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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 9 — May. 1, 2006
  • pp: 3730–3737
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Extraordinary optical reflection from sub-wavelength cylinder arrays

Raquel Gomez-Medina, Marine Laroche, and Juan José Sáenz  »View Author Affiliations


Optics Express, Vol. 14, Issue 9, pp. 3730-3737 (2006)
http://dx.doi.org/10.1364/OE.14.003730


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Abstract

A multiple scattering analysis of the reflectance of a periodic array of sub-wavelength cylinders is presented. The optical properties and their dependence on wavelength, geometrical parameters and cylinder dielectric constant are analytically derived for both s- and p-polarized waves. In absence of Mie resonances and surface (plasmon) modes, and for positive cylinder polarizabilities, the reflectance presents sharp peaks close to the onset of new diffraction modes (Rayleigh frequencies). At the lowest resonance frequency, and in the absence of absorption, the wave is perfectly reflected even for vanishingly small cylinder radii.

© 2006 Optical Society of America

1. Introduction

Since the observation of enhanced transmission through a metallic film perforated by a 2D array of sub-wavelength holes [7

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

], there has been a renewed interest in analyzing and understanding the underlying physics of both reflection and transmission “anomalies” in both 2D hole [8

8. E. Popov, M. Neviére, S. Enoch, and R. Reinisch,“Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000). [CrossRef]

, 9

9. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen,“Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114 (2001). [CrossRef] [PubMed]

, 10

10. M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003). [CrossRef]

, 11

11. F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwave-lenght hole arrays,” Phys. Rev. E , 72, 016608, (2005). [CrossRef]

, 12

12. J. B. Pendry, L. Martín-Moreno, and F.J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 (2004). [CrossRef] [PubMed]

, 13

13. F. J. García de Abajo and J. J. Sáenz, “Electromagnetic surface states in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901 (2005). [CrossRef]

, 14

14. F. J. García de Abajo, J.J. Sáenz, I Campillo, and J.S. Dolado, “Site and Lattice Resonances in Metallic Hole Arrays,” Opt. Express 14, 7 (2006). [CrossRef] [PubMed]

] and 1D slit [15

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

, 8

8. E. Popov, M. Neviére, S. Enoch, and R. Reinisch,“Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000). [CrossRef]

, 16

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

, 17

17. F. Yang and J.R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002). [CrossRef] [PubMed]

, 18

18. F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002) [CrossRef]

] arrays. Although the enhanced transmission is commonly associated to the excitation of surface plasmons [7

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

, 8

8. E. Popov, M. Neviére, S. Enoch, and R. Reinisch,“Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000). [CrossRef]

, 9

9. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen,“Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114 (2001). [CrossRef] [PubMed]

], dynamical diffraction resonances [10

10. M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003). [CrossRef]

, 19

19. M. M. J. Treacy,“Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002). [CrossRef]

, 20

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

] are also invoked as the origin of the effect. Recent theoretical and experimental works put forward that the excitation of any surface plasmons was not required [11

11. F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwave-lenght hole arrays,” Phys. Rev. E , 72, 016608, (2005). [CrossRef]

, 20

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

]. Consequently, there remains some controversy surrounding the transmission mechanism [21

21. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004). [CrossRef] [PubMed]

, 22

22. Q. Cao and P. Lalanne, “Negative Role of Surface Plasmons in the Transmission of Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 88, 057403(2002). [CrossRef] [PubMed]

, 23

23. 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 (2003). [CrossRef]

, 20

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

, 24

24. K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,“Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72, 045421 (2005). [CrossRef]

]. In this work we discuss the physics behind the (Babinet) complementary problem: the extraordinary reflection from a periodic array of sub-wavelength scatterers.

