def test_kerr():
"""More test than example. Show different approximations for the BPM
implementation of the Kerr effect."""
no = 1
lo = 1.5
length_z = 50
dist_z = 0.1
nbr_z_disp = 1
dist_x = 0.01
length_x = 400
bpm = Bpm(no, lo,
length_z, dist_z, nbr_z_disp,
length_x, dist_x)
[length_z, nbr_z, nbr_z_disp, length_x, nbr_x, x] = bpm.create_x_z()
dn = np.zeros((nbr_z, nbr_x))
fwhm = 6
field = bpm.gauss_light(fwhm)
irrad = 260e13 # if too high, see big difference between method
theta_ext = 0
[progress_pow] = bpm.init_field(field, theta_ext, irrad)
# Need to overwrite those variables due to changes
theta = asin(sin(radians(theta_ext)) / no) # angle in the guide
nu_max = 1 / (2 * dist_x) # max frequency due to sampling
# Spacial frequencies over x (1/µm)
nu = np.linspace(-nu_max,
nu_max*(1 - 2/nbr_x),
nbr_x)
intermed = no * cos(theta) / lo
fr = -2 * pi * nu**2 / (intermed + np.sqrt(
intermed**2
- nu**2
+ 0j))
bpm.phase_mat = fftshift(np.exp(1j * dist_z * fr))
bpm.phase_mat_demi = fftshift(np.exp(1j * dist_z / 2 * fr))
bpm.nl_mat = bpm.ko * bpm.dist_z * dn
# End overwrite
kerr_loop = 10
chi3 = 10 * 1E-20
nbr_step = nbr_z-1
print("\n dz/2+lens+dz/2")
field = bpm.field
for i in range(nbr_step):
# Linear propagation over dz/2
field = ifft(bpm.phase_mat_demi * fft(field))
# Influence of the index modulation on the field
field = field * np.exp(1j * bpm.nl_mat[nbr_step, :]) # No changes if
# no initial guide (exp=1)
# Linear propagation over dz/2
field = ifft(bpm.phase_mat_demi * fft(field))
cur_pow = bpm.epnc * abs2(field)
field_ref = field
cur_ref = cur_pow
print("\n dz+kerr")
field = bpm.field
for i in range(nbr_step):
# Linear propagation over dz
field = ifft(bpm.phase_mat * fft(field))
# Influence of the index modulation on the field
field_x = field * np.exp(1j * bpm.nl_mat[nbr_step, :])
cur_pow = bpm.epnc * abs2(field_x)
for k in range(1): # insensitive to correction loop
prev_pow = cur_pow
# influence of the beam intensity on the index modulation
dn_temp = dn[nbr_step, :] + (3*chi3)/(8*no)*(prev_pow/bpm.epnc)
nl_mat = bpm.ko * bpm.dist_z * dn_temp
# influence of the index modulation on the field
field_x = field * np.exp(1j*nl_mat) # No changes for the pow
cur_pow = bpm.epnc * abs2(field_x)
try:
bpm.variance(prev_pow, cur_pow)
except ValueError as error:
print(error)
field = field_x
field_1 = field
cur_1 = cur_pow
dn_1 = dn_temp
print("\n dz/2+kerr+dz/2")
field = bpm.field
for i in range(nbr_step):
# Linear propagation over dz/2
field = ifft(bpm.phase_mat_demi * fft(field))
# Influence of the index modulation on the field
field_x = field * np.exp(1j * bpm.nl_mat[nbr_step, :])
# Linear propagation over dz/2
field_x = ifft(bpm.phase_mat_demi * fft(field_x))
cur_pow = bpm.epnc * abs2(field_x)
for k in range(kerr_loop):
prev_pow = cur_pow
# influence of the beam intensity on the index modulation
dn_temp = dn[nbr_step, :] + (3*chi3)/(8*no)*(prev_pow/bpm.epnc)
nl_mat = bpm.ko * bpm.dist_z * dn_temp
# influence of the index modulation on the field
field_x = field * np.exp(1j * nl_mat)
# Linear propagation over dz/2
field_x = ifft(bpm.phase_mat_demi * fft(field_x))
cur_pow = bpm.epnc * abs2(field_x)
try:
bpm.variance(prev_pow, cur_pow)
except ValueError as error:
print(error)
field = field_x
field_2 = field
cur_2 = cur_pow
dn_2 = dn_temp
print("\n kerr+dz")
field = bpm.field
for i in range(nbr_step):
# Influence of the index modulation on the field
field_x = field * np.exp(1j * bpm.nl_mat[nbr_step, :])
# Linear propagation over dz
field_x = ifft(bpm.phase_mat * fft(field_x))
cur_pow = bpm.epnc * abs2(field_x)
for k in range(kerr_loop):
prev_pow = cur_pow
