Abstract

We experimentally demonstrate an interrogation procedure of a ring-resonator ultrasound sensor using a fiber Mach-Zehnder interferometer (MZI). The sensor comprises a silicon ring resonator (RR) located on a silicon-oxide membrane, designed to have its lowest vibrational mode in the MHz range, which is the range of intravascular ultrasound (IVUS) imaging. Ultrasound incident on the membrane excites its vibrational mode and as a result induces a modulation of the resonance wavelength of the RR, which is a measure of the amplitude of the ultrasound waves. The interrogation procedure developed is based on the mathematical description of the interrogator operation presented in Appendix A, where we identify the amplitude of the angular deflection Φ0 on the circle arc periodically traced in the plane of the two orthogonal interrogator voltages, as the principal sensor signal. Interrogation is demonstrated for two sensors with membrane vibrational modes at 1.3 and 0.77 MHz, by applying continuous wave ultrasound in a wide pressure range. Ultrasound is detected at a pressure as low as 1.2 Pa. Two optical path differences (OPDs) of the MZI are used. Thus, different interference conditions of the optical signals are defined, leading to a higher apparent sensitivity for the larger OPD, which is accompanied by a weaker signal, however. Independent measurements using the modulation method yield a resonance modulation per unit of pressure of 21.4 fm/Pa (sensor #1) and 103.8 fm/Pa (sensor #2).

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References

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2015 (5)

A. P. Freitas, G. B. Farias, F. G. Peternella, Y. R. R. Bustamante, D. A. Motta, and J. C. R. F. de Oliveira, “112 Gb/s compact silicon-on-insulator coherent receiver,” Proc. of SPIE 9390, 93900D (2015).
[Crossref]

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

N. Pavarelli, J. S. Lee, M. Rensing, C. Scarcella, S. Zhou, P. Ossieur, and P. A. O’Brien, “Optical and electronic packaging processes for silicon photonic systems,” J. Lightwave Technol. 33(5), 991–997 (2015).
[Crossref]

C. Zhang, S. L. Chen, T. Ling, and L. J. Guo, “Imprinted polymer microrings as high performance ultrasound detectors in photoacoustic imaging,” J. Lightwave Technol. 33(20), 4318–4328 (2015).
[Crossref]

A. Dhakal, A. Raza, F. Peyskens, A. Z. Subramanian, S. Clemmen, N. L. Thomas, and R. Baets, “Efficiency of evanescent excitation and collection of spontaneous Raman scattering near high index contrast channel waveguides,” Opt. Express 23(21), 27391–27404 (2015).
[Crossref] [PubMed]

2014 (2)

M. Boerkamp, T. van Leest, J. Heldens, A. Leinse, M. Hoekman, R. Heideman, and J. Caro, “On-chip optical trapping and Raman spectroscopy using a TripleX dual-waveguide trap,” Opt. Express 22(25), 30528–30537 (2014).
[Crossref]

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

2013 (1)

2012 (3)

E. Hallynck and P. Bienstman, “Integrated optical pressure sensors in silicon-on-insulator,” IEEE Photon. J. 4(2), 450–453 (2012).
[Crossref]

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

V. M. N. Passaro, C. Tullio, B. Troia, M. L. Notte, G. Giannoccaro, and F. De Leonardis, “Recent advances in integrated photonic sensors,” Sensors 12(11), 15558–15598 (2012).
[Crossref] [PubMed]

2011 (1)

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

2009 (1)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

2002 (1)

1998 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM Journal of Optimization 9(1), 112–147 (1998).
[Crossref]

1994 (2)

A. Dandridge, C. C. Wang, A. B. Tveten, and A. M. Yurek, “Performance of 3×3 couplers in fiber optic sensor systems,” Proc. of SPIE 2360, 549–552 (1994).
[Crossref]

W. Gander, G. H. Golub, and R. Strebel, “Least-squares fitting for circles and ellipses,” BIT Numerical Mathematics 34(4), 558–578 (1994).
[Crossref]

1982 (1)

R. G. Priest, “Analysis of fiber interferometer utilizing 3×3 fiber coupler,” IEEE Trans. Microw. Theory Techn. 30(10), 1589–1591 (1982).
[Crossref]

Baets, R.

