Abstract

A miniaturized homodyne laser Doppler vibrometer (LDV) with a compact 90° optical hybrid is experimentally demonstrated on a CMOS compatible silicon-on-insulator (SOI) platform. Optical components on this platform usually have inadequate suppressions of spurious reflections, which significantly influence the performance of the LDV. Numerical compensation methods are implemented to effectively decrease the impact of these spurious reflections. With the help of these compensation methods, measurements for both super-half-wavelength and sub-half-wavelength vibrations are demonstrated. Results show that the minimal detectable velocity is around 1.2 μm/s.

© 2013 OSA

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References

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  1. P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser Doppler vibrometry: development of advanced solution answering to technology’s needs,” Mech. Syst. Signal. Proc.20, 1265–1285 (2006).
    [CrossRef]
  2. J. W. Czarske, “Laser Doppler velocimetry using powerful solid-state light sources,” Meas. Sci. Technol.17, R71–R91 (2006).
    [CrossRef]
  3. A. T. Waz, P. R. Kaczarek, and K. M. Aramski, “Laser-fibre vibrometry at 1550 nm,” Meas. Sci. Technol.20, 105301 (2009).
    [CrossRef]
  4. S. M. Khanna, “Homodyne interferometer for basilar membrane measurements,” Hearing Res.23, 9–26 (1986).
    [CrossRef]
  5. J. La, S. Wang, K. Kim, and K. Park, “High-speed FM demodulator of a homodyne laser interferometer for measuring mechanical vibration,” Opt. Eng.43(6), 1341–1349 (2004).
    [CrossRef]
  6. R. Halir, G. Roelkens, A. Ortega-Mon̈ux, and J. G. Wangüemert-Pérez, “High-performance 90° hybrid based on a silicon-on-insulator multimode interference coupler,” Opt. Lett.36, 178–180 (2011).
    [CrossRef] [PubMed]
  7. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguide in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol.23, 401–402 (2005).
    [CrossRef]
  8. S. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun.284, 2141–2144 (2011).
    [CrossRef]
  9. H. Yu, W. Bogaerts, and A. De Keersgieter, “Optimization of ion implantation condition for depletion-type silicon optical modulators,” IEEE J. Quantum. Elect.46, 1763–1768 (2010).
    [CrossRef]
  10. L. Vivien, M. Rouvière, J-M Fédéli, D. Marris-Morini, J.-F. Damlencourt, J. Mangeney, P. Crozat, L. El Melhaoui, E. Cassan, X. Le Roux, D. Pascal, and S. Laval, “High speed and high responsivity germanium photodetector integrated in a Silicon-On-Insulator microwaveguide,” Opt. Express159843–9848 (2007).
    [CrossRef] [PubMed]
  11. S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
    [CrossRef]
  12. S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
    [CrossRef]
  13. Y. Li, S. Verstuyft, G. Yurtsever, S. Keyvaninia, G. Roelkens, D. Van Thourhout, and R. Baets, “Heterodyne laser Doppler vibrometers integrated on silicon-on-insulator based on serrodyne thermo-optic frequency shifters,” Appl. Opt.52, 2145–2152 (2013).
    [CrossRef] [PubMed]
  14. K. G. Krauter, G. F. Jacobson, J. R. Patterson, J. H. Nguyen, and W. P. Ambrose, “Single-mode fiber, velocity interferometry,” Rev. Sci. Instrum.82, 045110 (2011).
    [CrossRef] [PubMed]
  15. Y. Li, D. Vermeulen, Y. De Koninck, G. Yurtsever, G. Roelkens, and R. Baets, “Compact grating couplers on silicon-on-insulator with reduced backreflection,” Opt. Lett.37, 4356–4358 (2012).
    [CrossRef] [PubMed]
  16. Y. Li, L. Li, B. Tian, G. Roelkens, and R. Baets, “Reflectionless tilted grating couplers with improved coupling efficiency based on a silicon overlay,” to be published.
  17. http://www.epixfab.eu

2013 (1)

2012 (3)

S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
[CrossRef]

S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
[CrossRef]

