[en] The photoinjector test facility at DESY, Zeuthen site (PITZ) has been built for the development, testing and optimization of high brightness electron sources for Free Electron Lasers (FELs). A radio frequency (RF) photo gun is one of the key components for the successful operation of modern FELs. The PITZ RF gun consists of a 1.6 cell copper cavity with a Cs2Te photocathode. It is surrounded by two solenoids for generation a constant external magnetic field for beam focusing. The gun is operated at an RF field resonance frequency of 1.3 GHz with an electric field strength of 60 MV/m at the cathode. The RF cavity is fed through a coaxial coupler. An electron beam asymmetry has been observed at PITZ experimentally which could not be explained by imperfections of the photocathode laser transverse profile. An RF field asymmetry in the coupler section of the cavity generates a transverse RF field in the cavity which can deteriorate the transverse phase space of generated beams, therefore it is being considered as one of possible reasons of the observed electron beam distortions. The influence of the transverse fields on the beam dynamics was studied using CST Particle Studio simulation code. Several coupler concepts were suggested and their field asymmetry was studied. The results of simulations are presented in this work.