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A high-aspect-ratio metallic rod array is demonstrated to generate and propagate highly confined terahertz (THz) surface plasmonic waves under end-fire excitation. The transverse modal power distribution and spectral properties of the bound THz plasmonic wave are characterized in two metallic rod arrays with different periods and in two configurations with and without attaching a subwavelength superstrate. The integrated metallic rod array–based waveguide can be used to sense the various thin films deposited on the polypropylene superstrate based on the phase-sensitive mechanism. The sensor exhibits different phase detection sensitivities depending on the modal power immersed in the air gaps between the metallic rods. Deep-subwavelength SiO2 and ZnO nanofilms with an optical path difference of 252 nm, which is equivalent to λ/3968 at 0.300 THz, are used as analytes to test the integrated plasmonic waveguide. Analysis of the refractive index and thickness of molecular membranes indicates that the metallic rod array–based THz waveguide can integrate various biochip platforms for minute molecular detection, which is extremely less than the coherent length of THz waves.
© 2014 Optical Society of America
1. Introduction
Terahertz (THz) sensing has attracted considerable attention in recent years because THz radiation can be used for the noninvasive and label-free detection of diverse materials based on the molecular fingerprints of analytes, such as metals, polar molecules, and bio/chemical materials. However, THz sensing is not applicable for minute materials or ultra-thin films because the ultra-small optical path difference (OPD), which depends on the physical thickness and refractive index differences of analytes, is almost impossible to resolve using the traditional THz spectroscopic system [1]. Surface plasmon (SP) technology has undergone tremendous development; surface plasmon polaritons (SPPs) facilitate THz nanofilm sensing. SP waves excited by electromagnetic waves are resonant oscillations of conduction electrons at the metal–dielectric interface. Compared with the optical plasma frequency of metals, the plasmon frequency of semiconductors is located only at the THz frequency range; it depends on the carrier concentrations and is derived from the Drude model [2]. Hence, a semiconductor surface can act as a THz plasmonic waveguide that supports bound THz SP waves for micrometer-thick film sensing [3]. Another way to effectively support bound THz SP waves is to use metamaterials or spoof surface plasmon polaritons (SSPPs) from various patterned metal surfaces to generate strongly localized and enhanced fields [4]. The frequencies of the generated SSPPs can be adjusted from optical to microwave frequency ranges according to the sizes and shapes of the artificial metal. In addition, the effective propagation constants of SSPPs are influenced by the geometric parameters of a metal. Thus, the field confinement ability of SSPPs can be altered [5]. The highly confined and enhanced electromagnetic field is sensitive to the surrounding dielectric materials. It can surpass the diffraction limit of the electromagnetic field and route photons on a nano-scale circuit to realize system-on-a-chip [6–8] and near-field molecular/nanofilm sensing [9–11].
An integrated optical waveguide can be used for bio-chemical sensing applications. This waveguide sensor is composed of three main layers: waveguide, superstrate, and sensing analytes [12, 13]. The sensing mechanism of an integrated optical waveguide sensor is based on the evanescent field or decay length of waveguide modes strongly affected by the sensing layer, which may be constituted by bulk, thin film, or particle analytes. The detection sensitivity is significantly affected by the decay length of the evanescent waveguide mode, which is determined by the refractive indexes and thicknesses of the waveguide and superstrate layers. By analogy, the detection sensitivity of the SP sensor based on the metamaterial or textured metal surface can be optimized by adjusting the geometrical parameters of the metamaterial, which is equivalent to optimize the SSPP’s decay length.
In this presentation, we combine the concepts of integrated optical waveguide and textured metal surface to demonstrate a THz plasmonic waveguide sensor composed of metallic rod arrays (MRAs). According to the sensing scheme of SSPPs, the MRA-based plasmonic waveguide can effectively excite and support the THz SP waves to sensitively detect nanometer-thick thin films based on the phase-sensitive mechanism. MRAs, fabricated through bottom-up microstereolithography for a certain period, change the decay length of evanescent waveguide modes at the air–MRA interfaces by adjusting the air gaps between the metallic rods. A 100 µm-thick polypropylene (PP) film superstrate is top conjugated with the MRAs, forming an integrated THz plasmonic waveguide, to load various dielectric nanofilms for sensing. The phase detection sensitivity, which is dependent on the thickness of the PP superstrate, is also experimentally characterized by analyzing the THz electric field waveforms and the corresponding power spectra for the MRA plasmonic waveguides integrated with PP superstrates of different thicknesses. SiO2 and ZnO nanofilms (thickness: 300 nm) deposited on a 100 µm-thick PP superstrate are used as analytes. The nanofilms are successfully recognized by the integrated MRA waveguide sensor, where the OPD is 252 nm, which is equivalent to λ/3968 at 0.300 THz. The MRA-based waveguide sensor can potentially integrate various biochip platforms for the highly sensitive detection of molecular membranes with different thicknesses and refractive indices based on the sensing modality.
