We report on the fabrication and transmission properties of free-standing single-layer and double-layer THz bandpass filters. These filters are fabricated on aluminum foils using femtosecond laser micro-machining. The aluminum foils are periodically patterned with cross apertures with a total area of 1.75×1.75 cm2, also known as frequency-selective surfaces. Their terahertz transmission properties were simulated using the FDTD method and measured using a time-domain terahertz spectroscopy system. The simulation results agree with the measurements results very well. The performance of single-layer bandpass filters is as good as the commercial equivalents on the market. The double-layer filters show extraordinary transmission peaks with changing spacing between the two layers. We show the contour map of the electric field distribution across the apertures, and ascribe the new transmission peaks to the interference and coupling of surface plasmon polaritons between the two layers.
© 2017 Optical Society of America
Terahertz (THz) waves generally refer to the electromagnetic radiations in the 0.1-10 THz frequency range. THz waves have potential applications in bio-sensing, satellite communication, military radar, object imaging, environmental monitoring, and medical diagnosis [1–4]. To truly realize the applications of THz technology and effectively control THz waves, studies on THz functional devices such as: waveguides, polarizers, modulators, antennas, switches, and bandpass filters, are particularly important [5,6].
Frequency-selective surface (FSS) is composed of periodically arranged metal patches or apertures on a metal foil. FSS exhibits total reflection or full transmission characteristics at its resonant frequency, demonstrating excellent filtering performance. A filter based on the FSS has a controllable center frequency and a high transmittance, and can be precisely machined by laser direct writing technology, photolithography and other processing methods [7–9]. To improve filter performance, people also utilized multi-layer filters . In 2012, Rao L et al. used the numerical control machining to fabricate a terahertz bandpass filter based on circular holes and studied its transmission characteristics . In 2011, Ebrahimi A et al. used photolithography to fabricate bandpass filters with three layers of dielectric layers and two-layer frequency selective surface layers by alternately stacking dielectric and metal structures . The filter has a good angular stability, with the incident light angle in the range of 0 ° −45 °, and its terahertz transmittance is almost unaffected. All kind of THz bandpass filters based metamaterials also have been proposed and fabricated [13–15].
At present, most of the THz devices are fabricated using photolithography, which requires multiple steps such as spin-coating, pre-baking, the preparation of masks, and exposure, etc., resulting in a long preparation cycle and a high cost. In addition, most of these devices have a substrate which significantly lower the transmittance and cause internal interference [16,17]. Therefore, it is attractive to seek for a simple, low-cost, and efficient way to fabricate free-standing THz bandpass filters. With the development of ultrafast lasers, femtosecond laser micromachining technology provides an alternative choice for the preparation of THz devices. It has the characteristics of a small pulse width, a high peak power, and a small heat influence zone, well suitable for the high-precision machining requirements for THz devices.
In this paper, we employed femtosecond laser micro-machining to fabricate free-standing THz bandpass filters which are basically FSSs with cross apertures on an aluminum foil. We characterized these filters using a THz time-domain spectroscopy system, obtaining high transmittance at their central frequencies. Additionally, by stacking two layers of the single-layer filter to form a double-layer bandpass filter, we found Fabry-Perot resonant features induced by tuning the spacing between the two layers. We utilized the finite-difference time-domain (FDTD) method to carry out theoretical simulation on the single-layer and double-layer filters. Our experimental results and simulation results agree with each other very well. Unlike the metal-substrate structure  and the metal-substrate-metal sandwich structure  used in most FSS and metamaterial based THz filters, our THz filters employ a substrateless design to avoid blue shift due to substrate , as well as unwanted internal interference and energy loss associated with the substrate [16,17].
