Engineering the properties of terahertz filters using multilayer aperture arrays

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.


Introduction
Technology development within the terahertz (THz) spectral range (1 THz = 10 12 Hz) has lagged severely behind that of other regions of the electromagnetic spectrum [1,2].While reasonable progress has been made in developing sources and detectors, other device technologies are still at a rather rudimentary stage [1,2].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], allowing for low propagation losses.The field of plasmonics [4], and the use of surface plasmon polaritons (SPPs), is therefore particularly attractive for THz device development.As an example, single layer periodic [5] and aperiodic [6] arrays of subwavelength apertures fabricated in metal films have been shown to exhibit resonantly enhanced transmission approaching unity [7,8], 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], 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], there have been a number of experimental and theoretical studies of double-layer aperture arrays [10][11][12][13][14][15].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.

Experimental details
Two-dimensional (2D) aperture arrays were fabricated in 75 m thick, ~5x5 cm 2 area of freestanding 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.We used THz time-domain spectroscopy (THz-TDS) to measure the optical transmission spectra, t() of the perforated metal films, where the THz frequency  = /2 [7].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().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(), using the relation In this expression, E incident and E transmitted are the incident and transmitted THz fields, respectively, |t()| and () are the magnitude and phase of the amplitude transmission coefficient, respectively, and  /2 is the THz frequency.

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, AR 1 = 0.2 THz and second lowest ( ± 1, ± 1) AR frequency, AR 2 = 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].We note that although the fractional aperture area is only ~19%, the absolute resonant transmission amplitude at the lowest resonance, R 1 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 < d 1 = 0.75 mm (where d 1 = a/2), t() 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 > d 1 , 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 MFP 1 appears at frequencies  1 /2 < (R 1 )/2, and moves progressively to lower frequencies with increasing d.However when d > d 2 = 1.5 mm (where d 2 = a), we obtain a second new resonance, labeled MFP 2 (Fig. 2(b)) whose frequency,  2 /2 also decreases with d.The various new resonance frequencies are summarized in Fig. 2(c).
Fig. 2. THz electric field transmission spectra, t(), using a double layer periodic array (a) t() of a single layer periodic aperture array using the parameters given in 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 d 1 = (a/2) and d 2 = 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  ~-3x10 4 + i10 6 [3].The poor agreement with the experimental results demonstrates that a more sophisticated model for () response of the plasmonic lattice needs be considered.Fig. 3. Numerical calculations of t() for a double layer periodic aperture array, assuming that () is that of an unperforated metal at THz frequencies ( ~-3x10 4 + i10 6 ).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 () using the amplitude transmittance, |t()|, and the phase spectra, () [16], assuming that the effective permeability is frequency independent and of the order of 1 [17,18].As shown in Fig. 4(a), with fit parameters given in Table 1, the complex () response of the plasmonic lattices can be modeled using the general form: where P   is the effective plasma frequency, r  and p j  are associated with the relative contributions of all of the components,  is the plasma relaxation rate, L j  and 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  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 () along with the modeled () 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 ( P   ) that we will use later in describing () of the corresponding random aperture array.The TO frequencies ( T j  ) in the resonant contribution correspond to AR 1 and AR 2 frequencies (Fig. 2(a)), which can also be derived from the standard surface plasmon equation [4,5].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 > d 1 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 R 1 , MFP 1 and MFP 2 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 (), as shown in Fig. 5(c).() is essentially identical to that of the periodic array, but includes only the lossy plasma contribution (the first term of Eq. ( 2)) [19].The fit parameters are given in Table 2. Using this extracted () response we repeated the simulation mentioned above to obtain t() 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.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() vs. d for the ( ± 1,0) resonance, we expect larger transmission compared with that for d = 0.In fact, the R 1 transmission amplitude is nearly identical to that of the single layer array, although t() at other frequencies above and below the R 1 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 R 1 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 R 1 resonance [19].While the R 1 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 R 1 resonance is dramatically minimized compared with a single array.

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] as well as conductive non-metallic materials [20] 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.
Fig.2.THz electric field transmission spectra, t(), using a double layer periodic array (a) t() of a single layer periodic aperture array using the parameters given in Fig.1, where the resonances (Ri) and anti-resonances (ARi) are denoted.(b) t() 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, /2, for R1, MFP1 and MFP2 bands in t() as a function of d.

Table 1 .
The "best fit" parameters for the effective () 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, T j  , were set to the AR frequencies in the transmission spectra, while the LO resonant frequencies, L j  , were set to the frequencies corresponding to the resonance peaks, j R .

Fig. 4 .
Fig.4.Numerical calculations of t() for a double layer periodic aperture array.(a) Real and imaginary components of the effective () response for a single layer periodic aperture array extracted from the amplitude and phase of t() (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, /2 for R1, MFP1 and MFP2 bands in t() spectra, as a function of d.

Fig. 5 .
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() of a single layer random aperture array.(b) Experimentally measured t() 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 () components of the individual random array extracted from t() in (a).(d) Numerical simulation of t() 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, /2 for the MFP1 through MFP4 bands in t() as a function of d.

Fig. 6 .
Fig. 6. t() 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°.