Engineering the properties of terahertz filters using multilayer aperture arrays

doi:10.1364/OE.19.018678

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Engineering the properties of terahertz filters using multilayer aperture arrays

Tho Duc Nguyen, Shuchang Liu, Z. Valy Vardeny, and Ajay Nahata »View Author Affiliations

Optics Express, Vol. 19, Issue 19, pp. 18678-18686 (2011)
http://dx.doi.org/10.1364/OE.19.018678

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– Abstract
1. Introduction
2. Experimental details
3. Experimental results, simulation and discussion
4. Conclusion
– References and links

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Abstract

We experimentally demonstrate the ability to create additional transmission resonances in a double-layer aperture array by varying the interlayer gap spacing. In the case of periodic aperture arrays, these additional resonances are sharply peaked, while for random aperture arrays the resonances are broad. Surprisingly, these additional resonances only occur when the interlayer gap spacing is greater than half the aperture spacing on a single array. Since there is no corresponding periodicity in the random arrays, these resonances occur regardless of how small the gap spacing is made. This phenomenon can be accurately modeled only if the correct frequency-dependent complex dielectric function of a metal film perforated with subwavelength apertures is used. Using THz time-domain spectroscopy, we are able to directly obtain the complex dielectric response function from the THz experimental transmission measurements. We conclude by demonstrating several passive free-space THz filters using multilayer aperture arrays. Importantly, we show that the magnitude of the lowest order resonance can be approximately maintained, while the background transmission can be significantly suppressed leading to a significant improvement in the optical filter fidelity.

1. Introduction

Technology development within the terahertz (THz) spectral range (1 THz = 10¹² Hz) has lagged severely behind that of other regions of the electromagnetic spectrum [1

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002). [CrossRef] [PubMed]

]. While reasonable progress has been made in developing sources and detectors, other device technologies are still at a rather rudimentary stage [1

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002). [CrossRef] [PubMed]

]. A significant reason for this lies in the fact that dielectric materials typically used for passive and active device applications in microwave and optical applications tend to exhibit high loss at THz frequencies. Metals, on the other hand, are highly conductive at these frequencies [3

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–20 (1983). [CrossRef] [PubMed]

], allowing for low propagation losses. The field of plasmonics [4

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

], and the use of surface plasmon polaritons (SPPs), is therefore particularly attractive for THz device development. As an example, single layer periodic [5

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

] and aperiodic [6

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007). [CrossRef] [PubMed]

] arrays of subwavelength apertures fabricated in metal films have been shown to exhibit resonantly enhanced transmission approaching unity [7

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12(6), 1004–1010 (2004). [CrossRef] [PubMed]

J. W. Lee, M. A. Seo, J. Y. Sohn, Y. H. Ahn, D. S. Kim, S. C. Jeoung, Ch. Lienau, and Q.-H. Park, “Invisible plasmonic meta-materials through impedance matching to vacuum,” Opt. Express 13(26), 10681–10687 (2005). [CrossRef] [PubMed]

], even for relatively small fractional aperture areas. Here we show that when two or more aperture arrays are placed in close proximity to one another, new transmission resonances arise that are associated with the gap spacing between the arrays, offering an additional mechanism for tailoring their optical properties. Importantly, proper design of these additional resonances requires that the complex dielectric response of the single aperture array be determined. Furthermore, with appropriate layer spacing in multilayer structures, we obtained extremely high transmission at the primary resonance frequency, along with substantial suppression of the background transmission increasing the filtering fidelity.

