def basic_test():
"""
Compare with program I wrote previously in Mathematica. Also confirms
that I don't accidentally mess up the program by editing.
"""
n_list = [1, 2 + 4j, 3 + 0.3j, 1 + 0.1j]
d_list = [inf, 2, 3, inf]
th_0 = 0.1
lam_vac = 100
print('The following should all be zero (within rounding errors):')
s_data = coh_tmm('s', n_list, d_list, th_0, lam_vac)
print(df(s_data['r'], -0.60331226568845775 - 0.093522181653632019j))
print(df(s_data['t'], 0.44429533471192989 + 0.16921936169383078j))
print(df(s_data['R'], 0.37273208839139516))
print(df(s_data['T'], 0.22604491247079261))
p_data = coh_tmm('p', n_list, d_list, th_0, lam_vac)
print(df(p_data['r'], 0.60102654255772481 + 0.094489146845323682j))
print(df(p_data['t'], 0.4461816467503148 + 0.17061408427088917j))
print(df(p_data['R'], 0.37016110373044969))
print(df(p_data['T'], 0.22824374314132009))
ellips_data = ellips(n_list, d_list, th_0, lam_vac)
print(df(ellips_data['psi'], 0.78366777347038352))
print(df(ellips_data['Delta'], 0.0021460774404193292))
return
def sample2():
"""
Here's the transmitted intensity versus wavelength through a single-layer
film which has some complicated wavelength-dependent index of refraction.
(I made these numbers up, but in real life they could be read out of a
graph / table published in the literature.) Air is on both sides of the
film, and the light is normally incident.
"""
#index of refraction of my material: wavelength in nm versus index.
material_nk_data = array([[200, 2.1 + 0.1j], [300, 2.4 + 0.3j],
[400, 2.3 + 0.4j], [500, 2.2 + 0.4j],
[750, 2.2 + 0.5j]])
material_nk_fn = interp1d(material_nk_data[:, 0].real,
material_nk_data[:, 1],
kind='quadratic')
d_list = [inf, 300, inf] #in nm
lambda_list = linspace(200, 750, 400) #in nm
T_list = []
for lambda_vac in lambda_list:
n_list = [1, material_nk_fn(lambda_vac), 1]
T_list.append(coh_tmm('s', n_list, d_list, 0, lambda_vac)['T'])
plt.figure()
plt.plot(lambda_list, T_list)
plt.xlabel('Wavelength (nm)')
plt.ylabel('Fraction of power transmitted')
plt.title('Transmission at normal incidence')
plt.show()
def sample6():
"""
An example reflection plot with a surface plasmon resonance (SPR) dip.
Compare with http://doi.org/10.2320/matertrans.M2010003 ("Spectral and
Angular Responses of Surface Plasmon Resonance Based on the Kretschmann
Prism Configuration") Fig 6a
"""
# list of layer thicknesses in nm
d_list = [inf, 5, 30, inf]
# list of refractive indices
n_list = [1.517, 3.719 + 4.362j, 0.130 + 3.162j, 1]
# wavelength in nm
lam_vac = 633
# list of angles to plot
theta_list = linspace(30 * degree, 60 * degree, num=300)
# initialize lists of y-values to plot
Rp = []
for theta in theta_list:
Rp.append(coh_tmm('p', n_list, d_list, theta, lam_vac)['R'])
plt.figure()
plt.plot(theta_list / degree, Rp, 'blue')
plt.xlabel('theta (degree)')
plt.ylabel('Fraction reflected')
plt.xlim(30, 60)
plt.ylim(0, 1)
plt.title(
'Reflection of p-polarized light with Surface Plasmon Resonance\n'
'Compare with http://doi.org/10.2320/matertrans.M2010003 Fig 6a')
plt.show()
def sample1():
"""
Here's a thin non-absorbing layer, on top of a thick absorbing layer, with
air on both sides. Plotting reflected intensity versus wavenumber, at two
different incident angles.
