Gaussian_beam_waist_radius

plasmapy.formulary.laser.Gaussian_beam_waist_radius(

spot_size_FWHM: Annotated[Quantity, Unit('m')],

) → Annotated[Quantity, Unit('m')]

Calculate the beam waist radius \(w_0\) for the intensity profile of a Gaussian beam given the Full Width at Half Maximum spot size \(FWHM\).

At focus, \(w_0\) is the transverse distance from the center of the beam to where the intensity drops by a factor of \(1/e^2\).

The beam waist radius of a Gaussian beam is calculated using:

\[w_0=\frac{FWHM}{\sqrt{2 \ln {2}}},\]

where \(FWHM\) is the full width at half maximum spot size of the beam.

Aliases: w0_

Parameters:

spot_size_FWHM (Quantity) – Full Width at Half Maximum spot size of the Gaussian beam (convertible to m).

Returns:

w_0 – The beam waist radius of the Gaussian beam for the given FWHM spot size.

Return type:

Quantity

See also

Gaussian_spot_size_FWHM

Notes

For details, see Gaussian beam.

Examples

>>> import astropy.units as u
>>> Gaussian_beam_waist_radius(8.242 * u.um)
<Quantity 7e-6 m>