OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8514–8525
« Show journal navigation

Enhanced optical transmission through sub-wavelength centered-polygonal hole arrays in silver thin film on silica substrate

Hesam Edin Arabi, Minkyu Park, Marzieh Pournoury, and Kyunghwan Oh  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 8514-8525 (2011)
http://dx.doi.org/10.1364/OE.19.008514


View Full Text Article

Acrobat PDF (1629 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We numerically investigated the enhanced optical transmission through sub-wavelength centered-polygonal hole arrays (CPHA) in a thin Ag film deposited on the silica substrate. In octagonal and decagonal-CPHAs, we observed new hybrid transmission characteristics that were inherited from both crystalline and quasi-crystalline hole arrays. This peculiar nature was attributed to the unique arrangement of CPHAs which can be covered with copies of a single unit cell as in crystalline arrays, and their rotational symmetry as observed in quasi-crystalline arrays. Hybrid natures in CPHAs were further investigated in the transmission spectra and Fourier space representations of the arrays. Contributions from the nearest neighbor hole-to-hole distance to enhanced transmission were analyzed in order to quantify the plasmonic contributions from the Air/Ag interface and Silica/Ag interface. We also investigated the impact of layer structure, Air/Ag/Air versus Air/Ag/Silica in the transmissions and found that in CPHAs in Air/Ag/Silica structures, contributions from the Air/Ag interface became dominant in contrast to crystalline hole arrays with lower fold symmetry.

© 2011 OSA

1. Introduction

Thus far crystalline hole arrays in noble metal films such as square [7

7. F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16(13), 9571–9579 (2008). [CrossRef] [PubMed]

] and hexagonal hole arrays [8

8. G. Ctistis, P. Patoka, X. Wang, K. Kempa, and M. Giersig, “Optical transmission through hexagonal arrays of subwavelength holes in thin metal films,” Nano Lett. 7(9), 2926–2930 (2007). [CrossRef] [PubMed]

] have been studied and the influence of holes size, period of arrays [7

7. F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16(13), 9571–9579 (2008). [CrossRef] [PubMed]

,9

9. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004). [CrossRef] [PubMed]

], holes depth [10

10. J. H. Kim and P. J. Moyer, “Thickness effects on the optical transmission characteristics of small hole arrays on thin gold films,” Opt. Express 14(15), 6595–6603 (2006). [CrossRef] [PubMed]

,11

11. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength hole arrays,” Appl. Phys. Lett. 81(23), 4327–4329 (2002). [CrossRef]

], and metal film properties [4

4. S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77(7), 075401.1–075401.8 (2008). [CrossRef]

] have been investigated. In recent years quasi-crystalline hole arrays with 10-fold (Penrose) [12

12. F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through penrose subwavelength hole arrays,” Appl. Phys. Lett. 89(12), 121115.1–121115, 3 (2006). [CrossRef]

], 8-fold [13

13. D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cell,” J. Mod. Opt. 53(3), 407–416 (2006). [CrossRef]

], and 12-fold [14

14. A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24(9), 2545–2554 (2007). [CrossRef]

] rotationally symmetries have been explored. In contrast to crystalline hole arrays composed of successive copies of identical unit cells, quasi-crystalline hole arrays are covered by copies of more than one type of unit cells. For instance, Penrose hole array is made of two basic rhombi (skinny and fat) [12

12. F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through penrose subwavelength hole arrays,” Appl. Phys. Lett. 89(12), 121115.1–121115, 3 (2006). [CrossRef]

,15

15. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. Dela Rau, and P. Miller, “Two dimensional penrose-tiled photonic quasicrystals: from diffraction pattern to band structure,” Nanotechnology 11(4), 274–280 (2000). [CrossRef]

,16

16. J. Xue, W. Zhou, B. Dong, X. Wang, Y. Chen, E. Huq, W. Zeng, X. Qu, and R. Liu, “Surface Plasmon enhanced transmission through planar gold quasicrystals fabricated by focused ion beam technique,” Microelectronic Engineering. http://homepage.fudan.edu.cn/~fdnil/paper/Surface%20plasmon%20enhanced%20transmission%20through%20planar%20gold.PDF.

