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Experimental and numerical analysis on the optical resonance transmission properties of nano-hole arrays |
Optics Express, Vol. 18, Issue 21, pp. 22255-22270 (2010)
http://dx.doi.org/10.1364/OE.18.022255
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– Abstract
1. Introduction
2. Methods
3. Results
5. Discussion
6. Conclusion
– References and links
– Abstract
1. Introduction
2. Methods
3. Results
5. Discussion
6. Conclusion
– References and links
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Abstract
In this paper, we present experimental and numerical analysis on Extraordinary Optical Transmission (EOT) or optical resonance transmission through various nano-hole arrays constructed from an optically thick metal film within the visible and near infra-red spectrum. Nano-hole arrays with different geometrical parameters (hole size, hole shape, and hole periodicity) having their EOT properties in the visible and near-infrared regime were simulated based on Finite Difference Time Domain (FDTD). Large nano-hole arrays with geometric properties similar to the simulated arrays were fabricated using Electron Beam Lithography (EBL). The optical resonance transmission properties (resonance position, transmission efficiency, and spectral bandwidth of resonance peak) of the fabricated nano-hole arrays were characterized. Finally, the experimental and numerical results were analyzed to determine the dependencies and discrepancies between optical resonance transmission properties for various nano-hole arrays.
© 2010 OSA
1. Introduction
The interaction of light with perforated sub-wavelength holes in metallic films generates extraordinary effects that can be employed to miniaturize photonic devices to sub-wavelength scales. The optical characteristics of these sub-wavelength holes in a metallic film are created by the coupling of light with Surface Plasmon (SP) modes [1,2]. Surface Plasmon (SP) is the oscillation of free electrons at the interface of a metal and a dielectric and has been recognized to transmit light through sub-wavelength holes causing Extraordinary Optical Transmission (EOT) within the specific spectral range. Hence, a flat metal film, with a thickness that blocks light transmission (optically thick), can be perforated with an array of sub-wavelength holes to transmit light efficiently. EOT has been exploited in many applications such as Surface Enhanced Raman Spectroscopy (SERS), Surface Enhanced Fluorescence Spectroscopy (SEFS), focusing of light below the sub-wavelength regime, non-linear optics, and biosensors [2–6].
T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999). [CrossRef]
F. M. Huang, Y. Chen, F. J. Garcia de Abajo, and N. I. Zheludev, “Focusing of light by a Nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007). [CrossRef]
Recently, studies have investigated the dependence of EOT on a variety of parameters to improve optical transmission properties of nano-hole arrays [7–17]. Regarding geometrical parameters, the excitation of SP modes depends highly on the spacing between adjacent holes (periodicity) and dielectric constants of the metal and dielectric. Ebbessen [1,10] was first to derive an equation describing the dependence of the wavelength (λmax
) of the SP resonance modes (EOTs) on the arrangement of nano-holes for a square lattice when the incident light is normal to the plane of the nano-hole array:where a0
is the periodicity of holes, εd
and εm
are the dielectric constants of the incident medium (at the top or bottom surface of the nano-hole) and the metal film, and m and n are integers expressing the scattering mode indices. A transmission minimum is often observed before each EOT peak due to Wood’s anomaly [2]. It has been discovered that the nano-hole shape can robustly control both the polarization properties and the intensity of the EOT [7]. With regard to material properties, Ag, Au, and Cu have larger optical resonant transmission peaks than nano-hole arrays in a perfect metal conductor with the same geometrical parameters [8,9]. However for Ni and Cr, the transmittance is much smaller due to the absorption properties of these metals [8]. In addition, it is recognized that some metals particularly Au and Ag are more likely to display EOT properties compared to others such as Ni and Co [9]. Also, variations in the nano-hole radii, groove period, groove depth, locations of the grooves and slap thickness can significantly influence the transmission spectrum [11]. The optical transmission efficiency of the nano-hole array reaches an asymptotic upper value with a specific finite number of holes in the array [12,13]. The optical resonant transmission of a nano-hole array is enhanced by exploiting the same dielectric constant on the back and front surface of a nano-hole array as a result of the same Surface Plasmon energy on both sides [14]. Fabrication of a Bragg reflector on the boundary of a nano-hole array has been shown to enhance the optical resonance transmission of the array by preventing losses at the edges of the array such as those seen in classic optical diffraction filters [16].
