1. Introduction

In recent years, THz fibers and waveguides have attracted much attention. They have potential applications in communication, spectroscopy, imaging, and sensing. For the practical applications, functional devices such as switches, filters, and modulators are essential. A waveguide-based device enables both transmission and manipulation of the guided optical waves and has the advantages of fiber compatibility, compactness, and low insertion loss. Therefore, such a device can be more easily integrated in fiber-based systems than can other functional devices. In the THz frequency range, some waveguide-based filters have been demonstrated [1–4]. They include a PPWG with a 2D Bragg structure [1] and a slab waveguide with periodic gratings [2], which are operated at a fixed frequency. Frequency tunability is achieved by incorporating liquid crystal materials [3] or a semiconductor defect layer [5,6] into the THz photonic crystal waveguides to shift the bandgap of the waveguide in a manner that is controlled by an external stimulus, such as the electrical/magnetic field [3,5], temperature [6], or photoexcitation. A tunable metallic photonic crystal filter that operates in a frequency range of 365~385GHz is demonstrated by mechanically lateral-shifting the distance between two photonic crystal plates [7]. These THz filters rely on the insertion of a resonant structure inside the waveguide, such as a Bragg grating [1,2] or a photonic crystal [2,3,5,7], and an additional costly fabrication process or multiple dielectric layers are required. When such a resonant structure is introduced, its spectral properties can be tuned only over a certain frequency range, which is dominated by the materials and geometry of the waveguide [8].

Recently, Sun et al. developed a simple and low-loss THz pipe waveguide [9] from a cheap and easily acquired plastic tube, whose guidance mechanism is based on an anti-resonant reflecting optical waveguide (ARROW) [8]. THz waves are strongly confined in the low-index core by antiresonant reflection from a single high-index cladding layer that effectively acts as Fabry- Pérot (FP) etalon. Based on the FP resonance of the dielectric cladding, THz waves escape from the waveguide core and multiple periodic resonant dips are appeared in the transmission spectrum [8,9]. Therefore, no additional resonant structures have to be introduced in the waveguide for the THz filter application. The spectral positions of transmission dips are mainly determined by the refractive index and thickness of the waveguide cladding [8]. An ARROW-based filter in the optical regime for optofluidic sensing [10], operated at a fixed working frequency, was demonstrated. However, the device lacks frequency tunability owing to its specific waveguide geometry. An ARROW-like microstructure optical fiber in which micro-inclusions are filled with temperature-sensitive liquids was theoretically demonstrated, for use in a tunable photonic device [8]. The spectral positions of the transmission dips were continuously tuned by changing the temperature, and thereby continuously changing the cladding index of the ARROW.

In this presentation, a waveguide-based tunable THz notch filter without resonant structures is demonstrated, simply by exploiting the antiresonant reflecting wave-guidance in a hollow-core dielectric planar waveguide, to produce multiple narrow notch-dips with a uniform spectral period over a broad transmission spectrum. The continuous shifting of the spectral positions of notch-dips is for the first time experimentally achieved by adding movable metal layers outside the dielectric claddings of the waveguide and mechanically changing the spacing between the metal layer and the dielectric slab cladding. The performance of the filter is characterized by THz time-domain spectroscopy (THz-TDS). A tiny variation of the spacing caused an apparent shift in notch-frequency and a high mechanical frequency-tuning-sensitivity of 115GHz/mm was thus achieved by TE polarized THz waves. The measured maximum notch-frequency-tuning-range approached 50% of the bandwidth in every passband, and a 20dB rejection notch-depth with a linewidth as low as 6GHz at frequency of around 0.2THz was achieved. The spectral tuning mechanism is verified by theoretical simulation, which agrees closely with the measurements. The waveguide-based THz tunable notch filter has potential for applications that require the dynamic tuning of the rejection frequency for sensitive detection, such as biochips, optofluidic sensing, and microfluidic biosensing.

