A Photonic Spectrum Analyzer for Waveguide-Coupled Sources in the Terahertz Range

Signals in the terahertz range are mainly wireless, waveguide-bound or on-chip signals. To measure their spectral power, linewidth and harmonics, usually spectrum analyzers are used. Here we present a photonic spectrum analyzer for waveguide-bound signals for the frequency range from 450 GHz to 1.05 THz with the possibility to extend its operation to on-chip signals. Therefore, a photonically generated local oscillator frequency is used to downconvert the signal under test within a photoconductor. A Vivaldi antenna feeds the signal from a dielectric waveguide to the photoconductor. This allows the measurement of any signal that can be transported via a dielectric waveguide. We show details on the transition from a rectangular metallic hollow waveguide to a dielectric waveguide and spectral measurements of a rectangular metallic hollow waveguide source. The same transition can also be used to attach metallic waveguide-coupled ground-source-ground probes in order to characterize on-chip sources.


I. INTRODUCTION
W ITH rising interest in applications at Terahertz (THz) frequencies, reliable, versatile and affordable THz measurement equipment becomes more and more important. To date, frequency-extended microwave electronic measurement equipment, like spectrum analyzers (SAs) or vector network analyzers (VNAs), dominates the market. Extender modules are usually connected with metallic hollow waveguides (MHWGs) [1] limited to single-mode operation with a bandwidth of at best 50% of the center frequency. In order to cover a larger spectrum, e.g. from 100 GHz to 1 THz at least six extender modules are needed [2], [3]. Each band must be individually aligned and calibrated. The higher the THz frequency, the (exponentially) more expensive the extender will be.
With a photonically generated local oscillator (LO) and a photoconductive antenna (PCA) employed as a mixer, we have shown that a single setup is able to measure the full range from Manuscript  below 100 GHz to 1 THz at the example of a free-space photonic spectrum analyzer (PSA) [4] and a free-space photonic vector network analyzer [5]. The LO was generated by the difference frequency of two frequency-adjustable continuous-wave, distributed feedback laser diodes. So far, the photonic setup employed logarithmic-periodic antennas and a silicon lens, limiting measurements to free-space coupled sources under test. Many THz sources, in particular electronic ones, are frequently on-chip or mounted in a MHWG [6], [7] therefore requiring on-chip or in-waveguide measurement capabilities. In this paper, we demonstrate a PSA using a planar PCA, enabling the measurement of waveguide-bound signals. We verify this by the exemplary characterization of a WR2.2-coupled VNA head. For this we discuss the transition from the photonic circuit to a MHWG in detail. The very same transition can also be employed for characterization of on-chip sources via MHWG-coupled, commercially available ground-signal-ground (GSG) cascade probes.

A. Photonic Spectrum Analyzer
The PSA consists of two frequency-adjustable distributed feedback (DFB) laser diodes, a PCA, a trans-impedance amplifier (TIA) and an acquisition card (ACQC) as illustrated in Fig. 1. The PSA mixes the signal under test (SUT) with the beat signal of the two lasers within the PCA [4]. This results in an intermediate frequency signal whose spectral power at or around the laser beat frequency is obtained after filtering and squaring. Sweeping the beat signal frequency and simultaneously measuring the IF signal creates a frequency spectrum of the SUT. The difference to the PSA version in [4] is the PCA. The logarithmic-periodic antenna and the silicon lens are replaced by a broadband planar end-fire Vivaldi antenna (VA) [8], similar to the one shown in coupled to a dielectric waveguide [9], [10]. Both are designed to enable planar PSAs and photonic VNAs and operate between 450 GHz and 1.05 THz [9], [10], [11]. The dielectric waveguide is a planar rectangular waveguide consisting of highly resistive float zone silicon as this offers a low loss material with a high refractive index and a good surface roughness control. The implemented Si waveguides have a size of 200 μm × 50 μm, an attenuation of 0.1 dB/cm and support bending radii down to 2 mm [9].

