Abstract

A π phase shift between the incident wave and surface plasmon polariton (SPP) waves launched from a one-dimensional (slit or groove) subwavelength structure has been found in numerical simulations and invoked to explain recent measurements of optical transmission in slit arrays. Although groove launchers exhibit an overall phase shift that depends on the groove depth, it is shown here how magnetic field induction at the incident surface, and oscillating dipoles from the accumulated charge at the slit or groove edges on the entrance facet lead to an intrinsic π phase shift, independent of the groove or slit depth. Destructive interference between the π-shifted surface wave and the incident wave explains the observed transmission minima when the pitch of an array of slits becomes equal to an integer multiple of the SPP wavelength.

© 2008 Optical Society of America

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References

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  1. A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Surface plasmon polaritons on metallic surfaces,” Opt. Express 15, 183–197 (2007).
    [CrossRef] [PubMed]
  2. G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
    [CrossRef]
  3. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits” Phys. Rev. Lett. 83, 2845–2848 (1999).
    [CrossRef]
  4. Q. Cao and Lalanne, “Negative of Surface Plasmons in the Transmission of Metallic Gratins with Very Narrow Slits,” Phys. Rev. Lett. 88, 057403-1–4 (2002).
    [CrossRef] [PubMed]
  5. P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404-1–11 (2003).
    [CrossRef]
  6. D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Enhanced and Suppressed Transmission through Subwavelength Slit Arrays in Silver Films,” arXiv:0708.1886v2 [physics.optics] 15 Aug 2007.
  7. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629–3651 (2004).
    [CrossRef] [PubMed]
  8. O. T. A. Janssen, H. P. Urbach, and G. W.’t Hooft, “On the phase of plasmons excited by slits in a metal film,” Opt. Express 14, 11823–11832 (2006).
    [CrossRef] [PubMed]
  9. G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76, 155418-1–8 (2007).
    [CrossRef]
  10. G. Gay, O. Alloschery, B. Viaris de Lesegno, and J. Weiner, “Surface Wave Generation and Propagation on Metallic Subwavelength Structures Measured by Far-Field Interferometry,” Phys. Rev. Lett. 96, 213901-1–4 (2006).
    [CrossRef] [PubMed]
  11. J. S. StrattonElectromagnetic Theory, (McGraw-Hill, New York, 1941).
  12. H. RaetherSurface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, Berlin, 1988).
  13. M. Born and E. WolfPrinciples of Optics, 6th edition, (Pergamon, Oxford, 1980).
  14. F. Kalkum, G. Gay, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, “Surface-wave interferometry on single subwavelength slit-groove structures fabricated on Au films,” Opt. Express 15, 2613–261 (2007).
    [CrossRef] [PubMed]
  15. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

2007 (4)

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76, 155418-1–8 (2007).
[CrossRef]

A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Surface plasmon polaritons on metallic surfaces,” Opt. Express 15, 183–197 (2007).
[CrossRef] [PubMed]

F. Kalkum, G. Gay, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, “Surface-wave interferometry on single subwavelength slit-groove structures fabricated on Au films,” Opt. Express 15, 2613–261 (2007).
[CrossRef] [PubMed]

2006 (3)

O. T. A. Janssen, H. P. Urbach, and G. W.’t Hooft, “On the phase of plasmons excited by slits in a metal film,” Opt. Express 14, 11823–11832 (2006).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, and J. Weiner, “Surface Wave Generation and Propagation on Metallic Subwavelength Structures Measured by Far-Field Interferometry,” Phys. Rev. Lett. 96, 213901-1–4 (2006).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

2004 (1)

2003 (1)

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404-1–11 (2003).
[CrossRef]

2002 (1)

Q. Cao and Lalanne, “Negative of Surface Plasmons in the Transmission of Metallic Gratins with Very Narrow Slits,” Phys. Rev. Lett. 88, 057403-1–4 (2002).
[CrossRef] [PubMed]

1999 (1)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits” Phys. Rev. Lett. 83, 2845–2848 (1999).
[CrossRef]

Alloschery, O.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, and J. Weiner, “Surface Wave Generation and Propagation on Metallic Subwavelength Structures Measured by Far-Field Interferometry,” Phys. Rev. Lett. 96, 213901-1–4 (2006).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

Atwater, H. A.

