Comparisons of two subwavelength aperture arrays with different lattice structure for light transmission

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Comparisons of two subwavelength aperture arrays with different lattice structure for light transmission Nan Zhang, Peiheng Zhou ∗ , Jianliang Xie, Longjiang Deng State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, China

a r t i c l e

i n f o

Article history: Received 29 February 2012 Accepted 10 July 2012 Keywords: Surface plasmon polaritons Subwavlength grating Extraordinary optical transmission Mid-infrared

a b s t r a c t The transmission through subwavelength square and hexagonal lattice structure hole arrays in aluminum films at mid-infrared spectral range is reported experimentally in this work. Enhanced transmission peak is observed at wavelengths up to seven times of the hole’s diameter. Positions of the transmission peaks are coincide with the prediction of surface plasmon polaritons (SPPs) theory. Lattice structure is proved to be a decisive factor of the transmission spectra. Interface media on both sides of the metal structure also affect the transmission peak position. These results are meaningful for the aperture applications in infrared detection and frequency selective surfaces devices. © 2012 Elsevier GmbH. All rights reserved.

1. Introduction Light transmission through a metallic film perforated with subwavelength aperture arrays has been extensively studied since the extraordinary optical transmission (EOT) phenomenon was reported by Ebbesen [1]. Previous experiment results have revealed incredible high transmission obtained at wavelengths up to 10 times lager than the diameter of the holes. In contrast, according to Bethe’s diffraction theory [2], subwavlength apertures should have a low transmission efficiency: for a small hole in a perfectly conducting and infinitely thin metal screen, the transmission coef4 ficient T is given by: T = 64(kr) /272 , where k represents the wavevector of incident light; r is the hole’s radius. Note that, T scales as (r/)4 , so the transmission is extremely weak when (r < ). Therefore, numerous works have been focused on the potential physical mechanisms behind the EOT phenomenon [3–9]. Surface plasmon polaritons (SPPs) has been theoretically and experimentally certified to play an important role in arousing this resonant phenomenon [10–12]. Generally speaking, subwavelength aperture arrays resonantly couple incident light into surface waves, which conversely interfere with light directly incident on the apertures, and convert the transmission spectrum. These surface waves are either conventional surface plasmon polaritons (SPPs) for real metal or spoof SPPs for PEC [13]. However, most of previous works was studied in the visible and near infrared spectral range, since SPPs has a relatively low excitation efficiency in the mid-infrared [7] (2.5–25 ␮m). In this paper, we

∗ Corresponding author. Tel.: +86 28 83201574; fax: +86 28 83201575. E-mail address: [email protected] (P. Zhou).

present EOT of circular holes arranged in a square lattice structure and a hexagonal lattice structure respectively in aluminum films in the mid-infrared spectral range.

2. Experiment and measurement setup First, a 200 nm thick aluminum film was deposited on the doubly polished n-type silicon wafer (thickness ≈ 400 ␮m) and SeZn glass substrate (thickness ≈ 800 ␮m) respectively by electron beam evaporation. Positive photoresist was then spun on the metal films. After the patterns were transferred onto the photoresist from masks by lithography process, the final metal structures were yielded by wet etching. The whole sample is 15 mm × 15 mm, composed of periodic replicated units. Period and hole’s diameter of the two structures are identical, i.e., P = 6 ␮m, D = 3 ␮m. A 1 ␮m thick SiO2 film was deposited on the metal structure by Plasma Enhanced Chemical Vapor Deposition (PECVD) to investigate the impact of coating layer on the transmission spectrum. Fig. 1(a) and (b) shows the microscope view of the two subwavelength aperture arrays. Fig. 1(c) shows the transmission measurement setup. Sample plate lies in the XY plane with light incident from the metal side in the −Z direction, and the dispersion relation was measured by rotating the sample around Y axis 10◦ per step from 0◦ to 40◦ . Bruker Tensor 27 Fourier Transform Infrared Spectroscopy (FTIR) system was used to obtain the zero order transmission spectra, and a bare substrate plate was used for the measurement calibration.