2. THz plasmonic waveguide based on MRAs
An MRA-based structure is constructed using 2D periodically arranged uniform metal rods. The period of the rod array Λ is determined from the rod diameter D and the air-gap size G. The schematic structure is illustrated in Fig. 1(a). The rod diameter and height are 160 µm and 1 mm, respectively. The air gap size is varied to understand the dependence of modal confinement on geometry. In the edge-coupled configuration, the 1 mm-high MRAs are sufficiently thick because the focused THz wave spot is nearly diffraction limited. The propagation length of the MRA-based waveguide is 30 periods of rod array in the Y-axis, and the polarization of the input THz waves is perpendicular to the rod axis in the X-direction [Fig. 1(a)] [14]. The width of the MRA structure is approximately 9 mm in the X-direction, which is considerably larger than the rod height (1 mm in the Z-direction) and the input THz beam width. The configuration of the MRA structure resembles a thin dielectric slab waveguide that can confine THz waves in the Z-direction [15]. A metal blade is placed ahead of the input end of the MRAs to prevent the detection of leaky and scattered THz waves [Fig. 1(a)]. The fabrication process of the MRA structure is described as follows. First, cylinder polymer rods with a periodical arrangement in a square array are constructed through bottom-up 3D microstereolithography using a UV curable photopolymer [16, 17]. The MRA structure cannot be fabricated via a traditional mechanical or 3D printing method because of the large distinction ratio (6.25) between the rod diameter and height. After microstereolithography, a 100 nm-thick aluminum film is coated on the polymer rod arrays by sputtering. The thickness of the metal coating is sufficiently larger than the skin depth of the THz radiations within the spectral range of 0.1 THz to 1 THz [18]. Figures 1(b) and 1(c) show the top-view photos of the MRA devices with 420 and 620 µm periods, respectively. The periods in the X- and Y-dimension are nearly equal. Figures 1(d) and 1(e) illustrate the side-view microscopic photos of the devices.
Fig. 1 (a) Optical configuration of an MRA waveguide. Top-view microscopic photos of (b) 420 µm- and (c) 620 µm-period MRAs. Side-view microscopic photos of (d) 420 µm- and (e) 620 µm-period MRAs.
Figures 2(a) and 2(b) show the normalized transmission spectra (i.e. transmittance) of the 420 µm- and 620 µm-Λ MRA waveguides, respectively. The spectra were obtained through THz time-domain spectroscopy [19] and through comparison of the THz transmitted powers with and without an MRA device. Two transmission bands are found in both MRA structures within the spectral range of 0.1 THz to 0.6 THz. However, the transmittance of transmission band measured from the 620 µm-Λ MRA is obviously higher than that of the transmission band measured from the 420 µm-Λ MRA because of the high air-filling ratio among the rods. The rejection bands of the two MRAs within the spectral range of 0.1 THz to 0.6 THz are caused by the destructive interference of multiple reflections among the metal rods when THz waves transmit through the 30 arrays of the MRA waveguide. The central frequency of the rejection band is consistent with the Bragg frequency calculated from c/2nΛ, where c, n, and Λ are the light speed in vacuum, effective refractive index, and period of MRA, respectively. As shown in Fig. 2(a), the rejection band for the 420 µm-Λ MRA ranges from 0.284 THz to 0.425 THz, which corresponds to a 141 GHz bandwidth. As shown in Fig. 2(b), the rejection band for the 620 µm-Λ MRA ranges from 0.240 THz to 0.270 THz. These values are consistent with the results calculated using the finite-difference time-domain (FDTD) method.
