# Gaussian Beam

Lasers usually emit beams with a Gaussian profile. A Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are described by Gaussian functions.

For a Gaussian beam, the  amplitude of the complex electric field is given by where,

r       – radial distance from the centre axis of the beam

z       – axial distance from the beam’s narrowest point

i        – imaginary unit (for which i2 = − 1)

k       – wave number (in radians per meter).

w(z)    – radius at which the field amplitude drops to 1/e and field intensity to 1/e2 of their axial values, respectively.

w(0)   – waist size.

E0     =  |E( 0,0) |

R(z)     – radius of curvature of the beam’s wavefronts

ζ(z)   – Gouy phase shift. It is an extra contribution to the phase that is seen in  beams which obey Gaussian profiles.

The corresponding time-averaged intensity (or irradiance) distribution is where I0 = I(0,0) is the intensity at the center of the beam at its waist. The constant  is defined as the characteristic impedance of the medium through which the beam is propagating.

For vacuum,  Close