# Photonic-Assisted Scanning Receivers for Microwave Frequency Measurement
## 3 Experimental Results  
As a proof of concept, an experiment was conducted based on the setup depicted in Figure 1. The filter, which consists of two straight bus waveguides and a racetrack waveguide, was fabricated on a silicon-on-insulator (SOI) wafer via ePIXfab. The scanning electron microscope (SEM) image of this filter is shown in Figure 3a. The silicon core waveguides have a fixed height and width of 220 nm and 450 nm, respectively, and the coupling gap spacing between the bus waveguide and the racetrack ring resonator is designed to be about 620 nm to obtain a bus-to-ring cross power coupling coefficient of 0.0125. Additionally, the length of the straight sections and the bend radius of the curved sections of the racetrack ring resonator are designed to be 50 \(\upmu\)m and 100 \(\upmu\)m, respectively. The discrete spectral response of the optical filter, \(h(n)\), was measured by sweeping the optical carrier of the laser and measuring the power at filter output. The optical carrier was generated by a laser (Keysight 81960A, Santa Rosa, CA, USA) and was swept from 1546.6 nm to 1547.4 nm with a constant step of 0.1 pm, thus generating 8000 effective points recorded by an optical power meter (Keysight N7744A, Santa Rosa, CA, USA). Figure 3b shows the measured output power, where the horizontal axis represents the relative frequency counted from the step number of the tunable laser. For comparison, the simulated response of the filter is also plotted. The measured output shows a Lorentzian-shape with a 3-dB bandwidth of about 1.325 GHz, which agrees well with the simulated filter response. The corresponding quality factor, which is defined as the ratio of the resonance frequency to filter bandwidth, is around 1.5 \(\times\) 10\({}^{5}\). The discrete Fourier transform of the measured filter output \(H[k]\) was also computed and is displayed in Figure 3c. It should be mentioned that half of the transform \(H[k]\) is a mirror image caused by the Hermitian symmetry property, since \(h(n)\) is a real-valued sequence. Upon neglecting the mirror image symmetry, \(H[k]\) showed a low-pass effect with limited bandwidth, as illustrated in the inset of Figure 3c. To minimize the impact of noise on filter response, only the first 85 Fourier coefficients of \(H[k]\) are considered in the convolution theorem [27]. This facilitates a reconstruction with up to \(85/2\approx 44\) spectral lines including optical carrier and 1 st-order sidebands induced by RF tones [28]. First, a single-tone RF signal generated by a vector network analyzer (Keysight N5230A, Santa Rosa, CA, USA) was applied to a low-biased EOM (Sumitomo T.DEH1.5-40, Osaka, Japan) to evaluate the system performance. Figure 4a shows the measured power output of the scanning receiver \(y[n]\) (\(n\)=1,2... 8000) at an input RF frequency of 20 GHz. As expected, three peaks with the shape of filter response were observed, which was a result of the convolution product of the filter, the optical carrier, and two 1 st-order sidebands. Figure 4b plots the reconstructed optical spectrum of the modulated signal based on the matrix pencil method where the number of sinusoids \(M\) was set to 3 and the pencil parameter was set to 32, which were found to be the optimum values within the range recommended in Reference [29] to reduce the noise sensitivity of the matrix pencil method. Thanks to the linear mapping between frequency and time, the frequency of the input RF signal is proportional to the sweeping step difference between the upper sideband (USB) and lower sideband (LSB). In this experiment, the sweeping step of the laser was 0.1 pm and the step difference between the two sidebands was 3187, thus representing an estimated RF frequency of 19.9188 GHz and a measurement error of 81.2 MHz. Moreover, the proposed signal reconstruction based on deconvolution also provides amplitude information of the microwave signal.