Abstract

We present a new size-selective detection method for integrated optical interferometric biosensors that can strongly enhance their performance. We demonstrate that by launching multiple wavelengths into a Young interferometer waveguide sensor it is feasible to derive refractive index changes from different regions above the waveguide surface, enabling one to distinguish between bound particles (e.g. proteins, viruses, bacteria) based on their differences in size and simultaneously eliminating interference from bulk refractive index changes. Therefore it is anticipated that this new method will be ideally suited for the detection of viruses in complex media. Numerical calculations are used to optimize sensor design and the detection method. Furthermore the specific case of virus detection is analyzed theoretically showing a minimum detectable virus mass coverage of 4 × 102 fg/mm2 (typically corresponding to 5 × 101 particles/ml).

© 2012 OSA

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    [CrossRef] [PubMed]
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2011

P. Kozma, A. Hámori, S. Kurunczi, K. Cottier, and R. Horvath, “Grating coupled optical waveguide interferometer for label-free biosensing,” Sens. Actuators B Chem.155(2), 446–450 (2011).
[CrossRef]

K. E. Zinoviev, A. B. Gonzalez-Guerrero, C. Dominguez, and L. M. Lechuga, “Integrated Bimodal Waveguide Interferometric Biosensor for Label-Free Analysis,” J. Lightwave Technol.29(13), 1926–1930 (2011).
[CrossRef]

2010

M. S. Luchansky, A. L. Washburn, T. A. Martin, M. Iqbal, L. C. Gunn, and R. C. Bailey, “Characterization of the evanescent field profile and bound mass sensitivity of a label-free silicon photonic microring resonator biosensing platform,” Biosens. Bioelectron.26(4), 1283–1291 (2010).
[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]

2008

G. D. Kim, G. S. Son, H. S. Lee, K. D. Kim, and S. S. Lee, “Integrated photonic glucose biosensor using a vertically coupled microring resonator in polymers,” Opt. Commun.281(18), 4644–4647 (2008).
[CrossRef]

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev.108(2), 462–493 (2008).
[CrossRef] [PubMed]

S. C. Buswell, V. A. Wright, J. M. Buriak, V. Van, and S. Evoy, “Specific detection of proteins using photonic crystal waveguides,” Opt. Express16(20), 15949–15957 (2008).
[CrossRef] [PubMed]

2007

N. Skivesen, A. Têtu, M. Kristensen, J. Kjems, L. H. Frandsen, and P. I. Borel, “Photonic-crystal waveguide biosensor,” Opt. Express15(6), 3169–3176 (2007).
[CrossRef] [PubMed]

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt.46(18), 3811–3820 (2007).
[CrossRef] [PubMed]

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, and P. Meyrueis, “Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions,” Biosens. Bioelectron.22(11), 2591–2597 (2007).
[CrossRef] [PubMed]

2006

2003

A. Ymeti, J. S. Kanger, J. Greve, P. V. Lambeck, R. Wijn, and R. G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt.42(28), 5649–5660 (2003).
[CrossRef] [PubMed]

K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sensor Actuat Biol. Chem.91, 241–251 (2003).

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

2002

A. Ymeti, J. S. Kanger, R. Wijn, P. V. Lambeck, and J. Greve, “Development of a multichannel integrated interferometer immunosensor,” Sensor Actuat Biol. Chem.83, 1–7 (2002).

2001

F. Prieto, L. M. Lechuga, A. Calle, A. Llobera, and C. Dominguez, “Optimized silicon antiresonant reflecting optical waveguides for sensing applications,” J. Lightwave Technol.19(1), 75–83 (2001).
[CrossRef]

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

C. Worth, B. B. Goldberg, M. Ruane, and M. S. Unlu, “Surface desensitization of polarimetric waveguide interferometers,” IEEE J. Sel. Top. Quantum Electron.7(6), 874–877 (2001).
[CrossRef]

2000

A. Brandenburg, R. Krauter, C. Künzel, M. Stefan, and H. Schulte, “Interferometric sensor for detection of surface-bound bioreactions,” Appl. Opt.39(34), 6396–6405 (2000).
[CrossRef] [PubMed]

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

1998

C. Stamm, R. Dangel, and W. Lukosz, “Biosensing with the integrated-optical difference interferometer: dual-wavelength operation,” Opt. Commun.153(4-6), 347–359 (1998).
[CrossRef]

