Field in Focus with a Maximum Longitudinal Electric Component

Closed formulas are presented for the field in the lens pupil for which the longitudinal electric component at the focal point is larger than any other focused field with the same power. The full-width-at-half-maximum of the squared amplitude of the maximum longitudinal component is 15% to 30% less than that of the classical Airy spot.

Figure 1

(a) Normalized $|E_z{|}^2$ of the optimum field in the $z=0$ plane and (b) normalized electric energy distribution $|\mathbf{E}(\mathbf{r}){|}^2$ in the focal plane of an $x$-polarized focused plane wave. The total power flow is the same for both fields and $NA/n=0.9$.

Figure 2

Cross-sections of the optimum $|E_z(x,y,0){|}^2$ (solid curves) and of $|\mathbf{E}(x,0,0){|}^2$ (dashed) and $|\mathbf{E}(0,y,0){|}^2$ (dotted) for the Airy spot of the $x$-polarized focused plane wave, for $NA/n=0.9$.

Figure 3

FWHM of $|E_z(x,y,0){|}^2$ of the optimum field and FWHM in the $x$ and $y$ direction of the focused $x$-polarized plane wave as a function of $NA/n$.

Figure 4

Comparison of the maximum $E_z(\mathbf{0})$ and the maximum of $|E_x|$ in the focal point when a $x$-polarized plane wave is focused. The total flow of power is the same for both fields.

Figure 5

The electric field in the pupil that, when focused, yields the field with maximum longitudinal component at the focal point for $NA/n=0.9$.

Figure 6

Cross section of the intensity in the pupil as a function of the radial coordinate, for several values of $NA/n$.