Y. Li, D. Vermeulen, Y. De Koninck, G. Yurtsever, G. Roelkens, and R. Baets, “Compact grating couplers on silicon-on-insulator with reduced backreflection,” Opt. Lett.37, 4356–4358 (2012).
[CrossRef] [PubMed]

2011 (3)

K. G. Krauter, G. F. Jacobson, J. R. Patterson, J. H. Nguyen, and W. P. Ambrose, “Single-mode fiber, velocity interferometry,” Rev. Sci. Instrum.82, 045110 (2011).
[CrossRef] [PubMed]

R. Halir, G. Roelkens, A. Ortega-Mon̈ux, and J. G. Wangüemert-Pérez, “High-performance 90° hybrid based on a silicon-on-insulator multimode interference coupler,” Opt. Lett.36, 178–180 (2011).
[CrossRef] [PubMed]

S. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun.284, 2141–2144 (2011).
[CrossRef]

2010 (1)

H. Yu, W. Bogaerts, and A. De Keersgieter, “Optimization of ion implantation condition for depletion-type silicon optical modulators,” IEEE J. Quantum. Elect.46, 1763–1768 (2010).
[CrossRef]

2009 (1)

A. T. Waz, P. R. Kaczarek, and K. M. Aramski, “Laser-fibre vibrometry at 1550 nm,” Meas. Sci. Technol.20, 105301 (2009).
[CrossRef]

2007 (1)

2006 (2)

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser Doppler vibrometry: development of advanced solution answering to technology’s needs,” Mech. Syst. Signal. Proc.20, 1265–1285 (2006).
[CrossRef]

J. W. Czarske, “Laser Doppler velocimetry using powerful solid-state light sources,” Meas. Sci. Technol.17, R71–R91 (2006).
[CrossRef]

2005 (1)

2004 (1)

J. La, S. Wang, K. Kim, and K. Park, “High-speed FM demodulator of a homodyne laser interferometer for measuring mechanical vibration,” Opt. Eng.43(6), 1341–1349 (2004).
[CrossRef]

1986 (1)

S. M. Khanna, “Homodyne interferometer for basilar membrane measurements,” Hearing Res.23, 9–26 (1986).
[CrossRef]

Ambrose, W. P.

K. G. Krauter, G. F. Jacobson, J. R. Patterson, J. H. Nguyen, and W. P. Ambrose, “Single-mode fiber, velocity interferometry,” Rev. Sci. Instrum.82, 045110 (2011).
[CrossRef] [PubMed]

Aramski, K. M.

A. T. Waz, P. R. Kaczarek, and K. M. Aramski, “Laser-fibre vibrometry at 1550 nm,” Meas. Sci. Technol.20, 105301 (2009).
[CrossRef]

Baets, R.

Beckx, S.

Bienstman, P.

Bogaerts, W.

S. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun.284, 2141–2144 (2011).
[CrossRef]

H. Yu, W. Bogaerts, and A. De Keersgieter, “Optimization of ion implantation condition for depletion-type silicon optical modulators,” IEEE J. Quantum. Elect.46, 1763–1768 (2010).
[CrossRef]

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguide in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol.23, 401–402 (2005).
[CrossRef]

Cassan, E.

Castellini, P.

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser Doppler vibrometry: development of advanced solution answering to technology’s needs,” Mech. Syst. Signal. Proc.20, 1265–1285 (2006).
[CrossRef]

Crozat, P.

Czarske, J. W.

J. W. Czarske, “Laser Doppler velocimetry using powerful solid-state light sources,” Meas. Sci. Technol.17, R71–R91 (2006).
[CrossRef]

Damlencourt, J.-F.

De Keersgieter, A.

H. Yu, W. Bogaerts, and A. De Keersgieter, “Optimization of ion implantation condition for depletion-type silicon optical modulators,” IEEE J. Quantum. Elect.46, 1763–1768 (2010).
[CrossRef]

De Koninck, Y.

Dumon, P.

El Melhaoui, L.

Fédéli, J-M

Ghosh, S.

S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
[CrossRef]

Halir, R.

Heck, J. M.

S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
[CrossRef]

Jacobson, G. F.

