Gaussian_Rayleigh_length

plasmapy.formulary.laser.Gaussian_Rayleigh_length(
wavelength: Annotated[Quantity, Unit('m')],
beam_waist_radius: Annotated[Quantity, Unit('m')],
) → Annotated[Quantity, Unit('m')][source]

Calculate the Rayleigh length \(z_R\) from the beam waist radius \(w_0\) and the wavelength \(\lambda\).

The Rayleigh length of a Gaussian beam is calculated using:

\[z_R=\frac{\pi w_0 ^2}{\lambda},\]

where \(w_0\) is the beam waist and \(\lambda\) is the wavelength of the beam.

Parameters:

  • wavelength (Quantity) – Wavelength of the laser pulse (convertible to m).

  • beam_waist_radius (Quantity) – Beam waist of the laser pulse (convertible to m).

Returns:

z_R – The Rayleigh length of the Gaussian beam for the given wavelength and beam waist.

Return type:

Quantity

See also

Gaussian_beam_waist_radius, Gaussian_spot_size_FWHM

Notes

For details, see Rayleigh length.

Examples

>>> import astropy.units as u
>>> Gaussian_Rayleigh_length(800 * u.nm, 1 * u.um)
<Quantity 3.927e-06 m>