We present a tunable notch filter having a wide terahertz (THz) frequency range and a low-pass filter (LPF) having a 0.78 THz cutoff frequency. Single slit and multiple slits are positioned at the center of air gaps in tapered parallel-plate waveguides (TPPWG) to obtain the notch filter and LPF, respectively. The notch filter has a dispersion-free and low-loss transverse magnetic (TM) mode. The Q factor was proved to be 138, and the resonant frequency is easily tunable by adjusting the air gaps between TPPWG. On the other hand, the cut off frequency of the LPF was determined using a Bragg stop band, which depends on slit period. The LPF has a transition width of 68 GHz at the cutoff frequency and a dynamic range of 35 dB at stop bands. In addition, the characteristics of such filters were analyzed using finite-difference time-domain (FDTD) simulations.
©2011 Optical Society of America
Since the realization of low-loss and transverse electromagnetic (TEM) mode propagation in PPWGs within the THz region , various structures, such as resonant cavities [2,3], photonic crystals [4–6], grooves [7,8], and slits [9,10] on the waveguide plate surfaces have been used for THz research. In addition, development of TPPWG having high coupling-efficiency has allowed research into further application [11,12]. Due to the confined THz beam in the sub-wavelength region, the PPWG has not only played the role of coupling THz beams with a waveguide but has also been utilized to study potentially useful phenomena like THz filters. These THz filters will be useful in future research areas such as THz communication, sensors, and devices.
In the recent past, a high Q factor based on defect-mode resonance and Bragg resonance was employed by a periodic metal structure on a metal plate using standard lithographic and metallization techniques [7,8]. Using TE1 mode from the PPWG, a highly sensitive fluid refractive-index sensor , tunable universal THz filters [14,15] and a mechanically tunable THz notch filter [3,16] have been achieved. However, such studies have not been able to simultaneously satisfy conditions such as TEM mode, high Q factors, high signal-to-noise ratios, and tunable notch filters. Recently, Bragg and non-Bragg stop bands have been studied using metal slit arrays positioned at the center of the air gaps in TPPWG . An easily installable notch filter satisfying the above conditions was implemented in this study using the characteristics of the non-Bragg stop band. An LPF, which cuts off high frequency regions using metal slit arrays having multiple Bragg stop bands, was also implemented. Together with a high pass filter using TE mode with a two-cylinder waveguide , the LPF can be applicable in many research areas. Such THz filter studies (especially, the study of notch filters) are expected to be applied to gas detection, biochips, optofluidic sensing, and microfluidic bio-sensing.
2. Experimental setup
The experimental setup is similar to the one that was used to investigate THz propagation by using a stainless steel slit in TPPWG that is made by aluminum . Instead of the multiple slits used previously to study the band gap properties, a single stainless steel slit was employed as a notch filter. As shown in Fig. 1(a) , the slit has 30-μm thickness, 100-μm width, and 9-mm length where the propagated THz beam width is 7 mm. A vertically polarized (y direction) THz beam, which is perpendicular to the tapered surface (x × z surface) of the waveguide, generates a TM mode, becoming gradually confined through the 9-mm long flat area in the waveguide. As the total length of the stainless steel is 96 mm, the stainless steel protrudes toward the inlet and outlet of the tapered area by 43.5 mm. Identical metal spacers are used to make same upper and lower air gaps. Such a structure confines the THz beam to the two equal-width air gaps on opposite sides of the steel plate, as the incident THz beam is split into two parts by the protruded stainless steel before arriving at the air gap in the waveguide. Therefore, the incident THz beams are propagated simultaneously across the upper side and the lower side of the slit along each air gap. Figure 1(b) shows a photo image of the slit sample, which was made by micro-photochemical etching.
