def fig3():
""" Plot the average decay rate of layer(normalised to bulk n) vs n of semi-infinite
half space.
Note:
* we use the spe_layer function as we only care about the Er-doped layer.
* th_num option is specified to give a higher accuracy on the integration.
"""
# Vacuum emission wavelength
lam_vac = 1550
results = []
n_list = np.linspace(1, 2, 10)
for n in n_list:
print('Evaluating n={:g}'.format(n))
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam_vac)
st.add_layer(1550, 1.5)
st.add_layer(0, n)
# Calculate average total spontaneous emission of layer 0 (1st)
result = st.calc_spe_layer_leaky(layer=0, emission='Lower', th_pow=11)
spe = result['spe']['total']
result = st.calc_spe_layer_leaky(layer=0, emission='Upper', th_pow=11)
spe += result['spe']['total']
spe /= 2
spe = np.mean(spe)
# Normalise to bulk refractive index
spe -= 1.5
# Append to list
results.append(spe)
results = np.array(results)
# Plot results
f, ax = plt.subplots(figsize=(15, 7))
ax.plot(n_list, results)
ax.set_title('Average spontaneous emission rate over doped layer (d=1550nm) '
'normalised to emission rate in bulk medium.')
ax.set_ylabel('$\Gamma / \Gamma_1.5$')
ax.set_xlabel('n')
plt.tight_layout()
if SAVE:
plt.savefig('../Images/spe_vs_n.png', dpi=300)
np.savez('../Data/spe_vs_n', n=n_list, spe=results)
plt.show()
def example1():
""" Silicon to air semi-infinite half spaces.
"""
# Vacuum wavelength
lam0 = 1550
n_list = np.linspace(1, 2, 3)
spe_list = []
for n in n_list:
print('Evaluating n={}'.format(n))
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
st.add_layer(1550, 1.5)
st.add_layer(1550, n)
# Calculate spontaneous emission over whole structure
result = st.calc_spe_structure_leaky()
z = result['z']
spe = result['spe']['total']
# Only get spe rates in the active layer and then average
ind = np.where(z <= 1550)
spe = spe[ind]
spe = np.mean(spe) - 1.5
spe_list.append(spe)
spe_list = np.array(spe_list)
# Plot spontaneous emission rates vs n
f, ax = plt.subplots(figsize=(15, 7))
ax.plot(n_list, spe_list)
ax.set_title('Average spontaneous emission rate over doped layer (d=1550nm) compared to bulk.')
ax.set_ylabel('$\Gamma / \Gamma_1.5$')
ax.set_xlabel('n')
plt.legend()
plt.tight_layout()
if SAVE:
plt.savefig('../Images/spe_vs_n.png', dpi=300)
np.savez('../Data/spe_vs_n', n=n_list, spe=spe_list)
plt.show()
def guiding_plot():
""" Find the guiding modes (TE and TM) for a given structure.
First plot s_11 as a function of beta. When s_11=0 this corresponds
to a wave guiding mode. We then solve the roots (with scipy's brentq
algorithm) and plot these as vertical red lines. Check that visually there
is a red line at each pole so that none are missed.
"""
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
st.set_field('E')
st.set_leaky_or_guiding('guiding')
# st.add_layer(0 * lam0, air)
# st.add_layer(1 * lam0, si)
# st.add_layer(0 * lam0, air)
st.add_layer(300, sio2)
st.add_layer(100, si)
st.add_layer(20, sio2)
st.add_layer(100, si)
st.add_layer(300, air)
st.info()
# Prepare the figure
fig, (ax1, ax2) = plt.subplots(2, 1, sharex='col', sharey='none')
# TE modes
st.set_polarization('TE')
[beta, s_11] = st.s11_guided()
ax1.plot(beta, s_11, label='TE')
roots = st.calc_guided_modes(normalised=True)
for root in roots:
ax1.axvline(root, color='r')
# TM modes
st.set_polarization('TM')
[beta, s_11] = st.s11_guided()
ax2.plot(beta, s_11, label='TM')
roots = st.calc_guided_modes(normalised=True)
for root in roots:
ax2.axvline(root, color='r')
# Format plot
# fig.tight_layout()
ax1.set_ylabel('$S_{11}$')
ax1.axhline(color='k')
ax2.set_ylabel('$S_{11}$')
ax2.set_xlabel('Normalised parallel wave vector (k_11/k)')
ax2.axhline(color='k')
ax1.legend()
ax2.legend()
if SAVE:
plt.savefig('../Images/guided modes.png', dpi=300)
plt.show()
def spe():
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
# Add layers
# st.add_layer(lam0, 1)
st.add_layer(lam0, si)
st.add_layer(lam0, air)
st.add_layer(lam0, si)
# st.add_layer(lam0, 1)
# Get results
result = st.calc_spe_structure_leaky()
z = result['z']
spe = result['spe']
spe_TE = spe['TE_total']
spe_TM_p = spe['TM_p_total']
spe_TM_s = spe['TM_s_total']
# Plot spe rates
fig = plt.figure()
ax1 = fig.add_subplot(211)
ax1.plot(z, spe_TE, label='TE')
ax1.plot(z, spe_TM_p, label='TM')
ax1.plot(z, spe_TE + spe_TM_p, 'k', label='TE + TM')
ax2 = fig.add_subplot(212)
ax2.plot(z, spe_TM_s, label='TM')
ax1.set_title('Spontaneous Emission Rate. LHS n=3.48, RHS n=1.')
