Abstract

A biomolecular sensor consisting of a thin metallic grating deposited on a glass prism is studied in the formalism of poles and zeros of the scattering matrix. Surface plasmon resonance is used to increase the sensitivity of the device with respect to a variation of the refractive index of the substrate. It is shown that a direct coupling between counter propagating surface plasmons using double-harmonic Fourier gratings leads to an enhancement of the sensitivity. The result of the stronger coupling is the transfer of the working point from the lower to the upper edge of the band gap in the dispersion diagram.

© 2008 Optical Society of America

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  1. E. Kretschmann, "Determination of optical constants of metals by excitation of surface Plasmons," Z. Phys. 241, 313- (1971).
    [CrossRef]
  2. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-402 (1902)
  3. J. J. Cowan and E. T. Arakawa, "Dispersion of surface plasmons in dielectric-metal coatings on concave diffraction gratings," Z. Phys.  235, 97- (1970).
    [CrossRef]
  4. D. Maystre and R. C. McPhedran, "A detailed theoretical study of the anomalies of a sinusoidal diffraction grating," Optica Acta 21, 413-421 (1974).
    [CrossRef]
  5. M. Neviere, "The homogeneous problem," in Electromagnetic theory of gratings, R. Petit ed. (Springer-Verlag, 1980), ch.5
  6. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988)
  7. M. J. Jory, P. S. Vukusic, and J. R. Sambles, "Development of a prototype gas sensor using surface plasmon resonance on gratings," Sens. Actuators B 17, 203-209 (1994).
    [CrossRef]
  8. U. Schroter and D. Heitmann, "Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration," Phys. Rev. B 60, 4992-4999 (1999).
    [CrossRef]
  9. J. Homola, S. S. Yee and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Act. B 54, 3-15 (1999)
    [CrossRef]
  10. F. Pigeon, I. F. Salakhutdinov, A. V. Tishchenko, "Identity of long-range surface plasmons along asymetric structures and their potential for refractometric sensors," J. Appl. Phys. 90, 852-859 (2001)
    [CrossRef]
  11. C. J. Alleyne, A.G. Kirk, R. C. McPhedran, N-A. P. Nicorovici and D. Maystre, "Enhanced SPR sensitivity using periodic metallic structures," Opt. Express 15, 8163-8169 (2007).
    [CrossRef] [PubMed]
  12. D. Maystre, "General study of grating anomalies from electromagnetic surface modes", in Electromagnetic Surface Modes, A.D. Boardman, ed. (John Wiley, 1982), Chap. 17.
  13. M. Breidne and D. Maystre, "A systematic numerical study of Fourier gratings", J. Opt. 13, 71-79 (1982).
    [CrossRef]
  14. J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J.Opt. 11, 235-241 (1980).
    [CrossRef]
  15. L. Li, "Oblique-coordinate-system-based Chandezon method for modeling one-dimensionally periodic, multilayer, inhomogeneous, anisotropic gratings," J. Opt. Soc. Am. 16, 2521-2531 (1999).
    [CrossRef]
  16. D. Maystre and R. Petit, "Brewster incidence for metallic gratings," Opt. Commun. 17, 196-200 (1976).
    [CrossRef]
  17. M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976)
    [CrossRef]
  18. M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, "Chain Length Dependence and Sensing Capabilities of the Localized Surface Plasmon Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol Self-Assembled Monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001).
    [CrossRef]

2007

2001

M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, "Chain Length Dependence and Sensing Capabilities of the Localized Surface Plasmon Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol Self-Assembled Monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001).
[CrossRef]

F. Pigeon, I. F. Salakhutdinov, A. V. Tishchenko, "Identity of long-range surface plasmons along asymetric structures and their potential for refractometric sensors," J. Appl. Phys. 90, 852-859 (2001)
[CrossRef]

1999

U. Schroter and D. Heitmann, "Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration," Phys. Rev. B 60, 4992-4999 (1999).
[CrossRef]

J. Homola, S. S. Yee and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Act. B 54, 3-15 (1999)
[CrossRef]

L. Li, "Oblique-coordinate-system-based Chandezon method for modeling one-dimensionally periodic, multilayer, inhomogeneous, anisotropic gratings," J. Opt. Soc. Am. 16, 2521-2531 (1999).
[CrossRef]

