Crossref] [PubMed]

Yi, C. W.

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

Yu, M.

Zervas, M. N.

Zhang, A. P.

Zhou, Y.

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
[Crossref]

X. Wang, X. Dong, Y. Zhou, K. Ni, J. Cheng, and Z. Chen, “Hot-Wire Anemometer Based on Silver-Coated Fiber Bragg Grating Assisted by No-Core Fiber,” IEEE Photon. Technol. Lett. 25(24), 2458–2461 (2013).
[Crossref]

Zimmermann, L.

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

Zou, X.

Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
[Crossref] [PubMed]

Zylka, P.

P. Zyłka, P. Modrzynski, and P. Janus, “Vortex Anemometer Using MEMS Cantilever Sensor,” J. Micromechanical Syst. 19(6), 1485–1489 (2010).
[Crossref]

Electron. Lett. (2)

D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
[Crossref]

C. Holmes, D. O. Kundys, J. C. Gates, C. B. E. Gawith, and P. G. R. Smith, “150 GHz of thermo-optic tuning in direct UV written silica-on-silicon planar Bragg grating,” Electron. Lett. 45(18), 954 (2009).
[Crossref]

IEEE J. Quantum Electron. (3)

G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Quantum Electron. 17(3), 571–580 (2011).
[Crossref]

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

P. Dumais, “Thermal Stress Birefringence in Buried-Core Waveguides with Over-Etch,” IEEE J. Quantum Electron. 47(7), 989–996 (2011).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

C. Kopp, B. Ben Bakir, J. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, “Silicon Photonic Circuits : On-CMOS Integration, Fiber Optical Coupling, and Packaging,” IEEE J. Sel. Top. Quantum Electron. 17(3), 498–509 (2011).
[Crossref]

IEEE J. Sel. Top. Quantum Phys (1)

F. Rafiq, M. Adikan, S. R. Sandoghchi, C. W. Yi, R. E. Simpson, M. A. Mahdi, A. S. Webb, J. C. Gates, and C. Holmes, “Direct UV Written Optical Waveguides in Flexible Glass Flat Fiber Chips,” IEEE J. Sel. Top. Quantum Phys.  18, 1534–1539 (2012).

IEEE Photon. Technol. Lett. (1)

X. Wang, X. Dong, Y. Zhou, K. Ni, J. Cheng, and Z. Chen, “Hot-Wire Anemometer Based on Silver-Coated Fiber Bragg Grating Assisted by No-Core Fiber,” IEEE Photon. Technol. Lett. 25(24), 2458–2461 (2013).
[Crossref]

J. Fluid Mech. (1)

B. D. C. Collis and M. J. Williams, “Two-dimensional convection from heated wires at low Reynolds numbers,” J. Fluid Mech. 6(03), 357–384 (1959).
[Crossref]

J. Lightwave Technol. (1)

J. Micromech. Microeng. (3)

C. Holmes, L. G. Carpenter, J. C. Gates, and P. G. R. Smith, “Miniaturization of Bragg-multiplexed membrane transducers,” J. Micromech. Microeng. 22(2), 025017 (2012).
[Crossref]

C. Holmes, L. G. Carpenter, H. L. Rogers, J. C. Gates, and P. G. R. Smith, “Quantifying the optical sensitivity of planar Bragg gratings in glass micro-cantilevers to physical deflection,” J. Micromech. Microeng. 21(3), 035014 (2011).
[Crossref]

A. Saran, D. C. Abeysinghe, R. Flenniken, and J. T. Boyd, “Anodic bonding of optical fibers-to-silicon for integrating MEMS devices and optical fibers,” J. Micromech. Microeng. 13(2), 346–351 (2003).
[Crossref]

J. Micromechanical Syst. (1)

P. Zyłka, P. Modrzynski, and P. Janus, “Vortex Anemometer Using MEMS Cantilever Sensor,” J. Micromechanical Syst. 19(6), 1485–1489 (2010).
[Crossref]