] and other arrays made of rhombus-square and rhombus-triangular units have been reported [13

13. D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cell,” J. Mod. Opt. 53(3), 407–416 (2006). [CrossRef]

,14

14. A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24(9), 2545–2554 (2007). [CrossRef]

,17

17. S. Mei, T. Jie, L. Zhi-Yuan, C. Ying, Z. Dao-zhong, J. ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett. 23(2), 486–488 (2006). [CrossRef]

].

In this paper, we studied a different arrangement of sub-wavelength hole arrays called centered polygonal hole arrays (CPHA), where the rotational symmetry is preserved while the lattice can be covered by only unit rhombic cell. Note that CPHA carries a hybrid nature such that it shows aperiodicity in the x-y plane showing rotational symmetry about z-axis as in quasi-crystalline hole arrays, but composed of successive copies of identical unit cells similar to crystalline hole arrays. We analyzed this hybrid nature of CPHA in terms of EOT for the first time to the best knowledge of the authors.

2. The hole arrangements used in this study

In this paper, CPHAs with the octagonal and the decagonal symmetries are discussed, which are schematically shown in Fig. 1
Fig. 1 Schematic illustration of (a) Octagonal CPHA, (b) Decagonal CPHA, (c) Square array, and (d) Hexagonal array. Note the unit rhombic cells marked in red lines in (a), (b)
. The octagonal and decagonal CPHAs are characterized by the single rhombic unit cells, which are shown in solid red lines in Fig. 1(a) and 1(b). The unit cell of octagonal CPHA is a rhombus with vertex angles of 45° and 135° and the corresponding angles in the decagonal CPHA are 36° and 144°. Conventional square- and hexagonal-crystalline hole arrays are shown in Fig. 1(c) and 1(d), respectively. We will designate them as square and hexagonal arrays in the rest of this paper.

Instead of prior free standing metal film [7

7. F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16(13), 9571–9579 (2008). [CrossRef] [PubMed]

], we discussed the three-layer structure as shown in Fig. 2(a)
Fig. 2 (a) Structural parameters of the D-film, and hole arrangements over D-film of (b)Octagonal CPHA, (c)Decagonal CPHA, (d)Hexagonal array,(f) Square array.
, where the silver layer of thickness h is deposited on a silica glass substrate and is perforated with holes of diameter d .We will refer this structure as “D-film” and the prior free standing film as “F-film” in the following discussion. D-films would find more practical applications integrated with optical waveguides, in comparison to prior F-films which require delicate handling [18

18. A. Dhawan and J. F. Muth, “Engineering surface Plasmon based fiber-optics sensors,” Mater. Sci. Eng. B 149(3), 237–241 (2008). [CrossRef]

]. Scientifically D-film will also reveal more physics because it provides two different boundaries; Air/Ag and Silica/Ag interfaces. We assumed normal incidence of light from the silica side. We also assume the same hole parameters for the structures in Fig. 2: d and Λ.

In this paper, we investigated two key issues that have not been addressed thus far:

  • 1) What is the impact of centered polygonal hole arrays (CPHAs) in Fig. 1 in optical transmission? How would it differ from well-known crystalline and quasi-crystalline arrays?
  • 2) What is the impact of the layer structure-Air/Ag/Silica in Fig. 2? How the Plasmonic resonances in the two different interfaces-Air/Ag, Silica/Ag would contribute to output optical transmission?

In the following discussions, we employed two physical analyses tools 1) Fourier transformation to find our appropriate reciprocal vectors that excites the surface plasmons, 2) Finite difference time domain (FDTD) analysis to find out the optical transmission through the proposed CPHAs in Air/Ag/Silica structures. Based on the plasmonic dispersion relations we then assigned the transmission peaks in terms of SPPs and corresponding reciprocal vectors, which can answer the above questions.

