Abstract

Surface-plasmon resonance is examined for a periodic semi-infinite structure with metal-dielectric unit cells in slab geometry. Electromagnetic waves through this structure are analyzed for the frequencies close to but smaller than the metal’s plasma frequency. A distinguished limit is found to exist for a small metallic content along with a small metallic nature. As a result, even this narrow frequency interval reveals remarkable resonance characters including wave stability and group velocity dispersion, depending on the dielectric-constant contrast. Both the cut-off period and large-period behavior predicted in the absence of metal’s material damping are found to be appreciably altered when considering material damping, which can be interpreted in terms of the resonant tunneling associated with structural periodicity and the depthwise energy exchange among multilayers.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  2. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, phonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
    [CrossRef]
  3. S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructutres,” Phys. Rev. B 72, 085117 (2005).
    [CrossRef]
  4. P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
    [CrossRef]
  5. J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E 74, 046618 (2006).
    [CrossRef]
  6. H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
    [CrossRef]
  7. M. Scalora, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. Centini, A. Mandatori, C. Sibilia, N. Akozbek, M. G. Cappeddu, M. Fowler, and J. W. Haus, “Negative refraction and sub-wavelength focusing in the visible range using transparent metallo-dielectric stacks,” Opt. Express 15, 508-523 (2007).
    [CrossRef] [PubMed]
  8. J.-L. Zhang, H.-T. Jiang, W.-D. Shen, X. Lu, Y.-Y. Li, and P.-F. Gu, “Omnidirectional transmission bands of one-dimensional metal-dielectric periodic structures,” J. Opt. Soc. Am. B 25, 1474-1478 (2008).
    [CrossRef]
  9. H.-I. Lee and J. Mok, “Low-frequency surface-plasmon resonances in planar metal-dielectric periodic structures,” J. Opt. A, Pure Appl. Opt. 10, 125201 (2008).
    [CrossRef]
  10. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, 1978).
  11. H.-I. Lee, “Wave propagation and resonance in four-layer systems for organic electro-luminescent diodes,” J. Opt. Soc. Am. A 24, 3017-3035 (2007).
    [CrossRef]
  12. I. Tsukerman, “Negative refraction and the minimum lattice cell size,” J. Opt. Soc. Am. B 25, 927-936 (2008).
    [CrossRef]
  13. B. Gralak, S. Enoch, and G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012-1020 (2000).
    [CrossRef]
  14. A. Alu, M. G. Silverinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tayloring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
    [CrossRef]

2008 (3)

2007 (3)

2006 (3)

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E 74, 046618 (2006).
[CrossRef]

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

2005 (1)

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructutres,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

2000 (1)

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, phonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Akozbek, N.

Alu, A.

A. Alu, M. G. Silverinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tayloring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Belov, P. A.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Bender, C. M.

C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, 1978).

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, phonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Bloemer, M. J.

Cappeddu, M. G.

Centini, M.

D'Aguanno, G.

de Ceglia, D.

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, phonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Elson, J. M.

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructutres,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

Engheta, N.

A. Alu, M. G. Silverinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tayloring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Enoch, S.

Fan, S.

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

Feng, S.

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructutres,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

Fowler, M.

Gralak, B.

Gu, P.-F.

Hao, Y.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Haus, J. W.

Jiang, H.-T.

Lee, H.-I.

H.-I. Lee and J. Mok, “Low-frequency surface-plasmon resonances in planar metal-dielectric periodic structures,” J. Opt. A, Pure Appl. Opt. 10, 125201 (2008).
[CrossRef]

H.-I. Lee, “Wave propagation and resonance in four-layer systems for organic electro-luminescent diodes,” J. Opt. Soc. Am. A 24, 3017-3035 (2007).
[CrossRef]

Li, Y.-Y.

Lu, X.

Mandatori, A.

Mattiucci, N.

Mok, J.

H.-I. Lee and J. Mok, “Low-frequency surface-plasmon resonances in planar metal-dielectric periodic structures,” J. Opt. A, Pure Appl. Opt. 10, 125201 (2008).
[CrossRef]

Orszag, S. A.

C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, 1978).

Overfelt, P. L.

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructutres,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

Salandrino, A.

A. Alu, M. G. Silverinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tayloring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Scalora, M.

Schilling, J.

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E 74, 046618 (2006).
[CrossRef]

Shen, W.-D.

Shin, H.

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

Sibilia, C.

Silverinha, M. G.

A. Alu, M. G. Silverinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tayloring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Tayeb, G.

Tsukerman, I.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Zhang, J.-L.

Appl. Phys. Lett. (1)

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

H.-I. Lee and J. Mok, “Low-frequency surface-plasmon resonances in planar metal-dielectric periodic structures,” J. Opt. A, Pure Appl. Opt. 10, 125201 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Opt. Express (1)

Phys. Rev. B (3)

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructutres,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

A. Alu, M. G. Silverinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tayloring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Phys. Rev. E (2)

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E 74, 046618 (2006).
[CrossRef]

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, phonic band-gap structures,” Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Other (2)

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, 1978).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Periodic semi-infinite structures. The unit cells are counted starting with 0 at the interface ms to increasing integers. The period h ̃ u is equal to h ̃ m + h ̃ d .

Fig. 2
Fig. 2

FDR W ( Q 2 D ; R , H ) plotted against the modified propagation constant Q 2 D with H = 1 for a number of the DCC R. Both coordinates are drawn on the logarithmic scales in the intervals Q 2 D [ 10 2 , 10 2 ] and W [ 10 2 , 10 1 ] .