The resonant optical properties of subwavelength aperture arrays (also known as ‘plasmonic lattices’) have been explained in terms of SPPs that mediate the metal-light interaction via coupling to corrugated metal surfaces [5

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

], where the electromagnetic field associated with the SPPs decays exponentially from the metal-dielectric interface. While the nearly exclusive focus of both theoretical and experimental work has been on the transmission response of single layer plasmonic lattices [9

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

], there have been a number of experimental and theoretical studies of double-layer aperture arrays [10

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004). [CrossRef] [PubMed]

–15

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009). [CrossRef]

]. It was found that when the gap spacing, d between the two plasmonic lattices was large, the resulting transmission properties could be obtained by considering each array independently. However, when d becomes sufficiently small, it is expected that the coupling between the SPP waves on the inner, adjacent surfaces of the two layers would yield new and interesting spectral transmission characteristics. Here we show that this coupling forms additional resonances for small values of d that may be used in designing THz filters.

2. Experimental details

Two-dimensional (2D) aperture arrays were fabricated in 75 μm thick, ~5x5 cm² area of free-standing stainless steel metal foils by laser cutting using a frequency tripled Nd:YAG laser. Two different aperture array pairs, based on periodic and random hole patterns respectively, were designed and fabricated to have the same fractional aperture area of ~19%. One aperture array pair consisted of 2D periodically spaced circular holes on a square lattice, while the other pair consisted of 2D randomly distributed circular holes. In Fig. 1 , we show a schematic diagram of the double-layer aperture array with the relevant dimensions.

Fig. 1 Schematic diagram of a double layer aperture array with aperture diameter, D = 750µm, periodicity, a = 1500 µm, metal film thickness, h = 75 µm and gap spacing, d, taking on values between 0 and 3000 µm.

We used THz time-domain spectroscopy (THz-TDS) to measure the optical transmission spectra, t(ω) of the perforated metal films, where the THz frequency ν = ω/2π [7

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12(6), 1004–1010 (2004). [CrossRef] [PubMed]

]. A pair of off-axis paraboloidal mirrors was used to collect and collimate the THz radiation from the emitter, which was then normally incident on the aperture array structures. Each array was attached to a solid metal plate with a 5 cm x 5 cm opening that was placed in the path of the collimated THz beam and placed on a translation stage to vary the distance between the arrays. The 1/e THz beam diameter was smaller than the aperture opening in the metal holders and the spatial extent of the aperture array structures, thereby minimizing edge effects due to the finite size of the array sample. Reference transmission spectra were taken with just the metal holders in the THz beam path using the same setup. The metallic foils were completely opaque prior to fabrication of the arrays. Therefore transmission through the perforated metallic films was uniquely due to the apertures. The detected transient photocurrent was then Fourier transformed and normalized to the reference transmission, yielding the electric field transmission spectrum, t(ω). THz TDS allows for the direct measurement of the THz electric field, yielding both amplitude and phase information. By transforming the time-domain data to the frequency domain, we are able to determine independently both the magnitude and phase of the amplitude transmission coefficient, t(ω), using the relation

t (ω) = | t (ω) | \exp [φ (ω)] = \frac{E_{t r a n s m i t t e d} (ω)}{E_{i n c i d e n t} (ω)}

(1)

In this expression, E_incident and E_transmitted are the incident and transmitted THz fields, respectively, |t(ω)| and φ(ω) are the magnitude and phase of the amplitude transmission coefficient, respectively, and ω /2π is the THz frequency.

3. Experimental results, simulation and discussion

Figure 2 summarizes our experimental studies on the periodically perforated metallic films. We begin by characterizing the properties of a single periodic aperture array in which the center-to-center aperture spacing, a = 1.5 mm. This plasmonic lattice forms a lowest order ( ± 1,0) anti-resonance (AR) frequency, AR₁ = 0.2 THz and second lowest ( ± 1, ± 1) AR frequency, AR₂ = 0.28 THz, as shown in the measured transmission spectrum in Fig. 2(a). We have shown previously that the AR feature (i.e. the sharp dip immediately to the right of the resonance peak) is directly related with the underlying structure factor [6

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007). [CrossRef] [PubMed]

