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 = 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():
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():
# -- 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))
###############################################################################
# The figure below shows the dynamic evolution of the pulse in the time domain
# (top subfigure) and in the frequency domain (center subfigure). The subfigure
# at the bottom shows the conservation law (c-law) given by the normalized
# photon number variation
#
# .. math::
# \delta_{\rm{Ph}}(z) = \frac{ C_p(z)-C_p(0)}{C_p(0)}
#
# as function of the proapgation coordinate :math:`z`. For the considered
# discretization of the computational domain the normalized photon number
# variation is of the order :math:`\delta_{\rm{Ph}}\approx 10^{-7}` and thus
# very small. The value can be still decreased by decreasing the stepsize
# :math:`\Delta z`.
utz = change_reference_frame(solver.w, solver.z, solver.uwz, pc.vg(w0))
plot_claw(solver.z,
grid.t,
utz,
solver.ua_vals,
t_lim=(-25, 125),
w_lim=(0.5, 4.5))
###############################################################################
# **References:**
#
# [AD2010] Sh. Amiranashvili, A. Demircan, Hamiltonian structure of propagation
# equations for ultrashort optical pulses, Phys. Rev. E 10 (2010) 013812,
# http://dx.doi.org/10.1103/PhysRevA.82.013812.
#