"""
# list of wavenumbers to plot in nm^-1
ks=linspace(0.0025,.00125,num=800)
# list of layer thicknesses in nm
ks=linspace(0.0025,.00125,num=800)
d0 = inf
d1 = 92
d2 = 91
d3 = inf
d_list = [d0, d1, d2, d1, d2, d1, d2, d1, d2, d1, d2, d1, d2, d1, d3]
material_nk_data2 = array([[0.0025, 1.575+0.17j], # @400nm
[0.002, 1.5552+0.15j], # @500nm
[0.001667, 1.5444+0.14j], # @600nm
[0.001429, 1.53796+0.13j], # @700nm
[0.00125, 1.53375+0.12j]]) # @800nm
material_nk_fn2 = interp1d(material_nk_data2[:,0].real,
material_nk_data2[:,1], kind='quadratic')
material_nk_data1 = array([[0.0025, 1.705+0.06j], # @400nm
[0.002, 1.6852+0.04j], # @500nm
[0.001667, 1.6744+0.03j], # @600nm
[0.001429, 1.66796+0.02j], # @700nm
[0.00125, 1.66375+0.014j]]) # @800nm
material_nk_fn1 = interp1d(material_nk_data1[:,0].real,
material_nk_data1[:,1], kind='quadratic')
# initialize lists of y-values to plot
Rnorm=[]
R37=[]
for k in ks:
# For normal incidence, s and p polarizations are identical.
# I arbitrarily decided to use 's'.
n_list = [1, material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), 1.615+0.085j]
Rnorm.append(coh_tmm('s',n_list, d_list, 0, 1/k)['R'])
#R37.append(unpolarized_RT(n_list, d_list, 37*degree, 1/k)['R'])
kcm = ks * 1e7 #ks in cm^-1 rather than nm^-1
lamb = 1/ks
plt.figure()
plt.plot(lamb,Rnorm,'blue',expx,expy,'purple')
plt.xlabel('Wavelength (/nm)')
plt.ylabel('Fraction reflected')
plt.title('Simulated reflection of unpolarized light at 0$^\circ$ incidence (blue), '
'Experimental data (purple)')
plt.axis([400, 800, 0, 0.25])
def sample1():
"""
Here's a thin non-absorbing layer, on top of a thick absorbing layer, with
air on both sides. Plotting reflected intensity versus wavenumber, at two
different incident angles.
"""
# list of layer thicknesses in nm
d_list = [inf, 100, 300, inf]
# list of refractive indices
n_list = [1, 2.2, 3.3 + 0.3j, 1]
# list of wavenumbers to plot in nm^-1
ks = linspace(0.0001, .01, num=400)
# initialize lists of y-values to plot
Rnorm = []
R45 = []
for k in ks:
# For normal incidence, s and p polarizations are identical.
# I arbitrarily decided to use 's'.
Rnorm.append(coh_tmm('s', n_list, d_list, 0, 1 / k)['R'])
R45.append(unpolarized_RT(n_list, d_list, 45 * degree, 1 / k)['R'])
kcm = ks * 1e7 #ks in cm^-1 rather than nm^-1
plt.figure()
plt.plot(kcm, Rnorm, 'blue', kcm, R45, 'purple')
plt.xlabel('k (cm$^{-1}$)')
plt.ylabel('Fraction reflected')
plt.title('Reflection of unpolarized light at 0$^\circ$ incidence (blue), '
'45$^\circ$ (purple)')
plt.show()
def sample4():
"""
Here is an example where we plot absorption and Poynting vector
as a function of depth.
"""
d_list = [inf, 100, 300, inf] #in nm
n_list = [1, 2.2 + 0.2j, 3.3 + 0.3j, 1]
th_0 = pi / 4
lam_vac = 400
pol = 'p'
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
ds = linspace(-50, 400, num=1000) #position in structure
poyn = []
absor = []
for d in ds:
layer, d_in_layer = find_in_structure_with_inf(d_list, d)
data = position_resolved(layer, d_in_layer, coh_tmm_data)
poyn.append(data['poyn'])
absor.append(data['absor'])
# convert data to numpy arrays for easy scaling in the plot
poyn = array(poyn)
absor = array(absor)
plt.figure()
plt.plot(ds, poyn, 'blue', ds, 200 * absor, 'purple')
plt.xlabel('depth (nm)')
plt.ylabel('AU')
plt.title('Local absorption (purple), Poynting vector (blue)')
plt.show()
def sample1():
"""
Here's a thin non-absorbing layer, on top of a thick absorbing layer, with
air on both sides. Plotting reflected intensity versus wavenumber, at two
different incident angles.
