Broadband Terahertz Photonic Integrated Circuit with Integrated Active Photonic Devices

: Present-day photonic terahertz (100 GHz–10 THz) systems offer dynamic ranges beyond 100 dB and frequency coverage beyond 4 THz. They yet predominantly employ free-space Terahertz propagation, lacking integration depth and miniaturisation capabilities without sacriﬁcing their extreme frequency coverage. In this work, we present a high resistivity silicon-on-insulator-based multimodal waveguide topology including active components (e.g., THz receivers) as well as passive components (couplers/splitters, bends, resonators) investigated over a frequency range of 0.5–1.6 THz. The waveguides have a single mode bandwidth between 0.5–0.75 THz; however, above 1 THz, these waveguides can be operated in the overmoded regime offering lower loss than com-monly implemented hollow metal waveguides, operated in the fundamental mode. Supported by quartz and polyethylene substrates, the platform for Terahertz photonic integrated circuits (Tera-PICs) is mechanically stable and easily integrable. Additionally, we demonstrate several key components for Tera-PICs: low loss bends with radii ∼ 2 mm, a Vivaldi antenna-based efﬁcient near-ﬁeld coupling to active devices, a 3-dB splitter and a ﬁlter based on a whispering gallery mode resonator.


Introduction
In the past few decades, huge advances have been made in creating sources and detectors working to bridge the so-called THz gap (0.1-10 THz). Currently available table-top, non-cryogenic THz sources can generate up to tens of milliwatts of power at the lower end of the THz range [1][2][3][4]. Combined with highly sensitive THz receivers, both photonic and electronic THz systems provide dynamic ranges of 120-140 dB [5,6]. Similar to integrated circuits in the RF and microwave domain [7,8] or photonic integrated circuits at the telecom bands in the near infrared there exist integrated terahertz systems. These include electronic systems based on fundamental oscillators at the lower end of the terahertz range [9] or frequency multiplier-based systems [6], both frequently using hollow metallic waveguides with microstrip transitions to active elements, as well as dielectric waveguide-based systems [10][11][12]. While the waveguide concepts generally allow for large bandwidths, the lack of broadband characterization tools as well as comparatively narrowband transitions to active elements typically restrict the operational bandwidth to typically not more than 10-50% of the centre frequency.
To date, the most powerful systems in terms of dynamic range are electronic systems based on hollow metal waveguides, at least below ∼1 THz. Their success is based on the comparatively low loss as compared to coplanar waveguides and microstrip circuitry and well engineered transitions to active elements with typical losses lower than 1 dB [13]. These transitions are necessary as semiconductor-based active components such as Schottky diodes still have to be fabricated in a microstrip circuitry or similar [14]. The down side of these transitions is the requirement of strongly wavelength-dependent (mode) field matching techniques, such as positioning the transition at a local field maximum, and have an appreciable leakage-free bandwidth. We also show transitions to active elements integrated in a planar dielectric waveguide. The same transitions may be exploited as on-chip GS connections to THz circuits in the future. The support by rigid substrates ascertains mechanical rigidity and stability.

Waveguide Architecture
The waveguide architecture consists of a rectangular HRFZ-Si waveguide mounted on a low loss, low refractive index substrate as illustrated in Figure 1a). Dielectric waveguides theoretically offer infinite single-mode bandwidth; however a non-homogeneous surrounding media limits its lowest operating frequency [39]. The field of a selected mode experiences not only the refractive index of the rectangular waveguide core n WG but also that of the surrounding media due to the evanescent field components of the mode. This results in an effective refractive index, composed of an integral of the local refractive indices, weighted by the local power across the mode profile. Unlike metallic waveguides, the non-homogeneous waveguide topology as shown in Figure 1a,b, where air (n air ≈ 1) and a dielectric medium (n diel ) is situated above and below the waveguide, respectively, (n air < n diel < n WG ), a lower cut-off frequency is introduced when the evanescent field in the air is sufficiently large to cause the effective refractive index to drop below the value of the substrate n diel . This causes the wave to leak into the substrate and is not guided further. Figure 1c) shows the simulated propagation constant (β) for the propagating modes for such a designed waveguide. At f ≤ 0.5 THz, propagation constant of the fundamental mode HE x 11 is lower than that of bulk quartz, causing a part of the wave to leak towards the quartz substrate. The simulation snapshots in the inset concur with this behaviour. A polyethylene substrate ( r,PE = 2.4) reduces the lower 3-dB cut-off frequency to 0.411 THz. As frequency increases, the wave becomes strongly confined within the HRFZ-Si structure. Hence, the substrate leakage decreases and, as a result, the transmission losses depend only on material properties. and HE x 31 modes, respectively. Simulation snapshots in the inset shows waves leaking into the substrate for f THz ≤ 0.5 THz. The black rectangular outline represents the HRFZ-Si waveguide. The dielectric below is quartz (n = 2.13), the dielectric above is air (n = 1).