]. We note that although the fractional aperture area is only ~19%, the absolute resonant transmission amplitude at the lowest resonance, R₁ is >80%. In Fig. 2(b), we show the obtained THz transmission spectra for a double-layer plasmonic lattice structure versus the interlayer spacing, d. The basic features of the transmission spectra can be summarized as follows. For d < d₁ = 0.75 mm (where d₁ = a/2), t(ω) for the double layer aperture array is similar to that of the corresponding single aperture array. Specifically, the resonance and anti-resonance frequencies are identical for the single and double arrays (Figs. 2(a) and 2(b)), although the double layer structure exhibits lower overall transmissivity. For values of d > d₁, however, we obtain additional transmission resonances in the double layer array that are not present in the case of a single layer. We label these new resonances, meta-Fabry-Perot (MFP) resonances, as explained below. The new resonance, labeled MFP₁ appears at frequencies ω₁/2π < ω(R₁)/2π, and moves progressively to lower frequencies with increasing d. However when d > d₂ = 1.5 mm (where d₂ = a), we obtain a second new resonance, labeled MFP₂ (Fig. 2(b)) whose frequency, ω₂/2π also decreases with d. The various new resonance frequencies are summarized in Fig. 2(c).

Fig. 2 THz electric field transmission spectra, t(ω), using a double layer periodic array (a) t(ω) of a single layer periodic aperture array using the parameters given in ^{Fig. 1} , where the resonances (R_i) and anti-resonances (AR_i) are denoted. (b) t(ω) for the double layer structure as a function of the gap spacing, d. The new transmission bands are labeled MFP₁ and MFP₂ (see text). The plots are vertically offset from the origin in units of ~0.4 for clarity. (c) Summary of the experimental resonant frequencies, ω/2π, for R₁, MFP₁ and MFP₂ bands in t(ω) as a function of d.

In order to determine the origin of the additional MFP resonances we performed numerical simulations based on the experimental parameters (Fig. 1) and the interlayer spacing, d. Since the MFP resonances emerge at array distances associated with integer values of a/2, namely d₁ = (a/2) and d₂ = 2(a/2), it is reasonable to consider Fabry-Perot reflections as the underlying mechanism. These reflections, however, need be modified according to the dielectric response of the underlying plasmonic lattice, which is actually a ‘metamaterial’. In the study of plasmonic lattices, a common approach for determining the transmission resonance frequencies is to use the dielectric properties of the (unperforated) metal film, although this typically yields only approximate resonance frequencies. In Fig. 3 we calculate the resulting transmission spectra taking all Fabry-Perot reflections between the two aperture array films into account, assuming that the dielectric properties of the aperture arrays can be approximated by that of an unstructured metal film at THz frequencies having a dielectric response ε ~-3x10⁴ + i10⁶ [3

]. The poor agreement with the experimental results demonstrates that a more sophisticated model for ε(ω) response of the plasmonic lattice needs be considered.

Fig. 3 Numerical calculations of t(ω) for a double layer periodic aperture array, assuming that ε(ω) is that of an unperforated metal at THz frequencies (ε ~-3x10⁴ + i10⁶). The spectra are offset from the origin in units of 1 for clarity.

Using the THz-TDS complex transmission spectra associated with a single aperture array, we can simultaneously extract the real and imaginary components of the effective ε(ω) using the amplitude transmittance, |t(ω)|, and the phase spectra, φ(ω) [16

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008). [CrossRef] [PubMed]

], assuming that the effective permeability is frequency independent and of the order of 1 [17

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

,18

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

]. As shown in Fig. 4(a) , with fit parameters given in Table 1 , the complex ε(ω) response of the plasmonic lattices can be modeled using the general form:

\tilde{ε} (ω) = ε_{r} (1 - \frac{{\tilde{ω}}_{p}^{2}}{ω^{2} + i γ ω}) + \sum_{j} i ε_{p j} \frac{ω_{L}_{j}^{2} - ω^{2}}{ω_{T}_{j}^{2} - ω^{2} - i γ_{j} ω},

(2)

where

{\tilde{ω}}_{P}

is the effective plasma frequency,

ε_{r}

and

ε_{p j}

are associated with the relative contributions of all of the components, γ is the plasma relaxation rate,

