Optical transmission of planar metallic films coated by two-dimensional colloidal crystals

Optical transmissions through a continuous planar metal film (without holes) with two-dimensional colloidal crystals coated on one or both interfaces have been experimentally and numerically investigated. Enhanced optical transmissions in the near-infrared regime can be observed for the metal film with identical two-dimensional colloidal crystals coated on both sides, which occur due to the resonant tunneling of surface polariton Bloch eigenmodes excited on periodically structured interfaces. Numerical simulations of transmission spectra show an excellent agreement with the measured ones. Additionally, the numerical simulations reveal that the intensity of tunneling transmission is strongly dependent on the relative shift of the two-dimensional colloidal crystals on the opposite interfaces of the metallic film. ©2014 Optical Society of America OCIS codes: (120.7000) Transmission; (240.6680) Surface plasmons. References and links 1. T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. 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Introduction
Since the discovery by Ebbesen et al. [1] of extraordinary optical transmission (EOT) through subwavelength periodic hole arrays, metallic films perforated with different periodic structures have attracted much interest in the field of plasmonics [2,3].The EOT phenomenon was generally accepted as a result of diffractive coupling of incident light to evanescent surface plasmon polaritons (SPPs) leading to a strong concentration of light at the metal surface, which then evanescently tunnel through the apertures in the film, finally reradiating into optical far field via the inverse process on the exit side [4].In the past decade, extensive studies show that the structural parameters of perforated metallic films such as the type of lattice symmetry [5][6][7][8] and the shape of holes [1][2][3][4][9][10][11] have significant effects on the optical transmission.In addition to the study of optical transmission of perforated metallic films, periodically corrugated metallic films without any holes showing enhanced transmission peaks in certain wavelengths have also been reported [12][13][14][15][16][17], which could been attributed to surface-plasmon-assisted resonant tunneling of light via states of localized surface plasmons or SPP Bloch waves excited on these periodically nanostructured metallic film interfaces [14,18,19].More interestingly, optical enhanced transmissions of planar optically opaque metallic films coated symmetrically with periodically corrugated dielectric layers were predicted [20,21].Although conspicuous optical-enhanced-transmission phenomenon of a metallic film whose thickness is larger than the penetration length of light at corresponding frequency is predicted theoretically, very few experimental results have been demonstrated due to the obstacle of fabricating such a structure, especially in the regime of visible, even of near-infrared.In this paper, we for the first time demonstrate experimentally such a microstructure operated in the near-infrared regime consisting of a planar metallic film coated with a two-dimensional (2D) colloidal crystals (CCs) on both sides by using a simple and inexpensive self-assembly method [8,22,23].Here, we have experimentally proved that the light can be effectively coupled into surface polariton Bloch eigenmodes [14,18] by a hybrid colloidal plasmonic-photonic crystal consisting of a 2D CC covered only on top side of a flat metallic film [24,25], but the efficiency of surface polariton-enhanced resonant transmission is very low.In contrast, with 2D CCs on both sides of the planar metallic film, dramatic enhancement of optical transmission is observed experimentally.According to the simulation analysis, we have also confirmed further that the strong transmissions at certain wavelengths are mainly due to some surface modes including surface plasmon mode and waveguided-like mode [24][25][26][27][28] on two sides of the metallic film, which could be simultaneously excited on the two sides of the metallic film and eventually resonant tunneling to free space.