Figure 1c also shows that higher order modes HE x 21 and HE x 31 start propagating above 0.75 THz and 0.81 THz, respectively. Thus, like its metallic counterpart, a dielectric waveguide operating between 0.5-2 THz supports multiple modes at the higher frequency end. We show in the upcoming sections that with appropriate bend designs and controlled excitation, the dielectric waveguides can be practically operated in its fundamental mode even above its 3-dB dispersion bandwidth of 0.5-0.75 THz, without loss of functionality of integrated components such as splitters/combiners and filters. The presented waveguides are planar and hence, any modal perturbation in the horizontal dimension can be controlled by lateral structural modifications, which becomes much more difficult for the vertical dimension with planar processing techniques. Thus, we designed the waveguide to support multiple modes along its width, but only a single mode along its height up to a frequency of 2 THz, resulting in the rectangular structure depicted in Figure 1a). The waveguides characterised in this work are 200 µm wide and 50 µm tall.

Fabrication and Measurement Setup
Rectangular waveguide structures are etched out of a 50 µm thick HRFZ-Si wafer, glued on a 525 µm thick quartz 2 inch quarter-wafer with a thin layer of superglue. The waveguides are fabricated either by deep reactive ion etching (DRIE) of a lithographically defined hard mask (hard-baked AZ ® nLof 2035) on the silicon wafer or by laser ablation. DRIE employs a Bosch Process, which involves repetitive deposition and etching cycles using inductively coupled plasmas of C 4 F 8 and SF 6 . While processing, the silicon wafer is cooled to −10 • C from below, which necessitates the substrate to have high thermal conductivity. For laser ablation, the substrate material must feature a high melting point. Hence, both the processes were conducted using crystalline quartz as substrate. The main difference between waveguides produced by DRIE and laser ablation is the roughness of their side walls. In DRIE, the quality of the photolithographic layer determines the sidewall roughness, which is a few hundreds of nanometres for our case, whereas in ablation processes, wall roughness can be reduced to as low as tens of nanometres. Additionally, it is more difficult to maintain the stability of process parameters in DRIE than in laser ablation. However, DRIE processing of a 50 µm silicon quarter-wafer takes only 20-25 min to complete, and is chosen as the preferred method of fabrication. In comparison, laser ablation of a similar silicon wafer requires ∼7 h. After processing, some waveguide structures were transferred onto a HDPE substrate with lower dielectric constant and the former quartz substrate was removed. Figure 2a shows the schematic of the setup. It consists of a Tx module with a p-i-n diode-based THz transmitter (Fraunhofer Heinrich Hertz Institute/Toptica photonics) followed by a parabolic mirror in order to achieve a collimated terahertz beam. A TPX (Polymethylpentene) lens (L1) couples the signal to the waveguide that features a 90 • bend in order to exclude line-of-sight coupling. A second TPX lens (L2) couples the power to a Rx module, consisting of another parabolic mirror and a silicon lens-coupled ErAs:InGaAs photoconductive THz receiver with logarithmic-periodic antenna (Rx LP ) developed inhouse [40]. The transmission coefficient is calculated by referencing to a measurement without waveguide and Tx and Rx LP modules facing each other with both TPX lenses in between.

