def main():
# -- INITIALIZATION STAGE
# ... DEFINE SIMULATION PARAMETERS
t_max = 3000. # (fs)
t_num = 2**14 # (-)
z_max = 8.0e3 # (micron)
z_num = 10000 # (-)
z_skip = 10 # (-)
n2 = 3.0e-8 # (micron^2/W)
wS = 1.884 # (rad/fs)
tS = 10.0 # (fs)
NS = 10. # (-)
# ... PROPAGGATION CONSTANT
beta_fun = define_beta_fun_NLPM750()
pc = PropConst(beta_fun)
# ... COMPUTATIONAL DOMAIN, MODEL, AND SOLVER
grid = Grid( t_max = t_max, t_num = t_num, z_max = z_max, z_num = z_num)
model = FMAS_S_R(w=grid.w, beta_w=pc.beta(grid.w), n2 = n2)
solver = IFM_RK4IP( model.Lw, model.Nw)
# -- SET UP INITIAL CONDITION
A0 = NS*np.sqrt(np.abs(pc.beta2(wS))*model.c0/wS/n2)/tS
Eps_0w = AS(np.real(A0/np.cosh(grid.t/tS)*np.exp(1j*wS*grid.t))).w_rep
solver.set_initial_condition( grid.w, Eps_0w)
# -- PERFORM Z-PROPAGATION
solver.propagate( z_range = z_max, n_steps = z_num, n_skip = z_skip)
# -- SHOW RESULTS
utz = change_reference_frame(solver.w, solver.z, solver.uwz, pc.vg(wS))
plot_evolution( solver.z, grid.t, utz,
t_lim = (-100,100), w_lim = (0.5,8.), DO_T_LOG = True)
def main():
t_max = 2000. # (fs)
t_num = 2**14 # (-)
z_max = 0.06e6 # (micron)
z_num = 25000 # (-)
z_skip = 50 # (-)
chi = 1.0 # (micron^2/W)
c0 = 0.29979 # (micron/fs)
# -- PROPAGATION CONSTANT
beta_fun = define_beta_fun()
pc = PropConst(beta_fun)
# -- INITIALIZE DATA-STRUCTURES AND ALGORITHMS
grid = Grid(t_max=t_max, t_num=t_num, z_max=z_max, z_num=z_num)
model = FMAS(w=grid.w, beta_w=beta_fun(grid.w), chi=chi)
solver = IFM_RK4IP(model.Lw, model.Nw, user_action=model.claw)
# -- PREPARE INITIAL CONDITION AND RUN SIMULATION
w01, t01, A01 = 1.178, 30.0, 0.0248892 # (rad/fs), (fs), (sqrt(W))
w02, t02, A02 = 2.909, 30.0, 0.0136676 # (rad/fs), (fs), (sqrt(W))
A_0t_fun = lambda t, A0, t0, w0: np.real(A0 / np.cosh(t / t0) * np.exp(
1j * w0 * t))
E_0t = A_0t_fun(grid.t, A01, t01, w01) + A_0t_fun(grid.t, A02, t02, w02)
solver.set_initial_condition(grid.w, AS(E_0t).w_rep)
solver.propagate(z_range=z_max, n_steps=z_num, n_skip=z_skip)
# -- SHOW RESULTS IN MOVING FRAME OF REFERENCE
v0 = 0.0749641870819 # (micron/fs)
utz = change_reference_frame(solver.w, solver.z, solver.uwz, v0)
plot_evolution(solver.z, grid.t, utz, t_lim=(-100, 150), w_lim=(0.3, 3.8))
def main():
# -- DEFINE SIMULATION PARAMETERS
# ... COMPUTATIONAL DOMAIN
t_max = 3500. # (fs)
t_num = 2**14 # (-)
z_max = 0.10 * 1e6 # (micron)
z_num = 8000 # (-)
z_skip = 10 # (-)
# ... INITIAL CONDITION
P0 = 1e4 # (W)
t0 = 28.4 # (fs)
w0 = 2.2559 # (rad/fs)
E_0t_fun = lambda t: np.real(
np.sqrt(P0) / np.cosh(t / t0) * np.exp(-1j * w0 * t))
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
grid = Grid(t_max=t_max, t_num=t_num, z_max=z_max, z_num=z_num)
# ... CUSTOM PROPAGATION MODEL
model = CustomModelPCF(w=grid.w)
# ... PROPAGATION ALGORITHM
solver = IFM_RK4IP(model.Lw, model.Nw, user_action=model.claw)
solver.set_initial_condition(grid.w, AS(E_0t_fun(grid.t)).w_rep)
# -- RUN SIMULATION
solver.propagate(z_range=z_max, n_steps=z_num, n_skip=z_skip)
# -- SHOW RESULTS
plot_evolution(solver.z,
grid.t,
solver.utz,
t_lim=(-500, 2200),
w_lim=(1., 4.))