Meas. Sci. Technol. (1)

Y.-J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8(4), 355–375 (1997).
[Crossref]

Microsyst. Technol. (2)

M. Schwerter, T. Beutel, M. Leester-Schädel, S. Büttgenbach, and A. Dietzel, “Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings,” Microsyst. Technol. 20(4-5), 821–829 (2014).
[Crossref]

R. Knechtel, “Glass frit bonding: an universal technology for wafer level encapsulation and packaging,” Microsyst. Technol. 12(1-2), 63–68 (2005).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Opt. Quantum Electron. 22(5), 391–416 (1990).
[Crossref]

Rev. Sci. Instrum. (1)

J. Salort, A. Monfardini, and P.-E. Roche, “Cantilever anemometer based on a superconducting micro-resonator: application to superfluid turbulence,” Rev. Sci. Instrum. 83(12), 125002 (2012).
[Crossref] [PubMed]

Sens. Actuators A Phys. (1)

X. Wang, X. Dong, Y. Zhou, Y. Li, J. Cheng, and Z. Chen, “Optical fiber anemometer using silver-coated fiber Bragg grating and bitaper,” Sens. Actuators A Phys. 214, 230–233 (2014).
[Crossref]

Sensors (Basel) (1)

Y. Tian, W. Wang, N. Wu, X. Zou, C. Guthy, and X. Wang, “A miniature fiber optic refractive index sensor built in a MEMS-based microchannel,” Sensors (Basel) 11(12), 1078–1087 (2011).
[Crossref] [PubMed]

Other (5)

V. P. Wnuk, A. Méndez, C. Ave, S. Ferguson, and T. Graver, “Process for Mounting and Packaging of Fiber Bragg Grating Strain Sensors for use in Harsh Environment Applications,” Smart Struct. Conf.46, (2005).
[Crossref]

A. D. Yablon, Optical Fiber Fusion Splicing, Springer Series in Optical Sciences (Springer, 2005).

C. G. Lomas, Fundamentals of Hot Wire Anemometry (Cambridge University, 2011).

P. Caldas, P. A. S. Jorge, G. Rego, O. Frazão, J. L. Santos, L. A. Ferreira, and F. Araújo, “Fibre Optic Hot-Wire Flowmeter Based on a Metallic Coated Hybrid LPG-FBG Structure,” in Fourth European Workshop on Optical Fibre Sensors (2010), Vol. 7653, p. 76530B.
[Crossref]

T. H. Laby and G. W. C. Kaye, Tables of Physical and Chemical Constants, 16th ed. (Longman, 2005).

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 (7)

Fig. 1
Fig. 1 The three stage process to fabricate a fibre-FHD planar composite.
Fig. 2
Fig. 2 SEM images of the Fibre-FHD optical composite (FFOC) with an optical fibre diameter of 125µm.
Fig. 3
Fig. 3 The geometry of the hotwire anemometer consisting of an optical fibre surrounded by a conducting gold layer. Fibre Bragg gratings are located at A and B. Gold was sputtered resulting in a non-uniform coating around the fibre.
Fig. 4
Fig. 4 Spectral tunability with respect to operational power.
Fig. 5
Fig. 5 Spectral tunability for selected operational voltages, indicating presence of spectral chirp.
Fig. 6
Fig. 6 The spectral response of a Bragg grating located in a hot-wire element (1V operating potential) subject to increasing air-velocity.
Fig. 7
Fig. 7 Device sensitivity for a Bragg grating anemometer, with respect to operational voltage.

Equations (7)

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

Δ λ B λ 0 =(1 ρ α )Δ ε axial +ηΔT
dE dt =WH
I 2 R=hA( T w T a )
h=a+b v c
Δ λ B = I 2 R λ 0 η A(a+b v 0.45 )
R e = vd γ
R e > G r 1 3

Metrics