Abstract

Radiationless interference of an electromagnetic wave occurs in the near field when the feature sizes of the waves are at the deep subwavelength scale. We present the propagation in such a regime using a wave-vector space picture. Using this picture, we reproduce the condition to achieve near-field focusing. We also design the initial field distribution needed for near-field beaming, where an intensity distribution maintains its shape as it propagates. We conclude the discussion by proposing a possible implementation of the near-field beaming scheme.

© 2009 Optical Society of America

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References

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  1. R. Merlin, Science 317, 927 (2007).
    [CrossRef] [PubMed]
  2. A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
    [CrossRef] [PubMed]
  3. A. Grbic, and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
    [CrossRef]
  4. L. E. Helseth, Opt. Commun. 281, 1981 (2008).
    [CrossRef]
  5. E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

2008 (3)

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

A. Grbic, and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
[CrossRef]

L. E. Helseth, Opt. Commun. 281, 1981 (2008).
[CrossRef]

2007 (1)

R. Merlin, Science 317, 927 (2007).
[CrossRef] [PubMed]

Grbic, A.

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

A. Grbic, and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
[CrossRef]

Helseth, L. E.

L. E. Helseth, Opt. Commun. 281, 1981 (2008).
[CrossRef]

Jiang, L.

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

Merlin, R.

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

A. Grbic, and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
[CrossRef]

R. Merlin, Science 317, 927 (2007).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag. (1)

A. Grbic, and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
[CrossRef]

Opt. Commun. (1)

L. E. Helseth, Opt. Commun. 281, 1981 (2008).
[CrossRef]

Science (2)

R. Merlin, Science 317, 927 (2007).
[CrossRef] [PubMed]

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

Other (1)

E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (3)

Fig. 1
Fig. 1

Focusing occurs when the field spectrum in wave-vector space F ̃ ( k y , L ) (dotted curve) becomes flat. This occurs at z = L , where the exponentially growing part of F ̃ ( k y , 0 ) (dark line) cancels with the exponentially decaying part of T ( k y , L ) (light line).

Fig. 2
Fig. 2

a, Near-field beaming scheme in wave-vector space. Beaming occurs when F ̃ ( k y , z ) (dotted curve), which is the product of the Gaussian F ̃ ( k y , 0 ) (dark curve) and T ( k y , z ) (light curve), maintains the shape and width as z increases. b, Real part of the field in position space. It maintains the same Gaussian envelope (dark curve), but the spatial oscillation of F ( k y , z ) [dark gray (blue online) curve] has a longer period than that of F ( k y , 0 ) [light gray (red online) curve].

Fig. 3
Fig. 3

Beaming scheme using a TM-polarized Gaussian beam incident at an oblique angle inside an SiC prism. The wave undergoes total internal refraction and gives an evanescent wave with a Gaussian profile on the air side. Arrows in a and b show the direction of incident and reflected waves. b, Real part of E x ; c, absolute value of E x , normalized such that in each plane of constant z, the maximum amplitude is 1 to emphasize the constant Gaussian envelope.

Equations (19)

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F ( y , z ) = 1 2 π F ̃ ( k y , z ) exp ( i k y y ) d k y .
F ̃ ( k y , z ) = F ̃ ( k y , 0 ) exp ( i k z ( k y ) z ) F ̃ ( k y , 0 ) T ( k y , z ) ,
k z i k y .
F ̃ ( k y , z ) = F ̃ ( k y , 0 ) exp ( k y z ) .
F ̃ ( k y , 0 ) = exp ( + k y L ) ,
F ̃ ( k y , L ) = F ̃ ( k y , 0 ) exp ( k y L ) = const .
F ̃ ( k y , 0 ) = exp ( | k y q 0 | L ) ,
F ( y , 0 ) = L π exp ( i q 0 y ) y 2 + L 2 .
F ( y , 0 ) = exp ( i q 0 y ) exp ( y 2 2 σ ) .
F ̃ ( k y , 0 ) = 2 π σ exp ( σ 2 ( k y q 0 ) 2 ) .
F ̃ ( k y , z ) = 2 π σ exp ( z q 0 + z 2 2 σ ) exp ( σ 2 ( k y ( q 0 z σ ) ) 2 ) ,
F ( y , z ) = exp ( z q 0 + z 2 2 σ ) exp ( i ( q 0 z σ ) y ) exp ( y 2 2 σ ) .
z max ( q 0 k 0 ) σ .
exp ( z q 0 + z 2 2 σ ) = exp ( σ ( k 0 q 0 ) 2 2 ) ,
z max = q 0 σ ( 1 1 ( 1 k 0 q 0 ) 2 ) .
z max = q 0 σ .
d q d z = 1 M ̃ ( 0 ) .
z max = q 0 q 0 2 2 k 0 2 log ( 1 M ̃ ( q 0 k 0 ) ) .
1 2 d 2 W d z 2 = 1 M ̃ ( W 2 ) { 1 M ̃ ( 0 ) W 2 1 M ̃ ( W 2 ) W 2 4 ( 1 M ̃ ( W 2 ) 2 ( M ̃ ( W 2 ) 2 ) ) } .

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