We describe how laterally confined and axially stretched needles of light can be produced by focusing a radially polarized annular optical beam with a spherical mirror. Our analysis is based on an extension of the Richards-Wolf formalism appropriate for nonaplanetic focusing systems operated under nonparaxial conditions. While maintaining their lateral confinement near the theoretical limit of 0.36λ, the needles of light that are produced can extend axially over 1000's of λ, in full compliance with geometrical and electromagnetic considerations. Relationships are established between the thickness of the incident annular beam and the length of the needle of light.

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We present a new approach, based on Richards-Wolf formalism, to rigorously model nonparaxial focusing of radially and azimuthally polarized electromagnetic beams by axisymmetric systems without a single-point focus. Our approach is based on a combined method that uses ray tracing and diffraction integrals. Our method is validated by comparing known results obtained with a parabolic mirror. Our integral representation of the focused beams, compliant with diffraction theory, is thoroughly discussed and solved for various conics that, so far, have not been treated analytically. The extension of the method to other polarization states is straightforward.

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The phase shift imparted by a dielectric nanofin metasurface can be modelled following a semi-analytical assessment of the guiding properties. The model can be seen as a correction to the typically used Pancharatnam-Berry model.