def get_spectrum( self, t=None, iteration=None, pol=None,
m='all', plot=False, **kw ):
"""
Return the spectrum of the laser
(Absolute value of the Fourier transform of the fields.)
Parameters
----------
t : float (in seconds), optional
Time at which to obtain the data (if this does not correspond to
an available file, the last file before `t` will be used)
Either `t` or `iteration` should be given by the user.
iteration : int
The iteration at which to obtain the data
Either `t` or `iteration` should be given by the user.
pol : string
Polarization of the field. Options are 'x', 'y'
m : int or str, optional
Only used for thetaMode geometry
Either 'all' (for the sum of all the modes)
or an integer (for the selection of a particular mode)
plot: bool, optional
Whether to plot the data
**kw : dict, otional
Additional options to be passed to matplotlib's `plot` method
Returns
-------
A tuple with:
- The 1D spectrum on axis
- A FieldMetaInformation object
"""
# Check if polarization has been entered
if pol not in ['x', 'y']:
raise ValueError('The `pol` argument is missing or erroneous.')
if pol == 'x':
slicing_dir = 'y'
theta = 0
else:
slicing_dir = 'x'
theta = np.pi/2.
# Get field data
field, info = self.get_field( t=t, iteration=iteration, field='E',
coord=pol, theta=theta, m=m,
slicing_dir=slicing_dir )
# Get central field lineout
field1d = field[field.shape[0]/2, :]
# FFT of 1d data
dt = (info.z[1]-info.z[0])/const.c # Integration step for the FFT
fft_field = np.fft.fft(field1d) * dt
# Take half of the data (positive frequencies only)
spectrum = abs( fft_field[ :len(fft_field)/2 ] )
# Create a FieldMetaInformation object
T = (info.zmax-info.zmin)/const.c
spect_info = FieldMetaInformation( {0:'omega'}, spectrum.shape,
grid_spacing=( 2*np.pi/T, ), grid_unitSI=1,
global_offset=(0,), position=(0,))
# Plot the field if required
if plot:
plt.plot( spect_info.omega, spectrum, **kw )
plt.xlabel('$\omega \; (rad.s^{-1})$',
fontsize=self.plotter.fontsize )
plt.ylabel('Spectrum', fontsize=self.plotter.fontsize )
return( spectrum, spect_info )
def get_spectrogram( self, t=None, iteration=None, pol=None, theta=0,
slicing_dir='y', plot=False, **kw ):
"""
Calculates the spectrogram of a laserpulse, by the FROG method.
Mathematically:
$$ s(\omega, \tau) = | \int_{-\infty}^{\infty} E(t) |E(t-\tau)|^2
\exp( -i\omega t) dt |^2 $$
See Trebino, R: Frequency Resolved Optical Gating: The measurements of
Ultrashort Laser Pulses: year 2000: formula 5.2
The time is centered around the laser pulse.
Parameters
----------
t : float (in seconds), optional
Time at which to obtain the data (if this does not correspond to
an available file, the last file before `t` will be used)
Either `t` or `iteration` should be given by the user.
iteration : int
The iteration at which to obtain the data
Either `t` or `iteration` should be given by the user.