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Enhanced and Suppressed Transmission through Subwavelength Slit Arrays in Silver Films,” arXiv:0708.1886v2 [physics.optics] 15 Aug 2007.

Born, M.

M. Born and E. WolfPrinciples of Optics, 6th edition, (Pergamon, Oxford, 1980).

Cao, Q.

Q. Cao and Lalanne, “Negative of Surface Plasmons in the Transmission of Metallic Gratins with Very Narrow Slits,” Phys. Rev. Lett. 88, 057403-1–4 (2002).
[CrossRef] [PubMed]

Chavel, P.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404-1–11 (2003).
[CrossRef]

de Lesegno, B. Viaris

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

G. Gay, O. Alloschery, B. Viaris de Lesegno, and J. Weiner, “Surface Wave Generation and Propagation on Metallic Subwavelength Structures Measured by Far-Field Interferometry,” Phys. Rev. Lett. 96, 213901-1–4 (2006).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits” Phys. Rev. Lett. 83, 2845–2848 (1999).
[CrossRef]

Gay, G.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

F. Kalkum, G. Gay, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, “Surface-wave interferometry on single subwavelength slit-groove structures fabricated on Au films,” Opt. Express 15, 2613–261 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

G. Gay, O. Alloschery, B. Viaris de Lesegno, and J. Weiner, “Surface Wave Generation and Propagation on Metallic Subwavelength Structures Measured by Far-Field Interferometry,” Phys. Rev. Lett. 96, 213901-1–4 (2006).
[CrossRef] [PubMed]

Hooft, G. W.’t

Hugonin, J. P.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404-1–11 (2003).
[CrossRef]

Janssen, O. T. A.

Kalkum, F.

Lalanne,

Q. Cao and Lalanne, “Negative of Surface Plasmons in the Transmission of Metallic Gratins with Very Narrow Slits,” Phys. Rev. Lett. 88, 057403-1–4 (2002).
[CrossRef] [PubMed]

Lalanne, P.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404-1–11 (2003).
[CrossRef]

Lévêque, G.

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76, 155418-1–8 (2007).
[CrossRef]

Lezec, H. J.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

F. Kalkum, G. Gay, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, “Surface-wave interferometry on single subwavelength slit-groove structures fabricated on Au films,” Opt. Express 15, 2613–261 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629–3651 (2004).
[CrossRef] [PubMed]

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Enhanced and Suppressed Transmission through Subwavelength Slit Arrays in Silver Films,” arXiv:0708.1886v2 [physics.optics] 15 Aug 2007.

Mansuripur, M.

Martin, O. J. F.

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76, 155418-1–8 (2007).
[CrossRef]

Moloney, J. V.

O’Dwyer, C.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

Pacifici, D.

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Enhanced and Suppressed Transmission through Subwavelength Slit Arrays in Silver Films,” arXiv:0708.1886v2 [physics.optics] 15 Aug 2007.

Pendry, J. B.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits” Phys. Rev. Lett. 83, 2845–2848 (1999).
[CrossRef]

Porto, J. A.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits” Phys. Rev. Lett. 83, 2845–2848 (1999).
[CrossRef]

Raether, H.

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

Rodier, J. C.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404-1–11 (2003).
[CrossRef]

Sauvan, C.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404-1–11 (2003).
[CrossRef]

Seideman, T.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

Stratton, J. S.

J. S. StrattonElectromagnetic Theory, (McGraw-Hill, New York, 1941).

Sukharev, M.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

Thio, T.

Urbach, H. P.

Weiner, J.

F. Kalkum, G. Gay, J. Weiner, H. J. Lezec, Y. Xie, and M. Mansuripur, “Surface-wave interferometry on single subwavelength slit-groove structures fabricated on Au films,” Opt. Express 15, 2613–261 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76, 155418-1–8 (2007).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, and J. Weiner, “Surface Wave Generation and Propagation on Metallic Subwavelength Structures Measured by Far-Field Interferometry,” Phys. Rev. Lett. 96, 213901-1–4 (2006).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Enhanced and Suppressed Transmission through Subwavelength Slit Arrays in Silver Films,” arXiv:0708.1886v2 [physics.optics] 15 Aug 2007.

Wolf, E.

M. Born and E. WolfPrinciples of Optics, 6th edition, (Pergamon, Oxford, 1980).

Xie, Y.

Zakharian, A. R.

Nature Phys. (1)

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Phys.264–267 (2006).

