The electromagnetic fields associated with a beam splitter having two input arms and two output arms are quantized in terms of the spatial modes of the complete optical system. The continuum mode operators employed conveniently describe the flow of light through the beam splitter from sources to detectors. The formalism is used to determine the photocount fluctuations in difference detection of the two outputs, the effect of beam splitting on squeezed input light, and the distribution of output photocounts for a definite number of input quanta.