2. Filter design and fabrication
The unit structure of the single-layer THz FSS filter on an aluminum foil is shown in Fig. 1. The geometrical parameters of a cross unit include period P, cross arm width W, cross arm length L, and thickness T. The central wavelength of this cross-structured filter can be roughly determined by the following empirical formula :
One can see that the central frequency decreases with increasing the arm length L and period P, and increases with increasing the arm width W. In addition, increasing the material thickness T slightly reduces the center frequency . In the FDTD simulation, we use periodic boundary conditions for X and Y directions, and perfect matching layers along the Z direction. The material is Al with a plasma frequency of 2.24 × 1016 rad/s, and a damping coefficient of 1.12 × 1014 rad/s . The polarization of the terahertz waves is along the X direction. The transmitted terahertz signal is detected on the other side of the aluminum foil and a fast Fourier transform (FFT) is used to obtain the spectrum.
The schematic diagram of the femtosecond laser micro-machining system is shown in Fig. 2. The femtosecond laser has a wavelength of 800 nm, a pulse width of 45 fs, and a repetition rate of 1 KHz. The adjustment of the laser pulse energy can be achieved by using a half-wave plate and a Glan prism. A small aperture is employed to limit the diameter of the laser beam, and the on/off of the beam is controlled by an electronic shutter. The Al foil is placed on a computer-controlled, two-dimensional precision translation platform. The femtosecond laser is focused on the surface of the foil through an objective lens. The microstructure of any pattern can be prepared by moving the two-dimensional platform. The entire process can be monitored in real-time through a CCD imaging system, and displayed on the computer screen. We use pulse energy of 50 μJ, a focusing spot size of 10 μm, and a moving speed 1 mm/second for optimal machining quality. The Al foil with a thickness of 10 μm. is placed on a hollow square plate with tension to ensure that the foil is flat. Before the actual processing, we performed a trial cut on the corner area of the aluminum foil. The laser cutting was along the cross edge in order to dig out the cross aperture. The CCD camera imaging was used to measure the obtained cross width and length. By adjusting the stage moving distance, we could obtain the desired linewidth and length which match the simulation parameters. We use compressed nitrogen to blow away the residue and cool the material. An optical microscope is used to examine the processing quality and aperture sizes. Three types of single-layer THz bandpass filters were fabricated. The structural parameters of sample A are L = 280 μm, W = 65 μm, P = 350 μm; the structural parameters of sample B are L = 395 μm, W = 60 μm, P = 550 μm; the structural parameter of sample C are L = 440 μm, W = 89 μm, P = 700 μm. The image of sample C is shown in Fig. 3(a) and an enlarged microscopic image on a local area is shown in Fig. 3(b). It can be seen that the aperture edge is smooth and straight, and unit similarity is high, indicating a good processing quality.
3. Results of single-layer THz band-pass filters
We measured these single-layer samples using a time-domain THz spectroscopy system. We cut an empty hole on the aluminum foil, which has the same size as the sample patterned area, as our reference. We measured the THz waveforms of the three samples and the reference, and then performed FFT to obtain their THz spectra. FDTD simulations were performed using the geometrical parameters measured by an optical microscope. The results of the terahertz experiments and FDTD simulations are shown in Fig. 4. Figures 4(a)-4(c) show the electric field amplitude of the sample signal (red dot line, | ESample (f) |) and the reference signal (black solid line, | ERef (f) |). The power transmittance TP (f) is the square of the electric field amplitude ration | ESample (f) |/| ERef (f) |. It can be seen from the left figure that we can tune the central frequencies of the samples by changing their unit parameters. Figures 4(d)-4(f) show the power transmittance curves; the black solid lines are the FDTD simulation results, the red dot lines are the experimental results. One can see that the theoretical simulation results are in good agreement with the experimental results. However, the transmittances of the experiments are slightly smaller than those of the theoretical results, and the experimental results in high frequencies do not show oscillation phenomena as the theory has expected. Besides experimental errors, these disagreements may be due to scattering loss on the rough surface. Overall, femtosecond laser micro-machining is well suitable for fabricating THz bandpass filters. The performances of these filters, including center frequency fc, FWHM bandwidth, and transmittance T, are listed in Table 1, with “*” denoting for simulation results. It can be seen from Table 1 that the center-frequency transmittance of the filters is between 0.75 and 0.9, which are as good as the commercially available equivalents on the market.