1996

J. W. Mellors, C. R. Rinaldo, P. Gupta, R. M. White, J. A. Todd, and L. A. Kingsley, “Prognosis in HIV-1 infection Predicted by the Quantity of Virus in Plasma,” Science272(5265), 1167–1170 (1996).
[CrossRef] [PubMed]

1993

P. M. Nellen and W. Lukosz, “Integrated optical input grating couplers as direct affinity sensors,” Biosens. Bioelectron.8(3-4), 129–147 (1993).
[CrossRef]

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach-Zehnder interferometer immunosensor,” Sens. Actuators B Chem.10(3), 209–217 (1993).
[CrossRef]

1982

Ashe, A.

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

Bååk, T.

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]

Baets, R.

Bailey, R. 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. S. Luchansky, A. L. Washburn, T. A. Martin, M. Iqbal, L. C. Gunn, and R. C. Bailey, “Characterization of the evanescent field profile and bound mass sensitivity of a label-free silicon photonic microring resonator biosensing platform,” Biosens. Bioelectron.26(4), 1283–1291 (2010).
[CrossRef] [PubMed]

Balch, W. M.

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

Beumer, T. A. M.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

Bienstman, P.

Borel, P. I.

Brand, S.

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

Brandenburg, A.

K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, and P. Meyrueis, “Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions,” Biosens. Bioelectron.22(11), 2591–2597 (2007).
[CrossRef] [PubMed]

A. Brandenburg, R. Krauter, C. Künzel, M. Stefan, and H. Schulte, “Interferometric sensor for detection of surface-bound bioreactions,” Appl. Opt.39(34), 6396–6405 (2000).
[CrossRef] [PubMed]

Brynda, E.

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Buriak, J. M.

Buswell, S. C.

Calle, A.

Cottier, K.

P. Kozma, A. Hámori, S. Kurunczi, K. Cottier, and R. Horvath, “Grating coupled optical waveguide interferometer for label-free biosensing,” Sens. Actuators B Chem.155(2), 446–450 (2011).
[CrossRef]

K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sensor Actuat Biol. Chem.91, 241–251 (2003).

Cross, G. H.

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

Ctyroký, J.

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Daimon, M.

Dangel, R.

C. Stamm, R. Dangel, and W. Lukosz, “Biosensing with the integrated-optical difference interferometer: dual-wavelength operation,” Opt. Commun.153(4-6), 347–359 (1998).
[CrossRef]

Debackere, P.

Dominguez, C.

Dostálek, J.

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Drapeau, D. T.

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

Evoy, S.

Frandsen, L. H.

Freeman, N. J.

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

Gao, H.

K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sensor Actuat Biol. Chem.91, 241–251 (2003).

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]

Goldberg, B. B.

C. Worth, B. B. Goldberg, M. Ruane, and M. S. Unlu, “Surface desensitization of polarimetric waveguide interferometers,” IEEE J. Sel. Top. Quantum Electron.7(6), 874–877 (2001).
[CrossRef]

Gonzalez-Guerrero, A. B.

Greve, J.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, J. Greve, P. V. Lambeck, R. Wijn, and R. G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt.42(28), 5649–5660 (2003).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, R. Wijn, P. V. Lambeck, and J. Greve, “Development of a multichannel integrated interferometer immunosensor,” Sensor Actuat Biol. Chem.83, 1–7 (2002).

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach-Zehnder interferometer immunosensor,” Sens. Actuators B Chem.10(3), 209–217 (1993).
[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. S. Luchansky, A. L. Washburn, T. A. Martin, M. Iqbal, L. C. Gunn, and R. C. Bailey, “Characterization of the evanescent field profile and bound mass sensitivity of a label-free silicon photonic microring resonator biosensing platform,” Biosens. Bioelectron.26(4), 1283–1291 (2010).
[CrossRef] [PubMed]

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]

Gupta, P.

J. W. Mellors, C. R. Rinaldo, P. Gupta, R. M. White, J. A. Todd, and L. A. Kingsley, “Prognosis in HIV-1 infection Predicted by the Quantity of Virus in Plasma,” Science272(5265), 1167–1170 (1996).
[CrossRef] [PubMed]

Hámori, A.