def determine_error(mode):
# -- SET AXES
grid = Grid(t_max=50., t_num=2**12)
t, w = grid.t, grid.w
# -- INITIALIZATION STAGE
# ... SET MODEL
b2 = -1.
gamma = 1.
model = NSE(w, b2, gamma)
# ... SET SOLVER TYPE
switcher = {
'SiSSM': SiSSM(model.Lw, model.Nw),
'SySSM': SySSM(model.Lw, model.Nw),
'IFM': IFM_RK4IP(model.Lw, model.Nw),
'LEM': LEM_SySSM(model.Lw, model.Nw),
'CQE': CQE(model.Lw, model.Nw, del_G=1e-6)
}
try:
my_solver = switcher[mode]
except KeyError:
print('NOTE: MODE MUST BE ONE OF', list(switcher.keys()))
raise
exit()
# -- AVERAGE RELATIVE INTENSITY ERROR
_RI_error = lambda x, y: np.sum(
np.abs(np.abs(x)**2 - np.abs(y)**2) / x.size / np.max(np.abs(y)**2))
# -- SET TEST PULSE PROPERTIES (FUNDAMENTAL SOLITON)
t0 = 1. # duration
P0 = np.abs(b2) / t0 / t0 / gamma # peak-intensity
LD = t0 * t0 / np.abs(b2) # dispersion length
# ... EXACT SOLUTION
u_exact = lambda z, t: np.sqrt(P0) * np.exp(0.5j * gamma * P0 * z
) / np.cosh(t / t0)
# ... INITIAL CONDITION FOR PROPAGATION
u0_t = u_exact(0.0, t)
res_dz = []
res_err = []
for z_num in [2**n for n in range(5, 12)]:
# ... PROPAGATE INITIAL CONITION
my_solver.set_initial_condition(w, FT(u0_t))
my_solver.propagate(z_range=0.5 * np.pi * LD, n_steps=z_num, n_skip=8)
# ... KEEP RESULTS
z_fin = my_solver.z[-1]
dz = z_fin / (z_num + 1)
u_t_fin = my_solver.utz[-1]
u_t_fin_exact = u_exact(z_fin, t)
res_dz.append(dz)
res_err.append(_RI_error(u_t_fin, u_t_fin_exact))
# ... CLEAR DATA FIELDS
my_solver.clear()
return np.asarray(res_dz), np.asarray(res_err)
def main():
t_max = 2000. # (fs)
t_num = 2**14 # (-)
chi = 1.0 # (micron^2/W)
c0 = 0.29979 # (micron/fs)
# -- PROPAGATION CONSTANT
beta_fun = define_beta_fun()
pc = PropConst(beta_fun)
grid = Grid( t_max = t_max, t_num = t_num)
model = FMAS(w=grid.w, beta_w = beta_fun(grid.w), chi = chi )
solver = IFM_RK4IP( model.Lw, model.Nw, user_action = model.claw)
# -- FUNDAMENTAL SOLITON INTITIAL CONDITION
A_0t_fun = lambda t, A0, t0, w0: np.real(A0/np.cosh(t/t0)*np.exp(1j*w0*t))
# ... FIRST SOLITON: PROPAGATE AND CLEAN-UP PRIOR TO COLLISION
w01, t01, A01 = 1.2, 20.0, 0.0351187 # (rad/fs), (fs), (sqrt(W))
z_max, z_num, z_skip = 0.06e6, 6000, 200 # (micron), (-), (-)
A_0t_1 = A_0t_fun(grid.t, A01, t01, w01)
solver.set_initial_condition( grid.w, AS(A_0t_1).w_rep)
solver.propagate( z_range = z_max, n_steps = z_num, n_skip = z_skip)