K. G. Krauter, G. F. Jacobson, J. R. Patterson, J. H. Nguyen, and W. P. Ambrose, “Single-mode fiber, velocity interferometry,” Rev. Sci. Instrum.82, 045110 (2011).
[CrossRef] [PubMed]

Kaczarek, P. R.

A. T. Waz, P. R. Kaczarek, and K. M. Aramski, “Laser-fibre vibrometry at 1550 nm,” Meas. Sci. Technol.20, 105301 (2009).
[CrossRef]

Keyvaninia, S.

Y. Li, S. Verstuyft, G. Yurtsever, S. Keyvaninia, G. Roelkens, D. Van Thourhout, and R. Baets, “Heterodyne laser Doppler vibrometers integrated on silicon-on-insulator based on serrodyne thermo-optic frequency shifters,” Appl. Opt.52, 2145–2152 (2013).
[CrossRef] [PubMed]

S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
[CrossRef]

Khanna, S. M.

S. M. Khanna, “Homodyne interferometer for basilar membrane measurements,” Hearing Res.23, 9–26 (1986).
[CrossRef]

Kim, K.

J. La, S. Wang, K. Kim, and K. Park, “High-speed FM demodulator of a homodyne laser interferometer for measuring mechanical vibration,” Opt. Eng.43(6), 1341–1349 (2004).
[CrossRef]

Krauter, K. G.

K. G. Krauter, G. F. Jacobson, J. R. Patterson, J. H. Nguyen, and W. P. Ambrose, “Single-mode fiber, velocity interferometry,” Rev. Sci. Instrum.82, 045110 (2011).
[CrossRef] [PubMed]

La, J.

J. La, S. Wang, K. Kim, and K. Park, “High-speed FM demodulator of a homodyne laser interferometer for measuring mechanical vibration,” Opt. Eng.43(6), 1341–1349 (2004).
[CrossRef]

Laval, S.

Le Roux, X.

Li, L.

Y. Li, L. Li, B. Tian, G. Roelkens, and R. Baets, “Reflectionless tilted grating couplers with improved coupling efficiency based on a silicon overlay,” to be published.

Li, Y.

Luyssaert, B.

Mangeney, J.

Marris-Morini, D.

Martarelli, M.

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser Doppler vibrometry: development of advanced solution answering to technology’s needs,” Mech. Syst. Signal. Proc.20, 1265–1285 (2006).
[CrossRef]

Mizumoto, T.

S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
[CrossRef]

Nguyen, J. H.

K. G. Krauter, G. F. Jacobson, J. R. Patterson, J. H. Nguyen, and W. P. Ambrose, “Single-mode fiber, velocity interferometry,” Rev. Sci. Instrum.82, 045110 (2011).
[CrossRef] [PubMed]

Ortega-Mon¨ux, A.

Park, K.

J. La, S. Wang, K. Kim, and K. Park, “High-speed FM demodulator of a homodyne laser interferometer for measuring mechanical vibration,” Opt. Eng.43(6), 1341–1349 (2004).
[CrossRef]

Pascal, D.

Patterson, J. R.

K. G. Krauter, G. F. Jacobson, J. R. Patterson, J. H. Nguyen, and W. P. Ambrose, “Single-mode fiber, velocity interferometry,” Rev. Sci. Instrum.82, 045110 (2011).
[CrossRef] [PubMed]

Richard, J.

S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
[CrossRef]

Roelkens, G.

Y. Li, S. Verstuyft, G. Yurtsever, S. Keyvaninia, G. Roelkens, D. Van Thourhout, and R. Baets, “Heterodyne laser Doppler vibrometers integrated on silicon-on-insulator based on serrodyne thermo-optic frequency shifters,” Appl. Opt.52, 2145–2152 (2013).
[CrossRef] [PubMed]

S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
[CrossRef]

S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
[CrossRef]

Y. Li, D. Vermeulen, Y. De Koninck, G. Yurtsever, G. Roelkens, and R. Baets, “Compact grating couplers on silicon-on-insulator with reduced backreflection,” Opt. Lett.37, 4356–4358 (2012).
[CrossRef] [PubMed]

R. Halir, G. Roelkens, A. Ortega-Mon̈ux, and J. G. Wangüemert-Pérez, “High-performance 90° hybrid based on a silicon-on-insulator multimode interference coupler,” Opt. Lett.36, 178–180 (2011).
[CrossRef] [PubMed]

Y. Li, L. Li, B. Tian, G. Roelkens, and R. Baets, “Reflectionless tilted grating couplers with improved coupling efficiency based on a silicon overlay,” to be published.

