OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 3 — Feb. 5, 2007
  • pp: 1182–1190
« Show journal navigation

Interference of surface waves in a metallic nanoslit

Bora Ung and Yunlong Sheng  »View Author Affiliations


Optics Express, Vol. 15, Issue 3, pp. 1182-1190 (2007)
http://dx.doi.org/10.1364/OE.15.001182


View Full Text Article

Acrobat PDF (378 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate the interference of the surface plasmon polariton (SPP) with an incident beam on a metallic slit using the FDTD. We find that the bulk waves radiated at the slit edge by scattering of the SPP leak into the slit and induce accumulated charges within the skin depth, which excite new SPPs on the slit side-walls. The SPP on the top surface of aperture is coupled into the slit and induces the 2D asymmetric field distributions, including the horizontal and vertical Fabry-Perot multi-reflection resonator modes. We show that the addition of these modes with the slit waveguide modes induced by a normally incident beam is the interference between the SPP and the incident beam, which enhances or suppresses the slit transmission, depending on their relative phase.

© 2007 Optical Society of America

1. Introduction

The extraordinary enhancement of the light transmission through subwavelength aperture arrays in metal films [1

1. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391,667–669 (1998). [CrossRef]

], or through a single hole surrounded by a number of grooves [2

2. T. Thio, K.M. Pellerin, R.A. Linke, T.W. Ebbesen, and H.J. Lezec, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26,1972–1974 (2001). [CrossRef]

] excited enormous research interests. Among numerous theoretical explanations, Lezec et al. suggested that the enhancement of transmission could be a result of the interference of the composite diffracted evanescent waves with the normally incident light on the apertures. Their theory is within the scalar diffraction theory framework [3

3. 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]

]. Schouten et al. studied the optical transmission of two subwavelength slits as a function of wavelength and slit separation [4

4. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-Assisted Two-Slit Transmission: Young’s Experiment Revisited,” Phys. Rev. Lett. 94, 053901 (2005). [CrossRef] [PubMed]

]. They suggested that the interference of the surface plasmon polariton (SPP), which is excited at one slit and is propagated to another slit with the incident beam at the slit, is the source of modulation of the double-slit transmission. We notice that before their arrival to the slit, the impinging SPP and the normally incident beam have orthogonal polarizations and perpendicular wavevectors. It is then important to understand how their interference may occur. Generally speaking, this interference must be mediated by conversion between SPP and free-space bulk waves at the nanoslit. However, the coupling mechanism of the SPP into the slit and the interference with the incident wave has yet to be fully understood.

In this paper we investigate the behavior of the SPP impinging on a metallic nanoslit, using the full vectorial solutions of the Maxwell equations with the finite-difference time-domain method (FDTD). In particular, we are interested in the mechanism of coupling a part of the impinging SPP into the slit and its interference with the normally incident beam. The FDTD has been used to model the optical transmission of subwavelength hole [5

5. A.R. Zakharian, M. Mansuripur, and J.V. Moloney, “Transmission of light through small elliptical apertures,” Opt. Express 12,2631–2648 (2004). [CrossRef] [PubMed]

,6

6. Y. Xie, A.R. Zakharian, J.V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12,6106–6121 (2004). [CrossRef] [PubMed]

], array of slits [7

7. Y. Xie, A.R. Zakharian, J.V. Moloney, and M. Mansuripur, “Transmission of light through a periodic array of slits in a thick metallic film,” Opt. Express 13,4485–4491 (2005). [CrossRef] [PubMed]

6

6. Y. Xie, A.R. Zakharian, J.V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12,6106–6121 (2004). [CrossRef] [PubMed]

]. The scattering of SPP by surface defects or by discontinuities of the substrate's dielectric constant is a classical problem investigated by many authors [8

8. J. A. Sanchez-Gil and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60,8359–8367 (1999). [CrossRef]

,9

9. J. A. Sanchez-Gil and A. A. Maradudin, “Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects,” Opt. Express 12,883–894 (2004). [CrossRef] [PubMed]

]. It is well known that the incoming SPP to a surface defect or a material discontinuity, is partially reflected, transmitted, and scattered into the free space above the metal surface. This scattering is relevant to probing of the SPP in near-field optical microscopy. However, to our best knowledge no detailed analysis has been reported on the coupling of the SPP into the slit, and the interference at the slit between the incoming SPP and the incident free-space beam. We find that the bulk waves radiated at the slit edge by scattering of the SPP leak into the slit and induce accumulated charges and new SPPs on the slit side-walls. A sole incident SPP can induce bulk wave multi-reflection resonance cavity modes between the two slit walls, and the SPP slit waveguide modes along the slit axis, with their field distributions depending on the slit's geometry. The addition of those modes with the well-known slit waveguide mode induced by a single normally incident beam [14

14. Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86,5601–5603 (2001). [CrossRef] [PubMed]

], is equal to the field in the slit when both the SPP and the plane wave beam are incident on the slit. Therefore, we confirm the interference theory and demonstrate that the slit transmission is enhanced or suppressed, depending on the relative phases of the interfering fields.