P. Kozma, A. Hámori, S. Kurunczi, K. Cottier, and R. Horvath, “Grating coupled optical waveguide interferometer for label-free biosensing,” Sens. Actuators B Chem.155(2), 446–450 (2011).
[CrossRef]

Heideman, R. G.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, J. Greve, P. V. Lambeck, R. Wijn, and R. G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt.42(28), 5649–5660 (2003).
[CrossRef] [PubMed]

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach-Zehnder interferometer immunosensor,” Sens. Actuators B Chem.10(3), 209–217 (1993).
[CrossRef]

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]

Hoffmann, C.

K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, and P. Meyrueis, “Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions,” Biosens. Bioelectron.22(11), 2591–2597 (2007).
[CrossRef] [PubMed]

Homola, J.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev.108(2), 462–493 (2008).
[CrossRef] [PubMed]

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Horvath, R.

P. Kozma, A. Hámori, S. Kurunczi, K. Cottier, and R. Horvath, “Grating coupled optical waveguide interferometer for label-free biosensing,” Sens. Actuators B Chem.155(2), 446–450 (2011).
[CrossRef]

Iqbal, M.

M. S. Luchansky, A. L. Washburn, T. A. Martin, M. Iqbal, L. C. Gunn, and R. C. Bailey, “Characterization of the evanescent field profile and bound mass sensitivity of a label-free silicon photonic microring resonator biosensing platform,” Biosens. Bioelectron.26(4), 1283–1291 (2010).
[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]

Kanger, J. S.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, J. Greve, P. V. Lambeck, R. Wijn, and R. G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt.42(28), 5649–5660 (2003).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, R. Wijn, P. V. Lambeck, and J. Greve, “Development of a multichannel integrated interferometer immunosensor,” Sensor Actuat Biol. Chem.83, 1–7 (2002).

Kim, G. D.

G. D. Kim, G. S. Son, H. S. Lee, K. D. Kim, and S. S. Lee, “Integrated photonic glucose biosensor using a vertically coupled microring resonator in polymers,” Opt. Commun.281(18), 4644–4647 (2008).
[CrossRef]

Kim, K. D.

G. D. Kim, G. S. Son, H. S. Lee, K. D. Kim, and S. S. Lee, “Integrated photonic glucose biosensor using a vertically coupled microring resonator in polymers,” Opt. Commun.281(18), 4644–4647 (2008).
[CrossRef]

Kingsley, L. A.

J. W. Mellors, C. R. Rinaldo, P. Gupta, R. M. White, J. A. Todd, and L. A. Kingsley, “Prognosis in HIV-1 infection Predicted by the Quantity of Virus in Plasma,” Science272(5265), 1167–1170 (1996).
[CrossRef] [PubMed]

Kjems, J.

Kooyman, R. P. H.

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach-Zehnder interferometer immunosensor,” Sens. Actuators B Chem.10(3), 209–217 (1993).
[CrossRef]

Kozma, P.

P. Kozma, A. Hámori, S. Kurunczi, K. Cottier, and R. Horvath, “Grating coupled optical waveguide interferometer for label-free biosensing,” Sens. Actuators B Chem.155(2), 446–450 (2011).
[CrossRef]

Krauter, R.

Kristensen, M.

Kunz, R. E.

K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sensor Actuat Biol. Chem.91, 241–251 (2003).

Künzel, C.

Kurunczi, S.

P. Kozma, A. Hámori, S. Kurunczi, K. Cottier, and R. Horvath, “Grating coupled optical waveguide interferometer for label-free biosensing,” Sens. Actuators B Chem.155(2), 446–450 (2011).
[CrossRef]

Lambeck, P. V.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, J. Greve, P. V. Lambeck, R. Wijn, and R. G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt.42(28), 5649–5660 (2003).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, R. Wijn, P. V. Lambeck, and J. Greve, “Development of a multichannel integrated interferometer immunosensor,” Sensor Actuat Biol. Chem.83, 1–7 (2002).

Lapierre, J.

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

Lechuga, L. M.

Lee, H. S.

G. D. Kim, G. S. Son, H. S. Lee, K. D. Kim, and S. S. Lee, “Integrated photonic glucose biosensor using a vertically coupled microring resonator in polymers,” Opt. Commun.281(18), 4644–4647 (2008).
[CrossRef]

Lee, S. S.

