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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 15 — Jul. 20, 2009
  • pp: 12714–12722
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A method to design transmission resonances through subwavelength apertures based on designed surface plasmons

Jinsong Liu, Lan Ding, Kejia Wang, and Jianquan Yao  »View Author Affiliations


Optics Express, Vol. 17, Issue 15, pp. 12714-12722 (2009)
http://dx.doi.org/10.1364/OE.17.012714


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Abstract

A plasmonic metamaterial is proposed for which an array of subwavelength apertures is pierced into a metallic foil whose one flat surface has been made with periodic rectangle holes of finite depth. Designed surface plasmons sustained by the holes are explored when the size and spacing of the holes are much smaller than those of the apertures. The transmission property of electromagnetic waves through the metamaterials is analyzed. Results show that the designed surface plasmons characterized by the holes could support the transmission resonances of the incident wave passing through the subwavelength apertures, and that the peak transmission wavelengths could be designed by controlling the geometrical and optical parameters of the holes. Example is taken at THz regime. Our work proposes a method to design the peak wavelengths, and may affect further engineering of surface plasmon optics, especially in THz to microwave regimes.

© 2009 OSA

1. Introduction

DSPs promise the ability to engineer a SP on structured metal surfaces. It is the character distinguishes DSPs from SPs. This character allows us to actively design some relevant experiments, such as microwave reflectivity measurements [6

6. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005). [CrossRef] [PubMed]

] and highly confined guiding THz surface wave [11

11. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]

]. However, based on the DSP theory to actively design the transmission property of electromagnetic waves through subwavelength apertures have not been considered so far. This mainly originates from the fact that the analytical form of the dispersion relationship for DSPs has not been found when the DSPs are sustained by subwavelength apertures whose size and spacing are comparing to the incident wavelength. As we know that the analytical form is available for DSPs sustained by arrays of holes whose size and spacing are much smaller than the incident wavelength, we naturally address an idea as the following: Can we construct a kind of new plasmonic metamaterials by which we can use the DSP theory to actively design an experiment of the transmission resonances of electromagnetic waves through subwavelength apertures in THz domain? Such metamaterials are made of metallic foils. At first, some rectangle holes of finite depth are made on one flat surface of the foil with the size and spacing of the holes being much smaller than the incident wavelength. And then arrays of subwavelength apertures are pierced on the foil. We imagine that the DSP states sustained by the holes of finite depth could support the transmission resonances of incident radiation through the subwavelength apertures. In this paper, based on the DSP’s theory [5

5. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

,7

7. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: New plasmonic metamaterials,” J. Opt. A 7, S97–S101 (2005). [CrossRef]

], we obtain an analytical form of the dispersion relationship for the anisotropic DSP states sustained by the holes, and then analyze theoretically the transmission property of radiation through the subwavelength apertures. Results indicate that the DSP states characterized by the holes could support the transmission resonances of THz radiation through the subwavelength apertures. The formula of the peak transmission wavelengths is obtained, which involves the geometrical and optical parameters of the metamaterials, including those of the holes, indicating that the peak wavelengths could be designed by controlling the parameters of the holes. The shape of holes is chosen as rectangle because it involves three geometrical parameters, i.e., long side, short side and depth, more than that of square or circle shape, thus allowing us to adjust more parameters to design the peak wavelengths. Numerical examples are taken at THz regime. Our research propose a method to use the DSP theory to design experiments of transmission resonances, and may affect further engineering of surface plasmon optics, especially in THz to microwave regimes.

2. Theoretical model

At first, we pay our attention on the structure of a metallic foil pierced with periodic rectangle holes of infinite depth and are devoted to find the effective medium of this structure. A set of a × b rectangle holes arranged on a d × d lattice is made into a square metallic foil, as shown in Fig. 1 (a)
Fig. 1 (a) A set of a × b rectangle holes of infinite depth arranged on a d × d lattice is pierced into a square metallic foil. (b) A set of a × b rectangle holes with finite depth h arranged on a d × d lattice is made on one surface of a square metallic foil. (c) In the effective medium approximation the structure displayed in (b) behaves as a homogeneous but anisotropic layer of thickness h on top of a perfect conductor.
. A cartesian coordinate is built for which the x- and y-axis are parallel to the sides a and b, respectively, and the z-axis is normal to the surface of the foil. For such a structure, if a,b<d<<λ, where λ is the wavelength of radiation, externally incident radiation is insensitive to the details of the holes, which it can see only an average response that can be described by an effective anisotropic homogeneous medium with effective permittivity εx, εy, and εz, and effective permeability μx,μy, and μz, for which εz and μz were determined as εz= and μz= by observing that the dispersion of the waveguide mode in the holes is unaffected by parallel momentum [5

5. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

,7

7. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: New plasmonic metamaterials,” J. Opt. A 7, S97–S101 (2005). [CrossRef]

]. In what follows, we will endeavor to find the expressions of εx,εy, μy, and μz for the asymmetric structure.

For the waveguide modes excited by an incident wave, both electric and magnetic fields are zero inside the conductor but in the rectangle holes the electric fields of transverse electric (TE) waveguide modes TEmn have the form
{Ex=Ex0(mn)cos(mπax)sin(nπby)exp(ikzziωtiπ/2)Ey=Ey0(mn)sin(mπax)cos(nπby)exp(ikzziωt+iπ/2)Ez=0,x<a,y<b,
(1)
where Ex0(mn)=nπbE(mn),Ey0(mn)=mπaE(mn),E(mn)=ωμμh0H0/[(mπa)2+(nπb)2], m, n = 0,1,2,3⋯, μ0 is vacuum permeability,H0 is constant, x, y and z are cartesian coordinates, ω is the angular frequency, t is time, i=1and
kz=kz(mn)=i(mπa)2+(nπb)2(nhk0)2,
(2)
where k0 is the free space wave vector, nh=εhμh, εh and μh are the permittivity and permeability, respectively, of any material that may be filling the rectangle holes. The magnetic fields H=(Hx,Hy,Hz)T follow from Eq. (1), where the superscript T denotes the operation of transposition.

For these waveguide modes, only those modes TEm0 and TE0n (m, n ≥1) can sustain DSP states because the average fields at the surface are equal to zero for the modes TE mn with m≠0 and n ≠0. As we are interested in the limita,b<<λ, we assume that the fundamental modes will dominate because they are the least strongly decaying. We thereby only consider two modes: TE10 and TE01. For the mode TE10, we have H=(Hx,0,Hz)T and E=(0,Ey,0)T with
Ey=Ey0sin(πax)exp(ikzziωt+iπ2),0<x<a,0<y<b,
(3)
where Ey0=(π/a)E(10) . We then suppose that there exist effective homogeneous fields in the effective medium as H=(Hx,0,Hz)T and E=(0,Ey,0)T with
Ey=Ey0exp(ikzz+ikxxiωt),
(4)
in which kz is the same as in the waveguide, i.e., kz=kz, and kx is defined by the incident direction. If this effective field is to match to the incident and reflected fields external to the surface, Ey and Ey must give the same average fields at the surface. Hence, by the use of the two equations above, after matching to incident and reflected waves, we have
E¯y=0bdy0aEydxd2=Ey0bd20asin(πax)dx=2Ey0abπd2=Ey0.
(5)
By taking the same approach, we have Hz = 0 because H¯z=0and Hx≠0, indicating that the effective homogeneous fields only have two components Ey and Hx, thus we have kz=εyμxk0 and (E×H)z=Ey2kz/(ωμ0μx). We then consider the instantaneous flows of energy across the surface, (S)z=(E×H)z and (S)z=(E×H)z. They must be the same inside and outside the surface, both for the real and effective media, thus we have
(E×H)z¯=kzωμhμ0Ey02d20bdy0asin2(πax)dx=kzEy02ab2ωμhμ0d2=(E'×H')z¯=kzEy02ωμxμ0.
(6)
From the two equations above, we have
μx=8abπ2d2μh,
(7)
Substitute kz=εyμxk0 and Eq. (7) into Eq. (2) with m = 1 and n = 0, we have
εy=π2d28abεh(1ωa2ω2).
(8)
ωa=πcnha,
(9)
where c is the velocity of wave in a vacuo.

