Gaussian Laser Profile#

class lasy.profiles.GaussianProfile(wavelength, pol, laser_energy, w0, tau, t_peak, cep_phase=0, z_foc=0)[source]#

Class for the analytic profile of a Gaussian laser pulse.

More precisely, the electric field corresponds to:

\[E_u(\boldsymbol{x}_\perp,t) = Re\left[ E_0\, \exp\left( -\frac{\boldsymbol{x}_\perp^2}{w_0^2} - \frac{(t-t_{peak})^2}{\tau^2} -i\omega_0(t-t_{peak}) + i\phi_{cep}\right) \times p_u \right]\]

where \(u\) is either \(x\) or \(y\), \(p_u\) is the polarization vector, \(Re\) represent the real part, and \(\boldsymbol{x}_\perp\) is the transverse coordinate (orthogonal to the propagation direction). 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.
w0float (in meter): The waist of the laser pulse, i.e. \(w_0\) in the above formula.
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 Envelope 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)
z_focfloat (in meter), optional: Position of the focal plane. (The laser pulse is initialized at z=0.)

Examples

>>> import matplotlib.pyplot as plt
>>> from lasy.laser import Laser
>>> from lasy.profiles.gaussian_profile import GaussianProfile
>>> from lasy.utils.laser_utils import get_full_field
>>> # Create profile.
>>> profile = GaussianProfile(
...     wavelength=0.6e-6,  # m
...     pol=(1, 0),
...     laser_energy=1.,  # J
...     w0=5e-6,  # m
...     tau=30e-15,  # s
...     t_peak=0.  # s
... )
>>> # Create laser with given profile in `rt` geometry.
>>> laser = Laser(
...     dim="rt",
...     lo=(0e-6, -60e-15),
...     hi=(10e-6, +60e-15),
...     npoints=(50, 400),
...     profile=profile
... )
>>> # Visualize field.
>>> E_rt, extent = get_full_field(laser)
>>> extent[2:] *= 1e6
>>> extent[:2] *= 1e15
>>> tmin, tmax, rmin, rmax = extent
>>> vmax = np.abs(E_rt).max()
>>> plt.imshow(
...     E_rt,
...     origin="lower",
...     aspect="auto",
...     vmax=vmax,
...     vmin=-vmax,
...     extent=[tmin, tmax, rmin, rmax],
...     cmap='bwr',
... )
>>> plt.xlabel('t (fs)')
>>> plt.ylabel('r (µm)')