def BB(ω): #ω: eV
ε = 1 - Ωp**2 / (ω * (ω + 1j * Γ0))
α = (ω**2 + 1j * ω * Γ1)**.5
za = (α - ω1) / (2**.5 * σ1)
zb = (α + ω1) / (2**.5 * σ1)
ε += 1j * π**.5 * f1 * ωp**2 / (2**1.5 * α * σ1) * (w(za) + w(zb)) #χ1
α = (ω**2 + 1j * ω * Γ2)**.5
za = (α - ω2) / (2**.5 * σ2)
zb = (α + ω2) / (2**.5 * σ2)
ε += 1j * π**.5 * f2 * ωp**2 / (2**1.5 * α * σ2) * (w(za) + w(zb)) #χ2
α = (ω**2 + 1j * ω * Γ3)**.5
za = (α - ω3) / (2**.5 * σ3)
zb = (α + ω3) / (2**.5 * σ3)
ε += 1j * π**.5 * f3 * ωp**2 / (2**1.5 * α * σ3) * (w(za) + w(zb)) #χ3
α = (ω**2 + 1j * ω * Γ4)**.5
za = (α - ω4) / (2**.5 * σ4)
zb = (α + ω4) / (2**.5 * σ4)
ε += 1j * π**.5 * f4 * ωp**2 / (2**1.5 * α * σ4) * (w(za) + w(zb)) #χ4
α = (ω**2 + 1j * ω * Γ5)**.5
za = (α - ω5) / (2**.5 * σ5)
zb = (α + ω5) / (2**.5 * σ5)
ε += 1j * π**.5 * f5 * ωp**2 / (2**1.5 * α * σ5) * (w(za) + w(zb)) #χ5
return ε
def NormalizedVoigt(x, *params):
"""
The Voigt function. The result of the convolution of a Lorentzian with one or more
Gaussians. Often used to describe an intrinsically Lorentzian absorption profile blurred
by Gaussian broadening from thermal motions and turbulance and another Gaussian instrument
profile. The result is also the real part of the Faddevva function (the complex probability
function), implemented by Scipy as wofz in scipy.special
This returns a normalized profile. The name `NormalizedVoigt` is to keep the convention
for the rest of this module. The amplitude controlling Voigt profile `Voigt` evaluates
this function first for `x - x0 = 0` to empirically `un-normalize` it before scaling by the
requested amplitude
Reference:
Olivero, J.J; R.L. Longbothum. ``Empirical fits to the Voigt line width:
A brief review''. Journal of Quantitative Spectroscopy and Radiative Transfer. Vol 17.
Issue 2. pages 223-236. Feb 1977
Parameters: `x0, sigma, gamma = params`
x0 -> center of the profile
sigma -> the Gaussian width
gamma -> the Lorentzian width
"""
x0, sigma, gamma = params
return w( ((x-x0) + 1j*gamma) / (sigma * np.sqrt(np.pi)) ).real / (
sigma * np.sqrt(2 * np.pi) )
def BB(wl): #wl: eV
e = 1 - Omp**2 / (wl * (wl + 1j * L0))
a = (wl**2 + 1j * wl * L1)**.5
za = (a - w1) / (2**.5 * o1)
zb = (a + w1) / (2**.5 * o1)
e += 1j * p**.5 * f1 * wp**2 / (2**1.5 * a * o1) * (w(za) + w(zb)) #x1
a = (wl**2 + 1j * wl * L2)**.5
za = (a - w2) / (2**.5 * o2)
zb = (a + w2) / (2**.5 * o2)
e += 1j * p**.5 * f2 * wp**2 / (2**1.5 * a * o2) * (w(za) + w(zb)) #x2
a = (wl**2 + 1j * wl * L3)**.5
za = (a - w3) / (2**.5 * o3)
zb = (a + w3) / (2**.5 * o3)
e += 1j * p**.5 * f3 * wp**2 / (2**1.5 * a * o3) * (w(za) + w(zb)) #x3
a = (wl**2 + 1j * wl * L4)**.5
za = (a - w4) / (2**.5 * o4)
zb = (a + w4) / (2**.5 * o4)
e += 1j * p**.5 * f4 * wp**2 / (2**1.5 * a * o4) * (w(za) + w(zb)) #x4
return e
def bv(f, f0, b0, T, s):
'''
Function representing convolution of the lorentzian line shape of the red transition and gaussian maxwell
distribution. This is taken from 5.13 from Chang chi's thesis and added the effect of saturation parameter.
Args:
f: numpy.array, frequency vector
f0: float, resonance frequency or centre of the spectrum
b0: float, optical depth at resonance at zero temperature
T: float, temperature in micro K
s: float, saturation parameter of the probe, :math:`I/I_s`.
Returns:
optical depth for frequencies f in the shape f.
'''
gamma = 2 * pi * 7.5 * milli
vavg = np.sqrt(T * micro * Boltzmann / (87 * m_p))
k = 2 * pi / (689 * nano)
x = w((2 * pi * (f - f0) + 1j * gamma * np.sqrt(1 + s) / 2) * 1e6 /
(np.sqrt(2) * k * vavg))
return b0 * np.sqrt(pi / 8) * (1 /
(1 + s)) * (gamma * np.sqrt(1 + s) * 1e6 /
(k * vavg)) * x.real