In absence of resonant surface modes (or surface plasmons for metallic particles) the scattering cross section of subwavelength-sized particles is very small [25

25. H.C. van de Hulst, Light Scattering by small particles (Dover, New York, 1981).

, 26

26. C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1998). [CrossRef]

]. However, in a periodic array of small particles, the coupling of the scattered dipolar field with diffraction modes may induce a geometric resonance close to the onset of new propagating modes (i.e. close to the Rayleigh frequencies). Following a multiple scattering approach [27

27. V. Twersky, “Multiple scattering of waves and optical phenomena,” J. Opt. Soc. Am 52, 145 (1962). [CrossRef] [PubMed]

, 28

28. K. Ohtaka and H. Numata, “Multiple scattering effects in photon diffraction for an array of cylindrical dielectric,” Phys. Lett. 73A, 411 (1979).

, 29

29. Ch. Kunze and R. Lenk, “A single scatter in a quantum wire: compact reformulation of scattering and transmission,” Sol. State Comm. 84, 457 (1992). [CrossRef]

], we analytically derive the resonance conditions as a function of the geometry and the polarizabilities of each individual scatterer. As we will show, in absence of absorption, it is possible to have a perfect reflected wave even for vanishingly small scatterers.

2. Scattering theory for s-polarized waves (Electric field parallel to the cylinder axis)

Let us consider an infinite set of parallel cylinders with their axis along the z-axis, relative dielectric constant ε and radius a much smaller than the wavelength. The cylinders are located at r n = nD u x = xn u x (with n an integer number). For simplicity, we will assume incoming plane waves with wave vector k 0u z (i.e. the fields do not depend on the z-coordinate)

k0=ksinθux+kcosθuyQ0ux+q0uy,
(1)

and k =ω/c.

Let us first consider an incoming wave with the electric field parallel to the cylinder axis (s-polarized wave, see Fig. 1), E = E(r)u z = E0 e iQ0x e iq0y u z. The scattered field from a given cylinder n, can be written as [25

25. H.C. van de Hulst, Light Scattering by small particles (Dover, New York, 1981).

, 26

26. C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1998). [CrossRef]

]:

Enscatt(r)=αzzEin(rn)k2G0rrn
(2)

where

αzzπa2(ε1)[1iπ4(ka)2(ε1)]1,
(3)

G 0(r,r n) = (i/4)H 0(kr-r n∣) is the free-space Green function (H 0 is the Hankel function), and Ein(r n) is the incident field on the scatterer. Since for a periodic array Ein(r m) = Ein(r 0)e iQ0xm, the total scattered field can be written as

Escatt(r)=(αzzEin(r0))k2G(r)
(4)
Fig. 1. (s-polarization) Calculated reflectance R in a frequency ω versus in-plane wave number Q 0 = (ω/c)sin(θ). The reflectance along the vertical lines is shown in the inset.

where the total Green function G(r) is given by:

G(r)n=+eiQ0xnG0rrn=1Dm=ei(Q0Km)x(i2qmeiqmy)
(5)

with Km = 2πm/D and k 2 = qm2 +(Q 0 -Km )2.

Multiple scattering effects manifest themselves in the actual incident field on each cylinder [27

27. V. Twersky, “Multiple scattering of waves and optical phenomena,” J. Opt. Soc. Am 52, 145 (1962). [CrossRef] [PubMed]

, 29

29. Ch. Kunze and R. Lenk, “A single scatter in a quantum wire: compact reformulation of scattering and transmission,” Sol. State Comm. 84, 457 (1992). [CrossRef]

]: Ein(r 0) is given by the incoming plane wave plus the scattered fields from other cylinders, i.e.

Ein(r0)=E0+αzzk2m0Ein(rm)G0r0rm=E0+αzzk2Ein(r0)Gb
=(1αzzk2Gb)1E0
(6)

where Gb = limrr0 [G(r)-G 0(r,r 0)]. The calculation of Gb involves the sum of a (poorly converging) series of Hankel functions. The convergence can be improved by using the well known result ∑n=1 e -byn/n = -ln(1-e -by) [30

30. P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.

, 31

31. R.E. Collin and W.H. Eggimann,“Dynamic Interaction Fields in a Two-Dimensional Lattice,” IRE Trans. on Microwave Theory and Techniques , MTT-9, 110 (1961). [CrossRef]

]. Finally, Gb is found to be given by

Gb=i{12Dq014}+12Dm=1(iqm+iqm2Km)+12π(ln{kD4π}+γE).
(7)

