Partial Coherence Simulation

In order to simulate the temporal and spectral distribution of SASE pulses there is an easy way based random fluctuations filtered spectrally and temporally.

The only input parameters are the center wavelength, spectral bandwidth and the pulse duration.

Here you can find a small python script (by MartinB) implementing the partial coherence method as described in:

• Thomas Pfeifer et al. Partial-coherence method to model experimental free-electron laser pulse statistics, Opt. Lett. 35, 3441-3443 (2010); link to the paper

The pulse shapes in time AND corresponding spectral distribution can be easily created with:

• a python script

  Click here to expand the script ...

  import numpy as np
  import matplotlib.pyplot as plt

  def GetSASE(CentralEnergy, dE_FWHM, dt_FWHM, samples=0, Axis=True):
  h=4.135667662 #in eV*fs
  dE=dE_FWHM/2.355 #in eV, converts to sigma
  dt=dt_FWHM/2.355 #in fs, converts to sigma
  if samples == 0:
  samples=int(400.*dt*CentralEnergy/h)
  else:
  if (samples < 400.*dt*CentralEnergy/h):
  print("Number of samples is a little small, proceeding anyway. Got", samples, "prefer more than",400.*dt*CentralEnergy/h)

  EnAxis=np.linspace(0.,20.*CentralEnergy,num=samples)
  EnInput=np.zeros(samples, dtype=np.complex64)
  EnInput=np.exp(-(EnAxis-CentralEnergy)**2/2./dE**2+2*np.pi*1j*np.random.random(size=samples))
  En_FFT=np.fft.fft(EnInput)
  TAxis=np.fft.fftfreq(samples,d=(20.*CentralEnergy)/samples)*h
  TOutput=np.exp(-TAxis**2/2./dt**2)*En_FFT
  EnOutput=np.fft.ifft(TOutput)
  if (Axis):
  return EnAxis, EnOutput, TAxis, TOutput
  else:
  return EnOutput, TOutput

  
  

  # set the main parameters here:
  CentralEnergy=80. # in eV
  bandwidth=0.5 # bandwidth in %
  dt_FWHM=30. # FWHM of the temporal duration on average

  dE_FWHM=CentralEnergy/100 *bandwidth # calculate bandwidth of the spectrum in eV

  # calculate 3 SASE pulses
  EnAxis, EnOutput, TAxis, TOutput = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)
  EnAxis2, EnOutput2, TAxis2, TOutput2 = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)
  EnAxis3, EnOutput3, TAxis3, TOutput3 = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)

  # plot spectrum
  ax1 = plt.subplot(1, 2, 1)
  plt.plot(EnAxis,np.absolute(EnOutput),EnAxis2,np.absolute(EnOutput2),EnAxis3,np.absolute(EnOutput3) )
  plt.xlim(CentralEnergy-2.*dE_FWHM,CentralEnergy+2.*dE_FWHM)
  plt.title('Average pulse duration: %.1f fs' % dt_FWHM )
  ax1.set_xlabel('Photon energy in eV')
  ax1.set_ylabel('spectral intensity')

  # plot time structure
  ax1 =plt.subplot(1, 2, 2)
  plt.plot(TAxis,np.absolute(TOutput),TAxis2,np.absolute(TOutput2), TAxis3,np.absolute(TOutput3))
  plt.xlim(-2.*dt_FWHM,+2.*dt_FWHM)
  ax1.set_xlabel('time in fs')
  ax1.set_ylabel('pulse amplitude')

  plt.show()

• or the same as a Jupyter Notebook GenerateSASE.ipynb 

Some examples:

CentralEnergy=80 # in eV

bandwidth=0.5 # bandwidth in %

dt_FWHM=10, 30., 70  # FWHM of the temporal duration on average