3. Theory

3.1. Surface plasmon polarition (SPP) in crystalline hole arrays

In crystalline hole arrays, the free space resonant wavelengths of SPPs [19

19. L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86(6), 1110–1113 (2001). [CrossRef] [PubMed]

,20

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

] are given by the plasmonic dispersion equation:
λr=αΛεd(ω)εm(ω)(εd(ω)+εm(ω))(i2+j2+ηij)
(1)
where the hole period is denoted by Λ; εd and εm are electric permittivity of the dielectric and the metal; η and α are constant values; and as shown in Fig. 3
Fig. 3 Illustration of basic reciprocal vectors, G1 and G2, and their corresponding hole-to-hole distance, a1 and a2 for (a) Squre array, and (b) Hexagonal array. a1 and a2 are the distance between two adjacent holes.
i and j are integers for the corresponding reciprocal vector:

G=iG1+jG2
(2)

The index pairs (i, j) also indicate the order of SPP modes. For the square array: η=0 and α=1 and for the hexagonal array: η=1 and α=3/2. The SPP waves resonantly guided in dielectric/metal interface of crystalline hole arrays called surface plasmon polarition Bloch waves (SPP-BWs) [21

21. S. H. Chang, S. K. Gray, and G. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13(8), 3150–3165 (2005). [CrossRef] [PubMed]

].

In addition to SPP-BWs, Wood’s anomalies also occur in transmission at the wavelengths given by:
λW=Λm2+l2+ηmlεd
(3)
where m and l are integers for the corresponding reciprocal vector. Wood’s anomalies are located at the minima adjacent to EOT peaks [22

22. T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24(4), 256–258 (1999). [CrossRef]

].

3.2 Surface plasmon polarition (SPP) in qausi -crystalline hole arrays

The plasmonic dispersion equation in quasi-crystalline hole arrays [16

16. J. Xue, W. Zhou, B. Dong, X. Wang, Y. Chen, E. Huq, W. Zeng, X. Qu, and R. Liu, “Surface Plasmon enhanced transmission through planar gold quasicrystals fabricated by focused ion beam technique,” Microelectronic Engineering. http://homepage.fudan.edu.cn/~fdnil/paper/Surface%20plasmon%20enhanced%20transmission%20through%20planar%20gold.PDF.

] can be expressed as;

λr=2π|GSPP|εd(ω)εm(ω)εd(ω)+εm(ω)
(4)

Gspp is one of reciprocal vectors, G, which are linear superposition of the basis reciprocal vectors (Fi) in the reciprocal space. In a 2N-fold rotationally symmetric quasi-crystalline hole array, reciprocal vectors are given by [15

15. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. Dela Rau, and P. Miller, “Two dimensional penrose-tiled photonic quasicrystals: from diffraction pattern to band structure,” Nanotechnology 11(4), 274–280 (2000). [CrossRef]

]:

G=j=1,0,1{i=1NjFi}
(5)

Figure 4
Fig. 4 Reciprocal vectors in Fourier representation for (a) Octagonal CPHA, (b) Decagonal CPHA, (c) Penrose array. Basic reciprocal vectors denoted by Fis . The insets are real space representations.
shows the reciprocal space representation for octagonal CPHA, decagonal CPHA and 10-fold rotationally symmetric Penrose array, where reciprocal vectors are indicated by bright spots and the basis reciprocal vectors, Fi, are shown in arrows. It is noted that quasi-crystalline hole arrays such as Penrose array has reciprocal vectors in discrete points due to its spatial aperiodicity (Fig. 4(c)). In contrast, the octagonal and decagonal CPHAs have not only the discrete points (points marked by red cross signs in Fig. 4(a) and 4(b)), but also the back ground space filled by scattering patterns, which exhibits their semi-crystalline property [23

23. R. Komrska, “Finite crystal lattice and its Fourier transform. lattice amplitude and shape amplitude”. http://physics.fme.vutbr.cz/~komrska/Eng/KapF17.pdf.

] These reciprocal vectors in Fourier space and corresponding hole-to-hole distances in the real space were utilized to assign appropriate SPP modes for EOT peaks calculated by FDTD, which is discussed in the following sections.

4. Numerical analysis

The permittivity of air was assumed to be εa=1. The permittivity of silver and silica glass was obtained from data book [24

24. D. W. Lynch, and W. R. Hunter, Handbook of Optical Constants of Solids (E. D. Palick, Ed. Orlando, FL Academic, 1985).