ax1.set_ylabel('$\Gamma / \Gamma_0$')
ax2.set_ylabel('$\Gamma /\Gamma_0$')
ax2.set_xlabel('Position in layer (nm)')
ax1.axhline(y=1, linestyle='--', color='k')
ax2.axhline(y=1, linestyle='--', color='k')
# Plot layer boundaries
for z in st.get_layer_boundaries()[:-1]:
ax1.axvline(z, color='k', lw=2)
ax2.axvline(z, color='k', lw=2)
ax1.legend(title='Horizontal Dipoles')
ax2.legend(title='Vertical Dipoles')
plt.show()
def test2():
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
# st.add_layer(1e3, si)
st.add_layer(1900, sio2)
st.add_layer(100, si)
st.add_layer(20, sio2)
st.add_layer(100, si)
st.add_layer(1e3, air)
st.info()
result = st.calc_spe_structure_guided()
z = result['z']
spe = result['spe']
# Convert z into z/lam0 and center
z = st.calc_z_to_lambda(z)
fig, (ax1, ax2) = plt.subplots(2, 1, sharex='col', sharey='none')
ax1.plot(z, spe['TE'], label='TE')
ax1.plot(z, spe['TM_p'], label='TM')
ax1.plot(z, spe['TE'] + spe['TM_p'], label='TE + TM')
ax2.plot(z, spe['TM_s'], label='TM')
for z in st.get_layer_boundaries()[:-1]:
ax1.axvline(st.calc_z_to_lambda(z), color='k', lw=1, ls='--')
ax2.axvline(st.calc_z_to_lambda(z), color='k', lw=1, ls='--')
# ax1.set_ylim(0, 4)
# ax2.set_ylim(0, 6)
ax1.set_title('Spontaneous Emission Rate. Core n=3.48, Cladding n=1.')
ax1.set_ylabel('$\Gamma / \Gamma_0$')
ax2.set_ylabel('$\Gamma /\Gamma_0$')
ax2.set_xlabel('z/$\lambda$')
size = 12
ax1.legend(title='Horizontal Dipoles', prop={'size': size})
ax2.legend(title='Vertical Dipoles', prop={'size': size})
fig.tight_layout()
if SAVE:
plt.savefig('../Images/creatore_fig5.png', dpi=300)
plt.show()
def test():
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
# st.add_layer(1e3, si)
st.add_layer(1900, sio2)
st.add_layer(100, si)
st.add_layer(20, sio2)
st.add_layer(100, si)
# st.add_layer(1900, sio2)
st.add_layer(1e3, air)
st.info()
st.set_polarization('TM')
st.set_field('H')
st.set_leaky_or_guiding('guiding')
alpha = st.calc_guided_modes(normalised=True)
st.set_guided_mode(alpha[0])
result = st.calc_field_structure()
z = result['z']
z = st.calc_z_to_lambda(z)
E = result['field']
# Normalise fields
# E /= max(E)
plt.figure()
plt.plot(z, abs(E) ** 2)
for z in st.get_layer_boundaries()[:-1]:
z = st.calc_z_to_lambda(z)
plt.axvline(x=z, color='k', lw=1, ls='--')
plt.show()
def t2_leaky():
"""
T2 EDTS layer next to air.
