Abstract

We show that geometrical models may provide useful information on light propagation in wavelength-scale structures even if evanescent fields are present. We apply a so-called local plane-wave and local plane-interface methods to study a geometry that resembles a scanning near-field microscope. We show that fair agreement between the geometrical approach and rigorous electromagnetic theory can be achieved in the case where evanescent waves are required to predict any transmission through the structure.

© 2015 Optical Society of America

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References

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    [Crossref]
  4. A. v. Pfeil and F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).
    [Crossref]
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    [Crossref]
  6. G. J. Swanson, “Binary optics technology: theoretical limits of the diffraction efficiency of multilevel diffractive optical elements,” MIT Tech. Rep.914 (MIT, 1991).
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2009 (1)

2008 (1)

2006 (1)

2003 (1)

H. Lajunen, J. Tervo, J. Turunen, T. Vallius, and F. Wyrowski, “Simulation of light propagation by local spherical interface approximation,” App. Opt. 42, 6804–6810 (2003).
[Crossref]

2001 (1)

2000 (2)

A. v. Pfeil, F. Wyrowski, A. Drauschke, and H. Aagedal, “Analysis of optical elements with the local plane-interface approximation,” Appl. Opt. 39, 3304–3313 (2000).
[Crossref]

A. v. Pfeil and F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).
[Crossref]

1994 (1)

1993 (1)

1991 (1)

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Aagedal, H.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Brunner, R.

Cao, Q.

Chavel, P.

Cozens, J.

R. Syms and J. Cozens, Optical Guided Waves and Devices (McGraw-Hill, 1992).

Drauschke, A.

Fang, Z.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Goudail, F.

Grann, E. B.

Hugonin, J. P.

Ichikawa, H.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Kuang, D.

Lajunen, H.

H. Lajunen, J. Tervo, J. Turunen, T. Vallius, and F. Wyrowski, “Simulation of light propagation by local spherical interface approximation,” App. Opt. 42, 6804–6810 (2003).
[Crossref]

Lalanne, P.

Miller, J. M.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Moharam, M. G.

Moulin, G.

Noponen, E.

E. Noponen, J. Turunen, and A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[Crossref]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Pätz, D.

Pfeil, A. v.

A. v. Pfeil and F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).
[Crossref]

A. v. Pfeil, F. Wyrowski, A. Drauschke, and H. Aagedal, “Analysis of optical elements with the local plane-interface approximation,” Appl. Opt. 39, 3304–3313 (2000).
[Crossref]

Pommet, D. A.

Ruoff, J.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[Crossref]

Sandfuchs, O.

Silberstein, E.

Sinzinger, S.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: theoretical limits of the diffraction efficiency of multilevel diffractive optical elements,” MIT Tech. Rep.914 (MIT, 1991).

Syms, R.

R. Syms and J. Cozens, Optical Guided Waves and Devices (McGraw-Hill, 1992).

Taghizadeh, M. R.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[Crossref]

Tervo, J.

H. Lajunen, J. Tervo, J. Turunen, T. Vallius, and F. Wyrowski, “Simulation of light propagation by local spherical interface approximation,” App. Opt. 42, 6804–6810 (2003).
[Crossref]

Turunen, J.

H. Lajunen, J. Tervo, J. Turunen, T. Vallius, and F. Wyrowski, “Simulation of light propagation by local spherical interface approximation,” App. Opt. 42, 6804–6810 (2003).
[Crossref]

E. Noponen, J. Turunen, and A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[Crossref]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Vallius, T.

H. Lajunen, J. Tervo, J. Turunen, T. Vallius, and F. Wyrowski, “Simulation of light propagation by local spherical interface approximation,” App. Opt. 42, 6804–6810 (2003).
[Crossref]

Vasara, A.

E. Noponen, J. Turunen, and A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[Crossref]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Wang, H.

Westerholm, J.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Wyrowski, F.

H. Lajunen, J. Tervo, J. Turunen, T. Vallius, and F. Wyrowski, “Simulation of light propagation by local spherical interface approximation,” App. Opt. 42, 6804–6810 (2003).
[Crossref]

A. v. Pfeil and F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).
[Crossref]

A. v. Pfeil, F. Wyrowski, A. Drauschke, and H. Aagedal, “Analysis of optical elements with the local plane-interface approximation,” Appl. Opt. 39, 3304–3313 (2000).
[Crossref]

App. Opt. (1)

H. Lajunen, J. Tervo, J. Turunen, T. Vallius, and F. Wyrowski, “Simulation of light propagation by local spherical interface approximation,” App. Opt. 42, 6804–6810 (2003).
[Crossref]

