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 = 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 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(): # -- 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(): # -- 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 = 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(): # -- 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))
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) # -- z-PROPAGATION solver.propagate(z_range=z_max, n_steps=z_num, n_skip=z_skip) # -- KEEP ONLY LAST z-SLICE
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) ############################################################################### # For the FMAS_S :math:`z`-propagation model we consider a conserved quantity # that is related to the classical analog of the photon number, see Eq. (24) of # [AD2010] and the appendix of [BW1989]. In particular we here implement # # .. math:: # C_p(z) = \sum_{\omega>0} \omega^{-1} |u_\omega(z)|^2,
# :math:`t_{\rm{S}}=25.2\,\mathrm{fs}` and center frequency # :math:`\omega_{\rm{S}}=0.4709\,\mathrm{rad/fs}`, and a dispersive wave with # duration :math:`t_{\rm{DW}}=100\,\mathrm{fs}` and angular frequency # :math:`\omega_{\rm{DW}}=2.6177\,\mathrm{rad/fs}`. Both pulses exhibit an # amplitude ratio of :math:`A_{\rm{DW}}/A_{\rm{S}}=0.566`, and the soliton is # launched with deltay :math:`t_{\rm{off}}=450\,\mathrm{fs}`. wS, tS = 0.4709, 25.2 # (rad/fs), (fs) wDW, tDW = 2.6177, 100. # (rad/fs), (fs) t_off = -450. # (fs) rDW = 0.566 # (-) A0S = np.sqrt(abs(pc.beta2(wS)) * model.c0 / wS / model.n2) / tS E_0t = np.real(A0S * sech(grid.t / tS) * np.exp(1j * wS * grid.t) + # S rDW * A0S * sech( (grid.t - t_off) / tDW) * np.exp(1j * wDW * grid.t)) # DW Eps_0w = AS(E_0t).w_rep ############################################################################### # For :math:`z`-propagation we here use a variant of an integrating factor # method, referred to as the "Runge-Kutta in the interaction picture" method, # implemented as `IFM_RK4IP` in module `solver`. solver = IFM_RK4IP(model.Lw, model.Nw) solver.set_initial_condition(grid.w, Eps_0w) solver.propagate( z_range=0.35e6, # (micron) n_steps=4000, # (-) n_skip=10 # (-) )