Sample preparation and optical characterization
The fabrication process of the samples under study is depicted schematically in Fig. 1(a).In brief, the microstructure was formed by first self-assembling a 2D hexagonal-close-packed (HCP) CC of polystyrene (PS) microspheres (1.59 µm diameter) on a quartz substrate coated with an optically opaque silver film (about 100 nm thick) via a ion-beam sputtering deposition process (PECS-682, Gatan Corp.) using our previously reported method [8,21], as shown in Fig. 1(b).Sample microstructures were characterized by scanning electron microcopy (SEM, FEI Philips XL-30).After corrosion in the atmosphere of hydrofluoric acid for more than half an hour, a free-standing silver film coated by 2D PS CC as shown in the inset of Fig. 1(b), could be integrally lifted off on a water surface from the supporting quartz substrate, and then transferred to another prepared 2D PS CC on quartz substrate via a special process analogy to Langmuir-Blodgett (LB) technique.Note that the silver film would prefer to float unfolded on water because of interfacial tension, which is very important to get a planar free-standing silver film.A top-view image of a typical area of the as-prepared microstructure is shown in Fig. 1(c), and a cross-sectional image of the sample in the inset shows clearly that the silver film is coated by 2D CCs on both sides.The zero-order optical transmission spectra were measured at normal incidence in the near-infrared regime from 1.4 µm to 2.2 µm, using a far-field Fourier-transform infrared (FTIR) spectrometer (Nicolet 5700).The optical spot size of the incident beam on the sample was about 0.8 mm, and the numerical aperture of our optical setup was estimated to be less than 0.20.All transmission spectra have been normalized to the transmittance of a pure quartz substrate.Since the optical spot size was much larger than a single domain of the 2D CC, the measured area was basically a region of multi-domains, and as a consequence, the measured transmission spectra were insensitive to the polarization of the incident light.