Opt. Express (4)

Phys. Rev. B (2)

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76, 155418-1–8 (2007).
[CrossRef]

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404-1–11 (2003).
[CrossRef]

Phys. Rev. E (1)

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E 75, 016612-1–4 (2007) and references cited therein.
[CrossRef]

Phys. Rev. Lett. (3)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits” Phys. Rev. Lett. 83, 2845–2848 (1999).
[CrossRef]

Q. Cao and Lalanne, “Negative of Surface Plasmons in the Transmission of Metallic Gratins with Very Narrow Slits,” Phys. Rev. Lett. 88, 057403-1–4 (2002).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, and J. Weiner, “Surface Wave Generation and Propagation on Metallic Subwavelength Structures Measured by Far-Field Interferometry,” Phys. Rev. Lett. 96, 213901-1–4 (2006).
[CrossRef] [PubMed]

Other (4)

J. S. StrattonElectromagnetic Theory, (McGraw-Hill, New York, 1941).

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

M. Born and E. WolfPrinciples of Optics, 6th edition, (Pergamon, Oxford, 1980).

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Enhanced and Suppressed Transmission through Subwavelength Slit Arrays in Silver Films,” arXiv:0708.1886v2 [physics.optics] 15 Aug 2007.

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Figures (2)

Fig. 1.
Fig. 1.

Orientation of orthogonal coordinate axes is shown along with a light wave TM polarized (H field aligned along the 0 y axis). Incident and scattered E-field components are confined to the x-z plane. A subwavelength slit milled at the interface between the metal slab (m) and a dielectric (d) is also aligned along the y- axis.

Fig. 2.
Fig. 2.

Top panel is a numerical simulation of an incident plane wave TM polarized and incident on a two-slit structure from the top. The color map indicates the amplitude of the magnetic field component (red highest amplitude, dark blue lowest amplitude) and shows the standing wave set up by the incident and reflected wave. Note that the standing H-field is maximum at the surface. Middle and lower panels show how the time-oscillating H-field induces current in the skin depth δ of the metal slit structure, resulting in charge accumulation at the slit edges with widths d. Middle panel: first optical half-cycle; lower panel: second optical half-cycle.

Equations (30)

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

× E = B t
× H = D t
B = μ 0 μ H and D = ε 0 ε E
H y ( x , z , t ) = H 0 exp [ i ( k x x + k z z ω t ) ]
E x ( x , z , t ) = E x exp [ i ( k x x + k z z ω t ) ]
E z ( x , z , t ) = E z exp [ i ( k x x + k z z ω t ) ]
H y d = H y m
E x d = E x m
ε d E z d = ε m E z m
k z d ε d ω H y d = E x d
k x d ε d ω H y d = E z d
k z m ε m ω H y m = E x m
k x m ε m ω H y m = E z m
H y d H y m = 0
k z d ε d H y d + k z m ε m H y m = 0
k z d ε d = k z m ε m
k x d = k x m = k x
( k x d ) 2 + ( k z d ) 2 = ( ω c ) 2 ε d
( k x m ) 2 + ( k z m ) 2 = ( ω c ) 2 ε m
k x = ( ω c ) ε d ε m ε d + ε m
k x = k z d ε m ε d
k x = i k z d ε m ε d
E x = i ε d ε m E z d
H y = c ε d ( ε d + ε m ) ε m E z d
H y ( z , t ) = 2 H 0 exp ( i ω 0 t )
Φ ( t ) = 2 μ 0 H 0 exp ( i ω 0 t ) dS = μ 0 2 H 0 ( δ p ) exp ( i ω 0 t )
em f x = d Φ ( t ) d t = 2 μ 0 H 0 ω 0 ( δ p ) exp [ i ( ω 0 t π 2 ) ]
𝓘 x = emf x 𝓡 = 2 μ 0 H 0 ω 0 ( δ p ) 𝓡 exp [ i ( ω 0 t π 2 ) ]
𝒬 ( t ) = 2 μ 0 H 0 ( δ p ) 𝓡 0 t ω 0 exp [ i ( ω 0 t π 2 ) dt ] = 2 μ 0 H 0 ( δ p ) 𝓡 exp [ i ( ω 0 t π ) ]
𝒫 x ( t ) = 𝒬 ( t ) d = 2 d μ 0 H 0 ( δ p ) 𝓡 exp [ i ( ω 0 t π ) ]

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