The integral power distribution in the Z-axis was measured using the knife-edge method with the spatial resolution of 0.1 mm to 0.2 mm to understand the modal field confinement of the guided THz SP waves on the MRA structure. The actual power distribution was derived through differential calculations [20]. Figures 3(a) and 3(b) illustrate the measured cross section of the Z-axial power distribution for 0.226 and 0.520 THz waves, guided on the 420 µm-Λ MRA waveguide. The power decay length of the 0.520 THz wave near the air–MRAinterface is significantly smaller than that of the 0.226 THz wave. In other words, the 0.520 THz wave on the 420 µm-Λ MRA waveguide has stronger field confinement than the 0.226 THz wave. No significant power transmission is extended outside the MRA structure. FDTD is used to calculate the simulated power distributions of the 0.226 and 0.520 THz waves in the X-Z plane. The results are shown in Figs. 3(c) and 3(d), where the power confinements are similar to the results shown in Figs. 3(a) and 3(b). Figures 3(e) and 3(f) show the calculated modal patterns of the 0.226 and 0.520 THz waves, respectively, in the Y-Z plane. Results show that the electromagnetic field of the 0.520 THz wave is mostly covered in the MRA structure from the input (Y ~−6mm) end to the output (Y ~6 mm) end. The theoretical and experimental waveguide modal patterns show good consistency (Fig. 3). The THz radiations located in the high-frequency transmission band (0.420 THz to 0.550 THz) of the 420 µm-Λ MRA device are firmly trapped and are deliverable inside the periodic air gaps.
Fig. 3 Measured Z-axial power distribution at the output end of a 420 µm-Λ MRA waveguide for (a) 0.226 THz and (b) 0.520 THz waves. Simulated cross power distributions in the X-Z plane of (c) 0.226 THz and (d) 0.520 THz waves at the output end of the waveguide. Simulated cross power distributions in the Y-Z plane for (e) 0.226 THz and (f) 0.520 THz waves.
Figures 4(a) to 4(c) illustrate the measured results of Z-axial power distributions at the output end of the 620 µm-Λ MRA waveguide at frequencies of 0.226, 0.322, and 0.424 THz, respectively. The power confinements of the waveguide modes decrease with decreasing THz frequency [Figs. 4(a) to 4(c)]. Compared with the power distributions of the 420 µm-Λ MRA waveguide [Figs. 3(a) and 3(b)], the modal patterns of the 620 µm-Λ MRA waveguide extend more toward both the MRA and air-cladding region. In other words, most of the power of the propagated THz plasmonic wave is concentrated near the MRA–air interface of the 420 µm-Λ MRA waveguide. However, the guided plasmonic wave for the 620 µm-Λ MRA waveguide is not only extended evanescent to the air-cladding region but is also deeply immersed in the air gaps of the MRA structure. The frequency- and geometry-dependent field confinement [Fig. 3 and Figs. 4(a) to 4(c)] indicates that the MRA structure acts as the THz waveguide that delivers the THz plasmonic wave and that the modal field distribution can be tuned by adjusting the air gap size between adjacent metal rods. This phenomenon is similar to the dielectric slab waveguide described in waveguide theory, in which the modal confinement can be changed by varying the refractive index of the waveguide core. For sensing, the decay length of the waveguide mode should be comparable with the size of the analytes to ensure strong interaction. Therefore, a 100 µm-thick PP film superstrate top conjugated with an MRA waveguide is designed to load the nanofilm analytes onto the waveguide sensor, as sketched in Fig. 4(d). A MRA THz waveguide acts as an integrated optical sensor based on the evanescent wave detection scheme because the decay length of the THz plasmon wave in the air-cladding region can be properly tailored by changing the MRA geometry, thereby optimizing the detection sensitivity [12].
Fig. 4 Measured cross power distributions along the Z-direction and at the output end of a 620 µm-Λ MRA waveguide for (a) 0.226 THz, (b) 0.322 THz, and (c) 0.424 THz waves. (d) Side-view sketch of nanofilm sensing using the integrated MRA-based THz plasmonic waveguide.
