A comprehensive view of temporal domain interference and spectral interpretation of short pulse

The superposition of the number of waves in time-domain Fourier synthesis is a basis of the Fourier transform. The beat or modulation frequency component of the resultant undulation of superposed EM waves has been easily detected by a broadband solid-state material detector. On the contrary, neither a beat or modulation frequency or even an average frequency could be detected by a Fabry-Perot interferometer which is a popularly used device as a spectrometer to analyze different frequency components with high resolving power. In this dissertation, by revisiting the property of the superposition effect of electromagnetic fields, we can improve our understanding of the properties of light beams with an investigation of the condition for the Fourier synthesis. Through this research, the necessity of the atomic or other material detector is suggested. ^ Fourier analysis, which is the inverse process of Fourier synthesis, is discussed to analyze the frequency components of a time limited pulse. It has been known that those are linked by the Fourier transform. The explanation of the time-domain superposition effect of light beams through interferometric devices gives a direct interpretation of an impulse response function. The difference of the impulse response function in a continuous wave case and a time limited pulse case is easily ignored. Due to the spatial and temporal locality of interference, Spatio-Temporal Response (STR) function is suggested using the spatial and temporal domain limitation for the superposition of the time limited pulse through interferometer. Using this STR function, the fringe broadening effect due to changes in the temporal input pulse width is discussed with the analysis of the frequency components in the broadened fringe. Based on the understanding of the temporal superposition effect of the EM fields, Fourier theory is explained by an understanding of the Fourier synthesis and the Fourier analysis. These works can be broadly applied in fiber communication systems to overcome the limitations to the high data transfer rate. ^ Analysis of cavity ring-down spectroscopy (CRDS) is given by the time-domain interpretation using the STR function. The time domain analysis gives a more direct and heuristic method than the frequency domain interpretation.