Abstract

We present a productive method of designing specific diffraction gratings that ensure some predetermined energy redistributions between outgoing waves. It is based on the analytical solution of the direct and reverse diffraction problems under surface plasmon-polariton resonance and is supported by strict numerical calculations.

© 2011 Optical Society of America

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References

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  1. R. W. Wood, Proc. Phys. Soc. London 18, 269 (1902).
    [CrossRef]
  2. R. W. Wood, Phys. Rev. 48, 928 (1935).
    [CrossRef]
  3. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  4. M. Neviere and E. Popov, Light Propagation in Periodic Media. Differential Theory and Design (Marcel Dekker, 2003).
  5. A. V. Kats, P. D. Pavitskii, and I. S. Spevak, Radiophys. Quantum Electron. 35, 163 (1992).
    [CrossRef]
  6. A. V. Kats, P. D. Pavitskii, and I. S. Spevak, JETP 78, 42(1994).
  7. A. V. Kats and I. S. Spevak, Phys. Rev. B 65, 195406 (2002).
    [CrossRef]
  8. A. V. Kats, I. S. Spevak, and N. A. Balakhonova, Phys. Rev. B 76, 075407 (2007).
    [CrossRef]
  9. I. S. Spevak, A. Yu. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, Phys. Rev. B 79, 161406(R) (2009).
    [CrossRef]
  10. L. Li, J. Chandezon, G. Granet, and J.-P. Plumey, Appl. Opt. 38, 304 (1999).
    [CrossRef]
  11. S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 77, 075401 (2008).
    [CrossRef]

2009 (1)

I. S. Spevak, A. Yu. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, Phys. Rev. B 79, 161406(R) (2009).
[CrossRef]

2008 (1)

S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

2007 (1)

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, Phys. Rev. B 76, 075407 (2007).
[CrossRef]

2002 (1)

A. V. Kats and I. S. Spevak, Phys. Rev. B 65, 195406 (2002).
[CrossRef]

1999 (1)

1994 (1)

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, JETP 78, 42(1994).

1992 (1)

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, Radiophys. Quantum Electron. 35, 163 (1992).
[CrossRef]

1935 (1)

R. W. Wood, Phys. Rev. 48, 928 (1935).
[CrossRef]

1902 (1)

R. W. Wood, Proc. Phys. Soc. London 18, 269 (1902).
[CrossRef]

Balakhonova, N. A.

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, Phys. Rev. B 76, 075407 (2007).
[CrossRef]

Bezuglyi, E. V.

I. S. Spevak, A. Yu. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, Phys. Rev. B 79, 161406(R) (2009).
[CrossRef]

Chandezon, J.

Garcia-Vidal, F. J.

S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

Granet, G.

Kats, A. V.

I. S. Spevak, A. Yu. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, Phys. Rev. B 79, 161406(R) (2009).
[CrossRef]

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, Phys. Rev. B 76, 075407 (2007).
[CrossRef]

A. V. Kats and I. S. Spevak, Phys. Rev. B 65, 195406 (2002).
[CrossRef]

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, JETP 78, 42(1994).

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, Radiophys. Quantum Electron. 35, 163 (1992).
[CrossRef]

Levchenko, A.

I. S. Spevak, A. Yu. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, Phys. Rev. B 79, 161406(R) (2009).
[CrossRef]

Li, L.

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Martin-Moreno, L.

S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

Neviere, M.

M. Neviere and E. Popov, Light Propagation in Periodic Media. Differential Theory and Design (Marcel Dekker, 2003).

Nikitin, A. Yu.

I. S. Spevak, A. Yu. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, Phys. Rev. B 79, 161406(R) (2009).
[CrossRef]

Pavitskii, P. D.

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, JETP 78, 42(1994).

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, Radiophys. Quantum Electron. 35, 163 (1992).
[CrossRef]

Plumey, J.-P.

Popov, E.

M. Neviere and E. Popov, Light Propagation in Periodic Media. Differential Theory and Design (Marcel Dekker, 2003).

Rodrigo, S. G.

S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

Spevak, I. S.

