# Radially Polarized Laser Beam Intensity Distributions

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This Demonstration compares the axial and radial field intensities in the focal plane of a radially polarized (axicon) laser beam with increased focusing or, equivalently, as the diffraction angle is increased. Such a beam has two electric field components: axial (along the propagation direction) and radial (transverse to the propagation axis). When the beam is focused to a spot size smaller than would be allowed by the paraxial approximation, it develops a pencil-like axial focus within which the intensity increases (with further focusing) at the expense of the radial intensity.

Contributed by: Yousef I. Salamin (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Using the parameters of a Gaussian beam propagating along the axis of a cylindrical coordinate system, a radially polarized laser beam may be shown to have two electric field components: axial and radial . For tight focusing (e.g., to a spot size that is small compared to a wavelength) the paraxial approximation fails to accurately describe the fields. The so-called "truncated-series representation" is a better candidate for modeling the field components and intensity distributions. Within this description, the parameter that controls focusing is the diffraction angle , defined as the ratio of the beam-waist radius at focus () to the Rayleigh length (or depth of focus ).

In this Demonstration, the axial and radial intensity distributions in the focal plane (plane through the beam focus and transverse to the propagation axis) are shown as the diffraction angle is varied up to a maximum value of 0.8. (The validity of the truncated-series representation is in doubt as .)

Note that the intensities are normalized by the maximum values ( and ) they would have when the paraxial approximation is made.

Snapshots 1-3: paraxial field intensity distributions

Y. I. Salamin, "Accurate Fields of a Radially Polarized Gaussian Laser Beam," *New Journal of Physics*, 8(133), 2006.

## Permanent Citation