The total scattered field (eq. 4) can then be rewritten as

Escatt(r)=α̂zzE0k2G(r)
(8)

where all multiple scattering effects are included in the renormalized polarizability, α^ zz,

k2α̂zz=(1k2αzzGb)1.
(9)
Fig. 2. (s-polarization) (a) Plot of ℜ{Gb } and ℜ{1/(k 2αzz} versus frequency along the constant Q 0 line in Fig. 1 (Q 0 = 0.8π/D)). The crossing points (open circles) correspond to different resonant frequencies ω 0m. (b) Calculated reflectance R versus ω. The inset shows a zoom-out of the ω 01 resonance. Dashed lines corresponds to the approximate expression given in eq. 15 with no fitting parameters.

In order to calculate the transmittance/reflectance we consider the far-field limit (∣y∣→∞) where only propagating diffraction orders (or channels) contribute to the scattered power. The total field, for both s- and p-polarizations (see below) can be written in the general form

ψ(r)=ψ0eiQ0xeiq0y+ψ0mPropi4πf̂qmq02Dqmei(Q0Km)xeiqmy
(10)

where 4πf̂(qm ,q 0) is the scattering amplitude and the sum runs only over modes having ∣Q 0 -Km ∣ < k. The transmittance T (reflectance R), defined as the ratio between transmitted (reflected) power and incoming power is shown to be

T=12{4πf̂q0q0}2Dq0+1D2nProp(4πf̂q0q024qnq0)
(11)
R=1D2nProp(4πf̂qnq024qnq0).
(12)

For s-polarization (4πf̂(qm ,q 0) = α^ zz k 2) the scattering amplitude is isotropic and

R={G(0)}2Dq0α̂zzk22.
(13)

since {G(0)}=nProp12Dqn.

In absence of absorption (T +R = 1), ℑ{1/(k 2αzz) = - ℑ{G 0(0)}, we obtain

R=G(0)}2Dq0(2{1k2αzzGb}+2G(0)})1
(14)

(where ℜ2{x} = (Real{x})2 and ℑ2{x} = (Imag{x})2). Figure 1 presents the calculated reflectance in a ω vs. Q 0 map (frequency versus in-plane wave number Q 0 = ksin θ). For simplicity, we have considered a real dielectric constant (ε > 1) independent of the frequency (the results correspond to (2πa/D)2(ε - 1) ≈ 4/9). The physics of the reflectance/transmittance can be understood from a simple argument (see Fig. 2): For small cylinders and ε > 1, ℜ{1/(k 2αzz)} > 0 is large and dominates the renormalized polarizability. However, approaching the threshold of a new propagating channel (i.e. ωωm() = cQ 0 - Km ∣)qm goes to zero. Then, the contribution of the lowest evanescent mode to ℜ{Gb } outweighs all the others and ℜ{Gb } ≈ (2D qm )-1 diverging at the threshold. The precise compensation of these two large terms at ω = ω 0m (see Fig. 2(a)) gives rise to a geometric resonance. Very close to each resonance, the reflectance along the vertical lines in Fig. 1 (i.e. for a given Q 0) can then be approximated as

R(ωωm)Rmax(1γ2(1ωm2ωm2ωm2ω2)2+1)1
(15)

where R max=(2D q 0ℑ{G(0)})-1 and γ= ℑ{G(0)}/ℜ{1/(k 2αzz)}. As shown in Fig. 2(b), the reflection resonances present typical asymmetric Fano line shapes: The reflectance presents sharp maxima R = R max at frequencies ω = ω 0mωm . Just at the onset of a new diffraction channel, i.e. at the Rayleigh frequencies ω = ωm the reflectance goes to zero. For ω = ω 01, i.e. at the lowest resonance frequency, there is a perfect reflection (R = 1) even for vanishingly small cylinders (although, in these extreme cases, the resonance width Γ ≈ γ(ωm2 - ω0m2)/ωm goes to zero). Notice that for metallic cylinders or strips (with α < 0) there will be no sharp resonances. This is consistent with the Babinet complementary system of a periodic array of slits [15

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

, 8

8. E. Popov, M. Neviére, S. Enoch, and R. Reinisch,“Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000). [CrossRef]

, 16

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

,17

17. F. Yang and J.R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002). [CrossRef] [PubMed]

, 18

18. F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002) [CrossRef]

] where, for p-polarized waves, sharp transmittance peaks only appear for deep enough gratings (i.e. when the phase shift inside the slit changes the sign of the effective polarizability).