3. Superstrate-integrated MRA waveguides
The PP superstrate integrated to 420 µm- and 620 µm-Λ MRAs with different Z-axial modal fields should be individually analyzed and the correlated sensitivity of thickness detection should be derived to sense the a nanometer-thick membrane deposited on the 100 µm-thick PP superstrate. In this experiment, the PP superstrates with the width of 9 mm and lengths of 13 and 18 mm are separately covered on the top surfaces of the 420 µm- and 620 µm-Λ MRA structures without any adhesive. The thicknesses of the PP superstrates include 30, 50, 70, and 90 µm. Figure 5(a) shows the transmitted THz electric field oscillations (denoted as E) measured from the 420 µm-Λ MRA waveguide with PP superstrates of various thicknesses. The waveform of the blank device apparently changes when the PP-superstrate is top integrated on the waveguide. In addition, obvious time-delay shifts of the waveform main peaks can be observed as the superstrate thickness increases from 30 µm to 90 µm, as shown in Fig. 5(a). The main peaks for the 30, 50, 70, and 90 µm-thick superstrates are located at 19.8, 24.3, 24.8, and 29.3 ps, respectively. The apparent time-delay shift of the waveform originates from the phase retardation contributed by a PP film superstrate. The corresponding transmission spectra (denoted as |E|2) of the PP superstrates integrated on the 420 µm-Λ MRA waveguide are illustrated in Fig. 5(b). In each spectrum [Fig. 5(b)], the rejection band still manifests at approximately 0.284 THz to 0.425 THz, but the transmission power of the rejection and transmission bands increases as the thickness of the PP superstrate increases.
Fig. 5 (a) Electric field oscillations and (b) power spectra of THz waves propagated through a 420 µm-Λ MRA waveguide with and without attaching PP superstrates of various thicknesses.
Figure 6(a) shows the peak power (denoted as |Epeak|2) of the low- and high-frequency transmission bands (denoted as 1st and 2nd band) as a function of PP superstrate thickness. The peak power at the transmission band gradually increases with a slight sinusoidal fluctuation as the superstrate thickness increases. The increase in transmission spectral power with the thickness of the top-integrated PP superstrate implies that the partial THz power of the confined modal pattern, which is originally concentrated at the MRA–air interface [Fig. 3(b)], is coupled toward the air-cladding region via the PP superstrate and then the interference interaction inside the MRA structure decreases [21]. In other words, the partial transmitted power that originates from the constructive and deconstructive interference of MRA is guided in the air-cladding space when a PP superstrate is attached to the top of the MRA structure. Figure 6(b) illustrates the power distribution of the THz plasmonic wave guided on the 420 µm-Λ MRA waveguide with a PP superstrate thickness of >90 µm. A large fractional power is distributed in the air-cladding region with a modal pattern more extended than that of the blank device, thereby increasing the THz power transmission [Fig. 6(a)].Figures 7(a) and 7(b) show the measured THz time-domain waveforms and the corresponding transmitted power spectra for the integrated 620 µm-Λ MRA waveguide with PP superstrates of different thicknesses (30, 50, 70, and 90 µm). The measured waveforms in Fig. 7(a) are quite similar, except for the broadening of oscillations. Thus, a continuous time-delay shift can be observed. For example, the second electric field peaks at 17.2, 17.9, 19.3, 20.4, and 21.7 ps for the blank condition and the 30, 50, 70, and 90 µm-thick PP superstrates are presented as dashed lines in Fig. 7(a). The power spectra of the electric field oscillations in Figure 7(a) are illustrated in Fig. 7(b), where the MRA-contributed rejection and transmission bands still exist at similar spectral positions for all thickness conditions.
Fig. 6 (a) Peak power of the low- and high-frequency transmission bands denoted as the 1st and 2nd peaks, respectively, passing through a 420 µm-Λ MRA waveguide with PP superstrates of various thicknesses. (b) Schematic Z-axial power distribution of a 420 µm-Λ MRA waveguide top conjugated with a >90 µm-thick PP superstrate.
Fig. 7 (a) Electric field oscillations and (b) power spectra of THz waves propagated through a 620 µm-Λ MRA waveguide with and without attaching PP-film superstrates of various thicknesses.