A_0t_1_f = np.real(
np.where(
np.logical_and(grid.t>-15., grid.t<273.0),
solver.utz[-1],
0j
)
)
solver.clear()
# ... SECOND SOLITON: PROPAGATE AND CLEAN-UP PRIOR TO COLLISION
w02, t02, A02 = 2.96750, 15.0, 0.0289073 # (rad/fs), (fs), (sqrt(W))
z_max, z_num, z_skip = 0.06e6, 6000, 200 # (micron), (-), (-)
A_0t_2 = A_0t_fun(grid.t-800., A02, t02, w02)
solver.set_initial_condition( grid.w, AS(A_0t_2).w_rep)
solver.propagate( z_range = z_max, n_steps = z_num, n_skip = z_skip)
A_0t_2_f = np.real(
np.where(
np.logical_and(grid.t>435.0, grid.t<727.0),
solver.utz[-1],
0j
)
)
solver.clear()
# -- LET CLEANED-UP SOLITONS COLLIDE
z_max, z_num, z_skip = 0.22e6, 50000, 100 # (micron), (-), (-)
solver.set_initial_condition( grid.w, AS( A_0t_1_f + A_0t_2 ).w_rep)
solver.propagate( z_range = z_max, n_steps = z_num, n_skip = z_skip)
# -- SHOW RESULTS IN MOVING FRAME OF REFERENCE
v0 = 0.0749879876745 # (micron/fs)
utz = change_reference_frame(solver.w, solver.z, solver.uwz, v0)
plot_evolution( solver.z, grid.t, utz,
t_lim = (-1400,1400), w_lim = (0.3,3.8), DO_T_LOG=False)
def main():
# -- DEFINE SIMULATION PARAMETERS
# ... COMPUTATIONAL DOMAIN
t_max = 4000. # (fs)
t_num = 2**14 # (-)
z_max = 6.0e6 # (micron)
z_num = 75000 # (-)
z_skip= 100 # (-)
n2 = 3.0e-8 # (micron^2/W)
beta_fun = define_beta_fun_ESM()
pc = PropConst(beta_fun)
# -- INITIALIZATION STAGE
grid = Grid( t_max = t_max, t_num = t_num, z_max = z_max, z_num = z_num)
#print(grid.dz)
#exit()
model = FMAS_S_Raman(w=grid.w, beta_w=pc.beta(grid.w), n2=n2)
solver = IFM_RK4IP( model.Lw, model.Nw, user_action = model.claw)
# -- SET UP INITIAL CONDITION
t = grid.t
# ... FUNDAMENTAL NSE SOLITON
w0_S, t0_S = 1.5, 20. # (rad/fs), (fs)
A0 = np.sqrt(abs(pc.beta2(w0_S))*model.c0/w0_S/n2)/t0_S
A0_S = A0/np.cosh(t/t0_S)*np.exp(1j*w0_S*t)
# ... 1ST DISPERSIVE WAVE; UNITS (rad/fs), (fs), (fs), (-)
w0_DW1, t0_DW1, t_off1, s1 = 2.06, 60., -600., 0.35
A0_DW1 = s1*A0/np.cosh((t-t_off1)/t0_DW1)*np.exp(1j*w0_DW1*t)
# ... 2ND DISPERSIVE WAVE; UNITS (rad/fs), (fs), (fs), (-)
w0_DW2, t0_DW2, t_off2, s2 = 2.05, 60., -1200., 0.35
A0_DW2 = s2*A0/np.cosh((t-t_off2)/t0_DW2)*np.exp(1j*w0_DW2*t)
# ... 3RD DISPERSIVE WAVE; UNITS (rad/fs), (fs), (fs), (-)
w0_DW3, t0_DW3, t_off3, s3 = 2.04, 60., -1800., 0.35
A0_DW3 = s3*A0/np.cosh((t-t_off3)/t0_DW3)*np.exp(1j*w0_DW3*t)
