1. Introduction

The study of the extraordinary transmission through subwavelength small metallic hole arrays has been active since the first observation by the Ebbesen group [1]. The consequences of the high transmitted spectral signals have significant potential in nano-photonic applications ranging from chemical to medical science. Particularly, by controlling the coupling of light with the surface plasmon polaritons bound to the metal-dielectric interface, one might expect applications related to achieving nano-scaled and highly efficient electro-optical devices (e.g., electro-optic modulators), near-field microscopy, and photolithography, as well as a new class of all optical integrated devices [2–10].

The enhancement results from the light coupling with the surface waves along the hole array structure. Recently, some have considered the dominant surface wave as simply the diffracted evanescent field [11,12]. As such, it is argued, constructive interference of the waves can be related directly to the extraordinary transmission. On the other hand, the surface plasmon modes along the metal interface might have significant roles in the high transmission spectra. The excited surface plasmon modes are caused by the momentum conservation of the incident light’s wave vector with the two dimensional grating wave vectors which result from the periodic structure [13–15]. The wavelength of the surface plasmon is dependent upon the dielectric constant of the medium surrounding the metal film, and it is much shorter than the coupling light. In order to study the effects of localized surface plasmons, many scientists have investigated the transmission spectra with a single subwavelength hole surrounded with corrugated structures [16–18]. Furthermore, the dependence of hole shape and light polarization on the transmission enhancement has been carried out to study the importance of the localized surface plasmons inside holes in nanoarrays [19–22].

In this study, we characterize the significance of the transmission efficiency as a function of wavelength through the various hole structure arrays on different metal thicknesses, and we conclude that the optical transmission characteristics are strongly related to the excitation of a surface wave mode resonance inside of the apertures. In addition, the array pattern also acts as a diffraction grating which serves to superimpose further spectral features onto the transmission spectra. We conclude from our results that array periodicity is simply not enough information to determine the peak position or peak width of the transmission spectra. In this paper, we focus on the effects of film thickness in our evaluation. Ebbesen et al. have addressed the issue of thickness as being a determining factor in transmission spectra [1] but they comment that the periodicity of the array determines the peak positions and that the features can be appreciably effected by the type of lattice (i.e., square or triangular lattice). They provide spectra of various thicknesses that show a slight red-shift as film thickness increases. Our results show a much more dramatic dependence on film thickness and we address the efficiency of the transmission and suggest that aperture resonances (Plasmon or waveguide modes) play a role in transmission efficiency, effects which have not previous been addressed in thickness studies. Further, the presence of ‘localized modes’, as suggested by Kuipers et al. [21,22] is further validated by our results presented here. Kuipers papers address the effect of lateral hole parameters while we address the effect of axial hole dimension, both of which affect the aperture resonance.

2. Sample preparation and experimental setup

The metallic nano-hole array samples are prepared on a silica glass substrate by using a lithography process with electron beam and ion milling etch systems. The thin silica substrate is coated with gold after the familiar cleaning process involving a piranha solution and ultra sonic treatment. A reactive DC sputtering system was used to deposit the gold film, and the film deposition was achieved by using 20 W DC power and 3 mTorr of chamber pressure with an Ar reactive gas at room temperature. The deposition rate has been characterized to have a fairly linear relation to the deposition time. We generated two different film thicknesses, 60 nm and 130 nm, using deposition times of 10 minutes and 20 minutes, respectively.

 

Fig. 1. AFM and SEM images of rectangular, circular and triangular subwavelength hole arrays for our experimental characterization. The scale bar in each image indicates 3 um. The periodicity and widths of the holes are, (a) and (b) a₀=600 nm, d_rec=230 nm, (c) a₀=600 nm, d_cir=360 nm, (d) a₀=600 nm, d_tri=150 nm

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After deposition of the gold films, a PMMA photoresist film of 200 nm thickness was coated onto the thin metal film and baked in an atmosphere oven at 170 °C for 30 minutes. For the pre-bake process, an oven bake is preferred over a hot plate in order to prevent heat shock from the direct heat transition to the substrate and thin metal layer. In our experiments, when using the hot plate, the partial burns of the metal film due to heat shock frequently occur when the substrate has defects or has been stored in a relatively high humidity environment.