G. D. Kim, G. S. Son, H. S. Lee, K. D. Kim, and S. S. Lee, “Integrated photonic glucose biosensor using a vertically coupled microring resonator in polymers,” Opt. Commun.281(18), 4644–4647 (2008).
[CrossRef]

Llobera, A.

Luchansky, M. S.

M. S. Luchansky, A. L. Washburn, T. A. Martin, M. Iqbal, L. C. Gunn, and R. C. Bailey, “Characterization of the evanescent field profile and bound mass sensitivity of a label-free silicon photonic microring resonator biosensing platform,” Biosens. Bioelectron.26(4), 1283–1291 (2010).
[CrossRef] [PubMed]

Lukosz, W.

C. Stamm, R. Dangel, and W. Lukosz, “Biosensing with the integrated-optical difference interferometer: dual-wavelength operation,” Opt. Commun.153(4-6), 347–359 (1998).
[CrossRef]

P. M. Nellen and W. Lukosz, “Integrated optical input grating couplers as direct affinity sensors,” Biosens. Bioelectron.8(3-4), 129–147 (1993).
[CrossRef]

Martin, T. A.

M. S. Luchansky, A. L. Washburn, T. A. Martin, M. Iqbal, L. C. Gunn, and R. C. Bailey, “Characterization of the evanescent field profile and bound mass sensitivity of a label-free silicon photonic microring resonator biosensing platform,” Biosens. Bioelectron.26(4), 1283–1291 (2010).
[CrossRef] [PubMed]

Masumura, A.

Mellors, J. W.

J. W. Mellors, C. R. Rinaldo, P. Gupta, R. M. White, J. A. Todd, and L. A. Kingsley, “Prognosis in HIV-1 infection Predicted by the Quantity of Virus in Plasma,” Science272(5265), 1167–1170 (1996).
[CrossRef] [PubMed]

Meyrueis, P.

K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, and P. Meyrueis, “Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions,” Biosens. Bioelectron.22(11), 2591–2597 (2007).
[CrossRef] [PubMed]

Navotny, J.

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

Nekvindová, P.

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Nellen, P. M.

P. M. Nellen and W. Lukosz, “Integrated optical input grating couplers as direct affinity sensors,” Biosens. Bioelectron.8(3-4), 129–147 (1993).
[CrossRef]

Peel, L. L.

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

Popplewell, J. F.

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

Prieto, F.

Reeves, A. A.

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

Rinaldo, C. R.

J. W. Mellors, C. R. Rinaldo, P. Gupta, R. M. White, J. A. Todd, and L. A. Kingsley, “Prognosis in HIV-1 infection Predicted by the Quantity of Virus in Plasma,” Science272(5265), 1167–1170 (1996).
[CrossRef] [PubMed]

Ruane, M.

C. Worth, B. B. Goldberg, M. Ruane, and M. S. Unlu, “Surface desensitization of polarimetric waveguide interferometers,” IEEE J. Sel. Top. Quantum Electron.7(6), 874–877 (2001).
[CrossRef]

Scheerlinck, S.

Schirmer, B.

K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, and P. Meyrueis, “Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions,” Biosens. Bioelectron.22(11), 2591–2597 (2007).
[CrossRef] [PubMed]

Schmitt, K.

K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, and P. Meyrueis, “Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions,” Biosens. Bioelectron.22(11), 2591–2597 (2007).
[CrossRef] [PubMed]

Schröfel, J.

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Schulte, H.

Skalský, M.

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Skivesen, N.

Skvor, J.

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Son, G. S.

G. D. Kim, G. S. Son, H. S. Lee, K. D. Kim, and S. S. Lee, “Integrated photonic glucose biosensor using a vertically coupled microring resonator in polymers,” Opt. Commun.281(18), 4644–4647 (2008).
[CrossRef]

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]

Spirková, J.

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Stamm, C.

C. Stamm, R. Dangel, and W. Lukosz, “Biosensing with the integrated-optical difference interferometer: dual-wavelength operation,” Opt. Commun.153(4-6), 347–359 (1998).
[CrossRef]

Stefan, M.

Subramaniam, V.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

Swann, M. J.

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

Têtu, A.