Transmission Losses through Straight Sections
The total transmission loss is composed of two categories, namely losses proportional to the length of waveguides occurring at the straight sections and losses originating at waveguide bends or discontinuities due to radiation and mode conversion. To estimate losses of the first kind, losses introduced by the bends are removed by comparing waveguides of different lengths but subsets of same radius of curvature (ROC), similar to the cut back technique used for optical fibres, i.e., for two waveguides with same ROC but of lengths l 1 and l 2 , the power attenuation coefficient (α pow ) is calculated as: where I 1 and I 2 are the measured current at the receiver, which are proportional to the incident terahertz field. Several waveguides with same bend radius but different lengths l WG between 15-35 mm are characterized. Furthermore, different waveguide bend radii between 1-11 mm were implemented with varying lengths of the straight sections. Figure 2b depicts the calculated average power attenuation coefficient with excellent agreement with the simulated values. Only below 0.47 THz, i.e., below the lower cut-off frequency where the waveguides lost their guiding properties, there is a noteworthy discrepancy. The transmission losses decrease from ≈8 dB/cm at 0.5 THz to ≈0.4 dB/cm at 0.65 THz. Above 0.9 THz, standing waves in the waveguides affect the data quality. A further plausible origin of these oscillations is inter-mode coupling between the fundamental and higher order modes. We show in simulations in Section 4 of the supplemental information that the power in the higher order modes is suppressed by at least 15 dB in the frequency range of interest. Furthermore, mode-inter-coupling and standing waves can be discriminated by investigating the time-domain traces of the measured data, as illustrated in Section 5 of the supplementary material. We therefore conclude that standing waves are the dominant origin of the oscillations. The measured absorption coefficient is larger than the simulated value of a HRFZ-Si waveguide placed on crystalline quartz, i.e., ≈0.13 dB/cm, due to the presence of a 5-9 µm layer of ethyl cyanoacrylate-based superglue ( r = 2.72, tan δ = 0.067 at 1 THz [41]) underneath the waveguides. Excess loss due to superglue, though not detrimental to the waveguide operation, can be easily avoided using other low-loss adhesives, such as BCB [12]. Dielectric waveguides are prone to dispersion as the effective mode permittivity of the guided mode increases with increasing frequency as a larger fraction of the wave is concentrated within the high index HRFZ-Si guide. The dispersion depends on the group velocity of the travelling wave [42]. The dispersion factor D is given by [43] ( where β = 2π f THz e f f r ( f THz )/c 0 is the propagation constant of the guided mode, ω is the angular frequency and c 0 is the speed of light in vacuum. Total dispersion for a HRFZ-Si waveguide of length l WG and the setup can be calculated from the phase of the detected THz field, where l FS is distance travelled by the THz wave in free-space with a propagation constant β 0 = 2π f THz /c 0 , φ ant is an additional phase induced by dispersive emitting and receiving antennas [44] and φ 0 is a constant. Similarly, the phase of the reference signal (Φ re f ) is where φ 0 is another arbitrary constant and the free space propagation length, l FS may differ from that of Equation (3). By subtracting the reference phase, Φ re f , from the phase with waveguide, Φ WG , removes the dispersion caused by the antennas, yielding Figure 3a,b show the measured average dispersion of the waveguides on quartz and HDPE substrates, respectively. The measured dispersion is of the same order of magnitude and shows the same frequency-dependent behaviour as the simulated ones for both cases, but feature strong standing wave patterns. We remark that the standing waves are present over the whole investigated frequency range and therefore cannot originate from mode beating as higher order modes cannot propagate at the lower end of the investigated frequency range. Chromatic dispersion of the presented waveguides limits their applicability in pulsed-THz setups. However, dispersion compensation techniques can be further employed, e.g., by etching slits into the waveguide (slotted waveguides) [45] or by introducing photonic-crystal structures [46], for extending their applicability in THz pulsed systems. In CW systems, dispersion effects can easily be removed by normalization to a reference measurement without any influence on the data quality.

