Abstract

A conceptual lab-in-a-photonic-crystal biosensor is demonstrated that can multiplex four or more distinct disease-markers and distinguish their presence and combinations simultaneously with unique spectral fingerprints. This biosensor consists of a photonic-band-gap, multi-mode waveguide coupled to surface modes on either side, encased in a glass slide with microfluidic channels. The spectral fingerprints consist of multiple peaks in optical transmission vs. frequency that respond sensitively and uniquely in both frequency shift and nonmonotonic change of peak transmittance levels to various analyte bindings. This special property enables complete, logical determination of twelve different combinations of four distinct disease-markers through one scan of the transmission spectrum. The results reveal unique phenomena such as switching between the strong-coupling and weak-coupling combinations of surface states by analyte binding at different locations along the central waveguide. The unconventional transmission spectra are explained using a Landauer-Büttiker, multiple-scattering, transmission theory that reproduces the main features of the exact finite-difference-time-domain simulation.

© 2016 Optical Society of America

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References

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2015 (1)

A. Al Rashid and S. John, “Optical biosensing of multiple disease markers in a photonic-band-gap lab-on-a-chip: a conceptual paradigm,” Phys. Rev. Appl. 3(3), 034001 (2015).
[Crossref]

2014 (4)

S. Chakravarty, A. Hosseini, X. Xu, L. Zhu, Y. Zou, and R. T. Chen, “Analysis of ultra-high sensitivity configuration in chip-integrated photonic crystal microcavity bio-sensors,” Appl. Phys. Lett. 104, 191109 (2014).
[Crossref] [PubMed]

R.-M. Ma, S. Ota, Y. Li, S. yang, and X. Zhang, “Explosives detection in a lasing plasmon nanocavity,” Nat. Nanotechnol. 9(8), 600–604 (2014).
[Crossref] [PubMed]

J. H. Jiang and S. John, “Photonic crystal architecture for room-temperature equilibrium Bose-Einstein condensation of exciton polaritons,” Phys. Rev. X 4(3), 031025 (2014).

J. H. Jiang and S. John, “Equilibrium high-temperature Bose-Einstein condensation in dichalcogenide monolayers,” Sci. Rep. 4, 7432 (2014).
[Crossref]

2013 (1)

M. G. Scullion, T. F. Krauss, and A. Di Falco, “Slotted photonic crystal sensors,” Sensors 13(3), 3675–3710 (2013).
[Crossref] [PubMed]

2012 (2)

2010 (2)

M. E. Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18(22), 22702–22714 (2010).
[Crossref] [PubMed]

Y.-J. Hung, S.-L. Lee, and L. A. Coldren, “Deep and tapered silicon photonic crystals for achieving anti-reflection and enhanced absorption,” Opt. Express. 18(7), 6841–6852 (2010).
[Crossref] [PubMed]

2009 (3)

G. Peng, U. Tisch, O. Adams, M. Hakim, N. Shehada, Y. Y. Broza, S. Billan, R. Abdah-Bortnyak, A. Kuten, and H. Haick, “Diagnosing lung cancer in exhaled breath using gold nanoparticles,” Nature Nanotech. 4(10), 669–673 (2009).
[Crossref]

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[Crossref] [PubMed]

M. Huang, A. A. Yanik, T.-Y. Chang, and H. Altug, “Sub-wavelength nanofluidics in photonic crystal sensors,” Opt. Express 17(26), 24224–24233 (2009).
[Crossref]

2008 (3)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluid. Nanofluid. 4(1), 117–127 (2008).
[Crossref]

T.-M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

2007 (4)

V. N. Konopsky and E. V. Alieva, “Photonic crystal surface waves for optical biosensors,” Anal. Chem. 79(12), 4729–4735 (2007).
[Crossref] [PubMed]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[Crossref]

N. Skivesen, A. Tetu, M. Kristensen, J. Kjems, L. H. Frandsen, and P. I. Borel, “Photonic-crystal waveguide biosensor,” Opt. Express 15(6), 3169–3176 (2007).
[Crossref] [PubMed]

