def bFctV0(n1, n2, rho, b, V0, modes, delta):
NA = sqrt(n1**2 - n2**2)
pyplot.figure()
sim = Simulator(delta=delta)
sim.setWavelength(Wavelength(k0=(v0 / b / NA)) for v0 in V0)
sim.setMaterials(Fixed, Fixed, Fixed)
sim.setRadii((rho * b, ), (b, ))
sim.setMaterialsParams((n2, ), (n1, ), (n2, ))
fiber = fixedFiber(0, [rho * b, b], [n2, n1, n2])
for m in modes:
neff = sim.getNeff(m)
bnorm = (neff - n2) / (n1 - n2)
pyplot.plot(V0, bnorm, color=COLORS[m.family], label=str(m))
c = fiber.cutoffV0(m)
pyplot.axvline(c, color=COLORS[m.family], ls='--')
pyplot.xlim((0, V0[-1]))
pyplot.title("$n_1 = {}, n_2 = {}, \\rho = {}$".format(n1, n2, rho))
pyplot.xlabel("Normalized frequency ($V_0$)")
pyplot.ylabel("Normalized propagation constant ($\widetilde{\\beta}$)")
def getSimulator(self):
sim = Simulator(delta=self.delta)
sim.setWavelength(self.wavelength)
sim.setMaterials(Silica, SiO2GeO2, Silica)
sim.setMaterialParam(1, 0, (self.X, ))
sim.setRadii((self._a, ), (self._b, ))
return sim
def analyseFiber(f):
print(f.name)
# wl = numpy.linspace(2100e-9, 2400e-9, 1000)
wl = numpy.linspace(1500e-9, 5000e-9, 100)
# wl = numpy.linspace(7000e-9, 20000e-9, 50)
sim = Simulator(delta=f.delta)
sim.setWavelength(wl)
sim.setMaterials(*[Fixed] * len(f.n))
sim.setRadii(*f.rho)
for i, idx in enumerate(f.n):
sim.setMaterialParam(i, 0, idx)
V0 = sim.getV0()
# print(V0[0], V0[-1])
# return
# modes = sim.findLPModes()
modes = sim.findVModes()
# modes = [Mode("TM", 0, 1), Mode("TM", 0, 2)]
fiber = next(iter(sim))
for m in modes:
cutoff = sim.getCutoffV0(fiber, m)
if cutoff < V0[-1]:
continue
# pyplot.plot(V0, sim.getNeff(m), label=str(m))
pl, = pyplot.plot(V0, sim.getBnorm(m), label=str(m))
c = pl.get_color()
if str(m) in ("HE(1,1)", "LP(0,1)"):
continue
print(str(m), cutoff)
pyplot.axvline(cutoff, ls=':', color=c)
# if m.nu > 1:
# cutoffs = findCutoffs(f, m.nu, V0)
# for c in cutoffs:
# pyplot.axvline(c, ls=':', color='k')
# pyplot.legend(loc="best")
pyplot.xlim((2.5, 7))
# pyplot.ylim((0, 1))
pyplot.ylim((0, 0.3))
# pyplot.xlabel("Normalized frequency ($V_0$)")
# pyplot.ylabel("Normalized propagation constant ($b$)")
pyplot.title(f.name)
def compute_fiber(filename, nrho, R2, C2, wl, numax=None, mmax=None):
# Initialize simulators
sim = []
for i, r2 in enumerate(R2):
r1 = numpy.linspace(0, r2, nrho, endpoint=False)
factory = FiberFactory()
factory.addLayer(radius=r1, material='Silica')
factory.addLayer(radius=r2, material='SiO2GeO2', x=C2)
factory.addLayer(material='Silica')
sim.append(Simulator(factory, wl))
nr2 = R2.size
nc2 = C2.size
ckfile, _ = os.path.splitext(filename)
ckfile += '.ckp.npz'
if os.path.isfile(ckfile):
# Restore checkpoint
data = numpy.load(ckfile)
modes = [Mode(*a) for a in data['modes']]
results = {'modes': modes}
for fct in ('cutoff', 'neff', 'beta1', 'beta2', 'beta3'):
results[fct] = data[fct]
else:
# Find modes
sim[-1].numax = numax
sim[-1].mmax = mmax
modes = find_mode_list(sim[-1])
# Initialize arrays
shape = (nrho, nr2, C2.size, len(modes))
results = {'modes': modes}
for fct in ('cutoff', 'neff', 'beta1', 'beta2', 'beta3'):
results[fct] = numpy.empty(shape)
results[fct].fill(numpy.nan)
Rho = numpy.linspace(0, 1, nrho, endpoint=False)