Bends
Bends are essential waveguide structures, that are also an integral part of other passive components, such as splitters. Bend losses are caused by (i) radiative loss at lower frequencies, which is akin to substrate leakage, and (ii) mode conversion losses at higher frequencies. For case (i), the losses by a bend can be described by the conformal mapping technique that maps the bent structure with constant refractive index to a straight waveguide with spatially dependent refractive index [47], including the surrounding media. Conformal mapping is detailed in the Supplemental Materials. The main result is summarized in Figure 4a. The conformal-transformed refractive index of media increases exponentially outwards from the centre of the circular bend as shown in the inset of Figure 4a. The lower the frequency, the smaller the effective refractive index of the guided mode and the larger the evanescent field. At a certain distance away from the waveguide, the conformally mapped refractive index becomes larger than the effective refractive index of the guided mode, causing radiative losses as illustrated in Figure 4a for 0.6 THz. At higher frequencies, the mode concentrates more in the high index HRFZ-Si waveguide, resulting in larger effective refractive index of the guided mode and less extension of the evanescent fields. Consequently, the radiative losses decrease with increasing frequency [48] as demonstrated by the simulations for 0.8 and 1 THz.
For case (ii), mode conversion occurs as the power distribution of the guided mode increasingly shifts away from the waveguide centre with increasing frequency, as visible in the simulated power distribution for 1 THz in Figure 4a. This leads to mode mismatch at the transitions between straight and bent sections of the waveguide, which eventually leads to excitation of higher order modes at higher frequencies. These transition losses are inversely proportional to the square of the radius of curvature, ROC 2 [49]. Bends with decreasing ROC at intersections to straight waveguide sections [50] or bend-offsets [51] reduce these mode conversion losses while keeping the effective bend radius, i.e., the space required for a low-loss bend, almost unaffected.  In this work, we characterize waveguides with circular bends only in order to determine the minimum bend radius. Scattering losses, induced by surface roughness of the waveguides (<0.01λ THz digs/sleeks), are much smaller compared to the aforementioned propagation losses and are not considered in the analysis. We examine the total loss for three different waveguides of length l WG = 19.14 mm with bend radii of 1 (Q1), 2 (Q2), and 4 mm (Q4) on quartz. As the waveguides share the same length and transitions to free space, losses caused by the bends can be directly evaluated by comparing results from waveguides with different bend radii (Explicit calculation of bend losses per radian or per 90 • turn requires a comparison of waveguides with a single bend and multiple bends. Due to the lack of structures with multiple bends, we opted for comparing structures with one bend each but different radius of curvature.). To remove losses caused by the straight sections and the coupling transitions from the waveguides to free space, the total loss data are normalized to the data of straight waveguide on HDPE substrate of same length (The straight waveguide data are calculated from a measured waveguide on HDPE, corrected by the simulated reduction in transmission efficiency between a straight and bent waveguide of same length.), as depicted in Figure 4b). Additionally, a longer waveguide (Q5, l WG = 22.71 mm) with larger ROC = 5 mm is also plotted. We remark that below 0.5 THz the data quality for the waveguides on quartz suffers from increased loss by inand out-coupling transitions.
Among the waveguides with quartz substrate, we observe that the waveguide with ROC = 1 mm (Q1) shows 3-5 dB higher loss than the rest over the whole frequency range, whereas waveguides with ROC ≥ 2 mm have similar losses between 0.55-0.9 THz indicating that the wave loses negligible power through radiation at the bend. At f THz > 0.9 THz, we see losses for the waveguide with ROC = 2 mm (Q2), increasing with frequency with respect to waveguides with larger bend radii, which indicates the onset of mode conversion losses in Q2. The early onset of these losses compared to the simulations can be explained by the non-idealities in Q2, such as roughness of the side walls (c.f. Figure 1b)) and presence of adhesives between HRFZ-Si waveguide and quartz substrate, along with presence standing waves. The 5 mm ROC bends, as well as waveguides with larger ROC up to 10 mm (not depicted) show similar losses as Q4, proving that bend losses are negligible at radii ≥4 mm up to at least 1.05 THz and according to simulations even beyond 1.6 THz. Larger ROCs will further extend the higher frequency limit of the waveguides. In addition, Figure 4b) also depicts a bend with ROC = 1 mm (H1) on a HDPE substrate. Two dominant features are visible: first, the lower cut-off frequency shifts to around 0.45 THz despite having four times lower ROC. Similar to the straight sections, the lower refractive index of HDPE reduces radiative losses, both towards the substrate as well as at bends. Second, the observed loss over the whole frequency range is reduced by 5-7 dB. The lower transmission losses are partly due to the reduced usage of superglue between the waveguide and HDPE substrate. Additionally, the fundamental mode has a larger mode field diameter for H1, which also improves the in-and out-coupling efficiency at the intersections to free space.