"""
# list of wavenumbers to plot in nm^-1
ks=linspace(0.0025,.00125,num=800)
# list of layer thicknesses in nm
d0 = inf
d1 = 117
d2 = 73
d3 = inf
d_list = [inf, d1, d2, d1, d2, d1, d2, d1, d2, d1, d2, d1, d2, d3]
# list of refractive indices
#Light-constasted layers
material_nk_data1 = array([[0.0025, 1.6335+0.0564j], # @400nm
[0.002,1.61376+0.0366], # @500nm
[0.001667, 1.603+0.025844j], # @600nm
[0.001429,1.5965+0.01935j], # @700nm
[0.00125, 1.59231+0.001515j]]) # @800nm
material_nk_fn1 = interp1d(material_nk_data1[:,0].real,
material_nk_data1[:,1], kind='quadratic')
#Dark-contrasted layers
material_nk_data2 = array([[0.0025,1.5326+0.13955j], # @400nm
[0.002, 1.5128+0.11975j], # @500nm
[0.001667,1.5024+0.109j], # @600nm
[0.001429,1.4956+0.1025j], # @700nm
[0.00125,1.49135+0.0983j]]) # @800nm
material_nk_fn2 = interp1d(material_nk_data2[:,0].real,
material_nk_data2[:,1], kind='quadratic')
# initialize lists of y-values to plot
Rnorm=[]
R37=[]
for k in ks:
# For normal incidence, s and p polarizations are identical.
# I arbitrarily decided to use 's'.
n_list = [1, material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k),1.55+0.1j]
Rnorm.append(coh_tmm('s',n_list, d_list, 0, 1/k)['R'])
#R37.append(unpolarized_RT(n_list, d_list, 37*degree, 1/k)['R'])
kcm = ks * 1e7 #ks in cm^-1 rather than nm^-1
lamb = 1/ks
plt.figure()
plt.plot(lamb,Rnorm,'blue',expx,expy,'purple')
plt.xlabel('Wavelength (/nm)')
plt.ylabel('Fraction reflected')
plt.title('Simulated reflection of unpolarized light at 0$^\circ$ incidence (blue), '
'Experimental data (purple)')
plt.axis([400, 800, 0, 0.25])
def coh_overflow_test():
"""
Test whether very very opaque layers will break the coherent program
"""
n_list = [1., 2 + .1j, 1 + 3j, 4., 5.]
d_list = [inf, 50, 1e5, 50, inf]
lam = 200
alpha_d = imag(n_list[2]) * 4 * pi * d_list[2] / lam
print('Very opaque layer: Calculation should involve e^(-', alpha_d, ')!')
data = coh_tmm('s', n_list, d_list, 0, lam)
n_list2 = n_list[0:3]
d_list2 = d_list[0:3]
d_list2[-1] = inf
data2 = coh_tmm('s', n_list2, d_list2, 0, lam)
print('First entries of the following two lists should agree:')
print(data['vw_list'])
print(data2['vw_list'])
def calc_reflectances(n_fn_list, d_list, th_0, pol='s', spectral_range='narrow'):
"""
Calculate the reflection spectrum of a thin-film stack.
n_fn_list[m] should be a function that inputs wavelength in nm and
outputs refractive index of the m'th layer. In other words,
n_fn_list[2](456) == 1.53 + 0.4j mans that layer #2 has a refractive index
of 1.53 + 0.4j at 456nm. These functions could be defined with
scipy.interpolate.interp1d() for example.
pol, d_list and th_0 are defined as in tmm.coh_tmm ... but d_list
MUST be in units of nanometers
spectral_range can be 'full' if all the functions in n_fn_list can take
wavelength arguments between 360-830nm; or 'narrow' if some or all require
arguments only in the range 400-700nm. The wavelengths outside the
'narrow' range make only a tiny difference to the color, because they are
almost invisible to the eye. If spectral_range is 'narrow', then the n(400)
values are used for 360-400 and n(700) for 700-830nm
Returns a 2-column array where the first column is wavelength in nm
(360,361,362,...,830) and the second column is reflectivity (from 0
to 1, where 1 is a perfect mirror). This range is chosen to be
consistent with colorpy.illuminants. See colorpy.ciexyz.start_wl_nm etc.