2. Coupling surface plasmons polaritons into slit

We consider an infinitely long slit perforated in a real metal film, such as silver, along the z-axis. The surface plasmon polariton (SPP) is generated by a linearly p-polarized beam, with Ex and Hz components, of wavelength λ 0=500nm normally incident on a groove of width 250nm and depth 70nm. As shown on Fig. 1(a), SPPs are generated by diffraction in the groove and propagate away from the groove on the top metal surface in the ±x directions. The internal mechanism of the SPP generation in the groove is not our concern in this paper. Other SPP sources could also be used.

Fig. 1. (a) Model schematic. (b) Transmission Ts of the slit (a=250nm, t=300nm) with a single beam incident on the groove, as a function of SPP propagation distance L.
ε(ω)=εr,+k=0Kfkωp2ωk2ω2+Γk
(1)

where ε r,∞ is the dielectric constant at infinite frequencies, ωp the plasma frequency, and ωk, fk, and Γk are the resonance frequency, strength and damping frequency, respectively, of kth oscillator. The Lorentz-Drude model uses K damped harmonic oscillators to describe the small resonances observed in the metal’s frequency response. The values of the constants in Eq. (1) are taken from [11

11. Aleksandar D. Rakic, Aleksandra B. Djuristic, Jovan M. Elazar, and Marian L. Majewski, “Optical properties of metallic films,” Appl. Opt. 37,5271–5283 (1998). [CrossRef]

]. At λ 0=500nm, we obtain the complex permittivity of silver: ε=-7.6321+0.7306i. Perfectly-matched layer boundary conditions were applied at the limits of the computational domain [10

10. A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 2nd edition, Artech House, Boston, 2000.

]. The slit intensity transmission coefficient Ts is calculated by integrating the time-averaged modulus of the Poynting vector along a plane “detector” located at the slit bottom exit (0≤xa, y=-10nm), as shown on Fig. 1(a).

We computed the electromagnetic fields and electrical charge distributions induced by the sole incident SPP for a set of slit width a and thickness t with the FDTD. The following is our observations on the results.

2.1 Fabry-Perot resonator of SPP between groove and slit

The incident SPP on the metal top surface on the air side is described by Hz and Ey, which is parallel and normal to the top surface, respectively. At the slit top-left edge (x=0, y=t), the abrupt change of permittivity of the material from metal to vacuum partially reflects the incident SPP. The remaining SPP is converted to bulk radiation by scattering. As the groove is present, the reflected SPP is again partially reflected back towards the slit from the top-right edge of the groove (x=-L, y=t). The SPP characteristic propagation length [12

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

] Lspp=1/(2∙Im(kspp))=52μm is significantly longer than the propagation distance L in our experiments. Thus, the multiple reflections on the section -L<x<0 of the metal top surface create a Fabry-Perot (F-P) type interference of the SPP. In Fig. 1(b) we show the slit energy transmission Ts as a function of the cavity length L, when the sole SPP is incident to the slit from the left ridge. The main features of the curve are its initial rapid decay for 0<L<μm and the oscillation period of λspp/2, where the SPP wavelength λspp=λ 0/Re(nspp)=470nm. The resonance peaks of Ts have low magnitudes corresponding to small SPP reflectivities R at the slit and groove edges. At the left-end ridge of the metal film the SPP propagating in the −x direction is also partially reflected back. However, the propagation distance of the SPP in the −x direction, L’, is chosen to be 1.5λspp such that their interference is destructive and their perturbation to the +x propagating SPP on the right-side of the groove is minimized.

