We report experimental and finite-difference time-domain simulation studies on terahertz (THz) characteristics of band gaps by using metal grooves which are located inside the flare parallel-plate waveguide. The vertically localized standing-wave cavity mode (SWCM) between the upper waveguide surface and groove bottom, and the horizontally localized SWCM between two groove side walls (groove cavity) are observed. The E field intensity of the horizontally localized SWCM in grooves is very strongly enchanced which is three order higher than that of the input THz. The 4 band gaps except the Bragg band gap are caused by the π radian delay (out of phase) between the reflected THz field by grooves and the propagated THz field through the air gap. The measurement and simulation results agree well.
© 2012 OSA
The investigation of electromagnetic surface waves started at the beginning of the 20th century. Radio-frequency was used in the first theoretical surface plasmon polariton (SPP) studies by Sommerfeld  and Zenneck . About 60 year later, Otto  experimentally demonstrated that light was a good source to generate SPP. The theoretical and experimental approaches to SPP are still used by many researchers in the microwave, mm-wave and THz communities. Uses of a photonic bandgap structure, stop band in the microwave region, and TEM waveguide have already been demonstrated [4, 5]. These techniques for the microwave region are still used in the THz frequency region. Recently Grischkowsky  and Mittleman  show THz SPP using a single metal wire. After that, THz SPP was generated on a metal plate  and between parallel-plates . Since SPPs propagate along the metal-dielectric (air) interface, they are very sensitive to the metal surface conditions, such as conductivity, roughness, and geometry. Because the energy distributions normal to the structured surfaces are very important parameters to propagate SPPs, many nano- and micro-structures have been investigated in optical [10–17] and THz [18–23] frequency ranges, respectively. Groove structure waveguides are an especially interesting subject because the SPP transmission loss is very small compared to that of an upward step structure such as a barrier. The characteristics of SPP propagation in the optical region have been investigated by numerical calculation for various groove widths and depths [13–15, 24]. However, there have been few studies in THz region. One of the applications using SPP in the THz region was photonic crystals within waveguides [18, 25, 26]. When the THz SPP propagates through the photonic crystals, THz spectra show a very high Q-factor or THz band gaps. Recently, parallel plate waveguides (PPWGs) have been used to propagate THz SPPs in a direction parallel to the metal-air-metal interface  or used as an SPP coupling tool on a metal plate surface [8, 9, 21]. The first THz studies of columns or holes [18, 28] and slits [22, 29] in PPWG show the characteristics of band gaps using micron-size photonic structures. The properties of band gap and defect mode using a groove structure were done by the Grischkowsky group [19, 20]; however, the depth of grooves was very small compared to the air gap and wavelengths. Therefore they cannot found the SWCMs because of such a small depth. This paper details the first study of SWCM, which has an extremely narrow frequency in the THz region. The characteristics of SPP propagation in the optical region have been investigated only by numerical calculation for various groove widths and depths [13–15, 24]. However, we investigated the characteristics of SPPs propagated in deep grooves using both experimental and FDTD simulation studies and have demonstrated a better way to achieve SWCM in THz region.
Meanwhile any incoming THz energy from the input side directed toward the groove surface undergoes reflection. The magnitude and direction of reflected field energy from the upper and lower groove surfaces are controlled by the conductance of the material and the geometry of the grooves, respectively. Because a metal is considered almost perfect conductor in the THz frequency range, the reflected THz field energy from the upper and lower groove surfaces are not changed. Since the lower surfaces of grooves are flat, the image structure of grooves exists under the lower surfaces of grooves. Therefore, the groove waveguide is equivalent to a slit waveguide whose thickness is twice the depth of the groove . The height of air gaps of a slit waveguide, which are located above and below the slit, is the same as that of the groove waveguide. Therefore, the slits in the PPWG can be simulated to understand the properties of THz propagation on the grooves.
2. Experimental setup
The THz waveguide system used for our experiments is shown in Fig. 1 . Flare PPWG is located between the two parabolic mirrors in order to focus and emit THz beam. The utilized flare parallel plate waveguide has a 130 mm radius of curvature, 116 mm length, and 40 mm width. The total longitudinal length is comprised of two 50 mm length flare parts and a 16 mm flat part. The groove used in the measurement has a 84-μm depth (d), 58-μm width (w), and 142-μm period (p) with 15 grooves (N). The copper sample plate with a groove pattern is made by a deep etch X-ray lithography method. A vertically (y-direction) polarized THz beam is focused into the air gap by a flare PPWG which is also made of copper. A solid flare PPWG comprises of two areas, namely, a smoothly curved metal flare area and a flat area in the middle of the waveguide. The PPWG enables simple and precise measurement . The 40 mm wide (z-direction) and 12 mm length (x-direction) copper groove sample plate is embedded into the flat area of the lower waveguide. To reduce the boundary effect between the groove sample plate and the PPWG, a 16-μm thick thin aluminum foil covers the boundary. The grooves exist on only half of the copper groove sample plate to measure the output THz signal . The other half of the plate has no grooves in order to measure the reference THz signal. Therefore, the waveguide and the copper groove sample plate are one unit which is moved in the z direction to measure the reference and output THz signals, and this can reduce system errors.
