We analyzed optical-signal processing based on time-space conversion in an arrayed-waveguide grating (AWG). General expressions for the electric fields needed to design frequency filters were obtained. We took into account the effects of the waveguides and clearly distinguished the temporal frequency axis from the spatial axis at the focal plane, at which frequency filters were placed. Using the analytical results, we identified the factors limiting the input-pulse width and clarified the windowing effect and the effect of phase fluctuation in the arrayed waveguide.
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