M. 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]

2006 (4)

Y. Fang, A. M. Ferrie, N. H. Fontaine, J. Mauro, and J. Balakrishnan, “Resonant waveguide grating biosensor for living cell sensing,” Biophys. J. 91(5), 1925–1940 (2006).
[Crossref] [PubMed]

I. D. Block, L. L. Chan, and B. T. Cunningham, “Photonic crystal optical biosensor incorporating structured low-index porous dielectric,” Sens. and Actuators B 120(1), 187–193 (2006).
[Crossref]

M. Wilchek, E. A. Bayer, and O. Livnah, “Essentials of biorecognition: the (strept) avidinbiotin system as a model for proteinprotein and proteinligand interaction,” Immun. Lett. 103(1), 27–32 (2006).
[Crossref]

Y. Fang, “Label-free cell-based assays with optical biosensors in drug discovery,” Assay Drug Dev. Technol. 4(5), 583–595 (2006).
[Crossref] [PubMed]

2005 (1)

M. L. Adams, M. Loncar, A. Scherer, and Y. Qiu, “Microfluidic integration of porous photonic crystal nanolasers for chemical sensing,” IEEE J. Sel. Areas Commun. 23(7), 1348–1354 (2005).
[Crossref]

2004 (4)

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[Crossref]

V. Pavlov, Y. Xiao, B. Shlyahovsky, and I. Willner, “Aptamer-functionalized Au nanoparticles for the amplified optical detection of thrombin,” J. Am. Chem. Soc. 126(38), 11768–11769 (2004).
[Crossref] [PubMed]

E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultracompact biochemical sensor built with two-dimensional photonic crystal microcavity,” Opt. Lett. 29(10), 1093–1095 (2004).
[Crossref] [PubMed]

2003 (1)

2002 (2)

J. Vörös, J. J. Ramsden, G. Csucs, I. Szendrö, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23(17), 3699–3710 (2002).
[Crossref] [PubMed]

M. Liss, B. Petersen, H. Wolf, and E. Prohaska, “An aptamer-based quartz crystal protein biosensor,” Anal. Chem. 74(17), 4488–4495 (2002).
[Crossref] [PubMed]

2001 (1)

1999 (2)

Y. Imry and R. Landauer, “Conductance viewed as transmission,” Rev. Mod. Phys. 71(2), S306 (1999).
[Crossref]

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54(1), 3–15 (1999).
[Crossref]

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44(19), 10961–10964 (1991).
[Crossref]

1987 (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid- state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

1986 (1)

M. Büttiker, “Four-terminal phase-coherent conductance,” Phys. Rev. Lett. 57(14), 1761–1764 (1986).
[Crossref] [PubMed]

1984 (1)

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
[Crossref]

1980 (1)

M. E. Young, P. A. Carroad, and R. L. Bell, “Estimation of diffusion coefficients of proteins,” Biotechnol. Bioeng. 22(5), 947–955 (1980).
[Crossref]

1971 (1)

C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James, “Direct calculation of the tunneling current,” J. Phys. C: Solid St. Phys. 4(8), 916–929 (1971).
[Crossref]

Abdah-Bortnyak, R.

G. Peng, U. Tisch, O. Adams, M. Hakim, N. Shehada, Y. Y. Broza, S. Billan, R. Abdah-Bortnyak, A. Kuten, and H. Haick, “Diagnosing lung cancer in exhaled breath using gold nanoparticles,” Nature Nanotech. 4(10), 669–673 (2009).
[Crossref]

Adams, M. L.

M. L. Adams, M. Loncar, A. Scherer, and Y. Qiu, “Microfluidic integration of porous photonic crystal nanolasers for chemical sensing,” IEEE J. Sel. Areas Commun. 23(7), 1348–1354 (2005).
[Crossref]

Adams, O.