R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]
C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999). [CrossRef]
T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]
F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A, Pure Appl. Opt. 8(5), 458–463 (2006). [CrossRef]
F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A, Pure Appl. Opt. 8(5), 458–463 (2006). [CrossRef]
K. Shuford, M. A. Ratner, S. K. Gray, and G. C. Schatz, “Finite-difference time-domain studies of light transmission through nanohole structures,” Appl. Phys. B 84(1-2), 11–18 (2006). [CrossRef]
J. Bravo-Abad, L. Martín-Moreno, and F. J. Garcia-Vidal, “Resonant transmission of light through subwavelength holes in thick metal films,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1221–1227 (2006). [CrossRef]
F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16(13), 9571–9579 (2008). [CrossRef] [PubMed]
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]
R. Gordon and P. Marthandam, “Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film,” Opt. Express 15(20), 12995–13002 (2007). [CrossRef] [PubMed]
Not only can nano-hole arrays in a metal film be used for enhancing the transmission of light by a means of the Surface Plasmon properties [17], their bandpass properties provide the opportunity to construct miniaturized spectral filters. Some groups have investigated the use of nano-hole arrays as color coding devices [18,19]. Another potential application for miniaturized spectral filters is spectroscopic optical imaging such as multispectral fluorescence microscopy. Although many studies have investigated the dependence of EOT properties on various geometrical properties of the nano-hole array, a comprehensive and systematic analysis of the dependence of EOT on nano-hole array geometry and the impact of the geometric properties on usage of nano-hole arrays as miniaturized spectral filters has yet to be done. Hence, in this study, a more complete characterization of the optical properties related to EOT was performed. Properties of the nano-hole array in a thick metal film included the wavelength of the peak transmission (optical resonance position), the intensity of the transmitted light at the peak (optical resonance transmission efficiency), and the spectral bandwidth (optical resonance bandwidth).
C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
N. F. van Hulst, “Plasmonics: Sorting colours,” Nat. Photonics 2(3), 139–140 (2008). [CrossRef]
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
Our approach was to compare numerical and experimental analyses from a series of nano-hole arrays with various geometrical designs (hole size, hole shape and periodicity) having optical resonance properties in the visible and near infra-red spectral regions. Numerical analysis was performed with FDTD simulation. Large nano-hole arrays were fabricated with electron beam lithography and characterized with optical transmission spectroscopy.
2. Methods
2.1 FDTD simulation of nano-hole arrays
The three-dimensional (3D) FDTD method was employed to simulate the interaction between light and a nano-hole array in a thick metal film with the goal of predicting the optical transmission properties. FDTD is a numerical method to solve the two and three dimensional Maxwell’s equations in linear and non-linear dispersive media. We used the FDTD package from Lumerical Inc. (Vancouver, Canada). Computations were performed with a computing grid (West grid (www.westgrid.ca)). With Lumerical, the user can specify arbitrary geometric structures and various input excitation sources. The software represents the electric [E(x,y,z,t)], magnetic [H(x,y,z,t)] and current density fields [J(x,y,z,t)] on a spatial grid and employs time spacing algorithms to perform the FDTD [20,21]. The dielectric constants for each material were defined by the relative dielectric constant [εr(x,y,z,ω)]. Since absorption and permittivity for a metallic material depend highly on frequency, the dispersion properties of the metal were considered. We used the dielectric constant for metallic and dielectric materials provided by Palik [22].
K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]
As shown in Fig. 1(a)
, in the simulation model, a single periodicity of nano-holes was surrounded by a simulation area and the x-, y-, and z-axis boundary conditions were set to Periodic, Periodic, and PML, respectively. The Periodic boundary conditions of the x- and y-axes were chosen due to the symmetric properties of the physical structure and the electromagnetic field. Therefore, due to these properties, the periodic structure of a single period nano-hole was replicated into infinity. A non-uniform mesh was used with a highest accuracy of 5 nm. A plain wave source was used to illuminate the nano-hole array at normal incidence to the nano-hole array plane. Using this methodology, we simulated nano-hole arrays with various hole shapes (circular and square), hole sizes (150 nm, 200 nm, and 250 nm) and periodicities (375 nm, 400 nm, 425 nm, 450 nm, and 475 nm) in square lattice arrangements.
Fig. 1 (a) Set up and boundary conditions for FDTD simulation of nano-hole array, (b) Electron beam lithography (EBL) for fabrication of nano-hole arrays, (c) SEM of an array of photo-resist nano-pillars, (d) Set up for optical characterization of nano-hole arrays, and (e) SEM of a nano-hole array with the circular nano-holes.
2.2 Electron Beam Lithography (EBL) fabrication methodology
We used electron beam lithography (EBL) fabrication methodology for fabricating nano-hole arrays in a 100-nm optically thick gold film. The fabrication process used is shown in Fig. 1(b). Chromium (5 nm) was deposited on a Pyrex substrate in order to make the substrate surface conductive for the EBL process. Afterward, 500 nm photo-resist (Negative Tone photo-resist ma-N 2403) was spin-coated and soft-baked on the chromium layer. The nano-hole array pattern was written using an EBL machine (LEO, 1530 e-beam lithography), the sample was developed leaving behind photo-resist pillars. Chromium (10 nm) was then deposited as an adhesion layer followed by 100 nm deposition of gold on to the sample. A SEM image of the photo-resist pillars covered with gold is shown in Fig. 1(c). Finally, in a lift-off process, the sample was exposed to Acetone and Nano-stripper to remove the pillars. A SEM image of a fabricated nano-hole array is shown in Fig. 1(e). We fabricated nano-hole arrays with various hole shapes (circular and square), hole sizes (150 nm, 200 nm, and 250 nm) and hole periodicities (375 nm, 400 nm, 425 nm, 450 nm, and 475 nm) in a square lattice arrangement. These geometrical parameters were selected to enable optical resonance transmission of each array in the visible and near-infrared regime. The number of holes in each nano-hole array was 150 × 150.