Fig. 3
Fig. 3

W ( Q 2 D ; R , H ) in Fig. 2 allowed under the Bloch condition. The vertical broken two-way arrows indicate the respective FBGs without SPRs.

Fig. 4
Fig. 4

W ( Q 2 D ; R , H ) plotted against Q 2 D with H = 0.20 , allowed under the Bloch condition. Each curve is flanked by the R number. Numerically, the FBG opening for the R=1.50 curve is found to span the interval W ( 1.23 , 2.98 ) for Q ( 0.00562 , 64.9 ) in comparison to its narrower counterpart in Fig. 3 over the interval W ( 1.88 , 2.30 ) for Q ( 0.372 , 0.978 ) .

Fig. 5
Fig. 5

EFCs for the rescaled frequency S ( W ) in Eq. (12) plotted on the ( Q 2 D , H ) plane with the prescribed data; (a) R = 0.618 = R m ( 1 ) and a = 1 ; (b) R = 1.5 and a = 50 . Logarithmic scales are employed over the intervals Q 2 D [ 10 2 , 10 2 ] and H [ 10 2 , 10 2 ] . The whole display window Σ Q H is composed of Σ a + Σ f , where the upper allowed zone Σ a and the lower forbidden zone Σ f are indicated on the figure, respectively. The threshold W = 1 is equal to the boundary between the yellow and light green colored contours, as indicated by the arrow. Part of this boundary is the slightly slant line in (a), while it is hardly seen in (b) (located just above the forbidden zone in B/W prints).

Fig. 6
Fig. 6

(a) EFL on the ( Γ r , Γ i ) plane with varying H. (b) Γ , B r , and B i plotted against H. Input parameters are ( R , W ) = ( 2 , 1.8 + i 0.5 ) . Only the solution ( Γ r , Γ i ) in (a) or ( B r , B i ) in (b) with the minimum Γ is presented for a given H. Only the portions of the curve with Γ < 1 are physically realizable. Meanwhile, the remaining portions with Γ > 1 correspond to wave instability. The end points at H = 10 on the curves with Γ > 1 are indicated by the larger filled squares.

Fig. 7
Fig. 7

FDR W ( Q 2 D ; R , H ) and Bloch factor Γ ( Q 2 D ; R , H ) plotted against Q 2 D for ( H , R ) = ( 1 , 2 ) . The abscissa is defined to be Q 2 D = Q 2 in view of Eq. (8), and it runs over the interval Q 2 D [ 10 2 , 10 2 ] . Numerically, W [ 1.82 , 2.62 ) for Q 2 D ( 0 , 1.88 ] while W [ 1.82 , ) for Q 2 D [ 1.88 , ) . On the other hand, Γ ( 0.651 , 0.721 ] for Q 2 D ( 0 , 0.300 ] while Γ ( 0 , 0.721 ] for Q 2 D [ 0.300 , ) .

Fig. 8
Fig. 8

Γ plotted against κ for ( H , R , W r ) = ( 1 , 2 , 1.8 ) , where W r + i W i = ( 1.8 ) ( 1 + i κ ) . The inset displays B = ( B r , B i ) . Starting at B = ( 1.40 , 0.94 ) , B = ( 1.88 , 0.161 ) , and B = ( 1.42 , 0.00220 ) for κ = 0.01 , the three curves converge to the same point B = ( 0.82 , 0.00 ) as κ , in agreement with the convergence of Γ as κ in the main window.

Tables (1)

Tables Icon

Table 1 Summary of Key Parameters and Variables a

Equations (20)

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

Ω = ω ̃ ω ̃ p , ε m ( Ω ) = 1 1 Ω 2 , ϕ = 1 Ω 2 .
F j l ( X ) = Γ l F j 0 ( X l h u ) ,
( Π + Π ) coth ( D d h d ) + ( Π + + Π ) + 2 coth ( D m h m ) = 0 .
p d coth ( h d b 2 ε d ) p c + p c 2 p d 2 b tanh ( h m b ) ϕ + O ( ϕ 2 ) = 0
W = 1 ε d lim ϕ , f 0 + ( ϕ f ) .
W = R H Q R Q 1 coth ( H Q 1 ) Q R ( R 1 ) [ ( R + 1 ) Q R ] .
Γ = R Q 1 R Q 1 cosh ( H Q 1 ) Q R sinh ( H Q 1 ) .
Q 2 D = Q max ( 1 , R ) > 0 .
W R R H 1 R R 1 , Γ R R H 1 R as Q 1 + ,
W R H coth ( H R 1 ) R 1 , Γ 1 cosh ( H R 1 ) < 1
as Q R + .
W Q ( R 1 ) [ ( R + 1 ) Q R ] , Γ R R H Q R 1 + .
S ( W ) = { W , W [ 0 , 1 ] 1 + [ tanh ( W 1 ) ] a , W [ 1 , ] } .
ε m = 1 1 Ω 2 ( 1 i γ ) , γ = γ ̃ 1 ω ̃ p .
W i = 1 ε d lim γ , f 0 + ( γ f ) , κ = lim γ , ϕ 0 + ( γ ϕ ) .
G j l ( τ , X , Z ) = T A j ± exp ± D j HFL ( X l h u δ d j h m ) ,
T ( τ , Z ; l ) = Γ l exp ( i l μ ) exp ( b i Z ) exp [ i ( Ω τ b r Z ) ] .
Q i > 0 .
ε [ f ( ϕ ) + ( 1 f ) ε d ] = ε d ,
ε ( f ϕ + 1 f ε d ) 1 = W W 1 ε d .

Metrics