G. Peng, U. Tisch, O. Adams, M. Hakim, N. Shehada, Y. Y. Broza, S. Billan, R. Abdah-Bortnyak, A. Kuten, and H. Haick, “Diagnosing lung cancer in exhaled breath using gold nanoparticles,” Nature Nanotech. 4(10), 669–673 (2009).
[Crossref]

Al Rashid, A.

A. Al Rashid and S. John, “Optical biosensing of multiple disease markers in a photonic-band-gap lab-on-a-chip: a conceptual paradigm,” Phys. Rev. Appl. 3(3), 034001 (2015).
[Crossref]

Alieva, E. V.

V. N. Konopsky and E. V. Alieva, “Photonic crystal surface waves for optical biosensors,” Anal. Chem. 79(12), 4729–4735 (2007).
[Crossref] [PubMed]

Altug, H.

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[Crossref]

Baird, C.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

Balakrishnan, J.

Y. Fang, A. M. Ferrie, N. H. Fontaine, J. Mauro, and J. Balakrishnan, “Resonant waveguide grating biosensor for living cell sensing,” Biophys. J. 91(5), 1925–1940 (2006).
[Crossref] [PubMed]

Bayer, E. A.

M. Wilchek, E. A. Bayer, and O. Livnah, “Essentials of biorecognition: the (strept) avidinbiotin system as a model for proteinprotein and proteinligand interaction,” Immun. Lett. 103(1), 27–32 (2006).
[Crossref]

Beheiry, M. E.

Bell, R. L.

M. E. Young, P. A. Carroad, and R. L. Bell, “Estimation of diffusion coefficients of proteins,” Biotechnol. Bioeng. 22(5), 947–955 (1980).
[Crossref]

Billan, S.

G. Peng, U. Tisch, O. Adams, M. Hakim, N. Shehada, Y. Y. Broza, S. Billan, R. Abdah-Bortnyak, A. Kuten, and H. Haick, “Diagnosing lung cancer in exhaled breath using gold nanoparticles,” Nature Nanotech. 4(10), 669–673 (2009).
[Crossref]

Block, I. D.

I. D. Block, L. L. Chan, and B. T. Cunningham, “Photonic crystal optical biosensor incorporating structured low-index porous dielectric,” Sens. and Actuators B 120(1), 187–193 (2006).
[Crossref]

Borel, P. I.

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44(19), 10961–10964 (1991).
[Crossref]

Broza, Y. Y.

G. Peng, U. Tisch, O. Adams, M. Hakim, N. Shehada, Y. Y. Broza, S. Billan, R. Abdah-Bortnyak, A. Kuten, and H. Haick, “Diagnosing lung cancer in exhaled breath using gold nanoparticles,” Nature Nanotech. 4(10), 669–673 (2009).
[Crossref]

Büttiker, M.

M. Büttiker, “Four-terminal phase-coherent conductance,” Phys. Rev. Lett. 57(14), 1761–1764 (1986).
[Crossref] [PubMed]

Caroli, C.

C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James, “Direct calculation of the tunneling current,” J. Phys. C: Solid St. Phys. 4(8), 916–929 (1971).
[Crossref]

Carroad, P. A.

M. E. Young, P. A. Carroad, and R. L. Bell, “Estimation of diffusion coefficients of proteins,” Biotechnol. Bioeng. 22(5), 947–955 (1980).
[Crossref]

Chakravarty, S.

S. Chakravarty, A. Hosseini, X. Xu, L. Zhu, Y. Zou, and R. T. Chen, “Analysis of ultra-high sensitivity configuration in chip-integrated photonic crystal microcavity bio-sensors,” Appl. Phys. Lett. 104, 191109 (2014).
[Crossref] [PubMed]

W.-C. Lai, S. Chakravarty, Y. Zou, and R. T. Chen, “Silicon nano-membrane based photonic crystal microcavities for high sensitivity bio-sensing,” Opt. Lett. 37(7), 1208–1210 (2012).
[Crossref] [PubMed]

Chan, L. L.

