Combined Longitudinal and Transverse Profile

class lasy.profiles.CombinedLongitudinalTransverseProfile(wavelength, pol, laser_energy, long_profile, trans_profile)

Class that combines a longitudinal and transverse laser profile.

The combined profile is defined as the product of the longitudinal and transverse profile.

More precisely, the electric field corresponds to:

\[E_u(\boldsymbol{x}_\perp,t) = Re\left[ E_0\, \mathcal{T}(x, y) \times \mathcal{L}(t) e^{-i\omega_0 t} \times p_u \right]\]

where \(u\) is either \(x\) or \(y\), \(p_u\) is the polarization vector, \(Re\) represent the real part. The other parameters in this formula are defined below.

Parameters:

wavelengthfloat (in meter)

The main laser wavelength \(\lambda_0\) of the laser, which defines \(\omega_0\) in the above formula, according to \(\omega_0 = 2\pi c/\lambda_0\).

pollist of 2 complex numbers (dimensionless)

Polarization vector. It corresponds to \(p_u\) in the above formula ; \(p_x\) is the first element of the list and \(p_y\) is the second element of the list. Using complex numbers enables elliptical polarizations.

laser_energyfloat (in Joule)

The total energy of the laser pulse. The amplitude of the laser field (\(E_0\) in the above formula) is automatically calculated so that the pulse has the prescribed energy.

long_profileLongitudinalProfile

Defines the longitudinal envelope of the laser, i.e. the function \(\mathcal{L}(t)\) in the above formula.

transverse_profileTransverseProfile

Defines the transverse envelope of the laser, i.e. the function \(\mathcal{T}(x, y)\) in the above formula.

evaluate(x, y, t)

Return the envelope field of the laser.

Parameters:

x, y, t: ndarrays of floats

Define points on which to evaluate the envelope These arrays need to all have the same shape.

Returns:

envelope: ndarray of complex numbers

Contains the value of the envelope at the specified points This array has the same shape as the arrays x, y, t