Inverse focal shift in truncated cylindrical waves

We report on a general analytical procedure to analyze the axial focusing properties of uniform cylindrical waves truncated by a rectangular window. The resulting on axis diffraction pattern explicitly depends on the square of the window height-to-width ratio. Depending on the value of this parameter, different kinds of axial behavior are observed. In particular, it is found that for low values of this parameter and low Fresnel number, an inverse focal-shift phenomenon can appear.