I. D. Block, L. L. Chan, and B. T. Cunningham, “Photonic crystal optical biosensor incorporating structured low-index porous dielectric,” Sens. and Actuators B 120(1), 187–193 (2006).
[Crossref]

Chang, T.-Y.

Chen, R. T.

S. Chakravarty, A. Hosseini, X. Xu, L. Zhu, Y. Zou, and R. T. Chen, “Analysis of ultra-high sensitivity configuration in chip-integrated photonic crystal microcavity bio-sensors,” Appl. Phys. Lett. 104, 191109 (2014).
[Crossref] [PubMed]

W.-C. Lai, S. Chakravarty, Y. Zou, and R. T. Chen, “Silicon nano-membrane based photonic crystal microcavities for high sensitivity bio-sensing,” Opt. Lett. 37(7), 1208–1210 (2012).
[Crossref] [PubMed]

Chow, E.

Coldren, L. A.

Y.-J. Hung, S.-L. Lee, and L. A. Coldren, “Deep and tapered silicon photonic crystals for achieving anti-reflection and enhanced absorption,” Opt. Express. 18(7), 6841–6852 (2010).
[Crossref] [PubMed]

Combescot, R.

C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James, “Direct calculation of the tunneling current,” J. Phys. C: Solid St. Phys. 4(8), 916–929 (1971).
[Crossref]

Csucs, G.

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A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
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M. Liss, B. Petersen, H. Wolf, and E. Prohaska, “An aptamer-based quartz crystal protein biosensor,” Anal. Chem. 74(17), 4488–4495 (2002).
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M. Liss, B. Petersen, H. Wolf, and E. Prohaska, “An aptamer-based quartz crystal protein biosensor,” Anal. Chem. 74(17), 4488–4495 (2002).
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M. L. Adams, M. Loncar, A. Scherer, and Y. Qiu, “Microfluidic integration of porous photonic crystal nanolasers for chemical sensing,” IEEE J. Sel. Areas Commun. 23(7), 1348–1354 (2005).
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J. Vörös, J. J. Ramsden, G. Csucs, I. Szendrö, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23(17), 3699–3710 (2002).
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R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44(19), 10961–10964 (1991).
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C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James, “Direct calculation of the tunneling current,” J. Phys. C: Solid St. Phys. 4(8), 916–929 (1971).
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Scherer, A.

M. L. Adams, M. Loncar, A. Scherer, and Y. Qiu, “Microfluidic integration of porous photonic crystal nanolasers for chemical sensing,” IEEE J. Sel. Areas Commun. 23(7), 1348–1354 (2005).
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A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
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B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
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M. G. Scullion, T. F. Krauss, and A. Di Falco, “Slotted photonic crystal sensors,” Sensors 13(3), 3675–3710 (2013).
[Crossref] [PubMed]

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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
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G. Peng, U. Tisch, O. Adams, M. Hakim, N. Shehada, Y. Y. Broza, S. Billan, R. Abdah-Bortnyak, A. Kuten, and H. Haick, “Diagnosing lung cancer in exhaled breath using gold nanoparticles,” Nature Nanotech. 4(10), 669–673 (2009).
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V. Pavlov, Y. Xiao, B. Shlyahovsky, and I. Willner, “Aptamer-functionalized Au nanoparticles for the amplified optical detection of thrombin,” J. Am. Chem. Soc. 126(38), 11768–11769 (2004).
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J. Vörös, J. J. Ramsden, G. Csucs, I. Szendrö, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23(17), 3699–3710 (2002).
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Szendrö, I.

J. Vörös, J. J. Ramsden, G. Csucs, I. Szendrö, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23(17), 3699–3710 (2002).
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Textor, M.

