Abstract

The mechanism and design of p- and s- polarized ultra-long-range surface-plasmon-polariton (SPP) propagation in the configuration {prism/ equivalent coupling layer (ECL)/ silver film (20 nm)/ equivalent substrate (ES)} are investigated using a normalized admittance diagram (NAD). The excitation of ultra-long-range SPP waves is characterized as a huge open loop of the NAD of the metal film at a designated angle of incidence. We propose three kinds of ECLs to complete the multilayer ultra-long-range SPP design: the normalized admittance of the ECL is (i) real (ii) infinite (iii) imaginary. The ultra-long propagation lengths in the three designs are compared at a wavelength of 632.8 nm for p- and s-polarization states.

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References

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2009

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and T.-Y. Chan, “Multilayered structures for p- and s-polarized long-range surface-plasmon-polariton propagation,” J. Opt. Soc. Am. A 26(12), 2600–2606 (2009).
[CrossRef]

2007

2006

2005

2001

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63(12), 125417 (2001).
[CrossRef]

G. G. Nenninger, P. Tobiska, J. Homola, and S. S. Yee, “Long-range surface plasmons for high-resolution surface plasmon resonance sensors,” Sens. Act. B 74(1-3), 145–151 (2001).
[CrossRef]

1999

1991

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

1987

1986

L. Wedler and R. Haupt, “Long-range surface plasmon-polaritons in asymmetric layer structures,” J. Appl. Phys. 59(9), 3289–3291 (1986).
[CrossRef]

1981

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

1969

E. N. Economu, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Adato, R.

Anemogiannis, E.

Berini, P.

Boltasseva, A.

Bozhevolnyi, S.

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

Breukelaar, I.

Chan, T.-Y.

Charbonneau, R.

Economu, E. N.

E. N. Economu, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Fafard, S.

Gaylord, T. K.

Glytsis, E. N.

Guo, J.

Haupt, R.

L. Wedler and R. Haupt, “Long-range surface plasmon-polaritons in asymmetric layer structures,” J. Appl. Phys. 59(9), 3289–3291 (1986).
[CrossRef]

Homola, J.

G. G. Nenninger, P. Tobiska, J. Homola, and S. S. Yee, “Long-range surface plasmons for high-resolution surface plasmon resonance sensors,” Sens. Act. B 74(1-3), 145–151 (2001).
[CrossRef]

Jen, Y.-J.

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and T.-Y. Chan, “Multilayered structures for p- and s-polarized long-range surface-plasmon-polariton propagation,” J. Opt. Soc. Am. A 26(12), 2600–2606 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

Kjaer, K.

Kou, F. Y.

Lahoud, N.

Lakhtakia, A.

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and T.-Y. Chan, “Multilayered structures for p- and s-polarized long-range surface-plasmon-polariton propagation,” J. Opt. Soc. Am. A 26(12), 2600–2606 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

Larsen, M.

Leosson, K.

Lin, C.-F.

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

Mattiussi, G.

Nenninger, G. G.

G. G. Nenninger, P. Tobiska, J. Homola, and S. S. Yee, “Long-range surface plasmons for high-resolution surface plasmon resonance sensors,” Sens. Act. B 74(1-3), 145–151 (2001).
[CrossRef]

Nikolajsen, T.

Sambles, J. R.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

Sarid, D.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

Scales, C.

Tamir, T.

Tobiska, P.

G. G. Nenninger, P. Tobiska, J. Homola, and S. S. Yee, “Long-range surface plasmons for high-resolution surface plasmon resonance sensors,” Sens. Act. B 74(1-3), 145–151 (2001).
[CrossRef]

Wedler, L.

L. Wedler and R. Haupt, “Long-range surface plasmon-polaritons in asymmetric layer structures,” J. Appl. Phys. 59(9), 3289–3291 (1986).
[CrossRef]

Yang, F.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

Yee, S. S.

G. G. Nenninger, P. Tobiska, J. Homola, and S. S. Yee, “Long-range surface plasmons for high-resolution surface plasmon resonance sensors,” Sens. Act. B 74(1-3), 145–151 (2001).
[CrossRef]

Yu, C.-W.

J. Appl. Phys.

L. Wedler and R. Haupt, “Long-range surface plasmon-polaritons in asymmetric layer structures,” J. Appl. Phys. 59(9), 3289–3291 (1986).
[CrossRef]

J. Lightwave Technol.

J. Nanophoton.

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton. 3(1), 033506 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Rev.

E. N. Economu, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Phys. Rev. B

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range modes supported by thin films,” Phys. Rev. B 44(11), 5855–5872 (1991).
[CrossRef]

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63(12), 125417 (2001).
[CrossRef]

Phys. Rev. Lett.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

Sens. Act. B

G. G. Nenninger, P. Tobiska, J. Homola, and S. S. Yee, “Long-range surface plasmons for high-resolution surface plasmon resonance sensors,” Sens. Act. B 74(1-3), 145–151 (2001).
[CrossRef]

Other

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin Heidelberg, 1988).