3. Results and discussion
Four different air gaps, with g = 75, 95, 120, and 134 μm were used to study the characteristics of the band gaps. Figure 2 (a) and (b) show the reference pulse and the transmitted sample pulse for 75 μm air gap, respectively. The measured 66 ps data was extended to 1320 ps by adding zeros at the end of the data. Therefore, the frequency resolution increased up to 0.75 GHz. Figures 2 (c) to (f) show the spectra of each measured THz pulse. The upper black curves and lower red curves indicate the reference pulse spectra without grooves and the output spectra with grooves into the PPWG, respectively. The TM1 modes are detected as shown in the rapid oscillations in the reference and output spectra, especially large air gaps due to the imperfect odd mode of the THz field in the air gap. A 16-μm thick aluminum foil layer is used to cover the boundary between the groove sample plate and waveguide, which creates the imperfect odd mode in the air gap. However, the TM1 mode oscillation is small enough compared to the output resonances. The position and amplitude of the output resonances are gradually changed as the air gap increases. The measured power transmission spectra are shown in Fig. 2(g) to (j) with red lines, which show the variations of band gaps with increasing air gap. Band gaps have been reported in the THz region using photonic crystal slabs with very broad bandwidth [18, 25]. However, the bandwidths of the band gaps in this study are narrow and air gap dependent. Moreover, one of the band gaps has a turn-on and turn-off property by changing the air gap. The minimum transmitted signal power of the measurement is about −30 dB at the band gaps. Meanwhile, FDTD simulations are shown in the figures with black lines. The waveguide blocks and groove structure are defined as a perfect electrical conductor because the attenuation loss of the metal can be disregard in the THz frequency range. The measured and simulated results show good agreements. The Roman numerals I, II, III, and IV and letters A, B, and C are used to distinguish two groups of resonances. The band gaps of the Roman numerals group, as simulations will show, come from multiple grooves and the band gaps of the letters group originate from the first single groove. The vertical dashed lines indicate the constant band gap frequency with increasing air gap.
Band gap A has a narrow width but its center frequency is constant with increasing air gap. However, band gap B appears only for the 75-μm air gap. Band gap C displays a very narrow spectral width and its position remains unchanged with increasing air gap. The amplitude of band gap I-1 is decreased with increasing air gap, but that of band gap I-2 is changed little. Band gaps II-1 and II-2 are seen in 120-μm and 134-μm air gaps only. Band gaps III and IV both move to a low frequency range with increasing air gap. To understand the characteristic of the band gaps, FDTD simulation is used.
Figure 3 (a) shows FDTD simulation results for the 15 grooves used in the measurement with various air gaps. The air gaps used in the measurement are indicated by horizontal white lines. Figure 3 (b) shows another FDTD simulation for a single groove with various air gaps, which shows only A, B, and C band gaps in contrast with many more peaks in the multiple grooves sample. The A and B band gaps of the single groove have narrower widths and smaller power transmission than those of the multiple grooves because few wavelength fitted in the single groove involves to a buildup of the band gaps. However, band gap C has a very narrow band gap width for both multiple and single groove. Except band gaps A, B, and C in Fig. 3(a), band gaps I, II, III, and IV come from the multiple grooves. As the air gap increases, the frequencies of band gaps A, C, and I are fixed to the resonance frequency, which means a specific wavelength is involved to the each resonance. The other band gaps, namely, B, II, III, and IV shift to a lower frequency range with increasing air gap.
Band gap A can be explained by the THz field being canceled out between the straight propagated THz field by the air gap and the detour (reflected) THz field by the first grove. The incident THz field is separated into three parts at the first edge of the groove, namely: transmission, reflection, and splitting. The splitted THz field to the down side (-y direction) is reflected from the groove bottom and then splits again at the second edge of the groove and goes to the output direction (x direction) with the propagated THz field through the air gap. The phase difference between the detour THz field by splitting and propagated THz field through the air gap is π radian at the band gap A. Because the two THz fields are out of phase, the two combined THz fields disappear after the first groove as shown in Fig. 4(a) . The diagram in Fig. 4(a) shows the out of phase state between the detour and straight propagated THz fields.
Unlike band gap A, the position of band gap B shifts to a low frequency range with increasing air gap up to approximately 80 μm. When the air gaps are 50 μm and 75 μm, the band gap frequencies are 2.295 THz and 1.948 THz, respectively, corresponding to the wavelengths of 130.7 μm and 154 μm, respectively. These wavelengths are the same as the length summation of the air gap height (g) and groove depth (d). Therefore, the frequency ofthe band gap B, which we name vertically localized SWCM, is defined as c/(d + g), where c is the speed of light and the depth d = 84 μm. Figure 4 (b) shows the localized THz field which mainly exists near the first groove and the diagram of vertically localized standing wave. Only a small fraction of the incident THz field is propagated to the second groove. Therefore, the resonance frequency component of the band gap B cannot be detected at the end of multiple grooves. When only the air gap is smaller than the depth of the groove (g < d), the vertically localized SWCM exists in the groove shown in band gap B of Fig. 3(b). When the air gap increases, the band gab B shifts to lower frequency range corresponding to longer-wavelength standing wave. If the air gap is larger than the depth of the groove (d = 84 μm), the THz field energy at the air gap is larger than the THz field energy in the groove. Therefore, the THz field cannot be localized in the groove.
