Abstract

Sensing schemes based on Rayleigh anomalies (RAs) in metal nanogratings exhibit an impressive bulk refractive-index sensitivity determined solely by the grating period. However, the surface sensitivity (which is a key figure of merit for label-free chemical and biological sensing) needs to be carefully investigated to assess the actual applicability of this technological platform. In this paper, we explore the sensitivity of RAs in metal nanogratings when local refractive-index changes are considered. Our studies reveal that the surface sensitivity deteriorates up to two orders of magnitude by comparison with the corresponding bulk value; interestingly, this residual sensitivity is not attributable to the wavelength shift of the RAs, which are completely insensitive to local refractive-index changes, but rather to a strictly connected plasmonic effect. Our analysis for increasing overlay thickness reveals an ultimate surface sensitivity that approaches the RA bulk value, which turns out to be the upper-limit of grating-assisted surface-plasmon-polariton sensitivities

© 2013 OSA

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  2. L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag.14, 60–65 (1907).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2012

S. Feng, S. Darmawi, T. Henning, P. J. Klar, and X. Zhang, “A miniaturized sensor consisting of concentric metallic nanorings on the end facet of an optical fiber,” Small8(12), 1937–1944 (2012).
[CrossRef] [PubMed]

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

2011

K. M. Mayer and J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev.111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

2009

2008

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]

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

2007

2003

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B67(8), 085415 (2003).
[CrossRef]

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B68(20), 205103 (2003).
[CrossRef]

1998

1995

1965

1941

1907

L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag.14, 60–65 (1907).

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond.79(532), 399–416 (1907).
[CrossRef]

1902

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag.4, 269–275 (1902).

Aguirre, C. M.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B68(20), 205103 (2003).
[CrossRef]

Anderton, C. R.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

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]

Borriello, A.

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

Consales, M.

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

Crescitelli, A.

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

Cusano, A.

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

Cutolo, A.

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

Darmawi, S.

S. Feng, S. Darmawi, T. Henning, P. J. Klar, and X. Zhang, “A miniaturized sensor consisting of concentric metallic nanorings on the end facet of an optical fiber,” Small8(12), 1937–1944 (2012).
[CrossRef] [PubMed]

Djurišic, A. B.

Elazar, J. M.

Esposito, E.

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

Fano, U.

Feng, S.

S. Feng, S. Darmawi, T. Henning, P. J. Klar, and X. Zhang, “A miniaturized sensor consisting of concentric metallic nanorings on the end facet of an optical fiber,” Small8(12), 1937–1944 (2012).
[CrossRef] [PubMed]

Galdi, V.

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

Gao, H.

Gaylord, T. K.

Giordano, M.

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

Granata, C.

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

Grann, E. B.

Gray, S. K.

Hafner, J. H.

K. M. Mayer and J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev.111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

Halas, N. J.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B68(20), 205103 (2003).
[CrossRef]

Hall, W. P.

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]

Henning, T.

S. Feng, S. Darmawi, T. Henning, P. J. Klar, and X. Zhang, “A miniaturized sensor consisting of concentric metallic nanorings on the end facet of an optical fiber,” Small8(12), 1937–1944 (2012).
[CrossRef] [PubMed]

Henzie, J.

Hessel, A.

Klar, P. J.

S. Feng, S. Darmawi, T. Henning, P. J. Klar, and X. Zhang, “A miniaturized sensor consisting of concentric metallic nanorings on the end facet of an optical fiber,” Small8(12), 1937–1944 (2012).
[CrossRef] [PubMed]

Lee, A.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B68(20), 205103 (2003).
[CrossRef]

Lee, M. H.

Lyandres, O.

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]

Majewski, M. L.

Malachovská, V.

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

Maria, J.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Mayer, K. M.

K. M. Mayer and J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev.111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

McMahon, J. M.

Moharam, M. G.

Moran, C. E.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B68(20), 205103 (2003).
[CrossRef]

Nuzzo, R. G.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Odom, T. W.

Oliner, A. A.

Pilla, P.

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

Pommet, D. A.

Rakic, A. D.

Rayleigh, L.

L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag.14, 60–65 (1907).

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond.79(532), 399–416 (1907).
[CrossRef]

Ricciardi, A.

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

Rogers, J. A.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Ruvo, M.

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

Sandomenico, A.

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

Sarrazin, M.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B67(8), 085415 (2003).
[CrossRef]

Schatz, G. C.

Shah, N. C.

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]

Steele, J. M.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B68(20), 205103 (2003).
[CrossRef]

Stewart, M. E.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Thompson, L. B.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Van Duyne, R. P.

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]

Vigneron, J. P.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B67(8), 085415 (2003).
[CrossRef]

Vigoureux, J. M.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B67(8), 085415 (2003).
[CrossRef]

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag.4, 269–275 (1902).

Zhang, X.

S. Feng, S. Darmawi, T. Henning, P. J. Klar, and X. Zhang, “A miniaturized sensor consisting of concentric metallic nanorings on the end facet of an optical fiber,” Small8(12), 1937–1944 (2012).
[CrossRef] [PubMed]

Zhao, J.

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]

Adv. Funct. Mater.

A. Crescitelli, A. Ricciardi, M. Consales, E. Esposito, C. Granata, V. Galdi, A. Cutolo, and A. Cusano, “Nanostructured metallo-dielectric quasi-crystals: Towards photonic-plasmonic resonance engineering,” Adv. Funct. Mater.22(20), 4389–4398 (2012).
[CrossRef]

Appl. Opt.

Biosens. Bioelectron.