]. To solve the electromagnetic wave equations in sub-wavelength structure as shown in Fig. 2, FDTD method was applied using a commercially available program [25

25. FDTD Lumerical Solutions Inc, www.lumerical.com.

]. The total simulation size for FDTD analysis was 20×20× 2 μm3 along with the mesh-grid resolution of 15nm, which were specifically chosen large enough to diminish the diffraction effect at the Ag film edges. We assumed that the white light source is a normally incident plane wave with a linear polarization covering the area of 10 × 10 μm2 and placed at 1μm from the film inside the silica glass. The monitor was positioned in the air, 5nm from the metal surface to detect the near field. Note that the spectral position of EOT peaks is independent of the incident light polarization at normal incidence of light (Eq. (1) and (4)), and therefore the simulation routine was designed for an arbitrary polarization in the plane wave.

All the structures in Fig. 2 have the identical geometrical parameters: holes size d=200nm, hole pitch Λ=600nm, film thickness h=340nm. Finite-size arrays covered the area of 7.2×7.2 μm2 ~8.5 × 7.2 μm2 on the surface of a 20×20μm2 Ag film. We assumed that the silica substrate is extended to the infinity. Experiments showed that a N×N square array resulted in the asymptotic transmission spectra of an infinite array for N≥9 [26

26. M. Bai and N. García, “Transmission of light by a single subwavelength cylindrical hole in metallic films,” Appl. Phys. Lett. 89(14), 141110.1–1411110, 3 (2006). [CrossRef]

]. Here we will assume the hole number N=169, except decagonal CPHA of 211 holes, which is sufficiently large to provide the asymptotic transmission spectra.

5. Results

5.1 Optical transmission of square and hexagonal arrays in D- and F-films

Figure 5
Fig. 5 Transmission of (a) Square and (b) Hexagonal arrays in F-film and D-film at d= 200nm, Λ= 600 nm, and h=340 nm. Numbers 1~7 referred to spectral position of SPP-BWs and their assignments are summarized in Table1.
renders transmission spectra of square and hexagonal arrays for both F- and D-film structures. We could confirm the accuracy and consistency of our numerical analysis by verifying the reported EOT peaks in the F-film structure. In Table.1

Table1. Spectral Positions of SPP-BW (λr) and Wood’s Anomalies (λW), in Square and Hexagonal Arrays in D-film.

table-icon
View This Table
| View All Tables
we summarized the orders of SPP-BWs, Wood’s anomalies, and their corresponding free space resonant wavelengths calculated by FDTD in the D-film structures. We referred the SPP-BWs traveling at the air/Ag and the silica/Ag interfaces as (i,j)a and (i,j)s, respectively. Resonant wavelengths of SPP-BWs were estimated utilizing Plasmonic dispersion equation in Eq. (1), (2) and their values are shown in the parentheses. The location of Wood’s anomalies was estimated using Eq. (3). The difference in the wavelengths obtained by plasmonic dispersion equation and FDTD were 1~14%, which is attributed to the missing radiative damping term in plasmonic dispersion equation in Eq. (1) [27

27. 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]

].

In contrast to F-film, the D-film has asymmetric boundaries [28

28. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001). [CrossRef]

] and the resonance wavelengths were grouped by the Air/Ag interface (peak 1,2) and the silica/Ag interface (peak 3~7) in Table 1. The minimum adjacent to the peak ‘4’ of square array and minima adjacent to peaks ‘1’ and ‘3′ of hexagonal array are assigned to Wood’s anomalies using Eq. (3) [21

21. S. H. Chang, S. K. Gray, and G. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13(8), 3150–3165 (2005). [CrossRef] [PubMed]

].

It is note that in Fig. 5(a), the dominant transmission peak in F-film of Square array is ‘2’ originated from the Air/Ag interface. In contrast, the dominant peaks are ‘5′, ‘6’, and ‘7’ in D-film of Square array, which are originated from the Silica/Ag interface. In fact the peak ‘2’ is still present between dominant ‘6’ and ‘7’ peaks in D-film, and its intensity is about 1/2 of the peak ‘2’ in F-film. This is consistent with well-known physics reported in reference [28

28. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001). [CrossRef]

], where the symmetric layer structure Air/Ag/Air in F-film provides stronger transmission peaks. This phenomena is also observed in the case of hexagonal arrays, Fig. 5(b), where two peaks ‘1’, ‘2’ originated from the Air/Ag interface have weaker intensities in D-film.