The electron beam machine (Raith 150) was used for writing the small hole structures into the PMMA, and a standard photoresist develop process followed. To etch the developed metal layer, an ion milling etch system (Ar gas) is used with 300 W of rf power and 0.35 mTorr of chamber pressure. The etch rate characterized for the glass substrate is about 0.7 nm per minute. For the PMMA resist, the etch rate is much smaller and notably nonlinear with the applied time because of both the implantation of accelerated ions and the modification of the chemical structure which results from the process. Eventually, we removed the hole area on the metal layer by etching for 60 and 100 minutes in order for the metallic small hole arrays with 60 nm and 130 nm of metal thickness, respectively, to result.

The overall hole array areas are 60 μm × 60 μm with varying periodicity, hole size, and hole shape. For experiments reported here, periodicities are referred to as a₀, and they take on the values of 400 nm, 600 nm and 800 nm. The hole shapes are circular, square and triangular with different hole width d ranging from 46 nm to 370 nm. Figure 1 shows representative scanning electron microscopy (SEM) and atomic force microscopy (AFM) images of our fabricated arrays. The AFM image has been acquired with a high aspect ratio tip using tapping mode. The AFM image is a 5 μm x 5 μm image. The surface roughness of the metal film is about 2 nm, as determined with the AFM. The scale bar in each of the SEM images represents 3 μm.

The transmission spectra through the arrays have been obtained with a quartz-halogen fiber optic light source and a high resolution spectrometer equipped with a liquid nitrogen-cooled CCD. Two objective lenses have been set up in order to collimate the light onto the metal array layer and collect the transmitted light. The illumination light is focused onto the sample with a 0.1 NA objective and the collected light beam is connected to a multi-mode fiber with another objective lens of 0.1 NA. The transmission measurement is performed between 350 nm and 950 nm with < 1 nm spectral resolution. Figure 2 shows a schematic diagram for the apparatus used for the measurement of the optical transmission spectra through the hole arrays. The acquired transmission spectra are normalized to the transmission spectrum of a bare glass substrate and divided by the fraction of the open hole area on the array. This method of normalization provides us with a measure of the extraordinary light transmission factor. A factor of 1 indicates no enhancement or loss of transmission for the hole. For hole sizes much larger than the wavelength of light, we would expect a factor of exactly one unless an interaction with the metal film plays a role.

 

Fig. 2. Schematic diagram of the optical system used for the optical transmission spectral measurements.

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3. Results and discussion

Figure 3 shows transmission spectra of 60 nm and 130 nm planar gold films with no hole array. Note that the maximum signal occurs near 500 nm wavelength for both 60 nm and 130 nm thickness of metal, but the maximum of the normalized transmission is dependent on the film thickness. To compare the transmitted intensity with different metal thickness, the measured transmission spectrum is normalized to the maximum transmitted intensity from a glass substrate. We attribute the strong transmitted signal at 500 nm to the effect of the photoluminescence of the gold, which results from the electron transitions and recombination between the filled d-bands in metal and the Fermi level in conduction band [23–25]. These references clearly distinguish this PL transition from any possible plasmon behavior. From the measured data, we found that the peak position is 5 nm blue-shifted for the 130 nm thickness of metal. The blue shift is presumably related to the absorption mechanism in the thin film or the contribution of the surface morphology [26].

 

Fig. 3. Optical transmission spectra normalized to the transmission of a glass substrate for planar thin Au films. The maximum intensity occurs at the wavelength of 500 nm that is consistent with the photon energy 2.5 eV, the bandgap energy between the Fermi level and d-band in gold.

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Fig. 4. Transmission intensity change near the wavelength of 500 nm as a function of the fraction of the open hole surface (t_metal=60 nm). The transmission efficiency decays exponentially as the fraction increases for all different hole shapes. Fraction of hole area is defined as 0.0 being no hole at all in the metal film and 1.0 being no metal remaining between holes.