A. Dhakal, A. Raza, F. Peyskens, A. Z. Subramanian, S. Clemmen, N. L. Thomas, and R. Baets, “Efficiency of evanescent excitation and collection of spontaneous Raman scattering near high index contrast channel waveguides,” Opt. Express 23(21), 27391–27404 (2015).
[Crossref] [PubMed]

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Bienstman, P.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

E. Hallynck and P. Bienstman, “Integrated optical pressure sensors in silicon-on-insulator,” IEEE Photon. J. 4(2), 450–453 (2012).
[Crossref]

Boerkamp, M.

Bogaerts, W.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Bustamante, Y. R. R.

A. P. Freitas, G. B. Farias, F. G. Peternella, Y. R. R. Bustamante, D. A. Motta, and J. C. R. F. de Oliveira, “112 Gb/s compact silicon-on-insulator coherent receiver,” Proc. of SPIE 9390, 93900D (2015).
[Crossref]

Caro, J.

Chen, S. L.

Claes, T.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

Clemmen, S.

Dandridge, A.

A. Dandridge, C. C. Wang, A. B. Tveten, and A. M. Yurek, “Performance of 3×3 couplers in fiber optic sensor systems,” Proc. of SPIE 2360, 549–552 (1994).
[Crossref]

A. Dandridge, “Fiber optic sensors based on the Mach-Zehnder and Michelson Interferometers,” in Fiber Optic Sensors: An Introduction for Engineers and Scientists, E. Udd, ed. (Wiley, 1991).

de Heyn, P.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

de Jong, N.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

De Leonardis, F.

V. M. N. Passaro, C. Tullio, B. Troia, M. L. Notte, G. Giannoccaro, and F. De Leonardis, “Recent advances in integrated photonic sensors,” Sensors 12(11), 15558–15598 (2012).
[Crossref] [PubMed]

de Oliveira, J. C. R. F.

A. P. Freitas, G. B. Farias, F. G. Peternella, Y. R. R. Bustamante, D. A. Motta, and J. C. R. F. de Oliveira, “112 Gb/s compact silicon-on-insulator coherent receiver,” Proc. of SPIE 9390, 93900D (2015).
[Crossref]

DeVos, K.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

Dhakal, A.

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Dumon, P.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Farias, G. B.

A. P. Freitas, G. B. Farias, F. G. Peternella, Y. R. R. Bustamante, D. A. Motta, and J. C. R. F. de Oliveira, “112 Gb/s compact silicon-on-insulator coherent receiver,” Proc. of SPIE 9390, 93900D (2015).
[Crossref]

Freitas, A. P.

A. P. Freitas, G. B. Farias, F. G. Peternella, Y. R. R. Bustamante, D. A. Motta, and J. C. R. F. de Oliveira, “112 Gb/s compact silicon-on-insulator coherent receiver,” Proc. of SPIE 9390, 93900D (2015).
[Crossref]

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Gander, W.

W. Gander, G. H. Golub, and R. Strebel, “Least-squares fitting for circles and ellipses,” BIT Numerical Mathematics 34(4), 558–578 (1994).
[Crossref]

Giannoccaro, G.

V. M. N. Passaro, C. Tullio, B. Troia, M. L. Notte, G. Giannoccaro, and F. De Leonardis, “Recent advances in integrated photonic sensors,” Sensors 12(11), 15558–15598 (2012).
[Crossref] [PubMed]

Golub, G. H.

W. Gander, G. H. Golub, and R. Strebel, “Least-squares fitting for circles and ellipses,” BIT Numerical Mathematics 34(4), 558–578 (1994).
[Crossref]

Guo, L. J.

Hallynck, E.

E. Hallynck and P. Bienstman, “Integrated optical pressure sensors in silicon-on-insulator,” IEEE Photon. J. 4(2), 450–453 (2012).
[Crossref]

Heideman, R.