"""
lam_vac_list = arange(360, 831)
num_layers = len(n_fn_list)
def extend_spectral_range(n_fn):
"""
Starting with a narrow-spectrum refractive index function
n_fn(wavelength), create then return the corresponding full-spectrum
refractive index function
"""
def extended_n_fn(lam):
if lam < 400:
return n_fn(400)
elif lam > 700:
return n_fn(700)
else:
return n_fn(lam)
return extended_n_fn
if spectral_range == 'narrow':
n_fn_list = [extend_spectral_range(n_fn) for n_fn in n_fn_list]
final_answer = []
for lam_vac in lam_vac_list:
n_list = [n_fn_list[i](lam_vac) for i in range(num_layers)]
R = coh_tmm(pol, n_list, d_list, th_0, lam_vac)['R']
final_answer.append([lam_vac,R])
final_answer = array(final_answer)
return final_answer
def sample1():
"""
Here's a thin non-absorbing layer, on top of a thick absorbing layer, with
air on both sides. Plotting reflected intensity versus wavenumber, at two
different incident angles.
"""
# list of wavenumbers to plot in nm^-1
ks=linspace(0.0025,.00125,num=800)
d0 = inf
d1 = 92
d2 = 90
d3 = inf
d_list = [d0, d1, d2, d1, d2, d1, d2, d1, d2, d1, d2, d1, d2, d1, d3]
material_nk_data2 = array([[0.0025, 1.575+0.17j], # @400nm
[0.002, 1.5552+0.15j], # @500nm
[0.001667, 1.5444+0.14j], # @600nm
[0.001429, 1.53796+0.13j], # @700nm
[0.00125, 1.53375+0.12j]]) # @800nm
material_nk_fn2 = interp1d(material_nk_data2[:,0].real,
material_nk_data2[:,1], kind='quadratic')
material_nk_data1 = array([[0.0025, 1.705+0.06j], # @400nm
[0.002, 1.6852+0.04j], # @500nm
[0.001667, 1.6744+0.03j], # @600nm
[0.001429, 1.66796+0.02j], # @700nm
[0.00125, 1.66375+0.014j]]) # @800nm
material_nk_fn1 = interp1d(material_nk_data1[:,0].real,
material_nk_data1[:,1], kind='quadratic')
# initialize lists of y-values to plot
Rnorm=[]
R37=[]
for k in ks:
# For normal incidence, s and p polarizations are identical.
# I arbitrarily decided to use 's'.
n_list = [1, material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), material_nk_fn2(k), material_nk_fn1(k), 1.615+0.085j]
Rnorm.append(coh_tmm('s',n_list, d_list, 0, 1/k)['R'])
#R37.append(unpolarized_RT(n_list, d_list, 37*degree, 1/k)['R'])
kcm = ks * 1e7 #ks in cm^-1 rather than nm^-1
lamb = 1/ks
plt.figure()
plt.plot(lamb,Rnorm,'blue',expx,expy,'purple')
plt.xlabel('Wavelength (/nm)')
plt.ylabel('Fraction reflected')
plt.title('Simulated reflection of unpolarized light at 0$^\circ$ incidence (blue), '
'Experimental data (purple)')
plt.axis([400, 800, 0, 0.25])
def run(self, thicknesses, theta0, polarization=None):
"""
runs the model with specified parameters
:param thicknesses: list of thicknesses, first and last must be inf
:param theta0: input angle
:param polarization: polarization state 's', 'p', or None
:return: void
"""
self.index_array = np.array(self.mat_df[self.layers])
if polarization is None:
self.data = tmm.unpolarized_RT(self.index_array, thicknesses, theta0, self.wavelength)
elif polarization in ['p', 's']:
self.data = tmm.coh_tmm(polarization, self.index_array, thicknesses, theta0, self.wavelength)
def sample1():
"""
Here's a thin non-absorbing layer, on top of a thick absorbing layer, with
air on both sides. Plotting reflected intensity versus wavenumber, at two
different incident angles.