5.2 Optical transmission of octagonal and decagonal CPHA in D- and F-films

Transmission spectra were obtained using FDTD and the results are summarized in Fig. 8
Fig. 8 Transmission spectra of (a) Octagonal, and (b) Decagonal CPHAs for d=200nm, Λ = 600 nm, and h=340 nm. Roman numbers are resonant wavelengths calculated by FDTD and the assignments are summarized in Table 2, 3. Vertical scales are different for D-film on the left y-axis, and F-film on the right y-axis that is ~5 times larger.
. Here we considered both D-film (solid line) and F-film (dashed line). The EOT peaks calculated by FDTD were assigned using the Plasmonic dispersion equation of quasi-crystalline hole arrays in Eq. (4) and the results are summarized in Table 2

Table 2. Assignment of EOT Peaks in the Octagonal CPHA in D-film Structure for Fig. 8(a)

table-icon
View This Table
| View All Tables
and 3

Table 3. Assignment of EOT Peaks in the Decagonal CPHA in D-film Structure for Fig. 8(b)

table-icon
View This Table
| View All Tables
.

In Table 2 and 3, we referred the reciprocal vectors of SPPs traveling at the Air/Ag and the Silica/Ag interfaces as GL(A) and GL(S), respectively. For each EOT peak in Fig. 8, we assigned the reciprocal vector (GL) and its magnitude (|GL|), corresponding hole-to-hole distances (L) in the tables. The spectral positions of peaks (λr) in Fig. 8 were also listed in nanometer (nm) and the estimated wavelengths from the plasmonic dispersion equation in Eq. (4) are shown in the parentheses. In the square and hexagonal arrays, the resonant wavelengths, λr, predicted by plasmonic dispersion equation were ~14% shorter than those numerically obtained by FDTD analysis based on Fano interpretation [27

27. 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]

]. See Table 1. On the while, in octagonal and decagonal CPHAs the plasmonic dispersion predictions were ~18% longer than the FDTD results, which has been similarly observed in quasi-crystalline hole arrays [16

16. J. Xue, W. Zhou, B. Dong, X. Wang, Y. Chen, E. Huq, W. Zeng, X. Qu, and R. Liu, “Surface Plasmon enhanced transmission through planar gold quasicrystals fabricated by focused ion beam technique,” Microelectronic Engineering. http://homepage.fudan.edu.cn/~fdnil/paper/Surface%20plasmon%20enhanced%20transmission%20through%20planar%20gold.PDF.

]. See Table 2, 3. The reason of this discrepancy is not fully understood yet but this behavior represents the quasi-crystalline nature in the CPHAs.

5.3 Impact of silver D-film parameters over EOT peaks

It is experimentally reported that quasi-crystalline hole arrays showed major EOT peaks contributed from SPP modes on the Air/Ag interface and we could confirm that octagonal and decagonal CPHAs share the nature of quasi-crystalline hole arrays in this regard [16

16. J. Xue, W. Zhou, B. Dong, X. Wang, Y. Chen, E. Huq, W. Zeng, X. Qu, and R. Liu, “Surface Plasmon enhanced transmission through planar gold quasicrystals fabricated by focused ion beam technique,” Microelectronic Engineering. http://homepage.fudan.edu.cn/~fdnil/paper/Surface%20plasmon%20enhanced%20transmission%20through%20planar%20gold.PDF.

]. It has been shown that by increasing the hole fraction (d/Λ) in square arrays, peaks are enhanced as well as broadened [9

9. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004). [CrossRef] [PubMed]

]. In addition, as either the hole diameter, or the period of hole is increased, transmission maxima are shifted to longer wavelengths. By increasing the hole fraction from d/Λ=0.36 at Λ=700 nm (black line in Fig. 9(a)9(d)) to d/Λ=0.40 at Λ=600 nm (green line in Fig. 9(a)9(d)), maxima in CPHAs (Fig. 9(c) and 9(d)) as well as those of crystalline hole arrays (Fig. 9(a), 9(b)) broadened in such a way that adjacent maxima overlap each other.

