Abstract

In this paper, we propose a design for a 2D slab photonic crystal (PhC) virus sensor and an associated signal analysis methodology that together enable single-virus detection while rejecting false positives that occur due to non-specific interactions of serum proteins and small molecules with the sensor surface. The slab-PhC design takes advantage of both the optical and geometrical properties of its incorporated structures by physically limiting virus infiltration to only the most sensitive region of the PhC sensor, while allowing simultaneous measurement of both site-selective virus infiltration and non-specific small molecule accumulation across the device. Notably, the proposed sensor transducer is compatible with both standard semiconductor fabrication procedures and lab-on-a-chip style microfluidic delivery systems. 3D finite-difference time-domain electromagnetic field computation results are presented, the outcomes of which indicate that both specific (target) virus capture and non-specific (non-target) binding can be simultaneously measured and discerned from one another. This type of capacity for background-corrected, single-pathogen target detection would provide a new and novel advancement toward sensitive, label-free virus diagnostics.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. M. Zhang, C. Ge, M. Lu, Z. Zhang, and B. T. Cunningham, “A self-referencing biosensor based upon a dual-mode external cavity laser,” Appl. Phys. Lett. 102(21), 213701 (2013).
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2015 (1)

J. E. Baker, R. Sriram, and B. L. Miller, “Two-dimensional photonic crystals for sensitive microscale chemical and biochemical sensing,” Lab Chip 15(4), 971–990 (2015).
[Crossref] [PubMed]

2013 (2)

S. Pal, A. R. Yadav, M. A. Lifson, J. E. Baker, P. M. Fauchet, and B. L. Miller, “Selective virus detection in complex sample matrices with photonic crystal optical cavities,” Biosens. Bioelectron. 44, 229–234 (2013).
[Crossref] [PubMed]

M. Zhang, C. Ge, M. Lu, Z. Zhang, and B. T. Cunningham, “A self-referencing biosensor based upon a dual-mode external cavity laser,” Appl. Phys. Lett. 102(21), 213701 (2013).
[Crossref] [PubMed]

2012 (2)

C. Blaszykowski, S. Sheikh, and M. Thompson, “Surface chemistry to minimize fouling from blood-based fluids,” Chem. Soc. Rev. 41(17), 5599–5612 (2012).
[Crossref] [PubMed]

S. Pal, P. M. Fauchet, and B. L. Miller, “1-D and 2-D photonic crystals as optical methods for amplifying biomolecular recognition,” Anal. Chem. 84(21), 8900–8908 (2012).
[PubMed]

2011 (2)

M. Lundberg, A. Eriksson, B. Tran, E. Assarsson, and S. Fredriksson, “Homogeneous antibody-based proximity extension assays provide sensitive and specific detection of low-abundant proteins in human blood,” Nucleic Acids Res. 39(15), e102 (2011).
[Crossref] [PubMed]

J. A. Carter, S. D. Mehta, M. V. Mungillo, C. C. Striemer, and B. L. Miller, “Analysis of inflammatory biomarkers by Arrayed Imaging Reflectometry,” Biosens. Bioelectron. 26(9), 3944–3948 (2011).
[Crossref] [PubMed]

2010 (4)

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

V. Toccafondo, J. García-Rupérez, M. J. Bañuls, A. Griol, J. G. Castelló, S. Peransi-Llopis, and A. Maquieira, “Single-strand DNA detection using a planar photonic-crystal-waveguide-based sensor,” Opt. Lett. 35(21), 3673–3675 (2010).
[Crossref] [PubMed]

J. García-Rupérez, V. Toccafondo, M. J. Bañuls, J. G. Castelló, A. Griol, S. Peransi-Llopis, and Á. Maquieira, “Label-free antibody detection using band edge fringes in SOI planar photonic crystal waveguides in the slow-light regime,” Opt. Express 18(23), 24276–24286 (2010).
[Crossref] [PubMed]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

2009 (1)

E. Guillermain and P. M. Fauchet, “Multi-channel biodetection via resonant microcavities coupled to a photonic crystal waveguide,” Proc. SPIE 7167, 71670D (2009).
[Crossref]

2008 (1)

2007 (1)

2003 (1)

2001 (2)

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001).
[Crossref]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[Crossref] [PubMed]

1997 (1)

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[Crossref]

Assarsson, E.

M. Lundberg, A. Eriksson, B. Tran, E. Assarsson, and S. Fredriksson, “Homogeneous antibody-based proximity extension assays provide sensitive and specific detection of low-abundant proteins in human blood,” Nucleic Acids Res. 39(15), e102 (2011).
[Crossref] [PubMed]

Azizi, K.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001).
[Crossref]

Baker, J. E.