"""
# list of layer thicknesses in nm
d_list = [inf, 100, 80, 100, 80, 100, 80, 100, 80, 100, 80, 100, 80, inf]
# list of refractive indices
n_list = [
1, 1.68 + 0.03j, 1.55 + 0.14j, 1.68 + 0.03j, 1.55 + 0.14j,
1.68 + 0.03j, 1.55 + 0.14j, 1.68 + 0.03j, 1.55 + 0.14j, 1.68 + 0.03j,
1.55 + 0.14j, 1.68 + 0.03j, 1.55 + 0.14j, 1.61 + 0.085j
]
# list of wavenumbers to plot in nm^-1
ks = linspace(0.0025, .00125, num=800)
# initialize lists of y-values to plot
Rnorm = []
R37 = []
for k in ks:
# For normal incidence, s and p polarizations are identical.
# I arbitrarily decided to use 's'.
Rnorm.append(coh_tmm('s', n_list, d_list, 0, 1 / k)['R'])
R37.append(unpolarized_RT(n_list, d_list, 37 * degree, 1 / k)['R'])
kcm = ks * 1e7 #ks in cm^-1 rather than nm^-1
lamb = 1 / ks
plt.figure()
plt.plot(lamb, Rnorm, 'blue', lamb, R37, 'purple')
plt.xlabel('Wavelength (/nm)')
plt.ylabel('Fraction reflected')
plt.title('Reflection of unpolarized light at 0$^\circ$ incidence (blue), '
'37$^\circ$ (purple)')
# data file
import numpy
datafile_path = "/users/Olimpia/Desktop/datafile.txt"
datafile_id = open(datafile_path, 'w+')
data = numpy.array([lamb, Rnorm])
data = data.T
numpy.savetxt(datafile_id, data, fmt=['%.4f', '%.4f'])
datafile_id.close()
def absorp_analytic_fn_test():
"""
Test absorp_analytic_fn functions
"""
d_list = [inf, 100, 300, inf] #in nm
n_list = [1, 2.2 + 0.2j, 3.3 + 0.3j, 1]
th_0 = pi / 4
lam_vac = 400
layer = 1
d = d_list[layer]
dist = 37
print('The following should all be zero (within rounding errors):')
for pol in ['s', 'p']:
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
expected_absorp = position_resolved(layer, dist, coh_tmm_data)['absor']
absorp_fn = absorp_analytic_fn()
absorp_fn.fill_in(coh_tmm_data, layer)
print(df(absorp_fn.run(dist), expected_absorp))
absorp_fn2 = absorp_fn.copy().flip()
dist_from_other_side = d - dist
print(df(absorp_fn2.run(dist_from_other_side), expected_absorp))
return
def position_resolved_test():
"""
Compare with program I wrote previously in Mathematica. Also, various
consistency checks.
