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Chris Wong 2018-12-17 09:55:58 +08:00
parent 8d65c8622f
commit 6f212468af
6 changed files with 139 additions and 98 deletions
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3
microring_dynamics.py
View File

@ -7,8 +7,7 @@ K = 0.1
t = np.sqrt(T) + 0.0j
k = 0.0 - 1j * np.sqrt(K)
Coupler = np.array([[t, k],
[k.conjugate(), -t.conjugate()]])
Coupler = np.array([[t, k], [k.conjugate(), -t.conjugate()]])
num_cycle = 1000
a = np.zeros((num_cycle, 2), dtype=complex)

9
ref/simple_anim.py
View File

@ -11,22 +11,23 @@ import matplotlib.animation as animation
fig, ax = plt.subplots()
x = np.arange(0, 2*np.pi, 0.01)
x = np.arange(0, 2 * np.pi, 0.01)
line, = ax.plot(x, np.sin(x))
def init(): # only required for blitting to give a clean slate.
line.set_ydata([np.nan] * len(x))
return line,
return (line,)
def animate(i):
line.set_ydata(np.sin(x + i / 100)) # update the data.
return line,
return (line,)
ani = animation.FuncAnimation(
fig, animate, init_func=init, interval=2, blit=True, save_count=50)
fig, animate, init_func=init, interval=2, blit=True, save_count=50
)
# To save the animation, use e.g.
#

12
ref/strip_chart.py
View File

@ -21,7 +21,7 @@ class Scope(object):
self.ydata = [0]
self.line = Line2D(self.tdata, self.ydata)
self.ax.add_line(self.line)
self.ax.set_ylim(-.1, 1.1)
self.ax.set_ylim(-0.1, 1.1)
self.ax.set_xlim(0, self.maxt)
def update(self, y):
@ -36,18 +36,19 @@ class Scope(object):
self.tdata.append(t)
self.ydata.append(y)
self.line.set_data(self.tdata, self.ydata)
return self.line,
return (self.line,)
def emitter(p=0.03):
'return a random value with probability p, else 0'
"return a random value with probability p, else 0"
while True:
v = np.random.rand(1)
if v > p:
yield 0.
yield 0.0
else:
yield np.random.rand(1)
# Fixing random state for reproducibility
np.random.seed(19680801)
@ -56,7 +57,6 @@ fig, ax = plt.subplots()
scope = Scope(ax)
# pass a generator in "emitter" to produce data for the update func
ani = animation.FuncAnimation(fig, scope.update, emitter, interval=10,
blit=True)
ani = animation.FuncAnimation(fig, scope.update, emitter, interval=10, blit=True)
plt.show()

