| From 1905 in which year Albert Einstein first proposed the concept of photon to explain photoelectric effect, Quantum Optics has had a history about one century. There has been a great progress in both discrete variable regime and continuous variable regime of Quantum Information with the in-depth research of quantum theory and rapid technical renovation. Balanced homodyne detection (BHD) is an important technic in the detection of quantum noises and different kinds of state function.Many theory calculations indicate that the visibility of the fringes decreases quickly with the detection efficiency of the apparatus which can caused by the mode mismatching between signal wave and local wave coupled on the beam splitter. In this paper we aim to deal with the problem of mode mismatching in BHD with a continuous variable of nonclassical state as the signal wave.The content of this paper is as follows:The first chapter is an introduction, it expatiate on the significance, purpose, methods and international headway of the research on mode mismatching in BHD with a continuous variable of nonclassical state as the signal wave; chapter 2 describes the principle of BHD and discusses how the mode mismatching effect on BHD, besides, we give a detail description of our home-made time domain pulse BHD with a bandwidth of 1 MHz; in chapter 3, the spectral property in collinear type-II BBO crystal spontaneous parametric down-conversion with a femtosecond pulse laser pump is analyzed, and the problem of how to choose a proper crystal thick is solved by use of classical three wave coupling equation; in chapter 4, a useful technique named Synchronously pumped optical parametric oscillators (SPOPOs) which can be used to enhance the conversion efficiency of optical nonlinear process is discussed, meanwhile the home-made SPOPOs is given out, and the adjusting, locking of the SPOPOs is explained.
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