J. Vörös, J. J. Ramsden, G. Csucs, I. Szendrö, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23(17), 3699–3710 (2002).
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G. Peng, U. Tisch, O. Adams, M. Hakim, N. Shehada, Y. Y. Broza, S. Billan, R. Abdah-Bortnyak, A. Kuten, and H. Haick, “Diagnosing lung cancer in exhaled breath using gold nanoparticles,” Nature Nanotech. 4(10), 669–673 (2009).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
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J. Vörös, J. J. Ramsden, G. Csucs, I. Szendrö, S. M. De Paul, M. Textor, and N. D. Spencer, “Optical grating coupler biosensors,” Biomaterials 23(17), 3699–3710 (2002).
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B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
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W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
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M. Wilchek, E. A. Bayer, and O. Livnah, “Essentials of biorecognition: the (strept) avidinbiotin system as a model for proteinprotein and proteinligand interaction,” Immun. Lett. 103(1), 27–32 (2006).
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Willner, I.

V. Pavlov, Y. Xiao, B. Shlyahovsky, and I. Willner, “Aptamer-functionalized Au nanoparticles for the amplified optical detection of thrombin,” J. Am. Chem. Soc. 126(38), 11768–11769 (2004).
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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

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M. Liss, B. Petersen, H. Wolf, and E. Prohaska, “An aptamer-based quartz crystal protein biosensor,” Anal. Chem. 74(17), 4488–4495 (2002).
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N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluid. Nanofluid. 4(1), 117–127 (2008).
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V. Pavlov, Y. Xiao, B. Shlyahovsky, and I. Willner, “Aptamer-functionalized Au nanoparticles for the amplified optical detection of thrombin,” J. Am. Chem. Soc. 126(38), 11768–11769 (2004).
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S. Chakravarty, A. Hosseini, X. Xu, L. Zhu, Y. Zou, and R. T. Chen, “Analysis of ultra-high sensitivity configuration in chip-integrated photonic crystal microcavity bio-sensors,” Appl. Phys. Lett. 104, 191109 (2014).
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Figures (18)

Fig. 1
Fig. 1

Illustration of photonic crystal biosensor. The blue regions at the left and right sides are glasses. The surface layers are elliptical shaped to support surface modes. The distance between the center of the surface micro-pillars and the glass is a. The waveguide mode is introduced by a larger micro-pillar with radius 0.445a where a is the center-to-center distance between adjacent micro-pillars. The radius of normal micro-pillars is 0.25a. Adjacent elliptic micro-pillars at the surface have the same semi-minor axis 0.15a, while their semi-major axes are 0.25a and 0.28a, respectively. Three different types of disease markers α, β, and σ are attached to three different analyte binding sites (labeled as “L”, “R”, and “W” in the figure) at the left surface, the right surface, and the central waveguide layer, separately. The length of the photonic crystal in the y direction can be l = 3 (as shown in the figure) or l = 4 (not shown).

Fig. 2
Fig. 2

(a) Band structure of the photonic crystal sensor. The blue shaded regions denote the bulk photonic bands. The red (dashed), green (dotted) and blue (solid) curves in the PBG stand for the waveguide and (two) surface guided modes, separately. The yellow solid line denotes the light line in glass. Period doubling in the x direction folds the region π 2 a < q x π a back to the first Brillouin zone π 2 a < q x π 2 a. As a consequence the surface and waveguide modes originally below the light line are moved to above the light line which are then able to couple to light in glass. Since the structure possess left-right mirror symmetry, the two surface modes form the anti-symmetric (blue curve) and symmetric (green curve) modes, respectively. The field distribution of the waveguide and surface modes are illustrated in (c)–(e). The frequencies of the anti-symmetric surface mode, the symmetric surface mode and the waveguide mode at qx = 0 are 0.2605, 0.2613 and 0.2640 (in unit of 2 π c a) separately. The length of the photonic crystal in the y direction is l = 3.