Figure 8(a) illustrates the peak powers of the 1st and 2nd transmission bands in Fig. 7(b) for different thicknesses of superstrates to integrate the 620 µm-Λ MRA waveguide. Contrary to the result of the 420 µm-Λ MRA waveguide, the peak power of the transmission bands decreases even with a slight sinusoidal fluctuation as the thickness of the PP superstrate increases. This result indicates that the extended modal pattern of the blank 620 µm-Λ MRA waveguide becomes more concentrated near the air–MRA interface after integrating a thick superstrate. In other words, the superstrate top conjugated on the 620 µm-Λ MRA waveguide can confine the extending power in the air-cladding region toward the MRA structure. This phenomenon results in a more fractional THz power both inside the PP superstrate and the MRA structure to attenuate the transmission power [Fig. 8(a)] [15]. Figure 8(b) shows the modal power distribution of the integrated 620 µm-Λ MRA waveguide, illustrating that most of the modal power immerses inside the 620 µm-Λ MRA structure and that only a small amount of the modal power evanesces to the air-cladding region. It eventually reserves the strong interference interaction inside the MRA structure, similar to the blank configuration of the 620 µm-Λ MRA waveguide.
Fig. 8 (a) Peak powers of the 1st and 2nd transmission bands shown in Fig. 7(b). (b) Schematic Z-axial power distribution of a 620 µm-Λ MRA waveguide top conjugated with a >90 µm-thick PP superstrate.
4. Nanofilm detection based on a phase-sensitive mechanism
The transmission power variations [Figs. 6(a) and 8(a)] indicate that a certain thickness of the PP superstrate integrated on a 420 µm-Λ and a 620 µm-Λ MRA waveguide results in different Z-axial modal power distributions. The power distribution affects the sensitivity for detecting analytes deposited on the superstrate. The waveform evolution [Figs. 5(a) and 7(a)] indicates that the phase retardations of the THz electric field oscillations induced by the PP superstrates are approximately proportional to the thickness variation of the superstrate. Figures 9(a) to 9(d) show the phase retardations induced by the 30, 50, 70, and 90 µm-thick PP superstrates attached to the 420 µm-Λ and 620 µm-Λ MRA waveguides at frequencies of 0.520, 0.424, 0.322, and 0.226 THz, respectively. The normalized phase retardation, denoted as ΔΦ, is obtained by comparing the phases of the transmitted THz wave with and without attaching PP film superstrates on the MRA waveguides and normalized by the waveguide lengths. Some of the THz frequencies are in the rejection bands, experiencing strong Bragg reflection in the blank MRA device with the least transmission power. After the integration of the PP superstrates to the MRAs, the fractional powers of the frequencies are obviously evanescent toward the air-cladding region, thereby increasing the overall transmission power[Figs. 5(b) and 7(b)]. The additional phase retardations at the rejected frequencies can thus be produced via the generated evanescent field interacting with the PP superstrates. All the phase retardations at the four THz frequencies and along the two different MRAs are approximately proportional to the PP film thicknesses. The linearly fitting curves are shown in Figs. 9(a) to 9(d). The slopes represent the phase detection sensitivities of the two MRA waveguides at different frequencies. In other words, the phase retardation contributed by a PP film superstrate per micrometer thickness can be estimated from the linearly fit slopes. Figure 9(e) summarizes the phase detection sensitivities at different THz wave frequencies and with different MRA waveguide sensors. The sensitivity is approximately proportional to frequency within the range of 0.20 THz to 0.55 THz. Obviously, the phase detection sensitivity of the 620 µm-Λ MRA waveguide for different thicknesses is superior to that of the 420 µm-Λ waveguide at THz wave frequencies higher than 0.226 THz. The difference in phase detection sensitivity between the 420 µm- and 620 µm-Λ MRAs results from the different modal power distributions of the two superstrate-integrated MRA waveguides [Figs. 6(b) and 8(b)]. In the superstrate-integrated 620 µm-Λ MRA waveguide, the modal field has a considerably longer optical path in the 30 periods of MRA because most of the waveguide power is guided inside the MRA structure. Thus, the increased OPD induced by the thickness increment of the superstrate per micrometer [Fig. 9(b)] on the 620 µm-Λ MRA waveguidepromotes phase retardation. By contrast, most of the modal power guided on the superstrate-integrated 420 µm-Λ MRA waveguide extends toward the air-cladding region, thereby reducing the optical path in the 30 periods of MRA. Consequently, the superstrate-induced OPD per micrometer in the multiple reflections of the 420 µm-Λ MRA is smaller than that of the 620 µm-Λ device.