1994

M. J. Jory, P. S. Vukusic, and J. R. Sambles, "Development of a prototype gas sensor using surface plasmon resonance on gratings," Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

1982

M. Breidne and D. Maystre, "A systematic numerical study of Fourier gratings", J. Opt. 13, 71-79 (1982).
[CrossRef]

1980

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J.Opt. 11, 235-241 (1980).
[CrossRef]

1976

D. Maystre and R. Petit, "Brewster incidence for metallic gratings," Opt. Commun. 17, 196-200 (1976).
[CrossRef]

M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976)
[CrossRef]

1974

D. Maystre and R. C. McPhedran, "A detailed theoretical study of the anomalies of a sinusoidal diffraction grating," Optica Acta 21, 413-421 (1974).
[CrossRef]

1971

E. Kretschmann, "Determination of optical constants of metals by excitation of surface Plasmons," Z. Phys. 241, 313- (1971).
[CrossRef]

1970

J. J. Cowan and E. T. Arakawa, "Dispersion of surface plasmons in dielectric-metal coatings on concave diffraction gratings," Z. Phys.  235, 97- (1970).
[CrossRef]

1902

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-402 (1902)

Alleyne, C. J.

Arakawa, E. T.

J. J. Cowan and E. T. Arakawa, "Dispersion of surface plasmons in dielectric-metal coatings on concave diffraction gratings," Z. Phys.  235, 97- (1970).
[CrossRef]

Breidne, M.

M. Breidne and D. Maystre, "A systematic numerical study of Fourier gratings", J. Opt. 13, 71-79 (1982).
[CrossRef]

Chandezon, J.

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J.Opt. 11, 235-241 (1980).
[CrossRef]

Cowan, J. J.

J. J. Cowan and E. T. Arakawa, "Dispersion of surface plasmons in dielectric-metal coatings on concave diffraction gratings," Z. Phys.  235, 97- (1970).
[CrossRef]

Gauglitz, G.

J. Homola, S. S. Yee and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Act. B 54, 3-15 (1999)
[CrossRef]

Heitmann, D.

U. Schroter and D. Heitmann, "Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration," Phys. Rev. B 60, 4992-4999 (1999).
[CrossRef]

Homola, J.

J. Homola, S. S. Yee and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Act. B 54, 3-15 (1999)
[CrossRef]

Hutley, M. C.

M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976)
[CrossRef]

Jory, M. J.

M. J. Jory, P. S. Vukusic, and J. R. Sambles, "Development of a prototype gas sensor using surface plasmon resonance on gratings," Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

Kelly, K. L.

M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, "Chain Length Dependence and Sensing Capabilities of the Localized Surface Plasmon Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol Self-Assembled Monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001).
[CrossRef]

Kirk, A.G.

Kretschmann, E.

E. Kretschmann, "Determination of optical constants of metals by excitation of surface Plasmons," Z. Phys. 241, 313- (1971).
[CrossRef]

Li, L.

L. Li, "Oblique-coordinate-system-based Chandezon method for modeling one-dimensionally periodic, multilayer, inhomogeneous, anisotropic gratings," J. Opt. Soc. Am. 16, 2521-2531 (1999).
[CrossRef]

Malinsky, M. D.

M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, "Chain Length Dependence and Sensing Capabilities of the Localized Surface Plasmon Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol Self-Assembled Monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001).
[CrossRef]

Maystre, D.

C. J. Alleyne, A.G. Kirk, R. C. McPhedran, N-A. P. Nicorovici and D. Maystre, "Enhanced SPR sensitivity using periodic metallic structures," Opt. Express 15, 8163-8169 (2007).
[CrossRef] [PubMed]

M. Breidne and D. Maystre, "A systematic numerical study of Fourier gratings", J. Opt. 13, 71-79 (1982).
[CrossRef]

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J.Opt. 11, 235-241 (1980).
[CrossRef]

D. Maystre and R. Petit, "Brewster incidence for metallic gratings," Opt. Commun. 17, 196-200 (1976).
[CrossRef]

M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976)
[CrossRef]

D. Maystre and R. C. McPhedran, "A detailed theoretical study of the anomalies of a sinusoidal diffraction grating," Optica Acta 21, 413-421 (1974).
[CrossRef]

McPhedran, R. C.