J. E. Baker, R. Sriram, and B. L. Miller, “Two-dimensional photonic crystals for sensitive microscale chemical and biochemical sensing,” Lab Chip 15(4), 971–990 (2015).
[Crossref] [PubMed]

S. Pal, A. R. Yadav, M. A. Lifson, J. E. Baker, P. M. Fauchet, and B. L. Miller, “Selective virus detection in complex sample matrices with photonic crystal optical cavities,” Biosens. Bioelectron. 44, 229–234 (2013).
[Crossref] [PubMed]

Baker, S. E.

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

Bañuls, M. J.

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Blaszykowski, C.

C. Blaszykowski, S. Sheikh, and M. Thompson, “Surface chemistry to minimize fouling from blood-based fluids,” Chem. Soc. Rev. 41(17), 5599–5612 (2012).
[Crossref] [PubMed]

Bond, T. C.

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

Borel, P. I.

Buriak, J. M.

Buswell, S. C.

Cabrini, S.

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

Carter, J. A.

J. A. Carter, S. D. Mehta, M. V. Mungillo, C. C. Striemer, and B. L. Miller, “Analysis of inflammatory biomarkers by Arrayed Imaging Reflectometry,” Biosens. Bioelectron. 26(9), 3944–3948 (2011).
[Crossref] [PubMed]

Castelló, J. G.

Chang, A. S. P.

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

Cunningham, B. T.

M. Zhang, C. Ge, M. Lu, Z. Zhang, and B. T. Cunningham, “A self-referencing biosensor based upon a dual-mode external cavity laser,” Appl. Phys. Lett. 102(21), 213701 (2013).
[Crossref] [PubMed]

Dhuey, S. D.

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

Eriksson, A.

M. Lundberg, A. Eriksson, B. Tran, E. Assarsson, and S. Fredriksson, “Homogeneous antibody-based proximity extension assays provide sensitive and specific detection of low-abundant proteins in human blood,” Nucleic Acids Res. 39(15), e102 (2011).
[Crossref] [PubMed]

Evoy, S.

Fauchet, P. M.

S. Pal, A. R. Yadav, M. A. Lifson, J. E. Baker, P. M. Fauchet, and B. L. Miller, “Selective virus detection in complex sample matrices with photonic crystal optical cavities,” Biosens. Bioelectron. 44, 229–234 (2013).
[Crossref] [PubMed]

S. Pal, P. M. Fauchet, and B. L. Miller, “1-D and 2-D photonic crystals as optical methods for amplifying biomolecular recognition,” Anal. Chem. 84(21), 8900–8908 (2012).
[PubMed]

E. Guillermain and P. M. Fauchet, “Multi-channel biodetection via resonant microcavities coupled to a photonic crystal waveguide,” Proc. SPIE 7167, 71670D (2009).
[Crossref]

Frandsen, L. H.

Fredriksson, S.

M. Lundberg, A. Eriksson, B. Tran, E. Assarsson, and S. Fredriksson, “Homogeneous antibody-based proximity extension assays provide sensitive and specific detection of low-abundant proteins in human blood,” Nucleic Acids Res. 39(15), e102 (2011).
[Crossref] [PubMed]

García-Rupérez, J.

Ge, C.

M. Zhang, C. Ge, M. Lu, Z. Zhang, and B. T. Cunningham, “A self-referencing biosensor based upon a dual-mode external cavity laser,” Appl. Phys. Lett. 102(21), 213701 (2013).
[Crossref] [PubMed]

Griol, A.

Guillermain, E.

E. Guillermain and P. M. Fauchet, “Multi-channel biodetection via resonant microcavities coupled to a photonic crystal waveguide,” Proc. SPIE 7167, 71670D (2009).
[Crossref]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Jaskorzynska, B.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001).
[Crossref]

Joannopoulos, J.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Johnson, S.

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Karlsson, A.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001).
[Crossref]

Kjems, J.

Kristensen, M.

Létant, S. E.

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

Lifson, M. A.

S. Pal, A. R. Yadav, M. A. Lifson, J. E. Baker, P. M. Fauchet, and B. L. Miller, “Selective virus detection in complex sample matrices with photonic crystal optical cavities,” Biosens. Bioelectron. 44, 229–234 (2013).
[Crossref] [PubMed]

Lu, M.

M. Zhang, C. Ge, M. Lu, Z. Zhang, and B. T. Cunningham, “A self-referencing biosensor based upon a dual-mode external cavity laser,” Appl. Phys. Lett. 102(21), 213701 (2013).
[Crossref] [PubMed]

Lundberg, M.