114
split_step_fourier_method.py
View File

@ -12,58 +12,57 @@ import matplotlib.pyplot as plt
import time
# ---Specify input parameters
distance = 150. # Enter fiber length (in units of L_c)=
# Normalized 2nd-dispersion: kappa=beta2*f^2*L/2):
distance = 150.0 # Enter fiber length (in units of L_c)=
# Normalized 2nd-dispersion: kappa=beta2*f^2*L/2):
# +ve for normal,-ve for anomalous*)
kappa = -0.001
sigma = 0. # Normalized 3rd-dispersion: sigma=beta3*f^3*L/6
G = 1. # small signal gain of Ramam Amp: G=g*L
Is = 1. # gain saturation parameter
sigma = 0.0 # Normalized 3rd-dispersion: sigma=beta3*f^3*L/6
G = 1.0 # small signal gain of Ramam Amp: G=g*L
Is = 1.0 # gain saturation parameter
alpha = 0.4 # Normalized fiber amplitude absorption coeff: alpha=l*L
# Nonlinear parameter n=')
# sqrt(L_D/L_NL)=sqrt(gamma*P0*T0^2/|beta2|) or QT: n=kappa^0.5
n = 2. ** 0.5
n = 2.0 ** 0.5
# ---Specify filter parameters
bdwidth = 2. * np.pi * 6.
delta = 2. * np.pi * 0.5
bdwidth = 2.0 * np.pi * 6.0
delta = 2.0 * np.pi * 0.5
a = np.log(np.sqrt(0.95))
perta = 0.3
pertfsr = 0.17
T = 0.2
t = np.sqrt(T)
r = 1.j * np.sqrt(1. - T)
r = 1.0j * np.sqrt(1.0 - T)
# ---Specify input parameters
mshape = -1. # m=0 for sech,m>0 for super-Gaussian=
chirp0 = 0. # % input pulse chirp (default value)
mshape = -1.0 # m=0 for sech,m>0 for super-Gaussian=
chirp0 = 0.0 # % input pulse chirp (default value)
# P = 1/(gamma*L); (P is the ref peak power);
# uu = A/sqrt(P);
# uu = A/sqrt(P);
# z = z0/L_c; (z0 is the real length, L_c is the cavity length);
# tau = f*t; (t is the time of reference traveling frame);
# ---set simulation parameters
nt = 2 ** 13 # % FFT points (powers of 2)
Tmax = 100. # (half) window size
Tmax = 100.0 # (half) window size
stepno = 1 * round(20 * distance * n ** 2) # No.of z steps to
dz = distance / stepno # step size in z
dtau = (2. * Tmax) / nt # step size in tau
dtau = (2.0 * Tmax) / nt # step size in tau
Twin = 5.
fmax = (1. / (2. * Tmax)) * nt / 2.
fwin = 5.
Twin = 5.0
fmax = (1.0 / (2.0 * Tmax)) * nt / 2.0
fwin = 5.0
filterz = 0.5
plotz = 5
# ---tau and omega arrays
tau = np.arange(-nt / 2., nt / 2.) * dtau # temporal grid
tau = np.arange(-nt / 2.0, nt / 2.0) * dtau # temporal grid
# [(0:nt/2-1) (-nt/2:-1)]
omega = (np.pi / Tmax) * \
np.append(np.arange(0.0, nt / 2.), np.arange(-nt / 2., 0.0))
omega = (np.pi / Tmax) * np.append(np.arange(0.0, nt / 2.0), np.arange(-nt / 2.0, 0.0))