"""
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
st.add_layer(2 * lam0, sio2)
st.add_layer(d_etds, edts)
st.add_layer(2 * lam0, air)
st.info()
# Calculate spontaneous emission for leaky and guided modes
result = st.calc_spe_structure_leaky(th_pow=9)
z = result['z']
z = st.calc_z_to_lambda(z)
spe = result['spe']
# Plot spontaneous emission rates
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, sharex='col', sharey='row', figsize=(15, 7))
ax1.plot(z, spe['TE'], label='TE')
ax1.plot(z, spe['TM_p'], label='TM')
ax1.plot(z, spe['TE'] + spe['TM_p'], label='TE + TM')
ax2.plot(z, spe['TE_lower_full'] + spe['TM_p_lower_full'], label='Fully radiative lower outgoing')
ax2.plot(z, spe['TE_lower_partial'] + spe['TM_p_lower_partial'], label='Partially radiative lower outgoing')
ax2.plot(z, spe['TE_upper'] + spe['TM_p_upper'], label='Fully radiative upper outgoing')
ax3.plot(z, spe['TM_s'], label='TM')
ax4.plot(z, spe['TM_s_lower_full'], label='Fully radiative lower outgoing')
ax4.plot(z, spe['TM_s_lower_partial'], label='Partially radiative lower outgoing')
ax4.plot(z, spe['TM_s_upper'], label='Fully radiative upper outgoing')
# Plot internal layer boundaries
for z in st.get_layer_boundaries()[:-1]:
ax1.axvline(st.calc_z_to_lambda(z), color='k', lw=1, ls='--')
ax2.axvline(st.calc_z_to_lambda(z), color='k', lw=1, ls='--')
ax3.axvline(st.calc_z_to_lambda(z), color='k', lw=1, ls='--')
ax4.axvline(st.calc_z_to_lambda(z), color='k', lw=1, ls='--')
# ax1.set_ylim(0, 4)
# ax3.set_ylim(0, 6)
# ax1.set_title('Spontaneous Emission Rate. LHS n=3.48, RHS n=1.')
ax1.set_ylabel('$\Gamma / \Gamma_0$')
ax3.set_ylabel('$\Gamma /\Gamma_0$')
ax3.set_xlabel('z/$\lambda$')
ax4.set_xlabel('z/$\lambda$')
ax1.legend(title='Horizontal Dipoles', fontsize='small')
ax2.legend(title='Horizontal Dipoles', fontsize='small')
ax3.legend(title='Vertical Dipoles', fontsize='small')
ax4.legend(title='Vertical Dipoles', fontsize='small')
fig.tight_layout()
if SAVE:
plt.savefig('../Images/t2_leaky.png', dpi=300)
plt.show()
def purcell_factor():
"""
T2 next to two mediums.
Leaky and guided separate plots.
Evaluate purcell factor for randomly orientated dipole averaged over film thickness.
"""
# Medium 1
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
st.add_layer(2 * lam0, sio2)
st.add_layer(d_etds, edts)
st.add_layer(2 * lam0, air)
st.info()
# Calculate spontaneous emission for leaky and guided modes
result = st.calc_spe_structure(th_pow=11)
z = result['z']
z = st.calc_z_to_lambda(z)
# Plot results
fig, (ax1, ax2) = plt.subplots(2, 1, sharex='col', sharey='none')
ax1.plot(z, result['leaky']['avg'], label='leaky, air')
try:
ax2.plot(z, result['guided']['avg'], label='guided, air')
except KeyError:
pass
spe_air = result['leaky']['avg'] + result['guided']['avg']
# Medium 2
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
st.add_layer(2 * lam0, sio2)
st.add_layer(d_etds, edts)
st.add_layer(2 * lam0, water)
st.info()
# Calculate spontaneous emission for leaky and guided modes
result = st.calc_spe_structure(th_pow=11)
z = result['z']
z = st.calc_z_to_lambda(z)
# Plot results
ax1.plot(z, result['leaky']['avg'], label='leaky, water')
try:
ax2.plot(z, result['guided']['avg'], label='guided, water')
except KeyError:
pass
spe_water = result['leaky']['avg'] + result['guided']['avg']
fp = np.mean(spe_water) / np.mean(spe_air)
print('Purcell Factor: {:e}'.format(fp))
# Plot internal layer boundaries
for z in st.get_layer_boundaries()[:-1]:
z = st.calc_z_to_lambda(z)
ax1.axvline(z, color='k', lw=1, ls='--')
ax2.axvline(z, color='k', lw=1, ls='--')