Fig. 3
Fig. 3

Transmission responses to analyte binding for different binding configurations. The right-most peak is dominated by the central waveguide mode, whereas the central peak arises from the weak-coupling surface mode, and the left-most peak is dominated by the strong-coupling surface mode. (a) When analyte σ is bound to the W site at the central waveguide. (b) When analyte α is bound to the L site at the left surface of the photonic crystal. (c) When analytes α and β bind to the L and R sites at the surfaces with equal thickness. (d) When analytes α and σ bind to both the L and W sites. From red, blue, green to black, the thickness of analyte layer is 0, 0.05a, 0.1a, and 0.15a, respectively. For (a) and (c), the system has mirror symmetry and the strong-coupling (weak-coupling) surface mode is the anti-symmetric (symmetric) combination of the left and right surface modes. In comparison, for (b) and (d), the mirror symmetry is broken, the strong-coupling (weak-coupling) surface mode is no longer the anti-symmetric (symmetric combination of the left and right surface modes, but other mixture of the two. The length of the photonic crystal along the y direction is l = 3.

Fig. 4
Fig. 4

Calculation of transmission using a simplified three-mode Landauer-Büttiker model in the l = 3 chip with a single central waveguide mode. (a) Comparison between Landauer-Büttiker theory (dashed curve) and FDTD calculation (solid curve) for no analyte binding. Parameters are given in the main text. (b) Transmission from the Landauer-Büttiker theory for different analyte binding asymmetries Δℓrωωr (varying ω with ωr fixed). Δℓr = 0 (red), 0.4 (green), 0.8 (black), 1.2 (blue), and 1.6 (cyan) (in unit of 10−3 × (2πc)/a).

Fig. 5
Fig. 5

(a) Illustration of photonic crystal sensor with two central waveguide modes and enlarged unit cell. Four different analyte binding sites are labeled as “L”, “W1”, “W2”, and “R”. The radii of the two enlarged micro-pillars in the middle are r1 = 0.47a (W1) and r2 = 0.455a (W2), respectively. (b) and (c): Electric field Ez distribution of the waveguide and surface modes from plane-wave-expansion calculation for the case with no analyte binding. At qx = 0, the w1 waveguide mode has frequency 0.2591( 2 π c a), the w2 waveguide mode has frequency 0.2628( 2 π c a), the anti-symmetric surface mode has frequency 0.2614( 2 π c a), and the symmetric surface mode has frequency 0.2618( 2 π c a). Note that these frequencies are slightly different from the peak frequencies in the FDTD calculation. The length of the photonic crystal in the y direction is l = 4. The structure is periodically repeated in the x (vertical) direction.

Fig. 6
Fig. 6

Transmission spectra for different analyte binding combinations in the l = 4 photonic crystal biosensor with two central waveguide modes: (a) analyte σ1 is attached to the W1 site (see Fig. 5), (b) analyte σ2 is attached to the W2 site, (c) analyte α and β are attached to the L and R sites at the surfaces with equal thickness, (d) analyte α binds to the L site. The red, blue, green, orange, to black curves in each figure represent different thicknesses of disease markers: (a) 0.025a, 0.05a, 0.075a, and 0.1a; (b) 0.05a, 0.1a, 0.15a, and 0.2a; (c) 0.025a, 0.0375a, 0.05a, 0.0605a, 0.075a, and 0.1a; (d) 0, 0.025a, 0.05a, and 0.1a.

Fig. 7
Fig. 7

Electric field Ez distributions of the (a) central waveguide modes and (b) surface modes (from plane-wave-expansion calculations) for the case with disease marker σ2 binding to the W2 site with thickness 0.2a. At qx = 0, the upper waveguide mode (w1) has frequency 0.2591( 2 π c a), while the lower waveguide mode (w2) has frequency 0.2619( 2 π c a). The anti-symmetric surface mode has frequency 0.2613( 2 π c a), while the symmetric surface mode has frequency 0.2618( 2 π c a). Note that these frequencies are slightly different from the peak frequencies obtained by FDTD simulations.