Transitions to Active Devices
A key challenge is the realization of low loss transitions to sources and receivers as well as to other circuits such as electronic integrated circuits. The HDPE substrate already considerably improves the coupling efficiency. Still, the coupling loss at two positions (inand out-coupling) totals to 18-26 dB over the whole frequency range from 0.4-1.05 THz. While for narrow band systems (bandwidths <50% of the centre frequency), the waveguide parameters do not change considerably allowing for close to perfect impedance-matching and mode field diameter matching with losses <1 dB [52], it is challenging to achieve matching for systems with a frequency coverage of several octaves. For instance, the mode field diameter becomes comparable to the size of the HRFZ-Si waveguide in the high frequency limit but extends considerably beyond at the low frequency end (c.f. Figure 4a), and, as a consequence, the wave velocity also shows strong frequency dependence. As opposed to narrowband circuits, a broadband topology cannot use any resonant elements, leading to necessary compromises between acceptable loss and achievable bandwidth.
An example of a broadband concept is the dielectric rod waveguide (DRW) antenna, basically a rectangular waveguide with a sharpened tip with a very small taper angle [53]. A DRW antenna is in principle compatible with the proposed topology; however, the optimum coupling position is again strongly frequency-dependent: the projection to the far field shows that high frequencies are emitted at the tip while low frequencies are emitted rather close to the base of the taper. This complicates in-coupling with fixed free space optics. For waveguides without transitions, the coupling losses using free space optics are high: For the presented waveguides, the vertical dimension of the waveguide extends only 50 µm with little evanescent field outside the HRFZ-Si at 1 THz (see Figure 4a, bottom). The Gaussian spot diameter of the free-space THz beam at the foci of TPX lenses is ≈1300 µm at 0.5 THz and ≈1000 µm at 1 THz. Thus, the waveguide cross-section is more than an order of magnitude smaller than the smallest beam diameter in the setup. To improve the coupling in horizontal direction to increase the coupling efficiency, waveguides are tapered-out at the input and output apertures to 1000 × 50 µm 2 . With the given technology, however, the vertical axis cannot be tapered, causing the previously mentioned total loss of 18-26 dB for two transitions, even for the waveguide on HDPE and 22-28 dB for the waveguides on quartz. Such large losses are not acceptable for high dynamic range systems.
A detailed description of free-space coupling losses is given in section Section 4 of the supplemental material.
To circumvent this issue, we implement a near field coupling scheme at the receiver using planar end-fire Vivaldi antennas (VAs). Additionally, using this scheme eliminates the necessity of using optics such as lenses, parabolic mirrors or bulky silicon lenses, currently used in table-top THz sources and receivers. Consequently, this eases integration and miniaturisation of THz setups essential for manufacturing broadband THz photonic integrated circuits (PICs). Figure 5 shows an exemplary design of such a semi-integrated system. Within the operation range, VAs are frequency-independent [54], which means their beam pattern and impedance theoretically remain unaltered with frequency. Hence, VAs are suitable for broadband operation and the operating frequency range can be controlled simply by scaling the antenna dimensions. The tapered antenna structure slowly transforms an incoupled wave to a guided wave which then couples to the active photoconductive element represented by the finger-like structure of the ErAs:InGaAs photoconductive material with a width of D2 = 10 µm and a thickness of 1.62 µm grown on a semi-insulating InP substrate. The finger electrodes are 1.5 µm wide, with a spacing of 2 µm. Further details on the material and a theoretical description of the receiving process can be found elsewhere [55]. The shown VA is a modification of antennas proposed by Abdullah et al. [56], where instead of having a superstrate atop the antenna, we thin the InP substrate supporting the active ErAs:InGaAs device [40] down to h = 32 µm to increase the antenna directivity in end-fire direction (θ = 90 • , φ = 0) and to reduce squinting into the high index InP substrate (n InP ≈ 3.48). A substrate thickness h fulfilling 0.005λ 0 ≤ (n InP − 1) × h ≤ 0.03λ 0 is desired for improved impedance matching between the antenna and the radiated THz wave at the point of radiation [57]. For h = 32 µm, this condition is not fulfilled over the whole wavelength range. At the shortest wavelength, h ≥ 0.11λ 0,min , however, the resulting reduced directivity can be compensated by increasing the surface current at the inner edges of the antenna blade [58] using slotted and circular corrugation structures. Additionally, metal directors further enhance the antenna performance and directivity at f THz > 0.9 THz. The Vivaldi antenna is mounted on HDPE and directly brought in contact with the HDPE-mounted HRFZ-Si waveguide as shown in Figure 5c. Figure 5d shows a simulation at 0.875 THz proving very little mode mismatch and thus excellent coupling efficiency. The vast majority of the incoming power from the waveguide becomes absorbed by the finger structure located at position A. An insignificant amount of power (<−20 dB), escapes the antenna and is absorbed in the contact pads.