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, Bristol, 1986).

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Figures (11)

Fig. 1
Fig. 1

Locus of a metal film for ultra-long-range SPP propagation in the NAD.

Fig. 2
Fig. 2

The required thickness of the silver film d r e q against the initial part γ for the p-polarization state and the s-polarization state at θ i = 41.31 ° when (a) Re ( η m ' ) = 2 N i , (b) Re ( η m ' ) = N i , and (c) Re ( η m ' ) = Re ( η m ) . The refractive index of the prism is 1.51511 at λ = 632.8 nm.

Fig. 3
Fig. 3

ξ against γ for p- and s-polarization states for a silver film at θ i = 41.31 ° .The wavelength is 632.8 nm

Fig. 4
Fig. 4

Clockwise locus of the equivalent coupling layer for ultra-long-range SPP propagation in the NAD.

Fig. 5
Fig. 5

Near vertical locus of the equivalent coupling layer for ultra-long-range SPP propagation in the NAD.

Fig. 6
Fig. 6

Counter-clockwise locus of the equivalent coupling layer for ultra-long-range SPP propagation in the NAD.

Fig. 7
Fig. 7

| r p | 2 against θ i for the structure {prism/ [Ta2O5 (48.75 nm)/ SiO2 (142.78 nm)/ Ta2O5 (48.75 nm)]43/ silver film (20 nm)/ [Ta2O5 (150.48 nm)/ air]} with a clockwise coupling path at λ = 632.8 nm.

Fig. 8
Fig. 8

| r p | 2 against θ i for the structure {prism/ [Ta2O5 (48.74 nm)/ SiO2 (142.73 nm)/ Ta2O5 (48.74 nm)] 40/ silver film (20 nm)/ [Ta2O5 (150.98 nm)/ air]} with a near vertical coupling path at λ = 632.8 nm.

Fig. 9
Fig. 9

| r p | 2 against θ i for the structure {prism/ [Ta2O5 (48.44 nm)/ SiO2 (141.85 nm)/ Ta2O5 (48.44 nm)] 28/ silver film (20 nm)/ [Ta2O5 (157.86 nm)/ air]} with a counter-clockwise coupling path at λ = 632.8 nm.

Fig. 10
Fig. 10

The absolute value of the parallel electric field distribution for (a) the p-polarization state and (b) the s-polarization state for the counter-clockwise coupling case in Table 1 and Table 2 at θ i = 41.31 ° at λ = 632.8 nm, respectively.

Fig. 11
Fig. 11

| r s | 2 as a function of θ i for the structure {prism/ [Ta2O5 (157.78 nm)/SiO2 (53.88 nm)/Ta2O5 (157.78 nm)]13/ silver film (20 nm)/ [SiO2 (139.87 nm)/ air]} for the counter-clockwise coupling case in Table 2. The wavelength is 632.8 nm.

Tables (2)

Tables Icon

Table 1 Design parameters γ and η c , real parts of η m ' , large values ξ, effective mode indices n e , half-widths θ H W , and propagation lengths L of the p-polarization state for the three types of coupling at θ i = 41.31 ° and λ = 632.8 nm.

Tables Icon

Table 2 Design parameters γ and η c , real parts of η m ' , large values ξ, effective mode indices n e , half-widths θ H W , and propagation lengths L of the s-polarization state for the three types of coupling at θ i = 41.31 ° and λ = 632.8 nm.

Equations (8)

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η ˜ i = { η ˜ i c h a r / cos θ i η ˜ i c h a r cos θ i , η ˜ = { η ˜ c h a r / cos θ η ˜ c h a r cos θ , p o l a r i z a t i o n = { p s .
η = { ( η ˜ cos θ i ) / ε 0 / μ 0 ( η ˜ / cos θ i ) / ε 0 / μ 0 , p o l a r i z a t i o n = { p s ,
η m = { ( n i k ) 2 cos θ i / n 2 k 2 ( N i sin θ i ) 2 2 i n k n 2 k 2 ( N i sin θ i ) 2 2 i n k / cos θ i , p o l a r i z a t i o n = { p s ,
η m ' = i γ cos ( 2 π d m α / λ ) + i η m sin ( 2 π d m α / λ ) cos ( 2 π d m α / λ ) γ η m 1 sin ( 2 π d m α / λ ) ,
η c [ i η c sin δ + η m ' cos δ ] η c cos δ + i η m ' sin δ N i , where δ = { 2 π η c d c cos 2 θ / ( cos θ i λ ) 2 π η c d c cos θ i / λ , p o l a r i z a t i o n = { p s .
Re ( η m ' ) = 2 N i ,
Re ( η m ' ) = N i ,
Re ( η m ' ) = Re ( η m ) ,

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