Heldens, J.

Hoekman, M.

Itabashi, S.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

Johnston, M.

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Kou, R.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM Journal of Optimization 9(1), 112–147 (1998).
[Crossref]

Lee, J. S.

Leinders, S. M.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

Leinse, A.

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Li, Y.

Ling, T.

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Motta, D. A.

A. P. Freitas, G. B. Farias, F. G. Peternella, Y. R. R. Bustamante, D. A. Motta, and J. C. R. F. de Oliveira, “112 Gb/s compact silicon-on-insulator coherent receiver,” Proc. of SPIE 9390, 93900D (2015).
[Crossref]

Muilwijk, P. M.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

Niewczas, P.

Nishi, H.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

Notte, M. L.

V. M. N. Passaro, C. Tullio, B. Troia, M. L. Notte, G. Giannoccaro, and F. De Leonardis, “Recent advances in integrated photonic sensors,” Sensors 12(11), 15558–15598 (2012).
[Crossref] [PubMed]

O’Brien, P.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

O’Brien, P. A.

Olver, F. W. J.

F. W. J. Olver, “Bessel functions of integer order,” in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, M. Abramowitz and I.A. Stegun, eds. (Dover books on Mathematics, 1964).

Orr, P.

Ossieur, P.

Park, S.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

Passaro, V. M. N.

V. M. N. Passaro, C. Tullio, B. Troia, M. L. Notte, G. Giannoccaro, and F. De Leonardis, “Recent advances in integrated photonic sensors,” Sensors 12(11), 15558–15598 (2012).
[Crossref] [PubMed]

Pavarelli, N.

Perry, M.

Peternella, F. G.

A. P. Freitas, G. B. Farias, F. G. Peternella, Y. R. R. Bustamante, D. A. Motta, and J. C. R. F. de Oliveira, “112 Gb/s compact silicon-on-insulator coherent receiver,” Proc. of SPIE 9390, 93900D (2015).
[Crossref]

Peyskens, F.

Pozo, J.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

Priest, R. G.

R. G. Priest, “Analysis of fiber interferometer utilizing 3×3 fiber coupler,” IEEE Trans. Microw. Theory Techn. 30(10), 1589–1591 (1982).
[Crossref]

Raza, A.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM Journal of Optimization 9(1), 112–147 (1998).
[Crossref]

Rensing, M.

Scarcella, C.

Selvaraja, S.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

Shinojima, H.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

Snyder, B.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

Strebel, R.

W. Gander, G. H. Golub, and R. Strebel, “Least-squares fitting for circles and ellipses,” BIT Numerical Mathematics 34(4), 558–578 (1994).
[Crossref]

Subramanian, A. Z.

Thomas, N. L.

Troia, B.

V. M. N. Passaro, C. Tullio, B. Troia, M. L. Notte, G. Giannoccaro, and F. De Leonardis, “Recent advances in integrated photonic sensors,” Sensors 12(11), 15558–15598 (2012).
[Crossref] [PubMed]

Tsuchizawa, T.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

Tullio, C.

V. M. N. Passaro, C. Tullio, B. Troia, M. L. Notte, G. Giannoccaro, and F. De Leonardis, “Recent advances in integrated photonic sensors,” Sensors 12(11), 15558–15598 (2012).
[Crossref] [PubMed]

Tveten, A. B.

A. Dandridge, C. C. Wang, A. B. Tveten, and A. M. Yurek, “Performance of 3×3 couplers in fiber optic sensor systems,” Proc. of SPIE 2360, 549–552 (1994).
[Crossref]

Urbach, H. P.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

van den Dool, T. C.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

van Leest, T.

van Neer, P. L. M.J.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

Van Thourhout, D.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

van Vaerenbergh, T.

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

Verweij, M. D.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Wang, C. C.

A. Dandridge, C. C. Wang, A. B. Tveten, and A. M. Yurek, “Performance of 3×3 couplers in fiber optic sensor systems,” Proc. of SPIE 2360, 549–552 (1994).
[Crossref]

Watanabe, T.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

Westerveld, W. J.