Fig. 8
Fig. 8

Electric field Ez profiles of the (a) central waveguide modes and (b) surface modes (from plane-wave-expansion calculations) for analyte binding to the L and R sites with equal thickness 0.1a. At qx = 0, the w1 waveguide mode has frequency 0.2590( 2 π c a), the w2 waveguide mode has frequency 0.2628( 2 π c a), the anti-symmetric surface mode has frequency 0.2609( 2 π c a), and the symmetric surface mode has frequency 0.2601( 2 π c a). These frequencies are slightly different from the peak frequencies obtained by FDTD simulation.

Fig. 9
Fig. 9

Transmission responses of different two-analyte binding configurations for the l = 4 biosensor with two central waveguide modes: (a) analytes σ1 and α bind to the W1 and L sites, respectively (b) analytes σ2 and α bind to the W2 and L sites, respectively (c) analytes σ1 and σ2 bind to the W1 and W2 sites, respectively (d) analytes α, σ1, and σ2 bind to the L, W1, and W2 sites, respectively. The red, blue, green, and black curves in each figure represent different thicknesses of disease markers: (a) 0.025a, 0.05a, 0.1a, and 0.15a; (b) 0.025a, 0.05a, 0.1a, and 0.15a; (c) 0.025a, 0.05a, 0.1a, and 0.15a; (d) 0.025a, 0.05a, 0.1a, and 0.15a.

Fig. 10
Fig. 10

Transmission spectra for different three-analyte binding combinations: (a) analytes are bound to all sites with equal thickness, (b) analytes are bound to all except the W2 site with equal thickness, (c) analytes are bound to all except the W1 site with equal thickness. From the red, blue, green, orange, and black curves in each figure represent different thicknesses of disease markers: (a) 0.05a, 0.1a, 0.12675a, 0.15a, and 0.2a; (b) 0.025a, 0.05a, 0.0827a, 0.1a, and 0.15a; (c) 0.025a, 0.05a, 0.0828a, 0.1a, and 0.15a.

Fig. 11
Fig. 11

Electric field Ez distributions of the (a) central waveguide modes and (b) surface modes from plane-wave-expansion calculations for the case with analytes binding to the L, W1, and W2 sites with equal thickness 0.15a. At qx = 0, the upper waveguide mode (w1) has frequency 0.2590( 2 π c a), the lower waveguide mode (w2) has frequency 0.2620( 2 π c a), the left surface mode has frequency 0.2603( 2 π c a), and the right surface mode has frequency 0.2616( 2 π c a). These frequencies are slightly different from the peak frequencies obtained by FDTD simulations.

Fig. 12
Fig. 12

Importance of surface-waveguide coupling is demonstrated via the peak transmittance at the two surface modes when the disease marker α is attached to the left surface (the L binding site) for (a) l = 3 and (b) l = 4 chip. The solid curves (red and blue) are for structures with the (single-mode) central waveguide, whereas the dashed curves (black and green) are for structures without the central waveguide. Curves with • stands for peak transmittance at the lower frequency surface mode, whereas curves with △ represent peak transmittance at the higher frequency surface mode. The vertical axis of (b) is on log-scale.

Fig. 13
Fig. 13

Quantitative transmission spectral signatures of our biosensor with a single central waveguide and l = 4. (a) Resonance frequency of the central waveguide mode vs. analyte thickness for different binding configurations. (b) and (c): resonance frequencies of the strong-coupling surface mode (left peak) and the weak-coupling surface mode (central peak) as functions of analyte thickness. (d) and (e): transmission level of the strong-coupling surface mode and the weak-coupling surface mode as functions of analyte thickness.

Fig. 14
Fig. 14

Quantitative transmission spectral fingerprints of the l = 4 biosensor with two central waveguide modes in response to six different disease marker combinations. Resonance frequency (a) and transmission level (b) of the central waveguide mode w1 as functions of analyte binding thickness for various analyte binding configurations. Note that “W12” in the figure stands for W1+W2, i.e., analytes bind simultaneously to sites W1 and W2. Resonance frequency (c) and transmission level (d) of the surface mode s1 (left-central peak) as functions of analyte thickness. Resonance frequency (e) and peak transmittance (f) of the surface mode s2 (right-central peak) as functions of analyte thickness. Resonance frequency (g) and transmission level (h) of the central waveguide mode w2 as functions of analyte thickness.