For the mode TE01, we have H=(0,Hy,Hz)T and E=(Ex,0,0)T with
Ex=Ex0sin(πby)exp(ikzziωtiπ2),0<x<a,0<y<b,
(10)
where Ex0=(π/b)E(01). We then suppose that the effective homogeneous fields in the medium are H=(0,Hy,Hz)T and E=(Ex,0,0)T with
Ex=Ex0exp(ikzz+ikyyiωt),
(11)
in which kz=kz, too, and ky is defined by the incident direction. For this case, similarly, we have kz=εxμyk0. By the use of the same approach as above, we obtain
μy=8abπ2d2μh,
(12)
εx=π2d28abεh(1ωb2ω2).
(13)
ωb=πcnhb.
(14)
The results above show that εxεy. This is easy understood for the asymmetric structure. Taking a = b, we can get the results for the case of square holes [5

5. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

,7

7. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: New plasmonic metamaterials,” J. Opt. A 7, S97–S101 (2005). [CrossRef]

].

We then consider the DSP states sustained by a structured surface with rectangle holes of finite depth. As shown Fig. 1 (b), a set of a × b rectangle holes with depth h arranged on a d × d lattice is made into one surface of a square metallic foil. In the effective medium approximation the structure displayed in Fig. 1 (b) behaves as an homogeneous but anisotropic layer of thickness h on top of a perfect conductor, as shown in Fig. 1 (c). For an interface between the effective medium layer and an isotropic homogeneous dielectric medium with εin, there should be an anisotropic bound surface state, i.e., DSP state. Let β be the wave vector of the DSP state, which has two components βx and βy in the x and y directions, respectively, thus
β=βxex+βyey.
(15)
where ex and ey are the unit vectors in the x and y directions, respectively.

After some straightforward algebra the specular reflection coefficient, Ry, for a plane wave whose electric and magnetic fields have the form Ein=(0,Eyin,Ezin)T and Hin=(Hxin,0,0)T impinging at the surface of the homogeneous but anisotropic layer of thickness h with μx and εy given by Eqs. (7) and (8) can be written as
Ry=εin1kzinεy1kz+(εin1kzin+εy1kz)exp(2ikzh)εin1kzin+εy1kz(εy1kzεin1kzin)exp(2ikzh),
(16)
here kzin=iβy2(nink0)2 with nin=εin being the refractive index of the dielectric medium. By extending this formula to the case βy>nink0 and looking at the zeros of the denominator of Ry and note that kz=εyμxk0 for this case, we can obtain
βy=ninωc1+Paω2ωa2ω2,
(17)
wherePa=PHa2 forμh=1, P=64a2b2nin2π4d4nh2and Ha1exp(2πh/a)1+exp(2πh/a) for λ>>nha. For the plane wave whose electric and magnetic fields have the form Ein=(Exin,0,Ezin)T and Hin=(0,Hyin,0)T impinging at the surface of the homogeneous but anisotropic layer of thickness h with μy and εx given by Eqs. (12) and (13), the specular reflection coefficient, Rx, can be obtained as
Rx=εin1kzinεx1kz+(εin1kzin+εx1kz)exp(2ikzh)εin1kzin+εx1kz(εx1kzεin1kzin)exp(2ikzh),
(18)
here kzin=iβx2(nink0)2 . Note that kz=εxμyk0 for this case, similarly, we have
βx=ninωc1+Pbω2ωb2ω2.
(19)
wherePb=PHb2 for μh=1, and Hb1exp(2πh/b)1+exp(2πh/b) for λ>>nhb.

From Eqs. (17) and (19), we can obtain the dispersion curves of the anisotropic DSP waves, as shown in Fig. 2
Fig. 2 Dispersion curves obtained from Eqs. (17) and (19) for ω (in units of ωa=πc/a) varying with βy and βx, respectively, withnin=1,nh=1, a = 45μm, b = 45μm, h = 45μm, and d = 60μm.
. Notably, the asymptotic frequencies corresponding to βx and βy are different, in contrast to an array of square holes where such two asymptotic frequencies are the same [5

5. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

].