for i, r2 in enumerate(R2[::-1], 1):
print("Solving when r2={:.3f}µm".format(r2 * 1e6))
if numpy.all(numpy.isnan(results['cutoff'][:, nr2 - i, :, :])):
numax, mmax = compute_fiber_r2(results, modes, sim[-i], nr2 - i,
Rho, r2, nc2, numax, mmax)
numpy.savez_compressed(ckfile, **results) # Save checkpoint
os.rename(ckfile, filename)
return results
def plotDneffvsb():
global n1, n2
pyplot.figure()
B = numpy.linspace(2, 4.5, 200)
sim = Simulator(delta=1e-4)
sim.setWavelength(1550e-9)
sim.setMaterials(Silica, SiO2GeO2, Silica)
sim.setRadius(1, B * 1e-6)
sim.setRadiusFct(0, mul, ('value', rho), ('radius', 1))
sim.setMaterialParam(1, 0, X)
# modes = sim.findLPModes()
# for m in modes:
# b = (numpy.fromiter(sim.getNeff(m),
# dtype=numpy.float) - n1a) / (n2a - n1a)
# pyplot.plot(V0a, b, label=str(m))
modes = sim.findVModes()
neff = {}
for m in modes:
neff[m] = sim.getNeff(m)
for (m1, m2) in [(modes[1], modes[2]),
(modes[2], modes[3]),
(modes[4], modes[5])]:
dneff = numpy.abs(neff[m1] - neff[m2]) * 1e4
pyplot.plot(B, dneff, label="{} - {}".format(str(m1), str(m2)))
for i, bb in enumerate(b, 1):
pyplot.axvline(bb, ls='--')
pyplot.annotate('fiber {}'.format(i),
xy=(bb, 2),
xytext=(0, 5),
textcoords='offset points',
horizontalalignment='center')
pyplot.axhline(1, ls=":")
pyplot.xlabel("Outer core radius (um)")
pyplot.ylabel("Mode separation ($\\Delta n_{eff} \\cdot 10^{-4}$)")
pyplot.legend(loc="bottom right")
def plotBvsV0():
global n1, n2
pyplot.figure()
b = 4e-6
V0a = numpy.linspace(2, 5, 200)
NA = sqrt(n1*n1 - n2*n2)
sim = Simulator(delta=1e-4)
sim.setWavelength(Wavelength(k0=(v0 / b / NA)) for v0 in V0a)
sim.setMaterials(Silica, SiO2GeO2, Silica)
sim.setRadius(1, b)
sim.setRadiusFct(0, mul, ('value', rho), ('radius', 1))
sim.setMaterialParam(1, 0, X)
n1a = numpy.fromiter((f['index', 0] for f in iter(sim)),
dtype=numpy.float)
n2a = numpy.fromiter((f['index', 1] for f in iter(sim)),
dtype=numpy.float)
# modes = sim.findLPModes()
# for m in modes:
# b = (numpy.fromiter(sim.getNeff(m),
# dtype=numpy.float) - n1a) / (n2a - n1a)
# pyplot.plot(V0a, b, label=str(m))
modes = sim.findVModes()
for m in modes:
b = (numpy.fromiter(sim.getNeff(m),
dtype=numpy.float) - n1a) / (n2a - n1a)
pyplot.plot(V0a, b, label=str(m))
for i, v0 in enumerate(V0, 1):
pyplot.axvline(v0, ls='--')
pyplot.annotate('fiber {}'.format(i),
xy=(v0, 0.7),
xytext=(0, 5),
textcoords='offset points',
horizontalalignment='center')
pyplot.xlabel("Normalized frequency ($V_0$)")
pyplot.ylabel("Normalized propagation constant ($\\widetilde{\\beta}$)")
pyplot.legend(loc="upper left")
def plotNeff():
b = 4e-6
ncl = 1.444
nco = ncl + 0.05
wl = numpy.linspace(1500e-9, 5000e-9, 50)
V = 2 * numpy.pi / wl * b * numpy.sqrt(nco * nco - ncl * ncl)
sim = Simulator()
sim.setWavelength(wl)
sim.setMaterials(Fixed, Fixed)
sim.setMaterialParam(0, 0, nco)
sim.setMaterialParam(1, 0, ncl)
sim.setRadius(0, b)
modes = sim.findVModes()
for m in modes:
neff = sim.getBnorm(m)
pyplot.plot(V, neff, label=str(m))
pyplot.show()
def plotNgvsb():
global n1, n2
pyplot.figure()
B = numpy.linspace(2, 4.5, 200)
sim = Simulator(delta=1e-4)
sim.setWavelength(1550e-9)
sim.setMaterials(Silica, SiO2GeO2, Silica)
sim.setRadius(1, B * 1e-6)
