Cosine Longitudinal Profile#

Used to define a truncated cosine longitudinal laser profile (i.e., a profile described by the function \(\cos{\left( {\frac{\pi}{2} \frac{t - t_{peak}}{t_{fwhm}} } \right)}\), in the interval \([t_{peak} - t_{fwhm}/2, t_{peak} + t_{fwhm}/2]\)).


class lasy.profiles.longitudinal.cosine_profile.CosineLongitudinalProfile(wavelength, tau_fwhm, t_peak, cep_phase=0)[source]#

Class for the analytic longitudinal truncated cosine profile of a laser pulse.

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

\[\mathcal{L}(t) = \cos\left({ \frac{\pi}{2} \frac{t-t_{peak}}{\tau_{fwhm}} }\right) \theta\left({ \frac{t-t_{peak}}{\tau_{fwhm}} + 1 }\right) \theta\left({ 1 - \frac{t-t_{peak}}{\tau_{fwhm}}} \right) \exp\left({ + i (\phi_{cep} + \omega_0 t_{peak} ) }\right)\]
Parameters:
wavelengthfloat (in meter)

The main laser wavelength \(\lambda_0\) of the laser.

tau_fwhmfloat (in second)

The Full-Width-Half-Maximum duration of the intensity distribution of the pulse, i.e. \(\tau_{fwhm}\) in the above formula.

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. the phase of the laser oscillation, at the time where the laser envelope is maximum, \(\phi_{cep}\) in the above formula).

evaluate(t)[source]#

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.