As expected for quasi-crystalline hole arrays, decreasing the holes size allows enhancement of higher orders SPP modes [14

14. A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24(9), 2545–2554 (2007). [CrossRef]

]. In Fig. 9 by decreasing the hole size from d=250 nm(green lines) to d=200 nm(red lines), higher order peaks appear in the spectrum, such as peaks ‘iii’ and ‘iv’ in octagonal CPHA ; peaks ‘v” and ‘iii” in decagonal CPHA ; peak ‘2’ in hexagonal array ;and peak ‘7’ in square array appears.

Reduction in thickness of the film leads to coupling between sets of SP modes excited on two sides of the metal film and lifting modes degeneracy [11

11. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength hole arrays,” Appl. Phys. Lett. 81(23), 4327–4329 (2002). [CrossRef]

]. Therefore, a SPP mode in one side show sharp high energy peak and its counterpart in the either side shows broad low energy peak. In Fig. 9, by decreasing the film thickness from h=340nm (red line) to h=200nm (blue line), (1,0)s and (1,0)a in hexagonal array (Fig. 9(b)) are excited as a weak broad peak (peak ‘3′), and a strong sharp peak (peak ‘1’) respectively. For two CPHAs (Fig. 9(c), 9(d)), by reducing the film thickness from h=340nm (red lines) to h=200 nm (Blue lines), maxima corresponding to reciprocal vectors of GΛ(A) and GΛ(S) gave sharp intense peaks (peaks ‘iv’ and ‘iv'’) and broadened low energy peaks (peak ‘i’ and ‘i'’) respectively.

Figure 10
Fig. 10 Averaged spectral transmission (AST) of square array, hexagonal array, octagonal CPHA, and decagonal CPHA against hole fraction(d/Λ) for Λ=600nm and h=340 nm.
illustrates the variation of averaged spectral transmission (AST) against the variation of hole fraction(d/Λ) for D-film structure. Here, AST defined the mean value of transmission in its spectrum over spectral range of 350~1000nm which can indicate the averaged optical throughput of hole arrays. By increasing the hole fraction, the AST of square array surpasses that of the other structures. However, at hole fractions less than0.3 the AST of square array is dominated by that of other arrays.

Figure 11(a)
Fig. 11 Transmission variation of (a) EOT peaks: iii, iv, v, and vi in octagonal CPHA and (b) EOT peaks: iii', iv', vi', and vii’ in decagonal CPHA versus variation of film thickness.
illustrates the transmission variation of EOT peaks: iii, iv, v, and vi (as listed in Table 2) versus the variation of the film thickness for octagonal CPHA. Figure 11(a) quantitatively shows that by increasing the film thickness the transmission of EOT peaks decrease due to the decoupling between SPP modes excited on both sides of the film [11

11. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength hole arrays,” Appl. Phys. Lett. 81(23), 4327–4329 (2002). [CrossRef]

]. However, this trend was not evident for the modes corresponding to relatively outer reciprocal vectors such as ‘v’ and ‘vi’ (see Fig. 6(b)). Similarly, as shown in Fig. 11(b) in decagonal CPHA among EOT peaks: iii', iv', vi', and vii' (as listed in Table 3), transmission of peak ‘vii'’ shows oscillating variations. In inner reciprocal vectors, on the other hand, the transmission gently reduces by increasing the film thickness as expected for lower order SPP modes in crystalline hole arrays [11

11. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength hole arrays,” Appl. Phys. Lett. 81(23), 4327–4329 (2002). [CrossRef]

]. Once again these transmission variations as a function of film thickness indicate hybrid nature of CPHAs.

6. Conclusion

Acknowledgments

This work was supported in part by the Brain Korea 21 Project, in part by the NRF grant funded by the MEST (Nos. 2010-0018442, 2009-00479 EC-FP7/2007-2013 219299 GOSPEL, R15-2004-024-00000-0, F01-2009-000-10200-0, and 2009-00541), in part by the ITEP (Nos. 2009-8-0809 and 2010-8-1415).