2.2 Bulk waves Fabry-Perot resonator modes between slit walls

Of the bulk waves converted from the incident SPP at the slit top-left edge, a major part is scattered into the half-space above the metal film, see Fig. 1(a). Our FDTD computation shows that a small part of the scattered divergent bulk waves leak into the slit. The bulk waves, mainly consisting of the Hz and Ey components, as for the incident SPP, hit and are reflected from the right-side-wall of the slit, and are then reflected back by the left-side-wall of the slit. The multiple reflections between the two slit walls form F-P resonator modes with slightly inclined bulk wave input from the top of the cavity. When the slit width is close to integer multiples of λ 0/2, the cavity resonance creates strong standing wave fringes of Ey and Hz with a fringe period of λ 0/2 as shown in Fig. 2(a) and 2(c). The fringes of Hz are interlaced with the fringes of Ey. The maxima of Hz are at the slit walls, while the maxima of Ey are shifted by λ 0/4 from the slit walls [5

5. A.R. Zakharian, M. Mansuripur, and J.V. Moloney, “Transmission of light through small elliptical apertures,” Opt. Express 12,2631–2648 (2004). [CrossRef] [PubMed]

]. These fringes represent the energy stored in the slit cavity. At the resonance, the slit’s stored energy and transmission Ts are maximal. Out of the resonance, both Ey and Hz in the slit decrease to low intensities and Ts is minimal, as pictured in Fig. 2(b).

Sanchez-Gil et al. showed in the case of a simple surface defect (groove or bump) that the scattering efficiency S of the waves into the free space above the top surface depends on the SPP transmission T (Fig. 1). When the surface defect is replaced by a slit, we observed that the scattering S and its direction of maximum radiation both depend on the F-P resonator modes in the slit, which also determine the SPP transmission T on the top surface and the slit transmission Ts coefficients. The latter is the energy leaked from the slit’s bottom exit in the form of the transmitted bulk waves and of the SPPs excited on the bottom plane of the metal film (x<0 and x>a, y=0).

Fig. 2. Modulus of Ex, Ey, and Hz when a single SPP is incident on a slit (a) width a=500nm at resonance; (b) a =3S0nm out of resonance and (c) a=250nm at resonance. (d) Phase distribution for a=250nm. In all figures, slit thickness t=300nm and SPP propagation distance L=520nm.

2.3 Excitation of new SPPs on slit walls

As noted previously, the SPP on the air side of the top surface contains no Ex component. The scattered bulk waves entering the slit contains Ex which is responsible for the downward component of the bulk wave vector k0. In addition, new Ex fields are excited on the slit walls. Indeed, the Hz of the incident SPP induces surface currents parallel to the top metal surface (-Lx≤0, y=t), while the bulk Hz leaked into the slit induces surface currents parallel to the slit left-side wall (x=0, 0≤yt). The surface currents associated with the incoming SPP must turn around the top-left corner (x=0, y=t) as shown in Fig. 3. There is a corresponding sharp discontinuity in the amplitude of Hz on the top surface SPP and that of the leaked bulk Hz, in the vicinity of the slit top-left edge, as shown in Fig. 2. According to the charge conservation equation, ∁ ∙ J⃑ = -∂ρ/∂t, the corresponding current discontinuity creates the accumulation of electric charges at the slit corner as an oscillating monopole, which can be observed by a high concentration of Ey on the top surface (x≤0, y=t) and of Ex on the slit left-side wall (x=0, 0≤yt), as shown in Fig. 2. The oscillating monopole radiates waves which excites the SPP on the slit left-side wall (x=0, 0≤yt).

On the right-side wall of the slit (x=a, 0≤yt), there is no significant Ex when the slit width a>>λ 0. However, the scattered bulk Hz induces surface currents and accumulated charges on the slit right-side wall within the skin depth. The FDTD calculation shows that the phase of Hz is shifted by π from the left-side wall to the right-side wall of the slit, as shown in Fig. 2(d), so that the surface currents are in the same direction along both walls. As a consequence, the accumulated charges on the slit right-side wall are of the opposite sign to that at the slit top-left edge, and the two poles are in-phase in their oscillation with time resulting in an oblique dipole across the slit as shown on Fig. 3. This dipole is the source of excitation of new SPPs on both slit walls, although the two poles can have different amount of charges, and the rightside pole is not necessarily located at the slit bottom-right corner but near the middle of the right-side wall. The distributions of field components Ex and Hz and of the accumulated charges on the two walls vary with the slit geometry and are asymmetric with respect to the slit axis, see Fig. 2(c).

Fig. 3. Poynting S⃑ (blue arrows) and surface current density vectors J⃑ (red arrows) for single incident SPP illumination. The length of arrows is proportional to the amplitude. Signs +/- indicate polarities of accumulated electric charges, which are related to the gradient of J⃑. Slit width a=250nm, thickness t=300nm.