# frequency grid
delaytau = dtau * np.arange(-round(Twin / dtau), round(Twin / dtau) + 1)
@ -71,21 +70,22 @@ delaytau = dtau * np.arange(-round(Twin / dtau), round(Twin / dtau) + 1)
# Input Field profile
if mshape == 0:
# ;% soliton
uu = np.exp(-0.5j * chirp0 * tau ** 2.) / np.cosh(tau)
uu = np.exp(-0.5j * chirp0 * tau ** 2.0) / np.cosh(tau)
elif mshape > 0:
# super-Gaussian
uu = np.exp(-0.5 * (1. + 1.j * chirp0) * tau ** (2. * mshape))
uu = np.exp(-0.5 * (1.0 + 1.0j * chirp0) * tau ** (2.0 * mshape))
else:
# White noise
uu = (np.random.randn(nt) + 1.j * np.random.randn(nt)) * np.sqrt(0.5)
uu = (np.random.randn(nt) + 1.0j * np.random.randn(nt)) * np.sqrt(0.5)
# temp = np.fft.fftshift(np.fft.ifft(uu) * (nt * dtau) / np.sqrt(2. * np.pi))
tempomega = np.fft.fftshift(omega)
# ---store dispersive phase shifts to speedup code
# % nonlinear phase factor
dispersion = np.exp((-alpha + 1.j * kappa * omega ** 2. +
1.j * sigma * omega ** 3.) * dz)
dispersion = np.exp(
(-alpha + 1.0j * kappa * omega ** 2.0 + 1.0j * sigma * omega ** 3.0) * dz
)
# comb filter type
# original comb filter + BPF
@ -93,23 +93,27 @@ dispersion = np.exp((-alpha + 1.j * kappa * omega ** 2. +
# (1 - r ** 2 * np.exp(-1.j * (omega + delta) + a))
# perturbated comb filter + BPF
filtert = np.exp(-omega ** 2. / bdwidth ** 2. -
perta * np.sin(0.5 * omega / pertfsr) ** 2) * \
(t ** 2) / (1.0 - r ** 2 * np.exp(-1.j * (omega + delta) + a))
filtert = (
np.exp(-omega ** 2.0 / bdwidth ** 2.0 - perta * np.sin(0.5 * omega / pertfsr) ** 2)
* (t ** 2)
/ (1.0 - r ** 2 * np.exp(-1.0j * (omega + delta) + a))
)
fig1 = plt.figure()
plt.plot(tempomega / (2. * np.pi),
np.fft.fftshift(10. * np.log10(np.abs(filtert) ** 2.)))
plt.plot(
tempomega / (2.0 * np.pi), np.fft.fftshift(10.0 * np.log10(np.abs(filtert) ** 2.0))
)
plt.title("Perturbated comb filter + BPF")
plt.xlim(-fwin, fwin)
plt.xlim(-fwin, fwin)
plt.ylim(-30., 10.)
plt.ylim(-30.0, 10.0)
plt.show()
# %*********[Beginning of MAIN Loop]***********
# % scheme:1/2N\[Rule]D\[Rule]1/2N;first half step nonlinear
temp = uu * np.exp((1.j * np.abs(uu) ** 2. +
G / (1.0 + np.abs(uu) ** 2. / Is)) * dz / 2.)
temp = uu * np.exp(
(1.0j * np.abs(uu) ** 2.0 + G / (1.0 + np.abs(uu) ** 2.0 / Is)) * dz / 2.0
)
# % note hhz/2
start_time = time.time()
@ -136,7 +140,9 @@ for i in range(stepno):
ftemp = np.fft.ifft(temp) * dispersion
uu = np.fft.fft(ftemp)