# ... ANALYTIC SIGNAL OF FULL ININITIAL CONDITION
Eps_0w = AS(np.real(A0_S + A0_DW1 + A0_DW2 + A0_DW3)).w_rep
solver.set_initial_condition( grid.w, Eps_0w)
solver.propagate( z_range = z_max, n_steps = z_num, n_skip = z_skip)
# -- SHOW RESULTS
v0 = pc.vg(w0_S)
utz = change_reference_frame(solver.w, solver.z, solver.uwz, v0)
res = {
't': grid.t,
'w': grid.w,
'z': solver.z,
'v0': pc.vg(w0_S),
'utz': utz,
'Cp': solver.ua_vals
}
save_h5('out_file_HR.h5', **res)
def main():
# -- SET MODEL PARAMETERS
t_max = -50.0
Nt = 2**12
# ... PROPAGATION CONSTANT (POLYNOMIAL MODEL)
beta = np.poly1d([-0.5, 0.0, 0.0])
beta1 = np.polyder(beta, m=1)
beta2 = np.polyder(beta, m=2)
# ... NONLINEAR PARAMETER
gamma = 1.0
# ... SOLITON PARAMTERS
t0 = 1.0 # duration
t_off = 20.0 # temporal offset
w0 = 25.0 # detuning
P0 = np.abs(beta2(0)) / t0 / t0 / gamma # peak-intensity
LD = t0 * t0 / np.abs(beta2(0)) # dispersion length
# ... EXACT SOLUTION
u_exact = lambda z, t: np.sqrt(P0) * np.exp(0.5j * gamma * P0 * z
) / np.cosh(t / t0)
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
grid = Grid(t_max=t_max, t_num=Nt)
t, w = grid.t, grid.w
# ... NONLINEAR SCHROEDINGER EQUATION
model = NSE(w, beta(w), gamma)
# ... PROPAGATION ALGORITHM
solver = LEM(model.Lw, model.N, del_G=1e-7)
# ... INITIAL CONDITION
u0_t = u_exact(0.0, t + t_off) * np.exp(1j * w0 * t)
u0_t += u_exact(0.0, t - t_off) * np.exp(-1j * w0 * t)
solver.set_initial_condition(w, FT(u0_t))
# -- RUN SOLVER
solver.propagate(
z_range=0.5 * np.pi * LD,
n_steps=2**9,
n_skip=2 # propagation range
)
# -- STORE RESULTS
# ... PREPARE DATA DICTIONARY FOR OUTPUT FILE
results = {
"t": t,
"z": solver.z,
"w": solver.w,
"u": solver.utz,
"dz_integration": solver.dz_,
"dz_a": np.asarray(solver._dz_a),
"del_rle": np.asarray(solver._del_rle),
}
# ... STORE DATA
save_h5("./res_LEM_SolSolCollision.h5", **results)
def main():
# -- DEFINE SIMULATION PARAMETERS
# ... COMPUTATIONAL DOMAIN
t_max = 3500. # (fs)
t_num = 2**14 # (-)
z_max = 0.16 * 1e6 # (micron)
z_num = 4000 # (-)
z_skip = 10 # (-)
# ... INITIAL CONDITION
P0 = 1e4 # (W)
t0 = 28.4 # (fs)
w0 = 2.2559 # (rad/fs)
E_0t_fun = lambda t: np.real(
np.sqrt(P0) / np.cosh(t / t0) * np.exp(-1j * w0 * t))
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
grid = Grid(t_max=t_max, t_num=t_num, z_max=z_max, z_num=z_num)