"""
d_list = [inf, 100, 300, inf] #in nm
n_list = [1, 2.2 + 0.2j, 3.3 + 0.3j, 1]
th_0 = pi / 4
lam_vac = 400
layer = 1
dist = 37
print('The following should all be zero (within rounding errors):')
pol = 'p'
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
print(
df(coh_tmm_data['kz_list'][1],
0.0327410685922732 + 0.003315885921866465j))
data = position_resolved(layer, dist, coh_tmm_data)
print(df(data['poyn'], 0.7094950598055798))
print(df(data['absor'], 0.005135049118053356))
print(df(1, sum(absorp_in_each_layer(coh_tmm_data))))
pol = 's'
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
print(
df(coh_tmm_data['kz_list'][1],
0.0327410685922732 + 0.003315885921866465j))
data = position_resolved(layer, dist, coh_tmm_data)
print(df(data['poyn'], 0.5422594735025152))
print(df(data['absor'], 0.004041912286816303))
print(df(1, sum(absorp_in_each_layer(coh_tmm_data))))
#Poynting vector derivative should equal absorption
for pol in ['s', 'p']:
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data1 = position_resolved(layer, dist, coh_tmm_data)
data2 = position_resolved(layer, dist + 0.001, coh_tmm_data)
print(
'Finite difference should approximate derivative. Difference is ' +
str(
df((data1['absor'] + data2['absor']) /
2, (data1['poyn'] - data2['poyn']) / 0.001)))
#Poynting vector at end should equal T
layer = 2
dist = 300
for pol in ['s', 'p']:
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
print(df(data['poyn'], coh_tmm_data['T']))
#Poynting vector at start should equal power_entering
layer = 1
dist = 0
for pol in ['s', 'p']:
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
print(df(data['poyn'], coh_tmm_data['power_entering']))
#Poynting vector should be continuous
for pol in ['s', 'p']:
layer = 1
dist = 100
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
poyn1 = data['poyn']
layer = 2
dist = 0
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
poyn2 = data['poyn']
print(df(poyn1, poyn2))
return
def sample1():
"""
Here's a thin non-absorbing layer, on top of a thick absorbing layer, with
air on both sides. Plotting reflected intensity versus wavenumber, at two
different incident angles.
"""
# list of wavenumbers to plot in nm^-1
ks = linspace(0.0025, .00125, num=800)
# list of layer thicknesses in nm
d0 = inf
d1 = 117
d2 = 73
d3 = inf
d_list = [inf, d1, d2, d1, d2, d1, d2, d1, d2, d1, d2, d1, d2, d3]
# list of refractive indices
#Light-constasted layers
material_nk_data1 = array([
[0.0025, 1.6335 + 0.0564j], # @400nm
[0.002, 1.61376 + 0.0366], # @500nm
[0.001667, 1.603 + 0.025844j], # @600nm
[0.001429, 1.5965 + 0.01935j], # @700nm
[0.00125, 1.59231 + 0.001515j]
]) # @800nm
material_nk_fn1 = interp1d(material_nk_data1[:, 0].real,
material_nk_data1[:, 1],
kind='quadratic')
#Dark-contrasted layers
material_nk_data2 = array([
[0.0025, 1.5326 + 0.13955j], # @400nm
[0.002, 1.5128 + 0.11975j], # @500nm
[0.001667, 1.5024 + 0.109j], # @600nm
[0.001429, 1.4956 + 0.1025j], # @700nm
[0.00125, 1.49135 + 0.0983j]
]) # @800nm
material_nk_fn2 = interp1d(material_nk_data2[:, 0].real,
material_nk_data2[:, 1],
kind='quadratic')
# initialize lists of y-values to plot
Rnorm = []
R37 = []
for k in ks:
# For normal incidence, s and p polarizations are identical.
# I arbitrarily decided to use 's'.
n_list = [
1,
material_nk_fn1(k),
material_nk_fn2(k),
material_nk_fn1(k),
material_nk_fn2(k),
material_nk_fn1(k),
material_nk_fn2(k),
material_nk_fn1(k),
material_nk_fn2(k),
material_nk_fn1(k),
material_nk_fn2(k),
material_nk_fn1(k),
material_nk_fn2(k), 1.55 + 0.1j
]
Rnorm.append(coh_tmm('s', n_list, d_list, 0, 1 / k)['R'])
#R37.append(unpolarized_RT(n_list, d_list, 37*degree, 1/k)['R'])
kcm = ks * 1e7 #ks in cm^-1 rather than nm^-1
lamb = 1 / ks
plt.figure()
plt.plot(lamb, Rnorm, 'blue', expx, expy, 'purple')
plt.xlabel('Wavelength (/nm)')
plt.ylabel('Fraction reflected')
plt.title(
'Simulated reflection of unpolarized light at 0$^\circ$ incidence (blue), '
'Experimental data (purple)')
plt.axis([400, 800, 0, 0.25])
def incoherent_test():
"""
test inc_tmm(). To do: Add more tests.