3. Measurements and analysis: notch filter
Figure 2 shows each THz pulse and spectrum resulting from the 92-μm and 105-μm air gaps in order to study the tunable properties of the THz notch filter. The image inserted in the THz pulse in Figs. 2(a) and 2(d) displays the ringing related to the resonance of the notch filter existing after the main pulse. Now that the resonance of the notch filter in the spectrum region is very sharp, the THz ringing in the time domain has been measured over a sufficiently large period of time at about 66 ps. The amplitude of the ringing at 66 ps is reduced about 1/210 compared to the amplitude of the main THz pulse. The spectra of the THz signals after zero padding are shown in Figs. 2(b) and 2(e). The 66 ps data was extended to 1320 ps by adding zeros at the end of the data. As the air gap had changed from 92 μm to 105 μm, the resonance frequency of the notch filter had also moved to a low frequency region by 0.168 THz (from 1.519 THz to 1.351 THz). The frequency tuning sensitivity (FTS) is given as , where is the resonance frequency shift and is the air gap variation. Therefore, the FTS is 12.9 GHz/μm, which shows a tunable notch filter in the THz region. The FTS value is two orders higher compared to that determined from previous methods such as the Fabry-Perot resonance  and Bragg resonance  methods. Figures 2(c) and 2(f) show the absorbance of the resonance frequency; the arrows denote the FWHM of each absorbance, 11 GHz and 12 GHz, respectively. The calculated Q factors (resonance frequency divided by FWHM) are 138 and 113, respectively. The previous studies have tunable resonance frequency but small Q factor [15,16], high Q factor but fixed resonance frequency , and tunable resonance frequency but a low signal-to-noise ratio . However, the advantage of the notch filter used in this study is its tunable resonance frequency with high Q factor and high signal-to-noise ratio.
Unlike the Bragg resonance of the defect mode, the measured notch filter resonance can be explained by the canceling out of the THz beams due to the out-of-phase component between the straight THz beam and the THz beam passing through the slit. Figure 3 shows FDTD simulation results considered under the conditions of resonance frequency of 1.519 THz and 92-μm air gap. Figure 3(a) shows the electric field intensity (|E|2) when a THz beam propagates along the air gaps upper and lower the stainless steel slit sample. The electric field is intensely localized in the areas upper and lower the slit. The air gap regions after passing the slit show almost no distribution of the field. Therefore, the 1.519 THz source cannot be measured in the output spectrum that makes the notch filter. Figure 3(b) illustrates the z-direction of the magnetic field (Hz), showing a symmetric distribution in both the upward and downward directions. Such structural symmetry enables a beam in one gap to leak into another gap and propagate with the same pattern. For that reason, as shown in Fig. 3(c), the simulation was performed by incident Ey field of the THz beam lower the air gaps only. Though it is a single slit, the THz beam of the resonance frequency leaks through the slit and distributes across the area on the other side of the air gap. The phase difference caused by time delay is a π radian corresponding to wavelength/2. Therefore, the electric field emerging between the air gaps upper and lower is out of phase . When the THz beams incident upper and lower the air gaps at the same time as in the experiment, the THz beams are canceled out after the slit. This phenomenon generates a narrow dip in the spectrum region and turns it into a notch filter.
As shown in the images inserted in Fig. 4(a) , the resonance frequency shift of a notch filter according to 3 dimensions of a waveguide setup—100 μm air gap (g), 100 μm slit width (w), and 30 μm slit thickness (T)—were changed using an FDTD simulation. When only one variable among air gap, slit width, and slit thickness changed from 30 μm to 150 μm at a time, the resonance frequency shifts () are 2.4 THz, 0.09 THz and 0.59 THz, respectively. The calculated FTSs are 20 GHz/μm, 0.75 GHz/μm, and 4.91 GHz/μm, respectively. Since the phase shift of the THz beam mostly depends on the air gap, the variations of slit width and thickness are not very sensitive. However, the air gap variation is most sensitive for FTS. Moreover, the smaller the air gap, the bigger the FTS becomes. When the air gap is slightly asymmetrical, the amplitude of the notch filter decreases because the intensity of out-of-phase components is not same. Moreover the position of notch filter for asymmetry depends on larger air gap than the smaller one. According to the precise adjustment of the air gap, the resonance frequency of the notch filter can be controlled.
Figure 4(b) shows the resonance frequency shift from 1.41 to 0.88 THz when the refractive index changes from 1 to 1.6. In this case, a gases having high refractive index are filled in the waveguide channel instead of air. According to the data shown in the figure, the average FTS for the refractive index, where is the refractive index variation, becomes 0.883 THz/RIU (RIU is the abbreviation for reflective index unit), which is an order of magnitude larger value than that in the recently reported results . The inserted figure in Fig. 4(b) illustrates the resonance frequency with the change of the refractive index of the air gap from 1.0 to 1.3. In particular, the FTS is very sensitive (1.36 THz/RIU) when the refractive index is 1 in a vacuum. Therefore, it can be possible to distinguish air and other gases (gas detection) that occur in very small amounts in the air gap.
