## 2 Microwave Photonic Filters
### Two Tap MWP Filter Based on a Sagnac Loop Incorporating a Linearly Chirped FBG  
A Sagnac interferometer incorporating a linearly chirped FBG (LCFBG) can be used to implement a tunable single wavelength, two tap MWP filter, see Figure 9. Consider a single wavelength which is input to the Sagnac interferometer. There will be two reflected signals, one due to clockwise propagation and one due to counterclockwise propagation, in the interferometer before reflection from the LCFBG. The delay between the two reflected signals, which form the two taps of the MWP filter, depends on the input wavelength and the dispersion of the LCFBG. By tuning the input wavelength, the tap delay \(\Delta T\) can be varied, causing a change in the FSR of the MWP filter response. In Reference [5], [PERSON] et al. demonstrated interrogation of a single FBG sensor using this MWP filter. We can extend this approach for simultaneous interrogation of multiple FBG temperature sensors using superimposed LCFBGs in the Sagnac interferometer. The experimental setup is shown in Figure 9. The output from a BBS is spectrally sliced by two FBGs (again, we consider two sensors for a proof-of-principle demonstration) that define the two input wavelengths for the two MWP filters. The FBG temperature sensors have the following characteristics: The center wavelength and 3 dB bandwidth for Sensor 1 (FBG\({}_{1}\)) are 1543.7 nm and 0.3 nm, respectively, while the corresponding values for Sensor 2 (FBG\({}_{2}\)) are 1549.5 nm and 0.12 nm. The wavelengths are then amplitude modulated using an EOM before input into the Sagnac interferometer. The two superimposed LCFBGs have similar reflectivity of \(-\)80%; center wavelengths of 1545.4 nm and 1551.1 nm, corresponding 3 dB bandwidths of 4.4 nm and 4.9 nm, and dispersions of 53.3 ps/nm and 47.8 ps/nm. We use an optical bandpass filter to isolate the response from one FBG sensor prior to photodetection. First, we vary the temperature of Sensor 1 from 30 \({}^{\circ}\)C to 70 \({}^{\circ}\)C, while keeping Sensor 2 at a constant (room) temperature. Figure 10a,c shows the MWP filter responses for Sensor 1 and Sensor 2, respectively, while Figure 10b,d shows the normalized RF power at two different frequencies along the rising and falling edges of the filter responses. For Sensor 1, at frequencies of 3.8 GHz (rising edge) and 6.2 GHz (falling edge), we observe a linear relation between RF power and temperature with corresponding sensitivities of \(-\)11\(\cdot\)10\({}^{-3}\)/\({}^{\circ}\)C and 12.4\(\cdot\)10\({}^{-3}\)/\({}^{\circ}\)C. For Sensor 2, the RF power at frequencies of 3.8 GHz and 6.5 GHz exhibits negligible change. Next, we do the reverse and vary the temperature of Sensor 2 from 30 \({}^{\circ}\)C to 70 \({}^{\circ}\)C, while keeping Sensor 1 at a constant (room) temperature. The corresponding results are summarized in Figure 11. The sensitivities at frequencies of 4.6 GHz (rising edge) and 6.9 GHz (falling edge) are \(-\)12.8\(\cdot\)10\({}^{-3}\)/\({}^{\circ}\)C and 19.3\(\cdot\)10\({}^{-3}\)/\({}^{\circ}\)C, respectively. The difference in sensitivities between the two sensors arises in part to the difference in the grating dispersions, which causes the amount of shift in the tap delay and hence the variation in FSR of \(|H(f_{\mathrm{RF}})|\) as a function of temperature of the MWP responses to be different. The results clearly demonstrate that the sensors can be interrogated independently with negligible crosstalk, so that varying the temperature on one sensor does not impact the MWP filter response of the other. Figure 9: Experimental setup for implementing multiple two tap MWP filters based on superimposed LCFBGs in a Sagnac loop. Figure 11: Characteristics of Sensor 2 as the temperature is increased from 30 \({}^{\circ}\)C to 70 \({}^{\circ}\)C, while Sensor 1 is maintained at a constant (room) temperature.