2. Experimental setup

Figure 1 schematically illustrates the tunable THz notch filter device composed of a planar antiresonant reflecting hollow waveguide (ARRHW) and a pair of mechanically-movable metal plates placed outside of the dielectric claddings of the planar waveguide. The ARRHW is consisted of an 8mm-thick air-core and dielectric slab claddings made by polymethylmethacrylate (PMMA) with a measured refractive index of 1.59. Two PMMA slabs with thicknesses t of 1.42mm and 1mm are adopted as the dielectric claddings of the THz-ARRHWs to study the frequency tuning range. The metal plates are fabricated by the thermal evaporation of a 100nm-thick aluminum (Al) layer on a PMMA plate. The measured THz transmission power of the metallic layer on a 1.42mm-thick PMMA substrate is zero at 0.1~1THz, which indicates the thickness of the Al layer is greater than the THz skin depth [11] in this frequency range. In this experiment, the spectral response of the filter device was measured using a transmission-type THz time-domain spectrometer, which is schematically illustrated in Fig. 1, and consists of a pair of LT-GaAs-based photoconductive antennas as the THz emitter and receiver. The THz emitter was optically excited using a mode-locked Ti:sapphire laser with a pulse width of 100fs. The generated linear-polarized THz pulse was collected and directly coupled into the ARRHW-based THz notch filter using a pair of parabolic mirrors. The direction of the parallel plates of the planar-waveguide-filter was changed from horizontal to vertical to select the TE or TM-polarized excitation. The two Al plates of the waveguide filter are moved with respect to the PMMA claddings which are mechanically controlled by a translation stage to continuously change the spacing d between them. The propagated THz waves were transmitted to the output end of the waveguide filter, where they were collected and focused onto a photoconductive receiver using a PE lens (f = 5cm) and a parabolic mirror. We measured the different transmission spectrum of the metal-clad THz-ARRHW at different spacing d. The measured THz propagation loss in a bare planar THz-ARRHW with 1.42mm-thick PMMA cladding is around 0.1cm⁻¹ at transmission bands of 0.1~0.16THz and 0.18~0.25THz, performed by a standard cutback method, and the resulting value is larger than that of a dielectric THz-ARRHW tube (~0.01cm⁻¹) [9] because the THz waves are only subject to 1D confinement in the planar waveguide. The full-width-half-maximum of the THz mode size at 0.312THz measured at the output end of a 16cm-long planar ARRHW with an 8mm-thick air-core and a 1.42mm-thick PMMA cladding is 5.13x13.85mm². From calculation of the overlap integral of mode patterns [9,12], the theoretical coupling efficiency between the planar ARRHW and a PMMA pipe waveguide which has the same cladding and air-core dimensions as the planar ARRHW is estimated to be greater than 80%. Additionally, adding the high-loss Al plates outside the cladding layers of the planar THz-ARRHW doesn’t increase the measured propagation loss, revealing the device has a low insertion loss for integration with THz pipe waveguides [9].

 

Fig. 1 Transmission-type THz time-domain spectrometer for measuring the notch filter device. The planar ARRHW-based THz tunable notch filter was illustrated schematically, where t and d respectively denote the thickness of PMMA slab cladding and a variable spacing between the metal plate and the cladding layer.

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3. Experimental results

Figure 2(a) shows the measured THz transmission spectra of a 16cm-long bare planar ARRHW with t=1.42mm under TE-polarized excitation. Multiple transmission dips can be clearly identified with a frequency period of around 86GHz. As shown in Fig. 2(a), the four transmission dips of the bare planar waveguide are 0.084, 0.171, 0.256, and 0.342THz, which agree excellently with the theoretical values of 0.086, 0.171, 0.257, and 0.343THz with respective dip-orders m of 1~4, calculated according to the FP resonant condition [8] of a 1.42mm-thick PMMA slab cladding. Figures 2(b) and (c) present the theoretical THz modal patterns in the bare ARRHW, individually corresponding to transmission-minimum and transmission-maximum frequencies for m=2 indicated in Fig. 2(a), which are simulated using the finite-difference frequency-domain method (FDFD) [13]. In Fig. 2(b), the oscillation amplitudes of the mode patterns within the PMMA cladding are very close to those in the hollow core and extending outside the cladding region, revealing high leakage at the transmission dip frequency. It indicates that, at the boundaries between the air-core and cladding regions (position = ± 4mm shown in Fig. 2(b)), the phases of the oscillatory electric fields must be the peaks of oscillations (indicated by the blue arrow in Fig. 2(b)) for the transmission dip frequencies. The total phases of the oscillatory electric fields within the cladding layers associated with the transmission dip and peak, respectively, equal an even number and odd number of half-oscillations, as shown in Figs. 2(b) and (c). They are 2π and 2.5π in the case of m=2. Restated, when a 0.5π-phase-difference is introduced into the PMMA cladding layer, it transforms the high-loss leaky mode, which corresponds to the transmission dip, into the confined waveguiding mode, yielding the transmission maximum.

