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Figure 2
Left pane: Cartesian plot of the lens formula for Gaussian beams showing the normalized source distance s1/f versus the normalized image distance s2/f, with normalized Rayleigh length of the input beam zR/f as parameter. Dashed blue line: behavior of a hypothetical elliptical mirror with focal lengths f1/f, f2/f. The source lying at f1/f is imaged to a distance s2/f < f2/f depending on the Rayleigh length zR/f of the source, with a single image for each value of zR/f. The source lying at f2/f is imaged to a distance s1/f < f1/f with a number of solutions depending on the value zR/f. For a given couple of values (f2/f, zR/f),there is a minimum distance s2/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). F1, F2, F mark the points corresponding to the focal lengths f1, f2, f, respectively [equation (4)[link]]. (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 F1, F2. (f, h) The same as before but with a Gaussian beam. In an elliptical mirror (h), the waist at F1 is imaged into an intermediate position between F and F2.

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