I. S. Spevak, A. Yu. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, Phys. Rev. B 79, 161406(R) (2009).
[CrossRef]

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, Phys. Rev. B 76, 075407 (2007).
[CrossRef]

A. V. Kats and I. S. Spevak, Phys. Rev. B 65, 195406 (2002).
[CrossRef]

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, JETP 78, 42(1994).

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, Radiophys. Quantum Electron. 35, 163 (1992).
[CrossRef]

Wood, R. W.

R. W. Wood, Phys. Rev. 48, 928 (1935).
[CrossRef]

R. W. Wood, Proc. Phys. Soc. London 18, 269 (1902).
[CrossRef]

Appl. Opt. (1)

JETP (1)

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, JETP 78, 42(1994).

Phys. Rev. (1)

R. W. Wood, Phys. Rev. 48, 928 (1935).
[CrossRef]

Phys. Rev. B (4)

A. V. Kats and I. S. Spevak, Phys. Rev. B 65, 195406 (2002).
[CrossRef]

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, Phys. Rev. B 76, 075407 (2007).
[CrossRef]

I. S. Spevak, A. Yu. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, Phys. Rev. B 79, 161406(R) (2009).
[CrossRef]

S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

Proc. Phys. Soc. London (1)

R. W. Wood, Proc. Phys. Soc. London 18, 269 (1902).
[CrossRef]

Radiophys. Quantum Electron. (1)

A. V. Kats, P. D. Pavitskii, and I. S. Spevak, Radiophys. Quantum Electron. 35, 163 (1992).
[CrossRef]

Other (2)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

M. Neviere and E. Popov, Light Propagation in Periodic Media. Differential Theory and Design (Marcel Dekker, 2003).

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Figures (2)

Fig. 1
Fig. 1

Example of the resonance diffraction in the simplest geometry. (a) General view; the plane of incidence is perpendicular to the grating grooves. (b) Geometry of the “forward” resonance in the 1st diffraction order. Propagating waves correspond to the specular one, 1 st and 2 nd diffraction orders. (c) Geometry of the r = 2 “backward” resonance diffraction.

Fig. 2
Fig. 2

Spectral dependencies of energy fluxes s N and squared magnitude of the resonance wave | h r | 2 : dashed (solid) curves correspond to analytical (numerical) calculations. (a) Case 1: r = + 1 resonance, TSSR, s 0 , min = 0 , accompanied by equipartition between nonspecular propagating waves, s 1 , max = s 2 , max = 0.3 . (b) Case 2: r = 2 resonance, TSSR, s 0 , min = 0 , with channeling of the half of the incident energy into 1 st-order diffracted wave, s 1 , max = 0.5 , s 1 = 0 . Corresponding grating profiles ζ ( x ) are shown in the insets.

Equations (15)

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z = ζ ( x ) = n ζ n exp ( i n g x ) , ζ n = ζ n * , ζ 0 = 0 ,
H ( x , z ) = e y n = n = h n exp [ i k ( α n x + β n z ) ] , z ζ ( x ) ,
n D m n h n = V m ,
D m n = δ m , n ( β n + ξ ) ν m n ,
V m = δ m , 0 ( β 0 ξ ) + ν m 0 ,
ν m n = i k ( 1 α m α n ) ζ m n , ν n m = ν m n * ,
k 0 x + r g = ± | q spp | , q spp = k 1 + ( ξ ) 2 .
{ N D M N h N + D M r h r = V M , M r , D r r h r + N D r N h N = V r .
h r ( 1 + R ) ν r 0 ( β 0 + ξ ) ( β r + ξ + Γ r ) ,
h N δ N , 0 R + ν N 0 β N + ξ + ν N r h r β N + ξ .
s N = Re β N β 0 | h N | 2 ,
s N β 0 β N | δ N , 0 2 ν N r ν r 0 β 0 ( ξ + Γ r ) | 2 , N P ,
s + ξ | h r | 2 β 0 = 1 , s = N P s N .
| ζ r | = ξ cos θ k ( 1 α r α 0 ) 1 ± s 0 1 s ,
| ζ N r | = ξ β N k ( 1 α r α N ) s N 1 s , N P { 0 , r } .

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