z = grid.z
print(z[1] - z[0])
exit()
# ... CUSTOM PROPAGATION MODEL
model = CustomModelPCF(w=grid.w)
# ... PROPAGATION ALGORITHM
solver = IFM_RK4IP(model.Lw, model.Nw, user_action=model.claw)
solver.set_initial_condition(grid.w, AS(E_0t_fun(grid.t)).w_rep)
# -- RUN SIMULATION
solver.propagate(z_range=z_max, n_steps=z_num, n_skip=z_skip)
res = {
"dz_integration": solver.dz_,
"t": grid.t,
"z": solver.z,
"w": solver.w,
"utz": solver.utz,
"Cp": solver.ua_vals
}
save_h5('res_IFM_SC_Nz%d.h5' % (z_num), **res)
# -- SHOW RESULTS
plot_evolution(solver.z,
grid.t,
solver.utz,
t_lim=(-500, 2200),
w_lim=(1., 4.),
DO_T_LOG=False)
def main():
# -- DEFINE SIMULATION PARAMETERS
# ... COMPUTATIONAL DOMAIN
t_max = 3500. # (fs)
t_num = 2**14 # (-)
z_max = 0.10 * 1e6 # (micron)
z_num = 8000 # (-)
z_skip = 10 # (-)
# ... INITIAL CONDITION
P0 = 1e4 # (W)
t0 = 28.4 # (fs)
w0 = 2.2559 # (rad/fs)
E_0t_fun = lambda t: np.real(
np.sqrt(P0) / np.cosh(t / t0) * np.exp(-1j * w0 * t))
# -- INITIALIZATION STAGE
grid = Grid(t_max=t_max, t_num=t_num, z_max=z_max, z_num=z_num)
model = CustomModelPCF(w=grid.w)
solver = IFM_RK4IP(model.Lw, model.Nw, user_action=model.claw)
solver.set_initial_condition(grid.w, AS(E_0t_fun(grid.t)).w_rep)
# -- RUN SIMULATION
solver.propagate(z_range=z_max, n_steps=z_num, n_skip=z_skip)
# -- POSTPRICESSING: COMPUTE SPECTROGRAM USING OPTFROG
# ... Z-DISTANCE, Z-INDEX AND FIELD FOR WHICH TO COMPUTE TRACE
z0 = 0.08e6 # (micron)
z0_idx = np.argmin(np.abs(solver.z - z0))
Et = solver.utz[z0_idx]
# ... WINDOW FUNCTION FOR SIGNAL LOCALIZATION
def window_fun(s0):
return lambda t: np.exp(-t**2 / 2 / s0 / s0) / np.sqrt(2. * np.pi) / s0
# ... OPTFROG TRACE
res = optFrog(
grid.t, # TEMPORAL GRID
Et, # ANALYTIC SIGNAL
window_fun, # WINDOW FUNCTION
tLim=(-500.0, 3200.0, 10), # (tmin, fs) (tmax, fs) (nskip)
wLim=(0.9, 4.1, 3) # (wmin, fs) (wmax, fs) (nskip)
)
# ... SHOW SPECTROGRAM
plot_spectrogram(res.tau, res.w, res.P)
def main():
# -- INITIALIZATION STAGE
# ... DEFINE SIMULATION PARAMETERS
t_max = 3500. / 2 # (fs)
t_num = 2**14 # (-)
z_max = 50.0e3 # (micron)
z_num = 100000 # (-)
z_skip = 100 # (-)
c0 = 0.29979 # (micron/fs)
n2 = 1. # (micron^2/W) FICTITIOUS VALUE ONLY
wS = 2.32548 # (rad/fs)
tS = 50.0 # (fs)
NS = 3.54 # (-)
# ... PROPAGGATION CONSTANT
beta_fun = define_beta_fun_fluoride_glass_AD2010()