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM Journal of Optimization 9(1), 112–147 (1998).
[Crossref]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM Journal of Optimization 9(1), 112–147 (1998).
[Crossref]

Yamada, K.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

Yousefi, M.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

Yurek, A. M.

A. Dandridge, C. C. Wang, A. B. Tveten, and A. M. Yurek, “Performance of 3×3 couplers in fiber optic sensor systems,” Proc. of SPIE 2360, 549–552 (1994).
[Crossref]

Zhang, C.

Zhou, S.

BIT Numerical Mathematics (1)

W. Gander, G. H. Golub, and R. Strebel, “Least-squares fitting for circles and ellipses,” BIT Numerical Mathematics 34(4), 558–578 (1994).
[Crossref]

IEEE J. Sel. Topics Quantum Electron. (2)

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of silicon, germanium, and silica-based optical devices for telecommunications applications,” IEEE J. Sel. Topics Quantum Electron. 17(3), 516–525 (2011).
[Crossref]

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of integrated optical strain sensors based on silicon waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 5900110 (2014).
[Crossref]

IEEE Photon. J. (1)

E. Hallynck and P. Bienstman, “Integrated optical pressure sensors in silicon-on-insulator,” IEEE Photon. J. 4(2), 450–453 (2012).
[Crossref]

IEEE Trans. Microw. Theory Techn. (1)

R. G. Priest, “Analysis of fiber interferometer utilizing 3×3 fiber coupler,” IEEE Trans. Microw. Theory Techn. 30(10), 1589–1591 (1982).
[Crossref]

J. Lightwave Technol. (3)

Laser Photon. Rev. (1)

W. Bogaerts, P. de Heyn, T. van Vaerenbergh, K. DeVos, S. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6(1), 47–73 (2012).
[Crossref]

Nat. Photon. (1)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3(4), 216–219 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Proc. of SPIE (2)

A. P. Freitas, G. B. Farias, F. G. Peternella, Y. R. R. Bustamante, D. A. Motta, and J. C. R. F. de Oliveira, “112 Gb/s compact silicon-on-insulator coherent receiver,” Proc. of SPIE 9390, 93900D (2015).
[Crossref]

A. Dandridge, C. C. Wang, A. B. Tveten, and A. M. Yurek, “Performance of 3×3 couplers in fiber optic sensor systems,” Proc. of SPIE 2360, 549–552 (1994).
[Crossref]

Sci. Rep. (1)

S. M. Leinders, W. J. Westerveld, J. Pozo, P. L. M.J. van Neer, B. Snyder, P. O’Brien, H. P. Urbach, N. de Jong, and M. D. Verweij, “A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane,” Sci. Rep. 5, 14328 (2015).
[Crossref] [PubMed]

Sensors (1)

V. M. N. Passaro, C. Tullio, B. Troia, M. L. Notte, G. Giannoccaro, and F. De Leonardis, “Recent advances in integrated photonic sensors,” Sensors 12(11), 15558–15598 (2012).
[Crossref] [PubMed]

SIAM Journal of Optimization (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM Journal of Optimization 9(1), 112–147 (1998).
[Crossref]

Other (5)

To unwrap the phase we use the function unwrap of MATLAB R2014b, The MathWorks, Inc., Natick, Massachusetts, United States.

R. S. Evenblij and J. A. P. Leijtens, “Space gator, a giant leap for fiber optic sensing,” online Proceedings of the International Conference on Space Optics, Tenerife, Spain, 6–10 October 2014. Website http://www.icsoproceedings.org/ , accessed on June 8, 2017.

F. W. J. Olver, “Bessel functions of integer order,” in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, M. Abramowitz and I.A. Stegun, eds. (Dover books on Mathematics, 1964).

A. Dandridge, “Fiber optic sensors based on the Mach-Zehnder and Michelson Interferometers,” in Fiber Optic Sensors: An Introduction for Engineers and Scientists, E. Udd, ed. (Wiley, 1991).

ePIXfab website http://www.epixfab.eu/ , accessed on October 30, 2017.

