Gaussian Longitudinal Profile

class lasy.profiles.longitudinal.GaussianLongitudinalProfile(wavelength, tau, t_peak, cep_phase=0)

Class for the analytic profile of a longitudinally-Gaussian laser pulse.

More precisely, the longitudinal envelope (to be used in the CombinedLongitudinalTransverseProfile class) corresponds to:

\[\mathcal{L}(t) = \exp\left( - \frac{(t-t_{peak})^2}{\tau^2} + i\omega_0t_{peak} \right)\]

Parameters:

taufloat (in second)

The duration of the laser pulse, i.e. \(\tau\) in the above formula. Note that \(\tau = \tau_{FWHM}/\sqrt{2\log(2)}\), 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)

evaluate(t)

Return the longitudinal envelope.

Parameters:

t: ndarrays of floats

Define points on which to evaluate the envelope

Returns:

envelope: ndarray of complex numbers

Contains the value of the longitudinal envelope at the specified points. This array has the same shape as the array t.