Abstract

It is still a common belief that ultra-high quality-factors (Q-factors) are a prerequisite in optical resonant cavities for high refractive index resolution and low detection limit in biosensing applications. In combination with the ultra-short steps that are necessary when the measurement of the resonance shift relies on the wavelength scanning of a laser source and conventional methods for data processing, the high Q-factor requirement makes these biosensors extremely impractical. In this work we analyze an alternative processing method based on the fast-Fourier transform, and show through Monte-Carlo simulations that improvement by 2-3 orders of magnitude can be achieved in the resolution and the detection limit of the system in the presence of amplitude and spectral noise. More significantly, this improvement is maximum for low Q-factors around 104 and is present also for high intra-cavity losses and large scanning steps making the designs compatible with the low-cost aspect of lab-on-a-chip technology. Using a micro-ring resonator as model cavity and a system design with low Q-factor (104), low amplitude transmission (0.85) and relatively large scanning step (0.25 pm), we show that resolution close to 0.01 pm and detection limit close to 10−7 RIU can be achieved improving the sensing performance by more than 2 orders of magnitude compared to the performance of systems relying on a simple peak search processing method. The improvement in the limit of detection is present even when the simple method is combined with ultra-high Q-factors and ultra-short scanning steps due to the trade-off between the system resolution and sensitivity. Early experimental results are in agreement with the trends of the numerical studies.

© 2016 Optical Society of America

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References

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2013 (4)

S. S. Djordjevic, K. Shang, B. Guan, S. T. S. Cheung, L. Liao, J. Basak, H.-F. Liu, and S. J. B. Yoo, “CMOS-compatible, athermal silicon ring modulators clad with titanium dioxide,” Opt. Express 21(12), 13958–13968 (2013).
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[Crossref]

C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013).
[Crossref]

C. Guan, X. Tian, S. Li, X. Zhong, and J. Shi, “Long period fiber grating and high sensitivity refractive index sensor based on hollow eccentric optical fiber,” Sensor. Actuat. Biol. Chem. 188, 768–771 (2013).

2012 (4)

G. Senthil Murugan, J. S. Wilkinson, and M. N. Zervas, “Optical microdiscus resonators by flattening microspheres,” Appl. Phys. Lett. 101(7), 071106 (2012).
[Crossref]

R. Heideman, M. Hoekman, and E. Schreuder, “TriPleX-based integrated optical ring resonators for lab-on-a-chip and environmental detection,” IEEE J. Sel. Top. Quantum Electron. 18(5), 1583–1596 (2012).
[Crossref]

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

M. S. Luchansky and R. C. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. Chem. 84(2), 793–821 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (3)

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

N. A. Yebo, P. Lommens, Z. Hens, and R. Baets, “An integrated optic ethanol vapor sensor based on a silicon-on-insulator microring resonator coated with a porous ZnO film,” Opt. Express 18(11), 11859–11866 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

2007 (6)

2006 (5)

L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Hoiby, and O. Bang, “Photonic crystal fiber long-period gratings for biochemical sensing,” Opt. Express 14(18), 8224–8231 (2006).
[Crossref] [PubMed]

P. Debackere, S. Scheerlinck, P. Bienstman, and R. Baets, “Surface plasmon interferometer in Silicon-on-Insulator: novel concept for an integrated biosensor,” Opt. Express 14(16), 7063–7072 (2006).
[Crossref] [PubMed]

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-Q microcavities,” Opt. Lett. 31(12), 1896–1898 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (1)

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[Crossref] [PubMed]

2002 (1)

L. Gui and S. T. Wereley, “A correlation-based continuous window-shift technique to reduce the peak-locking in digital PIV evaluation,” Exp. Fluids 32(4), 506–517 (2002).
[Crossref]

Agarwal, A.

Aldridge, J. C.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Anthes-Washburn, M.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Armani, A. M.

Armenise, M. N.

C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013).
[Crossref]

Baehr-Jones, T.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Baets, R.

Bailey, R. C.

M. S. Luchansky and R. C. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. Chem. 84(2), 793–821 (2012).
[Crossref] [PubMed]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Bang, O.

Barrios, C. A.

Bartolozzi, I.

Basak, J.

Bauters, J. F.

Berghmans, F.

Bienstman, P.

Blumenthal, D. J.

Bogaerts, W.

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

Botsialas, A.

Bowers, J. E.