pc = PropConst(beta_fun)
chi = (8. / 3) * pc.beta(wS) * c0 / wS * n2
# ... COMPUTATIONAL DOMAIN, MODEL, AND SOLVER
grid = Grid(t_max=t_max, t_num=t_num, z_max=z_max, z_num=z_num)
model = BMCF(w=grid.w, beta_w=pc.beta(grid.w), chi=chi)
solver = IFM_RK4IP(model.Lw, model.Nw)
# -- SET UP INITIAL CONDITION
LD = tS * tS / np.abs(pc.beta2(wS))
A0 = NS * np.sqrt(8 * c0 / wS / n2 / LD)
Eps_0w = AS(np.real(A0 / np.cosh(grid.t / tS) *
np.exp(1j * wS * grid.t))).w_rep
solver.set_initial_condition(grid.w, Eps_0w)
# -- PERFORM Z-PROPAGATION
solver.propagate(z_range=z_max, n_steps=z_num, n_skip=z_skip)
# -- SHOW RESULTS
utz = change_reference_frame(solver.w, solver.z, solver.uwz, pc.vg(wS))
plot_evolution(solver.z,
grid.t,
utz,
t_lim=(-500, 500),
w_lim=(-10., 10.),
DO_T_LOG=True,
ratio_Iw=1e-15)
def main():
# -- DEFINE SIMULATION PARAMETERS
# ... COMPUTATIONAL DOMAIN
t_max = 2000. # (fs)
t_num = 2**13 # (-)
z_max = 1.0e6 # (micron)
z_num = 10000 # (-)
z_skip = 10 # (-)
n2 = 3.0e-8 # (micron^2/W)
c0 = 0.29979 # (fs/micron)
lam0 = 0.860 # (micron)
w0_S = 2 * np.pi * c0 / lam0 # (rad/fs)
t0_S = 20.0 # (fs)
w0_DW = 2.95 # (rad/fs)
t0_DW = 70.0 # (fs)
t_off = -250.0 # (fs)
sFac = 0.75 # (-)
beta_fun = define_beta_fun_poly_NLPM750()
pc = PropConst(beta_fun)
# -- INITIALIZATION STAGE
grid = Grid(t_max=t_max, t_num=t_num, z_max=z_max, z_num=z_num)
model = FMAS_S_R(w=grid.w, beta_w=pc.beta(grid.w), n2=n2)
solver = IFM_RK4IP(model.Lw, model.Nw, user_action=model.claw)
# -- SET UP INITIAL CONDITION
t = grid.t
A0 = np.sqrt(abs(pc.beta2(w0_S)) * c0 / w0_S / n2) / t0_S
A0_S = A0 / np.cosh(t / t0_S) * np.exp(1j * w0_S * t)
A0_DW = sFac * A0 / np.cosh((t - t_off) / t0_DW) * np.exp(1j * w0_DW * t)
Eps_0w = AS(np.real(A0_S + A0_DW)).w_rep
solver.set_initial_condition(grid.w, Eps_0w)
solver.propagate(z_range=z_max, n_steps=z_num, n_skip=z_skip)
# -- SHOW RESULTS
utz = change_reference_frame(solver.w, solver.z, solver.uwz, pc.vg(w0_S))
plot_evolution(solver.z,
grid.t,
utz,
t_lim=(-1200, 1200),
w_lim=(1.8, 3.2))
def main():
# -- DEFINE SIMULATION PARAMETERS
# ... WAVEGUIDE PROPERTIES
b2 = -1.0
gamma = 1.
# ... TEST PULSE PROPERTIES
t0 = 1. # soliton duration
P0 = np.abs(b2) / t0 / t0 / gamma # peak-intensity
LD = t0 * t0 / np.abs(b2) # dispersion length
N_sol = 3 # soliton order
# ... COMPUTATIONAL DOMAIN
t_max = 30.