Appl. Opt. (1)

J. Mod. Opt. (1)

A. v. Pfeil and F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).
[Crossref]

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, and J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[Crossref]

Opt. Lett. (1)

Other (5)

G. J. Swanson, “Binary optics technology: theoretical limits of the diffraction efficiency of multilevel diffractive optical elements,” MIT Tech. Rep.914 (MIT, 1991).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

R. Syms and J. Cozens, Optical Guided Waves and Devices (McGraw-Hill, 1992).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[Crossref]

Supplementary Material (1)

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Figures (9)

Fig. 1
Fig. 1 The geometry involving the generation of an evanescent field on top of the substrate and detection with a wedge-shaped core of a waveguide.
Fig. 2
Fig. 2 Geometrical model of the propagation of an evanescent wave into and inside the wedge, and coupling into the waveguide along a typical ray path ABCDE.
Fig. 3
Fig. 3 Computational box showing the quantization of the wedge region into J layers and the computational period d.
Fig. 4
Fig. 4 Distributions of magnetic field amplitude inside the structure for several combinations of the wedge angle α and core width 2a. Media 1 illustrates the temporal evolution of the real field within the structure. Here λ = 633 nm, n = 1.4569, θ = 44.91°, n1 = 1.52, and n2 = 1.49.
Fig. 5
Fig. 5 Normalized coupling efficiency into the fundamental mode of a single-mode waveguide with 2a = 1000 nm as a function of the wedge angle α. Solid black: FMM calculation. Solid blue: overlap integral method based on LPIA. Arrow: optimum angle given by the phase matching condition.
Fig. 6
Fig. 6 Same as Fig. 5, but for a two-mode waveguide with 2a = 1600 nm. (a) Fundamental mode m = 0. (b) First antisymmetric mode m = 1.
Fig. 7
Fig. 7 Same as Fig. 5, but for a three-mode waveguide with 2a = 2200 nm. (a) Fundamental mode m = 0. (b) First antisymmetric mode m = 1. (c) Second symmetric mode m = 2.
Fig. 8
Fig. 8 Observation of evanescent-wave interference patterns. Red circles: magnetic-field intensity given by Eq. (12). Normalized coupling efficiencies given by FMM (black crosses) and LPIA (solid blue) into (a) the fundamental mode m = 0 with α = 40° and (b) the antisymmetric mode m = 1 with α = 42°.
Fig. 9
Fig. 9 Ray propagation model inside the wedge.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

H y ( x , z ) = exp ( i k x x ) exp ( k z z ) ,
H y ( z ) = exp [ k z ( z h ) ] .
H 1 ( x ) = H 0 T ( α ) R S exp [ κ ( x x 0 ) ] exp [ i K x ( x x 0 ) ] ,
H 0 = exp ( k z h ) ,
κ = k z S ,
S = d z d x = cos α cos γ sin ( 3 α γ )
x 0 = H tan ϕ ,
ϕ = 3 α γ π / 2 .
K x = k 0 n 1 cos ( 3 α γ ) = k 0 n 1 sin ϕ
η = | H 1 ( x ) H 2 * ( x ) d x | 2 | H 1 ( x ) | 2 d x | H 2 ( x ) | 2 d x .
η = 2 k z C 2 | x 0 a H 1 ( x ) H 2 * ( x ) d x | 2 | H 2 ( x ) | 2 d x
I exp ( 2 k z z ) cos 2 ( k x x ) .
b = ( H + h z ) tan α ,
f = ( z h ) sec α .
ϕ = 3 α γ π / 2 .
x = c cos ( α γ ) d cos ( 3 α γ ) ( z h ) tan α
f sin ( 2 α ) = c cos ( 2 α γ ) ,
H = ( z h ) + c sin ( α γ ) + d sin ( 3 α γ ) .
c = ( z h ) sin ( 2 α ) cos α cos ( 2 α γ ) .
d = H ( z h ) cos γ sec ( 2 α γ ) sin ( 3 α γ ) .
x = ( z h ) cos γ cos α sin ( 3 α γ ) H cot ( 3 α γ )
( z h ) = cos α cos γ [ x sin ( 3 α γ ) + H cos ( 3 α γ ) ] .
c + d = ( z h ) sin ( 2 α ) cos α cos ( 2 α γ ) + H ( z h ) cos γ sec ( 2 α γ ) sin ( 3 α γ ) .
φ ( x ) = x k 0 n 1 cos ( 3 α γ ) = x k 0 n 1 sin ϕ .

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