C. J. Alleyne, A.G. Kirk, R. C. McPhedran, N-A. P. Nicorovici and D. Maystre, "Enhanced SPR sensitivity using periodic metallic structures," Opt. Express 15, 8163-8169 (2007).
[CrossRef] [PubMed]

D. Maystre and R. C. McPhedran, "A detailed theoretical study of the anomalies of a sinusoidal diffraction grating," Optica Acta 21, 413-421 (1974).
[CrossRef]

Nicorovici, N-A. P.

Petit, R.

D. Maystre and R. Petit, "Brewster incidence for metallic gratings," Opt. Commun. 17, 196-200 (1976).
[CrossRef]

Pigeon, F.

F. Pigeon, I. F. Salakhutdinov, A. V. Tishchenko, "Identity of long-range surface plasmons along asymetric structures and their potential for refractometric sensors," J. Appl. Phys. 90, 852-859 (2001)
[CrossRef]

Raoult, G.

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J.Opt. 11, 235-241 (1980).
[CrossRef]

Salakhutdinov, I. F.

F. Pigeon, I. F. Salakhutdinov, A. V. Tishchenko, "Identity of long-range surface plasmons along asymetric structures and their potential for refractometric sensors," J. Appl. Phys. 90, 852-859 (2001)
[CrossRef]

Sambles, J. R.

M. J. Jory, P. S. Vukusic, and J. R. Sambles, "Development of a prototype gas sensor using surface plasmon resonance on gratings," Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

Schatz, G. C.

M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, "Chain Length Dependence and Sensing Capabilities of the Localized Surface Plasmon Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol Self-Assembled Monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001).
[CrossRef]

Schroter, U.

U. Schroter and D. Heitmann, "Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration," Phys. Rev. B 60, 4992-4999 (1999).
[CrossRef]

Tishchenko, A. V.

F. Pigeon, I. F. Salakhutdinov, A. V. Tishchenko, "Identity of long-range surface plasmons along asymetric structures and their potential for refractometric sensors," J. Appl. Phys. 90, 852-859 (2001)
[CrossRef]

Van Duyne, R. P.

M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, "Chain Length Dependence and Sensing Capabilities of the Localized Surface Plasmon Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol Self-Assembled Monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001).
[CrossRef]

Vukusic, P. S.

M. J. Jory, P. S. Vukusic, and J. R. Sambles, "Development of a prototype gas sensor using surface plasmon resonance on gratings," Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

Wood, R. W.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-402 (1902)

Yee, S. S.

J. Homola, S. S. Yee and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Act. B 54, 3-15 (1999)
[CrossRef]

J. Am. Chem. Soc.

M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, "Chain Length Dependence and Sensing Capabilities of the Localized Surface Plasmon Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol Self-Assembled Monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001).
[CrossRef]

J. Appl. Phys.

F. Pigeon, I. F. Salakhutdinov, A. V. Tishchenko, "Identity of long-range surface plasmons along asymetric structures and their potential for refractometric sensors," J. Appl. Phys. 90, 852-859 (2001)
[CrossRef]

J. Opt.

M. Breidne and D. Maystre, "A systematic numerical study of Fourier gratings", J. Opt. 13, 71-79 (1982).
[CrossRef]

J. Opt. Soc. Am.

L. Li, "Oblique-coordinate-system-based Chandezon method for modeling one-dimensionally periodic, multilayer, inhomogeneous, anisotropic gratings," J. Opt. Soc. Am. 16, 2521-2531 (1999).
[CrossRef]

J.Opt.

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J.Opt. 11, 235-241 (1980).
[CrossRef]

Opt. Commun.

D. Maystre and R. Petit, "Brewster incidence for metallic gratings," Opt. Commun. 17, 196-200 (1976).
[CrossRef]

M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976)
[CrossRef]

Opt. Express

Optica Acta

D. Maystre and R. C. McPhedran, "A detailed theoretical study of the anomalies of a sinusoidal diffraction grating," Optica Acta 21, 413-421 (1974).
[CrossRef]

Philos. Mag.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-402 (1902)

Phys. Rev. B

U. Schroter and D. Heitmann, "Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration," Phys. Rev. B 60, 4992-4999 (1999).
[CrossRef]

Sens. Act. B

J. Homola, S. S. Yee and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Act. B 54, 3-15 (1999)
[CrossRef]

Sens. Actuators B

M. J. Jory, P. S. Vukusic, and J. R. Sambles, "Development of a prototype gas sensor using surface plasmon resonance on gratings," Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