2.3 Optical characterization setup
We used a standard inverted microscope (Nikon, TE300) attached to a photometer (PTI, D104), monochromator (PTI, 101), and photo-multiplier (PTI, 710) for the optical characterization of each nano-hole array as shown in Fig. 1(d). Unpolarized white light from a 100 W halogen lamp was focused on the sample using the bright-field and condenser lens (NA = 0.3) of the microscope. The scattered light was collected with a 20 × objective (NA = 0.45; Nikon, 93150) and guided with a beam splitter to the photometer. Using the aperture adjustment on the photometer, light from a desired region of a given sample was selected, then guided to the monochromator for spectral characterization, and detection by the photo-multiplier tube. The optical transmission spectra were obtained by first subtracting the background signals obtained from a hole-free region of the gold film from the spectra transmitted through a given nano-hole array, and then divided by the measured white light spectrum. The ratio cancels the wavelength variant signal caused by the light source, monochromator and the wavelength responsivity of the detector.
2.4 Analysis of the optical transmission spectra
In order to employ EOTs (optical resonance peaks) of a nano-hole array as a spectral filter, the optical characteristics of EOT related to spectral performance were analyzed. These optical properties consist of the center wavelength, the transmission efficiency of a center wavelength and the spectral bandwidth. In some instances, although the position of the peaks was measurable, the peak location was corrupted due to the large bandwidth of the spectral features and was not interpretable. In these cases, the peak positions were not reported. The spectral bandwidth of each EOT computed in such a way that the spectral bandwidth is the full width of the EOT where the optical transmission was of the optical transmission peak.
3. Results
3.1 Experimental observations in Nano-hole array fabrication
Prior to writing nano-hole patterns with EBL, initial tests were performed to optimize the EBL area dose used for fabrication of nano-hole arrays with specific feature parameters (hole size, hole shape, and periodicity of hole). The area dose required to fabricate each design was dependent on hole shape, hole size, periodicity, and the type and age of the photo-resist. The area dose varied from 70 µC/cm2 to 125 µC/cm2.
All nano-hole array devices were imaged with SEM. The SEM measurements verified that the hole size and periodicity were within 5-10% of the intended size and periodicity. The average corner radius for nano-holes with square hole shape was measured and was about 50 nm. As a result, square nano-holes less than 100 nm on a side were effectively circular in shape. Also, for the 500 nm photo-resist pillars, the ratio of the top to the bottom diameter was 1.18.
3.2 Simulation results
The simulation results for optical transmission spectra of the nano-hole arrays with square lattice arrangement, various hole shapes (circular and square), hole sizes (150 nm, 200 nm, and 250 nm), and periodicities (375 nm, 400 nm, 425 nm, 450 nm, and 475 nm) are shown in Fig. 2
. The optical transmission spectrum of each nano-hole array was normalized to the combined area of the holes relative to the area corresponding to the lattice (i.e. square in shape and determined by the periodicity and number of holes). The optical resonance peaks related to (1,0) and (1,1) SP excitation modes from the Pyrex-gold side and (1,0) SP excitation mode from the air-gold side were generally observed (see Table 1
) in the optical transmission spectrum of each nano-hole array and are indicated by two separate brown dashed lines (Pyrex-gold side resonance peaks) and blue dashed lines (air-gold side resonance peaks) in Fig. 2. The optical resonance peaks were observed in the visible and near infra-red regime. A transmission minimum was observed between the (1,0) and (1,1) optical resonance peaks related to the Pyrex-gold side and is indicated in Fig. 2 by the orange dashed line.
Fig. 2 Optical transmission spectra for nano-hole arrays with various hole shape (square and circular), diameters (150 nm, 200 nm, and 250 nm), and periodicities or P (375 nm, 400 nm, 425 nm, 450 nm, and 475 nm) based on FDTD simulation: (a) circular holes with 150 nm diameter, (b) circular holes with 200 nm diameter, (c) circular holes with 250 nm diameter, (d) square holes with 150 nm length, (e) square holes with 200 nm length, and (f) square holes with 250 nm length. (ag) represents the optical resonance peak from air-gold side. (Pg) represents the optical resonance peak from Pyrex-gold side.
Table 1 Summary of simulation results related to optical resonance peaks
Not Measurable (NM), - (not observed)
The position, transmission efficiency, and bandwidth of (1,0) optical resonance peaks related to the Pyrex-gold side was extracted from each optical transmission spectrum and shown in Fig. 3
. The optical resonance position related to the (1,0) SP excitation red-shifted as the periodicity increased [Fig. 3(a)]. For a given periodicity, the resonance position generally slightly red-shifted as the hole size increased, except for arrays with square holes and larger hole sizes (200 nm and 250 nm), which showed a minor blue-shift as the hole size increased. In Fig. 3(b), the optical resonance transmission efficiency related to the (1,0) SP excitation decreased as periodicity increased. For a given periodicity, the transmission efficiency increased as the hole size increased. In Fig. 3(c), the (1,0) optical resonance bandwidth (see Table 1) was generally unaffected (e.g., D200) or decreased as the periodicity increased. In two specific instances, the bandwidth was smaller for the arrays with square hole shape when the periodicity was 375 nm compared to 400 nm. For all arrays at a given periodicity, the bandwidth increased with hole size.