B. Dielectric to Metallic Hollow Waveguide Transition
Generalov et al. [12] demonstrated a low loss tapered dielectric rod waveguide antenna transition coupling to the T E 10 mode typically used in MHWGs. The T E 10 mode within the MHWG couples into the HE 11 mode within the dielectric rod waveguide antenna, i.e. the fundamental mode of the dielectric waveguide [13]. In order to estimate the coupling losses, the transition from a WR2.2 MHWG to a highly resistive float zone silicon (Si) waveguide using a taper length of 1 mm is simulated with CST microwave studio. Fig. 2 shows the setup where the full length of the taper is put inside the MHWG. The Si waveguide is placed partially onto a high density polyethylene (HDPE) carrier in order to mechanically stabilize the waveguide. The simulations are done only taking the aforementioned fundamental modes into account. Three different scenarios are simulated. First the transition from a WR2.2 MHWG to a Si waveguide with the aforementioned taper fully inside the WR2.2 waveguide. This is done for the supported frequencies of the WR2.2 waveguide, namely between 330 GHz and 500 GHz. Secondly, the same transition using a Si waveguide without taper, having the Si waveguide inserted 1 mm into the WR2.2 waveguide. As tapers get smaller towards their tips, it is possible to also use them for higher frequency MHWGs [14]. Therefore, thirdly, the transition from a WR1.5 MHWG (supported frequencies 500 GHz to 750 GHz) to a Si waveguide using the same taper is simulated. Since this MHWG features an inner cross section of 380 μm × 190 μm the taper is only inserted by 0.8 mm.
The VA, due to its physical size, in conjunction with the Si waveguide have a lower cut-off frequency of approximately 450 GHz [9] while the WR2.2 MHWG is used starting from 330 GHz. As frequencies below 450 GHz will not be detected efficiently, they are not discussed further. For the frequency range from 450 GHz to 500 GHz the simulation indicates transmission from the MHWG to the Si waveguide with taper being better than −1.3 dB Fig. 3. For the frequency range of the WR1.5 MHWG the simulated results also show better than −1.3 dB transmission. For the WR2.2 MHWG transition without taper the results drop down to values between −3 dB and −1.6 dB for the frequencies above 450 GHz. As the difference between the simulations with and without taper for the WR2.2 MHWG are minor, the simpler and easier to manufacture version without any taper will be used throughout this paper. In a first measurement the Si waveguide is inserted by approximately 1 mm into the MHWG in agreement with the simulation. The VNA with extender frequency is set to 480 GHz.   GHz, pointing to a miscalibration of the frequency of possibly both the PSA LO and the VNA with a total offset of 900 MHz. By recalibrating the look-up tables of the LO, we expect the offset to become less than 25 MHz. Please note that the Y-axis is given in units of V 2 , which is directly proportional to power. Unfortunately, no power calibration could be conducted as none of our available power meter allow for reliable power measurements within the WR2.2 MHWG. Previously [4], we determined the displayed average noise power of the PSA to be −100 dB/Hz at 500 GHz.

III. RESULTS
The signal shows an average noise level (ANL) that is more than ten times larger than the noise standard deviation σ N . The ANL consists not only of a noise offset that is generated from squaring the signal but also of any remaining offset from the IF circuit. The exact reasons for these offsets are not known to date but their removal will be part of future work. Nonetheless, σ N limits securely identifying the signal under test. To achieve this consistently, and even if standing waves are present, the limit of detection is set to five times σ N above the average noise level (ANL): AN L + 5 σ N . In order to compare the results from In order to examine the frequency response of the SUT and PSA combination, the frequency in the extender is set to 500 GHz and decreased by 10 GHz after each measurement until the SUT is below the limit of detection. For each of the measurements the frequency range of the PSA is set to match the SUT while keeping all of the other settings the same. Fig.  6 displays the detectability of the signal at different frequencies. The measured results show the highest detectability at a frequency of 470 GHz. Signals at and below 450 GHz are below the limit of detection while frequencies above 500 GHz are not supported by the SUT. The results shown in Fig. 6 are a combined outcome of the SUT power, the transition from the MHWG to the Si waveguide, the transition to the PCA and the responsivity of the PCA. Therefore, it is not possible to directly compare the measured results with the simulation results Fig. 3.
In order to determine the optimum insertion depth of the Si waveguide into the WR2.2 MHWG, the Si waveguide is first positioned 2.1 mm inside the waveguide and then pulled out in 200 μm steps. At each of the positions a spectrum of the SUT is taken, using the same settings and the same VNA frequency as the first measurement. In Fig. 7 the position Zero marks where the end facet of the silicon waveguide is in the plane of the MHWG port. Negative positions refer to increasing the distance between the Si waveguide end facet and the MHWG and positive values mean that it is moved inside the MHWG. The position Zero was visually determined with a microscope resulting in an error bar of 100 μm. The red line marks the limit of detection of 5 σ. This limit allows to still securely identify the signal, even when standing waves are present.
The 5 σ level is just reached at Zero. The further the Siwaveguide is inserted into the MHWG, the larger the (S − AN L)/σ N gets, with a maximum at 1.7 mm.

IV. CONCLUSION
We have demonstrated a photonic spectrum analyzer with a low-loss interface to metallic hollow waveguides. The transition is based on a rectangular, dielectric silicon waveguide connected to a Vivaldi-antenna with an ErAs:InGaAs photoconductor as mixer. The WR2.2 transition can be realized as a tapered dielectric rod waveguide or by a terminated straight end facet. The transition can serve to investigate WR-coupled devices by the photonic spectrum analyzer or to serve as an on-chip transition by using a WR-coupled GSG probe being the conventional means to interface circuits. Further applications are implementations in photonic vector network analyzers where they would serve as an interface to WR-coupled devices under test. If some losses are acceptable, the same dielectric waveguide can be used for several metallic hollow waveguide bands as demonstrated already in [15].