ω_{L}_{j}

and

ω_{T}_{j}

are the effective longitudinal optical (LO) and transverse optical (TO) frequencies associated with the ‘phonon-like’ resonant contributions in the effective medium, and γ_j is the relaxation rate (inversely proportional to the linewidth) of the jth resonance. The first term in Eq. (2) corresponds to a smooth ‘plasma-type’ response, and is the only term used in modeling the random arrays (discussed below), while the last (summation) term in Eq. (2) corresponds to the discrete resonances associated with the periodic aperture arrays. The calculated ε(ω) along with the modeled ε(ω) using Eq. (2) are shown in Fig. 4(a) of a periodic aperture array having a = 1.5 mm and D = 750 µm. In fitting the data for the periodic arrays, we used the same effective plasma frequency (

{\tilde{ω}}_{P}

) that we will use later in describing ε(ω) of the corresponding random aperture array. The TO frequencies (

ω_{T}_{j}

) in the resonant contribution correspond to AR₁ and AR₂ frequencies (Fig. 2(a)), which can also be derived from the standard surface plasmon equation [4

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

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

Fig. 4 Numerical calculations of t(ω) for a double layer periodic aperture array. (a) Real and imaginary components of the effective ε(ω) response for a single layer periodic aperture array extracted from the amplitude and phase of t(ω) (red traces). The fit (blue lines) is calculated using Eq. (2). (b) Numerical simulation of the transmission spectra for the double-layer structure using the dielectric properties obtained in (a). MFP1, MFP₂ and R₁ resonances are denoted (c) Summary of the experimental (red diamonds from Fig. 2(c)) and calculated (blue triangles) resonant frequencies, ω/2π for R₁, MFP₁ and MFP₂ bands in t(ω) spectra, as a function of d.

Table 1 The “best fit” parameters for the effective ε(ω) of periodic aperture arrays with lattice spacing, a = 1.5 mm and diameter, D = 750 µm. The parameters are defined in Eq. (2). In the fit, the TO resonant frequencies,

ω_{T}_{j}

, were set to the AR frequencies in the transmission spectra, while the LO resonant frequencies,

ω_{L}_{j}

, were set to the frequencies corresponding to the resonance peaks,

R_{j}

$ε_{r}$	${\tilde{ω}}_{P}$ (rad/ps)	γ (rad/ps)	$ε_{p 1}$	$ω_{L 1}$ (rad/ps)	$ω_{T 1}$ (rad/ps)	$γ_{1}$ (rad/ps)	$ε_{p 2}$	$ω_{L 2}$ (rad/ps)	$ω_{T 2}$ (rad/ps)	$γ_{2}$ (rad/ps)
10.6	0.73	0.35	12	1.19	1.26	0.42	1.5	1.68	1.78	0.07

We calculated the transmission spectra of the double layer array using the obtained dielectric response, taking multiple reflections into account and assuming a single cycle broadband THz pulse at normal incidence. While contributions from Fabry-Perot reflections typically need to take all four surfaces of the double layer structure into account, for d > d₁ we found that reflections between the inner array surfaces dominate. In Fig. 4(b), we show the resulting simulated spectra as a function of d; they are in good agreement with the experimental data. In Fig. 4(c), we plot the calculated frequencies associated with the R₁, MFP₁ and MFP₂ resonances as a function of d, and compare these to the experimental frequencies; once again, the excellent agreement between the simulation and experimental data validates our approach.