References and links

1.

L. Yin, V. Vlasov, A. Rydh, J. Pearson, U. Welp, S. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, and C. W. Kimball, “Surface plasmons at single nano holes in Au films,” Appl. Phys. Lett. 85(3), 467–469 (2004). [CrossRef]

2.

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

3.

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays,” Phys. Rev. B 67(15), 155314 (2003). [CrossRef]

4.

S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77(7), 075401.1–075401.8 (2008). [CrossRef]

5.

F. Leon-Perez, G. Brucoli, F. Garcia-Vidal, and L. Martin-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” N. J. Phys. 10, 1–22 (2008).

6.

J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93(22), 227401 (2004). [CrossRef] [PubMed]

7.

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16(13), 9571–9579 (2008). [CrossRef] [PubMed]

8.

G. Ctistis, P. Patoka, X. Wang, K. Kempa, and M. Giersig, “Optical transmission through hexagonal arrays of subwavelength holes in thin metal films,” Nano Lett. 7(9), 2926–2930 (2007). [CrossRef] [PubMed]

9.

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004). [CrossRef] [PubMed]

10.

J. H. Kim and P. J. Moyer, “Thickness effects on the optical transmission characteristics of small hole arrays on thin gold films,” Opt. Express 14(15), 6595–6603 (2006). [CrossRef] [PubMed]

11.

A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength hole arrays,” Appl. Phys. Lett. 81(23), 4327–4329 (2002). [CrossRef]

12.

F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through penrose subwavelength hole arrays,” Appl. Phys. Lett. 89(12), 121115.1–121115, 3 (2006). [CrossRef]

13.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cell,” J. Mod. Opt. 53(3), 407–416 (2006). [CrossRef]

14.

A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24(9), 2545–2554 (2007). [CrossRef]

15.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. Dela Rau, and P. Miller, “Two dimensional penrose-tiled photonic quasicrystals: from diffraction pattern to band structure,” Nanotechnology 11(4), 274–280 (2000). [CrossRef]

16.

J. Xue, W. Zhou, B. Dong, X. Wang, Y. Chen, E. Huq, W. Zeng, X. Qu, and R. Liu, “Surface Plasmon enhanced transmission through planar gold quasicrystals fabricated by focused ion beam technique,” Microelectronic Engineering. http://homepage.fudan.edu.cn/~fdnil/paper/Surface%20plasmon%20enhanced%20transmission%20through%20planar%20gold.PDF.

17.

S. Mei, T. Jie, L. Zhi-Yuan, C. Ying, Z. Dao-zhong, J. ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett. 23(2), 486–488 (2006). [CrossRef]

18.

A. Dhawan and J. F. Muth, “Engineering surface Plasmon based fiber-optics sensors,” Mater. Sci. Eng. B 149(3), 237–241 (2008). [CrossRef]

19.

L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86(6), 1110–1113 (2001). [CrossRef] [PubMed]

20.

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

21.

S. H. Chang, S. K. Gray, and G. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13(8), 3150–3165 (2005). [CrossRef] [PubMed]

22.

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24(4), 256–258 (1999). [CrossRef]

23.

R. Komrska, “Finite crystal lattice and its Fourier transform. lattice amplitude and shape amplitude”. http://physics.fme.vutbr.cz/~komrska/Eng/KapF17.pdf.

24.

D. W. Lynch, and W. R. Hunter, Handbook of Optical Constants of Solids (E. D. Palick, Ed. Orlando, FL Academic, 1985).

25.

FDTD Lumerical Solutions Inc, www.lumerical.com.

26.

M. Bai and N. García, “Transmission of light by a single subwavelength cylindrical hole in metallic films,” Appl. Phys. Lett. 89(14), 141110.1–1411110, 3 (2006). [CrossRef]

27.