Fig. 9 Phase retardations induced by PP superstrates on a 420 µm- and a 620 µm-Λ MRA waveguide for (a) 0.520 THz, (b) 0.424 THz, (c) 0.322 THz, and (d) 0.226 THz waves. (e) Phase detection sensitivities of a 420 µm- and a 620 µm-Λ MRA waveguide.
Basing on the sensitivity analysis in Fig. 9(e), we choose the 620 µm-Λ MRA waveguide integrated with a 100 µm-thick PP superstrate for nanofilm sensing. In this experiment, SiO2 and ZnO nanofilms sputter coated on the 100 µm-thick PP superstrate are prepared as standard samples to confirm the nanofilm-sensing capability of the MRA structure. Three samples each with an area of 9 mm × 18 mm are prepared on the same PP superstrate for continuous measurement by just moving the integrated position of the superstrate on the MRA waveguide to avoid inaccurate phase measurement induced by thickness variation in a superstrate. The three sample areas on one PP superstrate are the SiO2 nanofilm, ZnO nanofilm, and blank space. The thicknesses of the two dielectric nanofilms controlled by sputter coating are both 300 nm. The films are used to observe the refractive index–induced OPD in the sensing application. Figure 10(a) shows the propagation of THz electric field oscillations through the integrated MRA waveguide loaded with and without a nanofilm. The electric field oscillations in the duration of 25 ps to 70 ps are apparently distinct for the three waveforms. These results show that the SiO2 and ZnO films can be recognized based on their different refractive indices, which are 1.95 and 2.79, respectively, at 0.300 THz [22, 23]. Figure 10(b) shows the theoretical and measured transmittances of the blank device, as well as the phase retardations, induced by the two nanofilms. The measured phase retardation is obtained by comparing the measured phases of the integrated MRA loaded with and without a nano film [Fig. 10(b)]. Different nanofilms can be identified by using the integrated MRA waveguide based on the phase retardation in the transmission band of 0.300 THz to 0.450 THz. Otherwise, the phase retardation in the rejection bands at 0.200 THz to 0.300 THz and 0.450 THz to 0.550 THz is considerably chaotic without repeatable response in the sensing measurement. The phase retardations for sensing the SiO2 and ZnO nanofilms are apparently distinct because of the large OPD (approximately 252 nm) between the two nanofilms. Basing on the phase detection resolution of 0.39 rad in our THz time–domain spectroscopy system and the proportional relation between the phase retardation and thickness variation (Fig. 9), we find that the minimum detectable OPD for nanofilm sensing at 0.300 THz is reduced to approximately 64 nm, which corresponds to λ/15702. When the operation electromagnetic frequency increases to 0.400 THz, the OPD resolution is further decreased to 21 nm, which corresponds to λ/35714. This result can be attributed to the increase in detection sensitivity with increasing frequency (Fig. 9).
Fig. 10 (a) Electric field oscillations of THz waves passing through a 620 µm-Λ MRA waveguide integrated in a 100 µm-thick PP substrate with and without nanofilm coating. (b) Detected phase retardations induced by SiO2 and ZnO nanofilms.
5. Conclusion
An MRA-based THz plasmonic waveguide can detect nanofilms because of the optimized integration of an MRA structure with a nanofilm-loaded superstrate. The power distribution of the modal field can be adjusted by changing the air gap size of an MRA to produce the evanescent field, which has a significantly large optical path to interact with analytes and is highly sensitive to the phase variation of the surrounding analytes. The sensitive MRA THz waveguide sensor can detect 300 nm-thick SiO2 and ZnO nanofilms coated on a 100 µm-thick PP-film superstrate based on their OPD. The minimum detectable OPD values are 64 and 21 nm at 0.300 and 0.400 THz, respectively, in the general THz time–domain spectroscopy measurement with the phase resolution of 0.39 rad. The PP superstrate integrated in the MRA THz waveguide can be replaced by various biochips or lab-on-a-chip platforms for molecular sensing. The corresponding OPD can be considerably smaller than the coherent length of a THz wave for various sensing applications. For example, the sensor can be used to identify ligand–receptor binding in biochemical reactions or to recognize various powder and thin film analytes based on the effective thickness and refractive index variations of the analytes.
Acknowledgment
This work was supported by the Advanced Optoelectronic Technology Center, National Cheng Kung University, under projects from the Ministry of Education and the National Science Council (NSC 100-2221-E-006 −174 -MY3) of Taiwan.
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