# ax1.set_title('Spontaneous emission rate at boundary for semi-infinite media. LHS n=1.57.')
ax1.set_ylabel('$\Gamma / \Gamma_0$')
ax2.set_ylabel('$\Gamma / \Gamma_0$')
ax2.set_xlabel('Position z ($\lambda$)')
ax1.legend()
ax2.legend()
plt.tight_layout()
if SAVE:
plt.savefig('../Images/T2_purcell_factor.png', dpi=300)
fig, ax1 = plt.subplots()
z = result['z']
ax1.plot(z, spe_air, label='Air')
ax1.plot(z, spe_water, label='Water')
# Plot internal layer boundaries
for z in st.get_layer_boundaries()[:-1]:
z = st.calc_z_to_lambda(z)
ax1.axvline(z, color='k', lw=1, ls='--')
ax1.set_ylabel('$\Gamma / \Gamma_0$')
ax1.set_xlabel('Position z ($\lambda$)')
# ax1.get_xaxis().get_major_formatter().set_useOffset(False)
ax1.legend()
plt.tight_layout()
if SAVE:
plt.savefig('../Images/T2_purcell_factor_total.png', dpi=300)
plt.show()
def t2_spe_vs_n():
n_list = np.append(np.linspace(1, 1.45, num=25), np.linspace(1.45, 1.55, num=50))
n_list = np.append(n_list, np.linspace(1.55, 2, num=25))
# n_list = [1, 1.33, 1.37, 1.47]
spe_list = []
leaky_list = []
guided_list = []
for n in n_list:
print('Evaluating n={:g}'.format(n))
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
st.add_layer(0, sio2)
st.add_layer(d_etds, edts)
st.add_layer(0, n)
st.info()
# Calculate spontaneous emission of layer 0 (1st)
result = st.calc_spe_structure()
leaky = result['leaky']['avg']
try:
guided = result['guided']['avg']
except KeyError:
guided = 0
# Average over layer
leaky = np.mean(leaky)
guided = np.mean(guided)
# Append to list
leaky_list.append(leaky)
guided_list.append(guided)
spe_list.append(leaky + guided)
# Convert lists to arrays
n_list = np.array(n_list)
leaky_list = np.array(leaky_list)
guided_list = np.array(guided_list)
spe_list = np.array(spe_list)
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex='col', sharey='none')
ax1.plot(n_list, spe_list, '.-', label='leaky + guided')
ax2.plot(n_list, leaky_list, '.-', label='leaky')
ax3.plot(n_list, guided_list, '.-', label='guided')
ax3.set_xlim(1, 2)
ax1.set_title('Average Spontaneous Emission Rate for Random Orientated Dipole in T2.')
ax1.set_ylabel('$\Gamma / \Gamma_0$')
ax2.set_ylabel('$\Gamma / \Gamma_0$')
ax2.set_xlabel('n')
ax1.legend()
ax2.legend()
ax3.legend()
plt.tight_layout()
if SAVE:
plt.savefig('../Images/t2_vs_n.png', dpi=300)
np.savez('../Data/t2_vs_n', n=n_list, spe=spe_list, guided=guided_list, leaky=leaky_list)
plt.show()
def t2_fig4():
"""
Silicon to air semi-infinite half spaces.
"""
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
st.add_layer(2 * lam0, sio2)
st.add_layer(d_etds, edts)
st.add_layer(2 * lam0, air)
st.info()
# Calculate spontaneous emission over whole structure
result = st.calc_spe_structure_leaky(th_pow=9)
z = result['z']
spe = result['spe']
# Convert z into z/lam0 and center
z = st.calc_z_to_lambda(z)
# Plot spontaneous emission rates
fig, (ax1, ax2) = plt.subplots(1, 2, sharey='row', figsize=(15, 5))
ax1.plot(z, (spe['TM_p_lower'] + spe['TE_lower']) / (spe['TE'] + spe['TM_p']), label='Lower')
ax1.plot(z, (spe['TM_p_upper'] + spe['TE_upper']) / (spe['TE'] + spe['TM_p']), label='Upper')
ax2.plot(z, (spe['TM_s_lower']) / spe['TM_s'], label='Lower')
ax2.plot(z, (spe['TM_s_upper']) / spe['TM_s'], label='Upper')
# Plot internal layer boundaries
for z in st.get_layer_boundaries()[:-1]:
ax1.axvline(st.calc_z_to_lambda(z), color='k', lw=1, ls='--')
ax2.axvline(st.calc_z_to_lambda(z), color='k', lw=1, ls='--')