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According to the measured transmission spectra, any significant changes of the peak position at the wavelength of 500 nm could not observed with the various hole structure arrays. This peak is present in all of our spectra, independent of hole size, hole shape, or periodicity. It is the only spectral feature that remains unchanged as a function of all of our array parameters. This result indicates that the light coupling with surface plasmons which results from the periodic holes is not a dominant factor for the transmission characteristic at this 500 nm wavelength. However, the normalized peak intensity is related to the ratio of surface area of the gold film for both 60 nm and 130 nm of metal thickness. Therefore, in order to investigate what the relationship might be between the normalized intensity at the wavelength of 500 nm and the illuminated metal surface area, we characterized the transmission peak intensity as a function of the fraction of the open hole area. We performed this analysis for a film thickness of 60 nm, various periodicities, and hole shapes that are circular, square, and equilaterally triangular. As a result of this characterization, the peak intensity is found to decay exponentially as the open fraction increases for the 60 nm of metal thickness. The same feature has also been observed for the thicker metal film. Fig. 4 indicates that the intensity at maximum peak is independent of the hole periodicity, the aperture size and the hole shapes. In Fig. 4, fraction of hole area is defined such that 0.0 would be no hole at all (only metal film) and 1.0 would be no remaining metal between the holes (in fact no array at all but only plain glass). This curve is fit to an exponential, indicating the exponential decay of transmission upon fraction of hole area.

Furthermore, we have discovered the noteworthy enhancement of transmitted signals in the wavelength range from 700 nm to 850 nm with the triangular hole shape for both 60 nm and 130 nm film thicknesses. In particular, the transmission enhancement occurs when the lattice constant a₀ is 400 nm rather than 600 nm and 800 nm. The enhanced peak positions for the varied hole sizes are obtained differently in the range as shown in Fig. 5 and Fig. 6. These two figures indicate the transmission spectra for triangular holes (equilateral in nature) of three different sizes. Figure 5 shows the spectra for the hole arrays in a 60 nm thick film and Fig. 6 shows the spectra in a 130 nm thick film. Hole sizes for each of the spectra are very similar. In other studies, the peak located between 700 nm and 900 nm is designated as the (1,0) peak, which is so defined from the result of resonant excitation of the surface plasmons with the periodic structure [14]. In addition, there are small peaks in the range of wavelength from 550 nm to 700 nm. The peaks are not trivial since they fluctuate and broaden as the hole array parameters vary. The result of the transmission spectra in this range might be attributed to the light interaction between the diffraction modes from the periodic structure. However, we would like to note that the transmission characteristics around 700 nm to 850 nm are more significant in terms of the transmission efficiency that is connected to the extraordinary transmission with the implications of the light interactions through the nano-scale hole arrays.

 

Fig. 5. The normalized transmission spectra for the triangular hole shape arrays with different hole width (a₀=400 nm and t_metal=60 nm). The hole width is the length of one side for a triangle. When the pitch is 400 nm the transmission efficiency in the optical wavelength range from 700 nm to 850 nm is highly enhanced. Further, the peak positions are shifted to the longer wavelength as the hole size increases.

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Fig. 6. The normalized transmission spectra for triangular hole shape arrays with different hole width (a₀=400 nm and t_metal=130 nm). The transmission characteristics of the peak near the wavelength from 700 nm to 850 nm are similar to the t_metal=60 nm except the enhancement factor due to the optical loss of the waveguide mode.

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Considering Fig. 5 and Fig. 6, from the characterization for the extraordinary transmission vs. the metal thickness, especially in the range of wavelength from 700 nm to 850 nm, we have two meaningful consequences. First, as we would expect, the transmission efficiency decays as the metal thickness increases. The normalized transmission peak intensity for the 130 nm thickness of metal is about 40 % less when compared to that of the 60 nm thick film, and as normalized to account for the fractional area coverage of the open holes. With this consequence, the thickness is clearly a prominent factor in determining the transmission efficiency. We proposed that the waveguide mode of the aperture is critical to this analysis, since the mode is evanescent in this small hole regime, thus leading to an exponentially decaying propagation constant given by

where η is the transmission efficiency dependent on the coupling wavelength, α is the decay constant of the evanescent waveguide mode inside hole and t is the metal thickness.