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]

28.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(050.6624) Diffraction and gratings : Subwavelength structures
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 10, 2011
Revised Manuscript: April 4, 2011
Manuscript Accepted: April 5, 2011
Published: April 18, 2011

Virtual Issues
Vol. 6, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Hesam Edin Arabi, Minkyu Park, Marzieh Pournoury, and Kyunghwan Oh, "Enhanced optical transmission through sub-wavelength centered-polygonal hole arrays in silver thin film on silica substrate," Opt. Express 19, 8514-8525 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8514


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Yin, V. Vlasov, A. Rydh, J. Pearson, U. Welp, S. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, and C. W. Kimball, “Surface plasmons at single nano holes in Au films,” Appl. Phys. Lett. 85(3), 467–469 (2004). [CrossRef]
  2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolf, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
  3. F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays,” Phys. Rev. B 67(15), 155314 (2003). [CrossRef]
  4. S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77(7), 075401.1–075401.8 (2008). [CrossRef]
  5. F. Leon-Perez, G. Brucoli, F. Garcia-Vidal, and L. Martin-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” N. J. Phys. 10, 1–22 (2008).
  6. J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93(22), 227401 (2004). [CrossRef] [PubMed]
  7. F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16(13), 9571–9579 (2008). [CrossRef] [PubMed]
  8. G. Ctistis, P. Patoka, X. Wang, K. Kempa, and M. Giersig, “Optical transmission through hexagonal arrays of subwavelength holes in thin metal films,” Nano Lett. 7(9), 2926–2930 (2007). [CrossRef] [PubMed]
  9. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004). [CrossRef] [PubMed]
  10. J. H. Kim and P. J. Moyer, “Thickness effects on the optical transmission characteristics of small hole arrays on thin gold films,” Opt. Express 14(15), 6595–6603 (2006). [CrossRef] [PubMed]
  11. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength hole arrays,” Appl. Phys. Lett. 81(23), 4327–4329 (2002). [CrossRef]
  12. F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through penrose subwavelength hole arrays,” Appl. Phys. Lett. 89(12), 121115.1–121115, 3 (2006). [CrossRef]
  13. D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cell,” J. Mod. Opt. 53(3), 407–416 (2006). [CrossRef]
  14. A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24(9), 2545–2554 (2007). [CrossRef]
  15. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. Dela Rau, and P. Miller, “Two dimensional penrose-tiled photonic quasicrystals: from diffraction pattern to band structure,” Nanotechnology 11(4), 274–280 (2000). [CrossRef]
  16. J. Xue, W. Zhou, B. Dong, X. Wang, Y. Chen, E. Huq, W. Zeng, X. Qu, and R. Liu, “Surface Plasmon enhanced transmission through planar gold quasicrystals fabricated by focused ion beam technique,” Microelectronic Engineering. http://homepage.fudan.edu.cn/~fdnil/paper/Surface%20plasmon%20enhanced%20transmission%20through%20planar%20gold.PDF .
  17. M. Sun, J. Tian, Z-Y. Li, B-Y. Cheng, D-Z. Zhang, A-Z. Jin, and H-F. Yang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett. 23(2), 486–488 (2006). [CrossRef]
  18. A. Dhawan and J. F. Muth, “Engineering surface Plasmon based fiber-optics sensors,” Mater. Sci. Eng. B 149(3), 237–241 (2008). [CrossRef]
  19. L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86(6), 1110–1113 (2001). [CrossRef] [PubMed]
  20. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
  21. S. H. Chang, S. K. Gray, and G. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13(8), 3150–3165 (2005). [CrossRef] [PubMed]
  22. T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24(4), 256–258 (1999). [CrossRef]
  23. R. Komrska, “Finite crystal lattice and its Fourier transform. lattice amplitude and shape amplitude”. http://physics.fme.vutbr.cz/~komrska/Eng/KapF17.pdf .
  24. D. W. Lynch, and W. R. Hunter, Handbook of Optical Constants of Solids (E. D. Palick, Ed. Orlando, FL Academic, 1985).
  25. FDTD Lumerical Solutions Inc, www.lumerical.com .
  26. M. Bai and N. García, “Transmission of light by a single subwavelength cylindrical hole in metallic films,” Appl. Phys. Lett. 89(14), 141110.1–1411110, 3 (2006). [CrossRef]
  27. 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]
  28. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001). [CrossRef]

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