4. Results of double-layer THz band-pass filters
We stacked two single-layer filters to form a double-layer filter, in order to improve the performance of the filters and study the frequency response of double-layer THz filters. The schematic diagram of a double-layer metal cross unit is shown in Fig. 5. To precisely assemble the two FSS layers, we first put one layer clinging to the other layer (spacing = 0); visible light projection is used to align the cross aperture arrays; then we move one filter which is mounted on a one-dimensional translation stage, with respect to the other filter which is fixed, to control the spacing between the two layers. Figures 6(a)-6(c) show the transmittance results of the double-layer filters (red dot line) and the FDTD simulation results (black solid lines) at spacings of 90 μm, 220 μm and 280 μm, respectively. The FDTD simulation results are in good agreement with the experimental results. Figures 6(d)-6(f) show the experimental transmittance results of the single-layer filters (black solid lines) and the double-layer filters (red dot line) for comparison.
It can be seen from Fig. 6(a) that there is only one main transmission peak f1 at 550 GHz when the spacing of the double-layer filter is 90 μm, and the shape of the peak has an approximately trapezoidal shape. Compared with the single-layer filter, the double-layer filter has steep cut-off characteristics, and the bandwidth is significantly reduced. As the spacing increases, it can be seen from Figs. 6(b) and 6(c) that two transmission peaks appear at f2 (491 GHz) and f3 (542 GHz) when the two-layer filter is spaced at 220 μm, and three transmittance peaks appear at f4 (442 GHz), f5 (546 GHz) and f6 (660 GHz) when the two-layer filter is spaced at 280 μm. On the whole, the simulation results are in good agreement with the experimental results, but there are still some deviations. In addition to the error of the experiment itself, the main reasons for the deviations are as follows: (1) the two filters are not exactly identical; (2) it is difficult to ensure that the two filters are completely parallel and the unit slits are perfectly aligned during the experiment.
In order to explore the cause of these double and triple peaks, we have simulated the THz transmittance at different spacings using the FDTD method. Figure 7 shows the contour map of the transmittance with changing spacing from 50 to 1100 μm and a THz range from 0.1 to 1.5 THz. It can be seen from the figure that the high transmission area (red) is centered at about 550 GHz, as highlighted by the vertical black dash dot line. This frequency does not change with changing spacing, corresponding to the f1 (550 GHz) peak in Fig. 6(a), the f3 (542 GHz) peak in Fig. 6(b) and the f5 (546 GHz) peak on Fig. 6(c). We see tilted wing-like patterns on both sides of the center frequency which appear cyclically with changing spacing. We draw three horizontal lines (black dash dot lines) on the contour map at spacings equal to 90, 220, and 280 μm, respectively. One can see that the horizontal line for a spacing of 90 mm only crosses the high transmission area, however the line for a spacing of 220 μm crosses a left-side wing and the high transmission area, the line for a spacing of 280 μm crosses two wings on both sides and the high transmission area. It is clear that the double peak and triple peak are related to the wings originating from the spacing change. Therefore, we can preliminarily conclude that the peaks at f1, f3and f5 which show up for all the cases including the single-layer filter, are due to the surface plasma polaritions (SPPs) coupling on the metal surface, whose frequencies depend on the structural parameters of the cross apertures . However, the peaks at f2, f4and f6 which are highly related to the spacing change, may originate from the Fabry-Perot resonance of the SPPs between the two filter layers [24–26].
In order to further explore the origin of the wing patterns showing on the contour map in Fig. 7, we plotted the simulated electric field distribution for a spacing of 220 μm along the cross arm through the center of one cross unit (XZ plane in Fig. 5), at frequencies equal to f2 (491 GHz) and f3 (542 GHZ), as shown in Figs. 8(a) and 8(b), respectively. From Fig. 8(a), one can see that the electric fields of SPPs are concentrated at the cross apertures of the two layers and there is a coupling between the electric fields of the SPPs on the two layers. However, as we can see from the electric field distribution at f3 (542 GHz) in Fig. 8(b), the coupling is not observed and we only see the concentrated electric fields in the two apertures. For comparison, Figs. 9(a)-9(c) shows the electric field distribution (XZ plane in Fig. 5) at f4 (442 GHz), f5 (546 GHz) and f6 (660 GHz). One can see that the electric filed distributions at f4 and f5 in Figs. 9(a) and 9(b) are quite similar to those at f2 and f3 in Figs. 8(a) and 8(b). However, from the electric field distribution at f6 (660 GHz) in Fig. 9(c), we find that there is a strong coupling between the electric fields of the SPPs inside the metal layers. The electric field distribution at f1 (550 GHz) which is not shown is similar to those at f3 (542 GHZ) and f5 (546 GHz).