3. Scattering theory for p-polarized waves (Magnetic field parallel to the cylinder axis)

Let us now consider an incoming wave with the magnetic field parallel to the cylinder axis (p-polarized wave), H = H(r)u z = H0 e iQ0x e iq0y u z. The scattered (magnetic) field from a given cylinder [25

25. H.C. van de Hulst, Light Scattering by small particles (Dover, New York, 1981).

, 26

26. C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1998). [CrossRef]

] can be cast in the form:

Hnscatt(r)={αyyxHin(r)}r=rnxG0rrn{αxxyHin(r)}r=rnyG0rrn
(16)

where

αxx=αyy2πa2ε1ε+1[1iπ4(ka)2ε1ε+1]1
(17)
αxy=αyx=0
(18)

and Hin(r n) = Hin(r 0)e iQ0xn is the incident field on the scatterer. For p-polarization, multiple scattering effects manifest themselves in the actual incident magnetic field gradient on each cylinder, ∇Hin(r)∣r=rn:

Fig. 3. (p-polarization) Calculated reflectance R in a frequency ω versus in-plane wave number Q 0 = (ω/c)sin(θ). The reflectance along the vertical lines is shown in the inset.
limrr0xHin(r)=iQ0H0αyyxHin(rr=r0x2Gb=iQ0H0(1+αyyx2Gb)1
(19)

where x2 = limrr0 x2[G(r) - G 0(r, r 0)]. The resulting series can be written as [31

31. R.E. Collin and W.H. Eggimann,“Dynamic Interaction Fields in a Two-Dimensional Lattice,” IRE Trans. on Microwave Theory and Techniques , MTT-9, 110 (1961). [CrossRef]

]:

x2Gb=12Dm=1{i(KmQ0)2qm+i(Km+Q0)2qm2Kmk2Km}
k24π(ln{kD4π}+γE12)+16πD2+i(k28Q022Dq0)
(20)
y2Gb=12Dm=1{iqm+iqm+2Kmk2Km}
k24π(ln{kD4π}+γE+12)+16πD2+i(k28q022Dq0)
(21)

(notice that ∇2 Gb +k 2 Gb = 0). The total scattered field can now be written as

Hnscatt(r)=iH0α̂yyQ0xG(r)iH0α̂xxq0yG(r)
(22)

where all the multiple scattering effects have been included in a renormalized polarizability tensor α̂:

α̂xx=(1+αxxy2Gb)1αxx
(23)
α̂yy=(1+αyyx2Gb)1αyy.
(24)

The transmittance/reflectance are given by the general equations 11 and 12 with a non-isotropic scattering amplitude

4πf̂qmq0=α̂yyQ0(Q0Km)+α̂xxq0qm.
(25)

Figure 3 presents the calculated reflectance in a ω - Q 0 map. (The results correspond to non-absorbing cylinders with (2πa/D)2(ε - 1)/(ε + 1) ≈ 8/9). The physics behind the reflectance presents significant differences with respect to s-polarization Sharp peaks in the reflectance (which now appear for ε > 1 or ε < - 1) are associated to the resonant coupling of electric dipoles pointing along the y-axis which lead to the divergence of ℜ{x2 Gb } ≈ - (Q 0 - Km )2(2D qm )-1 at the Rayleigh frequencies (in contrast ℜ{y2 Gb } remains finite). In absence of absorption, the reflectance at the lowest resonant frequency can be very large but, in contrast with s-waves, strictly less than 1.