P. Pilla, A. Sandomenico, V. Malachovská, A. Borriello, M. Giordano, A. Cutolo, M. Ruvo, and A. Cusano, “A protein-based biointerfacing route toward label-free immunoassays with long period gratings in transition mode,” Biosens. Bioelectron.31(1), 486–491 (2012).
[CrossRef] [PubMed]

Chem. Rev.

K. M. Mayer and J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev.111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nat. Mater.

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]

Opt. Express

Philos. Mag.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag.4, 269–275 (1902).

L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag.14, 60–65 (1907).

Phys. Rev. B

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B68(20), 205103 (2003).
[CrossRef]

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B67(8), 085415 (2003).
[CrossRef]

Proc. R. Soc. Lond.

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond.79(532), 399–416 (1907).
[CrossRef]

Small

S. Feng, S. Darmawi, T. Henning, P. J. Klar, and X. Zhang, “A miniaturized sensor consisting of concentric metallic nanorings on the end facet of an optical fiber,” Small8(12), 1937–1944 (2012).
[CrossRef] [PubMed]

Other

D. Maystre, “Theory of Wood’s anomalies,” in Plasmonics, S. Enoch and N. Bonod, eds. (Springer, 2012), pp. 39–83.

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Figures (9)

Fig. 1
Fig. 1

Schematic of the hybrid metallo-dielectric 1-D nanograting (cross section view) considered in the experimental study, consisting of a gold film of thickness t Au =30nm (yellow layers) deposited on a 1-D patterned ZEP layer of thickness t ZEP =370nm and RI n ZEP =1.54 with period Λ=1500nm and DC=w/Λ =0.25 (light grey layers), backed by a silicon substrate ( n s =3.4 ). Dielectric (SiO2, n d =1.45 ) overlays (red layers) of thickness t d =30nm and 60nm are deposited on the top surface of the nanograting in order to estimate its surface sensitivity. Also shown is the unit cell considered in the numerical simulations, as well as the illumination from air.

Fig. 2
Fig. 2

SEM image (top view) of the fabricated device, with indication of its period Λ=1.5μm . The inset shows a magnified view and the widths of the ridges (380 nm) and grooves (1.12μm).

Fig. 3
Fig. 3

Comparison among measured (solid curves with markers) and numerical (dashed curves with markers) reflectivity spectra pertaining to the device in Figs. 1 and 2, for different values of thickness t d of the SiO2 overlay ( n d =1.45 ): t d =0 (i.e., no overlay; black curves with circles), t d =30nm (red curves with squares), and t d =60nm (blue curves with triangles).

Fig. 4
Fig. 4

Schematic of the sensor configuration considered in the numerical study, constituted by a linear gold (RI = n Au , yellow layers) grating in the x,z plane, with period Λ=900nm , thickness t Au =30nm , and DC=w/Λ , laid on a fused-silica ( n s =1.45 ) substrate. A dielectric-analyte ( n d =1.33 , red layers) overlay of thickness t d , surrounded by air (RI = 1), is assumed. Also shown is the unit cell considered in the numerical simulations, as well as the illumination from the substrate.

Fig. 5
Fig. 5

(a) Numerical reflectivity spectra (magnified in the inset) pertaining to the device in Fig. 4, with DC=0.35 , and for different values of thickness t d of the dielectric ( n d =1.33 ) overlay: t d =0 (i.e., no overlay; black curves), t d =10nm (red curves), and t d =20nm (blue curves). The responses are obtained by averaging those pertaining to the TM and TE polarizations, shown separately in (b) and (c), respectively.

Fig. 6
Fig. 6

(a), (d) Reflectivity spectra (TM polarization) pertaining to the device in Fig. 4, with DC=0.35 , in the absence and presence of a dielectric ( n d =1.33 ) overlay of thickness t d =150nm , respectively. (b), (c) Numerically-computed electric-field (z-component) magnitude maps within a unit cell, in the absence of the overlay, at wavelengths 900nm and 926 nm, respectively. (e), (f) Same of (b), (c), but in the presence of the overlay, at wavelengths 900 nm and 1010 nm, respectively. The thick horizontal line indicates the gold metallization at the interface between the substrate ( z<0 ) and analyte ( z>0 ) regions.

Fig. 7
Fig. 7

Numerical surface sensitivity [estimated via Eq. (3)] pertaining to the device in Fig. 4, as a function of the thickness t d of the dielectric ( n d =1.33 ) overlay, for different DC values: DC = 0.35 (circles), DC = 0.45 (triangles), and DC = 0.55 (squares).

Fig. 8
Fig. 8

Reflectivity spectra contour plot (TM polarization) of the structure in Fig. 5 for a dielectric ( n d =1.33 ) with thickness t d varying within the range 0-3 μm. The white-dashed reference line corresponds to λ R,d ( 1 ) = n d Λ=1197nm .

Fig. 9
Fig. 9

Numerical surface sensitivity [estimated via Eq. (3)] pertaining to the device in Fig. 4, with DC=0.35 , as a function of the thickness t d of the dielectric ( n d =1.33 ) overlay. The dashed horizontal line corresponds to the theoretical bulk-sensitivity limit S t =Λ=900 nm / RIU .

Tables (1)

Tables Icon

Table 1 Numerical and experimental surface sensitivities [estimated via Eq. (3)] pertaining to the device in Figs. 1 and 2, for two values of thickness of the SiO2 overlay. Also given, as a reference, is the theoretical estimate of the bulk (i.e., td → ∞) sensitivity [cf. Eq. (2)].

Equations (3)

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λ R ( m ) = Λ n a ( sin θ i ±1 ) m ,m=±1,±2,...,
S t = λ R,d ( 1 ) λ R,air ( 1 ) n d 1 =Λ=1500( nm / RIU ),
S= λ d ( peak ) λ air ( peak ) n d 1 ( nm / RIU ),

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