Fig. 3 (1,0) and (1,1) optical resonance analyses of the nano-hole arrays for simulation results (in the graphs legend, D circular hole diameter and L square hole length): (a) (1,0) Pyrex-gold side optical resonance position versus periodicity, (b) (1,0) Pyrex-gold side optical resonance transmission efficiency versus periodicity, (c) (1,0) Pyrex-gold side optical resonance bandwidth versus periodicity, (d) (1,1) Pyrex-gold side optical resonance position versus periodicity, (e) (1,1) Pyrex-gold side optical resonance transmission efficiency versus periodicity, and f) (1,0) air-gold side optical resonance transmission versus periodicity.
The optical resonance position versus periodicity for the (1,1) optical resonance peaks from the Pyrex-gold side and the (1,1) optical resonance transmission efficiency from the Pyrex-gold side are shown in Fig. 3(d) and 3(e), respectively. The (1,1) resonance peaks red-shifted as the hole periodicity increased. However, at a given periodicity, all arrays of various hole shape and hole size had identical (1,1) optical resonance positions (therefore, only one line is plotted). In Fig. 3(e), the optical resonance transmission efficiency related to (1,1) SP excitation increased as the hole size increased. Also, as the hole size increased a transition from a decrease in transmission efficiency with periodicity to an increase in transmission efficiency with periodicity was observed in the simulation results. For example, the array with square hole size of 250 nm increased in transmission efficiency as a function of periodicity from 375 nm to 450 nm. The (1,0) optical resonance peak related to the air-gold side was observed for all arrays with circular hole shape, but only observed at higher periodicities for arrays with square hole shape [Table 1; Fig. 3(f)]. In Fig. 3(f), the (1,0) optical resonance peak related to the air-gold side red-shifted as the periodicity of the holes increased. Also, as the hole size increased for arrays with square and circular holes, the (1,0) optical resonance position increased and this effect was more apparent for arrays with larger periodicities. For arrays with circular holes and smaller periodicities, no dependence on hole size was observed.
4.3 Experimental results
The experimental results and analysis for optical transmission spectra of the nano-hole arrays with various hole shapes (circular and square), hole sizes (150nm, 200nm, and 250nm) and periodicities (375nm, 400nm, 425nm, 450nm, and 475nm) in the square lattice arrangement are shown in Figs. 4
and 5
. The experimental results (see Fig. 4) are presented in a format that is similar to the presentation of the simulation results (see Fig. 2). In general, the experimental optical transmission spectra were qualitatively similar to the simulated spectra. For example, the (1,0) and (1,1) optical resonance peaks related to the SP excitation from the Pyrex-gold side and Wood’s anomaly were observed. However, there were differences in the number of observable peaks and measurable bandwidths (compare Table 2
to Table 1). For instance, the (1,0) resonance peak from the air-gold side was not clearly observed in the experimentally measured spectra for the most of the arrays except the arrays with 150 nm circular hole and periodicities of 450 nm and 475 nm. Furthermore, the (1,1) optical resonance peaks from Pyrex-gold side had measurable bandwidths for the most of the arrays in the experimental results, which were not generally measurable in simulation studies (compare Table 2 to Table 1).
Fig. 4 Optical transmission spectra for nano-hole arrays with various hole shape (square and circular), diameters (150nm, 200nm, and 250nm), and periodicities or P(375nm, 400nm, 425nm, 450nm, and 475nm) in experimental results: (a) circular holes with 150nm diameter, (b) circular holes with 200nm diameter, (c) circular holes with 250nm diameter, (d) square holes with 150nm length, (e) square holes with 200nm length, and (f) square holes with 250nm length. (ag) represents the optical resonance peak from air-gold side. (Pg) represents the optical resonance peak from Pyrex-gold side.
Fig. 5 (1,0) and (1,1) Pyrex-gold side optical resonance analyses of the nano-hole arrays for experimental results (in the graphs legend, D circular hole diameter and L square hole length): (a) (1,0) optical resonance position versus periodicity, (b) (1,0) optical resonance transmission efficiency versus periodicity, (c) (1,0) optical resonance bandwidth versus periodicity, (d) (1,1) optical resonance position versus periodicity, (e) (1,1) optical resonance transmission versus periodicity, and (f) (1,1) optical resonance bandwidth versus periodicity.
Table 2 Summary of experimental results related to optical resonance peaks
Not Measurable (NM), - (not observed)
The dependence of the (1,0) optical resonance position, (1,0) optical resonance transmission efficiency, and (1,0) optical resonance bandwidth on periodicity, hole size and hole shape were generally similar to the corresponding metrics derived from simulations (see Fig. 3 and 5). Both simulation and experimental results agreed with respect to the red-shift of the (1,0) optical resonance position as the periodicity of the holes increased [see Fig. 3(a) and Fig. 5 (a)]. Also, the (1,0) optical resonance position derived from the simulation results was in good agreement with the experimental results. However, the experimental results showed less dependence of the (1,0) optical resonance position on hole size compared to the simulation results for the arrays with the same periodicity. The red-shift was generally observed for the (1,0) resonance position as hole size increased in the simulation results, while there was no systematic dependence of resonance position on hole size for the experimental results (both blue-shifts and red-shifts were observed). With respect to the (1,0) optical resonance transmission efficiency, both the simulation and experimental results were generally in agreement for the smallest hole size [see Fig. 3(b) and Fig. 5(b)]. However, as the hole size increased a transition from a decrease in transmission efficiency with periodicity to an increase in transmission efficiency with periodicity was observed in the experimental results. For example, the transmission efficiency of the array with 250 nm square hole size increased as a function of periodicity. This was largely true for the circular hole shaped arrays with 250 nm holes, except for devices with periodicities of 425 nm and higher where the transmission efficiency was observed to be relatively constant. Although the optical resonance bandwidth was not highly dependent on periodicity in the simulations, the bandwidth decreased with periodicity in the experimental results and bandwidths were significantly smaller (compare Tables 1 and 2) and [see Fig. 3(c) and Fig. 5(c)]. Furthermore, the dependence of bandwidth on hole size was greater for the experimental results compared to the simulations. For example, for simulations, arrays with circular holes of 200 nm and 250 nm, the bandwidths were measured to be 149 and 178 nm, respectively, while the corresponding experimental observations resulted in bandwidths of 86 and 143 nm, respectively.