 

Fig. 7. The peak wavelength characterization for different metal thicknesses (a₀=400 nm)

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On the other hand, in terms of the resonance peak position, we can clearly observe the red-shift as the hole size is increased for both 60 nm and 130 nm of metal thicknesses. It means that the light coupling with the localized surface plasmon mode is significantly dependent on the metal thickness. Additionally, comparing the different thicknesses of metal films, a red-shift of about 30 nm occurs at the same hole width for the thicker film as shown in Fig. 7. The peak wavelength is red-shifted with a constant ratio to the different hole widths. With these characterizations for the different metal thicknesses, the enhanced peak position and intensity are attributed to the notable light coupling with the localized surface plasmon mode inside the holes.

Likewise, as is the case with the triangular hole shape arrays, for the case of square and circular hole shape arrays with the 400 nm of lattice constant, we obtained strong transmission efficiency and the red-shift effect as the hole width increases at the range of wavelength from 700 nm to 850 nm. On the other hand, when the lattice constant a₀ is 600 nm and 800 nm the normalized transmission is less than unity at the wavelength range even though the hole width is as large as 260 nm. At the same time, the transmission efficiency is generally small for the thick metal film due to the optical loss of the evanescent waveguide mode. For a certain condition, however, the hole arrays on the 130 nm thick film, without reference to the hole shape, have the higher efficiency; as much as 2.2 times than the 60 nm thick film near the 750 nm wavelength. For instance, Fig. 8 indicates the transmitted signals as a function of wavelength for the square hole arrays with different metal thicknesses. Similarly the transmission characteristic occurs for the circle and triangular hole shape on condition that the lattice constant a₀ is 800 nm and the diameter d_hole is over 200 nm.

 

Fig. 8. The normalized transmission spectra for the square hole shape with different metal thicknesses (a₀=800 nm). The transmission feature occurs similarly for the circle and triangular hole shape on condition that a₀=800 nm and d_hole>200 nm.

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4. Conclusion

In conclusion, we have characterized the light transmission through subwavelength small hole arrays on different Au thin films. First, the transmitted spectral signal induced by the photoluminescence effect of the thin Au film has been observed on the opposite side of the layer. The transmission characteristics near the wavelength of 500 nm, which is consistent with the bandgap energy from the d-band in metal to the Fermi level in the conduction band, are dependent only on the fraction of the open hole apertures as if the surface wave modes are not significant. As a matter of fact, the various hole shapes and structures have almost no effect on the spectral signal at the wavelength of 500 nm.

Additionally, we have discovered the significant transmission enhancement at the wavelength ranged from 700 nm to 850 nm when the hole periodicity is 400 nm rather than 600 nm and 800 nm. The transmission characteristics in this spectral range are very dependent on the hole shape and the hole size as well as the metal thickness. The resonant frequency of the surface plasmons with the periodic structures is highly dependent on the depth of hole. This indicates that the localized surface plasmon inside the hole has a significant coupling with the evanescent waveguide mode. In terms of the transmission efficiency, it decreases as the metal thickness increases due to the loss of waveguide mode. Moreover, we found that the transmission efficiency for even 130 nm thickness near the wavelength of 750 nm is higher than the 60 nm thickness of metal in a certain condition of the periodicity of 800 nm and over 200 nm of the hole width. In summary, we conclude that the transmission efficiency depends on the optical loss of the waveguide mode, and the coupling of the surface plasmon modes with the periodic subwavelength small hole structures have important roles in determining the transmission characteristics.

These results are intended to provide additional information into the complex nature of white light transmission properties of metallic hole arrays. The complicated nature of these spectra, considering the dependence on periodicity, film thickness, hole shape, metal film material, etc., is still without a comprehensive theory that allows one to predict the transmission spectrum with knowledge of the film characteristics. A comprehensive model, including a determination into the role of plasmons and the nature of the hole resonance (whether it be a waveguide mode or other type of aperture resonance), could provide significant insight into the use of these films for displays, spectroscopic substrates, or near-field optical parallel imaging arrays.