Fig. 15
Fig. 15

Quantitative transmission spectral signatures of the l = 4 biosensor with two central waveguide modes in response to further disease marker combinations.

Fig. 16
Fig. 16

Transmission spectral responses in the l = 4 chip with one central waveguide mode, to different disease-marker configurations: (a) disease marker σ attached to the site W, (b) disease marker α bound to the binding site L, (c) disease markers α and β attached to the binding sites L and R with equal thickness, respectively, (d) disease markers α and σ bound to the sites L and W with equal thickness, respectively. Red, blue, green, magenta, and black curves correspond to the thicknesses of the disease marker layers of 0, 0.025a, 0.05a, 0.075a, and 0.1a, respectively.

Fig. 17
Fig. 17

Transmission spectral responses to different disease-marker configurations for photonic crystal biosensor with two central waveguide modes and (reduced) width l = 3 in the y direction: (a) analyte σ1 attached to the W1 site, (b) analyte σ2 attached to the W2 site. Red, blue, green, and black curves in each figure represent different thickness of disease markers: 0, 0.05a, 0.1a, and 0.15a.

Fig. 18
Fig. 18

Transmission spectra from Landauer-Büttiker theory for the l = 3 chip with single central waveguide mode, T(ω) (red) and Ti(ω) [or i(ω)], i = w, , r, for different analyte binding asymmetries Δℓr = 0 (a) and (b), Δℓr = 0.8 × 10−3(2πa/c) (c) and (d), Δℓr = 2 × 10−3(2πa/c) (e) and (f).

Tables (2)

Tables Icon

Table 1 Diagnostic logic table using three disease markers in the l = 3 biosensor with a single central waveguide mode. Changes in peak frequencies and transmittance in response to various analyte-binding configurations are tabulated. The frequency shift of the waveguide mode, Ωw, (right peak), the strong-coupling surface mode, Ωsc, (left peak), and the weak-coupling surface mode, Ωwc, (central peak), together with changes in peak transmission levels, Tsc and Twc, of the latter two surface modes, provide distinct spectral fingerprints of different analyte-binding configurations. The symbol ↓:↑ denotes that peak transmission first decreases then increases.

Tables Icon

Table 2 Logic table for enhanced medical diagnosis using four disease markers in the l = 4 biosensor with two central waveguide modes. Here we show how the peak frequencies and transmission levels change in response to the increase of analyte-layer thickness for the 12 analyte-binding configurations. The leftmost, middle-left, middle-right, and rightmost peaks in the transmission spectrum are denoted as w1, s1, s2, and w2. Their frequencies are denoted as Ωw1, Ωs1, Ωs2, and Ωw2, and their peak transmission levels are denoted as Tw1, Ts1, Ts2, and Tw2. We use the symbol ↓:↑ to represent that the transmission level first decreases then increases.

Equations (9)

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S m δ ω m τ ω m m .
t m ( lim ) η m Q m ,
H ^ = ( ω t r t w t r ω r t r w t w t r w ω w ) ,
H ^ = ( ω AS 0 2 t w 0 ω S 0 2 t w 0 ω w ) ,
Ω w = ω w + 2 | t w | , Ω AS = ω t r 2 | t w | , Ω S = ω + t r ,
T ( ω ) = Tr ( Γ ^ L G ^ r Γ ^ R G ^ a ) .
G ^ r = [ ω H ^ + i 2 ( Γ ^ L + Γ ^ R ) ] 1 , G ^ a = G ^ r .
Γ ^ ν = 2 π ρ ν V ν V ν , ν = L , R
V L , = V R , r , V L , r = V R , , V L , w = V R , w .

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