For a foil with arrays of holes of finite depth made on its one surface, when an incident wave with λ>>d>a,b impinges at the surface, this wave will see only an average response that can be described by the effective anisotropic homogeneous medium layer as described above. If the foil is pierced with arrays of subwavelength apertures with size A and spacing D, as shown in Fig. 3
Fig. 3 Schematic structure of the proposed plasmonic metamaterial. A set of subwavelength square apertures with size A arranged on a D × D lattice is cut into a metallic foil whose one surface has been made with rectangle holes whose sizes a and b, depth h, and spacing d are smaller than A and D at least one order of magnitude.
, the incident wave will passes through the apertures. The DSP states sustained by the holes could support the transmission resonances of incident wave through the subwavelength apertures. The dispersion relation for DSPs associated with this case is not well established. Nevertheless, it has been shown experimentally that the SP dispersion relation for a plane metal-dielectric interface without subwavelength apertures allows one to determine the locations of the transmission peaks when the interface is perforated at optical frequencies to good approximation. Therefore, we assume that such an approximation is equally valid here, thus the conservation of momentum is then given by [4

4. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

]
β=±jGx±lGy,
(20)
for radiation normally incident of the interface, where j and l are zero and integers, Gx and Gy are the reciprocal lattice vectors for a square lattice with Gx=Gy=2π/D. From the two equations above, we find that the locations of transmission peak wavelengths are given by
λ=λjl=ninDj2+l22+Paλa2λ2λa2+Pbλb2λ2λb2.
(21)
where λa=2nha, and λb=2nhb. Note that the peak wavelengths depend on the geometrical and optical parameters of the pierced foils, especially on those of the holes, thus allowing us to design the peak wavelengths by adjusting the parameters of the holes.

It is necessary to point out that Eq. (21) is obtained following the approach presented in Ref. 4

4. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

, in which only the momentum-matching condition was considered. This equation hence does not take into account the boundary condition between the transmission region and inside the aperture. As a consequence, it neglects some physical processes [19

19. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

], such as the interference that gives rise to a resonance shift [20

20. C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003). [CrossRef]

].

3. Numerical results

In order to establish a concept of magnitude, we carried out the calculations of λ10, λ11 and λ12 for nh, a, b, h, and d with nin=1 and D = 500 μm. Figures 4
Fig. 4 The normalized peak wavelengths λ10/λ100, λ11/λ110 and λ12/λ120 vary with the parameters nh, d and h. (a) a = b = h = 45μm, and d = 60μm. (b) a = b = h = 45μm, and nh=1. (c) a = b = 45μm, d = 60μm, and nh=1. The normalized parameters are taken as λ100=707.10 μm, λ110=500.0 μm and λ120=316.22 μm.
and 5
Fig. 5 The peak wavelengths vary with the parameters a and b for h = 45μm, d = 60μm, and nh=1. (a) λ10. (b) λ11. (c) λ12
show the parameter dependence of these peak wavelengths. In Fig. 4, we use λ100=707.10 μm, λ110=500.0 μm and λ120=316.22 μm to normalize the values of λ10, λ11 and λ12, respectively. In fact, these parameters are those ones of λ10, λ11 and λ12 at Pa=Pb=0, corresponding to the peak wavelengths of the subwavelength square apertures without the rectangle holes. As can be seen from Fig. 4 (a), λ10will increase from 708.30 μm to 708.48 μm for nh increasing from 1 to 3, having a wavelength shift Δλ10=0.18 μm, while the corresponding values forλ11 and λ12being Δλ11=0.61 μm and Δλ12=5.27 μm, respectively, meaning that the higher the peak wavelength’s order is, the more sensitively the peak wavelength varies with nh. If we took a nematic liquid crystal as the material to fill the holes, we could adjust the peak wavelength via controlling the refractive index of the crystal by applying a magnetic field [21

21. C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, “Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal,” Opt. Express 13(11), 3921–3930 (2005). [CrossRef] [PubMed]

]. The biggest advantage lies in here is that there is no any materials filling the subwavelength square apertures for which the THz wave will pass through. For the other parameters (that is, a, b, h, and d), the higher the order of the peak wavelength is, the more sensitively the peak wavelength varies with these parameters, which is the same as that of the parameternh. These numerical examples indicate that the peak wavelengths could be designed in a certain extent by adjusting the geometrical and optical parameters of the array of the rectangle holes, indicating that the DPS states sustained by the rectangle holes would affect the transmission property of electromagnetic wave passing through the subwavelength apertures.

