Abstract

We have explicated the Goos-Hänchen (GH) shift in a μm-order Kretchmann-Raether configuration embedded in an optical waveguide structure by using the finite-difference time-domain method. For optical waveguide-type surface plasmon resonance (SPR) devices, the precise derivation of the GH shift has become critical. Artmann’s equation, which is accurate enough for bulk optics, is difficult to apply to waveguide-type SPR devices. This is because Artmann's equation, based on the differentiation of the phase shift, is inaccurate at the critical and resonance angles where drastic phase changes occur. In this study, we accurately identified both the positive and the negative GH shifts around the incidence angle of resonance. In a waveguide-type Kretchmann-Raether configuration with an Au thin film of 50 nm, positive and negative lateral shifts of −0.75 and + 1.0 μm are obtained on the SPR with the incident angles of 44.4 ° and 47.5 °, respectively, at a wavelength of 632.8 nm.

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  1. E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).
  2. A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Zeitschrift fur Physik A Hadrons and Nuclei 216, 398–410 (1968).
  3. B. Liedberg, I. Lundstrom, and E. Stenberg, “Principles of biosensing with an extended coupling matrix and surface plasmon resonance,” Sens. Actuators B Chem. 11(1-3), 63–72 (1993).
    [CrossRef]
  4. F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
    [CrossRef]
  5. P. Drude, “Zur Elektronentheorie I/II,” Ann. Phys. 3, 4 (1900).
  6. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
    [CrossRef]
  7. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
    [CrossRef]
  8. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  9. S. K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68(4), 045415 (2003).
    [CrossRef]
  10. H. M. Lai, F. C. Cheng, and W. K. Tang, “Goos-Hänchen effect around and off the critical angle,” J. Opt. Soc. Am. A 3(4), 550–557 (1986).
    [CrossRef]
  11. P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 067603 (2002).
    [CrossRef]
  12. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the goos-Hanchen effect,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7330–7339 (2000).
    [CrossRef]
  13. M. Merano, A. Aiello, G. W. ‘t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15(24), 15928–15934 (2007).
    [CrossRef]

2007 (1)

2003 (1)

S. K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68(4), 045415 (2003).
[CrossRef]

2002 (1)

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 067603 (2002).
[CrossRef]

2000 (1)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the goos-Hanchen effect,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7330–7339 (2000).
[CrossRef]

1993 (1)

B. Liedberg, I. Lundstrom, and E. Stenberg, “Principles of biosensing with an extended coupling matrix and surface plasmon resonance,” Sens. Actuators B Chem. 11(1-3), 63–72 (1993).
[CrossRef]

1986 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1968 (2)

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Zeitschrift fur Physik A Hadrons and Nuclei 216, 398–410 (1968).

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[CrossRef]

1900 (1)

P. Drude, “Zur Elektronentheorie I/II,” Ann. Phys. 3, 4 (1900).

‘t Hooft, G. W.

Aiello, A.

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

Berman, P. R.

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 067603 (2002).
[CrossRef]

Cheng, F. C.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Drude, P.

P. Drude, “Zur Elektronentheorie I/II,” Ann. Phys. 3, 4 (1900).

Eliel, E. R.

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[CrossRef]

Gray, S. K.

S. K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68(4), 045415 (2003).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kretschmann, E.

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Kupka, T.

S. K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68(4), 045415 (2003).
[CrossRef]

Kwok, C. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the goos-Hanchen effect,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7330–7339 (2000).
[CrossRef]

Lai, H. M.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the goos-Hanchen effect,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7330–7339 (2000).
[CrossRef]

H. M. Lai, F. C. Cheng, and W. K. Tang, “Goos-Hänchen effect around and off the critical angle,” J. Opt. Soc. Am. A 3(4), 550–557 (1986).
[CrossRef]

Liedberg, B.

B. Liedberg, I. Lundstrom, and E. Stenberg, “Principles of biosensing with an extended coupling matrix and surface plasmon resonance,” Sens. Actuators B Chem. 11(1-3), 63–72 (1993).
[CrossRef]

Loo, Y. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the goos-Hanchen effect,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7330–7339 (2000).
[CrossRef]

Lundstrom, I.

B. Liedberg, I. Lundstrom, and E. Stenberg, “Principles of biosensing with an extended coupling matrix and surface plasmon resonance,” Sens. Actuators B Chem. 11(1-3), 63–72 (1993).
[CrossRef]

Merano, M.

Otto, A.

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Zeitschrift fur Physik A Hadrons and Nuclei 216, 398–410 (1968).

Raether, H.

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Stenberg, E.

B. Liedberg, I. Lundstrom, and E. Stenberg, “Principles of biosensing with an extended coupling matrix and surface plasmon resonance,” Sens. Actuators B Chem. 11(1-3), 63–72 (1993).
[CrossRef]

Tang, W. K.

van Exter, M. P.

Woerdman, J. P.

Xu, B. Y.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the goos-Hanchen effect,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7330–7339 (2000).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Ann. Phys. (3)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[CrossRef]

P. Drude, “Zur Elektronentheorie I/II,” Ann. Phys. 3, 4 (1900).

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

S. K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: Finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68(4), 045415 (2003).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 067603 (2002).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the goos-Hanchen effect,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7330–7339 (2000).
[CrossRef]

Sens. Actuators B Chem. (1)

B. Liedberg, I. Lundstrom, and E. Stenberg, “Principles of biosensing with an extended coupling matrix and surface plasmon resonance,” Sens. Actuators B Chem. 11(1-3), 63–72 (1993).
[CrossRef]

Z. Naturforsch. A (1)

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Zeitschrift fur Physik A Hadrons and Nuclei (1)

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Zeitschrift fur Physik A Hadrons and Nuclei 216, 398–410 (1968).

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