It is known that a SPP is an electromagnetic surface wave travelling along the interface between a smooth metal surface and the dielectric air. We can call it external SPP. For a metal layer with apertures, external SPPs go through the apertures by tunneling and propagate along the inner surface [10,27]. When two metal layers with apertures are placed closer, the SPPs that propagate along each of the two inner surfaces couple to each other, thus creating a mode called internal SPPs whose dispersion relation differs from that of the traditional external SPPs on a single interface . The electric fields of external SPPs are located on the outer metal-air interfaces, being particularly concentrated in the aperture areas as shown in Fig. 8(b) and Fig. 9(b). The peak at about 550 GHz shows up for any spacing including the single-layer filter, are simply due to the surface plasma polaritions (SPPs) coupling on the metal surface, whose frequency depends on the structural parameters of the cross apertures . The peaks at f2 (491 GHz) and f4 (442 GHz) can be attributed to the coupling between the electric fields of external SPPs, which resonates at a slightly lower frequency, corresponding to a larger spacing, and the peak at f6 (660 GHz) can be attributed to the coupling between the electric fields of internal SPPs, which resonates at a slightly higher frequency, corresponding to a smaller spacing inside the metal layers. These extraordinary peaks appear cyclically with changing spacing and must be associated with the Fabry-Perot resonance of the external and internal SPPs between the two filter layers [24–27].
Reference  also presented a double-layer THz bandpass filter design with a similar assembly concept. The transmittance of our single-layer filter is up to 90%, and the transmittance of the double-layer bandpass filter is up to 80% [see Fig. 6(d)] with a steep cut-off and a narrower bandwidth than that of a single-layer filter, while the transmittance in the literature is about 60% for the single-layer filters and 30% for the double-layer filters. In addition, we have observed one additional extraordinary transmission peak at higher frequencies which was not reported in the past. This difference might be due to the unit shape difference (hole vs. cross). We have ascribed the peak to the coupling between the electric fields of internal SPPs. For a metal layer with apertures, external SPPs go through the apertures by tunneling and propagate along the inner surface to form internal SPPs which propagate along inner metal surfaces. Hole apertures have a curved edge, while the cross apertures have a straight edge. Therefore, internal SPPs through hole apertures propagate divergently due to the curved edge, while the internal SPPs through cross apertures propagate along the same direction, which is conducive to the internal coupling of the internal SPPs, resulting in the observed additional extraordinary peak. Further theoretical analysis would be needed for understanding the details of this phenomenon.
We have fabricated single-layer and double-layer THz bandpass filters on aluminum foils, using the femtosecond laser micromachining technique. We have characterized the frequency response of these filters using a time-domain terahertz system. The experimental results are in good agreement with the FDTD simulation results, indicating that femtosecond laser micro-machining is a promising method for making terahertz devices. Especially, the substrateless design of the filters makes the spacing tuning easier, and one can avoid the absorption and resonance caused by the substrate. The performance of the single-layer filters is comparable to that of the commercially available equivalents on the market. For double-layer filters, with changing spacing between the two layers, extraordinary transmission peaks appear. These peaks are mainly due to the resonance and coupling of the SPPs between the two metal layers. Complete understanding the coupling of the SPPs in complex double-layer metallic cross aperture arrays is of fundamental interest and practical importance in designing THz devices.
Fujian Natural Science Foundation (grant # 2015J01246); State Key Laboratory of Photo-catalysis on Energy and Environment (grant # SKLPEE-KF201719).
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