In order to further demonstrate that the emergence of the MFP transmission resonances can be explained by using the correct complex dielectric function of the perforated metal film rather than the unperforated metallic response, we measured the transmission properties of a commensurate pair of random aperture arrays. First, we show the transmission spectrum of a single random array (Fig. 5(a) ). As expected, the transmission spectrum does not show evidence of any resonance, which is consistent with the fact that the Fourier transform of this geometry does not contain any discrete Fourier components. When two such arrays are separated by d, however we observe broad resonances in the otherwise smoothly varying transmission spectrum, as shown in Fig. 5(b). Using the magnitude and phase of the transmission spectrum associated with a single random array, we again extract the real and imaginary components of the effective ε(ω), as shown in Fig. 5(c). ε(ω) is essentially identical to that of the periodic array, but includes only the lossy plasma contribution (the first term of Eq. (2)) [19

T. D. Nguyen, A. Nahata, and Z. V. Vardeny, “THz anomalous transmission in plasmonic lattices: incidence angle dependence,” Proc. SPIE 7394, 73940H , 73940H-7 (2009). [CrossRef]

]. The fit parameters are given in Table 2 . Using this extracted ε(ω) response we repeated the simulation mentioned above to obtain t(ω) as a function of d, as shown in Fig. 5(d), and summarized in Fig. 5(e). We again see excellent agreement between our experimental data and numerical computations. In contrast to what was observed with the periodic arrays, there does not appear to be a minimum d associated with the appearance of MFP resonances. This is consistent with the lack of periodicity in this double layer structure.

Fig. 5 Electric field transmission spectra as in Figs. 2 and 4, but for a commensurate double layer random hole array with apertures of diameter, D = 750µm, metal thickness, h = 75 µm and spacing, d that varies between 0 and 3000 µm. (a) Experimentally measured t(ω) of a single layer random aperture array. (b) Experimentally measured t(ω) for the double layer structure for three different values of d. MFP1 through MFP4 represent the different orders of MFP resonances. (c) Experimental (red line) and calculated (blue line) real and imaginary ε(ω) components of the individual random array extracted from t(ω) in (a). (d) Numerical simulation of t(ω) for the double-layer hole array structure using the same parameters as in (c). (e) Summary of the experimental (red diamonds) and calculated (blue triangles) resonant frequencies, ω/2π for the MFP1 through MFP4 bands in t(ω) as a function of d.

Table 2 The “best fit” parameters for the effective ε(ω) of random aperture arrays with D = 750 µm. The parameters are defined in Eq. (2).

$ε_{r}$	${\tilde{ω}}_{P}$ (rad/ps)	γ (rad/ps)
37	0.73	0.35

Based on the existence of MFP resonances between closely spaced aperture arrays, we are now able to extend this general idea for demonstrating highly efficient free-space THz filters, as summarized in Fig. 6 . In Fig. 6(a), we show the transmission properties of two 0.75 mm thick periodic arrays having d = 0 and d = 0.75 mm, respectively. For d = 0, the double-layer aperture array is equivalent to a single, 1.5 mm thick periodic aperture array. In fact the transmission spectrum is identical to what is observed for a single layer array (Fig. 2(a)), albeit with somewhat reduced amplitude. For d = 0.75 mm, no MFPs are expected. However, since d = 0.8 mm corresponds to a local maxima in t(ω) vs. d for the ( ± 1,0) resonance, we expect larger transmission compared with that for d = 0. In fact, the R₁ transmission amplitude is nearly identical to that of the single layer array, although t(ω) at other frequencies above and below the R₁ resonance is dramatically reduced. Similar behavior is expected for other array spacings that correspond to local maxima (i.e. the reflections yield constructive interference). The notion of maintaining high transmission response for the R₁ resonance while reducing the background transmission can be implemented also using multiple arrays. In this case, the spacing between the arrays is significantly larger (~1 cm), as shown in Fig. 6(b). We introduce a small 5° rotation in the center array to further minimize the transmission away from the R₁ resonance [19

T. D. Nguyen, A. Nahata, and Z. V. Vardeny, “THz anomalous transmission in plasmonic lattices: incidence angle dependence,” Proc. SPIE 7394, 73940H , 73940H-7 (2009). [CrossRef]

]. While the R₁ transmission for the triple array is slightly smaller than that of the single array, the resonance quality factor is higher, and the transmission away from the R₁ resonance is dramatically minimized compared with a single array.