M. Lundberg, A. Eriksson, B. Tran, E. Assarsson, and S. Fredriksson, “Homogeneous antibody-based proximity extension assays provide sensitive and specific detection of low-abundant proteins in human blood,” Nucleic Acids Res. 39(15), e102 (2011).
[Crossref] [PubMed]

Mandelshtam, V. A.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[Crossref]

Maquieira, A.

Maquieira, Á.

McNab, S.

Mehta, S. D.

J. A. Carter, S. D. Mehta, M. V. Mungillo, C. C. Striemer, and B. L. Miller, “Analysis of inflammatory biomarkers by Arrayed Imaging Reflectometry,” Biosens. Bioelectron. 26(9), 3944–3948 (2011).
[Crossref] [PubMed]

Miller, B. L.

J. E. Baker, R. Sriram, and B. L. Miller, “Two-dimensional photonic crystals for sensitive microscale chemical and biochemical sensing,” Lab Chip 15(4), 971–990 (2015).
[Crossref] [PubMed]

S. Pal, A. R. Yadav, M. A. Lifson, J. E. Baker, P. M. Fauchet, and B. L. Miller, “Selective virus detection in complex sample matrices with photonic crystal optical cavities,” Biosens. Bioelectron. 44, 229–234 (2013).
[Crossref] [PubMed]

S. Pal, P. M. Fauchet, and B. L. Miller, “1-D and 2-D photonic crystals as optical methods for amplifying biomolecular recognition,” Anal. Chem. 84(21), 8900–8908 (2012).
[PubMed]

J. A. Carter, S. D. Mehta, M. V. Mungillo, C. C. Striemer, and B. L. Miller, “Analysis of inflammatory biomarkers by Arrayed Imaging Reflectometry,” Biosens. Bioelectron. 26(9), 3944–3948 (2011).
[Crossref] [PubMed]

Moll, N.

Mungillo, M. V.

J. A. Carter, S. D. Mehta, M. V. Mungillo, C. C. Striemer, and B. L. Miller, “Analysis of inflammatory biomarkers by Arrayed Imaging Reflectometry,” Biosens. Bioelectron. 26(9), 3944–3948 (2011).
[Crossref] [PubMed]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Pal, S.

S. Pal, A. R. Yadav, M. A. Lifson, J. E. Baker, P. M. Fauchet, and B. L. Miller, “Selective virus detection in complex sample matrices with photonic crystal optical cavities,” Biosens. Bioelectron. 44, 229–234 (2013).
[Crossref] [PubMed]

S. Pal, P. M. Fauchet, and B. L. Miller, “1-D and 2-D photonic crystals as optical methods for amplifying biomolecular recognition,” Anal. Chem. 84(21), 8900–8908 (2012).
[PubMed]

Peransi-Llopis, S.

Pocha, M. D.

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

Qiu, M.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001).
[Crossref]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Sheikh, S.

C. Blaszykowski, S. Sheikh, and M. Thompson, “Surface chemistry to minimize fouling from blood-based fluids,” Chem. Soc. Rev. 41(17), 5599–5612 (2012).
[Crossref] [PubMed]

Sirbuly, D. J.

S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
[Crossref]

Skivesen, N.

Sriram, R.

J. E. Baker, R. Sriram, and B. L. Miller, “Two-dimensional photonic crystals for sensitive microscale chemical and biochemical sensing,” Lab Chip 15(4), 971–990 (2015).
[Crossref] [PubMed]

Striemer, C. C.

J. A. Carter, S. D. Mehta, M. V. Mungillo, C. C. Striemer, and B. L. Miller, “Analysis of inflammatory biomarkers by Arrayed Imaging Reflectometry,” Biosens. Bioelectron. 26(9), 3944–3948 (2011).
[Crossref] [PubMed]

Swillo, M.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001).
[Crossref]

Taylor, H. S.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[Crossref]

Têtu, A.

Thompson, M.

C. Blaszykowski, S. Sheikh, and M. Thompson, “Surface chemistry to minimize fouling from blood-based fluids,” Chem. Soc. Rev. 41(17), 5599–5612 (2012).
[Crossref] [PubMed]

Toccafondo, V.

Tran, B.

M. Lundberg, A. Eriksson, B. Tran, E. Assarsson, and S. Fredriksson, “Homogeneous antibody-based proximity extension assays provide sensitive and specific detection of low-abundant proteins in human blood,” Nucleic Acids Res. 39(15), e102 (2011).
[Crossref] [PubMed]

Van, V.

Vlasov, Y.

Wright, V. A.

Yadav, A. R.

S. Pal, A. R. Yadav, M. A. Lifson, J. E. Baker, P. M. Fauchet, and B. L. Miller, “Selective virus detection in complex sample matrices with photonic crystal optical cavities,” Biosens. Bioelectron. 44, 229–234 (2013).
[Crossref] [PubMed]

Zhang, M.

