Gaussian profile

class fbpic.lpa_utils.laser.GaussianLaser(a0, waist, tau, z0, zf=None, theta_pol=0.0, lambda0=8e-07, cep_phase=0.0, phi2_chirp=0.0, propagation_direction=1)[source]

Define a linearly-polarized Gaussian laser profile.

More precisely, the electric field near the focal plane is given by:

\[E(\boldsymbol{x},t) = a_0\times E_0\, \exp\left( -\frac{r^2}{w_0^2} - \frac{(z-z_0-ct)^2}{c^2\tau^2} \right) \cos[ k_0( z - z_0 - ct ) - \phi_{cep} ]\]

where \(k_0 = 2\pi/\lambda_0\) is the wavevector and where \(E_0 = m_e c^2 k_0 / q_e\) is the field amplitude for \(a_0=1\).

Note

The additional terms that arise far from the focal plane (Gouy phase, wavefront curvature, …) are not included in the above formula for simplicity, but are of course taken into account by the code, when initializing the laser pulse away from the focal plane.

Parameters:

  • a0 (float (dimensionless)) – The peak normalized vector potential at the focal plane, defined as \(a_0\) in the above formula.

  • waist (float (in meter)) – Laser waist at the focal plane, defined as \(w_0\) in the above formula.

  • tau (float (in second)) – The duration of the laser (in the lab frame), defined as \(\tau\) in the above formula.

  • z0 (float (in meter)) – The initial position of the centroid of the laser (in the lab frame), defined as \(z_0\) in the above formula.

  • zf (float (in meter), optional) – The position of the focal plane (in the lab frame). If zf is not provided, the code assumes that zf=z0, i.e. that the laser pulse is at the focal plane initially.

  • theta_pol (float (in radian), optional) – The angle of polarization with respect to the x axis.

  • lambda0 (float (in meter), optional) – The wavelength of the laser (in the lab frame), defined as \(\lambda_0\) in the above formula. Default: 0.8 microns (Ti:Sapph laser).

  • cep_phase (float (in radian), optional) – The Carrier Enveloppe Phase (CEP), defined as \(\phi_{cep}\) in the above formula (i.e. the phase of the laser oscillation, at the position where the laser enveloppe is maximum)

  • phi2_chirp (float (in second^2)) – The amount of temporal chirp, at focus (in the lab frame) Namely, a wave packet centered on the frequency \((\omega_0 + \delta \omega)\) will reach its peak intensity at \(z(\delta \omega) = z_0 - c \phi^{(2)} \, \delta \omega\). Thus, a positive \(\phi^{(2)}\) corresponds to positive chirp, i.e. red part of the spectrum in the front of the pulse and blue part of the spectrum in the back.

  • propagation_direction (int, optional) – Indicates in which direction the laser propagates. This should be either 1 (laser propagates towards positive z) or -1 (laser propagates towards negative z).