Particle production by a relativistic semitransparent mirror of finite transverse size

Production of massless scalar particles by a relativistic semitransparent mirror of finite transverse size in (1+3)D flat spacetime is studied. The finite-size effect on the mode function is compared to the conventional scalar diffraction theory in optics. The derived particle spectrum formula is applied to two specific trajectories. One is the gravitational collapse trajectory commonly invoked in (1+1)D perfectly reflecting moving mirror literature, and the other is the plasma mirror trajectory proposed to be realizable in future experiments. We illustrate the finite-size effect on the particle spectrum, which should help to provide a guidance to the expectation in future flying mirror analog black hole experiments.