Z. Phys

J. J. Cowan and E. T. Arakawa, "Dispersion of surface plasmons in dielectric-metal coatings on concave diffraction gratings," Z. Phys.  235, 97- (1970).
[CrossRef]

Z. Phys.

E. Kretschmann, "Determination of optical constants of metals by excitation of surface Plasmons," Z. Phys. 241, 313- (1971).
[CrossRef]

Other

M. Neviere, "The homogeneous problem," in Electromagnetic theory of gratings, R. Petit ed. (Springer-Verlag, 1980), ch.5

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988)

D. Maystre, "General study of grating anomalies from electromagnetic surface modes", in Electromagnetic Surface Modes, A.D. Boardman, ed. (John Wiley, 1982), Chap. 17.

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Figures (13)

Fig. 1.
Fig. 1.

Periodically corrugated prism of refractive index n3 = 1.5 coated by a metallic layer of thickness t (t=40 nm) and refractive index equal to 0.1 + i 5.85, corresponding to silver at a wavelength of 850 nm. Grooves have a sinusoidal geometry with height h1 and period d. The substrate is made of water with refractive index n1 = 1.33 or 1.34.

Fig. 2.
Fig. 2.

Real (a) and imaginary parts (b) of the poles satisfying eq.(1) as a function of h1, for two refractive indices of the substrate 1.33 (blue) and 1.34 (red). Dashed line: surface plasmon excited by the 0th order, full line surface plasmon excited by the −1st order.

Fig. 3.
Fig. 3.

Similar to Fig. 2 with the zeros satisfying Eq.(2).

Fig. 4.
Fig. 4.

Difference between the real parts of the zeros with refractive index of 1.34 and 1.33 as a function of h1 (full black curve with the right scale) with imaginary parts of the zeros associated with the surface plasmon excited by the 0th order (dashed lines with the left scale).

Fig. 5.
Fig. 5.

Reflected efficiency as a function of the angle of incidence θ, with h1=0.017 μm.

Fig. 6.
Fig. 6.

Same as Fig. 1 with a second periodical modulation of height h2.

Fig. 7.
Fig. 7.

Real (a) and imaginary parts (b) of the zeros satisfying eq.(2) as a function of h1, for two refractive index of the substrate 1.33 (blue) and 1.34 (red). Dashed line: surface plasmon excited by the 0th order, full line surface plasmon excited by the −1st order. t = 40 nm and φ = π/2.

Fig. 8.
Fig. 8.

Real (a) and imaginary parts (b) of the zeros satisfying eq.(2) as a function of h, for two refractive indices of the substrate: 1.33 (blue) and 1.34 (red). Zeros are associated with the surface plasmon excited by the 0th order. t=40 nm and φ=π/2.

Fig. 9.
Fig. 9.

Reflected efficiency as a function of the angle of incidence θ. h1=35 nm, h2 = 59 nm, t = 40 nm, φ=π/2.

Fig. 10.
Fig. 10.

Sensitivity of the device per Δn = 1/1000. (a) Change of the reflectivity R at a fixed angle of incidence (the values given in the insert). (b) Change in the incident angle corresponding to the minimum of reflectivity

Fig. 11.
Fig. 11.

Variation of the device performance with 5% error in the groove height. (a) Same as in Fig.9 but for h increased by 5% and t = 50 nm. (b) Position of the angle of minimum reflectivity for the original groove profile (h = 35 nm) and for the profile with h increased by 5% and t = 50 nm

Fig. 12.
Fig. 12.

(a) Colour map dependence of the intensity of the 0th reflected order of a single-harmonic grating with h1 = 20 nm (h2 = 0). Thick blue lines, real part of the constant of propagation of the plasmon surface waves excited on the substrate-metal layer interface. Purple line, working point at λ = 0.85 μm. (b) Imaginary parts of the surface wave propagation constants as a function of ω/c.

Fig. 13.
Fig. 13.

Same as in Fig. 12, but for a double-harmonic grating with h1 = 35 nm, h2 = 59 nm, and φ = π/2.

Equations (5)

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S 1 ( α p ) D = 0 ,
S 0,0 ( α z ) = 0 .
α p λ d = α spp 1 2
α p = α spp 1 2
h ( sin ( 2 π d x ) + 59 35 sin ( 4 π d x π 2 ) ) .

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