temp = uu * np.exp((1.j * np.abs(uu) ** 2. + G / (1.0 + np.abs(uu) ** 2 / Is)) * dz)
temp = uu * np.exp(
(1.0j * np.abs(uu) ** 2.0 + G / (1.0 + np.abs(uu) ** 2 / Is)) * dz
)
z = z + dz
if round((z % plotz) / dz) == 0 or round(((z % plotz) - plotz) / dz) == 0:
@ -144,7 +150,7 @@ for i in range(stepno):
print("Z: " + str(z))
# fig2.suptitle("i = " + str(i) + ", z = " + str(z) + " Time: " + str(time_used))
line1.set_data(tau, np.abs(temp) ** 2.)
line1.set_data(tau, np.abs(temp) ** 2.0)
ax1.relim()
ax1.autoscale_view(True, True, True)
ax1.set_xlim([-Twin, Twin])
@ -152,7 +158,9 @@ for i in range(stepno):
ftemp0 = np.fft.fftshift(ftemp * (nt * dtau) / np.sqrt(2 * np.pi))
line2.set_data(tempomega / (2. * np.pi), 10. * np.log10(np.abs(ftemp0) ** 2.))
line2.set_data(
tempomega / (2.0 * np.pi), 10.0 * np.log10(np.abs(ftemp0) ** 2.0)
)
#
ax2.relim()
ax2.autoscale_view(True, True, True)
@ -165,14 +173,20 @@ for i in range(stepno):
ax3.set_xlim([-Tmax, Tmax])
ax3.set_title("Time domain (Full Scale)")
line4.set_data(tempomega / (2. * np.pi), 10. * np.log10(np.abs(ftemp0) ** 2.))
line4.set_data(
tempomega / (2.0 * np.pi), 10.0 * np.log10(np.abs(ftemp0) ** 2.0)
)
ax4.relim()
ax4.autoscale_view(True, True, True)
ax4.set_xlim([-fmax, fmax])
ax4.set_title("Spectrum (Full Scale)")
autocorr0 = np.fft.fftshift(
np.fft.ifft(np.fft.fft(np.abs(temp) ** 2) * np.conjugate(np.fft.fft(np.abs(temp) ** 2))))
np.fft.ifft(
np.fft.fft(np.abs(temp) ** 2)
* np.conjugate(np.fft.fft(np.abs(temp) ** 2))
)
)
line5.set_data(tau, np.abs(autocorr0) / max(np.abs(autocorr0)))
ax5.relim()
@ -187,7 +201,23 @@ plt.show()
# Exporting results
fname = "result" # file name
np.savetxt(fname + "_time.csv", (tau, np.real(uu), np.imag(uu), np.abs(uu) ** 2), delimiter=",")
np.savetxt(fname + "_freq.csv", (tempomega / (2. * np.pi), np.real(temp), np.imag(temp),
np.abs(temp) ** 2, np.fft.fftshift(np.abs(filtert) ** 2.)), delimiter=",")
np.savetxt(fname + "_autocorr.csv", (tau, np.abs(autocorr0), np.abs(autocorr0) / max(np.abs(autocorr0))), delimiter=",")
np.savetxt(
fname + "_time.csv", (tau, np.real(uu), np.imag(uu), np.abs(uu) ** 2), delimiter=","
)
np.savetxt(
fname + "_freq.csv",
(
tempomega / (2.0 * np.pi),
np.real(temp),
np.imag(temp),
np.abs(temp) ** 2,
np.fft.fftshift(np.abs(filtert) ** 2.0),
),
delimiter=",",
)
np.savetxt(
fname + "_autocorr.csv",
(tau, np.abs(autocorr0), np.abs(autocorr0) / max(np.abs(autocorr0))),
delimiter=",",
)

