1. Introduction

Filters are used throughout the electromagnetic (EM) spectrum for applications such as noise reduction, (de)multiplexing, and signal processing [1,2]. Filter design is a well established field for the electrical [3] and optical [4] frequencies. Within the terahertz (THz) gap (0.1-10 THz), filter design has primarily focused on THz-bulk optical components which are used with radiated waves commonly associated with THz-time domain spectroscopy (TDS) [5]. While these THz-bulk optical filters are useful, they do not integrate with miniaturized planar guided wave transmission lines (TLs) such as the coplanar striplines (CPS) and coplanar waveguides (CPW) [6–8].

Microwave filter synthesis is applicable at THz frequencies; however, current literature is lacking validating experiments. This gap in literature likely originates from the difficulty associated with performing experiments at THz frequencies. To the authors knowledge, there are three main methods for characterizing a device-under-test (DUT) at frequencies above 1 THz while remaining inside the THz gap. First, electronic vector network analyzers (VNAs) are typically limited to less than 100 GHz, but this range can be increased using extender modules up-to 1.5 THz [9–12]. This method is attractive because it uses techniques that are commonplace in microwave engineering and does not require the use of photonics. However, the rectangular feedlines are dispersive and band-limited, thus many extension modules (costly) are required to perform broadband measurements. Next, THz optics (free-space radiation) can be used to to perform investigation of a DUT [13–15]. The source of THz radiation could be a photoconductive antenna or mixer, quantum cascade laser, free-electron laser, etc. [16]. The detector could be another photoconductive antenna, electro-optic crystal (ZnTe), Golay cell, bolometer, etc. [17]. THz optics provides valuable information about the DUT, but experiments are adversely impacted by field coupling errors which can be difficult to manage depending on the feedline geometry. Lastly, planar transmission lines (TLs) can be integrated with an transmitter and receiver used to investigate a DUT [18–22]. Typically these structures are integrated into a CPS or CPW TL with an shunt or series photoconductive switch. There are some key benefits using this method; namely, the structure is inherently compatible with planar structures, the propagating mode is quasi-TEM which does not exhibit significant dispersion, and the overall system cost is relatively inexpensive. In this work we investigate filters using photoconductive switches integrated with CPS TLs. Currently, this combination allows for characterization of DUTs up-to 3 THz [22].

In previous works, planar filter demonstrations at THz frequencies do not perform network filter synthesis, that is, selecting the filter geometry to obtain a specific transfer function [23]. Instead, authors perform filter analysis which generally involves designing a periodic device [21] or metastructure [22,24–27], then confirming the transmission and reflection characteristics. While filter analysis is acceptable, it is generally advantageous to begin the design process by specifying targets such as cut-off frequency, minimal pass-band ripple, phase response, or roll-off rates. Here, we aim to demonstrate that microwave network synthesis filter design methods are valid at THz frequencies for planar structures. We note that many others have performed filter synthesis at THz frequencies using non-planar rectangular waveguides [28–30]. These non-planar filters are more common because they can be directly interfaced with a VNA equipped with extension modules. These filters are typically limited to operation as a band-pass filter due to the nature of wave propagation in a rectangular waveguide. We emphasize that the presented planar network synthesis filter utilizes the quasi-TEM mode and can be designed as a low-pass, high-pass, band-pass, or band-stop filter. A Bessel configuration has been selected for this proof-of-concept because it has desirable characteristics for pulsed THz systems. The linear phase response results in minimal pulse distortion which ensures the transmitted pulse is not significantly broadened. Reduction of pulse broadening improves the systems performance by reducing the impact of reflections and interference of the signal at the receiver which ultimately affects the spectral resolution.

We note that it is not straightforward to characterize devices at THz frequencies due to limitations such as source and detector availability and signal loss from potential substrate radiation. We have had success using our THz system-on-chip (TSoC) platform that uses planar CPS TLs on a thin Si$_3$N$_4$ substrate to overcome these challenges [31]. This methodology enables device characterization from DC to frequencies beyond 3 THz and is compatible with several planar TL configurations. In this work, we integrate a synthesized Bessel stepped-impedance low-pass filters (LPF) into a CPS TL. Other TL configurations (i.e. CPW, slotline, etc.) are equally viable; however, the CPS configuration is best suited to work with photoconductive switches as a sliding contact source and detector [6].