Todd, J. A.

J. W. Mellors, C. R. Rinaldo, P. Gupta, R. M. White, J. A. Todd, and L. A. Kingsley, “Prognosis in HIV-1 infection Predicted by the Quantity of Virus in Plasma,” Science272(5265), 1167–1170 (1996).
[CrossRef] [PubMed]

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]

Unlu, M. S.

C. Worth, B. B. Goldberg, M. Ruane, and M. S. Unlu, “Surface desensitization of polarimetric waveguide interferometers,” IEEE J. Sel. Top. Quantum Electron.7(6), 874–877 (2001).
[CrossRef]

Vaillancourt, R.

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

Van, V.

van Hövell, S. W. F. M.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

Vaughn, J.

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

Voirin, G.

K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sensor Actuat Biol. Chem.91, 241–251 (2003).

Washburn, A. L.

M. S. Luchansky, A. L. Washburn, T. A. Martin, M. Iqbal, L. C. Gunn, and R. C. Bailey, “Characterization of the evanescent field profile and bound mass sensitivity of a label-free silicon photonic microring resonator biosensing platform,” Biosens. Bioelectron.26(4), 1283–1291 (2010).
[CrossRef] [PubMed]

White, R. M.

J. W. Mellors, C. R. Rinaldo, P. Gupta, R. M. White, J. A. Todd, and L. A. Kingsley, “Prognosis in HIV-1 infection Predicted by the Quantity of Virus in Plasma,” Science272(5265), 1167–1170 (1996).
[CrossRef] [PubMed]

Wijn, R.

A. Ymeti, J. S. Kanger, J. Greve, P. V. Lambeck, R. Wijn, and R. G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt.42(28), 5649–5660 (2003).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, R. Wijn, P. V. Lambeck, and J. Greve, “Development of a multichannel integrated interferometer immunosensor,” Sensor Actuat Biol. Chem.83, 1–7 (2002).

Wijn, R. R.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

Wiki, M.

K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sensor Actuat Biol. Chem.91, 241–251 (2003).

Wink, T.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

Worth, C.

C. Worth, B. B. Goldberg, M. Ruane, and M. S. Unlu, “Surface desensitization of polarimetric waveguide interferometers,” IEEE J. Sel. Top. Quantum Electron.7(6), 874–877 (2001).
[CrossRef]

Wright, V. A.

Ymeti, A.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, J. Greve, P. V. Lambeck, R. Wijn, and R. G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt.42(28), 5649–5660 (2003).
[CrossRef] [PubMed]

A. Ymeti, J. S. Kanger, R. Wijn, P. V. Lambeck, and J. Greve, “Development of a multichannel integrated interferometer immunosensor,” Sensor Actuat Biol. Chem.83, 1–7 (2002).

Zinoviev, K. E.

Appl. Opt.

Biosens. Bioelectron.

P. M. Nellen and W. Lukosz, “Integrated optical input grating couplers as direct affinity sensors,” Biosens. Bioelectron.8(3-4), 129–147 (1993).
[CrossRef]

K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, and P. Meyrueis, “Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions,” Biosens. Bioelectron.22(11), 2591–2597 (2007).
[CrossRef] [PubMed]

M. S. Luchansky, A. L. Washburn, T. A. Martin, M. Iqbal, L. C. Gunn, and R. C. Bailey, “Characterization of the evanescent field profile and bound mass sensitivity of a label-free silicon photonic microring resonator biosensing platform,” Biosens. Bioelectron.26(4), 1283–1291 (2010).
[CrossRef] [PubMed]

G. H. Cross, A. A. Reeves, S. Brand, J. F. Popplewell, L. L. Peel, M. J. Swann, and N. J. Freeman, “A new quantitative optical biosensor for protein characterisation,” Biosens. Bioelectron.19(4), 383–390 (2003).
[CrossRef] [PubMed]

Chem. Rev.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev.108(2), 462–493 (2008).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron.

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]

C. Worth, B. B. Goldberg, M. Ruane, and M. S. Unlu, “Surface desensitization of polarimetric waveguide interferometers,” IEEE J. Sel. Top. Quantum Electron.7(6), 874–877 (2001).
[CrossRef]

J. Lightwave Technol.

Limnol. Oceanogr.