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Figures (7)

Fig. 1
Fig. 1

Schematic view of the silicon ring-resonator sensor fabricated on a circular silicon oxide membrane. Width of coupling waveguides and racetrack is w = 400 nm, while the gap of the directional couplers is 200 nm. Radius of bends is R = 5 μm. The length of the straight part of the racetrack 0 varies among the devices.

Fig. 2
Fig. 2

(a) Transmission spectrum of sensor #1, showing three resonance dips. (b) Zoom-in of the central dip in (a). The blue curve is a fit of Eq. (3) to the data points. On the linear part of the dip’s left flank the operation point λop. is shown, the static wavelength to which the laser is tuned in the modulation method (section 4.2).

Fig. 3
Fig. 3

Schematic of the fiber interrogator, based on a Mach-Zehnder interferometer with a 2×2 coupler and a 3×3 coupler. BBS is the broadband source, FBG the fiber Bragg grating, EDFA the erbium doped amplifier and AWG the arbitrary waveform generator. Sensor #1 is placed at 135 mm from the transducer and sensor #2 is placed at 149 mm. The lenses L1 and L2 are part of the variable optical path length of one MZI arm, ranging from 4 to 13.5 mm. PD + TIA denotes combination of photodetector and transimpedance amplifier. V1, V2 and V3 are the three output voltages used to calculate the orthogonal voltages Vx and Vy and the angular deflection Φ(t) (see section 4.1). The signal spectrum has been indicated at the BBS, after the circulator and before the MZI. The water tank with sensor and transducer shows the setup for ultrasound measurements.

Fig. 4
Fig. 4

(a) FBG reflection spectrum and combined FBG reflection and RR transmission spectrum, both normalized to their maximum value, and a fit of Eq. (7) to the FBG spectrum for N = 8. (b) Traces of the interrogator outputs Vi as a function of wavelength, with data points shown as crosses. Due to the way of plotting, the DC component of the Vi is not visible. The oscillatory functions are fits of Ai cos(ξλ + φi + ψe) to the data points. The fits give: Ai = 63.4, 68.9 and 68.7 mV (i = 1, 2, 3) and φi + ψe = 176°, 59° and −67° (i = 1,2,3). The traces were used in obtaining the correction factors and in Eqs. (9) and (10). (c) Corrected (Vx, Vy) points, together with the fitted circle. The circle radius is 181 mV.

Fig. 5
Fig. 5

(a) Part of traces of Vi(t) (i = 1, 2, 3) for sensor #1, sampled while interrogating the sensor, and of the mutual orthogonal voltages Vx and Vy, for OPD = 12.9 mm and p0 = 2280 Pa. (b) Plot of the points (Vx, Vy), which trace a circle arc, together with the fitted circle. (c) Fourier transforms of the Vi(t) and of the angular deflection Φ(t) for OPD = 12.9 mm and p0 = 2280 Pa (sensor #1) and p0 = 312 Pa (sensor #2). The weak signals at the third harmonic are indicated as 3 f0,#1 and 3 f0,#2 for sensor #1 and #2, respectively.

Fig. 6
Fig. 6

Main results of the interrogation of the sensors: (a) amplitude of the angular deflection Φ0 for sensor #1 as a function of the pressure amplitude p0 of 1.3 MHz ultrasound. (b) Zoom-in of (a) for the pressure range 0–30 Pa. (c) Amplitude of the angular deflection Φ0 for sensor #2 as a function of the pressure amplitude p0 of 0.77 MHz ultrasound. (d) Zoom-in of (c) for the pressure range 0–15 Pa. In (a)–(d) OPDs of the MZI are as stated and the lines are fitted straight lines through the origin. (e) Sensitivity as a function of frequency of sensor #2 for OPD = 12.9 mm.

