A laser with 4 parameters is ok?

[zk-fdu]

Hi! Except laser envelope model, based on manual ,I want to define a laser with 4 parameter(x,y,z,t), ie. vortex light Laguerre-Gauss laser propagating along x direction with its formula \begin{eqnarray} u_{p\ell}(r,\phi, z,t) &=& C_{p\ell} \frac{w_0}{w(z)}\exp(-\frac{r^2}{w^2(z)})(\frac{\sqrt{2}r}{w(z)})^{|\ell|} L_p^{|\ell|}[\frac{2 r^2}{w^2(z)}] \nonumber \\ && \times \exp(-i\frac{zr^2}{z_R w^2(z)}+i(2p+|\ell|+1)\varphi_G(z)) \nonumber \\ && \times \exp(-i\ell\phi) \times exp(-i\omega t).However, I didn't make it. The run error is following: So I want to know whether a laser defined with 4 paramaters (x,y,z,t ) is ok , not based on laser envelope model ? I would appreciate it very much if you could give some help!

[mccoys]

Hi A laser is a boundary condition. Thus it cannot have four variable x,y,z,t. For instance, if you are injecting your laser from xmin, the variables are y,z,t. You have to take a portion of your formula corresponding to this

[zk-fdu]

Hi A laser is a boundary condition. Thus it cannot have four variable x,y,z,t. For instance, if you are injecting your laser from xmin, the variables are y,z,t. You have to take a portion of your formula corresponding to this

However, following your description, if a physical quantity is associated with position x and varies enormously with x in a laser propagating along x direction with its injection from xmin , how to deal with it?

[mccoys]

The propagation of laser for x>0 is obtained by solving Maxwell equations. If the laser depends strongly on x, it means there was a strong dependence on time at the boundary x=0. This dependence is propagated by the solver

[zk-fdu]

ok, I see. Thanks!