Gaussian profile

The GaussLaser type contains the parameters required for describing a Gaussian laser pulse. The spatial profile of the electric field is given by

\[\newcommand{\ii}{\mathrm{i}} % imaginary unit \begin{aligned} E_x (r,z) &= \xi_x E_0 \frac{w_0}{w} \exp\left[-\ii k z -\frac{r^2}{w^2} -\ii \left(\frac{k r^2}{2 R} - \arctg{\frac{z}{z_R}} + \phi_0\right)\right]\\ E_y (r,z) &= \frac{\xi_y}{\xi_x} E_x(r,z) \\ E_z (r,z) &= \frac{2 \left(\ii -\frac{z}{z_R}\right)}{kw^2 (z)} \left[xE_x (r,z) +yE_y(r,z)\right]\,, \end{aligned}\]

where

• $E_0$ is the amplitude of the electric field
• $ξ_x$ and $ξ_y$ give the polarization (choosing $ξ_x=1$ and $ξ_y=0$ for example, would give a linearly polarized field along the $x$ axis while taking them $1/\sqrt{2}$ and $±\mathrm{i}/\sqrt{2}$would give right and left-handed circular polarization)
• $w(z)$ is the beam radius at $z$
• $w_0$ is the beam waist
• $k$ is the wavenumber
• $R$ is the radius of curvature
• $\arctg{\frac{z}{z_R}}$ is the Gouy phase
• $ϕ_0$ is the initial phase

The magnetic field field is given by

\[\newcommand{\ii}{\mathrm{i}} % imaginary unit \begin{aligned} B_x(r,z) &= -\frac{1}{c}E_y(r,z)\\ B_y(r,z) &= \frac{1}{c}E_x(r,z)\\ B_z (r,z) &= \frac{2 \left(\ii -\frac{z}{z_R}\right)}{ckw^2 (z)} [yE_x (r,z) - xE_y(r,z)] \end{aligned}\]