## 3 Chirped Microwave Pulse Generation and Compression
### Chirped Microwave Pulse Generation
Thus, within the spectral windows of the ASGWSI defined by the spectral response of the OBPFs, the wavelength dependent path length changes. In turn, the frequency components of the chirped microwave signal will change while the chirp rate will remain constant, as given by Equations (3) and (4). In our experiments, we use a wavelength-tunable mode-locked femtosecond laser generating pulses with a 3 dB bandwidth of \(\sim\)6 nm at a repetition rate of 16 MHz and centered at \(\sim\)1540 nm as the pulsed BBS. The dispersive medium is a length of dispersion compensating fiber with a dispersion of \(-\)1719 ps/nm. The two LCFBGs, LCFBG\({}_{1}\) (for Sensor 1) and LCFBG\({}_{2}\) (for Sensor 2), have very similar spectral characteristics: They are centered at 1540 nm with a 3 dB bandwidth of 10 nm, a dispersion of 140 ps/nm, and a peak reflectivity of \(\sim\)80%. The two pairs of identical OBPFs are used to select a \(\sim\)1 nm wide spectral slice within the LCFBG reflection spectrum. The two channels in the AWGSI are separated spectrally by 2 nm, which corresponds to a temporal separation of \(\sim\)3.4 ns between the generated chirped microwave signals. We use an optical sampling module with 65 GHz bandwidth connected to a digital communications analyzer (DCA) with a corresponding impulse response time of \(\sim\)7 ps to record the temporal waveforms. The recorded waveforms are then processed offline to calculate the spectrograms and correlations with the reference signal to obtain the compressed pulses. Figure 13a,b shows the chirped microwave waveforms when two different temperatures, 30 \({}^{\circ}\)C and 50 \({}^{\circ}\)C, are applied to Sensor 1, while Sensor 2 is kept at room temperature. Figure 14a,b shows the corresponding waveforms when temperatures of 21 \({}^{\circ}\)C and 50 \({}^{\circ}\)C are applied to Sensor 2, while keeping Sensor 1 at room temperature. We calculate the spectrograms of the chirped waveforms and extract an RF chirp of \(\sim\)\(\pm\)14 GHz/ns, as shown by the slopes of the red lines in Figures 13c and 14c. These values of RF chirp are used to define the reference signals, shown in Figures 13d and 14d, which are used to compress the measured waveforms in Figure 13a,b and Figure 14a,b, respectively. As observed from the plots of the compressed pulses in Figure 15a,b, there is a linear shift in the correlation peak corresponding to the sensor experiencing a temperature change. There are small drifts in the correlation peaks for the sensor that is maintained at room temperature (ideally, the correlation peaks should not vary), the results generally show low cross-talk between the two sensors. These drifts/fluctuations are caused by other environmental perturbations in our experimental setup, such as vibrations. In a practical system, the sensors will need to be properly packaged to avoid such drifts while there is a negligible shift in the correlation peak for the sensor that is kept at a constant temperature. Figure 12: Setup for generating two chirped microwave signals using an AWGSI incorporating multiple LCFBGs, followed by WTT mapping. PC: Polarization controller, VOA: Variable optical attenuator, EDFA: Erbium-doped fiber amplifier, PD: Photodetector. Figure 14: Correlation signals (compressed pulses) for the waveforms measured when LCFBG\({}_{1}\) is at 30 \({}^{\circ}\)C (Figure 2a) and 50 \({}^{\circ}\)C (Figure 2b). Correlation signals (compressed pulses) for the waveforms measured when LCFBG\({}_{2}\) is at 21 \({}^{\circ}\)C (Figure 4a) and 50 \({}^{\circ}\)C (Figure 4b) (after Reference [13]). Figure 13: Measured chirped microwave waveforms when applying a temperature of (**a**) 30 \({}^{\circ}\)C and (**b**) 50 \({}^{\circ}\)C to Sensor 1, while keeping Sensor 2 at constant temperature; (**c**) Calculated spectrogram for the waveform in (**a**); (**d**) Reference signal used to compress the waveforms in (**a**,**b**).