4. Conclusion

Similar resonances to the ones discussed above appear in very different contexts under the label of Fano or Feshbach geometric resonances [3

3. U. Fano, “The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves),” J. Opt. Soc. Am. 31, 213 (1941). [CrossRef]

, 32

32. H. Feshbach,“Unified theory of nuclear reactions, I”, Ann. Phys. (N.Y.) 5, 357 (1958); “A unified theory of nuclear reactions, II,” Ann. Phys. (N.Y.) 19, 287 (1962).

, 33

33. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961). [CrossRef]

]: Geometric resonances had been discussed in the context of electronic transport in waveguides [34

34. J.U. Nöckel and A.D. Stone, “Resonance line shapes in quasi-one-dimensional scattering,” Phys. Rev. B 50, 17415 (1994). [CrossRef]

], ultracold atomic collisions [37

37. M. Olshanii, “Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons,” Phys. Rev. Lett. 81, 938 (1998). [CrossRef]

] and light-atom interactions in confined geometries [35

35. R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Saénz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275 (2001). [CrossRef] [PubMed]

, 36

36. R. Gómez-Medina and J.J. Sáenz, “Unusually strong optical interactions between particles in quasi-one-dimensional geometries,” Phys. Rev. Lett. 93, 243602 (2004). [CrossRef]

, 38

38. P. Horak, P. Domokos, and H. Ritsch, “Giant Lamb shift of atoms near lossy multimod optical micro-waveguides,” Europhys. Lett. 61, 459 (2003). [CrossRef]

]. In general, Fano-Feshbach resonances occur when the energy (frequency) of the incoming wave is tuned to the energy (frequency) of a quasi-bound-state (QBS). These QBS may have a (multiple scattering -dynamical diffraction-) geometrical origin or can be an internal property of each scatterer. From the discussion above, reflectance resonances, for both s and p polarized waves, have a geometrical origin for dielectric cylinders. The existence of particle surface modes or plasmons would reflect itself in a resonant behavior of the bare polarizabilities (for p-polarized fields) and ℜ{1/αii} would present sharp maxima and minima around each internal resonant frequency. Surface modes would then induce new peaks in the reflectance or, when the surface resonance frequency is close to a Rayleigh frequency, they would mix with geometrical resonances leading to more complex reflectance patterns.

To summarize, in this work we have discussed the optical properties of an array of sub-wavelength Rayleigh cylinders. In absence of particle resonant modes, the cross-section of a single non-resonant cylinder can be extremely small and resonant effects are associated to geometrical resonances. We have shown that, for non-absorbing scatterers, it is possible to have a perfect reflected wave even for vanishingly small cylindrical radii. We believe that our study of reflectance resonances provide a new physical insight into the general mechanisms of light interactions with periodic structures of sub-wavelength objects.

Acknowledgements

We thank S. Albaladejo, R. Carminati, J. García de Abajo, J.J. Greffet, L. Froufe-Pérez and M. Thomas for interesting discussions. This work has been supported by the Spanish MCyT (Ref No. BFM2003-01167) and the EU Integrated Project “Molecular Imaging” (EU contract LSHG-CT-2003-503259).

References and links

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R.W. Wood, “On the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London A 18, 269 (1902).

2.

R.W. Wood, “Anomalous Diffraction Gratings,” Phys. Rev. 15, 928 (1935). [CrossRef]

3.

U. Fano, “The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves),” J. Opt. Soc. Am. 31, 213 (1941). [CrossRef]

4.

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. Roy. Soc. (London) A79, 399 (1907).

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A. Hessel and A.A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275 (1965) [CrossRef]

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M. Neviére, D. Maystre, and P. Vincent,“Application du calcul des modes de propagation a letude theorique des anomalies des reseaux recouverts de dielectrique,” J. Opt. (Paris) 8, 231 (1977).

7.

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

8.

E. Popov, M. Neviére, S. Enoch, and R. Reinisch,“Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000). [CrossRef]

9.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen,“Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114 (2001). [CrossRef] [PubMed]

10.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003). [CrossRef]

11.

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwave-lenght hole arrays,” Phys. Rev. E , 72, 016608, (2005). [CrossRef]

12.