M. Zhang, C. Ge, M. Lu, Z. Zhang, and B. T. Cunningham, “A self-referencing biosensor based upon a dual-mode external cavity laser,” Appl. Phys. Lett. 102(21), 213701 (2013).
[Crossref] [PubMed]

Zhang, Z.

M. Zhang, C. Ge, M. Lu, Z. Zhang, and B. T. Cunningham, “A self-referencing biosensor based upon a dual-mode external cavity laser,” Appl. Phys. Lett. 102(21), 213701 (2013).
[Crossref] [PubMed]

Anal. Chem. (1)

S. Pal, P. M. Fauchet, and B. L. Miller, “1-D and 2-D photonic crystals as optical methods for amplifying biomolecular recognition,” Anal. Chem. 84(21), 8900–8908 (2012).
[PubMed]

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S. E. Baker, M. D. Pocha, A. S. P. Chang, D. J. Sirbuly, S. Cabrini, S. D. Dhuey, T. C. Bond, and S. E. Létant, “Detection of bio-organism simulants using random binding on a defect-free photonic crystal,” Appl. Phys. Lett. 97(11), 113701 (2010).
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J. A. Carter, S. D. Mehta, M. V. Mungillo, C. C. Striemer, and B. L. Miller, “Analysis of inflammatory biomarkers by Arrayed Imaging Reflectometry,” Biosens. Bioelectron. 26(9), 3944–3948 (2011).
[Crossref] [PubMed]

S. Pal, A. R. Yadav, M. A. Lifson, J. E. Baker, P. M. Fauchet, and B. L. Miller, “Selective virus detection in complex sample matrices with photonic crystal optical cavities,” Biosens. Bioelectron. 44, 229–234 (2013).
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J. E. Baker, R. Sriram, and B. L. Miller, “Two-dimensional photonic crystals for sensitive microscale chemical and biochemical sensing,” Lab Chip 15(4), 971–990 (2015).
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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, (2008).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic representation of simulated slab-PhC sensor design, including the patterned top oxide and device layers, supported by a planar buried oxide layer. (b) Electromagnetic field profiles for the optical mode resonance used for sensing. Cross sections are taken at the center plane of the high-RI device layer and demonstrate that the field strength is localized in and around the large-hole defect of PhC. Because of required periodic boundary conditions for the method, the W1 waveguide was not included in the geometry for frequency-domain computation. The waveguide was included for FDTD calculations.
Fig. 2
Fig. 2 Dispersion diagram (left) and optical transmission spectrum (right) for the slab-PhC sensor design, as computed using FDTD methods.
Fig. 3
Fig. 3 Various infiltration schemes of material into the slab-PhC sensor (a-d) for which optical spectra (e,f) were simulated using FDTD methods. (a-d) The green sphere in the large-hole defect represents a virus-like particle with radius of 0.3a, the smallest particle for which infiltration into non-lattice PhC holes cannot occur. Orange cylindrical shells represent an aggregated layer of bound small-molecules (thickness of a/50). (e) The shift in frequency for the optical resonance that is localized to the large-defect structure depends on both particle infiltration and small-molecule accumulation. (f) The high-frequency band edge shifts due to the presence of an accumulated material monolayer, but is insensitive to the presence of the virus particle in the large-hole defect.
Fig. 4
Fig. 4 Dependence of features in the optical transmission spectrum on infiltration schemes within the slab-PhC sensor. Monolayer thickness and particle infiltration arrangements correspond to the schematic images in Fig. 3(a-d). Arrows on the inset graphs show where minima/maxima are selected. (a) Frequencies for the optical mode localized to the large-hole PhC defect. (b) Frequencies of the trough and peak spectrum features found in the high-frequency transmission band edge. The two features exhibit the same trend; both are shown to demonstrate flexibility in the selection of the band-edge feature. (a,b) Dashed lines indicate polynomial fits to each data set (R2 = 1).
Fig. 5
Fig. 5 Dispersion diagrams corresponding to different monolayer thicknesses on the sidewalls of PhC lattice holes. Note that the lower boundary of the low-RI dielectric band is the feature most strongly affected by monolayer accumulation.

Equations (3)

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Δf f 1 2 d 3 r Δε(r) | E(r) | 2 d 3 r ε(r) | E(r) | 2 Δn n ( fraction of ε | E | 2 in perturbed region )
Δ f be = j=1 c j x j = c 1 x+ c 2 x 2 +
Δ f def =my+ k=1 d k x k =my+ d 1 x+ d 2 x 2 +

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