# RF Frequency Selective Switch by Multiple PMIM Conversions
## 2 Materials and Methods  
Our frequency selective switch scheme is derived from the phase modulation to intensity modulation conversion based on a single pair of notch optical filters and a continuous wave (CW) light source [15]. When a single-frequency lightwave is phase-modulated by the RF signal, a positive and negative first-order sideband will be generated. This pair of optical sidebands has the same power value, but their phase is opposite to the original optical carrier. When the modulated light is opto-electrically converted, the pair of recovered RF signals also has the same power value and opposite phase, so they will cancel each other out and the photodetector will output an RF signal with zero power. If an optical filter is introduced after the phase modulator, the amplitude or phase balance of the positive and negative first-order sidebands will be destroyed, resulting in the change of the RF amplitude behind the photodetector. When the optical filter is a notch type, this imbalance will only appear at a narrow band optical frequency, so after the photodetector,a narrow band RF filter will be obtained. The PMIM conversion has many advantages. On the one hand, it can give full play to the wide range tunability of the light source, which can make the microwave photonic filter have a large tuning range. On the other hand, because the current optical resonator can achieve a high quality factor and high frequency selectivity, the bandwidth of the microwave photonic filter can be less than 100 MHz, which can match the channel bandwidth of current RF communication. Compared with the FIR structure, the resulting RF spectrum processor has smaller volume and loss, and also has incoherent stability. Many interesting applications have been implemented based on this principle [17], such as the Fourier domain mode-locked optoelectronic oscillator [18]. However, only one narrowband microwave spectrum filtering process can be obtained by a single PMIM conversion. On this basis, we extend the number of spectral channels by an optical frequency comb, so as to achieve greater bandwidth and channel reconfigurability. The principle is shown in Figure 1. An optical frequency comb has many comb teeth, all of which have different but strictly equidistant carrier frequencies. When the optical comb is modulated by a phase modulator, the RF signal is carried around each comb tooth. Then, the modulated optical frequency comb passes through a single periodic notch filter. The filter can be a single ring resonator, Fabry Perot resonator, and so on, which takes advantage of the natural periodicity of these optical devices. In this way, each pair of comb tooth and notch frequency response constitutes a PMIM conversion, and a band-pass filter can be formed in the RF spectrum. In order to achieve broadband RF spectrum coverage, we make the comb spacing of the optical frequency comb slightly different from the FSR of the periodic notch filter. Typically, it can be set like this: such a difference is approximately equal to the bandwidth of a single notch frequency response. Obviously, if the number of frequency tooth and notch pairs is \(N\), the bandwidth of the RF processor will be \(N\Delta\), where \(\Delta=|S_{\text{{OFF}}}-FSR_{\text{{n notch}}}|\). Here we assume \(S_{\text{{OFF}}}\) is the comb spacing, and \(FSR_{\text{{n notch}}}\) is the FSR of the periodic notch filter. Assuming that the difference between the optical carrier frequency and the central frequency of the notch frequency response is \(f_{c}\) at the center tooth-notch pair, then \(f_{c}\) is also the central frequency of the RF spectrum processor. Note that \(f_{c}\) must be larger than half of the total bandwidth, which means \(N_{\text{max}}=2f_{c}/\Delta\). In other words, although we can increase the processing bandwidth by increasing the number of comb-notch pairs, there is an upper limit on the number. In the above design, we have mapped each frequency channel in the RF spectrum with the corresponding comb tooth of the optical frequency comb, one by one.