We demonstrate the methods for increasing the observed squeezing level in the generation of squeezed states of light at 1064 nm with periodically poled KTiOPO4 (PPKTP) crystal. We analyze the technical limits to the reduction of noise in the squeezed quadrature theoretically, including the intra-cavity loss of the optical parametric amplifier (OPA) cavity, the normalized amplitude, the detection frequency, and the mode matching on the balanced homodyning stage. To observe a high degree of squeezing, we improve the quality of mode matching into the OPA cavity and the mode cleaning (MC) cavity experimentally. By optimizing mode matching of the light into cavities, the finesse of the cavities would be higher in practice and the desirable spatial mode can be realized. As the intensity noise of the laser light reach the shot noise limit above the frequency of 1 MHz, which is sufficient for our experiment, so the MC cavity is incorporated to filter higher-order transverse modes of the local oscillator (LO) beam for the balanced homodyne detection. The experimental and theoretical results show that it is essential to optimize the mode matching efficiency to generate and detect high degree of squeezing otherwise an inefficiency mode matching will throw away the squeezing and transform the squeezed field into a vacuum field.