sim.setRadiusFct(0, mul, ('value', rho), ('radius', 1))
sim.setMaterialParam(1, 0, X)
# modes = sim.findLPModes()
# for m in modes:
# b = (numpy.fromiter(sim.getNeff(m),
# dtype=numpy.float) - n1a) / (n2a - n1a)
# pyplot.plot(V0a, b, label=str(m))
modes = [Mode('HE', 1, 1),
Mode('TE', 0, 1), Mode('HE', 2, 1), Mode('TM', 0, 1),
Mode('EH', 1, 1), Mode('HE', 3, 1)]
for m in modes:
ng = sim.getNg(m)
pyplot.plot(B, ng, label=str(m))
for i, bb in enumerate(b, 1):
pyplot.axvline(bb, ls='--')
pyplot.annotate('fiber {}'.format(i),
xy=(bb, 1.505),
xytext=(0, 5),
textcoords='offset points',
horizontalalignment='center')
pyplot.xlabel("Outer core radius (um)")
pyplot.ylabel("Group index ($n_g$)")
pyplot.legend(loc="bottom right")
pyplot.ylim((1.48, 1.505))
def plotDvsb():
global n1, n2
pyplot.figure()
wl = Wavelength(1550e-9)
V0a = numpy.linspace(2, 5, 100)
NA = sqrt(n1*n1 - n2*n2)
ba = V0a / wl.k0 / NA
sim = Simulator(delta=1e-4)
sim.setWavelength(wl)
sim.setMaterials(Silica, SiO2GeO2, Silica)
sim.setRadius(1, ba)
sim.setRadiusFct(0, mul, ('value', rho), ('radius', 1))
sim.setMaterialParam(1, 0, X)
modes = sim.findVModes()
for m in modes:
D = sim.getD(m)
pyplot.plot(ba*1e6, D, label=str(m))
for i, bb in enumerate(b, 1):
pyplot.axvline(bb, ls='--')
pyplot.annotate('fiber {}'.format(i),
xy=(bb, 50),
xytext=(0, 5),
textcoords='offset points',
horizontalalignment='center')
pyplot.ylim((-100, 50))
pyplot.axhspan(-100, -40, color='k', alpha=0.3)
pyplot.axhspan(40, 100, color='k', alpha=0.3)
pyplot.xlabel("Ring-core outer radius (µm)")
pyplot.ylabel("Dispersion (ps / (nm km) )")
pyplot.legend(loc="lower left")
def plotRhoVsV0():
global n1, n2
pyplot.figure()
wl = Wavelength(1550e-9)
V0a = numpy.linspace(2, 5, 15) # 75
NA = sqrt(n1*n1 - n2*n2)
b = V0a / wl.k0 / NA
rho = numpy.linspace(0, 1, 15) # 75
sim = Simulator(delta=1e-4)
sim.setWavelength(wl)
sim.setMaterials(Silica, SiO2GeO2, Silica)
sim.setMaterialParam(1, 0, X)
# coupures
sim.setRadius(1, b[-1])
sim.setRadius(0, rho * b[-1])
modes = sim.findVModes()
for m in modes:
coupure = numpy.zeros(rho.size)
for i, fiber in enumerate(iter(sim)):
coupure[i] = fiber.cutoffV0(m)
if coupure[i] > 5:
break
coupure = numpy.ma.masked_equal(coupure, 0)
pyplot.plot(coupure, rho, label=str(m), color='k')
# dneff
sim.setRadius(1, b)
neff = numpy.empty((len(modes), len(rho), len(b)))
for j, r in enumerate(rho):
sim.setRadiusFct(0, mul, ('value', r), ('radius', 1))
for i, m in enumerate(modes):
neff[i, j] = sim.getNeff(m).filled(0)
if numpy.sum(neff[i, j]) == 0:
break
if i == 1:
break
dneff = numpy.ones((len(rho), len(b)))
for i in range(len(rho)):
for j in range(len(b)):
for k in range(2, len(modes)):
if neff[k, i, j]:
if abs(neff[k, i, j] - neff[k-1, i, j]) < dneff[i, j]:
dneff[i, j] = abs(neff[k, i, j] - neff[k-1, i, j])
dneff = numpy.ma.masked_greater(dneff, 5e-4)
pyplot.imshow(dneff, aspect='auto', extent=(V0a[0], V0a[-1], 1, 0))
pyplot.colorbar()
pyplot.axhline(0.35, ls='--', color='k')
pyplot.plot(V0, [0.35] * V0.size, 'ok')
pyplot.xlim((V0a[0], V0a[-1]))
pyplot.ylim((0, 1))
pyplot.xlabel("Normalized frequency ($V_0$)")
pyplot.ylabel("Inner / outer radius ratio ($\\rho = a / b$)")