"""
print('The following should all be zero (within rounding errors):')
#3-incoherent-layer test, real refractive indices (so that R and T are the
#same in both directions)
n0 = 1
n1 = 2
n2 = 3
n_list = [n0, n1, n2]
d_list = [inf, 567, inf]
c_list = ['i', 'i', 'i']
th0 = pi / 3
th1 = snell(n0, n1, th0)
th2 = snell(n0, n2, th0)
lam_vac = 400
for pol in ['s', 'p']:
inc_data = inc_tmm(pol, n_list, d_list, c_list, th0, lam_vac)
R0 = abs(interface_r(pol, n0, n1, th0, th1)**2)
R1 = abs(interface_r(pol, n1, n2, th1, th2)**2)
T0 = 1 - R0
RR = R0 + R1 * T0**2 / (1 - R0 * R1)
print(df(inc_data['R'], RR))
print(df(inc_data['R'] + inc_data['T'], 1))
#One finite layer with incoherent layers on both sides. Should agree with
#coherent program
n0 = 1 + 0.1j
n1 = 2 + 0.2j
n2 = 3 + 0.4j
n_list = [n0, n1, n2]
d_list = [inf, 100, inf]
c_list = ['i', 'c', 'i']
n00 = 1
th00 = pi / 3
th0 = snell(n00, n0, th00)
lam_vac = 400
for pol in ['s', 'p']:
inc_data = inc_tmm(pol, n_list, d_list, c_list, th0, lam_vac)
coh_data = coh_tmm(pol, n_list, d_list, th0, lam_vac)
print(df(inc_data['R'], coh_data['R']))
print(df(inc_data['T'], coh_data['T']))
print(df(1, sum(inc_absorp_in_each_layer(inc_data))))
#One finite layer with three incoherent layers. Should agree with
#manual calculation + coherent program
n0 = 1 + 0.1j
n1 = 2 + 0.2j
n2 = 3 + 0.004j
n3 = 4 + 0.2j
d1 = 100
d2 = 10000
n_list = [n0, n1, n2, n3]
d_list = [inf, d1, d2, inf]
c_list = ['i', 'c', 'i', 'i']
n00 = 1
th00 = pi / 3
th0 = snell(n00, n0, th00)
lam_vac = 400
for pol in ['s', 'p']:
inc_data = inc_tmm(pol, n_list, d_list, c_list, th0, lam_vac)
coh_data = coh_tmm(pol, [n0, n1, n2], [inf, d1, inf], th0, lam_vac)
th2 = snell(n0, n2, th0)
th3 = snell(n0, n3, th0)
coh_bdata = coh_tmm(pol, [n2, n1, n0], [inf, d1, inf], th2, lam_vac)
R02 = coh_data['R']
R20 = coh_bdata['R']
T02 = coh_data['T']
T20 = coh_bdata['T']
P2 = exp(-4 * pi * d2 * (n2 * cos(th2)).imag /
lam_vac) #fraction passing through
R23 = interface_R(pol, n2, n3, th2, th3)
T23 = interface_T(pol, n2, n3, th2, th3)
#T = T02 * P2 * T23 + T02 * P2 * R23 * P2 * R20 * P2 * T23 + ...
T = T02 * P2 * T23 / (1 - R23 * P2 * R20 * P2)
#R = R02
# + T02 * P2 * R23 * P2 * T20
# + T02 * P2 * R23 * P2 * R20 * P2 * R23 * P2 * T20 + ...
R = R02 + T02 * P2 * R23 * P2 * T20 / (1 - R20 * P2 * R23 * P2)
print(df(inc_data['T'], T))
print(df(inc_data['R'], R))
#The coherent program with a thick but randomly-varying-thickness substrate
#should agree with the incoherent program.