Fig. 7
Fig. 7

Plots of the functions , Ĝ, and 0 in the complex plane for (a) OPD=6.9 mm and (b) OPD=12.9 mm. Zero angular deflection of the functions occurs for the point where Im(function) = 0. The black dash-dotted curve is a fit of a circle to the data points of , giving radii of 54.3 and 32.6 pm for the OPDs of 6.9 and 12.9 mm, respectively. For 0 the radii are 60.1 and 23.2 pm, for these OPDs. In the plot the total bi-directional angular deflections 2ξδ0 and Φ0 for the functions 0 and , respectively, are indicated. In calculating the functions, the following parameters were used: γr = 122 pm, γFBG = 207 pm, ε = 0.043 (the three values in section 2 for sensor #1) and δ0 = 40 pm.

Tables (1)

Tables Icon

Table 1 Parameters obtained for sensors #1 and #2: Φ0/∂p0 is the sensor sensitivity, ∂δ0/∂p0 is the amplitude of the resonance-wavelength modulation of the sensor per unit of pressure, while κexp. and κtheo. are the experimental and theoretical correction factors, respectively, which relate to Eq. (13). The uncertainty in ∂δ0/∂p0 was omitted, since its contribution to the uncertainty of κexp. is negligible.

Equations (37)

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

T pass ( θ ) = r 2 + r 2 a 2 2 r 2 a cos θ 1 + r 4 a 2 2 r 2 a cos θ .
θ = 2 π λ n eff ( λ ) L 2 π m 2 π n g L λ λ r λ r 2 .
T pass ( λ ) ( λ λ r ) 2 + ε ( γ r / 2 ) 2 ( λ λ r ) 2 + ( γ r / 2 ) 2 .
γ r = λ r 2 ( 1 a r 2 ) π n g L r a = FWHM
ε = r 2 ( 1 a ) 2 ( 1 a r 2 ) 2 .
T MZI , i = 1 3 [ p + q cos ( 2 π λ OPD + φ i + φ e ) ] 1 3 [ p + q cos ( ξ λ + φ i + ψ e ) ] .
R FBG ( λ ) = [ 1 + ( λ λ 0 γ FBG / 2 ) N ] 1 .
V x = 2 V 1 c 2 V 2 c 3 V 3
V y = 3 ( c 3 V 3 c 2 V 2 ) .
V x ( t ) = 2 V 1 ( t ) V 2 ( t ) V 3 ( t ) = 3 R K cos ( Φ ( t ) + ψ e ) + x 0 ( ψ e )
V y ( t ) = 3 ( V 3 ( t ) V 2 ( t ) ) = 3 R K sin ( Φ ( t ) + ψ e ) + y 0 ( ψ e ) .
Φ ( t ) wr . = atan 2 ( V y y 0 , V x x 0 ) ψ e .
δ 0 = κ Φ 0 ξ = κ λ r 2 Φ 0 2 π OPD .
T pass ( λ , δ λ r ˜ ) = ( λ λ r δ λ r ˜ ( t ) ) 2 + ε ( γ r / 2 ) 2 ( λ λ r δ λ r ˜ ( t ) ) 2 + ( γ r / 2 ) 2
T MZI , i ( λ ) = 1 3 [ p + q cos ( ξ λ + φ i + ψ e ) ]
R FBG ( λ ) = 1 1 + ( λ λ r γ FBG / 2 ) 8 .