96
split_step_fourier_method_v0.py
View File

@ -12,63 +12,62 @@ import matplotlib.pyplot as plt
import time
# ---Specify input parameters
distance = 150. # Enter fiber length (in units of L_c)=
# Normalized 2nd-dispersion: kappa=beta2*f^2*L/2):
distance = 150.0 # Enter fiber length (in units of L_c)=
# Normalized 2nd-dispersion: kappa=beta2*f^2*L/2):
# +ve for normal,-ve for anomalous*)
kappa = -0.001
sigma = 0. # Normalized 3rd-dispersion: sigma=beta3*f^3*L/6
G = 1. # small signal gain of Ramam Amp: G=g*L
Is = 1. # gain saturation parameter
kappa = -0.001
sigma = 0.0 # Normalized 3rd-dispersion: sigma=beta3*f^3*L/6
G = 1.0 # small signal gain of Ramam Amp: G=g*L
Is = 1.0 # gain saturation parameter
alpha = 0.4 # Normalized fiber amplitude absorption coeff: alpha=l*L
# Nonlinear parameter n=')
# sqrt(L_D/L_NL)=sqrt(gamma*P0*T0^2/|beta2|) or QT: n=kappa^0.5
n = 2. ** 0.5
n = 2.0 ** 0.5
# ---Specify filter parameters
bdwidth = 2. * np.pi * 6.
delta = 2. * np.pi * 0.5
bdwidth = 2.0 * np.pi * 6.0
delta = 2.0 * np.pi * 0.5
a = np.log(np.sqrt(0.95))
perta = 0.3
pertfsr = 0.17
T = 0.2
t = np.sqrt(T)
r = 1.j * np.sqrt(1. - T)
r = 1.0j * np.sqrt(1.0 - T)
# ---Specify input parameters
mshape = -1. # m=0 for sech,m>0 for super-Gaussian=
chirp0 = 0. # % input pulse chirp (default value)
mshape = -1.0 # m=0 for sech,m>0 for super-Gaussian=
chirp0 = 0.0 # % input pulse chirp (default value)
# P = 1/(gamma*L); (P is the ref peak power);
# uu = A/sqrt(P);
# P = 1/(gamma*L); (P is the ref peak power);
# uu = A/sqrt(P);
# z = z0/L_c; (z0 is the real length, L_c is the cavity length);
# tau = f*t; (t is the time of reference traveling frame);
# ---set simulation parameters
nt = 2 ** 13 # % FFT points (powers of 2)
Tmax = 100. # (half) window size
Tmax = 100.0 # (half) window size
stepno = 1 * round(20 * distance * n ** 2) # No.of z steps to
dz = distance / stepno # step size in z
dtau = (2. * Tmax) / nt # step size in tau
dtau = (2.0 * Tmax) / nt # step size in tau
Twin = 5.
fmax = (1. / (2. * Tmax)) * nt / 2.
fwin = 5.
Twin = 5.0
fmax = (1.0 / (2.0 * Tmax)) * nt / 2.0
fwin = 5.0
filterz = 0.5
plotz = 5
# ---tau and omega arrays
tau = np.arange(-nt / 2., nt / 2.) * dtau # temporal grid
tau = np.arange(-nt / 2.0, nt / 2.0) * dtau # temporal grid
# [(0:nt/2-1) (-nt/2:-1)]
omega = (np.pi / Tmax) * \
np.append(np.arange(0.0 , nt / 2.), np.arange(-nt / 2., 0.0))
omega = (np.pi / Tmax) * np.append(np.arange(0.0, nt / 2.0), np.arange(-nt / 2.0, 0.0))
# frequency grid
@ -78,23 +77,24 @@ delaytau = dtau * np.arange(-round(Twin / dtau), round(Twin / dtau) + 1)
# Input Field profile
if mshape == 0:
# ;% soliton
uu = np.exp(-0.5j * chirp0 * tau ** 2.) / np.cosh(tau)
uu = np.exp(-0.5j * chirp0 * tau ** 2.0) / np.cosh(tau)
elif mshape > 0:
# super-Gaussian
uu = np.exp(-0.5 * (1. + 1.j * chirp0) * tau ** (2. * mshape))
uu = np.exp(-0.5 * (1.0 + 1.0j * chirp0) * tau ** (2.0 * mshape))
else:
# White noise
uu = (np.random.randn(nt) + 1.j * np.random.randn(nt)) * np.sqrt(0.5)
uu = (np.random.randn(nt) + 1.0j * np.random.randn(nt)) * np.sqrt(0.5)
temp = np.fft.fftshift(np.fft.ifft(uu) * (nt * dtau) / np.sqrt(2.* np.pi))
temp = np.fft.fftshift(np.fft.ifft(uu) * (nt * dtau) / np.sqrt(2.0 * np.pi))
tempomega = np.fft.fftshift(omega)
