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The quantum efficiency from a metal cathode is strongly dependent on the field at the cathode due to the Schottky effect. Since the field is time dependent the quantum efficiency is also time dependent. Thus the laser pulse shape used to generate electrons in a photocathode rf gun is not the same as the electron bunch shape. In addition since the thermal emittance and quantum efficiency are related, the thermal emittance is also time dependent.
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Schmerge et al. (2007) studied this question.
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