t_num = 2**12
z_max = 0.5 * np.pi * LD
z_num = 1000
z_skip = 2
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
grid = Grid(t_max=t_max, t_num=t_num, z_max=z_max, z_num=z_num)
# ... NSE MODEL
model = NSE(grid.w, b2, gamma)
# ... Z-PROPAGATION USING SYMMETRIC SPLIT-STEP FOURIER METHOD
solver = SySSM(model.Lw, model.Nw)
# ... INITIAL CONDITION
u_0t = N_sol * np.sqrt(P0) / np.cosh(grid.t / t0)
solver.set_initial_condition(grid.w, FT(u_0t))
# -- RUN SIMULATION
solver.propagate(z_range=z_max, n_steps=z_num, n_skip=z_skip)
plot_evolution(solver.z,
grid.t,
solver.utz,
t_lim=(-4, 4),
w_lim=(-50, 50),
DO_T_LOG=False)
# -- COMPUTATIONAL DOMAIN
t_max = 3500. # (fs)
t_num = 2**14 # (-)
z_max = 0.10 * 1e6 # (micron)
z_num = 8000 # (-)
z_skip = 10 # (-)
# -- INITIAL CONDITION
P0 = 1e4 # (W)
t0 = 28.4 # (fs)
w0 = 2.2559 # (rad/fs)
E_0t_fun = lambda t: np.real(
np.sqrt(P0) / np.cosh(t / t0) * np.exp(-1j * w0 * t))
# -- COMPUTATIONAL DOMAIN
grid = Grid(t_max=t_max, t_num=t_num, z_max=z_max, z_num=z_num)
# -- PROPAGATION MODEL
model = CustomModelPCF(w=grid.w)
# -- ANALYTIC SIGNAL INITIAL CONDITION
ic = AS(E_0t_fun(grid.t))
###############################################################################
# We first perfom a simulation run using the default Raman response model
# implemented with `CustomModelPCF`. This is also implemented in terms of the
# Blow-Wood type response model `h_BW` in module `raman_response`. From the
# simulation results we will only keep the final :math:`z`-slice.
# -- INITIALIZE MODEL
solver = IFM_RK4IP(model.Lw, model.Nw, user_action=model.claw)
# -- SET INITIAL CONDITION
solver.set_initial_condition(grid.w, AS(E_0t_fun(grid.t)).w_rep)
is used. .. codeauthor:: Oliver Melchert <*****@*****.**> """ import fmas import numpy as np from fmas.solver import IFM_RK4IP from fmas.analytic_signal import AS from fmas.grid import Grid from fmas.propagation_constant import PropConst, define_beta_fun_ESM from fmas.tools import sech, change_reference_frame, plot_claw beta_fun = define_beta_fun_ESM() pc = PropConst(beta_fun) grid = Grid(t_max=5500.0, t_num=2**14) # (fs) # (-) Ns = 8.0 # (-) t0 = 7.0 # (fs) w0 = 1.7 # (rad/fs) n2 = 3.0e-8 # (micron^2/W) A0 = Ns * np.sqrt(abs(pc.beta2(w0)) * pc.c0 / w0 / n2) / t0 E_0t_fun = lambda t: np.real(A0 * sech(t / t0) * np.exp(1j * w0 * t)) Eps_0w = AS(E_0t_fun(grid.t)).w_rep ############################################################################### # As model we here consider the simplified forward model for the analytic # signal (FMAS_S) from fmas.models import FMAS_S model = FMAS_S(w=grid.w, beta_w=pc.beta(grid.w), n2=n2)
# -- EQUIP THE SUPERCLASS
super().__init__(w, self.beta_fun(w), n2, fR, tau1, tau2)
###############################################################################
#
# Next, we use the implemente class to reproduce the interaction between a
# soliton and a dispersive wave in absence of the Raman effect. In particular,
# we here reproduce the collision scenario underlying Fig. 2 of Ref. [3].
#
# Therefore, we initialize an adequate computational domain and an instance of
# the `ZBLAN` model, for which the fractional contribution of the Raman effect
# is set to zero
grid = Grid(
t_max=4500., # (fs)
t_num=2**14 # (-)
)
model = ZBLAN(grid.w, fR=0.0)
###############################################################################
# To visually assess the group-velocity (GV) and group-velocity dispersion
# (GVD) of the propagation constant in the relevant angular frequency range we
# use the convenience class `PropConst` and pre-implemented plotting functions
# that are implemented in module `tools`
w = grid.w[np.logical_and(grid.w > 0.5, grid.w < 5.)]
pc = PropConst(model.beta_fun)
plot_details_prop_const(w, pc.vg(w), pc.beta2(w))
###############################################################################
def Lw(self):
return 1j*self.beta_w
def Nw(self, uw):
ut = IFT(uw)
return 1j*self.gamma*FT(np.abs(ut)**2*ut)
###############################################################################
# Next, we initialize the computational domain and use a simple split-step
# Fourier method to propagate a single fundamental soliton for ten soliton
# periods.
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
grid = Grid( t_max = 30., t_num = 2**10)
t, w = grid.t, grid.w
# ... NSE MODEL
model = NSE(w, b2=-1., gamma=1.)
