Clarifications on the Gouy phase of radially polarized laser beams

The Gouy phase, which describes how a field accumulates an additional phase shift around the focus compared to a spherical wave, is investigated for the strongly focused TM₀₁ beam in free space. It is shown, using both analytical and numerical solutions, that when the effects of the edges of focusing optics are small, the complete variation of the on-axis Gouy phase of the longitudinal electric field is 2π. It is true even in the strongly focused limit. Moreover, we show, using an appropriate effective wavevector, how to retrieve the Gouy phase when the diffraction caused by the edges is dominant at the focus. We further investigate the off-axis Gouy phase of the TM₀₁ beam and show that any slight variation from the optical axis causes a variation of the Gouy phase of the longitudinal electric field to reduce to π.