Abstract

When an electromagnetic wave is obliquely incident on the interface between two homogeneous media with different refractive indices, the requirement of phase continuity across the interface generally leads to a shift in the trajectory of the wave. When a linearly position-dependent phase shift is imposed at the interface, the resulting refraction may be described using a generalized version of Snell’s law. In this Letter, we establish a formal equivalence between generalized refraction and blazed diffraction gratings, further discussing the relative merits of the two approaches.

© 2012 Optical Society of America

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References

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  1. D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, Phys. Rev. E 71, 036609 (2005).
    [CrossRef]
  2. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
    [CrossRef]
  3. R. Magnusson and T. K. Gaylord, J. Opt. Soc. Am. 68, 806 (1978).
    [CrossRef]
  4. P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, Opt. Lett. 23, 1081 (1998).
    [CrossRef]
  5. Y.-J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, Opt. Express 19, 24411 (2011).
    [CrossRef]
  6. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef]
  7. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
    [CrossRef]
  8. D. R. Smith, Y.-J. Tsai, and S. Larouche, IEEE Antennas Wirel. Propag. Lett. 10, 1605 (2011).
    [CrossRef]

2012 (1)

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[CrossRef]

2011 (3)

D. R. Smith, Y.-J. Tsai, and S. Larouche, IEEE Antennas Wirel. Propag. Lett. 10, 1605 (2011).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Y.-J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, Opt. Express 19, 24411 (2011).
[CrossRef]

2005 (1)

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, Phys. Rev. E 71, 036609 (2005).
[CrossRef]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

1998 (1)

1978 (1)

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Astilean, S.

Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[CrossRef]

Cambril, E.

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Chavel, P.

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[CrossRef]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Gaylord, T. K.

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Jokerst, N. M.

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Kildishev, A. V.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[CrossRef]

Lalanne, P.

Larouche, S.

D. R. Smith, Y.-J. Tsai, and S. Larouche, IEEE Antennas Wirel. Propag. Lett. 10, 1605 (2011).
[CrossRef]

Y.-J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, Opt. Express 19, 24411 (2011).
[CrossRef]

Launois, H.

Lipworth, G.

Magnusson, R.

Mock, J. J.

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Ni, X.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[CrossRef]

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Schurig, D.

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Shalaev, V. M.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[CrossRef]

Smith, D. R.

Y.-J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, Opt. Express 19, 24411 (2011).
[CrossRef]

D. R. Smith, Y.-J. Tsai, and S. Larouche, IEEE Antennas Wirel. Propag. Lett. 10, 1605 (2011).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Starr, A. F.

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Tsai, Y.-J.

D. R. Smith, Y.-J. Tsai, and S. Larouche, IEEE Antennas Wirel. Propag. Lett. 10, 1605 (2011).
[CrossRef]

Y.-J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, Opt. Express 19, 24411 (2011).
[CrossRef]

Tyler, T.

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett. (1)

D. R. Smith, Y.-J. Tsai, and S. Larouche, IEEE Antennas Wirel. Propag. Lett. 10, 1605 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E (1)

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Science (2)

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic representation of general refraction. When a surface between two media introduces a phase shift Φ(x) depending linearly on x, the refraction angle is different than that given by the standard Snell’s law.

Fig. 2.
Fig. 2.

(a) Transmission amplitude (red) and phase (blue) and (b) diffraction pattern of the motif of a blazed diffraction grating. The intensity has been normalized by d2.

Fig. 3.
Fig. 3.

(a) Transmission amplitude (red) and phase (blue) and (b) diffraction pattern of an eight-period blazed grating. The intensity has been normalized by (8d)2.

Fig. 4.
Fig. 4.

Diffraction angles for λ=8μm, d=15μm, silicon input medium, and air output medium. The m=0 line and m=+1 lines correspond to normal and general refraction, respectively. Shaded regions correspond to negative refraction.

Fig. 5.
Fig. 5.

(a) Transmission amplitude (red) and phase (blue) and (b) diffraction pattern of an eight-period blazed grating with suboptimal phase thickness. The intensity has been normalized by (8d)2.

Equations (7)

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

nosinθonisinθi=λ2πdΦ(x)dx,
nosinθonisinθi=mλd,
m=δ(αmd),
α=nosinθonisinθiλ.
tmotif(x)=rect(xd)×expi2π(xd12).
F{tmotif(x)}=dsinc(α1d).
F{expi2πxd}=δ(α1d),

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