# Experimental Study on Partially Coherent Optical Coherent Detection
## 1 Introduction  
In a coherent optical communication system, if the polarization state of the signal light is uncertain [1], but the optical mixer is sensitive to the polarization state of the signal light and the local polarization light, and the polarization state of the signal light does not match with the local polarization light, it will reduce the heterodyne's efficiency and seriously affect the performance of the whole communication system [2]. In coherent optical communication systems, the generation of intermediate frequency signals relies on an optical mixing process, which is the nonlinear interaction between local oscillator light and signal light in the photodetector. This interaction facilitates the frequency transformation of the signal to the intermediate frequency range, facilitating subsequent signal processing in the form of lower-frequency electrical signals. Due to the fact that the mixing rate process depends on the phase relationship between the local oscillator light and the signal light, different polarization states may also introduce phase uncertainty, which can affect the phase of the intermediate frequency signal and thus affect the demodulation quality of the signal. Polarization mismatch may result in some components of the signal not being effectively mixed, which may cause a decrease in signal quality, such as amplitude or phase distortion, further reducing the signal-to-noise ratio (SNR) and bit error rate (BER) performance of the signal. [PERSON] [3] used the properties of the cross spectral density matrix of an EGSM source characterized by 10 parameters to derive the necessary and sufficient conditions that must be met to produce this type of physically achievable beam source. [PERSON] [4] derivedanalytical formulas for the root mean square spatial width, root mean square angular width, and M\({}^{2}\)-factor of EGSM beams in turbulence using the Wigner distribution function and the extended Huygens Fresnel integration second-order moment formula. The results indicate that the relative M\({}^{2}\)-factor of EGSM beams decreases with a decreasing zenith angle, initial coherence length, and initial polarization degree, as well as an increasing beam width and intrinsic scale. [PERSON] [5] investigated the effects of anisotropic atmospheric turbulence on the propagation characteristics of an electromagnetic twisted Gaussian Schell-model array beam. They derived an analytical expression for the cross-spectral density function of the beam propagating through anisotropic turbulent atmosphere and utilized it to explore the evolutionary behavior of the spectral intensity, degree of polarization, and degree of coherence. [PERSON] [6] has outlined a method based on first-order interference and two-point Stokes parameters for measuring the polarization states of electromagnetic Gaussian Schell-model beams, and has applied second-order field correlations to determine the complex magnitude and phase of their electromagnetic coherence. The effectiveness of this method was demonstrated experimentally using an EGSM beam generated by a laser beam passing through a rotating ground glass diffuser. [PERSON] [7] studied the evolution of the degree of polarization of EGSM beams. The interaction between EGSM beams and Gaussian cavities was analyzed. The results indicate that the behavior of the degree of polarization depends on the statistical properties of the source generating the EGSM beams and the parameters of the cavity. [PERSON] [8] studied the polarization properties of electromagnetic Gaussian Schell-model beams propagating through the anisotropic non-Kolmogorov turbulence of a marine-atmosphere channel based on the cross-spectral density matrix of the beam. The electromagnetic Gaussian Schell-model beam with smaller \(\delta\)yy, \(\delta\)xx, and Ax parameters, but a larger Ay, will reduce the interference of turbulence. [PERSON] et al. [9] investigated the behavior of coherent detection systems in the case of partially coherent beams containing both local oscillator light and signal light.