4. Measurements and analysis: low-pass filter
A THz beam propagating along slits with a period P inside a TPPWG has a Bragg stop band with strong resonance at a Bragg frequency fBragg = mc/(2P), where m is an integer and c is the speed of light. The bandwidth of the Bragg stop band broadens as the period gets narrower at the Bragg stop band positions in the high frequency range. Using such characteristics, if slits with different periods are arrayed in a line on a metal sheet, an LPF can be implemented to completely eliminate the high frequency component after cutoff frequency. To design such an LPF, slits with equal width of 60 μm and 7 different periods of slit pattern were designed as shown in Table 1 . Since each region has 10 identical slits, the total number of the slits is 70. Figure 5(a) shows images of some of the slits in region I and region VII; slits were made of stainless steel with a thickness of 30 μm.
Figure 5(b) shows the FDTD simulation results for Bragg stop bands when the air gap is 38 μm. As shown in the figure, the first and second Bragg resonance frequencies corresponding to the slits of region I are located at 0.85 and 1.7 THz, respectively. The bandwidths of each Bragg stop band are 0.19 THz and 0.24 THz, where the bandwidths are measured at a width at 3 dB. The first and second Bragg stop bands of each of the 7 slit patterns are overlapped. Moreover, the first Bragg stop band of region VII (from 1.23 THz to 1.62 THz) and the second Bragg stop band of region I (from 1.58 THz to 1.82 THz) overlap. Only a THz field whose frequency range is below the first Bragg stop band of the slits of region I can propagate to the exit of the waveguide. Therefore, the characteristics of LPF depend on the first Bragg stop band of region I. The LPF can be predicted to have a 0.76 THz cutoff frequency, 55 dB power transmission in the cutoff region, and 84 GHz transition width (a drop from 90% to 10%) at the cutoff region.
In order to confirm that the slits block the propagation of this particular THz component, FDTD simulation was performed using a THz continuous wave (CW) source. As shown in the red vertical dashed line in Fig. 5(b), a 2.3 THz CW source propagates through regions I, II, and III. However, the Bragg stop band of the slits of region IV includes 2.3 THz, which prevents the THz beam propagation along the air gap. Figure 5(c) displays a simulation with a 38-μm air gap and a 2.3 THz CW source. Region IV prevents the THz beam propagation to the higher regions.
Figure 6(a) shows the measured reference THz pulse (black) without slits in the stainless steel sheet and output of a THz pulse (red) with slits in the stainless steel sheet where the thickness of the sheet and air gap are 30 μm and 38 μm, respectively. The oscillation of the output THz pulse is much broader than that of the reference THz pulse, whereby a large number of low-frequency components can be assumed. Moreover, the output THz pulse has a time delay compared to the reference THz pulse, caused by the group velocity delay at the time of passing the slits. The spectra of the measured THz pulses are shown in Fig. 6(b). The amplitude of the output spectrum (red) is cut off at 0.78 THz, which is consistent with the simulation results in Fig. 5(b). As shown in the inserted figure, the magnitude response changes from pass band to stop band. The transition width is about 68 GHz. On the other hand, the amplitude of the output spectrum is larger than that of the reference spectrum. The summation of total slit width (60 μm x 70 ea = 4200 μm) allows a small propagation loss because one large air gap (38 μm + 30 μm + 38 μm = 106 μm) between two waveguide plates has smaller attenuation than the two small (38 μm) air gaps. Therefore, a power transmission, as shown in Fig. 6(c), was obtained by using numerical modification of the reference amplitude, expressed as a dotted line in Fig. 6(b). The power transmission in the cutoff region of the LPF is measured at about 35 dB, as shown by the red line. The experimental result is in good agreement with the FDTD simulation, which is represented with a black line in Fig. 6(c).
The non-Bragg and Bragg stop bands obtained from the slits embedded between the two surfaces of the TPPWG can be used as notch filters and LPFs. A tunable notch-filter with a good FTS and high Q factor with TM mode can be implemented by adjusting air gaps. Using such characteristics of notch filters, gas detection may be possible for a very small amount of gas of which the refractive index is different from that of air. Moreover, we performed the first LPF based on multiple Bragg stop bands using different slit width. The transition width of the cutoff is only 68 GHz and the cutoff region of power transmission is 35 dB. As the bandwidth of a Bragg stop band becomes broader as the air gap gets narrower , the cutoff frequency is tunable despite the fact that the tunable range is minute. Future work will investigate utilizing this structure as a gas detection sensor with a notch filter.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0001053, No. 2010-0009070), the Grant of the Korean Health Technology R&D Project; Ministry for Health, Welfare & Family Affairs of Korea (A101954), and the Photonics 2020 Research Project through a grant provided by the GIST in 2011.
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