Both simulation and experimental results agreed with respect to the red-shift of the (1,1) optical resonance position as the periodicity of the holes increased [see Fig. 3(d) and Fig. 5(d)]. However, for a given periodicity, the (1,1) optical resonance position was slightly (blue-shifted or red-shifted) as the hole size increases in the experimental results which no change was observed in the simulation results. With respect to the (1,1) optical resonance transmission efficiency, similar behavior between simulation and experimental results was observed [see Fig. 3(e) and Fig. 5(e)]; however, the increase in transmission efficiency with increasing hole size was not as apparent for the arrays with the largest hole size (e.g. 200 to 250 nm) and some instances decreases in efficiency were observed as the hole size increased (e.g. 200 to 250 nm at periodicity of 400 nm). As shown in Fig. 5(f), the (1,1) resonance bandwidth increased with periodicity, except for smaller periodicities (375 nm and 400 nm). For a given periodicity, the (1,1) resonance bandwidths were similar for various hole sizes and shapes.
5. Discussion
The (1,0) and (1,1) optical resonance positions related to the Pyrex-gold side of nano-hole arrays for various periodicities were calculated using Eq. (1). The (1,0) optical resonance positions for the periodicities of 375 nm, 400 nm, 425 nm, 450 nm, and 475 nm were 659 nm, 682 nm, 710 nm, 742 nm, and 776 nm, respectively. Also, the (1,1) optical resonance positions were computed to be 536 nm, 547 nm 561 nm, 584 nm, and 616 nm for the corresponding periodicities. The resonance peak positions observed in experiment and simulation were in good qualitative agreement with the theoretical estimates.
Although there was general agreement between the optical properties of nano-hole arrays studied by experiment and simulation, there were several notable differences. First, the transmission efficiency for (1,0) and (1,1) resonance peaks related to the Pyrex-gold side obtained through simulation was significantly lower compared to the experimental results. This was likely due to the high sensitivity of the simulated transmission spectra on presence of the chromium layer. For example, sharp resonance peaks were observed when the chromium layer was excluded (data not shown) in a manner similar to other work [8]. It is possible that the selection of the mesh accuracy, although small enough to adequately sample the chromium layer, resulted in an underestimation of the transmission efficiency. The slight discrepancy between simulation and experimental results due to the selection of the mesh accuracy enabled manageable computation times. Second, although the optical resonance peaks related to the (1,0) air-gold side were observed in the simulation studies, they were not observed consistently in the experimental studies. This was most likely on account of the closeness of the (1,1) resonance peak position to (1,0) resonance and the poorer transmission efficiency of the (1,0) resonance from air-gold side. As a result, the (1,0) resonance peaks on the air-gold side were not observed for all of the arrays, except for the arrays with 150 nm circular hole size and higher periodicities (450 nm and 475 nm). Since the arrays with 150 nm holes and higher periodicities (450 nm and 475 nm) had a smaller total hole area compared to the other tested arrays, the resonance peaks of longer wavelength had lower transmission efficiency compared to other arrays with larger hole sizes. As a result, the (1,1) resonance peak from the Pyrex-gold side and the (1,0) resonance peak from air-gold side appeared at longer and shorter wavelengths, respectively. This effect resulted in more pronounced (1,0) resonance peaks from the air-gold side for these arrays (150 nm circular hole with 450 nm and 475 nm periodicities) and suppression of the (1,1) resonance peak from the Pyrex-gold side. Third, in the simulations, the transmission efficiency of the (1,0) Pyrex-gold side resonance peak improved with hole size. Based on geometric considerations, the transmission behaviour was consistent with the total effective aperture of the nano-hole array, i.e. larger holes and closer hole spacing resulted in larger total opening size compared to nano-hole arrays with smaller holes and wider hole spacing. This geometric dependence of the optical transmission efficiency on hole area has been known for over a decade [10]. Although this general optical transmission behaviour was observed in experiments performed with nano-hole arrays with circular holes, the transmission efficiency determined through experiment did not increase in a manner consistent with the effective aperture hypothesis. The discrepancy was most apparent for nano-hole arrays with square holes. For example, nano-hole arrays with square holes 200 nm in size had greater transmission efficiency than arrays of identical periodicity with square holes either 150 nm or 250 nm in size. Although the reason for this behaviour is not fully understood, it may be related to more efficient coupling of the light to the SP with this specific hole size in the visible and near infra-red regime, which could potentially result in a higher transmission efficiency.