Results and discussion
Figure 2(a) shows the measured transmission spectrum at normal incidence for the metallic microstructure composed of 2D PS CC only coated on top of 100 nm-thick silver film supported by a quartz substrate.Comparing with a pure flat silver film without any dielectric coating (black line in Fig. 2(a)), the transmission is considerably modified owing to the introduction of an array of 2D HCP PS microspheres self-assembled on the silver surface.A series of optical modes appearing as sharp transmission peaks and dips are clearly seen.All these modes correspond to the coupling of free-space light into propagating surface modes via 2D periodic dielectric coating.Actually, it has been predicted theoretically that flat metal surface decorated with periodic dielectric microstructure could support propagating surface plasmon modes bounded at the metal surface, guided modes confined in the periodic dielectric up-layer and their hybrids as well [24][25][26][27][28].
To well understand the optical properties of these metallic microstructures, numerical simulations were performed using the electromagnetic wave layer-multiple scattering theory formalism [29] and finite-element method based software package (COMSOL Multiphysics).The former numerical method was used to obtain the transmission spectra and the latter simulation method was adopted to calculate the field distributions of desired optical modes.The calculation domain of COMSOL Multiphysics constitutes one complete and four quarter PS microspheres in the xy-plane, and periodic boundary conditions are applied to the four sides of the rectangular calculation domain to mimic the periodicity of the whole structures.In the simulations, a plane wave with linear polarization (with the electric field parallel to the x-direction, shown in Fig. 1(a)) is normally illuminated on the microstructures, the diameter (d) of the PS microsphere is 1.59 µm as the experiments and the thickness of the silver film is 100 nm.The refractive index of the PS ( ps n ) is 1.59, which is considered as a constant in the wavelength regime of interest, and the permittivity of silver is taken from well accepted experimental data of Johnson and Christy [30].The calculated transmission spectrum for the sample consisting of a 2D CC on a silver film is presented in Fig. 2(b), which shows an excellent agreement with the experimental results.In the calculated spectrum, there are four distinct transmission peaks located at the wavelengths of 1527 nm, 1672 nm, 1879 nm, and 1945 nm, corresponding to the wavelengths of transmission peaks of the measured spectrum at 1528 nm, 1688 nm, 1884 nm, and 1929 nm, respectively.To achieve the physical nature of these transmission peaks supported by the microstructure in Fig. 1(a), the normalized electric field distributions (|E/E 0 |) on a cross-sectional (xz-plane) cut through the center of a PS microsphere for these four resonance modes are plotted.For the convenience of comparison, the normalized electric field intensity distributions are mapped using the same scale.From them, it is fairly clear that two types of optical surface modes are excited by the incident light in this microstructure: plasmonic resonant mode (SPP-like modes) and photonic modes (WGlike modes) [24][25][26][27][28].As marked in Fig. 2(c), for the WG-like modes (GM1, GM2), the electric fields are mainly confined inside the PS microspheres, while for the SPP-like modes (SPM1, SPM2), the electric fields are strongly bounded at the interface between the silver surface and the periodic PS microsphere arrays.Note that the optical features of such a microstructure could be easily scaled proportionally with the diameter of the PS microspheres (results not shown here).It's well known that the role of the top 2D PS CC is a diffraction grating which provides conservation of wave vectors needed for light from free space coupling to SPP modes.These SPP-like and WG-like modes will be evanescently tunneled through the optically opaque silver film and converted back into free space light with the help of silver surface roughness, which leads to the transmission peaks as shown in Fig. 2.However, such conversion efficiency is quite low and notoriously difficult to control, since it largely depends on the morphology of silver film with randomly rough interface.To achieve remarkable enhancement of transmissions, a symmetric structure was recommended because it could permit resonant coupling of SPP waves excited on both interfaces of the metallic film [20,31,32].The measured transmission spectrum for the as-prepared 100-nm-thick silver film sandwiched by 2D PS CCs on both sides is shown in Fig. 3(a).In this architecture, SPPs at both metallic surfaces may couple each other if the metallic film is not very thick.Comparing with silver interface with random roughness, the coupled SPPs would be effectively scattered out by the 2D PS CC on the other side of silver film, reradiating into outgoing light.Thus, for the planar silver film coated with the identical 2D PS CCs on both sides, its transmission spectrum shows tremendous enhancement at certain wavelengths.Figure 3(b) shows the calculation results of the transmission spectra for 100-nm-thick silver films with a 2D PS CC on one or both interfaces, which are, overall, in an excellent agreement with the corresponding measured spectra.Both in experiment and calculation, the transmission peaks of a silver film coated with PS microspheres on both sides have huge enhancement compared with just on one side.Two strong transmission peaks are found at wavelengths of 1676 nm and 1976 nm in the experiment, corresponding to that of 1669 nm and 1954 nm in the simulation (marked as SPM2', SPM1'), due to the resonant tunneling via SPPs excited on two periodically structured interfaces.In Fig. 3(c), we also plot the of electric field distributions of the PS microspheres above and under the silver film; all the modes are nearly as same as the fields described in Fig. 2(b), which shows a symmetric distributions of the electric fields on both sides of the silver film.Besides, we also can also observe the other two obvious resonant transmission peaks at wavelengths of 1516 nm and 1877 nm in Fig. 3(a), which might stem from the excitations of WG-like modes of the 2D CCs at 1529 nm and 1879 nm in the simulation.These WG-like modes as one kind of surface polariton Bloch modes, can also excite the composite diffracted evanescent wave at the interface of the silver film [33].After the propagating surface wave tunneling through the silver film, it would be reconverted to WG-like modes (GM2', GM1') by the PS microspheres array at the interface of silver film, which leads to the enhancement of the other two peaks.In Fig. 3(b), the transmission is plotted in logarithmic scale.It should be noted that the enhancement of the GM1' (or GM2') is actually lower than that of the SPM1' (or SPM2') if we use the linear scale to present the transmittance.The maximum of the electric fields locates directly at the metal/air interface for SPM modes, while for GM modes the maximum locates around the center of the microsphere, as shown in Fig. 3(c).For both SPM and GM modes, however, the electric fields will decay exponentially from its maximum to the adjacent medium.At the top metal/air interface the electric fields for SPM1' (or SPM2') are stronger than that for GM1' (or GM2'), which is very clear in the Fig. 3(c).Therefore, the tunneled electric fields are also stronger for the case of SPM modes, resulting in a relatively larger transmission enhancement.In Fig. 3, it is obvious that the calculated transmission peaks are much higher than the measured ones.In our simulation, identical 2D PS CCs are symmetrically coated on both sides of the silver film.Nevertheless, considering the real condition of our experiment, the 2D CCs on both sides of the silver film might be laterally shifted with respect to each other.The numerical simulation of evolutions for the transmission spectra dependent on the relative shift of the 2D CCs on the opposite interfaces of the silver film was performed.The relative shift is defined by x  and y  , which is the distance between the PS microspheres on opposite interfaces along x-direction and y-direction, respectively, as shown in the inset of Fig. 4(a).
Note that the simulated model with 0 x   or 0 y   is correspondence to a perfect microstructure, in which the 2D CCs coated on two sides are exactly symmetrical about the silver plane.Figures 4(a) and 4(b) demonstrate that variation of the relative shift of the 2D CCs on the opposite interfaces does not have an obvious effect on the spectral position of the resonant tunneling transmission, but significantly influences the peak transmittance of the microstructure.It is reasonable that the coupling efficiencies of the resonant surface modes on the opposite interfaces might be strongly dependent on the phase difference, although the surface polariton Bloch eigenmodes are only determined by the interface geometry [14].In addition, we simulated the transmission spectra for the different distances between the bottom PS microspheres array and the silver film, which might be formed inevitably by the wrinkle of silver film during our fabrication process, as shown in Fig. 4(c).Obviously, as the distance ( z  ) increases, the peak transmission would be suppressed continuously, as the coupling strength of the surface modes on both sides of metallic film decreases, which results in a low tunneling efficiency.