The novelty of this work can be summarized as the first demonstration of an THz integrated planar guided-wave all-pole filter (Bessel) using network filter synthesis using methods adopted from microwave engineering. We note that we have selected a common filter topology (stepped-impedance LPF) for this proof-of-concept verification at THz frequencies.

2. Design

In this work we implement and test several linear-phase stepped-impedance low-pass filters on the TSoC. This filter consists of alternating sections of low and high characteristic impedance of varying lengths which depending on the specific filter configuration (Butterworth, Bessel, Chebyshev, etc.). Figure 1 illustrates this concept. Here, we focus on the Bessel filter because of the short physical length and minimal pulse distortion characteristics.

 

Fig. 1. Stepped Impedance Filter

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Figure 2 illustrates cross section of a CPS TL on a thin substrate. The conductor width, separation, thickness, and conductivity are given by $W$, $S$, $T = 200$ nm, and $\sigma _c = 4.1\times 10^7$ S/m, respectively. The selection of $W$ and $S$ is discussed below. The substrate thickness, relative permittivity, and loss tangent are given by $H=1\mu m$, $\varepsilon _r = 7.6$, and tan $\delta _e = 0.0056$, respectively [32].

 

Fig. 2. Coplanar strip transmission cross section

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We are interested in the systematic design and experimental results of a planar low-pass Bessel filter which has a uniquely high cut-off frequency ($f_c > 500$ GHz) . This can be demonstrated by fabrication on a thin substrate. The design procedure consists of specifying the desired cut-off frequency ($f_c$) and filter order ($N$), then selecting the appropriate feedline impedance ($Z_0$), low impedance ($Z_L$), and high impedance ($Z_H$), then calculating the section lengths ($l_n$).

In this work, we select $f_c = 0.8$ THz and fabricate 3rd, 4th, and 5th order filters ($N$ = 3, 4, 5). Figure 3 illustrates the overall structure and the three different filters. The manufacturing procedure consisted of depositing a 1 µm layer of Si$_3$N$_4$ onto a 500 µm thick Silicon wafer then etching regions where THz bandwidth signals propagates. This process results in a 1 µm thick Si$_3$N$_4$ substrate suspended in air which is supported on the edges by the Silicon frame. Next, the conductors were placed using mask alignment physical vapour deposition (Ti/Au, 10/200 nm). Lastly, the photoconductive switches (PCSs) were aligned with the conductors using a micromanipulator and bonded to the surface using Van der Waals bonding [33,34].

 

Fig. 3. Microscope images of the TSoC structure with integrated filters. $V_B$ is the bias voltage with respect to ground (GND).

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The feedline impedance, $Z_0$, was selected to correspond to a low loss ($\alpha \approx$ 0.8 dB/mm at $\approx$800 GHz [21]) configuration which occurs when $S_0 = 70 \mu m$ and $W_0 = 45 \mu m$. For a stepped impedance LPF, it is desired to maximize the $Z_H/Z_L$ ratio. Note that selection of $Z_L$ and $Z_H$ are subject to limitations. Also, we opted to keep the conductor center spacing constant ($S$+$W$=const.) throughout the filter length. Structures must have dimensions larger than 2 $\mu$m because of our photolithography resolution. At the upper end, given that we selected $S_0 = 70 \mu m$ and $W_0 = 45 \mu m$, this implies $S+W=115\mu m$ and that $2\mu m<S_{L,H}<113\mu m$ and $2\mu m<W_{L,H}<113\mu m$.

In the past work [31], we found that structures with $W=10 \mu m$ behave well with acceptable resistive loss. Thus, for this work, we selected our high impedance sections to have $W_H = 10 \mu m$ and $S_H = 105 \mu m$. For the low impedance sections, dielectric breakdown must be considered because the CPS TL also functions to DC bias the transmitting photoconductive switch. To ensure proper DC biasing, $S_L$ should be larger than $S$ at the transmitter ($S_{Tx} = 10 \mu m$). For this work, we have selected $S_L = 15 \mu m$ and $W_L = 100 \mu m$.