Burla, M.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Campanella, C. E.

C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013).
[Crossref]

Campanella, C. M.

C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013).
[Crossref]

Casquel, R.

Chao, C.-Y.

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

Chbouki, N.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Cheung, S. T. S.

Chow, E.

Chu, S.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Ciminelli, C.

C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013).
[Crossref]

Claes, T.

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

Dale, P. S.

De Heyn, P.

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

De Pauw, B.

De Vos, K.

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

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
[Crossref] [PubMed]

Debackere, P.

Dekker, R.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Dell’Olio, F.

C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013).
[Crossref]

Desai, T. A.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Djordjevic, S. S.

Dufva, M.

Dumon, P.

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

Falke, F.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Fan, X.

Fauchet, P. M.

Fung, W.

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

Geuzebroek, D. H.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Gill, D.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Girolami, G.

Gleeson, M. A.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Goldberg, B. B.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Griol, A.

Grot, A.

Guan, B.

Guan, C.

C. Guan, X. Tian, S. Li, X. Zhong, and J. Shi, “Long period fiber grating and high sensitivity refractive index sensor based on hollow eccentric optical fiber,” Sensor. Actuat. Biol. Chem. 188, 768–771 (2013).

Gui, L.

L. Gui and S. T. Wereley, “A correlation-based continuous window-shift technique to reduce the peak-locking in digital PIV evaluation,” Exp. Fluids 32(4), 506–517 (2002).
[Crossref]

Gunn, L. C.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Gunn, W. G.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Guo, L. J.

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

Gylfason, K. B.

Han, M.

Heck, M. J. R.

Heideman, R.

R. Heideman, M. Hoekman, and E. Schreuder, “TriPleX-based integrated optical ring resonators for lab-on-a-chip and environmental detection,” IEEE J. Sel. Top. Quantum Electron. 18(5), 1583–1596 (2012).
[Crossref]

Heideman, R. G.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Hens, Z.

Hochberg, M.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Hoekman, M.

K. Misiakos, I. Raptis, A. Salapatas, E. Makarona, A. Botsialas, M. Hoekman, R. Stoffer, and G. Jobst, “Broad-band mach-zehnder interferometers as high performance refractive index sensors: theory and monolithic implementation,” Opt. Express 22(8), 8856–8870 (2014).
[Crossref] [PubMed]

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

R. Heideman, M. Hoekman, and E. Schreuder, “TriPleX-based integrated optical ring resonators for lab-on-a-chip and environmental detection,” IEEE J. Sel. Top. Quantum Electron. 18(5), 1583–1596 (2012).
[Crossref]

Hoiby, P. E.

Holgado, M.

Homola, J.

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[Crossref] [PubMed]

Hryniewicz, J.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Hu, J.

Iqbal, M.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Jensen, J. B.

Jobst, G.

Kimerling, L. C.

King, O.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Klein, E. J.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Kumar Selvaraja, S.

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

Lamberti, A.

Lee, M. R.

Leinse, A.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Li, S.

C. Guan, X. Tian, S. Li, X. Zhong, and J. Shi, “Long period fiber grating and high sensitivity refractive index sensor based on hollow eccentric optical fiber,” Sensor. Actuat. Biol. Chem. 188, 768–771 (2013).

Liao, L.

Little, B. E.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Liu, H.-F.

Lommens, P.

Luchansky, M. S.

M. S. Luchansky and R. C. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. Chem. 84(2), 793–821 (2012).
[Crossref] [PubMed]

Makarona, E.

Marpaung, D.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Miri, N.

N. Miri and M. Mohammadzaheri, “Optical sensing using microspheres with different size and material,” IEEE Sens. J. 14(10), 3593–3598 (2014).
[Crossref]

Mirkarimi, L. W.

Misiakos, K.

Mohammadzaheri, M.

N. Miri and M. Mohammadzaheri, “Optical sensing using microspheres with different size and material,” IEEE Sens. J. 14(10), 3593–3598 (2014).
[Crossref]

Oldenbeuving, R. M.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Pedersen, L. H.

Popat, K. C.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Raptis, I.

Rindorf, L.

Roeloffzen, C. G. H.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Salapatas, A.

Sánchez, B.

Schacht, E.

Scheerlinck, S.

Schreuder, E.