J. B. Pendry, L. Martín-Moreno, and F.J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 (2004). [CrossRef] [PubMed]

13.

F. J. García de Abajo and J. J. Sáenz, “Electromagnetic surface states in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901 (2005). [CrossRef]

14.

F. J. García de Abajo, J.J. Sáenz, I Campillo, and J.S. Dolado, “Site and Lattice Resonances in Metallic Hole Arrays,” Opt. Express 14, 7 (2006). [CrossRef] [PubMed]

15.

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

16.

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

17.

F. Yang and J.R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002). [CrossRef] [PubMed]

18.

F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002) [CrossRef]

19.

M. M. J. Treacy,“Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002). [CrossRef]

20.

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

21.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004). [CrossRef] [PubMed]

22.

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

23.

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 (2003). [CrossRef]

24.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,“Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72, 045421 (2005). [CrossRef]

25.

H.C. van de Hulst, Light Scattering by small particles (Dover, New York, 1981).

26.

C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1998). [CrossRef]

27.

V. Twersky, “Multiple scattering of waves and optical phenomena,” J. Opt. Soc. Am 52, 145 (1962). [CrossRef] [PubMed]

28.

K. Ohtaka and H. Numata, “Multiple scattering effects in photon diffraction for an array of cylindrical dielectric,” Phys. Lett. 73A, 411 (1979).

29.

Ch. Kunze and R. Lenk, “A single scatter in a quantum wire: compact reformulation of scattering and transmission,” Sol. State Comm. 84, 457 (1992). [CrossRef]

30.

P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.

31.

R.E. Collin and W.H. Eggimann,“Dynamic Interaction Fields in a Two-Dimensional Lattice,” IRE Trans. on Microwave Theory and Techniques , MTT-9, 110 (1961). [CrossRef]

32.

H. Feshbach,“Unified theory of nuclear reactions, I”, Ann. Phys. (N.Y.) 5, 357 (1958); “A unified theory of nuclear reactions, II,” Ann. Phys. (N.Y.) 19, 287 (1962).

33.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961). [CrossRef]

34.

J.U. Nöckel and A.D. Stone, “Resonance line shapes in quasi-one-dimensional scattering,” Phys. Rev. B 50, 17415 (1994). [CrossRef]

35.

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Saénz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275 (2001). [CrossRef] [PubMed]

36.

R. Gómez-Medina and J.J. Sáenz, “Unusually strong optical interactions between particles in quasi-one-dimensional geometries,” Phys. Rev. Lett. 93, 243602 (2004). [CrossRef]

37.

M. Olshanii, “Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons,” Phys. Rev. Lett. 81, 938 (1998). [CrossRef]

38.

P. Horak, P. Domokos, and H. Ritsch, “Giant Lamb shift of atoms near lossy multimod optical micro-waveguides,” Europhys. Lett. 61, 459 (2003). [CrossRef]

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(290.4210) Scattering : Multiple scattering

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 14, 2006
Revised Manuscript: April 7, 2006
Manuscript Accepted: April 13, 2006
Published: May 1, 2006

Citation
Raquel Gómez-Medina, Marine Laroche, and Juan J. Sáenz, "Extraordinary optical reflection from sub-wavelength cylinder arrays," Opt. Express 14, 3730-3737 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3730