Next we must obtain $Z_0$, $Z_H$, and $Z_L$ which requires the use of full-wave simulations to obtain the impedance at the cut-off frequency ($f_c$ = 0.8 THz). Using ANSYS HFSS, we find $Z_0 = 234 \Omega$, $Z_L = 131 \Omega$, and $Z_H = 362 \Omega$. We note that it is possible to use a quasi-static analytic models [35] to approximate these the characteristic impedances, but the frequency-dependence degrades the accuracy, for example, we find the quasi-static characteristic impedances to be $Z_0^{qs} = 264 \Omega$, $Z_L^{qs} = 128 \Omega$, and $Z_H^{qs} = 470 \Omega$ which are not representative of the characteristic impedances at 0.8 THz.

Next we calculate the lengths of the individual sections. This is accomplished using well known methods [1]; we will quickly review the procedure here. Alternating low-impedance and high-impedance sections behave like alternating series inductors and shunt capacitors in a ladder circuit which exhibits low-pass behavior. The length of the individual sections are calculated using:

Table 1. $g_n$ for maximally flat Time Delay LPF prototype [1]

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Table 2. Section lengths for filters

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3. Experiment

To characterize the filters we use a method similar to our previous work [22]. The experiment (Fig. 4) consists of a modified THz-time domain spectroscopy (TDS) system which requires the use of electrical and optical components.

 

Fig. 4. Simplified experimental setup.

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The transmitter is a thin (1.5 $\mu$m) DC-biased (24V) PCS made of low-temperature grown gallium arsenide (LT-GaAs) that is Van der Waals (VDW) bonded to CPS TLs. A sub-picosecond (THz-bandwidth) electrical pulse is generated by illuminating the transmitter PCS with an 80 femtosecond (10 mW average) optical pulse from a mode-locked fiber laser. The electrical pulse propagates along the CPS TL and through the filters, or device-under-test (DUT), prior to arriving at the receiver. The receiver is another thin LT-GaAs PCS which is partially isolated from the transmitter circuit using a DC block. The receiver PCS is illuminated by the same optical pulse from the same mode-locked fiber laser, however, the pulse arrival time is made variable by the use of a mechanical delay line. Translation of the mechanical delay line reconstructs the transmitted signal which is given by the convolution of the incident electrical signal and receiver photoconductance which is measured by a lock-in amplifier (LIA) referenced to an optical chopper which modulates the optical beam in the transmitter path.

4. Results and discussion

Figure 5 plots the normalized experimental temporal and spectral responses for the filters illustrated in Fig. 3. The temporal response illustrates minimal pulse distortion which is consistent with the linear phase response of the designed filters. This property is desired in a transient system because the ringing associated with a non-linear phase response can adversely impact the spectral resolution. The spectral response is obtained by applying the discrete Fourier transform to the temporal response. Recognizing that finite duration transient pulses do not have a flat spectral response, we expect an inherent roll-off. This concept is illustrated by the dotted lines in Fig. 5. It is seen that the spectral response experiences a change of slope near the designed cut-off frequency at 0.8 THz. This effect is illustrated by the dashed lines. The exponential coefficients for the dotted and dashed lines are noted in the legend of Fig. 5. The increasing difference between the exponential coefficients for increasing filter order is expected since the higher order filters have a larger roll-off rate. Lastly, we note that any minor reflections which may occur between the receiver and other discontinuities are removed by windowing of the temporal response.

 

Fig. 5. Normalized experimental results for the N=3,4,5 Bessel filters.

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5. Conclusion

In this work we have designed, fabricated, and tested several integrated planar stepped-impedance low-pass Bessel filters for THz applications. Characterization at THz frequencies was enabled by the use of the TSoC platform. We found that the experimental results align well with theory which illustrates the great potential for further experiment and developing other network synthesis filters at THz frequencies. To the authors knowledge, this work demonstrates the first time a guided-wave planar filter designed using network synthesis has been demonstrated in the THz gap.