# influence of the beam intensity on the index modulation
dn_temp = dn[nbr_step, :] + (3*chi3)/(8*no)*(prev_pow/bpm.epnc)
nl_mat = bpm.ko * bpm.dist_z * dn_temp
# influence of the index modulation on the field
field_x = field * np.exp(1j * nl_mat)
# Linear propagation over dz
field_x = ifft(bpm.phase_mat * fft(field_x))
cur_pow = bpm.epnc * abs2(field_x)
try:
bpm.variance(prev_pow, cur_pow)
except ValueError as error:
print(error)
field = field_x
field_3 = field
cur_3 = cur_pow
dn_3 = dn_temp
plt.figure(num="Impact order kerr")
ax1 = plt.subplot(211)
ax2 = plt.subplot(212)
ax1.set_title("phase: comparison")
ax2.set_title("power: comparison")
ax1.set_xlim(-15, 15)
ax2.set_xlim(-15, 15)
ax1.plot(x, np.angle(field_ref), label="no kerr")
ax1.plot(x, np.angle(field_1), label="dz+kerr")
ax1.plot(x, np.angle(field_2), label="dz/2+kerr+dz/2")
ax1.plot(x, np.angle(field_3), label="kerr+dz")
ax2.plot(x, cur_ref, label="no kerr")
ax2.plot(x, cur_1, label="dz+kerr")
ax2.plot(x, cur_2, label="dz/2+kerr+dz/2")
ax2.plot(x, cur_3, label="kerr+dz")
ax1.legend(loc="upper right")
ax2.legend(loc="upper right")
plt.show()
dn_ref = dn[nbr_step, :]
plt.figure(num="Impact on dn order kerr")
ax1 = plt.subplot(111)
ax1.set_title("dn: comparison")
ax1.set_xlim(-15, 15)
ax1.plot(x, dn_ref, label="no kerr")
ax1.plot(x, dn_1, label="dz+kerr")
ax1.plot(x, dn_2, label="dz/2+kerr+dz/2")
ax1.plot(x, dn_3, label="kerr+dz")
ax1.legend(loc="upper right")
plt.show()
def stability():
"""Show the possible BPM approximations for implementing a refractive
index variation"""
width = 6
no = 2.14
wavelength = 1.55
delta_no = 0.0014
length_z = 200
dist_z = 1
nbr_z_disp = 1
dist_x = 0.2
length_x = 1000
bpm = Bpm(no, wavelength,
length_z, dist_z, nbr_z_disp,
length_x, dist_x)
[length_z, nbr_z, nbr_z_disp, length_x, nbr_x, x] = bpm.create_x_z()
shape = bpm.squared_guide(width)
nbr_p = 1
p = 0
[peaks, dn] = bpm.create_guides(shape, delta_no, nbr_p, p)
fwhm = 6
lo = 1.5
field = bpm.gauss_light(fwhm)
irrad = 1
theta_ext = 0
[progress_pow] = bpm.init_field(field, theta_ext, irrad)
nbr_step = nbr_z-1
# Need to overwrite those variables due to changes
theta = asin(sin(radians(theta_ext)) / no) # angle in the guide
nu_max = 1 / (2 * dist_x) # max frequency due to sampling
# Spacial frequencies over x (1/µm)
nu = np.linspace(-nu_max,
nu_max * (1 - 2/nbr_x),
nbr_x)
intermed = no * cos(theta) / lo
fr = -2 * pi * nu**2 / (intermed + np.sqrt(
intermed**2
- nu**2
+ 0j))
bpm.phase_mat = fftshift(np.exp(1j * dist_z * fr))
bpm.phase_mat_demi = fftshift(np.exp(1j * dist_z / 2 * fr))
bpm.nl_mat = bpm.ko * bpm.dist_z * dn
# End overwrite
field = bpm.field
for i in range(nbr_step):
field = ifft(bpm.phase_mat * fft(field))
field *= np.exp(1j * bpm.nl_mat[nbr_step, :])
test1 = field
field = bpm.field
for i in range(nbr_step):
field = ifft(bpm.phase_mat_demi * fft(field))
field *= np.exp(1j * bpm.nl_mat[nbr_step, :])
field = ifft(bpm.phase_mat_demi * fft(field))
test2 = field
field = bpm.field
for i in range(nbr_step):
field *= np.exp(1j * bpm.nl_mat[nbr_step, :])
field = ifft(bpm.phase_mat * fft(field))
test3 = field
plt.figure("Power")
plt.title("Power: Impact of the chosen algorithm on the free propagation")
plt.xlim(-20, 20)
# plt.ylim(-1, 350)
plt.plot(x, abs2(test1), label='dz+lens')
plt.plot(x, abs2(test2), label='dz/2+lens+dz/2')
plt.plot(x, abs2(test3), label='lens+dz')
plt.legend()
plt.show()
plt.figure("Phase")
plt.title("Phase: Impact of the chosen algorithm on the free propagation")
plt.xlim(-30, 30)
plt.plot(x, np.angle(test1), label='dz+lens')
plt.plot(x, np.angle(test2), label='dz/2+lens+dz/2')
plt.plot(x, np.angle(test3), label='lens+dz')
plt.legend()
plt.show()