In fast ignition laser fusion, a high-intensity picosecond laser heats a compressed dense core to achieve ignition. It is theoretically expected that the energy coupling efficiency from the heating laser to the compressed core becomes higher as the wavelength of the heating laser is shorter. This prediction is ready to be experimentally demonstrated using second harmonic generation at Institute of Laser Engineering (ILE), Osaka University. Fundamental and converted second harmonic waves irradiate a target simultaneously in the experiment because crystals for wavelength conversion is installed after a final optical system. In addition, the polarization of the second harmonic wave becomes perpendicular to the original fundamental wave after the wavelength conversion. These features make laser-plasma-interactions complicated. Therefore, three-dimensional particle-in-cell simulations have been conducted to investigate effects of conversion to short wavelength and mixed-beam irradiation with different wavelengths. Simulation results show that the temperature of the generated fast electrons decreases for second harmonic conversion compared to the case of pure fundamental wave and the laser propagates deeper as the wavelength conversion efficiency becomes high. In the case of mixed-beam irradiation, it is found that the second harmonic wave drills the plasma and guides the fundamental wave to the deep region, where pure fundamental wave cannot reach.