R. Heideman, M. Hoekman, and E. Schreuder, “TriPleX-based integrated optical ring resonators for lab-on-a-chip and environmental detection,” IEEE J. Sel. Top. Quantum Electron. 18(5), 1583–1596 (2012).
[Crossref]

Schreuder, F.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Senthil Murugan, G.

G. Senthil Murugan, J. S. Wilkinson, and M. N. Zervas, “Optical microdiscus resonators by flattening microspheres,” Appl. Phys. Lett. 101(7), 071106 (2012).
[Crossref]

Shang, K.

Shi, J.

C. Guan, X. Tian, S. Li, X. Zhong, and J. Shi, “Long period fiber grating and high sensitivity refractive index sensor based on hollow eccentric optical fiber,” Sensor. Actuat. Biol. Chem. 188, 768–771 (2013).

Sigalas, M.

Sohlström, H.

Spaugh, B.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Spencer, D. T.

Stoffer, R.

Sun, X.

Suter, J. D.

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
[Crossref] [PubMed]

H. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. Fan, “Integrated refractive index optical ring resonator detector for capillary electrophoresis,” Anal. Chem. 79(3), 930–937 (2007).
[Crossref] [PubMed]

Tian, X.

C. Guan, X. Tian, S. Li, X. Zhong, and J. Shi, “Long period fiber grating and high sensitivity refractive index sensor based on hollow eccentric optical fiber,” Sensor. Actuat. Biol. Chem. 188, 768–771 (2013).

Tien, M.-C.

Tybor, F.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

Ünlü, M. S.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Vahala, K. J.

Van, V.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Van Dijk, P. W. L.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Van Thourhout, D.

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

Van Vaerenbergh, T.

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

Vanlanduit, S.

Wang, A.

Wereley, S. T.

L. Gui and S. T. Wereley, “A correlation-based continuous window-shift technique to reduce the peak-locking in digital PIV evaluation,” Exp. Fluids 32(4), 506–517 (2002).
[Crossref]

White, I. M.

Wilkinson, J. S.

G. Senthil Murugan, J. S. Wilkinson, and M. N. Zervas, “Optical microdiscus resonators by flattening microspheres,” Appl. Phys. Lett. 101(7), 071106 (2012).
[Crossref]

Yalçin, A.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

Yebo, N. A.

Yoo, S. J. B.

Zervas, M. N.

G. Senthil Murugan, J. S. Wilkinson, and M. N. Zervas, “Optical microdiscus resonators by flattening microspheres,” Appl. Phys. Lett. 101(7), 071106 (2012).
[Crossref]

Zhong, X.

C. Guan, X. Tian, S. Li, X. Zhong, and J. Shi, “Long period fiber grating and high sensitivity refractive index sensor based on hollow eccentric optical fiber,” Sensor. Actuat. Biol. Chem. 188, 768–771 (2013).

Zhu, H.

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
[Crossref] [PubMed]

H. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. Fan, “Integrated refractive index optical ring resonator detector for capillary electrophoresis,” Anal. Chem. 79(3), 930–937 (2007).
[Crossref] [PubMed]

Zhuang, L.

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Zourob, M.

H. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. Fan, “Integrated refractive index optical ring resonator detector for capillary electrophoresis,” Anal. Chem. 79(3), 930–937 (2007).
[Crossref] [PubMed]

Anal. Bioanal. Chem. (1)

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[Crossref] [PubMed]

Anal. Chem. (2)

M. S. Luchansky and R. C. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. Chem. 84(2), 793–821 (2012).
[Crossref] [PubMed]

H. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. Fan, “Integrated refractive index optical ring resonator detector for capillary electrophoresis,” Anal. Chem. 79(3), 930–937 (2007).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

G. Senthil Murugan, J. S. Wilkinson, and M. N. Zervas, “Optical microdiscus resonators by flattening microspheres,” Appl. Phys. Lett. 101(7), 071106 (2012).
[Crossref]

Exp. Fluids (1)

L. Gui and S. T. Wereley, “A correlation-based continuous window-shift technique to reduce the peak-locking in digital PIV evaluation,” Exp. Fluids 32(4), 506–517 (2002).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (5)

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006).
[Crossref]

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[Crossref]

R. Heideman, M. Hoekman, and E. Schreuder, “TriPleX-based integrated optical ring resonators for lab-on-a-chip and environmental detection,” IEEE J. Sel. Top. Quantum Electron. 18(5), 1583–1596 (2012).
[Crossref]

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

IEEE Sens. J. (1)