pol : string
Polarization of the laser field. Options are 'x', 'y'
plot: bool, optional
Whether to plot the spectrogram
**kw : dict, otional
Additional options to be passed to matplotlib's `imshow` method
Returns
-------
- A 2d array with spectrogram
- info : a FieldMetaInformation object
(see the corresponding docstring)
"""
# Get the field envelope
env, _ = self.get_laser_envelope(t=t, iteration=iteration, pol=pol)
# Get the field
E, info = self.get_field( t=t, iteration=iteration, field='E',
coord=pol, theta=theta,
slicing_dir=slicing_dir )
# Get central slice
E = E[E.shape[0] / 2, :]
Nz = len(E)
# Get time domain of the data
tmin = info.zmin / const.c
tmax = info.zmax / const.c
T = tmax - tmin
dt = T / Nz
# Normalize the Envelope
env /= np.sqrt(np.trapz(env ** 2, dx=dt))
# Allocate array for the gating function and the spectrogran
E_shift = np.zeros_like(E)
spectrogram = np.zeros((2 * Nz, Nz))
# Loop over the time variable of the spectrogram
for i in range( Nz * 2):
itau = i % Nz
# Shift the E field and fill the rest with zeros
if i < Nz:
E_shift[:itau] = env[ Nz - itau: Nz]
E_shift[itau:] = 0
else:
E_shift[itau:] = env[: Nz - itau]
E_shift[:itau] = 0
EE = E * E_shift ** 2
fft_EE = np.fft.fft(EE)
spectrogram[i, :] = np.abs(fft_EE) ** 2
# Rotate and flip array to have input form of imshow
spectrogram = np.flipud(np.rot90(spectrogram[:, Nz / 2:]))
# Find the time at which the wigner transform is the highest
maxi, maxj = np.unravel_index(spectrogram.argmax(), spectrogram.shape)
tmin = -(T - T / spectrogram.shape[1] * maxj)
info = FieldMetaInformation( {0:'omega', 1:'t'}, spectrogram.shape,
grid_spacing=( 2*np.pi/T, dt/2. ), grid_unitSI=1,
global_offset=(0, tmin), position=(0, 0))
# Plot the result if needed
if plot:
iteration = self.iterations[ self.current_i ]
time_fs = 1.e15*self.t[ self.current_i ]
plt.imshow( spectrogram, extent=info.imshow_extent, aspect='auto',
**kw)
plt.title("Spectrogram at %.1f fs (iteration %d)" \
%(time_fs, iteration ), fontsize=self.plotter.fontsize)
plt.xlabel('$t \;(s)$', fontsize=self.plotter.fontsize )
plt.ylabel('$\omega \;(rad.s^{-1})$',
fontsize=self.plotter.fontsize )
return( spectrogram, info )
def get_current( self, t=None, iteration=None, species=None, select=None,
bins=100, plot=False, **kw ):
"""
Calculate the electric current along the z-axis for selected particles.
Parameters
----------
t : float (in seconds), optional
Time at which to obtain the data (if this does not correspond to
an available file, the last file before `t` will be used)
Either `t` or `iteration` should be given by the user
iteration : int
The iteration at which to obtain the data
Either `t` or `iteration` should be given by the user
species : string
Particle species to use for calculations
select : dict, optional
Either None or a dictionary of rules
to select the particles, of the form
'x' : [-4., 10.] (Particles having x between -4 and 10 microns)
'z' : [0, 100] (Particles having x between 0 and 100 microns)
bins : int, optional
Number of bins along the z-axis in which to calculate the current
plot : bool, optional
Whether to plot the requested quantity
**kw : dict, otional
Additional options to be passed to matplotlib's `plot` method
Returns
-------
A tuple of arrays containig
- The current in each bin in Ampere
- A FieldMetaInformation object (See object's docstring for more details)
"""
# Get particle data
z, uz, uy, ux, w, q = self.get_particle(
var_list=['z', 'uz', 'uy', 'ux', 'w', 'charge'],
t=t, iteration=iteration,
species=species, select=select )
# Calculate Lorentz factor for all particles
gamma = np.sqrt(1 + ux ** 2 + uy ** 2 + uz ** 2)
# Calculate particle velocities
vz = uz / gamma * const.c
# Length to be seperated in bins
len_z = np.max(z) - np.min(z)
vzq_sum, _ = np.histogram(z, bins=bins, weights=(vz*w*q))
# Calculete the current in each bin
current = np.abs(vzq_sum * bins / (len_z * 1.e-6))
# Info object with central position of the bins
info = FieldMetaInformation( {0: 'z'}, current.shape,
grid_spacing=(len_z/bins, ), grid_unitSI=1,
global_offset=(np.min(z)+len_z/bins/2,), position=(0,))
# Plot the result if needed
if plot:
iteration = self.iterations[ self.current_i ]
time_fs = 1.e15*self.t[ self.current_i ]
plt.plot( info.z, current, **kw)
plt.title("Current at %.1f fs (iteration %d)"
%(time_fs, iteration ), fontsize=self.plotter.fontsize)
plt.xlabel('$z \;(\mu m)$', fontsize=self.plotter.fontsize)
plt.ylabel('$I \;(A)$', fontsize=self.plotter.fontsize)
# Return the current and bin centers
return(current, info)