4. Discussion and conclusion

The present experiments at THz regime cannot be used to check the theoretical results above because only those subwavelength apertures with the size and spacing being hundred-micron dimension were cut in freestanding 75 µm thick stainless steel foils [22

22. H. Cao and A. Nahata, “Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures,” Opt. Express 12(16), 3664–3672 (2004). [CrossRef] [PubMed]

]. Some suitable experiments are expected for which the samples should be pierced with subwavelength apertures and drilled with holes whose size and spacing should be taken as ten-micron dimension or less. Such experiments not only can be used to check the results above, but also would provide evidences for the existence of DSP states at THz regime. Our research proposes a way to connect the DSP theory to the engineering of surface plasmon optics, for which the creation of designer SPs with expectant resonant peaks could readily be realized by controlling the parameters of the holes, especially in THz to microwave regimes.

Acknowledgments

The Research Foundation of Wuhan National Laboratory under Grant No. P080008 and National “973” Project under Grant No. 2007CB310403 have supported this research.

References and links

1.

S. A. Maier, Plasmonics—Fundamentals and Applications (Springer, New York, 2007).

2.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

3.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

4.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

5.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

6.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005). [CrossRef] [PubMed]

7.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: New plasmonic metamaterials,” J. Opt. A 7, S97–S101 (2005). [CrossRef]

8.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401–197404 (2005). [CrossRef] [PubMed]

9.

D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23(3), 391–403 (2006). [CrossRef]

10.

M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, “Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays,” Opt. Lett. 30(10), 1210–1212 (2005). [CrossRef] [PubMed]

11.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]

12.

L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]

13.

Y. C. Lan and R. L. Chern, “Surface plasmon-like modes on structured perfectly conducting surfaces,” Opt. Express 14(23), 11339–11347 (2006). [CrossRef] [PubMed]

14.

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88(25), 251120 (2006). [CrossRef]

15.

F. J. García de Abajo and J. J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95(23), 233901 (2005). [CrossRef]

16.

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008). [CrossRef]

17.

Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90(20), 201906 (2007). [CrossRef]

18.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008). [CrossRef] [PubMed]

19.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

20.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003). [CrossRef]

21.

C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, “Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal,” Opt. Express 13(11), 3921–3930 (2005). [CrossRef] [PubMed]

22.

H. Cao and A. Nahata, “Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures,” Opt. Express 12(16), 3664–3672 (2004). [CrossRef] [PubMed]

OCIS Codes
(120.7000) Instrumentation, measurement, and metrology : Transmission
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(260.2110) Physical optics : Electromagnetic optics
(310.2790) Thin films : Guided waves
(040.2235) Detectors : Far infrared or terahertz

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 12, 2009
Revised Manuscript: June 24, 2009
Manuscript Accepted: July 3, 2009
Published: July 20, 2009

Citation
Jinsong Liu, Lan Ding, Kejia Wang, and Jianquan Yao, "A method to design transmission resonances through subwavelength apertures based on designed surface plasmons," Opt. Express 17, 12714-12722 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12714


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References

  1. S. A. Maier, Plasmonics—Fundamentals and Applications (Springer, New York, 2007).
  2. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
  3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
  4. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]
  5. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]
  6. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005). [CrossRef] [PubMed]
  7. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: New plasmonic metamaterials,” J. Opt. A 7, S97–S101 (2005). [CrossRef]
  8. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401–197404 (2005). [CrossRef] [PubMed]
  9. D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23(3), 391–403 (2006). [CrossRef]
  10. M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, “Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays,” Opt. Lett. 30(10), 1210–1212 (2005). [CrossRef] [PubMed]
  11. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]
  12. L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]
  13. Y. C. Lan and R. L. Chern, “Surface plasmon-like modes on structured perfectly conducting surfaces,” Opt. Express 14(23), 11339–11347 (2006). [CrossRef] [PubMed]
  14. S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88(25), 251120 (2006). [CrossRef]
  15. F. J. García de Abajo and J. J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95(23), 233901 (2005). [CrossRef]
  16. E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008). [CrossRef]
  17. Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90(20), 201906 (2007). [CrossRef]
  18. Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008). [CrossRef] [PubMed]
  19. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
  20. C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003). [CrossRef]
  21. C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, “Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal,” Opt. Express 13(11), 3921–3930 (2005). [CrossRef] [PubMed]
  22. H. Cao and A. Nahata, “Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures,” Opt. Express 12(16), 3664–3672 (2004). [CrossRef] [PubMed]

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