# n2 = Silica.n(wl)
# n1 = n2 + dn
# X = SiO2GeO2.xFromN(wl, n1)
# Values as 1550 nm
wl = Wavelength(1550e-9)
n2 = Silica.n(wl)
n1 = n2 + dn
X = SiO2GeO2.xFromN(wl, n1)
# n1 = SiO2GeO2.n(wl, X)
V0 = wl.k0 * b * 1e-6 * sqrt(n1*n1 - n2*n2)
# dn = n1 - n2
n02 = n1**2 / n2**2
sim = Simulator(delta=1e-4)
sim.setWavelength(wl)
sim.setMaterials(Silica, SiO2GeO2, Silica)
# sim.setMaterials(Fixed, Fixed, Fixed)
sim.setRadius(1, b * 1e-6)
sim.setRadiusFct(0, mul, ('value', rho), ('radius', 1))
sim.setMaterialParam(1, 0, X)
# sim.setMaterialsParams((1.444,), (1.474,), (1.444,))
modes = sim.findVModes()
# modes = [Mode('LP', 0, 1), Mode('LP', 1, 1), Mode('LP', 2, 1)]
def latexSI(value, unit=None):
if unit:
return "\\SI{{{}}}{{\\{}}}".format(value, unit)
def plotCMap(dn):
V0 = numpy.linspace(2, 5, 50)
rho = numpy.linspace(0, 1, 50)
wl = Wavelength(1550e-9)
n1 = Silica.n(wl)
n2 = n1 + dn
X = SiO2GeO2.xFromN(wl, n2)
b = 6e-6
a = b * rho
sim = Simulator(delta=1e-4)
sim.setWavelength(wl)
sim.setMaterials(Silica, SiO2GeO2, Silica)
sim.setMaterialParam(1, 0, X)
sim.setRadii(a, (b, ))
ssif = SSIF(wl, (SiO2GeO2, b, X), (Silica, b))
cutoffs = {}
for m in MODES[1:]:
cutoffs[m] = []
for i, fiber in enumerate(iter(sim)):
if i == 0:
cutoffs[m].append(ssif.cutoffV0(m, 2))
else:
if cutoffs[m][i - 1] > V0[-1]:
cutoffs[m].append(cutoffs[m][i - 1])
else:
cutoffs[m].append(fiber.cutoffV0(m, 2))
pyplot.plot(cutoffs[m], rho, label=str(m))
wl = constants.tpi * b * ssif.na / V0
sim.setWavelength(wl)
neff = {}
for m in MODES:
neff[m] = numpy.zeros((rho.size, V0.size))
for i, r in enumerate(rho):
if i == 0:
sim.setMaterials(SiO2GeO2, Silica)
sim.setMaterialParam(0, 0, X)
sim.setRadius(0, b)
else:
sim.setMaterials(Silica, SiO2GeO2, Silica)
sim.setMaterialParam(1, 0, X)
sim.setRadii((a[i], ), (b, ))
if m in cutoffs and cutoffs[m][i] > V0[-1]:
continue
neff[m][i, :] = sim.getNeff(m)
dneff = numpy.zeros((rho.size, V0.size))
for i, r in enumerate(rho):
for j, v in enumerate(V0):
n = []
mm = []
for m in MODES:
if m in cutoffs and cutoffs[m][i] > v:
continue
if neff[m][i, j]:
n.append(neff[m][i, j])
mm.append(m)
if len(n) > 1:
n = numpy.array(n)
n.sort()
dneff[i, j] = min(n[1:] - n[:-1])
numpy.save('dneff', dneff)
dneff = numpy.ma.masked_greater(dneff, 1e-3)
pyplot.imshow(dneff, aspect='auto', extent=(V0[0], V0[-1], 1, 0))
pyplot.title("$\Delta n = {}$".format(dn))
pyplot.xlim((V0[0], V0[-1]))
pyplot.ylim((0, 1))
pyplot.colorbar()
from fibermodes import Wavelength, Mode, constants
from fibermodes.material import Silica, SiO2GeO2, Fixed
from fibermodes.simulator import PSimulator as Simulator
import numpy
from matplotlib import pyplot
wl = numpy.linspace(800e-9, 1800e-9, 200)
print(wl[1] - wl[0])
sim = Simulator(delta=1e-4, epsilon=1e-12)
sim.setWavelength(wl)
sim.setMaterials(SiO2GeO2, Silica)
sim.setMaterialParam(0, 0, 0.05)
sim.setRadii(4.5e-6)
modes = sim.findVModes()
#modes = [Mode('HE', 1, 2)]
### Neff ###
pyplot.figure()
pyplot.subplot(221)
pyplot.title("Neff")
for m in modes:
pyplot.plot(wl * 1e6, sim.getNeff(m), '-', label=str(m))
n1 = sim.getIndex(0)
n2 = sim.getIndex(1)
pyplot.plot(wl * 1e6, n1, ls='--', label="Core")
pyplot.plot(wl * 1e6, n2, ls='--', label="Cladding")
pyplot.legend()
### Ng ###