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Please cite this article in press as: N. Zhang, et al., Comparisons of two subwavelength aperture arrays with different lattice structure for light transmission, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.019

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Fig. 2. Transmission spectra of the square lattice structure arrays (a) and the hexagonal lattice structure arrays (b).

reciprocal lattice vectors of the aperture arrays. For different lattice structure there will be different reciprocal lattice vectors, thus, ៝ = 2 x៝ , G x a

៝ = 2 y៝ G y a

(3)

are the reciprocal lattice vectors of the square lattice structure arrays with period a, and, √    4   1   4   1  3 ៝ = √ ៝ = √ ៝ G x + y៝ , G x៝ x y 2 2 2 3a 3a

√   3 2

+

Fig. 1. Subwavelength circular hole arrays with square lattice structure (a) and hexagonal lattice structure (b) and the schematic view of the transmission measurement setup (c). Period constant is P and hole’s diameter is D.

y៝

(4)

are associated with the hexagonal lattice structure arrays. At normal incident,  = 0◦ , so the SPPs resonant mode appears at wavelength: spp = a(i2 + j2 )

−1/2

 ε ε 1/2 d m εd + εm

3. Theories

for the square lattice structure arrays, and,

For a smooth metallic film, the SPPs wavevector ksp is given by [14]:

spp = a



4 3

−1/2  ε ε 1/2 d m

(i2 − ij + j2 )

εd + εm

(5)

(6)

Here ω is the frequency of incident light, c is the velocity of light in vacuum, εm and εs are the dielectric constants of the metal and interface medium respectively. This dispersion relation is also applicable for the perforated metallic film, even though the fact that the holes in the film may cause both a significant change in the plasmon dispersion and a large coupling between the front and back surfaces of the metal film [14]. However, for a smooth metal surface, light does not couple to surface plasmons because surface plasmons have a longer wavevector than the incident light at same frequency propagating along the metal surface. The presence of a periodic structure on the metal surface makes up the momentum gap and enables the direct coupling of light to surface plasmons. This supernumerary momentum could provide the needed momentum for the momentum conservation [14]:

for the hexagonal lattice structure arrays. Note that, dielectric constants of the interface media on two sides of the metal structure are different due to the different contacting media, e.g. at wavelength of 20 ␮m, dielectric constants are: εair = 1 and εsilicon = 11.7 [15]. Therefore, for a certain lattice structure, there will be two sets of transmission peaks corresponding to the selected values of (i, j), distinguished as metal/substructure or metal/dielectric SPPs mode, which represent the propagating SPPs mode on the bottom and upper contact surface of the metal structure, respectively. Furthermore, according to Eqs. (2), (5) and (6), SPPs resonant transmission peaks are determined by several factors, such as period, lattice structure, incident angles, dielectric constants of the media on both sides of the metal structure, etc. In the following part of this article, characterizations of the transmission spectra, dispersion relations and symmetry properties due to the lattice structure are discussed. Other decisive factors on the transmission spectrum, like the hole’s diameter and contacting media, are also investigated.

៝ ± jG ៝ k៝ sp = k៝ x ± iG x y

4. Results and discussion

|ksp | =

ω c

εd × εm εd + εm

(1)

(2)

where |kx | = (2/) sin  is the wavevector of incident light in the x direction,  is the incident angle, i and j are the integers corresponding to the specific order of SPPs mode, Gx and Gy are the

Fig. 2(a) and (b) shows the transmission spectra of square and hexagonal lattice structure arrays at normal incidence, with the corresponding SPPs resonant mode (i, j) indicated following the

Please cite this article in press as: N. Zhang, et al., Comparisons of two subwavelength aperture arrays with different lattice structure for light transmission, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.019

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Fig. 3. Transmission spectra of the square lattice structure arrays with the same period (P = 6 ␮m) and three different hole’s diameters (D = 3 ␮m, 4 ␮m, 5 ␮m).

theories shown in the previous section. A simple glance at the two figures shows two completely different spectra, even though the two structures have same period and hole’s diameter. According to Eqs. (5) and (6), different lattice structures will yield different peak positions for the same SPPs resonant mode. Theoretically, transmission peaks of the (1, 0) Al/Si, (1, −1) Al/Si and (1, 0) Al/Air SPPs modes appear at wavelengths of 20.5 ␮m, 14.5 ␮m, and 6 ␮m