Band gap C is another SWCM where the field is horizontally localized in the groove cavities. The field is confined between both side walls and the bottom of the groove as shown in Fig. 4(c). Since the band gap frequency of a horizontally localized SWCM is determined by twice the groove width , the mode frequency is independent of the air gap. The diagram in Fig. 4(c) shows the wavelength of a horizontally localized SWCM in a groove. The groove width in the experiment was 58 μm which corresponds to the 2.62 THz band gap frequency as shown in the band gap C of Figs. 3(a) and (b). After the horizontally localized SWCM forms at the first groove, like band gap B, some of THz field is propagated to the second groove. The propagated THz field makes another horizontally localized SWCM at the next groove and so on. The THz field at the horizontally localized SWCM cannot arrive to the end of the groove. Therefore, the power transmission of multiple grooves is smaller than that of a single groove. The field is localized in some of multiple grooves, but the other grooves are not exist the field as shown in Fig. 4(c). Because we used single frequency for the simulation, the phase of an incoming THz field is periodically changed such as + , 0, and -. Therefore, the horizontally localized SWCM repeatedly appears and disappears in the grooves. Figure 4 (c) shows a snapshot when E field intensity in the grooves is at a maximum. The THz field energy is accumulated in the grooves until saturation because of the equilibrium between incoming and leaking THz field energy. The maximum E field intensity in the grooves is about 1400 times higher than the E field intensity in the input channel. Figure 4 (d)–(f) show the E field intensity when the condition of simulation are identical with (a)–(c), except that the simulation is performed for the single groove sample.
Meanwhile, band gaps I-1 and I-2 show Bragg band gaps which are given by mc/2p, where m is an integer, and p is the period of the groove. Because Bragg band gaps depend only on the period of grooves, not the air gaps, the first and the second Bragg band gap frequencies are always located around 1.06 THz and 2.11 THz, respectively, as show in Fig. 3(a). Band gaps II, III, and IV are caused by the π radian delay (out of phase) between the THz field reflected by the grooves and the THz field propagated through the air gap . Figures 4 (g) and (h) show the magnetic field Hz field distributions of band gaps II-1 and II-2, respectively. The Hz field pattern repeats every 3rd grooves. After two or three repetitions of the Hz field patterns, as shown by the dashed arrow lines, the field uniformly distributes to the y-direction, which makes it out of phase to the THz fields between the THz field reflected by the grooves and the THz field propagated through the air gap. Therefore, band gaps II-1 and II-2 have air gap dependent characteristics. The Hz field pattern of band gap II-2 is the same as that of band gap II-1 except the wavelength. Because the wavelength of band gap II-2 is half as long as that of band gap II-1, the position of band gap II-2 is located at a frequency two times higher as shown in Fig. 3(a). Band gaps III and IV have an out of phase mechanism which is similar to that of band gap II, but it shows very complicated and irregular field patterns. Many band gaps also come out after 3 THz ; however, more study is required to understand the higher frequency band gaps completely. Meanwhile, the slit waveguide can be considered a mirror image by the groove bottom as mentioned in the introduction. It is helpful to understand the principle of band gaps by using the THz field which supplies only one side of the air gap to the slit waveguide .
4. Summary and conclusions
This work has demonstrated the characteristic of band gaps using metal grooves in a flare PPWG with increasing air gap. The observed vertically and horizontally localized SWCMs in measurement showed good agreement with the FDTD simulations. Vertically localized SWCMs only exist when the air gap is smaller than the depth of the groove (g < d) which is the condition of turn-on and turn-off of the band gap. The transition air gap for turn-on and turn-off is about 3 μm. Horizontally localized SWCMs depend only on the groove width, not the air gap. In the case of a single groove, the simulated linewidth and Q-factor are 6 GHz and 437, respectively. The stop band is extremely narrow compared to that in previous results, which had a Q-factor of 430 by the Bragg resonance on groove  and a Q-factor of 1065 by photonic crystal waveguide . Since the band gap width of horizontally localized SWCM is so narrow, it is recommended to be used as a notch filter with very high quality factor. The grooves function as THz field energy containers for SWCMs. Other band gaps except Bragg band gaps can be explained by the field being canceled out by the out of phase between detour THz fields reflected by grooves and/or air gap and THz fields propagated through air gaps. The FDTD simulation is a powerful tool to understand the characteristics of band gaps. Understanding the mode characteristics into grooves can give us more useful applications in the THz region, such as THz filters or THz sensors, in the future.
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, and No. 2011-0001291), the Korea Science and Engineering Foundation (KOSEF) (M10755020001-08N5502-00110), and the Grant of the Korean Health Technology R&D Project; Ministry for Health, Welfare & Family Affairs of Korea (A101954).
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