We present a theoretical model of a physically pixellated nonlinear interference filter illuminated by a Gaussian laser beam. The plane-wave model figure of merit of a previous paper is redefined as a function of spot size, pixel dimensions, and the thermal conductivities of the pixel and substrate. We present detailed calculations of switching powers, and actual values are obtained for the cases of glass and polyimide pixels on a sapphire substrate. The theory predicts that switching powers of the order of less than 1 mW can be achieved for the polyimide-sapphire combination and 10 mW for the glass-sapphire combination. An upper limit of the order of 107 gate Hz/cm 2 in an array of pixels is projected.