Gaussian Beam Half-Width

`w = w_0 sqrt(1+(( lambda * z )/(pi* w_0 ^2))^2)`

Enter a value for all fields

The Gausian Beam Half-Width calculator computes the beam half width for a Gausian Beam based on the beam waist, distance on the axis, and the wavelength.

INSTRUCTIONS: Choose units and enter the following:

(w₀) Gausian Beam Waist
(z) Distance along the optical axis from the beam waist
(`lambda`) Beam Wavelength

Gausian Beam Half-Width(w): The calculator return the beam half-width in nano-meters. However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

This Gaussian Beam Half-Width equation¹ calculates the beam half-width for a Gaussian Beam. The beam half-width (`w`) is used as an indicator of the "size" of a Gaussian Beams. Gaussian Beams to extend to infinity, but they approach zero as they do so. It's convenient for us to establish a finite measure of the beam's width. We use the beam half-width, the radial distance (`w`) from the central axis such that `E(w) = E_0/e` (where the electric field is `1/e` of its value at the central axis). For more information on beam half-width and Gaussian Beams in general, please see the Gaussian Beam Calculator.

Gaussian Beam Calculators

^ Hecht, Eugene. "Modern Optics: Lasers and Other Topics." Optics. Reading, MA: Addison-Wesley, 2002. 618. Print.