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respectively for the square lattice structure arrays, and 17.8 ␮m, 10.3 ␮m, and 5.2 ␮m for the hexagonal lattice structure arrays. These peak positions are coincide quite well with the measured data, says, 21.1 ␮m, 14.9 ␮m, 6.6 ␮m for the square lattice structure arrays, and 18.4 ␮m, 10.6 ␮m, 5.8 ␮m for the hexagonal one. Only a little red-shift is observed, because the theoretical calculation is done without taking into account the coupling of SPPs mode between the two contact surfaces of the metal structure. This coupling is quite strong when the film is optically thick [14]. Note that, position of the transmission peak of the (1, 0) Al/Si SPPs mode of the hexagonal lattice structure arrays is about seven times of the hole’s diameter, where no diffraction can occur from the arrays or the individual hole [1]. Therefore, it is evident that the unusual optical properties are due to the coupling of light with surface plasmon polaritons. Another remarkable difference between the two spectra is the transmission intensity: transmission intensity of the hexagonal lattice structure arrays is generally higher than the square one. We attribute this to the effective area of the holes occupied in the Al film. Holes of the hexagonal lattice structure arrays possess a lager area per unit cell than the square one. Therefore, the observed transmission intensity of the hexagonal lattice structure is correspondingly higher. To verify this point, we compare the transmission intensity of square lattice structure arrays with the same

Fig. 4. Transmission spectra (a) and dispersion relation of SPPs (c) of the hexagonal lattice structure arrays, transmission spectra (b) and dispersion relation of SPPs (d) of the square lattice structure arrays at oblique incidence. The units of kx are normalized to 2␲/a, and the sample was rotated around Y axis by 10◦ , 20◦ , 30◦ and 40◦ .

Fig. 5. Transmission spectra of the hexagonal lattice structure arrays (a) and the square lattice structure arrays (b) under polarized incident light (E-field parallel to the Y axis). The sample was rotated by 30◦ , 45◦ and 90◦ around Z axis. Inset: details of the peak information at 18.4 ␮m and 21.1 ␮m of the two structures respectively.

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period (P = 6 ␮m) but three different hole diameters (D = 3 ␮m, 4 ␮m, 5 ␮m). As can be seen in Fig. 3, transmission intensity within the whole transmission spectral range increases along with the hole’s diameter, and FWHM (Full Width at Half Maximum) of the transmission peaks are broadened simultaneously. Since positions of the transmission peaks are determined by Eqs. (5) and (6), independent of the hole’s diameter, there is no peak shift for the three spectra in Fig. 3. Different lattice structure will also result in different dispersion relation. Fig. 4(a) and (b) shows the transmission spectra of the two structures by rotating the samples around the Y axis 10◦ per step from 0◦ to 40◦ . Fig. 4(c) and (d) are the corresponding dispersion relations of SPPs. The degenerated SPPs mode at normal incidence will split at oblique incidence, for kx in Eq. (2) is no longer zero, and SPPs waves interfere with each other in this direction. With the increment of the incident light angles, transmission peaks of the (1, 0) Al/Si SPPs mode of the two structures decrease in intensity and split into several peaks which move in opposite directions. The sixfold degenerated SPPs modes [(−1, −1), (1, 1), (1, 0), (0, 1), (0, −1), and (−1, 0)] identified as the (1, 0) Al/Si SPPs mode at normal incidence of the hexagonal lattice structure split into four peaks at 40◦ incidence [Fig. 4(a)], while the fourfold degenerated SPPs modes [(1, 0), (0, 1), (0, −1), and (−1, 0)] which is also identified as the (1, 0) Al/Si SPPs mode at normal incidence of the square lattice structure split into three peaks at 40◦ incidence [Fig. 4(b)]. Notably, the [(1, 0), (0, 1)], [(−1, 0), (0, −1)] Al/Si SPPs modes of the hexagonal lattice structure and the [(0, 1), (0, −1)] Al/Si SPPs modes of the square lattice structure remain degenerated at 40◦ incidence, which could be also clearly reflected in the dispersion relations of SPPs in Fig. 4(c) and (d). Besides, as can be seen in Fig. 4(b) and (d), transmission peaks of the (1, 0) Al/Si SPPs mode branch happen to merge into the (1, −1) Al/Si SPPs peaks at lower angles. Therefore, it’s hard to distinguish transmission peaks of (1, 0) from (1, −1) Al/Si SPPs mode in both Fig. 4(b) and (d), until it moves away from the (1, −1) Al/Si SPPs transmission peaks at incidence angles lager than 30◦ (∼12.6 ␮m, corresponding to an energy of 0.98 eV). We also study the symmetry of arrays from the view point of polarized incident light. Fig. 5(a) shows the transmission spectra of the hexagonal lattice structure arrays under polarized incident light (E-field parallel to the Y axis), the sample was rotated by 30◦ , 45◦ and 90◦ around Z axis. The transmission spectra are almost identical, only with a negligible discrepancy on the transmission intensity as can be seen in the inset of Fig. 5(a), providing that the sample owns a highly symmetrical structure under polarized incident light. The symmetry property of the square lattice structure arrays is as good as the hexagonal one [seen in Fig. 5(b)], although apparently that the symmetry of the square lattice structure is slightly worse than the hexagonal one. Considering that the asymmetry of the two structures that caused by rotating the samples under polarized light can be neglected comparing with the wavelength of the incident light, the discrepancy of the symmetry property is negligible. As mentioned above, two sets of transmission peaks exist in the transmission spectra, since the interface media on both sides of the metal structure may have significant effect on the SPPs resonant mode. According to Eqs. (5) and (6), resonant peaks will be modified by changing the medium’s dielectric constants. Ref. [16] investigated the sensitivity of the resonant transmission of the gratings to the cladding environment with the help of matching fluids. Hence the SiO2 layer deposited above the metal structure tends to play the same role as the matching fluids. Transmission spectra of the Air/Al/Si and SiO2 /Al/Si sandwich hexagonal lattice structure arrays are both shown in Fig. 6(a). The 1 ␮m thick SiO2 medium layer on top of the metal structure is 5 times thicker than the 200 nm Al film, and the roughness of the SiO2 surface is negligible comparing to the wavelength of incident light, which means that the SiO2 surface can be considered as optically