nair = 1 + 0.1j
nfilm = 2 + 0.2j
nsub = 3
nf = 3 + 0.4j
n_list = [nair, nfilm, nsub, nf]
n00 = 1
th00 = pi / 3
th0 = snell(n00, n0, th00)
lam_vac = 400
for pol in ['s', 'p']:
d_list_inc = [inf, 100, 1, inf] #sub thickness doesn't matter here
c_list = ['i', 'c', 'i', 'i']
inc_data = inc_tmm(pol, n_list, d_list_inc, c_list, th0, lam_vac)
coh_Rs = []
coh_Ts = []
for dsub in np.linspace(10000, 30000, 357):
d_list = [inf, 100, dsub, inf]
coh_data = coh_tmm(pol, n_list, d_list, th0, lam_vac)
coh_Rs.append(coh_data['R'])
coh_Ts.append(coh_data['T'])
print('Coherent with random thickness should agree with incoherent. ' +
'Discrepency is: ' + str(df(average(coh_Rs), inc_data['R'])))
print('Coherent with random thickness should agree with incoherent. ' +
'Discrepency is: ' + str(df(average(coh_Ts), inc_data['T'])))
#The coherent program with a thick substrate and randomly-varying wavelength
#should agree with the incoherent program.
n0 = 1 + 0.0j
n_list = [n0, 2 + 0.0002j, 3 + 0.0001j, 3 + 0.4j]
n00 = 1
th00 = pi / 3
th0 = snell(n00, n0, th00)
d_list = [inf, 10000, 10200, inf]
c_list = ['i', 'i', 'i', 'i']
for pol in ['s', 'p']:
inc_absorp = array([0., 0., 0., 0.])
coh_absorp = array([0., 0., 0., 0.])
num_pts = 234
for lam_vac in np.linspace(40, 50, num_pts):
inc_data = inc_tmm(pol, n_list, d_list, c_list, th0, lam_vac)
inc_absorp += array(inc_absorp_in_each_layer(inc_data))
coh_data = coh_tmm(pol, n_list, d_list, th0, lam_vac)
coh_absorp += array(absorp_in_each_layer(coh_data))
inc_absorp /= num_pts
coh_absorp /= num_pts
print(
'Coherent with random wavelength should agree with incoherent. ' +
'The two rows of this array should be the same:')
print(vstack((inc_absorp, coh_absorp)))
def position_resolved_test2():
"""
Similar to position_resolved_test(), but with initial and final medium
having a complex refractive index.
"""
d_list = [inf, 100, 300, inf] #in nm
# "00" is before the 0'th layer. This is easy way to generate th0, ensuring
#that n0*sin(th0) is real.
n00 = 1
th00 = pi / 4
n0 = 1 + 0.1j
th_0 = snell(n00, n0, th00)
n_list = [n0, 2.2 + 0.2j, 3.3 + 0.3j, 1 + 0.4j]
lam_vac = 400
layer = 1
dist = 37
print('The following should all be zero (within rounding errors):')
for pol in ['s', 'p']:
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
print(df(1, sum(absorp_in_each_layer(coh_tmm_data))))
#Poynting vector derivative should equal absorption
for pol in ['s', 'p']:
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data1 = position_resolved(layer, dist, coh_tmm_data)
data2 = position_resolved(layer, dist + 0.001, coh_tmm_data)
print(
'Finite difference should approximate derivative. Difference is ' +
str(
df((data1['absor'] + data2['absor']) /
2, (data1['poyn'] - data2['poyn']) / 0.001)))
#Poynting vector at end should equal T
layer = 2
dist = 300
for pol in ['s', 'p']:
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
print(df(data['poyn'], coh_tmm_data['T']))
#Poynting vector at start should equal power_entering
layer = 1
dist = 0
for pol in ['s', 'p']:
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
print(df(data['poyn'], coh_tmm_data['power_entering']))
#Poynting vector should be continuous
for pol in ['s', 'p']:
layer = 1
dist = 100
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
poyn1 = data['poyn']
layer = 2
dist = 0
coh_tmm_data = coh_tmm(pol, n_list, d_list, th_0, lam_vac)
data = position_resolved(layer, dist, coh_tmm_data)
poyn2 = data['poyn']
print(df(poyn1, poyn2))
return
