Super-Gaussian Longitudinal Profile#
Used to define a super-Gaussian transverse laser profile.
The shape of the profile is characterised by the duration \(\tau\) and by one “order parameter” \(n\), where \(n=2\) gives a standard Gaussian profile, and the profile converges to a square pulse when \(n\) goes to infinity.
- class lasy.profiles.longitudinal.SuperGaussianLongitudinalProfile(wavelength, tau, t_peak, n_order, cep_phase=0)[source]#
Class for the analytic profile of a longitudinally-super-Gaussian laser pulse.
More precisely, the longitudinal envelope (to be used in the
CombinedLongitudinalTransverseProfileclass) corresponds to:\[\mathcal{L}(t) = \exp\left( -\left(\frac{(t-t_{peak})^2}{\tau^2}\right)^{n/2} + i\omega_0t_{peak} \right)\]- Parameters:
- taufloat (in second)
The duration of the laser pulse, i.e. \(\tau\) in the above formula. Note that \(\tau = \tau_{FWHM}/(\sqrt{2}\log(2)^{1/n})\), where \(\tau_{FWHM}\) is the Full-Width-Half-Maximum duration of the intensity distribution of the pulse.
- t_peakfloat (in second)
The time at which the laser envelope reaches its maximum amplitude, i.e. \(t_{peak}\) in the above formula.
- cep_phasefloat (in radian), optional
The Carrier Enveloppe Phase (CEP), i.e. \(\phi_{cep}\) in the above formula (i.e. the phase of the laser oscillation, at the time where the laser envelope is maximum)
- n_orderfloat (in meter)
The shape parameter of the super-gaussian function, i.e. \(n\) in the above formula. If \(n=2\) the super-Gaussian becomes a standard Gaussian function. If \(n=1\) the super-Gaussian becomes a Laplace function.