Rouvière, M.

Selvaraja, S.

S. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun.284, 2141–2144 (2011).
[CrossRef]

Shoji, Y.

S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
[CrossRef]

Stankovic, S.

S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
[CrossRef]

Sysak, M. N.

S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
[CrossRef]

Taillaert, D.

Tian, B.

Y. Li, L. Li, B. Tian, G. Roelkens, and R. Baets, “Reflectionless tilted grating couplers with improved coupling efficiency based on a silicon overlay,” to be published.

Tomasini, E. P.

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser Doppler vibrometry: development of advanced solution answering to technology’s needs,” Mech. Syst. Signal. Proc.20, 1265–1285 (2006).
[CrossRef]

Van Campenhout, J.

Van Roy, W.

S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
[CrossRef]

Van Thourhout, D.

Y. Li, S. Verstuyft, G. Yurtsever, S. Keyvaninia, G. Roelkens, D. Van Thourhout, and R. Baets, “Heterodyne laser Doppler vibrometers integrated on silicon-on-insulator based on serrodyne thermo-optic frequency shifters,” Appl. Opt.52, 2145–2152 (2013).
[CrossRef] [PubMed]

S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
[CrossRef]

S. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun.284, 2141–2144 (2011).
[CrossRef]

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguide in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol.23, 401–402 (2005).
[CrossRef]

Vermeulen, D.

Verstuyft, S.

Vivien, L.

Wang, S.

J. La, S. Wang, K. Kim, and K. Park, “High-speed FM demodulator of a homodyne laser interferometer for measuring mechanical vibration,” Opt. Eng.43(6), 1341–1349 (2004).
[CrossRef]

Wangüemert-Pérez, J. G.

Waz, A. T.

A. T. Waz, P. R. Kaczarek, and K. M. Aramski, “Laser-fibre vibrometry at 1550 nm,” Meas. Sci. Technol.20, 105301 (2009).
[CrossRef]

Wiaux, V.

Yu, H.

H. Yu, W. Bogaerts, and A. De Keersgieter, “Optimization of ion implantation condition for depletion-type silicon optical modulators,” IEEE J. Quantum. Elect.46, 1763–1768 (2010).
[CrossRef]

Yurtsever, G.

Appl. Opt. (1)

Hearing Res. (1)

S. M. Khanna, “Homodyne interferometer for basilar membrane measurements,” Hearing Res.23, 9–26 (1986).
[CrossRef]

IEEE J. Quantum. Elect. (1)

H. Yu, W. Bogaerts, and A. De Keersgieter, “Optimization of ion implantation condition for depletion-type silicon optical modulators,” IEEE J. Quantum. Elect.46, 1763–1768 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

S. Stankovic, J. Richard, M. N. Sysak, J. M. Heck, G. Roelkens, and D. Van Thourhout, “Hybrid III-V/Si distributed-feedback laser based on adhesive bonding,” IEEE Photon. Technol. Lett.24, 2155–2158 (2012).
[CrossRef]

S. Ghosh, S. Keyvaninia, Y. Shoji, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Compact Mach-Zehnder interferometer Ce:YIG/SOI optical isolators,” IEEE Photon. Technol. Lett.24, 1653–1656 (2012).
[CrossRef]

J. Lightwave Technol. (1)

Meas. Sci. Technol. (2)

J. W. Czarske, “Laser Doppler velocimetry using powerful solid-state light sources,” Meas. Sci. Technol.17, R71–R91 (2006).
[CrossRef]

A. T. Waz, P. R. Kaczarek, and K. M. Aramski, “Laser-fibre vibrometry at 1550 nm,” Meas. Sci. Technol.20, 105301 (2009).
[CrossRef]

Mech. Syst. Signal. Proc. (1)