 

Fig. 2 (a) Measured THz transmission spectra of bare planar ARRHW with t = 1.42mm. Normalized THz electric field profiles at frequencies of transmission dip (b) and peak (c) Region shaded with oblique lines represents PMMA slab claddings. The blue arrows indicate the phases of oscillatory electric fields corresponding to transmission dip and peak frequencies are peak and valley of the oscillations, respectively.

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Figure 3(a) presents the TE-polarized THz transmission spectra of the ARRHW-based tunable notch filter with different spacings, d, between the metal layer and the 1.42mm-thick PMMA slab cladding. The notch dips associated with the TE-polarized waves are apparently blue-shifted as d decreases, as shown in Fig. 3(a). As shown in Figs. 3(b) and (c), the measured spectral positions of the notch dips agree closely with the theoretical calculations based on FDFD in different passbands (m=2 and m=3). The simulated THz modal patterns in the planar-waveguide-filter can effectively explain the continuous spectral shift. The inset figures in Fig. 3(a) individually illustrate the half-THz modal patterns that correspond to the notch dips (m = 2), labeled (1)~(4) in Fig. 3(a), which are simulated based on FDFD. The inset (1) in Fig. 3(a) presents the leakage of THz waves with large power loss both inside and outside the PMMA cladding of the bare ARRHW without metal plates. As shown in insets (2)~(4) of Fig. 3(a), the high loss of the metal plate prevents the electric field oscillations from appearing in the region outside (right-side) the Al plate when Al plates are added. However, the phases at the boundaries between the air-core and cladding regions are still the oscillatory peaks in insets (1)~(4), revealing the transmission dips characteristics at these frequencies as mentioned in Fig. 2(b) regardless of the metal layers’ addition. As the distance d between the Al plate and the PMMA cladding gradually declines, the cladding region is forced to accommodate more oscillations of the electric field and thus it reduces the oscillation period. The decrease in the wavelength of the electric field causes the notch dip frequency to move toward the high-frequency range.

 

Fig. 3 (a) Measured TE-polarized THz transmission spectra of ARRHW-based notch filter with various spacings d. Inset Figs. (1, 2, 3, 4) present half-simulated normalized THz modal patterns at frequencies of notch dips, 0.172, 0.190, 0.194, and 0.216THz. The cyan and orange regions represent the PMMA cladding and movable metal layer, respectively, and the hollow core of the waveguide is located at positions of 0~4mm. Comparison of measured (solid line) and simulated (dashed line) dip-frequency positions at (b) 2nd and (c) 3rd -order passband. Vertical dot lines indicate theoretical notch dip frequencies.

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A comparison of inset (1) with inset (4) in Fig. 3(a) reveals that the total phase of the electric field in the cladding region increases from 2π to 2.5π as d changes from infinity to 0mm, and the 0.5π phase-difference causes the notch dip frequency in the latter case (at a total phase of 2.5π) to coincide with the central frequency of the transmission maximum in the former case (at a total phase of 2π), which condition is similar to that in Fig. 2. The resulting 0.5π phase-difference between the m^th-order transmission dip and the transmission-peak frequency reveals that the maximum spectral shift of the notch dip can be tuned up to 50% of transmission bandwidth for each passband of THz-ARRHW, by mechanically moving the Al plates relative to the PMMA claddings from infinity to d = 0mm. The spectral response of the THz ARRHW-based notch filter, obtained by THz-TDS as shown in Fig. 3(a), reveals that the continuous frequency shift phenomenon, which can be remotely controlled using a metal plate, under TE polarization. As shown in Fig. 3(a), the measured maximum rejection depth exceeds 20dB with a linewidth as narrow as 6GHz at a frequency of 0.194THz when d = 0.54mm. A deeper rejection could be achieved by transmission of a longer waveguide.