Fig. 6. Transmission spectra of the Air/Al/Si and SiO2/Al/Si sandwich hexagonal lattice structure arrays (a) and transmission spectra of the hexagonal lattice structure arrays on Si and SeZn glass substrate (b).

flat and the roughness have little influence on the optical properties of the structure [17]. Transmission peaks of the (1, 0) Al/Si SPPs mode of the two structures both appear at 18.4 ␮m, since the Al/Si SPPs mode is determined by the surface waves on the Al/Si interface, and this is identical for the two structures. However, for the introduction of the SiO2 medium layer, the (1, 0) Al/Air SPPs mode disappears and the (1, 0) Al/SiO2 SPPs mode emerges. So there will be a resonant peak of the (1, 0) Al/SiO2 SPPs mode at 11.1 ␮m theoretically, and this is experimentally proved by the peak at 10.7 ␮m in Fig. 6. Besides, the disappearance of the (1, 0) Al/Air SPPs mode at 5.8 ␮m induces a transmission dip. Similarly, different substrate will bring about different transmission properties. Fig. 6(b) shows the transmission spectra of the hexagonal lattice structure arrays on Si and SeZn glass substrate. SeZn glass has a relatively low dielectric constants (␧d = 5.4 [15] at wavelength of 20 ␮m), therefore resonant transmission peak of the (1, 0) Al/SeZn SPPs mode blue-shifts to 13.03 ␮m, comparing with the resonant transmission peak at 18.4 ␮m of the (1, 0) Al/Si SPPs mode. Resonant transmission peak of the (1, 0) Al/Air SPPs mode of the two spectra are almost at the same wavelengths, since the Air/Al/SeZn sandwich structure does not change the interface medium (air) above the metal film.

5. Conclusions We have demonstrated the extraordinary optical transmission of two subwavelength aperture arrays with different lattice structure in the mid-infrared spectral range. The experiment results have shown that the lattice structure determines the transmission properties, as well as the interface media on both sides of the metal structure. Modulation of the transmission peak position by lattice structure and interface media on both sides of the metal structure provide a more flexible choice of light transmission; good symmetry of these two structure arrays under polarized incident light is also meaningful in cases that the stability of the transmission shape are needed. These discussions may have multiple application values in the relevant fields, such as infrared detection and frequency selective surfaces devices.

Acknowledgments This work was supported by the Natural Science Foundation of China (Grant Nos. 61001026 and 51025208), the Fundamental Research Funds for the Central Universities of China.

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Please cite this article in press as: N. Zhang, et al., Comparisons of two subwavelength aperture arrays with different lattice structure for light transmission, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.08.019