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References

  1. R.W. Wood, "On the remarkable case of uneven distribution of light in a diffraction grating spectrum," Proc. R. Soc. London A 18, 269 (1902).
  2. R.W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 15, 928 (1935). [CrossRef]
  3. U. Fano, "The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves)," J. Opt. Soc. Am. 31, 213 (1941). [CrossRef]
  4. Lord Rayleigh, "On the dynamical theory of gratings," Proc. Roy. Soc. (London) A79, 399 (1907).
  5. A. Hessel and A.A. Oliner, "A new theory of Wood’s anomalies on optical gratings," Appl. Opt. 4, 1275 (1965) [CrossRef]
  6. M. Nevière, D. Maystre, P. Vincent,"Application du calcul des modes de propagation a letude theorique des anomalies des reseaux recouverts de dielectrique," J. Opt. (Paris) 8, 231 (1977).
  7. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio and P.A. Wolf, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667 (1998). [CrossRef]
  8. E. Popov, M. Nevière, S. Enoch and R. Reinisch,"Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100 (2000). [CrossRef]
  9. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen," Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001). [CrossRef] [PubMed]
  10. M. Sarrazin, J.-P. Vigneron and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003). [CrossRef]
  11. F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelenght hole arrays," Phys. Rev. E,  72, 016608, (2005). [CrossRef]
  12. J. B. Pendry, L. Martín-Moreno, F.J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847 (2004). [CrossRef] [PubMed]
  13. F. J. García de Abajo, and J. J. Sáenz, "Electromagnetic surface states in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233901 (2005). [CrossRef]
  14. F. J. García de Abajo, J.J. Sáenz, I Campillo and J.S. Dolado, "Site and Lattice Resonances in Metallic Hole Arrays," Opt. Express 14, 7 (2006). [CrossRef] [PubMed]
  15. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845 (1999). [CrossRef]
  16. Y. Takakura, "Optical Resonance in a Narrow Slit in a Thick Metallic Screen," Phys. Rev. Lett. 86, 5601 (2001). [CrossRef] [PubMed]
  17. F. Yang and J.R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901 (2002). [CrossRef] [PubMed]
  18. F. J. García-Vidal and L. Martín -Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002) [CrossRef]
  19. M. M. J. Treacy,"Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002). [CrossRef]
  20. H. Lezec and T. Thio,"Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629 (2004). [CrossRef] [PubMed]
  21. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004). [CrossRef] [PubMed]
  22. Q. Cao and P. Lalanne, "Negative Role of Surface Plasmons in the Transmission of Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 88, 057403(2002). [CrossRef] [PubMed]
  23. 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 (2003). [CrossRef]
  24. K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers,"Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory," Phys. Rev. B 72, 045421 (2005). [CrossRef]
  25. H.C. van de Hulst, Light Scattering by small particles (Dover, New York, 1981).
  26. C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles (JohnWiley & Sons, New York, 1998). [CrossRef]
  27. V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am 52, 145 (1962). [CrossRef] [PubMed]
  28. K. Ohtaka and H. Numata, "Multiple scattering effects in photon diffraction for an array of cylindrical dielectric," Phys. Lett. 73A, 411 (1979).
  29. Ch. Kunze, and R. Lenk, "A single scatter in a quantum wire: compact reformulation of scattering and transmission," Sol. State Comm. 84, 457 (1992). [CrossRef]
  30. P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.
  31. R.E. Collin and W.H. Eggimann,"Dynamic Interaction Fields in a Two-Dimensional Lattice," IRE Trans.On Microwave Theory and Techniques, MTT- 9, 110 (1961). [CrossRef]
  32. H. Feshbach,"Unified theory of nuclear reactions, I", Ann. Phys. (N.Y.) 5, 357 (1958); "A unified theory of nuclear reactions, II," Ann. Phys. (N.Y.) 19, 287 (1962).
  33. U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866 (1961). [CrossRef]
  34. J.U. Nöckel and A.D. Stone, "Resonance line shapes in quasi-one-dimensional scattering," Phys. Rev. B 50, 17415 (1994). [CrossRef]
  35. R. G Gómez-Medina, P. San Jose, A. García- Martín, M. Lester, M. Nieto-Vesperinas, and J.J. Sáenz, "Resonant radiation pressure on neutral particles in a waveguide," Phys. Rev. Lett. 86, 4275 (2001). [CrossRef] [PubMed]
  36. R. Gómez-Medina, and J.J. Sáenz, "Unusually strong optical interactions between particles in quasi-onedimensional geometries," Phys. Rev. Lett. 93, 243602 (2004). [CrossRef]
  37. M. Olshanii, "Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons," Phys. Rev. Lett. 81, 938 (1998). [CrossRef]
  38. P. Horak, P. Domokos and H. Ritsch, "Giant Lamb shift of atoms near lossy multimod optical micro-waveguides," Europhys. Lett. 61, 459 (2003). [CrossRef]

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