**Figure 2**
Left pane: Cartesian plot of the lens formula for Gaussian beams showing the normalized source distance *s*_{1}/*f* versus the normalized image distance *s*_{2}/*f*, with normalized Rayleigh length of the input beam *z*_{R}/*f* as parameter. Dashed blue line: behavior of a hypothetical elliptical mirror with focal lengths *f*_{1}/*f*, *f*_{2}/*f*. The source lying at *f*_{1}/*f* is imaged to a distance *s*_{2}/*f* < *f*_{2}/*f* depending on the Rayleigh length *z*_{R}/*f* of the source, with a single image for each value of *z*_{R}/*f*. The source lying at *f*_{2}/*f* is imaged to a distance *s*_{1}/*f* < *f*_{1}/*f* with a number of solutions depending on the value *z*_{R}/*f*. For a given couple of values (*f*_{2}/*f*, *z*_{R}/*f*),there is a minimum distance *s*_{2}/*f* < δ beyond which no real image is produced. Right pane: comparison of a thin lens and elliptical mirror when illuminated by a spherical wave (upper row) and a Gaussian wave (lower row). *F*_{1}, *F*_{2}, *F* mark the points corresponding to the focal lengths *f*_{1}, *f*_{2}, *f*, respectively [equation (4)]. (*a*, *c*) Collimating a point source to a plane wave. (*e*, *g*) Waist-to-waist imaging. (*b*, *d*) Extrafocus-to-intrafocus imaging. In an elliptical mirror (*c*), the relevant extrafocal/intrafocal points are the focii *F*_{1}, *F*_{2}. (*f*, *h*) The same as before but with a Gaussian beam. In an elliptical mirror (*h*), the waist at *F*_{1} is imaged into an intermediate position between *F* and *F*_{2}. |