T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
It has been reported in early literature that the optical resonance position is not dependent on hole size [1]. However, we found experimentally that the (1,0) optical resonance position varied slightly (blue-shifted or red-shifted) with hole size. In agreement with our results, it has been reported for nano-hole arrays with square hole shape that a similar shift in resonance position behavior occurs, which was attributed to a cutoff behavior related to the hole size [23]. Also, in agreement with literature (see ref [10].), we also observed that the (1,0) optical resonance bandwidth became larger for larger holes and narrower for larger periodicities.
T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999). [CrossRef]
K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004). [CrossRef]
T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
Using the EBL fabrication methodology, the pattern on the photoresist for a nano-hole array 1 mm by 1 mm can be written in a couple of hours with reasonable cost. However, compared to other methods such as Focused Ion Beam (FIB) milling technology, EBL fabrication methodology requires a thicker adhesion layer (such as 8 nm to 20 nm Chromium or Titanium) to allow for an aggressive lift-off process without damaging an array. Since the adhesion layer is deposited between the gold and Pyrex substrate, the optical performance of the nano-hole array is affected. For example, we observed that the bandwidth of the (1,0) and (1,1) resonance peak was broadened and the transmission efficiency was lower. However, deposition of metal materials such as aluminum or silver on the Pyrex substrate does not require an adhesion layer, but these materials are sensitive to oxidization that leads to loss of the SP properties. Also, unlike other methods for nano-hole-array fabrication, patterns such as grooves, corrugations, and dimples cannot be fabricated about the holes easily with EBL. Other fabrication methodologies such as Nano-Imprint Lithography (NIL) and FIB are proven methods for fabrication of nano-hole arrays [24–27]. FIB fabrication methodology can be used to fabricate arbitrary nano-hole array designs with fine resolution, but at the cost of speed. Alternatively, very large nano-hole arrays can be fabricated with NIL methodology very quickly, but with poorer resolution and higher cost. Therefore, EBL provides a rapid and competitive fabrication solution for nano-hole arrays of intermediate size where fidelity of nanostructures is important.
Z. Yu, H. Gao, W. Wu, H. Ge, and S. Y. Chou, “Fabrication of large area subwavelength antireflection structures on Si using trilayer resist nanoimprint lithography and liftoff,” J. Vac. Sci. Technol. B 21(6), 2874–2877 (2003). [CrossRef]
J. Chen, J. Shi, D. Decanini, E. Cambril, Y. Chen, and A. Haghiri-Gosnet, “Gold nanohole arrays for biochemical sensing fabricated by soft UV nanoimprint lithography,” Microelectron. Eng. 86(4-6), 632–635 (2009). [CrossRef]
Although the motivation for this study was the potential development of nano-hole arrays as spectral filters. The analysis of the EOT properties of various nano-hole array designs revealed that the band-pass characteristics of the devices simulated and tested was far from optimal when compared to conventional commercially available interference filters. Typically, it was observed that the nano-hole arrays had at least two pass bands with poor blocking between and on either side. Poor out of band blocking would result in bleed through of out of band wavelengths and corruption of spectroscopic data, for example. To improve band-pass performance several options remain including manipulation of the dielectrics on either side of the gold and incorporation of nano-scale features to enhance wavelength selectivity and transmission efficiency. For example, a nano-hole array surrounded with the material of the same dielectric constant on both sides is known to increase the transmission efficiency of the resonance peak due to SP energy coincidence on both sides of a nano-hole array [14]. Also, structures such as grooves, corrugations, and dimples about the holes of a nano-hole array or surrounding an entire nano-hole array can enhance transmission efficiency of the resonance peak [11,16]. For example, it has been shown that a nano-hole array surrounded by dimples with the same size and shape as the holes and at half periodicity of the holes can improve transmission efficiently by a factor of two [16]. In addition to the hole size effect on the bandwidth of the resonance peaks, the bandwidth can be reduced if the nano-hole array is fabricated in a thicker metal film. However, the transmission efficiency of the resonance peak decays as thickness of metal film increases [1]. Also, a 10 to 20 nm adhesion layer of Chromium can cause broadening of the bandwidth of the resonance peaks related to the Pyrex-gold side of the nano-hole array. As a result, by exploiting other materials such as Ag or Al [8], the need for a Chromium layer can be eliminated and narrower bandwidths can be achieved.
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]
K. Shuford, M. A. Ratner, S. K. Gray, and G. C. Schatz, “Finite-difference time-domain studies of light transmission through nanohole structures,” Appl. Phys. B 84(1-2), 11–18 (2006). [CrossRef]
R. Gordon and P. Marthandam, “Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film,” Opt. Express 15(20), 12995–13002 (2007). [CrossRef] [PubMed]
R. Gordon and P. Marthandam, “Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film,” Opt. Express 15(20), 12995–13002 (2007). [CrossRef] [PubMed]
T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999). [CrossRef]
Regardless of the poor blocking characteristics of the nano-hole arrays studied here, an interesting aspect of nano-hole arrays is their scalable size. The nano-hole array dimension can be varied from several microns to several centimeters in size. This provides interesting opportunities to utilize the same base technology for applications that work at microscopic scales to applications that work at macroscopic scales. For example, the optical resonance of nano-hole arrays for various geometrical parameters can be exploited in applications such as SEFS and bio-sensing applications, where the optical resonance transmission properties of the nano-hole arrays can enhance the detectability of fluorescence emission and bio-molecules [2–5].