Conclusion
In summary, we have fabricated a structure consisting of a silver film coated with monolayer HCP array of PS microspheres on its one and both sides and demonstrated the extraordinary optical transmission of the latter microstructure both experimentally and theoretically.From our simulations, the extraordinary transmission is ascribed to the resonance tunneling of surface polariton Bloch eigenmodes, including surface plasmon modes and waveguided-like modes, excited by the diffracted evanescent wave at the interface of the silver film.It is the first time to demonstrate experimentally the extraordinary optical transmission of such a structure, especially in the regime of visible and near-infrared, and our work also elucidates further the plasmonic interactions in nano-coated metallic films.Clearly, by changing the parameters of the microspheres such as their sizes, refractive index and lattice structure as well, these optical modes can be tuned, and the huge enhancement of transmission at these optical modes suggests this microstructure has the potential applications in photonic devices.

Fig. 1 .
Fig. 1.(a) Fabrication procedure and schematic geometry of our microstructure.(b) Top-view SEM image of a planar silver film (about 100 nm of thickness) coated with monolayer array of PS microspheres (with 1.59 µm in diameter) on one side, and inset is tilted view of a freestanding silver film coated by 2D PS CC.(c) Top-view SEM image of 2D HCP PS microspheres arrays on both sides of the silver film, and the inset shows the cross-sectional SEM image.

Fig. 2 .
Fig. 2. (a) The experimental transmission spectra for a planar metal film (black line) and a planar film coated by a 2D CC on one side (red line).(b) The corresponding calculated results for a planar film with 100 nm (black line) and for the 2D CC on one side (red line).(c) Calculated distributions of normalized electric fields (|E/E0|) for four transmission peaks at corresponding wavelengths of (b), marked as GM1, SPM1, GM2, and SPM2.White circles and rectangles outline the PS microsphere and the silver films.

Fig. 3 .
Fig. 3. (a) Measured transmission spectra for a pure planar silver film with about 100 nm thickness (black line), a planar film (about 100 nm) coated with 2D CC on only one side (blue line) and on both sides (red line).The blue line is plotted by the left hand axes to display its details clearly.(b) The corresponding calculated results for a planar silver film with 100 nm thickness (black line), the 2D CC on one side (blue line) and both sides (red line) of a planer silver film (100 nm), respectively.(c) The different calculated distributions of normalized electric fields of the PS microspheres arrays above and under the silver film at the wavelengths of four transmission peaks marked as GM1', SPM1', GM2', and SPM2' in (b).The color maps are in linear scale as shown at the right of top panel and the under panel, respectively.

Fig. 4 .
Fig. 4. Calculated transmission spectra of the 100-nm-thick-silver film coated by 2D HCP CCs on both sides.The relative lateral shifts of these two 2D CCs along x-direction (a) and ydirection (b) are set to be 0   (black line),