N. Miri and M. Mohammadzaheri, “Optical sensing using microspheres with different size and material,” IEEE Sens. J. 14(10), 3593–3598 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

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

Opt. Express (11)

N. A. Yebo, P. Lommens, Z. Hens, and R. Baets, “An integrated optic ethanol vapor sensor based on a silicon-on-insulator microring resonator coated with a porous ZnO film,” Opt. Express 18(11), 11859–11866 (2010).
[Crossref] [PubMed]

M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19(14), 13551–13556 (2011).
[Crossref] [PubMed]

S. S. Djordjevic, K. Shang, B. Guan, S. T. S. Cheung, L. Liao, J. Basak, H.-F. Liu, and S. J. B. Yoo, “CMOS-compatible, athermal silicon ring modulators clad with titanium dioxide,” Opt. Express 21(12), 13958–13968 (2013).
[Crossref] [PubMed]

A. Lamberti, S. Vanlanduit, B. De Pauw, and F. Berghmans, “A novel fast phase correlation algorithm for peak wavelength detection of fiber Bragg grating sensors,” Opt. Express 22(6), 7099–7112 (2014).
[Crossref] [PubMed]

K. Misiakos, I. Raptis, A. Salapatas, E. Makarona, A. Botsialas, M. Hoekman, R. Stoffer, and G. Jobst, “Broad-band mach-zehnder interferometers as high performance refractive index sensors: theory and monolithic implementation,” Opt. Express 22(8), 8856–8870 (2014).
[Crossref] [PubMed]

P. Debackere, S. Scheerlinck, P. Bienstman, and R. Baets, “Surface plasmon interferometer in Silicon-on-Insulator: novel concept for an integrated biosensor,” Opt. Express 14(16), 7063–7072 (2006).
[Crossref] [PubMed]

L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Hoiby, and O. Bang, “Photonic crystal fiber long-period gratings for biochemical sensing,” Opt. Express 14(18), 8224–8231 (2006).
[Crossref] [PubMed]

M. R. Lee and P. M. Fauchet, “Two-dimensional silicon photonic crystal based biosensing platform for protein detection,” Opt. Express 15(8), 4530–4535 (2007).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

Opt. Lett. (4)

Proc. SPIE (1)

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. Van Dijk, and R. M. Oldenbeuving, “TriPleX™ waveguide platform: Low-loss technology over a wide wavelength range,” Proc. SPIE 8767, 87670E (2013).
[Crossref]

Prog. Quantum Electron. (1)

C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013).
[Crossref]

Sensor. Actuat. Biol. Chem. (1)

C. Guan, X. Tian, S. Li, X. Zhong, and J. Shi, “Long period fiber grating and high sensitivity refractive index sensor based on hollow eccentric optical fiber,” Sensor. Actuat. Biol. Chem. 188, 768–771 (2013).

Other (2)

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley Interscience, 2002).

M. Nentwig, “Signal fitting with subsample resolution,” http://www.dsprelated.com/showcode/207.php .

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Figures (13)

Fig. 1
Fig. 1

(a) Layout of a typical MRR, (b) indicative transfer functions at drop port for different Q-factors and round-trip amplitude transmission coefficients α, (c) optical power transmission at resonance as a function of Q-factor and α, (d) waveguiding structure of the reference MRR in this work based on the TriPleX platform.

Fig. 2
Fig. 2

(a) Qualitative representation of the resonance shift at drop port, (b) method for estimating the system sensitivity based on resonance shift measurements. Zoom inside the resonance spectrum of the transfer function and representation of the effect of (c) the amplitude noise, and (d) the spectral noise.

Fig. 3
Fig. 3

Phase difference between the Fourier transforms of two transfer functions Td1 and Td2 in the case of delay between these functions that is shorter than one sample, exactly equal to one sample and longer than one sample. In the last case the curve wraps around the [-π + π] range. The delay can be calculated in principle from the slope of each curve.

Fig. 4
Fig. 4

System resolution of FFT and peak-search method in the case of amplitude noise as a function of the Q-factor and Δλ. In all cases, the amplitude transmission is 0.85.

Fig. 5
Fig. 5

System resolution of FFT and peak-search method in the case of amplitude noise as a function of the Q-factor and Δλ. In all cases, the amplitude transmission is 0.90.