A. Lesuffleur, H. Im, N. C. Lindquist, K. S. Lim, and S. H. Oh, “Laser-illuminated nanohole arrays for multiplex plasmonic microarray sensing,” Opt. Express 16(1), 219–224 (2008). [CrossRef] [PubMed]
In the future, additional studies will need to be directed at improving the optical resonance transmission efficiency of nano-hole arrays and reducing bandwidth if nano-hole arrays are to be used as spectral band-pass filters for biomedical applications. Probably the most success will come from examining new substrates and dielectric matching of the top and bottom layers. As a result, in future work, we are planning to do a comprehensive experimental and numerical analyses on optical transmission of nano-hole arrays when they are surrounded by transparent materials such as Polymethyl methacrylate (PMMA), transparent SU-8, and silicon dioxide.
6. Conclusion
We presented a comprehensive experimental and numerical (FDTD) study on Extraordinary Optical Transmission (EOT) through various nano-hole arrays in a thick metal film within the visible and near infra-red spectral regions. Large nano-hole arrays were fabricated using EBL methodology and they were optically characterized. We analyzed the simulation and the optical characterization results of optical resonance of nano-hole arrays with respect to optical resonance peak position, optical resonance transmission efficiency, and optical resonance bandwidth. As a result, regarding these parameters, the simulation results showed relatively good agreement with the experimental analyses although there were some notable differences. The hole size was recognized as a main factor in the appearance of the optical resonance peaks in the transmission spectra. There were no significant differences between optical transmission spectra of nano-hole arrays with circular or square hole shapes. However, the opening area of the hole had a major effect on the optical resonance transmission properties. The effect of the chromium adhesion layer between the gold film and the Pyrex substrate reduced the transmission efficiency for the optical resonance peaks related to SP excitation from Pyrex-gold side. Finally, the analyses showed that for macroscopic applications such as optical band-pass filters, improved out of band blocking are needed. One possibility for achieving this optical characteristic is the matching of the SP energy on both sides of the array by index-matching.
References and links
T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999). [CrossRef] | |
R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. , 1–25 (2009). | |
A. G. Brolo, S. C. Kwok, M. G. Moffitt, R. Gordon, J. Riordon, and K. L. Kavanagh, “Enhanced fluorescence from arrays of nanoholes in a gold film,” J. Am. Chem. Soc. 127(42), 14936–14941 (2005). [CrossRef] [PubMed] | |
J. R. Lakowicz, M. H. Chowdhury, K. Ray, J. Zhang, Y. Fu, R. Badugu, C. R. Sabanayagam, K. Nowaczyk, H. Szmacinski, K. Aslan, and C. D. Geddes, “Plasmon-controlled fluorescence: A new detection technology,” Proc SPIE 6099, 9–1-9–14 (2009). | |
A. Lesuffleur, H. Im, N. C. Lindquist, K. S. Lim, and S. H. Oh, “Laser-illuminated nanohole arrays for multiplex plasmonic microarray sensing,” Opt. Express 16(1), 219–224 (2008). [CrossRef] [PubMed] | |
F. M. Huang, Y. Chen, F. J. Garcia de Abajo, and N. I. Zheludev, “Focusing of light by a Nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007). [CrossRef] | |
R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed] | |
S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. Lett B 77, 075401 (2008). | |
F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A, Pure Appl. Opt. 8(5), 458–463 (2006). [CrossRef] | |
T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef] | |
K. Shuford, M. A. Ratner, S. K. Gray, and G. C. Schatz, “Finite-difference time-domain studies of light transmission through nanohole structures,” Appl. Phys. B 84(1-2), 11–18 (2006). [CrossRef] | |
J. Bravo-Abad, L. Martín-Moreno, and F. J. Garcia-Vidal, “Resonant transmission of light through subwavelength holes in thick metal films,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1221–1227 (2006). [CrossRef] | |
F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16(13), 9571–9579 (2008). [CrossRef] [PubMed] | |
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] | |
F. J. Garcia de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10(25), 1475–1484 (2002). [PubMed] | |
R. Gordon and P. Marthandam, “Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film,” Opt. Express 15(20), 12995–13002 (2007). [CrossRef] [PubMed] | |
C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed] | |
N. F. van Hulst, “Plasmonics: Sorting colours,” Nat. Photonics 2(3), 139–140 (2008). [CrossRef] | |
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed] | |
K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef] | |
A. Taflove, and S. C. Hagness, Computational electrodynamics: The Finite-Difference Time-Domain method , 2nd Ed” (Artech House Publishers, Boston, 2000). | |
E. D. Palik, Handbook of Optical Constants of Solids , Academic Press, New York, (1985). | |