# ---store dispersive phase shifts to speedup code
# % nonlinear phase factor
dispersion = np.exp((-alpha + 1.j * kappa * omega **2. + \
1.j * sigma * omega ** 3.) * dz)
dispersion = np.exp(
(-alpha + 1.0j * kappa * omega ** 2.0 + 1.0j * sigma * omega ** 3.0) * dz
)
# comb filter type
# original comb filter + BPF
@ -102,22 +102,26 @@ dispersion = np.exp((-alpha + 1.j * kappa * omega **2. + \
# (1 - r ** 2 * np.exp(-1.j * (omega + delta) + a))
# perturbated comb filter + BPF
filtert = np.exp(-omega ** 2. / bdwidth ** 2. - \
perta * np.sin(0.5 * omega / pertfsr) ** 2) * \
(t ** 2) / (1.0 - r ** 2 * np.exp(-1.j*(omega + delta) + a))
filtert = (
np.exp(-omega ** 2.0 / bdwidth ** 2.0 - perta * np.sin(0.5 * omega / pertfsr) ** 2)
* (t ** 2)
/ (1.0 - r ** 2 * np.exp(-1.0j * (omega + delta) + a))
)
plt.figure()
plt.plot(tempomega / (2. * np.pi),
np.fft.fftshift(10. * np.log10(np.abs(filtert) ** 2.)))
plt.plot(
tempomega / (2.0 * np.pi), np.fft.fftshift(10.0 * np.log10(np.abs(filtert) ** 2.0))
)
plt.xlim(-fwin, fwin)
plt.xlim(-fwin, fwin)
plt.ylim(-30., 10.)
plt.ylim(-30.0, 10.0)
plt.show()
# %*********[Beginning of MAIN Loop]***********
# % scheme:1/2N\[Rule]D\[Rule]1/2N;first half step nonlinear
temp = uu * np.exp((1.j * np.abs(uu) ** 2. +
G / (1.0 + np.abs(uu) ** 2. / Is )) * dz / 2.)
temp = uu * np.exp(
(1.0j * np.abs(uu) ** 2.0 + G / (1.0 + np.abs(uu) ** 2.0 / Is)) * dz / 2.0
)
# % note hhz/2
start_time = time.time()
@ -131,13 +135,15 @@ z = 0
plt.ion()
fig, ((ax1, ax2), (ax3, ax4), (ax5, ax6)) = plt.subplots(3, 2)
for i in range(stepno):
if round((z % 1 - filterz)/dz) == 0:
if round((z % 1 - filterz) / dz) == 0:
ftemp = np.fft.ifft(temp) * filtert * dispersion
else:
ftemp = np.fft.ifft(temp) * dispersion
uu = np.fft.fft(ftemp)
temp = uu*np.exp((1.j * np.abs(uu)**2. + G / (1.0 + np.abs(uu)**2 / Is)) * dz)
temp = uu * np.exp(
(1.0j * np.abs(uu) ** 2.0 + G / (1.0 + np.abs(uu) ** 2 / Is)) * dz
)
z = z + dz
if round((z % plotz) / dz) == 0 or round(((z % plotz) - plotz) / dz) == 0:
@ -145,29 +151,33 @@ for i in range(stepno):
print(i)
ax1.clear()
ax1.plot(tau, np.abs(temp)**2.)
ax1.plot(tau, np.abs(temp) ** 2.0)
ax1.set_xlim([-Twin, Twin])
ax1.set_title("i = " + str(i) + ", z = " + str(z))
ftemp0 = np.fft.fftshift(ftemp * (nt * dtau) / np.sqrt(2 * np.pi))
ax2.clear()
ax2.plot(tempomega / (2. * np.pi), 10. * np.log10(np.abs(ftemp0)**2.))
ax2.plot(tempomega / (2.0 * np.pi), 10.0 * np.log10(np.abs(ftemp0) ** 2.0))
ax2.set_xlim([-fwin, fwin])
ax2.set_title(" Time = " + str(time_used))
ax3.clear()
ax3.plot(tau, np.abs(temp)**2)
ax3.plot(tau, np.abs(temp) ** 2)
ax3.set_xlim([-Tmax, Tmax])
ax3.set_title("i = " + str(i) + ", z = " + str(z))
ax4.clear()
ax4.plot(tempomega / (2. * np.pi), 10. * np.log10(np.abs(ftemp0)**2.))
ax4.plot(tempomega / (2.0 * np.pi), 10.0 * np.log10(np.abs(ftemp0) ** 2.0))
ax4.set_xlim([-fmax, fmax])
ax4.set_title(" Time = " + str(time_used))
autocorr0 = np.fft.fftshift(
np.fft.ifft(np.fft.fft(np.abs(temp)**2) * np.conjugate(np.fft.fft(np.abs(temp)**2))))
np.fft.ifft(
np.fft.fft(np.abs(temp) ** 2)
* np.conjugate(np.fft.fft(np.abs(temp) ** 2))
)
)
ax5.clear()
ax5.plot(tau, autocorr0 / max(autocorr0))

3
tmp.py
View File

@ -1 +1,2 @@
print(1.3%1.0)
print(1.3 % 1.0)