## 2 Operation and Principle  
The architecture of the proposed microwave photonic channelized receiver is illustrated in Figure 1. The system is composed of a laser diode (LD), a pair of polarization modulators (POLMs), a pair of erbium-doped fiber amplifiers (EDFAs), an acousto-optic modulator (AOM), a dual-parallel Mach-Zehnder modulator (DPMZM), a quartet of polarization controllers (PCs), a couple of wavelength division multiplexers (WDMs), and a set of four dual-polarization image rejection receivers (DP-IRRs). Each DP-IRR is assembled with two polarization beam splitters (PBSs), a dual-polarization quadrature optical hybrid (Dpol-QOH), a quartet of balanced photodetectors (BPDs), a pair of electrical hybrid couplers (EHCs), and four electrical band pass filters (EBPFs). The light carrier wave can be expressed as \(E_{c}(t)=E_{0}\exp(j\omega_{c}t)\), where \(E_{0}\) and \(\omega_{c}\) represent the amplitude and angular frequency of the optical signal, respectively. The  
Figure 1: Schematic diagram of the proposed microwave photonic RF channelizer. optical carrier is divided into two paths--upper and lower--by a 50:50 optical coupler. The upper path optical carrier enters POLM\({}_{1}\) and is modulated by a single-tone signal. POLM\({}_{1}\) has opposite modulation indices in its upper and lower arms, primarily used for generating a polarization multiplexed three-line optical frequency comb. The optical signal output from POLM\({}_{1}\) can be represented as follows:  
\[ \begin{array}{ll}E_{POLM_{1}}(t)&=\left\{\begin{array}{ll}E_{ OFC-X}(t)\cdot\overset{-}{e}_{x}\\ E_{ OFC-Y}(t)\cdot\overset{-}{e}_{y}\end{array}\right.\\ &=\left\{\begin{array}{ll}\sum\limits_{n=2m-1}A_{n}\exp\left\{j2\pi\big{[}f_{ RF1}+(n-1)f_{sig}\big{]}t\right\}\cdot\overset{-}{e}_{x}\\ \sum\limits_{n=2m}A_{n}\exp\left\{j2\pi\big{[}f_{RF1}+(n-1)f_{sig}\big{]}t\right\} \cdot\overset{-}{e}_{y}\end{array}\right.m=1,2\end{array}  \tag{1}\]  
In the context of the provided information, the amplitude of the optical comb is represented by a specific term \(A_{n}\); \(f_{RF1}\) denotes the frequency of the RF1 signal; and \(f_{sig}\) is the free spectral range (FSR) of the three-line optical comb. By adjusting the polarization direction of PC\({}_{2}\) to form a 45\({}^{\circ}\) angle with the principal axes of POLM\({}_{2}\), the odd and even order sidebands of the polarization-multiplexed comb are separated by the upper and lower arms of POLM\({}_{2}\). The broadband RF signal, RF\({}_{2}\), to be received is loaded onto the RF port of POLM\({}_{2}\) for signal replication. The output of POLM\({}_{2}\) can be expressed as follows:  
\[E_{POLM_{2}}(t)=\left\{ \begin{array}{ll}E_{ OFC-X}(t)\cdot\exp j[m_{s}s(t)]\overset{-}{e}_{x}\\ E_{ OFC-Y}(t)\cdot\exp j[-m_{s}s(t)]\cdot\overset{-}{e}_{y}\end{array} \right. \tag{2}\]  
In the given context, lets denote the modulation index of POLM\({}_{2}\) to be \(m_{s}\), the RF\({}_{2}\) signal to be \(s(t)\!=\!\text{V}_{RF_{2}}\sin(\omega_{2}t)\), and the angular frequency of the RF\({}_{2}\) signal to be \(\omega_{RF}\). Assuming the starting and ending frequencies of the RF\({}_{2}\) signal are \(f_{1}\) and \(f_{n}\), respectively, when \(f_{sig}=2f_{1}+[f_{n}-f_{1}]\), the RF sidebands along the orthogonal polarization state completely overlap, as shown in Figure 2a. The lower path optical carrier, after entering the AOM, is modulated by a single-tone signal \(f_{s}\) with a frequency that can be expressed as \(V_{f_{s}}(t)=V_{f_{s}}\sin\!\left(\omega_{f_{s}}t\right)\), where \(V_{f_{s}}\) represents the amplitude of the single-tone signal and \(\omega_{f_{s}}\) represents its angular frequency. The AOM then downshifts the optical carrier by a frequency interval of \(f_{s}\).