W. M. Balch, J. Vaughn, J. Navotny, D. T. Drapeau, R. Vaillancourt, J. Lapierre, and A. Ashe, “Light scattering by viral suspensions,” Limnol. Oceanogr.45(2), 492–498 (2000).
[CrossRef]

Nano Lett.

A. Ymeti, J. Greve, P. V. Lambeck, T. Wink, S. W. F. M. van Hövell, T. A. M. Beumer, R. R. Wijn, R. G. Heideman, V. Subramaniam, and J. S. Kanger, “Fast, ultrasensitive virus detection using a young interferometer sensor,” Nano Lett.7(2), 394–397 (2007).
[CrossRef] [PubMed]

Opt. Commun.

C. Stamm, R. Dangel, and W. Lukosz, “Biosensing with the integrated-optical difference interferometer: dual-wavelength operation,” Opt. Commun.153(4-6), 347–359 (1998).
[CrossRef]

G. D. Kim, G. S. Son, H. S. Lee, K. D. Kim, and S. S. Lee, “Integrated photonic glucose biosensor using a vertically coupled microring resonator in polymers,” Opt. Commun.281(18), 4644–4647 (2008).
[CrossRef]

Opt. Express

Science

J. W. Mellors, C. R. Rinaldo, P. Gupta, R. M. White, J. A. Todd, and L. A. Kingsley, “Prognosis in HIV-1 infection Predicted by the Quantity of Virus in Plasma,” Science272(5265), 1167–1170 (1996).
[CrossRef] [PubMed]

Sens. Actuators B Chem.

P. Kozma, A. Hámori, S. Kurunczi, K. Cottier, and R. Horvath, “Grating coupled optical waveguide interferometer for label-free biosensing,” Sens. Actuators B Chem.155(2), 446–450 (2011).
[CrossRef]

R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach-Zehnder interferometer immunosensor,” Sens. Actuators B Chem.10(3), 209–217 (1993).
[CrossRef]

J. Dostálek, J. Ctyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Spirková, J. Skvor, and J. Schröfel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem.76(1-3), 8–12 (2001).
[CrossRef]

Sensor Actuat Biol. Chem.

K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sensor Actuat Biol. Chem.91, 241–251 (2003).

A. Ymeti, J. S. Kanger, R. Wijn, P. V. Lambeck, and J. Greve, “Development of a multichannel integrated interferometer immunosensor,” Sensor Actuat Biol. Chem.83, 1–7 (2002).

Other

E. F. Schipper, “Waveguide immunosensing of small molecules,” Ph.D. Thesis, University of Twente (1997).

A. Ymeti, “Development of a multichannel integrated Young interferometer immunosensor,” Ph.D. Thesis, University of Twente (2004).

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics: Fundamentals, techniques, and design (McGraw-Hill, 1995), pp. 33.61–33.66.

M. Green, M. Piña, R. Kimes, P. C. Wensink, L. A. MacHattie, and C. A. Thomas, “Adenovirus DNA. I. Molecular weight and conformation,” Proceedings of the National Academy of Sciences of the United States of America 57, 1302-& (1967).

E. Hecht, in Optics (Addison-Wesley, 1998), pp. 385–388.

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Figures (6)

Fig. 1
Fig. 1

The principle of a Young interferometer, where light is coupled in and guided through an integrated channel waveguide structure and projected onto a CCD camera by a cylindrical lens, giving an interference pattern. Figure adapted from [17].

Fig. 2
Fig. 2

Structure definition of waveguide with on top N introduced imaginary layers and a guided mode profile (dashed line), where d is the thickness and n the refractive index.

Fig. 3
Fig. 3

Guided mode profiles of three different wavelengths propagating through a waveguide structure with three layers introduced on top of the sensing window to distinguish between the non-specific protein binding, the specific virus binding, and the bulk solution changes.

Fig. 4
Fig. 4

Relative precision as a function of the core thickness and core refractive index (given at a wavelength of 550 nm) for a) the virus layer using two layers, b) the bulk using two layers, c) the virus layer using three layers, d) the bulk using three layers and e) the non-specific binding layer using three layers.

Fig. 5
Fig. 5

Mean relative precision as a function of the number of layers, which is equal to the number of wavelengths, for a core thickness of 70 nm and Si3N4 as core material.