# ... INITIAL CONDITION
u_0t = 1./np.cosh(t)
###############################################################################
# In a first numerical experiment, the stepsize is intentionally kept very
# large in order to allow the numerical istabilities to build up.
solver = SySSM(model.Lw, model.Nw)
solver.set_initial_condition(w, FT(u_0t))
solver.propagate(z_range = 10*np.pi, n_steps = 511, n_skip = 1)
z, utz = solver.z_, solver.utz
return 1j*self.gamma*FT(np.abs(ut)**2*ut)
###############################################################################
# Next, we initialize the computational domain and use a simple split-step
# Fourier method to propagate a single third-order soliton for six soliton
# periods.
# In this first numerical experiment, the extend of the frequency domain is so
# small that, when the solitons spectrum broadens, it exceeds the bounds of the
# frequency domain. Errors stemming from truncation of the spectrum accumulate
# over subsequent soliton periods, giving an erroneous account of the true
# dynamics (see the subsequent figure).
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
grid = Grid( t_max = 34., t_num = 2**9)
t, w = grid.t, grid.w
# ... NSE MODEL
model = NSE(w, b2=-1., gamma=1.)
# ... INITIAL CONDITION
u_0t = 3./np.cosh(t)
solver = SiSSM(model.Lw, model.Nw)
solver.set_initial_condition(w, FT(u_0t))
solver.propagate(z_range = 6*np.pi/2, n_steps = 10000, n_skip = 50)
z, utz = solver.z_, solver.utz
plot_evolution( solver.z, grid.t, solver.utz,
t_lim = (-5,5), w_lim = (-60,60), DO_T_LOG=False)
beta2 = np.polyder(beta, m=2)
# ... NONLINEAR PARAMETER
gamma = 1.
# ... SOLITON PARAMTERS
t0 = 1. # duration
t_off = 20. # temporal offset
w0 = 25. # detuning
P0 = np.abs(beta2(0)) / t0 / t0 / gamma # peak-intensity
LD = t0 * t0 / np.abs(beta2(0)) # dispersion length
# ... EXACT SOLUTION
u_exact = lambda z, t: np.sqrt(P0) * np.exp(0.5j * gamma * P0 * z) / np.cosh(
t / t0)
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
grid = Grid(t_max=t_max, t_num=Nt)
t, w = grid.t, grid.w
# ... NONLINEAR SCHROEDINGER EQUATION
model = NSE(w, beta(w), gamma)
# ... PROPAGATION ALGORITHM
solver = LEM(model.Lw, model.N, del_G=1e-7)
# ... INITIAL CONDITION
u0_t = u_exact(0.0, t + t_off) * np.exp(1j * w0 * t)
u0_t += u_exact(0.0, t - t_off) * np.exp(-1j * w0 * t)
solver.set_initial_condition(w, FT(u0_t))
# -- RUN SOLVER
solver.propagate(
z_range=0.5 * np.pi * LD, # propagation range
n_steps=512,
n_skip=2)
return 1j * self.beta_w
def Nw(self, uw):
ut = IFT(uw)
return self._de_alias(1j * self.gamma * FT(np.abs(ut)**2 * ut))
###############################################################################
# Next, we initialize the computational domain and use a symmetric split-step
# Fourier method to propagate a single third-order soliton for six soliton
# periods.
# For this numerical experiment, the extend of the time domain and the number
# of sample points is chosen large enough to allow for a zero padding
# anti-aliasing technique without cropping important parts of the spectrum.
grid = Grid(t_max=34., t_num=2**12)
t, w = grid.t, grid.w
model = NSE(w, b2=-1., gamma=1.)
u_0t = 4. / np.cosh(t)
solver = SySSM(model.Lw, model.Nw)
solver.set_initial_condition(w, FT(u_0t))
solver.propagate(z_range=3 * np.pi / 2, n_steps=10000, n_skip=50)
z, utz = solver.z_, solver.utz
plot_evolution(solver.z,
grid.t,
solver.utz,
t_lim=(-5, 5),
w_lim=(-60, 60),
DO_T_LOG=False)