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser Doppler vibrometry: development of advanced solution answering to technology’s needs,” Mech. Syst. Signal. Proc.20, 1265–1285 (2006).
[CrossRef]

Opt. Commun. (1)

S. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun.284, 2141–2144 (2011).
[CrossRef]

Opt. Eng. (1)

J. La, S. Wang, K. Kim, and K. Park, “High-speed FM demodulator of a homodyne laser interferometer for measuring mechanical vibration,” Opt. Eng.43(6), 1341–1349 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

K. G. Krauter, G. F. Jacobson, J. R. Patterson, J. H. Nguyen, and W. P. Ambrose, “Single-mode fiber, velocity interferometry,” Rev. Sci. Instrum.82, 045110 (2011).
[CrossRef] [PubMed]

Other (2)

Y. Li, L. Li, B. Tian, G. Roelkens, and R. Baets, “Reflectionless tilted grating couplers with improved coupling efficiency based on a silicon overlay,” to be published.

http://www.epixfab.eu

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Figures (7)

Fig. 1
Fig. 1

The schematic show of a typical homodyne LDV. In this figure, ISO stands for optical isolator, BPD stands for balanced photo detector, oc stands for optical coupler, os1 and os2 stand for two optical splitters, and hybrid stands for 90° optical hybrid.

Fig. 2
Fig. 2

The PIC design and microscope images of the 90° optical hybrid and of the 2gc light receiving components.

Fig. 3
Fig. 3

The configuration of the 1gc type and the 2gc type light receiver.

Fig. 4
Fig. 4

(a) The average light power values at each output port (DCj) for the homodyne 1gc LDV. (b) DCj for the homodyne 2gc LDV.

Fig. 5
Fig. 5

(a) The average light power values at each output port (DCj) as a function of device temperature (2gc LDV). (b) DCj as a function of the input power (2gc LDV).

Fig. 6
Fig. 6

(a) Demodulated signals for two vibrations in time domain. (b) I&Q Lissajous curve.

Fig. 7
Fig. 7

Power spectral densities.

Tables (1)

Tables Icon

Table 1 Performance of 1gc and 2gc LDVs, all values are compared with the light power of the reference light.

Equations (11)

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

( E 1 ( t ) E 2 ( t ) E 3 ( t ) E 4 ( t ) ) = ( κ 1 , 1 κ 1 , 2 e i ϕ 1 , 2 κ 2 , 1 κ 2 , 2 e i ϕ 2 , 2 κ 3 , 1 κ 3 , 2 e i ϕ 3 , 2 κ 4 , 1 κ 4 , 2 e i ϕ 4 , 2 ) ( E r ( t ) E m ( t ) ) ,
I ( t ) i 1 ( t ) i 2 ( t ) = η E 0 2 ( t ) r m ( t ) cos [ θ D ( t ) ]
Q ( t ) i 3 ( t ) i 4 ( t ) = η E 0 2 ( t ) r m ( t ) sin [ θ D ( t ) ] .
i j ( t ) = C j ( t ) + S j ( t ) + R ( t ) ,
C j ( t ) = ζ j ( t ) [ κ j , 1 2 r 2 + κ j , 2 2 m 2 ( t ) ]
S j ( t ) = 2 ζ j ( t ) κ j , 1 κ j , 2 m ( t ) r cos [ θ D ( t ) + ϕ j , 2 ] ,
I ( t ) = I 0 + a cos [ θ D ( t ) + φ 1 ] cos ( φ 0 ) b sin [ θ D ( t ) + φ 1 ] sin ( φ 0 )
Q ( t ) = Q 0 + a cos [ θ D ( t ) + φ 1 ] sin ( φ 0 ) + b sin [ θ D ( t ) + φ 1 ] cos ( φ 0 ) ,
I 1 ( t ) = I ( t ) I 0 Q 1 ( t ) = Q ( t ) Q 0 .
I ( t ) = b [ I 1 ( t ) cos ( φ 0 ) + Q 1 ( t ) sin ( φ 0 ) ]
Q ( t ) = a [ I 1 ( t ) sin ( φ 0 ) + Q 1 ( t ) cos ( φ 0 ) ] .

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