Longitudinal shaping for the creation of tunable dark spots with high-order radially polarized beams

We present a systematic method for the creation of tunable three-dimensional dark spots in the focal volume by focusing high-order radially polarized transverse modes (R-TEM). By applying the binary phase mask of opposite phases, it works as a polarization filter and tailors the focal field structure by suppressing the longitudinal components. The dark focal spots of variable sizes are created for different high-order modes, such as <i>R</i>-<i>T</i><i>E</i><i>M</i>₀₁, <i>R</i>-<i>T</i><i>E</i><i>M</i>₁₁, <i>R</i>-<i>T</i><i>E</i><i>M</i>₂₁, <i>R</i>-<i>T</i><i>E</i><i>M</i>₀₂, <i>R</i>-<i>T</i><i>E</i><i>M</i>₁₂, and <i>R</i>-<i>T</i><i>E</i><i>M</i>₂₂, by focusing through the optical system over a range of low numerical apertures (NAs). Our approach extends the functionality of binary phase modulation to achieve localized 3D intensity nulls with high spatial precision. These tunable dark focus structures hold significant potential for advanced applications, including optical trapping of low-index particles, high-resolution imaging with reduced background illumination, and structured light-matter interaction.