The current designs are optimized with respect to the lower cut-off frequency of the waveguides (≈0.5 THz) and the estimated frequency coverage of the CW photomixing setup. Optimum dimensions of the VAs are obtained by CST simulations for an operational frequency range of 0.5-1.5 THz. The dimensions are D1 = 112.5 µm and D2 = 10 µm corresponding to the maximum and minimum desired half effective-wavelengths, respectively. The operational bandwidth can be easily increased by scaling D1 and D2 appropriately. The antenna consists of an ≈400 nm thick layer of Gold, with a Titanium adhesion layer. The VAs further feature extended metallic contacts behind the active element to extract the rectified THz current as shown in Figure 5a. The manufactured device is orders of magnitude smaller than commercially available state-of-the-Art THz lens-integrated receivers and is comparable in size to a strand of human hair as shown in Figure 5b.
To characterize the performance of the Vivaldi antenna, the receiver side of the waveguide setup shown in Figure 2a is replaced by the Vivaldi antenna as illustrated in Figure 5c. As we have no access to decent photomixer source material, we could not fabricate a VAcoupled source. Therefore, the source side of the setup is kept unaltered. For impedance matching reasons, a HDPE-mounted waveguide is used in conjunction with the HDPEmounted receiver VA, where the receiver InP substrate de facto becomes an extension of the waveguide with n Si = 3.417 ≈ n InP = 3.48.
To estimate the performance of the VA transition, Figure 6a shows the following plots for comparison: The bottommost plot (violet) shows the measured transmission losses through the waveguides using free space, lens-assisted coupling at both in-and out-coupling positions of a waveguide as illustrated in Figure 2a. The measured losses are about 22-26 dB over the whole operation band, in agreement with the previous findings. The middle (blue) line represents the setup with the Vivaldi-antenna receiver as shown in Figure 5c. Compared to the lens-coupled setup, the losses are 5-14 dB less between 0.4-1.05 THz with a peak improvement of 14 dB around 0.68 THz. The topmost plot (black) shows the simulated achievable coupling efficiency when VAs are used for both inand out-coupling to the waveguides. The plot shows a minimum insertion loss of ≈2 dB at 0.74 THz per VA-waveguide interface and a 3-dB bandwidth between 0.55-0.99 THz (relative bandwidth = 57.1%). The simulated coupling losses are however higher than the measured values in free-space and VA setup at frequencies above 1.2 THz, which indicates the necessity for further optimization of the VAs at the upper end of the operational band. Furthermore, simulations indicate that when a VA is implemented on the source side, the waveguide should support only one mode in the vertical dimension in order to prevent excitation of higher order modes. This imposes another limit on the upper cut-off frequency of about 2 THz for a 50 µm tall waveguide.  In summary, the VA features an improvement of the coupling efficiency of 5-14 dB above 0.4 THz per coupling position. Using VA at one coupling position extends the operational range of the demonstrated system with a waveguide-coupled detector and a lens-coupled commercial p-i-n diode source to 1.6 THz as shown in Figure 6b. We expect an increase of the operational bandwidth of the system to at least 2 THz if nearfield coupled devices are implemented at both the source and receiver side. The VA also shows a less pronounced roll-off than logarithmic-periodic or spiral antennas as the radiation resistance is smaller. Furthermore, there is no requirement for a silicon lens, simplifying and compacting the setup. Experimental findings also show reduced reflections by the VA antenna due to improved mode field diameter-and impedance matching, reducing the amplitude of undesired standing waves in the waveguide. By replacing the active element by a short transmission line with enforced end contacts a GS coupler to a metal-based electronic integrated circuit can be realised. This may enable future on-chip measurement systems such as photonic vector network analysers with operational bandwidths as demonstrated here.