Fig. 6
Fig. 6

Relative precision as a function of the number of wavelengths for two layers, a core thickness of 70 nm and SiO2 as the substrate material, Si3N4 as the core material, and water on top of this core.

Tables (2)

Tables Icon

Table 1 Waveguide structure details for all the simulations, where the RI of the layers is determined by the Sellmeier equations (see Appendix A).

Tables Icon

Table A.1 Sellmeier equations for the different materials used in the waveguide structure

Equations (26)

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

Δφ= 2π λ lΔ N eff = 2π λ l ( N eff n ) λ Δn,
Δφ= Μ s Δn with Δφ=[ Δ φ 1 Δ φ j Δ φ N λ ], Δn=[ Δ n 1 Δ n i Δ n N layer ],
M s =2πl[ 1 λ 1 S 1,1 1 λ 1 S 2,1 1 λ 1 S 3,1 1 λ 1 S N layer ,1 1 λ 2 S 1,2 1 λ 2 S N layer ,2 1 λ 3 S 1,3 1 λ j S i,j 1 λ 3 S N layer ,3 1 λ N λ S 1, N λ 1 λ N λ S 2, N λ 1 λ N λ S 3, N λ 1 λ N λ S N layer , N λ ] with S i,j = ( N eff n i ) λ j ,
Δn= M s 1 Δφ,
Φ i = σ Δ n i σ Δφ = [ j=1 N λ ( M s,ij 1 ) 2 ] 1/2 .
C v = 1 β (Δ n 2 Δ n 3 ),
Δ C v = 2 β σ Δ n virus ,
β= ( n virus n solution ) d virus 2 / m virus .
( N eff n c ) λ j =( n c N eff )( n core 2 N eff 2 n core 2 n c 2 )( Y 0c ( λ j ) d core + Y 0c ( λ j )+ Y 0s ( λ j ) ),
Y 0c,s ( λ j )=( λ 2π ) ( N eff 2 n c,s 2 ) 1/2 ,
S i,j = z i1 z i exp( 2z Y 0c ( λ j ) ) dz 0 exp( 2z Y 0c ( λ j ) ) dz ( N eff n c ) λ j ,
S i,j =[ exp( 2 z i1 Y 0c ( λ j ) )exp( 2 z i Y 0c ( λ j ) ) ]( n c N eff )( n core 2 N eff 2 n core 2 n c 2 )( Y 0c ( λ j ) d core + Y 0c ( λ j )+ Y 0s ( λ j ) ).
Δn= M s 1 Δφ.
σ 2 ( Δn )=( M s 1 M s 1 ) σ 2 ( Δφ ),
( M s 1 M s 1 ) ij = ( M s,ij 1 ) 2 .
[ σ( Δn ) ] i = σ Δ n i = [ ( M s 1 M s 1 ) σ 2 ( Δφ ) ] i 1/2 = [ j=1 N λ ( M s,ij 1 ) 2 σ Δ φ j 2 ] 1/2 .
Φ i = σ Δ n i σ Δϕ = 1 σ Δϕ [ j=1 N ( M s,ij 1 ) 2 σ Δϕ 2 ] 1/2 = [ j=1 N ( M s,ij 1 ) 2 ] 1/2 .
[ Δ n 1 Δ n 2 Δ n 3 ]= M C [ C p C v C b ],with M C =[ α β γ 0 β γ 0 0 γ ],
[ C p C v C b ]= M C 1 [ Δ n 1 Δ n 2 Δ n 3 ],with M C 1 =[ 1/α 1/α 0 0 1/β 1/β 0 0 1/γ ].
C v = 1 β (Δ n 2 Δ n 3 ),
C v = 1 β Δ n virus .
C v = N virus m virus wl ,
N virus = Δ n virus Δ n max N max = Δ n virus wl ( n virus n solution ) d 2 .
β= ( n virus n solution ) d virus 2 / m virus .
Δ C v = [ | ( f ( Δ n 2 ) )Δ( Δ n 2 ) | 2 + | ( f ( Δ n 3 ) )Δ( Δ n 3 ) | 2 ] 1/2 = 1 β [ | Δ( Δ n 2 ) | 2 + | Δ( Δ n 3 ) | 2 ] 1/2 .
Δ C v = 2 β σ Δ n virus .

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