K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004). [CrossRef] | |
Z. Yu, H. Gao, W. Wu, H. Ge, and S. Y. Chou, “Fabrication of large area subwavelength antireflection structures on Si using trilayer resist nanoimprint lithography and liftoff,” J. Vac. Sci. Technol. B 21(6), 2874–2877 (2003). [CrossRef] | |
V. Malyarchuk, F. Hua, N. Mack, V. Velasquez, J. White, R. Nuzzo, and J. Rogers, “High performance plasmonic crystal sensor formed by soft nanoimprint lithography,” Opt. Express 13(15), 5669–5675 (2005). [CrossRef] [PubMed] | |
A. A. Tseng, “Recent developments in nanofabrication using focused ion beams,” Small 1(10), 924–939 (2005). [CrossRef] | |
J. Chen, J. Shi, D. Decanini, E. Cambril, Y. Chen, and A. Haghiri-Gosnet, “Gold nanohole arrays for biochemical sensing fabricated by soft UV nanoimprint lithography,” Microelectron. Eng. 86(4-6), 632–635 (2009). [CrossRef] |
OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(220.4241) Optical design and fabrication : Nanostructure fabrication
(250.5403) Optoelectronics : Plasmonics
ToC Category:
Optics at Surfaces
History
Original Manuscript: August 4, 2010
Revised Manuscript: August 28, 2010
Manuscript Accepted: August 29, 2010
Published: October 6, 2010
Citation
Mohamadreza Najiminaini, Fartash Vasefi, Bozena Kaminska, and Jeffrey J. L. Carson, "Experimental and numerical analysis on the optical resonance transmission properties of nano-hole arrays," Opt. Express 18, 22255-22270 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-21-22255
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References
- T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999). [CrossRef]
- R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. , 1–25 (2009).
- A. G. Brolo, S. C. Kwok, M. G. Moffitt, R. Gordon, J. Riordon, and K. L. Kavanagh, “Enhanced fluorescence from arrays of nanoholes in a gold film,” J. Am. Chem. Soc. 127(42), 14936–14941 (2005). [CrossRef] [PubMed]
- J. R. Lakowicz, M. H. Chowdhury, K. Ray, J. Zhang, Y. Fu, R. Badugu, C. R. Sabanayagam, K. Nowaczyk, H. Szmacinski, K. Aslan, and C. D. Geddes, “Plasmon-controlled fluorescence: A new detection technology,” Proc SPIE 6099, 9–1-9–14 (2009).
- A. Lesuffleur, H. Im, N. C. Lindquist, K. S. Lim, and S. H. Oh, “Laser-illuminated nanohole arrays for multiplex plasmonic microarray sensing,” Opt. Express 16(1), 219–224 (2008). [CrossRef] [PubMed]
- F. M. Huang, Y. Chen, F. J. Garcia de Abajo, and N. I. Zheludev, “Focusing of light by a Nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007). [CrossRef]
- R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]
- S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. Lett B 77, 075401 (2008).
- F. Przybilla, A. Degiron, J. Y. Laluet, C. Genet, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A, Pure Appl. Opt. 8(5), 458–463 (2006). [CrossRef]
- T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
- K. Shuford, M. A. Ratner, S. K. Gray, and G. C. Schatz, “Finite-difference time-domain studies of light transmission through nanohole structures,” Appl. Phys. B 84(1-2), 11–18 (2006). [CrossRef]
- J. Bravo-Abad, L. Martín-Moreno, and F. J. Garcia-Vidal, “Resonant transmission of light through subwavelength holes in thick metal films,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1221–1227 (2006). [CrossRef]
- F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16(13), 9571–9579 (2008). [CrossRef] [PubMed]
- 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]
- F. J. Garcia de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10(25), 1475–1484 (2002). [PubMed]
- R. Gordon and P. Marthandam, “Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film,” Opt. Express 15(20), 12995–13002 (2007). [CrossRef] [PubMed]
- C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
- N. F. van Hulst, “Plasmonics: Sorting colours,” Nat. Photonics 2(3), 139–140 (2008). [CrossRef]
- W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
- K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]
- A. Taflove, and S. C. Hagness, Computational electrodynamics: The Finite-Difference Time-Domain method, 2nd Ed” (Artech House Publishers, Boston, 2000).
- E. D. Palik, Handbook of Optical Constants of Solids, Academic Press, New York, (1985).
- K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004). [CrossRef]
- Z. Yu, H. Gao, W. Wu, H. Ge, and S. Y. Chou, “Fabrication of large area subwavelength antireflection structures on Si using trilayer resist nanoimprint lithography and liftoff,” J. Vac. Sci. Technol. B 21(6), 2874–2877 (2003). [CrossRef]
- V. Malyarchuk, F. Hua, N. Mack, V. Velasquez, J. White, R. Nuzzo, and J. Rogers, “High performance plasmonic crystal sensor formed by soft nanoimprint lithography,” Opt. Express 13(15), 5669–5675 (2005). [CrossRef] [PubMed]
- A. A. Tseng, “Recent developments in nanofabrication using focused ion beams,” Small 1(10), 924–939 (2005). [CrossRef]
- J. Chen, J. Shi, D. Decanini, E. Cambril, Y. Chen, and A. Haghiri-Gosnet, “Gold nanohole arrays for biochemical sensing fabricated by soft UV nanoimprint lithography,” Microelectron. Eng. 86(4-6), 632–635 (2009). [CrossRef]
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