The excited SPPs are sustained by the Ex and Hz on the slit side walls. In contrast with the Ey, whose maximum is shifted from the reflecting wall surfaces by λ 0/4, the Ex is stuck on the walls. Apparently, the multiple reflection resonances of the bulk waves between the two slit walls have little effect to the Ex on the walls. When the bulk wave is out of resonance, Ey is minimum inside the slit while the Ex and Hz components are non null on the slit walls, as shown in Fig. 2(b), where they sustain the SPPs on the slit side walls and contribute to coupling the incoming SPP on the top surface into the slit cavity.

2.4 Coupling the incident SPP into the slit

Figure 3 shows the Poynting vectors S⃑ associated with a single SPP incident on the slit. Since the magnetic field has only Hz component, the direction of S⃑ is determined by the local ratio of Ex and Ey. On the top surface, the S⃑ of the incident SPP is in +x direction. The S⃑ then enters inside the slit by turning around the positively charged pole at the slit top-left edge due to the strong presence of accumulated charges at the edge. The S⃑ then flows downward supported by the excited SPP (Ex) on the slit left-side wall. After propagating through a small depth in the slit, the magnitude of Ex diminishes, and S⃑ changes the direction right conducted by the rising of Ey in the middle of the slit, as shown in Fig. 2(c), to meet the right-side wall of the slit where the negatively charged pole and the excited SPP, sustained by Ex and Hz, leads the S⃑ flux towards the bottom-right edge and to the slit bottom exit. In addition, new SPPs are excited on the bottom-right metal plane (xa, t=0).

2.5 Fabry-Perot resonator modes along the slit axis

It is well known that when a plane wave beam is normally incident on a nanoslit from free-space, the impedance mismatch between the region in the slit and the free-space region outside the slit is sufficiently important to allow strong F-P resonance modes along the slit axis [14

14. Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86,5601–5603 (2001). [CrossRef] [PubMed]

]. Our FDTD computation shows that the incident SPP on the top surface may alone excite the slit waveguide modes for sufficiently thick films. When the slit width aλ 0/4, the Ex distribution is oblique only at the top of the slit inside the first period, (t-λspp)/2<y<t, of the standing-wave fringes. As shown in Fig. 4(b), the standing-wave fringes of Ex become uniform across the slit width for the remaining slit length, 0<y<(t-λspp/2), as in the conventional slit F-P waveguide modes for the slit illuminated by a normal incident beam.

2.6 Field distributions inside the slit

The pure bulk wave resonator modes between the two slit walls (horizontal F-P), as shown in Fig. 4(c), and the pure SPP resonator modes along the slit axis (vertical F-P), as shown in Fig. 4(b), represent the two extreme cases for wide and narrow slit, characterized by aλ 0 and aλ0/4 respectively. In general, a single incident SPP on the top surface induces 2D field distributions in the slit, which are asymmetric with respect to the slit axis.

Figure 4(a) shows the slit energy transmission Ts normalized by the slit width a as a function of slit width a and thickness t, when a single SPP on the top surface impinges on the slit. Peak transmission occurs when both the vertical and horizontal F-P resonator modes are at resonance. Our computations show that the values of a and t for the resonances are shifted from those for the classical cavity resonances, a=n(λ 0/2) and t=m(λeff/2), where m and n are integers and λeff=λspp/neff is the effective wavelength with slit waveguide mode effective index neff[14

14. Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86,5601–5603 (2001). [CrossRef] [PubMed]

]. For slit widths aλ 0/4, the F-P resonances along the slit thickness t are clearly visible in Fig. 4(a), which occur when t is m(λeff/2). The peak regions of Ts have an inclined shape because λeff and neff are functions of the slit width a. With increasing of the slit thickness t, Ts decreases due to attenuation losses of the SPPs’ propagation along the slit walls. When the slit width a is around λ 0/2, the F-P resonances along the slit thickness t are clearly visible in Fig. 4(a), which occur when t is m(λeff/2). The peak regions of Ts have an inclined shape because λeff and neff are functions of the slit width a. With increasing of the slit thickness t, Ts decreases due to attenuation losses of the SPPs’ propagation along the slit walls. When the slit width a is around λ 0/2, the F-P resonances as a function of t are still present, but with different shapes and locations of the Ts peaks in the a-t map due to the onset of bulk wave horizontal F-P modes. When the slit width a is around λ 0 and 3λ 0/4, the peaks of Ts with t dependence can still be seen in Fig. 4(a). However, the appearance of the resonances with variation of t are not as regular as for small widths, aλ 0/4, because of the 2D asymmetric nature of the field distributions in the slit region and the weak confinement ability of the slit cavities for large widths a and small thicknesses t.

