# RF Frequency Selective Switch by Multiple PMIM Conversions
## 2 Materials and Methods
We have noticed that a similar resolution enhancement phenomenon has been reported in previous literature, such as the so-called bandwidth scaling method [28; 29]. However, in the previous scheme, all of the RF channels were coherently synthesized in the optical domain. In other words, the phase of the local oscillation optical frequency comb will affect the phase of RF channels after synthesis; this will lead to the instability of the phase of the output signal, and even lead to the random change of the phase among the channels after combining, resulting in the failure of RF combining. In our scheme, although the operation of the optical sideband is also involved in each optical channel, it is an incoherent synthesis. This is because in PMIM conversion, the RF signal is transmitted through the disappearance of the optical sideband; the regenerated RF signal is obtained by beating the optical carrier and the sideband that has not disappeared. Both the carrier and the sideband are reflected (in the case of a [PERSON] cavity) or transmitted (in the case of a ring resonator) by the notch filter and pass through the same optical path from beginning to end. This is fundamentally different from the scheme in the literature [28], where the regeneration of RF signal is obtained through the transmission of an optical sideband. This will make our scheme maintain excellent phase stability and phase consistency in the process of reconfigurable filtering and FSS. Another problem that needs to be noted is that other beat frequencies can also be generated in the optical carrier or sideband between different optical channels. However, when the interval between optical frequency combs is wide enough, the beat frequency between these channels will be beyond the signal bandwidth and can be ignored. It can be seen that the proposed scheme and the conventional incoherent synthetic FIR filter both use multi-wavelength light source or optical frequency comb, but their principles are very different. In a FIR filter, each wavelength corresponds to a tap in the time domain, and the desired frequency response is obtained by weighted interference between taps with different delays. The relationship between tap weight and spectrum response is Fourier transform, so if we want to update the target frequency response, we need to update the weights of all taps. Moreover, the Fourier transform relationship puts forward special requirements for tap weights. For example, the spectral response close to a rectangle requires some taps to have a \(\pi\) phase, which is also the difficulty of various incoherent synthetic FIR filters. In order to achieve a negative tap, the device has to be much more complex [30; 31; 32]. In our scheme, each wavelength directly corresponds to a channel in the broadband RF spectrum, that is to say, the amplitude of each channel can be directly realized by controlling the corresponding optical tooth power of the channel. In practice, it can be obtained by operating the insertion loss of the optical WSS at the optical frequency. This makes it easier to update the target frequency response, and can achieve a higher update rate and more accurate target frequency response. Moreover, because the channel frequency response and tap weight are of one-to-one correspondence, the frequency response can be directly changed by controlling the power of the optical frequency comb. Therefore, any amplitude frequency characteristics such as rectangle and serration can be realized without any complex taps, as long as the target resolution is above the bandwidth of a single notch filter. We demonstrate the principle of broadband RF FSS and obtain the frequency selective switching with 50 MHz resolution and five channels at most. The experimental setup is shown in Figure 2. The frequency comb spacing is about 50 GHz, and the number of comb teeth is 21. After the Erbium-doped fiber amplifier (EDFA), the optical power is increased to about 20 dBm. The RF signal is loaded on each comb tooth of the optical frequency comb through a phase modulator.