# ax1.set_ylim(0, 1.1)
# ax1.set_title('Spontaneous Emission Rate. LHS n=3.48, RHS n=1.')
ax1.set_ylabel('$\Gamma / \Gamma_0$')
ax1.set_xlabel('z/$\lambda$')
ax2.set_xlabel('z/$\lambda$')
ax1.legend(title='Horizontal Dipoles')
ax2.legend(title='Vertical Dipoles')
fig.tight_layout()
if SAVE:
plt.savefig('../Images/t2_fig4.png', dpi=300)
plt.show()
def t2():
"""
T2 EDTS layer next to air.
"""
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam0)
st.add_layer(2 * lam0, sio2)
st.add_layer(d_etds, edts)
st.add_layer(2 * lam0, air)
st.info()
# Calculate spontaneous emission for leaky and guided modes
result = st.calc_spe_structure(th_pow=9)
z = result['z']
z = st.calc_z_to_lambda(z)
# Plot results
fig, (ax1, ax2) = plt.subplots(2, 1, sharex='col', sharey='none')
ax1.plot(z, result['leaky']['avg'], label='leaky')
try:
ax2.plot(z, result['guided']['avg'], label='guided')
except KeyError:
pass
# Plot internal layer boundaries
for z in st.get_layer_boundaries()[:-1]:
z = st.calc_z_to_lambda(z)
ax1.axvline(z, color='k', lw=1, ls='--')
ax2.axvline(z, color='k', lw=1, ls='--')
# ax1.set_title('Spontaneous emission rate at boundary for semi-infinite media. LHS n=1.57.')
ax1.set_ylabel('$\Gamma / \Gamma_0$')
ax2.set_ylabel('$\Gamma / \Gamma_0$')
ax2.set_xlabel('Position z ($\lambda$/2$\pi$)')
ax1.legend()
ax2.legend()
plt.tight_layout()
if SAVE:
plt.savefig('../Images/t2.png', dpi=300)
plt.show()
def fig4():
""" n=3 or n=1 (air) to n=1.5 (Erbium deposition) semi-infinite half spaces.
Plot the average total spontaneous emission rate of dipoles as a function of
distance from the interface.
"""
# Vacuum wavelength
lam_vac = 1550
# Plotting units
units = lam_vac / (2 * pi)
# Create plot
f, ax = plt.subplots(figsize=(15, 7))
for n in [1, 3]:
print('Evaluating n={:g}'.format(n))
# Create structure
st = LifetimeTmm()
st.set_vacuum_wavelength(lam_vac)
st.add_layer(4 * units, n)
st.add_layer(4 * units, 1.5)
st.info()
# Calculate spontaneous emission over whole structure
result = st.calc_spe_structure_leaky()
z = result['z']
# Shift so centre of structure at z=0
z -= st.get_structure_thickness() / 2
spe = result['spe']['total']
# Plot spontaneous emission rates
ax.plot(z/units, spe, label=('n='+str(n)), lw=2)
ax.axhline(y=n, xmin=0, xmax=0.4, ls='dotted', color='k', lw=2)
# Plot internal layer boundaries
for z in st.get_layer_boundaries()[:-1]:
# Shift so centre of structure at z=0
z -= st.get_structure_thickness() / 2
ax.axvline(z/units, color='k', lw=2)
ax.axhline(1.5, ls='--', color='k', lw=2)
ax.set_title('Spontaneous emission rate at boundary for semi-infinite media. RHS n=1.5.')
ax.set_ylabel('$\Gamma / \Gamma_0$')
ax.set_xlabel('Position z ($\lambda$/2$\pi$)')
plt.legend()
plt.tight_layout()
if SAVE:
plt.savefig('../Images/spe_vs_n.png', dpi=300)
plt.show()