V i ( δ λ r ˜ ) = α P BBS R ph G 0 R FBG ( λ ) T pass ( λ , δ λ r ˜ ) T MZI , i ( λ ) d λ .
I i = 0 R ( λ ) T ( λ , δ λ r ˜ ) [ p + q cos ( ξ λ + φ i + ψ e ) ] d λ = p 0 R ( λ ) T ( λ , δ λ r ˜ ) d λ + q 0 R ( λ ) T ( λ , δ λ r ˜ ) cos ( ξ λ + φ i + ψ e ) d λ = p I α ( δ λ r ˜ ) + q I β , i ( δ λ r ˜ ) .
I α ( δ λ r ˜ ) = 0 R ( λ ) T ( λ , δ λ r ˜ ) d λ
I β , i ( δ λ r ˜ ) = 0 R ( λ ) T ( λ , δ λ r ˜ ) cos ( ξ λ + φ i + ψ e ) d λ = Re { e i ( φ i + ψ e ) 0 + R ( λ ) T ( λ , δ λ r ˜ ) e i ξ λ d λ } .
J ^ 0 R ( λ ) T ( λ , δ λ r ˜ ) e i ξ λ d λ = 0 ( λ λ r δ λ r ˜ ) 2 + ε ( γ r / 2 ) 2 ( λ λ r δ λ r ˜ ) 2 + ( γ r / 2 ) 2 e i ξ λ 1 + ( λ λ r γ FBG / 2 ) 8 d λ .
I α ( t ) = J ^ | ξ = 0
I β , i ( t ) = Re { e i ( φ i + ψ e ) J ^ } .
J ^ / e i ξ λ r K ^ = C ( z δ λ r ˜ ) 2 + ε ( γ r / 2 ) 2 ( z δ λ r ˜ ) 2 + ( γ r / 2 ) 2 e i ξ z 1 + ( z γ FBG / 2 ) 8 d z = C f ( z ) d z .
C f ( z ) d z = F ^ ( δ λ r ˜ ) + G ^ ( δ λ r ˜ ) .
F ^ ( δ λ r ˜ ) = π γ r 2 ( 1 ε ) e ξ γ r / 2 1 + ( δ λ r ˜ + i γ r / 2 γ FBG / 2 ) 8 e i ξ δ λ r ˜ E ^ δ λ r ˜ e i ξ δ λ r ˜
G ^ δ λ r ˜ = i π 4 k = 0 3 z FBG , k [ ( z FBG , k δ λ r ˜ ) 2 + ε ( γ r / 2 ) 2 ] ( z FBG , k δ λ r ˜ ) 2 + ( γ r / 2 ) 2 e i ξ Re ( z FBG , k ) e ξ Im ( z FBG , k ) .
L c , FBG k = λ r 2 2 π Im ( z FBG , k ) = λ r 2 π γ FBG sin [ π 4 ( k + 1 / 2 ) ] .
K ^ ( δ λ r ˜ ) = E ^ ( δ λ r ˜ ) e i ξ δ λ r ˜ + G ^ ( δ λ r ˜ ) F ^ 0 ( δ λ r ˜ ) + z 0 = R F 0 e i ξ δ λ r ˜ + z 0 .
V x ( t ) = 2 V 1 ( t ) V 2 ( t ) V 3 ( t ) ,
V y ( t ) = 3 ( V 3 ( t ) V 2 ( t ) ) .
I β , i = Re { e i ( φ i + ψ e ) J ^ } = Re { e i ( φ i + ψ e + ξ λ r ) [ E ^ ( δ λ r ˜ ) e i ξ δ λ r ˜ + G ^ ( δ λ r ˜ ) ] } Re { e i ( φ i + ψ e + ξ λ r ) [ R K e i Φ ( t ) + z 0 ] } .
V x ( t ) = 3 R K cos ( Φ ( t ) + ψ e + ξ λ r ) + 3 | z 0 | cos ( φ z 0 + ψ e + ξ λ r ) = 3 Re { e i ( ξ λ r + ψ e ) K ^ ( δ λ r ˜ ) } ,
V y ( t ) = 3 R K sin ( Φ ( t ) + ψ e + ξ λ r ) + 3 | z 0 | sin ( φ z 0 + ψ e + ξ λ r ) = 3 Im { e i ( ξ λ r + ψ e ) K ^ ( δ λ r ˜ ) } .
x 0 = 3 | z 0 | cos ( φ z 0 + ψ e + ξ λ r ) ,
y 0 = 3 | z 0 | sin ( φ z 0 + ψ e + ξ λ r ) .
δ λ r ˜ ( t ) T pass 0 ( λ op . ) T pass ( λ op . , t ) T pass 0 / λ | λ op .