Fig. 6
Fig. 6

System resolution of FFT and peak-search method in the case of amplitude noise as a function of the Q-factor and Δλ. In all cases, the amplitude transmission is 0.95. The legend in all diagrams is as in Fig. 6(a).

Fig. 7
Fig. 7

System resolution of FFT and peak-search method in the case of amplitude noise as a function of the Q-factor and Δλ. In all cases, the amplitude transmission is 1. The legend in all diagrams is as in Fig. 7(a).

Fig. 8
Fig. 8

Gain in system resolution of the FFT over the peak-search method in the case of amplitude noise for Q-factor equal to 104 and SNRmax equal to: (a) 40 and (b) 60 dB. The gain is calculated against the amplitude transmission α and the scanning step Δλ.

Fig. 9
Fig. 9

System resolution of FFT and peak-search method in the case of spectral noise with σλ equal to: a) 0.3∙Δλ, b) 0.4∙Δλ, c) 0.5∙Δλ, and d) 0.6∙Δλ. System resolution is shown for amplitude transmission equal to 1, but it is in fact independent from this parameter. The legend in all diagrams is as in Fig. 9(a).

Fig. 10
Fig. 10

Mean error in the estimation of the real resonance shift using: a) the FFT method, and b) the peak-search method with Lorentzian fitting. In both cases the Q-factor is 104 and the SNRmax 40 dB.

Fig. 11
Fig. 11

Mean error in the estimation of the real resonance shift using: a) the FFT method, and b) the peak-search method with Lorentzian fitting. In both cases the Q-factor is 104 and the SNRmax 60 dB.

Fig. 12
Fig. 12

Gain in the standard deviation of the measurement for the FFT method over the peak-search method with Lorentzian fitting. The results correspond to Q-factor 104 and SNRmax equal to: (a) 40, and (b) 60 dB.

Fig. 13
Fig. 13

a) Experimental setup used for early experiments, b) Photograph of TriPleX chip with sensing and reference MRR used in early experiments, c) Transfer functions of the reference and sensing MRRs within a 990-pm spectral window, d) Experimental curve regarding the dependence of system resolution on the scanning step and comparison against numerical curves for a similar set of design parameters and two SNRmax levels (20 and 40 dB). The scanning window for extracting the experimental curve was 400 pm.

Tables (1)

Tables Icon

Table 1 Comparison of the detection limit using the FFT and the peak-search method.

Equations (26)

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Td(φ)= (1 r 1 2 )(1 r 2 2 )a 12 r 1 r 2 acos(φ)+ ( r 1 r 2 a) 2
Td(λ)= (1 r 1 2 )(1 r 2 2 )a 12 r 1 r 2 acos( 2π n eff L λ )+ ( r 1 r 2 a) 2
λ res = n eff L m , m=1,2,3...
FSR= λ 0 2 n g L
n g = n eff λ 0 d n eff dλ
FWHM= (1 r 1 r 2 a) λ res 2 π n g L r 1 r 2 a
Qfactor= λ res FWHM = π n g L r 1 r 2 a λ res (1 r 1 r 2 a)
DL= R S
3 σ measn =3 σ ampln 2 + σ spectn 2 + σ tempn 2
σ shotn = 2q(RP)Δf and SNR= (RP) 2 σ shotn 2
R limit = Δλ 2
F 1 ( f k )= j=1 N T d1 ( λ j ) e 2πi N (j1)(k1)
F 2 ( f k )= j=1 N T d2 ( λ j ) e 2πi N (j1)(k1)
T d1 ( λ j ) T d2 ( λ j )= F 1 { F 1 ( f k ) F 2 ( f k )}= F 1 {U( f k )}
U rotated ( f k )=U( f k ) e j2πn f k ^
phase{ U rotated ( f k )}=phase{ U rotated ( f k )}| U rotated ( f k ) | x
TotalDelay=nΔλ+FractionalDelay
3 σ measn =3 σ ampln
σ shotnmax = 1 SN R max
σ shotnsample = P sample P max σ shotnmax = P sample 1 σ shotnmax
Gai n amplFFT = 3 σ amplnps 3 σ amplnFFT
3 σ meann =3 σ spectn
Gai n spectFFT = 3 σ spectnps 3 σ spectnFFT
f(x)= 1 2π a (xb) 2 + ( c 2 ) 2
Gai n amplFFTLorFitting = 3 σ amplnLorFitting 3 σ amplnFFT
ηA= 2π n eff λ res Q A

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