Fig. 6 t(ω) spectra of multi-layer periodic aperture arrays. (a) Comparison between a double layer structure with spacing d = 0 (blue line) and d = 0.8 mm (red line). (b) Comparison between a single layer periodic array (black line) and a triple layer aperture array structure (red line) with d ~1 cm. (Inset) Schematic diagram of the triple-layer transmission measurement. The middle plate is rotated from the normal by 5°.

4. Conclusion

Our results demonstrate that carefully designed multilayer aperture arrays can allow for two important device capabilities: (1) the introduction of additional resonances associated with the layer spacing, which may be used to generate more complex THz spectral filtering properties, and (2) the ability to create high quality narrow bandpass THz filters. These capabilities were illustrated primarily using double-layer aperture arrays, although multilayer structures may allow for additional refinement of the transmission properties. In addition, the use of aperiodic geometries [6

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007). [CrossRef] [PubMed]

] as well as conductive non-metallic materials [20

T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006). [CrossRef]

] may allow for greater control over the MFP resonance frequencies, as well as the potential for active THz optoelectronic devices applications. Finally, it should be noted that interesting “three dimensional” structures using stacks of aperture arrays layers in a variety of geometries may give rise to new and interesting optical interference phenomena.

Acknowledgements

This work was supported in part by the National Science Foundation under Grant # ECCS- 0801965 and the CEMRI program at the University of Utah. We gratefully acknowledge funding from the University of Utah Open Access Publishing Fund.

References and Links

1.	M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]
2.	B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002). [CrossRef] [PubMed]
3.	M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–20 (1983). [CrossRef] [PubMed]
4.	W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
5.	T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
6.	T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007). [CrossRef] [PubMed]
7.	H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12(6), 1004–1010 (2004). [CrossRef] [PubMed]
8.	J. W. Lee, M. A. Seo, J. Y. Sohn, Y. H. Ahn, D. S. Kim, S. C. Jeoung, Ch. Lienau, and Q.-H. Park, “Invisible plasmonic meta-materials through impedance matching to vacuum,” Opt. Express 13(26), 10681–10687 (2005). [CrossRef] [PubMed]
9.	F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]
10.	A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004). [CrossRef] [PubMed]
11.	H. B. Chan, Z. Marcet, K. Woo, D. B. Tanner, D. W. Carr, J. E. Bower, R. A. Cirelli, E. Ferry, F. Klemens, J. Miner, C. S. Pai, and J. A. Taylor, “Optical transmission through double-layer metallic subwavelength slit arrays,” Opt. Lett. 31(4), 516–518 (2006). [CrossRef] [PubMed]
12.	F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B 71(16), 165408 (2005). [CrossRef]
13.	Y. H. Ye and J. Y. Zhang, “Enhanced light transmission through cascaded metal films perforated with periodic hole arrays,” Opt. Lett. 30(12), 1521–1523 (2005). [CrossRef] [PubMed]
14.	H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008). [CrossRef]
15.	R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009). [CrossRef]
16.	A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008). [CrossRef] [PubMed]
17.	J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]
18.	F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]
19.	T. D. Nguyen, A. Nahata, and Z. V. Vardeny, “THz anomalous transmission in plasmonic lattices: incidence angle dependence,” Proc. SPIE 7394, 73940H , 73940H-7 (2009). [CrossRef]
20.	T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006). [CrossRef]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(240.6680) Optics at surfaces : Surface plasmons
(260.3090) Physical optics : Infrared, far

ToC Category:
Optical Devices

History
Original Manuscript: July 1, 2011
Revised Manuscript: July 29, 2011
Manuscript Accepted: July 30, 2011
Published: September 9, 2011

Citation
Tho Duc Nguyen, Shuchang Liu, Z. Valy Vardeny, and Ajay Nahata, "Engineering the properties of terahertz filters using multilayer aperture arrays," Opt. Express 19, 18678-18686 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18678

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