Fig. 4. Variation of (a) squared transmitted intensity normalized with slit width a for various slit widths a and thicknesses t for a sole incident SPP. Standing wave fringes inside the slit in (b) vertical F-P modes (a=120nm, t=1μm) and (c) horizontal F-P modes (a=1μm, t=310nm).

For a given slit thickness tλspp/2=235nm, the peaks of Ts for the slit widths a around λ 0/2, λ 0 and 3λ 0/2, are due to the horizontal bulk wave F-P resonances. The peaks at aλ 0/2 and ⃑∼λλ 0 are spaced with an interval slightly larger than λ 0/2.

3. Enhancement and suppression of transmission through field interference

We first computed the fields of Ex, Ey, Hz and electrical charge distributions when a single p-polarized narrow beam is normally incident on the groove. As described in Section 2, this beam generates the SPP propagating on the top metal surface and impinging on the slit from the left side.

Fig. 5. Poynting S⃑ (blue arrows) and surface current density vectors J⃑ (red arrows) for a single normal incident beam on the slit (a=250nm, t=300nm). The length of arrows is proportional to the amplitude. Signs +/- indicate polarities of accumulated electric charges.

Then, we computed the field distributions when a single p-polarized narrow beam is normally incident on the slit. For this latter configuration, the FDTD results have been well described in [5

5. A.R. Zakharian, M. Mansuripur, and J.V. Moloney, “Transmission of light through small elliptical apertures,” Opt. Express 12,2631–2648 (2004). [CrossRef] [PubMed]

,6

6. Y. Xie, A.R. Zakharian, J.V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12,6106–6121 (2004). [CrossRef] [PubMed]

]. The incident beam induces surface currents and accumulated electrical charges in the vicinity of the slit, which form two electric dipoles of nearly the same phase on the top and the bottom ridges of the aperture and parallel to the film surfaces. Fig. 5 shows the computed Poynting vectors, surface currents and induced electric dipoles in the vicinity of the slit for this case. The waves traveling along the slit axis form the F-P slit waveguide modes. In addition, the SPPs are excited and propagate away from the nanoslit in the ±x directions on both the top and bottom metal film surfaces.

We added the two individual field distributions by the instantaneous amplitudes of each component in the slit neighborhood, and then we computed the field distributions produced when the two beams are normally incident on the groove and the slit respectively and simultaneously. We found that the addition of the two individual field and charge distributions resulting from the two respective incident beams is identical to that resulting from the two simultaneously incident beams. Thus, we confirm that the interference between the normally incident beam and the incident SPP does occur around and inside the slit. This is natural since the structure responds linearly to the two individual incident beams when nonlinear effects are not taken into account.

The 2D field interference pattern on the top and bottom metal planes and inside the slit varies with the slit width a, thickness t and the incident SPP propagation distance L, which controls the relative phase of the SPP-induced distribution with respect that induced by the normally incident beam. The slit transmission is enhanced by the incident SPP, when the two distributions are superposed constructively. It is reduced when the two distributions are superposed destructively.

Fig. 6. Slit transmittance Ts (normalized on the transmission of a single normal beam on the slit) as a function of the slit-groove distance L. Slit parameters: a=250nm, t=300nm.

Figure 6 shows the slit intensity transmission coefficient Ts with the two incident beams, on the groove and on the slit, normalized by that of a single beam normally incident on the slit, as a function of the SPP propagation distance L. For constructive interference, the bare slit transmittance can be enhanced by more than 1.3 by the incident SPP on the slit. When the two distributions are superposed destructively, the transmittance can drop as low as 0.72 compared to the bare slit transmittance.

