## 2 Principle  
Figure 1a shows a possible RoF system, where RF signals are received at the RAU. After electro-optical conversion and amplification in the RAU, the optical signals are transmitted to the CO through a length of fiber for complex signal processing, including up/downconversion, phase shifting, and frequency and phase measurement. This setup significantly simplifies the complexity of RAUs. However, in this scenario of remote fiber transmission, the receiving system must be capable of anti-chromatic dispersion transmission. In this work, we propose an image-free photonic mixer, which can transmit the received RF signal to the CO for frequency downconversion without introducing power fading. Meanwhile, the image interference signal can be eliminated by establishing Hartley architecture in the CO.  
To clearly illustrate the principle of our approach, we will use the structure of one RAU as an example. The schematic diagram of our proposed image-free microwave photonic sub-harmonic downconverter is presented in Figure 1b. A linearly polarized  
Figure 1: **(a)** Architectural diagram for a possible radio-over-fiber (RoF) system. RAU, remote antenna unit; **(b)** the schematic diagram of the proposed image-free microwave photonic sub-harmonic downconverter. LD, laser diode; DP–QPSK, dual-polarization quadrature phase-shift keying; PBC, polarization beam combiner; LO, local oscillator; PS, phase shifter; EDFA: erbium-doped fiber amplifier, PC, polarization controller; Pol, polarizer; PD, photodetector; 90\({}^{\circ}\) EHC, 90\({}^{\circ}\) electrical hybrid coupler. lightwave, denoted by \(E_{in}(t)=E_{0}\exp(j\omega_{c}t)\) is emitted from a laser diode (LD) and then injected into the DP-QPSK modulator. The DP-QPSK modulator consists of two QPSK modulators (X-QPSK and Y-QPSK), a 90\({}^{\circ}\) polarization rotator (PR), and a polarization beam combiner (PBC). The target RF signal is divided into two channels via a 90\({}^{\circ}\) electrical PS. The two RF signals with a 90-degree phase difference are fed to the two RF ports of the X-QPSK modulator, respectively. The target RF signal, including the unwanted image signal, is expressed as \(V(t)=V_{RF}\sin(\omega_{RF}t)+V_{IM}\sin(\omega_{IM}t)\). Both sub-MZMs of the X-QPSK modulator are biased at the minimum transmission point. The parent modulator of X-QPSK is biased at the quadrature transmission point. Thus, the CS-SSB modulation of the RF signal is achieved at the output of the X-QPSK modulator. The optical field of the upper arm can be written as follows:  
\[E_{X-QPSK}=\frac{\sqrt{2}\eta_{E_{\text{int}}(t)}}{4}\left\{ \begin{array}{l}\left[\begin{array}{l}\exp(j(m_{RF}\sin\omega_{RF}t+m_{IM }\sin\omega_{IM}t))\\ -\exp(-j(m_{RF}\sin\omega_{RF}t+m_{IM}\sin\omega_{IM}t))\end{array}\right]+\\ \left[\begin{array}{l}\exp(j(m_{RF}\cos\omega_{RF}t+m_{IM}\cos\omega_{IM}t) \\ -\exp(-j(m_{RF}\cos\omega_{RF}t+m_{IM}\cos\omega_{IM}t)\end{array}\right]\cdot \exp(j\frac{\pi}{2})\end{array} \right\} \tag{1}\] \[= \sqrt{2}\eta_{E_{\text{int}}}(t)[-J_{0}(m_{RF})I_{1}(m_{IM})exp(- j\omega_{IM}t)-J_{1}(m_{RF})J_{0}(m_{IM})exp(-j\omega_{RF}t)]\]  
where \(J_{n}()\) represents the nth-order Bessel function of the first kind. It should be noted that in the derivation of Formula (1), the higher-order terms of Bessel functions of the first kind are ignored due to the lower powers. \(m_{RF}\) and \(m_{IM}\) represent the modulation indices of the target RF signal and the image signal, respectively. \(\eta\) denotes the insertion losses of each QPSK modulator. In the lower arm, the Y-QPSK modulator is driven by the LO signal, which is equally separated into two channels by a tunable PS. The phase difference between the two channels is \(\pi/4\). The three biases of the Y-QPSK modulator are biased at maximum, maximum, and quadrature transmission points. Under this bias setting, the first-order sidebands of the LO signal are suppressed, while the optical carrier and second-order sidebands are dominant.