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(): 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 = 4.0e6 # (micron) z_num = 50000 # (-) 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) model = FMAS_S(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) plot_evolution(solver.z, grid.t, utz, t_lim=(-4000, 1000), w_lim=(1.1, 2.4))
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 = 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)
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 # (-) ) ############################################################################### # Finally, the :math:`z`-propagation characteristics of the interaction process # can be obtained by utz = change_reference_frame(solver.w, solver.z, solver.uwz, pc.vg(wS)) plot_evolution(solver.z, grid.t, utz, t_lim=(-3000, 2000), w_lim=(0.2, 3.3)) # sphinx_gallery_thumbnail_number = 2 ############################################################################### # # References: # [1] C. Agger, C. Petersen, S. Dupont, H. Steffensen, J. K. Lyngso, C. L. # Thomsen, J. Thogersen, S. R. Keiding, O. Bang, Supercontinuum generation # in ZBLAN fibers—detailed comparison between measurement and simulation, J. # Opt. Soc. Am. B 29 (2012) 635, https://doi.org/10.1364/JOSAB.29.000635. # # [2] L. Liu, G. Qin, Q. Tian, D. Zhao, W. Qin, Numerical investigation of # mid-infrared supercontinuum generation up to 5 μm in single mode fluoride # fiber, Opt. Exp. 19 (2011) 10041, https://doi.org/10.1364/OE.19.010041. #
# 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) ############################################################################### # **References:** # # .. [B2001] J.P. Boyd, Chebychev and Fourier Spectral Methods, Dover, New York (2001) # # .. [HCL2008] H. Holmas, D. Clamond, H.P. Langtangen, A pseudospectral Fourier # method for a 1D incompressible two-fluid model, Int. J. Numer. # Meth. Fluids 58 (2008) 639, https://doi.org/10.1002/fld.1772 # # .. [FCGK2005] D. Fuctus, D. Clamond, J. Grue, O. Kristiansen, An efficient # model for three-dimensional surface wave simulations Part I: Free # space problems, J. Comp. Phys. 205 (2005) 665,
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) ############################################################################### # The figure below shows the propagation dynamics of the above initial # condition: plot_evolution(solver.z, grid.t, solver.utz, t_lim=(-30, 30), w_lim=(-50., 50.)) ############################################################################### # Below we prepare a figure showing the variation of the local relative error # upon propagation (top figure), and the decrease of the local stepsize in the # vicinity of the soliton-soliton collision (bottom subfigure). # In the top figure, the shaded region indicates the local goal error range. # Aim of the LEM method is to keep the conservation quantity error within that # range. # sphinx_gallery_thumbnail_number = 2 import matplotlib as mpl import matplotlib.pyplot as plt
solver.set_initial_condition(grid.w, Eps_0w) solver.propagate( z_range=0.12e6, # (micron) n_steps=2000, # (-) n_skip=10 # (-) ) ############################################################################### # Once the :math:`z`-propagation algorithm terminates we can perform a shift to # a frame of reference in which the initial pulse is stationary, i.e. to a # moving frame of reference with velocity :math:`v_0=v_g(\omega_0)`. The # evolution of the analytic signal can then be visualized using the function # `plot_evolution` defined in module `tools`: utz = change_reference_frame(solver.w, solver.z, solver.uwz, pc.vg(w0)) plot_evolution(solver.z, grid.t, utz, t_lim=(-200, 2500), w_lim=(0.6, 3.4)) ############################################################################### # This reproduces Fig. 1 of Ref. [1]. # # Analytic signal spectrograms that show the time-frequency characteristics of # the field can be constructed using the function `spectrogram` defined in # module `tools`. These spectrograms are computed by using a Gaussian function # for localizing the analytic signal along the time-axis. The root-mean-square # (rms) width of this window-function needs to be chosen carefully, as # demonstrated below. Consider, e.g., the propagation distance # :math:`z=0.12~\mathrm{m}`, for which the analytic signal can be obtained as z0_idx = np.argmin(np.abs(solver.z - 0.12e6)) Et = utz[z0_idx]
############################################################################### # An example that shows how an adequate input file can be generated via python # is shown under the link below: # # :ref:`sphx_glr_auto_tutorials_basics_ng_generate_infile.py` # # After the proapgation algorithm (specified in `input_file.h5`) terminates, # a simple dictionary data structure with the following keys is available print(res.keys()) ############################################################################### # A simple plot that shows the result of the simulation run can be produced # using function `plot_evolution` implemented in module `tools` from fmas.tools import plot_evolution plot_evolution(res['z'], res['t'], res['u'], t_lim=(-500, 2200), w_lim=(1., 4.)) ############################################################################### # The results can be stored for later postprocessing using the function # `save_h5` implemented in module `data_io`. It will generate a file # `out_file.h5` with HDF5 format in the current working directory from fmas.data_io import save_h5 save_h5('out_file.h5', **res)