def test_born_newton(self):
"""Tests whether born and newton methods get the same result"""
n0 = 3.4
omega = 2*np.pi*200e12
dl = 0.01
chi3 = 2.8E-18
width = 1
L = 5
L_chi3 = 4
width_voxels = int(width/dl)
L_chi3_voxels = int(L_chi3/dl)
Nx = int(L/dl)
Ny = int(3.5*width/dl)
eps_r = np.ones((Nx, Ny))
eps_r[:, int(Ny/2-width_voxels/2):int(Ny/2+width_voxels/2)] = np.square(n0)
nl_region = np.zeros(eps_r.shape)
nl_region[int(Nx/2-L_chi3_voxels/2):int(Nx/2+L_chi3_voxels/2), int(Ny/2-width_voxels/2):int(Ny/2+width_voxels/2)] = 1
simulation = Simulation(omega, eps_r, dl, [15, 15], 'Ez')
simulation.add_mode(n0, 'x', [17, int(Ny/2)], width_voxels*3)
simulation.setup_modes()
simulation.add_nl(chi3, nl_region, eps_scale=True, eps_max=np.max(eps_r))
srcval_vec = np.logspace(1, 3, 3)
pwr_vec = np.array([])
T_vec = np.array([])
for srcval in srcval_vec:
simulation.setup_modes()
simulation.src *= srcval
# Newton
simulation.solve_fields_nl(solver_nl='newton')
E_newton = simulation.fields["Ez"]
# Born
simulation.solve_fields_nl(solver_nl='born')
E_born = simulation.fields["Ez"]
# More solvers (if any) should be added here with corresponding calls to assert_allclose() below
assert_allclose(E_newton, E_born, rtol=1e-3)
def test_chi3(self):
"""Tests whether we get a nonlinear phase shift (self phase modulation) which agrees with analytical predictions"""
# Set simulation parameters
n0 = 3.4
omega = 2 * pi * 200e12
dl = 0.01
chi3 = 2.8E-18
width = 1 # WG width
L = 5 # WG length
L_chi3 = 4 # WG nonlinear length
# Convert to voxels
width_voxels = int(width / dl)
L_chi3_voxels = int(L_chi3 / dl)
Nx = int(L / dl)
Ny = int(3.5 * width / dl)
# Setup
eps_r = ones((Nx, Ny))
eps_r[:,
int(Ny / 2 -
width_voxels / 2):int(Ny / 2 +
width_voxels / 2)] = square(n0)
nl_region = zeros(eps_r.shape)
nl_region[int(Nx / 2 - L_chi3_voxels / 2):int(Nx / 2 +
L_chi3_voxels / 2),
int(Ny / 2 - width_voxels / 2):int(Ny / 2 +
width_voxels / 2)] = 1
simulation = Simulation(omega, eps_r, dl, [15, 15], 'Ez')
simulation.add_mode(n0, 'x', [17, int(Ny / 2)], width_voxels * 3)
simulation.setup_modes()
simulation.solve_fields()
# Probe field from linear simulation to get phase
fld0 = simulation.fields['Ez'][20, int(Ny / 2)]
fld1 = simulation.fields['Ez'][Nx - 20, int(Ny / 2)]
T_linear = fld1 / fld0
# Set nonlinear functions
kerr_nonlinearity = lambda e: 3 * chi3 / square(simulation.L0
) * square(abs(e))
dkerr_de = lambda e: 3 * chi3 / square(simulation.L0) * conj(e)
# Sweep source power and record nonlinear phase accumulation
srcval_vec = logspace(1, 3, 3)
pwr_vec = array([])
T_vec = array([])
for srcval in srcval_vec:
simulation.setup_modes()
simulation.src *= srcval
simulation.solve_fields_nl(kerr_nonlinearity,
nl_region,
dnl_de=dkerr_de,
timing=False,
averaging=True,
Estart=None,
solver_nl='newton')
fld0 = simulation.fields['Ez'][20, int(Ny / 2)]
fld1 = simulation.fields['Ez'][Nx - 20, int(Ny / 2)]
T_vec = append(T_vec, fld1 / fld0)
pwr = simulation.flux_probe('x', [Nx - 20, int(Ny / 2)],
width_voxels * 3)
pwr_vec = append(pwr_vec, pwr)
# Analytically calculate the expected nonlinear phase accumulation
n2 = 12 * square(pi) * chi3 * 1e4 / square(n0)
n2 *= 1e-4 / square(simulation.L0)
width = dl * width_voxels
height = width
Aeff = width * height
L = dl * L_chi3_voxels
gamma_spm = (omega / 299792458 * simulation.L0) * n2 / Aeff
P = pwr_vec * height # Power
Phi_fdfd = -unwrap(angle(T_vec) -
angle(T_linear)) / pi # Nonlinear phase in FDFD
Phi_analytic = (
pwr_vec * height) * L * gamma_spm / pi # Analytic nonlinear phase
# If our simulation is correct, these values should be equal
assert_allclose(Phi_fdfd, Phi_analytic, rtol=1e-3)