Couplers
Power splitters and combiners are essential components for photonic circuits. Figure 7a shows a 3-dB coupler/splitter consisting of two symmetrically designed output arms, with sinusoidal and circular bends with 1 mm bend radii. The structure is fabricated on a quartz substrate. The splitter is characterized in the free-space setup (c.f. Figure 2a) between 0.45-1.05 THz. It shows an equal splitting ratio at a power level of 4.8-6 dB in its two arms, which is in excellent agreement with the simulation. Since, the coupler was designed with ROC < 4 mm, higher order modes are excited at frequencies <0.9 THz resulting in excess losses and an undulating transmission characteristics. The performance can thus be further improved by increasing the bend radii. The simulated isolation between the two output arms is >40 dB for frequencies >0.65 THz, and reaches a minimum of 32 dB at 0.582 THz.

Frequency-Selective Filter Example
A whispering gallery mode (WGM) resonator is measured between 0.45-0.65 THz with a VA receiver. The resonator structure is a 50 µm high silicon disk, matching the height of the waveguide, with a design radius of 400 µm. It is placed in direct contact with the straight section of a waveguide. Figure 7b shows the transmission coefficient, normalized to a reference measurement of the bare waveguide without the resonator. Resonance peaks in the measured and simulated data match excellently; however to a simulated resonator radius of 408 µm. The resonator has a free spectral range of around 45 GHz and the steepest resonance peak at 0.482 THz shows a quality factor of 38.9. The simulated quality factor is slightly lower than the measured value. These may have several causes, such as a slight misalignment (i.e., slight distance between WGM and waveguide), non-straight sidewall of the WGM, causing a small gap at the coupling position, or simply non-zero losses of all involved materials. We remark that for all modes, the coupling was under-critical as critical coupling cannot be achieved with the given waveguide width and considerably small amount of evanescent field in the horizontal direction. Resonators incorporated within the waveguides or non-planar WGM resonators [59] can serve as better alternatives. Attaching a second waveguide to the WGM results in an add drop filter for specific frequencies [60]. Multiple resonators with different mode spectra allow engineering wavelength division multiplexers [61].

Conclusions
We demonstrated broadband characterization of a dielectric waveguide architecture based on HRFZ-Si waveguides on crystalline quartz and HDPE substrates between 0.4-1.05 THz in a free-space setup. Waveguides on quartz substrates show a very low attenuation constant below 0.4 dB/cm between 0.65-0.9 THz. At higher frequencies, standing waves introduce measurement errors that only allow to provide an upper bound of about 1.7 dB/cm. The minimum bend radius for low loss circular curved sections is found to be larger than 2 mm, whereas 4 mm bends already show close to ideal performance. HDPE substrates reduce leakage and coupling losses as compared to quartz and decrease the lower cut-off frequency to ≈0.41 THz. The challenge of low loss transitions to sources, receivers and planar metallic waveguide-based components in general was addressed with end-fire Vivaldi antennas where we have demonstrated a reduction of the coupling losses compared to a free space transition by 5-14 dB per coupling position. Furthermore, the reduced losses increase the operation range of the waveguide-based homodyne THz system consisting of a waveguide-coupled VA detector and a commercial lens-coupled p-i-n diode source, from 0.5-1.6 THz, which is the largest reported operational bandwidth of such an integrated THz setup up until now. Further characterized components include a 3-dB splitter and a filter based on a whispering gallery mode resonator. The proposed waveguides and waveguide components will significantly facilitate development of miniaturized table-top broadband THz systems, such as photonic THz-VNAs and photonic spectrum analysers.