In the case of t=1.42mm, the measured and simulated frequency shifts of the 1^st~4^th-order dip frequencies (0.084, 0.171, 0.257, and 0.343THz) as the cladding-metal spacing d increased from 0 to 2.5mm are illustrated in Fig. 4(a) and 4(b). Both the measured and simulated results indicated that the spectral blueshift of the notch dip decreased nonlinearly as d increased, and are in good agreement with each other. The measured maximum frequency shift in the THz ARRHW-based filter with 1.42mm-thick PMMA slab claddings is 47.4GHz, which is about 50% of its transmission bandwidth (~86GHz). As shown in Fig. 4, the decrease in the frequency shift is caused by the reduced effect of the metal plate on the cladding mode of the THz-ARRHW at large d. Additionally, the spectral shift is larger for the lower-order notch-frequency at a given d, as shown in Fig. 4, indicating the better remote-controllability of the evanescent cladding mode at the low-order notch-frequency using the metal plate. The frequency tuning sensitivity is defined as Δf/Δd, where Δf and Δd represent the frequency shift of the notch dip and the variation in d. The frequency tuning sensitivity of the filter with t=1.42mm is 36, 44, 58, and 99 GHz/mm for m=1~4, respectively. The sensitivity increases with the order of the notch dip because the higher-order notch-frequencies have shorter field-decay distances outside the cladding layers. Therefore, notch-frequency tuning is effective only at low d or Δd to achieve a frequency tuning range of 50% of the bandwidth, corresponding to a 0.5π-phase-difference in the PMMA cladding.

 

Fig. 4 (a) Measured and (b) theoretical frequency shifts, Δf, of notch dips with various spacings d. The zero frequency shifts for TM polarization are shown in the case of t=1.42mm at 0.171THz.

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The spectral shift decreased with d is also observed in the case of t=1mm for m=1 notch dip shown in Fig. 4. In this experiment, a measured maximum dynamic notch-frequency tuning range and tuning sensitivity of 60GHz and 115GHz/mm at m=2 were both achieved using the THz-ARRHW-based filter with a dielectric cladding thickness t=1mm, because its spectral-dip period (or transmission bandwidth~120GHz) was larger than that of the waveguide-filter with t=1.42mm. Theoretically, the increase of the transmission bandwidth which is inversely proportional to the cladding thickness t [9] will increase the spectral tuning range.

We also examined the TM polarized excitation, whose measured spectral shift is almost zero, and it doesn’t change with d as shown in Fig. 4(a) and 4(b). This is because placing a metal plate outside the cladding layer alters the cutoff properties of the cladding modes [14,15]. Therefore, the notch-dips positions of the TE and TM waves become increasingly different between the two orthogonal polarizations as d varies. In fact, the different cutoff shifts of TE and TM waves, caused by a coated thin metal layer, are also observed in the optical regime [14,15]. Therefore, the spectral tunability only occurred in TE polarization which is selected for the frequency-tunable THz notch filter application.

4. Conclusion

In conclusion, we have shown a dynamic tunable notch filter based on a planar ARRHW in the THz frequency range. The continuous spectral tuning of the notch dip has been experimentally demonstrated by mechanically changing the spacing between dielectric and metal plates, and the mechanism is confirmed in FDFD simulations due to the increased phase-change in the dielectric-slab remotely driven by the metal plate. The spectral tuning scheme could be extended to other electromagnetic ranges as well. The integrated waveguide-based device has the advantages of low loss, broad frequency tuning range for THz pulses, strong light-confinement [9], efficient connection with other THz waveguides [9], and remote-controlled capability, which could be potentially applied to various terahertz applications.