def test(self):
# With initial condition y(1) = 2, solution is
def exact(x):
return np.power(x + x**2 * (0.5 * 2**(2. / 3.) - 1), -3)
ystart = np.ones((1, ))
ystart[:] = [2.0]
rtol = 1.0e-13
atol = 1.0e-13
x0 = 1.0
x1 = 4.0
hmin = 0.0
h1 = 0.01
out = ode_solve.Output(1)
a = ode_solve.ODEint(ystart, x0, x1, atol, rtol, h1,hmin, out,\
dopr853.StepperDopr853, integrand() )
a.integrate()
y_calc = a.out.ysave[a.out.count - 1]
y_exct = exact(a.out.xsave[a.out.count - 1])
self.assertAlmostEqual(y_calc, y_exct, delta=2 * atol * y_exct)
integrand = dfg_problem(pump_in,
sgnl_in,
idlr_in,
crystal,
disable_SPM=True,
waist=beamwaist)
# Set up integrator
rtol = 1.0e-6
atol = 1.0e-6
x0 = 0.0
x1 = crystallength
hmin = 0.0
h1 = 0.00001
out = ode_solve.Output(n_saves)
a = ode_solve.ODEint(integrand.ystart, x0, x1, atol, rtol, h1,hmin, out,\
dopr853.StepperDopr853, integrand)
a.integrate()
print 'integrated!'
pump_out = a.out.ysave[0:a.out.count, 0:npoints].T
sgnl_out = a.out.ysave[0:a.out.count, npoints:2 * npoints].T
idlr_out = a.out.ysave[0:a.out.count, 2 * npoints:3 * npoints].T
z = a.out.xsave[0:a.out.count]
pump_power_in = np.round(
1e3 * np.trapz(abs(IFFT_t(pump_out[:, 0]))**2, pump_in.T) * pump_in.frep,
decimals=4)
sigma = 10.0
R = 28.0
b = 8.0 / 3.0
dydx[0] = sigma * (y[1] - y[0])
dydx[1] = R * y[0] - y[1] - y[0] * y[2]
dydx[2] = -b * y[2] + y[0] * y[1]
ystart = np.ones((3, ), dtype=np.complex128)
ystart[:] = [10.0, 1.0, 1.0]
dydxstart = np.ones((3, ), dtype=np.complex128)
xstart = np.zeros((1, ))
rtol = 1.0e-9
atol = 1.0e-9
x0 = 0.0
x1 = 250.0
hmin = 0.0
h1 = 0.01
out = ode_solve.Output(5000)
a = ode_solve.ODEint(ystart, x0, x1, atol, rtol, h1,hmin, out,\
dopr853.StepperDopr853, integrand())
a.integrate()
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(a.out.ysave[:a.out.count, 0], a.out.ysave[:a.out.count, 1],
a.out.ysave[:a.out.count, 2])
plt.show()
def test_fn(self):
npoints = 2**6
# Physical lengths are in meters
crystallength = 0.010
crystal = crystals.AgGaSe2()
crystal = crystals.AgGaSe2(length=crystallength)
n_saves = 10
# Wavelengths are in nanometers
pump_wl_nm = 1560. + 10.0 * np.random.rand()
sgnl_wl_nm = 2200. + 10.0 * np.random.rand()
theta, idlr_wl_nm = crystal.phasematch(pump_wl_nm,
sgnl_wl_nm,
None,
return_wavelength=True)
crystal.set_theta(theta)
pump_power = (1 + np.random.rand()) * 5000.0
sgnl_power = 0.10 * np.random.rand()
twind = 25.
beamwaist = 100e-3
pump_in = CWPulse(pump_power,
pump_wl_nm,
NPTS=npoints,
time_window_ps=twind)
sgnl_in = CWPulse(sgnl_power,
sgnl_wl_nm,
NPTS=npoints,
time_window_ps=twind)
integrand = dfg_problem(pump_in,
sgnl_in,
crystal,
disable_SPM=True,
pump_waist=beamwaist,
apply_gouy_phase=True)
# Set up integrator
rtol = 1.0e-12
atol = 1.0e-12
x0 = 0.0
x1 = crystallength
hmin = 0.0
h1 = 0.0000001
out = ode_solve.Output(n_saves)
# From Boyd section 2.8, also my One Note
omega = lambda l_nm: 2.0 * np.pi * speed_of_light / (l_nm * 1.0e-9)
w_1 = omega(sgnl_wl_nm)
w_2 = omega(idlr_wl_nm)
k_1 = np.mean(2 * np.pi * crystal.n(sgnl_wl_nm, 'o') /
(sgnl_wl_nm * 1.0e-9))
k_2 = np.mean(2 * np.pi * crystal.n(idlr_wl_nm, 'o') /
(idlr_wl_nm * 1.0e-9))
n_1 = crystal.n(sgnl_wl_nm, 'o')
n_2 = crystal.n(idlr_wl_nm, 'o')
n_3 = crystal.n(pump_wl_nm, 'mix')
A_3 = np.sqrt(pump_power) * integrand.pump_beam.rtP_to_a(
crystal.n(pump_wl_nm, 'mix'))
A_1 = np.sqrt(sgnl_power) * integrand.sgnl_beam.rtP_to_a(
crystal.n(sgnl_wl_nm, 'o'))
kappa = np.mean(
np.sqrt(4 * crystal.deff**2 * w_1**2 * w_2**2 /
(k_1 * k_2 * speed_of_light**4)) * A_3)
a = ode_solve.ODEint(integrand.ystart, x0, x1, atol, rtol, h1,hmin, out,\
dopr853.StepperDopr853, integrand, dtype = np.complex128)
a.integrate()
pump_out = a.out.ysave[0:a.out.count, 0:npoints].T
sgnl_out = a.out.ysave[0:a.out.count, npoints:2 * npoints].T
idlr_out = a.out.ysave[0:a.out.count, 2 * npoints:3 * npoints].T
z = a.out.xsave[0:a.out.count]
pump_power_in = np.sum(np.abs(pump_out[:, 0]), axis=0)**2
sgnl_power_in = np.sum(np.abs(sgnl_out[:, ])**2, axis=0)
idlr_power_in = np.sum(np.abs(idlr_out[:, 0]), axis=0)**2
pump_power_out = np.sum(np.abs(pump_out[:, -1]))**2
sgnl_power_out = np.sum(np.abs(sgnl_out[:, -1]))**2
idlr_power_out = np.sum(np.abs(idlr_out[:, -1]))**2
# Compare integrated and analytic values for signal power
numeric_sgnl = np.sum(np.abs(sgnl_out[:, :])**2, axis=0)
analytic_sgnl = sgnl_power_in * np.cosh(kappa * z)**2
self.assertLess(
abs(
np.sum(numeric_sgnl - analytic_sgnl) /
np.sum(abs(analytic_sgnl))), 0.01)
# Compare integrated and analytic values for idler power
numeric_idlr = np.sum(np.abs(idlr_out[:, :])**2, axis=0)
analytic_idlr = n_1 * w_2 / (n_2 * w_1) * sgnl_power_in * np.sinh(
kappa * z)**2
self.assertLess(
abs(
np.sum(numeric_idlr - analytic_idlr) /
np.sum(abs(analytic_idlr))), 0.02)
