## 2 Microwave Photonic Filters
### Single Bandpass MWP Filter  
First, we consider interrogating a temperature sensor based on an in-fiber FP cavity formed with two near-identical low-reflectivity FBGs, as shown in Figure 3a. The reflection spectrum of the FBG structure is a sinusoidal-like pattern characterized by an FSR of \(\Delta\lambda_{FSR}=\frac{\lambda^{2}}{2n_{eff}L}\) where \(n_{eff}\) is the effective refractive index, \(L\) is the center-to-center length between the FBGs, and \(\lambda\) is the center wavelength of the reflection response of each FBG. Figure 3b illustrates the reflection spectrum of such an in-fiber FP cavity where the peak reflectivity of each FBG is \(\sim\)17% and \(L=10\) mm. When the in-fiber FP cavity is exposed to a change in temperature, both the length and the refractive index of the fiber separating the FBGs, as well as the FBGs themselves, will vary due to thermal expansion and thermo-optic effects. Thus, the FSR of the reflection response \(\Delta\lambda_{FSR}\) will change, resulting in a shift in the MWP filter response \(|H(f_{RF})|\), i.e., in the value of \(f_{0}\). For multiple sensor operations, we can wavelength multiplex multiple in-fiber FP cavity temperature sensors, each having its own FSR, and track temperature changes on the individual sensors by monitoring changes in their corresponding MWP filter passbands. Note that the use of an in-fiber FP cavity as the sensing element is more compact compared to the use of a Mach-Zehnder interferometer as demonstrated in [10]. Figure 4a illustrates the experimental setup used to demonstrate the ability to interrogate multiple temperature sensors using the MWP filter system (two sensors were considered in our proof-of-principle demonstration) [12]. The output from a BBS is spectrally sliced using two in-fiber-FP cavity sensors, one with \(L_{1}=10\) mm (Sensor 1) and the other with \(L_{2}=20\) mm (Sensor 2), that are placed at different locations and exposed to different temperature conditions. The spectrally sliced spectra are shown in Figure 4b. Sensor 1 operates at longer wavelengths and occupies a broader optical spectrum, while Sensor 2 operates at shorter wavelengths. The corresponding FSRs for Sensor 1 and Sensor 2 are \(\Delta\lambda_{FSR,1}\approx 80\) pm and \(\Delta\lambda_{FSR,2}\approx 40\) pm, respectively. Figure 4: (**a**) Experimental setup for interrogating two temperature sensors based on single bandpass MWP filtering and (**b**) spectral response of the two in-fiber FP cavity sensors. Figure 3: (**a**) Structure of an in-fiber FP cavity formed by two near-identical Fiber Bragg gratings (FBGs) and (**b**) zoom of the spectral fringe pattern of a typical device. We use an EOM for amplitude modulation and dispersion compensating fiber (DCF) with a dispersion of \(|D|\) = 1719 ps/nm (at 1550 nm) as the dispersive medium. The calculated frequencies of the MWP filter passbands are \(f_{0,1}\) = 7.27 GHz and \(f_{0,2}\) = 14.54 GHz for Sensors 1 and 2, respectively. Figure 5 shows the measured MWP filter responses. The measured passband peaks are 7.38 GHz for Sensor 1 and 15.12 GHz for Sensor 2, in good agreement with the calculate values. First, we characterize the response of each sensor separately. Figure 6a shows the change in normalized RF power at frequencies \(f_{RF}\) of 7.48 GHz and 7.24 GHz, which are at the falling and rising edges of the MWP filter response, respectively, as the temperature of Sensor 1 is increased from room temperature (22 \({}^{\circ}\)C) to 100 \({}^{\circ}\)C. For these two frequencies, the RF power varies linearly with temperature, and the sensitivities are 2\(\cdot\)10\({}^{-4}\)/\({}^{\circ}\)C at 7.48 GHz and \(-\)4\(\cdot\)10\({}^{-4}\)/\({}^{\circ}\)C at 7.24 GHz. Note that, for the frequency on the falling (rising) edge of \(|H(f_{RF})|\), the slope of the change in RF power with increasing temperature is positive (negative), thereby indicating that MWP filter response shifts to higher frequencies.