4. Conclusion

We have investigated the interference of the surface plasmon polariton (SPP) with an incident beam on a metallic nanoslit using the FDTD. The incident SPP on the film top surface is coupled into the slit by inducing oscillating electric charges at the slit edges which can emulate an oblique dipole that reradiates bulk waves inside and out of the slit, and excites new SPPs on the slit walls. The scattered bulk waves leaked into the slit form Fabry-Perot (F-P) resonator modes between the two slit walls. The excited new SPPs on the slit walls create the F-P resonator modes along the slit axis. The values of the slit width and thickness for the two types of cavity resonances are shifted from that of the standard F-P resonance conditions because of the asymmetric nature of the field distributions in the slit. We have demonstrated the interference between the impinging SPP and the normally incident beam by addition of their respectively induced modes in the slit through SPP/bulk-wave conversion. The slit transmission is enhanced or suppressed by the interference, depending on the relative phase between the incident SPP and the incident beam.

References and links

1.

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391,667–669 (1998). [CrossRef]

2.

T. Thio, K.M. Pellerin, R.A. Linke, T.W. Ebbesen, and H.J. Lezec, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26,1972–1974 (2001). [CrossRef]

3.

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]

4.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-Assisted Two-Slit Transmission: Young’s Experiment Revisited,” Phys. Rev. Lett. 94, 053901 (2005). [CrossRef] [PubMed]

5.

A.R. Zakharian, M. Mansuripur, and J.V. Moloney, “Transmission of light through small elliptical apertures,” Opt. Express 12,2631–2648 (2004). [CrossRef] [PubMed]

6.

Y. Xie, A.R. Zakharian, J.V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12,6106–6121 (2004). [CrossRef] [PubMed]

7.

Y. Xie, A.R. Zakharian, J.V. Moloney, and M. Mansuripur, “Transmission of light through a periodic array of slits in a thick metallic film,” Opt. Express 13,4485–4491 (2005). [CrossRef] [PubMed]

8.

J. A. Sanchez-Gil and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60,8359–8367 (1999). [CrossRef]

9.

J. A. Sanchez-Gil and A. A. Maradudin, “Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects,” Opt. Express 12,883–894 (2004). [CrossRef] [PubMed]

10.

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 2nd edition, Artech House, Boston, 2000.

11.

Aleksandar D. Rakic, Aleksandra B. Djuristic, Jovan M. Elazar, and Marian L. Majewski, “Optical properties of metallic films,” Appl. Opt. 37,5271–5283 (1998). [CrossRef]

12.

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

13.

T. A. Leskova, “Theory of a Fabry-Perot Type Interferometer for Surface Polaritons,” Solid State Commun. 50,869–873 (1984). [CrossRef]

14.

Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86,5601–5603 (2001). [CrossRef] [PubMed]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(260.3160) Physical optics : Interference
(260.3910) Physical optics : Metal optics

ToC Category:
Optics at Surfaces

History
Original Manuscript: November 14, 2006
Revised Manuscript: January 19, 2007
Manuscript Accepted: January 22, 2007
Published: February 5, 2007

Citation
Bora Ung and Yunlong Sheng, "Interference of surface waves in a metallic nanoslit," Opt. Express 15, 1182-1190 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-3-1182


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T.W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667-669 (1998). [CrossRef]
  2. T. Thio, K. M. Pellerin, R. A. Linke, T. W. Ebbesen, and H. J. Lezec, "Enhanced light transmission through a single subwavelength aperture," Opt. Lett. 26, 1972-1974 (2001). [CrossRef]
  3. 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]
  4. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005). [CrossRef] [PubMed]
  5. A. R. Zakharian, M. Mansuripur, and J. V. Moloney, "Transmission of light through small elliptical apertures," Opt. Express 12, 2631-2648 (2004). [CrossRef] [PubMed]
  6. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through slit apertures in metallic films," Opt. Express 12, 6106-6121 (2004). [CrossRef] [PubMed]
  7. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through a periodic array of slits in a thick metallic film," Opt. Express 13, 4485-4491 (2005). [CrossRef] [PubMed]
  8. J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359-8367 (1999). [CrossRef]
  9. J. A. Sanchez-Gil and A. A. Maradudin, "Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects," Opt. Express 12, 883-894 (2004). [CrossRef] [PubMed]
  10. A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 2nd edition, (Artech House, Boston, 2000).
  11. A. D. Rakic, A. B. Djuristic, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films," Appl. Opt. 37, 5271-5283 (1998). [CrossRef]
  12. H. Raether, Surface Polaritons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  13. T. A. Leskova, "Theory of a Fabry-Perot Type Interferometer for Surface Polaritons," Solid State Commun. 50, 869-873 (1984). [CrossRef]
  14. Y. Takakura, "Optical resonance in a narrow slit in a thick metallic screen," Phys. Rev. Lett. 86, 5601-5603 (2001). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited